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master thesis in crystallography Yazan Maswadeh [email protected]
Citation preview
STRUCTURAL ANALYSIS OF HEXAFERRITE MATERIALS
By
Yazan Osama Maswadeh
Supervisor
Prof. Sami Husain Mahmood
This Thesis was Submitted in Partial Fulfillment of the Requirements for the
Master’s Degree of Physics
Faculty of Graduate Studies
The University of Jordan
August 2014
IV
AKNOWLEDGEMENT
I would like to express my deep gratitude to Professor Sami Mahmood, my research supervisor, for his patient guidance, enthusiastic encouragement and useful critiques of this research work. I would also like to warmly thank my friend Dr. Ahmad Awadallah, for his advice and assistance in keeping my progress on schedule. Also my special thanks to my friend Dr. Feres Ben Jemaa for his assistance and guidance and patience in the refinement. As well, my thanks to Ms. Aynoor Oqaily for her assistance in the labs.
I would also like to extend my thanks to Mr. Yousef Abu Salha the technician of the XRD and XRF laboratory in the geology department for his help in offering me the XRD data.
Finally, I wish to thank my parents for their support and encouragement throughout my study.
V
List of Contents
Page Subject
ii Committee Decision
iii Thesis Publishing
iv Acknowledgement
v List of Contents
vii List of Tables
ix List of Figures
xv Abstract (English
1 Chapter 1 - Introduction
2 - 1.1 Magnetic material
2 - 1.2 Hexagonal Ferrites
3 - 1.3 Building blocks of hexagonal ferrites
6 - 1.4 The M-type hexaferrites
9 - 1.5 Our study
10 - 1.6 X-ray crystallography
11 - 1.7 Powder Diffraction
11 - 1.8 Rietveld Fitting
14 - 1.9 Literature Review
18 Chapter 2 - Methodology
19 - 2.1 Preparation of non-stoichiometric Barium hexaferrite samples
19 - 2.2 Structural and characterization
27 - 2.3 Preparation of non-stoichiometric Barium hexaferrite samples
with iron to barium ratio = 9 and 7
VI
28 Chapter 3 – Result
29 - Result of non-stoichiometric barium hexaferrite Samples
Iron to barium ratio (Fe+3 : Ba+2) ≥ 11.5
37 - XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite
Samples with Iron to Barium ratio = 9
52 - XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite
Samples with Iron to Barium ratio = 7
67 Chapter 4 – Analysis and Discussion
68 - Non-stoichiometric barium hexaferrite samples
with Fe:Ba ratio ≥ 11.5
78 - Non-stoichiometric barium hexaferrite samples
with Fe:Ba ratio = 9
85 - Non-stoichiometric barium hexaferrite samples
with Fe:Ba ratio = 7
90 Chapter 5 – Conclusions and Recommendations
91 - Conclusions
92 - Recommendations for Future Work
93
100
REFERANCES
Abstract (Arabic)
VII
PAGE TABLE CAPTION NUMBER
6 Table 1.1: Types of Compositions and building blocks of barium
hexaferrites. 1
9 Table 1.2: Metallic sub-lattices of M-type hexaferrite 2
19 Table (2.1) the iron to barium ratio for each sample. 3
26 Table (2.2) outputs compatibility between Rietveld and Profile
matching methode. 4
42
Table (3.1) Structural phases existing in the samples with Fe:Ba =
9 sintered at different temperatures
5
56 Table (3.2) Structural phases existing in the samples with Fe:Ba =
7 sintered at different temperatures 6
70
Table (4.1) The integrated intensity of all structural peaks of BaM
(IBaM) and of α-Fe2O3 (Iα), and the ratio (Iα/IBaM) for the samples
with different Fe:Ba ratio. 7
71
Table (4.2) The integrated intensities of the main peaks of BaM
(IMB), α-Fe2O3 (IMα), and the peak ratios of the two phases for all
samples. 8
73
Table (4.3) α-Fe2O3 α-Fe2O3 wt% determined from Rietveld
refinement of the diffraction patterns and the corresponding
relative main peak integrated intensity.
9
80
Table (4.4) the calculated ratios for each phase according to the
sintering temperature.
10
81
Table (4.5) the total sites multiplicity and the unit cell volume of
each phase at 1000° C sintering temperature.
11
83 Table (4.6) the unit cell volume at each sintering degree. 12
87 Table (4.7) the calculated ratios for each phase according to the
sintering temperature. 13
VIII
PAGE FIGURE CAPTION NUMBER
4 Figure (1.1) a close-packed layer of spheres occupying positions A. 1
5 Figure (1.2) a two close-packed layers of spheres stacking on
each other occupying positions A and B. 2
5
Figure (1.3) a three close-packed layers of spheres stacking on each
other occupying positions A, B and C with the two stacking form
(ABAB.., ABCABC..).
3
5 Figure (1.4) a three dimensional modeling for the (ABAB..,
ABCABC..) stacking 4
7
Figure (1.5) S block structure in barium hexaferrite, (a) Top oxygen
R layer viewed from above to determine the unit cell shape. (b) The
two S block layers with their oxygen ions and cations and the top R
layer.
5
8 Figure (1.6) R block structure in barium hexaferrite with the ions and
cations sites. 6
9 Figure (1.7) T block structure in barium hexaferrite with the ions and
cations sites. 7
10 Figure (1.8) Constructive Interference of reflected waves following
Bragg law terms. 8
20 Figure (2.1) XRD pattern of barium hexaferrite sample with Fe:Ba
ratio = 11.5 9
IX
21
Figure (2.2) XRD pattern matching for the sample with Fe:Ba ratio
of 11.5.
10
22 Figure (2.3) XRD pattern matching for the sample with Fe:Ba ratio
of 16.16. 11
24 Figure (2.4) The fitted XRD pattern using profile matching method
for the sample with Fe:Ba ratio of 11.5. 12
24 Figure (2.5) The fitted XRD pattern using profile matching method
for the sample with Fe:Ba ratio of 16.16. 13
30 Figure (3.1) Fitted XRD pattern using Rietveld method for the
sample with Fe:Ba ratio = 11.5. 14
31 Figure (3.2) Fitted XRD pattern using Rietveld method for the
sample with Fe:Ba ratio = 12.24. 15
32 Figure (3.3) Fitted XRD pattern using Rietveld method for the
sample with Fe:Ba ratio = 13.05 16
34 Figure (3.4) Fitted XRD pattern using Rietveld method for the
sample with Fe:Ba ratio = 13.97. 17
34 Figure (3.5) Fitted XRD pattern using Rietveld method for the
sample with Fe:Ba ratio = 14.99. 18
37 Figure (3.6) Fitted XRD pattern using Rietveld method for the
sample with Fe:Ba ratio = 16.16. 19
38 Figure (3.7) XRD pattern for the sample with Fe:Ba = 9 sintered at
1200° C. 20
X
38 Figure (3.8) XRD pattern for the sample with Fe:Ba = 9 sintered at
1100° C. 21
39 Figure (3.9) XRD pattern for the sample with Fe:Ba = 9 sintered at
1000° C. 22
40 Figure (3.10) XRD pattern for the sample with Fe:Ba = 9 sintered
at 900° C. 23
41 Figure (3.11) XRD pattern for the sample with Fe:Ba = 9 sintered
at 800° C. 24
45 Figure (3.12) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1200° C
25
45 Figure (3.13) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1100° C
26
47 Figure (3.14) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1000° C
27
49 Figure (3.15) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 900° C
28
51 Figure (3.16) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 800° C
29
52 Figure (3.17) XRD pattern for the sample with Fe:Ba = 7 sintered at 1200° C.
30
53 18) XRD pattern for the sample with Fe:Ba = 7 sintered at 1100° C. 31
53 19) XRD pattern for the sample with Fe:Ba = 7 sintered at 1000° C. 32
54 Figure (3.20) XRD pattern for the sample with Fe:Ba = 7 sintered at 900° C.
33
55 Figure (3.21) XRD pattern for the sample with Fe:Ba = 7 sintered at 800° C.
34
59 Figure (3.22) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 1200° C
35
59 Figure (3.23) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 1100° C
36
61 Figure (3.24) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 1000° C
37
64 Figure (3.25) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 900° C
38
XI
64 Figure (3.26) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 800° C
39
69
Figure (4.1) XRD patterns of all samples added with different
amounts of α-Fe2O3. The main structural peaks of iron oxide phase
are shaded in yellow
40
70 Figure (4.2) A plot of Iα/IBaM (%) vs Fe:Ba ratio for all samples 41
72 Figure (4.3) A plot of IMα/IMB (%) vs Fe:Ba ratio for all samples 43
73 Figure (4.4) A plot of IMα/IMB (%) as a function of α-Fe2O3
wt% evaluated from the refinement of the patterns of all samples 44
74 Figure (4.5) Linear fit of Fe:Ba ratio vs α-Fe2O3 wt% obtained from the refinement of the diffraction patterns.
45
75 Figure (4.6) the calculated XRD stick pattern for BaFe12O19 phase
compared with other standard patterns in ICDD library. 46
76 Figure (4.7) the crystal structure of BaFe12O19 unit cell in 3D. 47
76 Figure (4.8) the crystal structure of Fe2O3 unit cell in a 3D. 48
77 Figure (4.9) Compression of tow barium hexaferrite structures,
samples zero and twenty-five percent. 49
79
Figure (4.10) XRD patterns samples with Fe:Ba of 9 sintered at
different temperatures. α-Fe2O3 was highlighted in yellow, the
barium spinel (BaFe2O4) in blue, and the barium iron oxide
(Ba3Fe2O6) in green.
50
81
Figure (4.11) a schematic representation for each phase calculated
ratios according to the sintering temperature, Fe:Ba ratio =9.
51
XII
82 Figure (4.12) the XRD stick pattern of barium iron oxide
(Ba3Fe2O6) phase. 52
82 Figure (4.13) the calculated XRD stick pattern for Ba3Fe2O6 phase
compared with other standard pattern in ICDD library. 53
83 Figure (4.14) the calculated XRD stick pattern for BaFe2O4
phase compared with other standard patterns in ICDD library. 54
84 Figure (4.15) the crystal structure of Ba3Fe2O6 unit cell in 3D. 55
84 Figure (4.16) the crystal structure of BaFe2O4 unit cell in 3D. 56
85 Figure (4.17) Compression of tow barium hexaferrite structures sintered at 800° & 1200° C.
57
86
Figure (4.18) XRD patterns samples with Fe:Ba of 7 sintered at
different temperatures. α-Fe2O3 was highlighted in yellow, the
barium spinel (BaFe2O4) in blue, and the barium iron oxide
(Ba3Fe2O6) in green.
58
88 Figure (4.19) a schematic representation for each phase calculated
ratios according to the sintering temperature, Fe:Ba ratio = 7. 59
XIII
Structural Analysis of Hexaferrite Materials
By
Yazan Maswadeh
Supervisor
Prof. Sami Mahmood
ABSTRACT
The main essence of this study is about the structural analysis of barium hexaferrite
material, based on XRD pattern fitting using Rietveld refinement. Our methodology start by
preparing a samples of barium iron oxide materials, with different stoichiometric ratios, under
different laboratory conditions. In an attempt to understand the formation of barium hexaferrite
phases, in order to synthesis a pure phase of M-type barium hexaferrite (BaFe12O19). As well
as to understand the effect of temperature and impurities on the resulted phases.
In the beginning, a precursor material was prepared in order to obtain M-type barium
hexaferrite (BaFe12O19) samples, and modifying the proportion of Fe:Ba ratio in each sample
ascending from (11.5) to (16:16), for five samples and synthesizing them under the same
laboratory conditions. The analysis of these samples shows that the M-type barium hexa ferrite
was not affected structurally or quantitatively, and the increase of the iron oxide quantity in the
precursor material, appeared as separate phase (impurity) in each sample, which increases with
increasing the Fe:Ba ratio in the precursor material. According to these results, a reference
scheme measures the weight ratio of iron oxide to the M-type barium hexaferrite was created,
depending on the main peaks ratio for each phase.
XIV
To study these samples in a wider range according to the barium to iron ratio in the
precursor material, we prepared samples with barium to iron ratio of (1:9) and (1:7), and five
samples of each proportion were sintered at different temperatures (800, 900, 1000, 1100,
1200° C).
The analysis results showed the formation of four phases in different proportions at each
sintering temperature. A scheme representing the phases evolution according to sintering
temperature was plotted depending on the analysis results. The XRD stick pattern for each
phase was obtained, in addition to building a three-dimensional model of each crystalline
structure with an indication to the structural differences that have occurred depending on the
variation of sintering temperature.
1
CHAPTER 1
Introduction
1.1 Magnetic materials
1.2 Hexagonal Ferrites
1.3 Building blocks of hexagonal ferrites
1.4 The M-type hexaferrites
1.5 Our study
1.6 X-ray crystallography
1.7 Powder Diffraction
1.8 Rietveld Fitting
1.9 Literature Review
2
1.1 Magnetic materials
Magnetic materials are widely used in our everyday life, covering the range from
being employed in components of electronic devices and equipment to refrigerator
stickers and parts of children toys. Ferrites are magnetic ceramics based on iron oxides,
and form a class of important magnetic materials due to their desirable magnetic and
electrical properties, chemical stability, and low cost of production. Ferrites exist in
different forms such as cubic ferrites, hexagonal ferrites, orthoferrites and garnets [1 – 3].
These materials play an important role in the technological and industrial progress, and
the evolution of new applications, where for example they were efficiently used in
telecommunication and radar technologies, digital storage devices, and motor industry.
The demand for low-cost novel magnetic materials with properties required to satisfy the
specific needs of the various technological and industrial applications had therefore
generated a great interest in the synthesis and characterization of hexagonal ferrites due
to their improved and tunable properties [4 – 7].
1.2 Hexagonal Ferrites
These ferrites with hexagonal structure (also known as hexaferrites) were first
discovered in the 1950s, and the barium-based hexaferrites are composed of special
stacking sequence of close-packed oxygen layers with barium ions partially substituting
oxygen ions at specific positions in the unit cell, and the small metallic ions occupying
interstitial positions [1 – 3]. Owing to their interesting properties and wide range of
applications, hexagonal ferrites had attracted special interest which grew exponentially
until they become probably the most important magnetic materials today [7]. The
3
properties of the hexaferrites were found to depend crucially on the method of preparation
and experimental conditions as well as on the cationic substitution for iron ions [8 – 16].
Further, the substitution of Ba2+ ions by other ions such as Sr2+, Pb2+ and Ca2+ was also
found to influence the properties of the hexaferrites [16 – 20].
1.3 Building blocks of hexagonal ferrites
Visualizing the ion in the crystal structure of the hexaferrite as a hard sphere, the
large oxygen ions are closely packed in hexagonal layers as illustrated by figure (1.1). If
the ions in the first layer occupy positions labelled by (A), close packing of an over-layer
can be achieved by placing oxygen ions at any of the two positions labelled by (B) and
(C). If the second layer is at position (B), a third layer can then be placed on top of the
second layer either at position A (forming an ABA stacking) or C (forming an ABC
stacking) as illustrated by Figure (1.2) [21]. An infinite stacking of the type (ABABAB…)
then reproduces the hexagonal close-packed structure, whereas an infinite stacking of the
type (ABCABC…) reproduces the face-centered cubic (fcc) structure as explained by
general undergraduate solid state text books, see Figure (1.3 - 4). These two types of
stacking are the simplest special cases. An infinite number of stacking sequences can,
however, be produced by variations of the positions of the over-layers.
The crystal structure of the different types of hexagonal ferrites is based on the
sequential stacking of three main blocks of close-packed oxygen layers (with Ba partially
substituting oxygen in some of these layers) as demonstrated by Figure (1.5). The spinel
(S) block consists of two oxygen layers with ABCABC… stacking sequence. The
hexagonal (R) consists of three oxygen layers (ABAB… stacking) with one Ba ion
substituting an oxygen in the middle layer [22], Figure (1.6). On the other hand, the
4
hexagonal (T) block consists of four oxygen layers with one barium ion substituting an
oxygen ion in each of the two middle layers, Figure (1.7) [7]. The metal ions (primarily
Fe3+) occupy the interstitial positions in these blocks, and in the interface between the
different blocks in the hexaferrite structure. Table (1.1) summarizes the stacking
sequences of the blocks of the six known types of hexaferrites, where the starred block is
rotated by 180° about the c-axis, and the primed and double primed block is rotated by
120° [23].
Figure (1.1) a close-packed layer of spheres occupying positions A.
5
Figure (1.2) a two close-packed layers of spheres stacking on each other occupying
positions A and B.
Figure (1.3) a three close-packed layers of spheres stacking on each other occupying
positions A, B and C with the two stacking form (ABAB.., ABCABC..).
Figure (1.4) a three dimensional modeling for the (ABAB.., ABCABC..) stacking.
6
Table 1.1: Types of Compositions and building blocks of barium hexaferrites.
Hexaferrite Combination Chemical formula Stacking
M M BaFe12O19 RSR*S*
Y Y Ba2Me2Fe12O22 TST’S’T”S”
W MS BaMe2Fe16O27 SSRS*S*R*
X M2S Ba2Me2Fe28O46 3(SRS*S*R*)
Z MY Ba3Me2Fe24O41 STSRS*T*S*R*
U M2Y Ba4Me2Fe36O60 SRS*R*S*T
1.5 The M-type hexaferrites
The M-type barium hexaferrite (also known as Ferroxdure or BaM) is a
ferrimagnetic material with chemical formula BaFe12O19, melting point of 1390° C, and
theoretical density of 5.3 g/cm3 [7]. The unit cell consists of the sequence RSR*S* and
contains two molecules. BaM hexaferrite is the most important hexaferrite in terms of
production (more than 50% of the total market share of the magnetic materials [7]). The
symmetry of the barium hexaferrite crystal structure is characterized by the space group
(P63/mmc) with lattice parameter a = b = 5.89Å, c = 23.17 Å, β = α = 90°, γ = 120° [7].
The unit cell of M-type barium hexaferrite is built by stacking S and R blocks along
the hexagonal c-axis, the S block consisting of two close-packed plans have eight oxygen
ions, four ions in each, one iron cation at (2a) octahedral site, two iron cations at (4f1)
tetrahedral sites and three iron cations at (12k) octahedral sites, following the stacking
(A, B, C) where the (C) here belongs to the next R block. As a result, the S block has the
chemical formula Fe6O8, see Figure (1.5) [23].
The R block consists of three close-packed layers in an hcp stacking sequence as
shown above. The chemical formula for this block is BaFe6O11, containing one iron cation
at the (2b) trigonal site, two iron cations at the (4f2) octahedral sites and three iron cations
7
at (12k) octahedral sites. Table (1.2) summarizes the M-type barium hexaferrite
(BaFe12O19) structure and the iron ions sites at the sublattices coordinations.
Figure (1.5) S block structure in barium hexaferrite, (a) Top oxygen R layer viewed
from above to determine the unit cell shape. (b) The two S block layers with their
oxygen ions and cations and the top R layer.
The unit cell of M-type barium hexaferrite contains two BaFe12O19 molecules, one
in SR blocks and the other in the S*R* blocks rotated by 180° about the c-axis.
8
Figure (1.6) R block structure in barium hexaferrite with the ions and cations sites.
Figure (1.7) T block structure in barium hexaferrite with the ions and cations sites.
9
Table 1.2: Metallic sub-lattices of M-type hexaferrite
Block Sublattice Formula Coordination Cations / Site Spin
S 4f1
2(Fe3O4) Tetrahedral 2 2 ↓
2a Octahedral 1 1 ↑
R 4f2
BaFe6O11 Octahedral 2 2 ↓
2b Bi-pyramidal 1 1 ↑
(S-R) (R-S*) 12k SHARED Octahedral 6 (3↑) (3↑)
S* 4f1
2(Fe3O4) Tetrahedral 2 2 ↓
2a Octahedral 1 1 ↑
R* 4f2
BaFe6O11 Octahedral 2 2 ↓
2b Bi-pyramidal 1 1 ↑
(S*-R*) (R*-S) 12k SHARED Octahedral 6 (3↑) (3↑)
1.5 Our study
Our study is mainly concerned with the identification and the structural analyses of
the phases evolving in the process of synthesizing barium hexaferrite samples using
different Fe:Ba ratios. Further, the weight ratios of the different coexisting phases were
determined as a function of Fe:Ba ratio in the precursor powder. Extrapolation of the
weight ratio of the impurity phases in samples with Fe:Ba ≥ 11.5 was used to determine
the optimal ratio necessary to produce single M-type barium hexaferrite phase.
Another objective of this study was to identify and analyze the phases evolving in
samples prepared from precursors with Fe:Ba ratios of 9 and 7. The effect of sintering
temperature on the development of phases was investigated, and a phase diagram was
obtained.
1.6 X-ray crystallography
X-ray diffraction (XRD) is a non-destructive technique that is often used for the
structural analyses of solids owing to its availability, accessibility, and low cost of
operation. Regular arrays of atoms in a crystal diffract the x-ray beam into certain
directions determined by the angular positions of the diffraction peaks in a given pattern.
10
Analysis of the diffracted beam intensities into different angular positions gives
information on the atomic arrangement in a crystalline material, and allows the
construction of a three-dimensional image of the unit cell. This analysis gives full
structural information including the local atomic positions in the crystal structure,
chemical bond lengths and angles, cell deformation, and atomic order-disorder
phenomena.
When directing the x-rays to the crystalline material, the electrons of the atoms
scatter the x-rays in all directions forming a secondary spherical wave in a process similar
to the rebound of water waves after hitting a barrier. The scattered x-ray waves usually
cancel each other in most directions via destructive interference, and in some directions
(Fig. 1.8) they add up constructively, giving peaks in the intensity profile at angular
positions given by Bragg’s law [24]:
𝓃 λ = 2 𝒹 sinθ (1)
Here (λ) is the incident beam wavelength, θ the angle between the direction of the x-ray
beam and the surface of the sample, and n is an integer [25].
Figure (1.8) Constructive Interference of reflected waves following Bragg law terms.
11
1.7 Powder Diffraction
XRD is considered as one of the most common techniques to identify and analyze
the crystalline phases in a given material. A small amount of the material is required for
such analysis, and the time taken in this analysis is relatively short.
The diffraction pattern involving the peak positions and diffracted intensity profile
of a given crystalline phase is unique. Therefore, XRD provides the means to identify the
components of the study sample without pre-knowledge of the chemical elements that
constitute the sample. The d-spacing between parallel planes responsible for a given
diffraction peak (dhkl) is readily determined from the position by using Bragg’s law. This
parameter is a function of Miller indices (hkl) of the parallel reflecting planes, the unit
cell dimensions, and the type of the crystal structure of the phase [24]. Further, the
intensity of a diffraction peak is dependent on the types and positions of atoms in the
crystal, the crystal structure, the angular position of the peak, and the multiplicity of the
reflecting atomic planes [24].
The XRD sample should be made of fine powder of the material, so that the particles
are randomly oriented over the sample surface and every possible crystalline orientation
will be quite equally represented in the powder sample. Accordingly, XRD pattern with
relative intensity ratios representative of a powder sample is obtained.
1.8 Rietveld Fitting
Although crystal structure determination from powder diffraction data is simple in
theory, it is highly challenging in the case of multi-phase analysis due to overlapped
12
reflections. Rietveld method, which is also known as full pattern analysis technique, is
used to refine the crystal structure of a material and obtain accurate structural parameters
of the different phases in the sample under investigation.
Rietveld method uses the least squares minimization technique to fit the observed
XRD pattern with a theoretical pattern, which is generated using the crystal structure
information along with the microstructural and instrumental information. Other
specialized techniques to determine unknown structures from powder data are also
available [26].
Even though there are many primary terms that are frequently used in the pattern
refinement field, we will only address and interpret the most important ones as outlined
by Rodriguez [27]:
(I) The Chi squared value (𝜒2) represents the goodness of the fit. This value is given
by [28-29]:
𝜒2 = ∑(𝒪 − ℰ)2
ℰ (2)
Where 𝒪 is the observed value and ℰ is the calculated value. Therefore, low values
of 𝜒2 indicate that the proposed theoretical model represents the crystal structure
satisfactorily, while higher values indicate the model should not be accepted as
representative of the structure of the crystalline phase.
(II) Pearson's chi-squared test (Person’s r) is a statistical test applied to sets of
categorical data to evaluate how likely it is that any observed difference between the sets
arose by chance. It is suitable for unpaired data from large samples [30].
Pearson's correlation is computed by dividing the sum of the 𝓍𝓎 column by the
square root of the product of the sum of the 𝓍2 and 𝓎2, following the formula [31]:
𝓇 =∑𝓍𝓎
√(∑𝓍2∑𝓎2) (3)
13
(III) RF-factor (ℛℱ) , which is also known as Crystallographic RF-Factor, is a
measure of the agreement between the crystallographic model and the experimental X-
ray diffraction data. In other words, it is a measure of how well the refined structure
predicts the observed data. RF -factor is given by [32]:
ℛℱ = 100∑ |′ℱobs,𝑘′ − ℱcalc,ℎ|
ℎ
∑ |′ℱobs,ℎ′|ℎ
(4)
Where ℱ is the structure factor.
(IV) Bragg R-factor (ℛℬ) is a measure of the agreement between the reflected
intensities calculated from a crystallographic model and those measured experimentally.
This is given by [33]:
ℛℬ = 100∑ |′ℐobs,ℎ′ − ℐcalc,ℎ|
ℎ
∑ |′ℐobs,ℎ′|ℎ
(5)
Here ℐ is the integrated intensity.
(V) PSEUDOVOIGT peak shape, (pVx) function is a linear combination of a
Lorentzian (ℒ′) and a Gaussian (𝒢′) of the same FWHM.
𝒱(𝓍) = ℒ(𝓍) ⨂ 𝒢(𝓍) = ∫ −∞
+∞
ℒ(𝓍 − 𝓊)𝒢(𝓊)𝒹𝓊 (6)
(VI) Biso or isotropic Debye-Waller factors, is used to describe the attenuation of x-
ray scattering caused by thermal motion.
(VII) Occ, Occupation number i.e. (chemical occupancy × site multiplicity) can be
normalized to the multiplicity of the general position of the group.
(VIII) Wyckoff position of a space group G consists of all points X for which the
site-symmetry groups are conjugate subgroups of G, the Wyckoff positions tell us where
the atoms in a crystal can be found.[34].
14
(IIX) The lattice constant, or lattice parameter, refers to the physical dimension of
unit cells in a crystal lattice. Lattices in three dimensions generally have three lattice
constants, referred to as a, b, and c.[35].
(IX) In quantitative analysis, noting that in a mixture of N crystalline phases, the
weight fraction Wj of phase j is given by:
Wj ={ Sj Zj Mj Vj / tj} / Sum(i)[Si Zi Mi Vi /ti] (7)
Where Sj is the scale factor of phase j, Zj is the number of formula units per unit
cell for phase j, Mj is the mass of the formula unit, Vj is the unit cell volume and tj is the
Brindley particle absorption contrast factor for phase j.
The 𝒜𝒯𝒵 coefficient, which is used to calculate the phase weight percent, depends
on several parameters, and is given by:
𝒜𝒯𝒵 = 𝒵 ℳ𝒲 f 2/𝓉 (8)
Here 𝒵 is the number of formula units per unit cell, ℳ𝒲 the molecular weight, and 𝓉 is
the Brindley coefficient.For a stoichiometric phase f = 1 if these multiplicities are
calculated by dividing the Wyckoff multiplicity 𝓂 of the site by the general
multiplicity ℳ. Otherwise
f = 𝒪𝒸𝒸. ℳ 𝓂⁄ (9)
where 𝒪𝒸𝒸 is the occupation number, lastly.
1.9 Literature Review
The existence of impurity phases in barium hexaferrite sample, mainly α-Fe2O3 and
barium spinel (BaFe2O4) phases were reported by several investigators [36 - 40]. These
phases affect the properties of the prepared hexaferrites samples negatively. The presence
15
of such phases was shown to depend on the method of fabrication and the experimental
conditions, such as the heat treatment.
Sözeri et al. [37] synthesized BaFe12O19 particles by citrate sol–gel combustion
route with a sintering temperature ranging from 800 to 1200° C. The Fe:Ba ratio in this
study was varied from 2 to 12. They observed that the sample with Fe:Ba ratio of 12
sintered at 800° C contains a Ba-hexaferrite phase with a minor α-Fe2O3 impurity phase.
The sintering temperature of 900° C was high enough to crystallize barium hexaferrite
phase in the sol–gel route. They also observed that the annealing temperature up to 1100°
C would increase both the specific saturation magnetization and coercivity, where a
transition from single to multi domain structure occurs. Furthermore, they reported the
appearance of two peaks at about two-theta of 37° and 44°, in the sample sintered at 1200°
C, which they claimed to be associated with BaM phase. The peaks were reported to
become narrower with increasing the temperature, which they associated with increasing
the crystallite size.
Suastiyant, et al. [38] used the sol gel auto combustion method to synthesis barium
hexaferrite powder, then investigating the powder crystallite and grain size, crystal
structure and magnetic properties. They found that the Fe:Ba ratio in the precursor
material has an important influence on the diffraction pattern, magnetic properties and
crystallite size. They reported that the ratio 11.5 is the best ratio which gives the well-
crystalline powder with the smallest crystallite size 22 nm as they found. Nevertheless,
they did not use an accurate fitting method for the structural study and phase
identification.
Wang and Zhang [39] studied the Ba:Fe ratio effect on synthesizing a barium
hexaferrite powder using the citrate–EDTA complexing method. Powders with Fe:Ba
16
ratios of 6.5, 7,11, 11.5, and 12, calcined at 1000° C for five hours were synthesized. They
reported that the Fe:Ba ratio value is very important in developing the BaFe12O19 phase.
They claimed that they obtained pure barium hexaferrite phase with Fe:Ba ratios of 11
and 11.5. For other ratios, BaFe2O4 and Fe2O3 were observed, in addition to the hexagonal
barium ferrite major phase. However, they did not investigate the phase purity of the
samples treated at higher temperatures. Also their results showed that the calcination
temperature for samples with Fe:Ba ratio of 11.5 is lower than for other ratios.
Topal et al. [40] investigated the structural and magnetic properties of BaFe12O19
prepared by the ammonium nitrate melt technique (ANMT) with tuning the Fe:Ba ratio
from 2 to 13, and treated them at different temperatures from 800° C to 1200° C. They
reported that the BaFe2O4 impurity phase is formed at low Fe:Ba ratios (Fe:Ba = 2–6), in
addition to BaFe12O19 phase, and Fe2O3 is the only impurity phase that appears at high
Fe:Ba ratios (Fe:Ba = 8–13). They also claimed to obtain a high-quality single crystalline
BaFe12O19 successfully using ANMT, while keeping the Fe:Ba ratio between 2 and 6, and
washing the samples with diluted HCl after the heat treatment in order to get rid of the
BaFe2O4 impurity.
Other researchers used mixing and physical milling technique to prepare the barium
hexaferrite powder. Zlatkov, et al. [41] investigated the barium hexaferrite permanent
magnets prepared using the powder injection molding. The starting barium hexaferrite
powder was prepared by calcination followed by milling.
Suarez et al. [42] studied the magnetization for barium ferrite powders with
increasing the heating temperature from 1000° C to 1200° C with Fe:Ba ratios varying
from 7 to 15 and. They found that increasing the heating temperature was effective in
increasing the magnetization of the powders for the ratios larger than 10. For lower ratios,
17
the magnetization increased initially and then decreased with increasing temperature
“presumably due to the formation of BaFe2O4” as they predicted. Furthermore, they
investigated the effect of the milling time on the magnetic properties and powder
characteristics and found that forty hours of milling was enough to obtain samples with
less volume fraction of other phases.
Janasi, et al. [43] prepared MnZn ferrites using co-precipitation and solid state
reaction. They investigated the effect of the calcination temperature on the magnetic
properties of the ferrites.
Campbell, et al. [44] investigated the effects of dry-milling BaM in air on the
particle properties using X-ray diffraction. They reported that the sizes of the particles
decrease, and a partial decomposition of BaFe12O19 to α-Fe2O3 was found to take place
upon extended milling for 1000 h.
Using the XRD pattern refinement technique, Ashima, et al. [45] used the Rietveld
refinement of X-ray powder diffraction data of Ca–Sr substituted barium hexaferrites and
found that the samples possess single hexagonal phase with space group consistent that
for BaM phase having the composition BaFe12O19. On the other hand, Brando, et al. [46]
used X-ray data to determine the cation distributions Ir-Co and Ir-Zn on the various Fe
sites of the substituted BaM-hexaferrites. They used their XRD results concerning the
preferred sites and multiplicity of the different cations to explain the magnetization data.
Also, Suminar Pratapa, [47] analyzed the phase composition of ceramic powder using
Rietveld refinement method.
18
CHAPTER 2
Methodology
2.1 Preparation of non-stoichiometric Barium hexaferrite samples
With high iron to barium ratio (11.5 – 16.16)
2.2 Structural characterization
2.3 Preparation of non-stoichiometric Barium hexaferrite samples with iron to
barium ratio = 9 and 7
19
2.1 Preparation of non-stoichiometric Barium hexaferrite samples
With high iron to barium ratio (11.5 – 16.16)
About 10 g of a mixture of the of high purity (≥ 99%) BaCO3 and α-Fe2O3 powders
with Fe:Ba molar ratio of 11.5 was prepared using high energy ball milling. Appropriate
amounts of the powder precursors were weighed accurately (to five decimal places) and
mixed in two zirconia cups and milled for 16 hours in an acetone bath using a (Fritsch
Pulverisette 7) ball mill. Seven zirconia balls were used for the milling with a ball-to-
powder ratio of 14. The rotational speed was 250 rpm. The milled powder was left to dry
at room temperature. This powder was used to synthesize six different barium hexaferrite
samples with Fe to Ba ratio ranging from 11.5 to 16.16. About one gram of the dry powder
was pressed into 1.3 mm diameter disc under a 50 kN force, and sintered at 1100° C for 2
hours. This sample is labled (0%) as shown in Table 2.1. Then five different samples with
different Fe:Ba ratios were prepared by mixing portions of the original powder with
different weight ratios of α-Fe2O3 (from 5% to 25%) for about an hour using an agate
mortar and pestle, pressing into discs and sintering at 1100° C (Table 2.1).
Table (2.1) the iron to barium ratio for each sample.
Sample name 25% 20% 15% 10% 5% 0%
Fe:Ba Ratio 16.158 14.993 13.699 13.053 12.236 11.500
2.2 Structural characterization
The structure of the samples was investigated by θ-2θ x-ray diffraction (XRD) using
Shimadzu X-ray Diffraction Instrument, with Cu-Kα ray (λα1 = 1.540560 Å and λα2 =
1.544390 Å). The XRD scan configuration was, (2θ = 20° – 70°) for the scan range, with
step time of 1.2 s and 0.01° sampling pitch. A divergence slit of width DF = 2.4 mm, a
scattering slits of width SS = 1.25 mm, and a receiving slit of width RS = 0.9 mm were
used for the data collection.
20
XRD patterns of the samples were initially analyzed beginning with Panalytical
X'Pert Highscore plus software based on PDF-2 ICDD library. This analysis revealed the
phases in each sample by matching the observed pattern with those included in the library.
It was found that the sample with Fe:Ba ratio of 11.5 consisted of a single phase of
M-type barium hexaferrite (Fig 2.1). However, all samples added with α-Fe2O3 consisted
of two phases; the M-type barium hexaferraite, and the iron oxide (α-Fe2O3). Figures (2.2)
and (2.3) show the patterns of the samples 0% (Fe:Ba = 11.5) and 25% (Fe:Ba = 16.16)
analyzed using the X’pert software.
Figure (2.1) XRD pattern of barium hexaferrite sample with Fe:Ba ratio = 11.5
21
Figure (2.2) XRD pattern matching for the sample with Fe:Ba ratio of 11.5.
22
Figure (2.3) XRD pattern matching for the sample with Fe:Ba ratio of 16.16.
23
The process of determining the phases in a pattern using X'Pert Highscore plus
software begins by matching two things, first by matching the peak positions of the XRD
pattern, secondly by matching the height of these peaks with reference patterns in the
software database. It should be noted that the software cannot determine the phases
automatically; it needs a user's hand and eye to match those profiles.
The second step of the analysis begins by fitting these data to a theoretical pattern
of the structure, based on the space group, cell dimension, and other parameters that play
a role in the fitting routine. Initially, the patterns were fitted using the whole-pattern
decomposition (Profile Matching) procedure in FullProf software (this procedure is also
known as Lebail Fitting) [48]. It has been used in Profile Matching with the constant scale
factor technique. This technique makes data entry much easier and significantly expands
the scope of the powder pattern profile refinement. However, the restriction applicable to
the refinement is much less severe than the Rietveld refinement, and the Profile Matching
is therefore more prone to instability, but it is a very useful initial step in the refinement
process, due to the speed and the ease of the refinement, and the validity confirmation of
the input information. Furthermore, the output of this process is excellent.
The five samples were fitted using the Profile Matching refinement routine. The
difference in the impurity phase’s integrated intensities between the samples was obvious,
and the fitting came up with a very good chi square value, the Bragg R-factor and RF-
factor were rather low, indicating the reliability of the fit. The goodness of fit can be
concluded directly by observing the difference pattern between the observed and the
theoretical patterns (Yobs - Ycal) as shown in Figures (2.4) and (2.5).
24
Figure (2.4) The fitted XRD pattern using profile matching method for the sample with
Fe:Ba ratio of 11.5.
Figure (2.5) The fitted XRD pattern using profile matching method for the sample with
Fe:Ba ratio of 16.16.
25
The first fitted pattern for the sample of Fe:Ba ratio of 11.5 in figure (2.4) has a Chi
squared value = 1.24, (BaFe12O19) Brag R-factor= 0.442 and RF-factor= 0.601. The
second pattern for the sample of Fe:Ba ratio of 16.16 in figure (2.5) has a Chi squared
value = 1.344. The BaFe12O19 Brag RB-factor = 0.434 and RF-factor = 0.523, while the α-
Fe2O3 Brag RB-factor = 0.523 and RF-factor = 0.517.
The output parameters of the previous operation include the cell parameters (a, b,
c) and some other important parameters necessary for the next fitting step. Rietveld
refinement process is then performed using the previous output. Several other parameters
were necessary for the process, Wyckoff positions being the most important.
Although the Rietveld profile refinement is rather simple in theory, it requires some
expertise and good scientific background in crystallography to be implemented properly.
Many characteristics of this refinement technique make it a tough starting refinement
method and may lead to incorrect starting steps. The correlation between the structure
parameters in this refinement may readily cause a premature divergence, and the least-
squares minimization algorithm often falls into fake minima. In order to avoid these
weaknesses, a particular procedure should be followed, using the cell parameters obtained
from the previous refinement method (Profile Matching). In addition, this procedure
shortens the time required for the development of the cell refinement prototype, and ends
up with a good pattern fit.
Shift relaxation factors, which include the instrumental zero-shift, displacement and
transparency, pattern background information and parameters, are all picked from the
outputs of the previous refinement technique (Profile Matching). The cell parameters,
angles and the FWHM (Full width at half maximum) parameters for each phase are also
being taken from the previous outputs. Next, the atomic positions and related parameters
represented by the element, the Wyckoff positions, the occupancy and the isotropic
26
temperature parameter (Debye–Waller factor) for each site are used in the structural
refinement.
In the absence of sufficient crystallographic information regarding the structure, the
atomic positions are manually calculated to approximate numbers depending on the
theoretical reference of each space group, by taking the Wyckoff sites and their
multiplicities and coordinates. In addition, the normalized occupancies are manually
calculated. Initially the isotropic temperature parameters for all atoms are given the same
value, and then the refinement procedure leads to the final accurate refined values.
Table (2.2) shows the compatibility of the parameters after refinement by Profile
Matching method and Rietveld method. The word helpful means it helps in the fitting
process if it is used as an initial value.
Table (2.2) outputs compatibility between Rietveld and Profile matching method.
Parameters Compatibility Parameters Compatibility
Cell Parameters (a,b,c) 99.90% FWHM (U,V,W) peaks
parameters
Helpful, Don’t
match
Cell Angles, Space
group 100%, no change Scale Factor Unmatched
Pattern Background Helpful , 70% Preferred orientation Unmatched
Zero-shift,
displacement,
Transparency.
95%
Eta0, X
Unmatched (Additional shape parameters,
Lorentzian isotropic strain)
In all refinement methods, it is important to plot and compare the changes in the
fitted pattern. The difference between the fitted patterns after each refinement step is an
efficient and fast way to detect the fault-fitting step, and modify the refinement procedure
to obtain the best sequence and most reliable results.
27
2.3 Preparation of non-stoichiometric Barium hexaferrite samples with iron to
barium ratio = 9 and 7
Precursor powders with Fe:Ba ratios of 9 and 7 (significantly lower than the
stoichiometric ratio of 12) were prepared following the same procedure for preparing the
sample with Fe:Ba = 11.5 as outlined in section 2.1. The sample with Fe:Ba ratio of 7 has
the stoichiometry of Fe2-Y barium hexaferrite (Ba2Fe2Fe12O22) [7]. Therefore, the choice
of these two compositions was motivated by the fact that they extend between the
stoichiometries of the Y-type and the M-type hexaferrites. The effect of the sintering
temperature on the evolution of the structural phases in these samples was investigated
by analyzing the structure of different portions of the powder sintered at different
temperatures (800, 900, 1000, 1100 and 1200° C).
28
CHAPTER 3
Results
3.1 Result of non-stoichiometric barium hexaferrite Samples, Iron to barium
ratio (Fe+3 : Ba+2) ≥ 11.5
3.2 XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite
Samples with Iron to Barium ratio = 9
3.3 XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite
Samples with Iron to Barium ratio = 7
29
3.1 Result of non-stoichiometric barium hexaferrite Samples.
Iron to barium ratio (Fe+3 : Ba+2) ≥ 11.5
This section is concerned with the structural refinement of barium iron oxide sample
with Fe:Ba = 11.5. Rietveld profile refinement was performed using some of the fitting
parameters reported elsewhere [50 - 53]. A reliable fit was obtained Figure (3.1) with a
rather low Chi-Squared value, and the corresponding main structural output parameters
are listed below. The atomic positions obtained in this refinement process are in good
agreement with previously reported results [50-51].
Phase data Chi2 = 1.254
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8909 Å c=23.2087 Å
c/a=3.9398
V=697.50 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850
Fe +3 2a -3m. 1.02874 0.00000 0.00000 0.00000 0.00640
Fe +3 2b -6m2 0.95243 0.00000 0.00000 0.25027 0.00860
Fe +3 4f 3m. 0.97621 0.33333 0.66667 0.02660 0.00240
Fe +3 4f 3m. 0.99455 0.33333 0.66667 0.19027 0.00970
Fe +3 12k .m. 0.99554 0.16930 0.33856 0.89165 0.00590
O -2 4e 3m. 1.04014 0.00000 0.00000 0.15157 0.01460
O -2 4f 3m. 1.05451 0.33333 0.66667 0.94388 0.00020
O -2 6h mm2 0.97985 0.17590 0.35188 0.25000 0.00830
O -2 12k .m. 1.06558 0.15414 0.30820 0.05200 0.00790
O -2 12k .m. 1.04840 0.50185 1.00368 0.14928 0.00490
As it appears, there is no such difference between the figures (2.4) and (3.1), the two
fitted figures for the same sample (Zero Percent) done by the two different refinement
methods, the Profile Matching and Rietveld Refinement.
Sample Zero Percent (0%)
30
Figure (3.1) Fitted XRD pattern using Rietveld method for the sample with Fe:Ba ratio
= 11.5.
In what follows we show the fitted patterns and present the main structural results
of the two phase appearing in the patterns of the samples added with different weight
ratios of α-Fe2O3.
Sample Five Percent (5%)
Current global Chi2 (Bragg contrib.) = 1.312
Phase: 1 - BaFe12O19
Bragg R-factor : 2.64 Vol: 698.311 Fract(%): 95.35
Rf-factor : 2.51 ATZ: 47.727 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8928 Å c=23.2207 Å
c/a=3.9405
V=698.31 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 -0.00450
Fe +3 2a -3m. 1.03856 0.00000 0.00000 0.00000 -0.00330
Fe +3 2b -6m2 0.89774 0.00000 0.00000 0.25027 -0.00180
Fe +3 4f 3m. 0.95977 0.33333 0.66667 0.02722 -0.01350
Fe +3 4f 3m. 1.09681 0.33333 0.66667 0.19067 0.01280
Fe +3 12k .m. 1.01411 0.16838 0.33653 0.89167 0.00050
31
O -2 4e 3m. 0.98114 0.00000 0.00000 0.14998 -0.02330
O -2 4f 3m. 1.13034 0.33333 0.66667 0.94643 0.03240
O -2 6h mm2 1.10925 0.18134 0.36263 0.25000 0.00610
O -2 12k .m. 1.18231 0.15705 0.31385 0.05151 0.01520
O -2 12k .m. 1.19880 0.50313 1.00634 0.14946 0.01820
Phase: 2 - Fe2O3
Bragg R-factor : 5.13 Vol: 298.864 Fract(%): 4.65
Rf-factor : 4.06 ATZ: 30.8 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=4.9908 Å c=13.8549 Å
c/a=2.7761
V=298.86 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.37484 0.00810
O -2 18e 0.2 1.04882 0.45368 0.00000 0.25000 0.01200
Figure (3.2) Fitted XRD pattern using Rietveld method for the sample with Fe:Ba ratio
= 12.24.
32
Figure (3.3) Fitted XRD pattern using Rietveld method for the sample with Fe:Ba ratio
= 13.05
Sample Ten Percent (10%)
Current global Chi2 (Bragg contrib.) = 1.134
Phase: 1 - BaFe12O19
Bragg R-factor : 1.65 Vol: 698.363 Fract(%): 92.04
Rf-factor : 1.86 ATZ: 45.649 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8933 Å c=23.2186 Å
c/a=3.9398
V=698.36 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.00000 -0.00290
Fe +3 2a -3m. 1.02491 0.00000 0.00000 0.00000 -0.00880
Fe +3 2b -6m2 0.90808 0.00000 0.00000 0.25027 -0.00300
Fe +3 4f 3m. 0.96735 0.33333 0.66667 0.02734 -0.00800
Fe +3 4f 3m. 1.08892 0.33333 0.66667 0.19063 0.01590
Fe +3 12k .m. 1.01904 0.16928 0.33841 0.89179 -0.00040
O -2 4e 3m. 0.97380 0.00000 0.00000 0.15076 -0.01660
O -2 4f 3m. 1.15979 0.33333 0.66667 0.94475 0.04390
O -2 6h mm2 1.13459 0.17995 0.35989 0.25000 0.01810
O -2 12k .m. 1.18657 0.15524 0.31029 0.05176 0.02230
O -2 12k .m. 1.21664 0.50398 1.00803 0.14867 0.02910
33
Phase: 2 - Fe2O3
Bragg R-factor : 3.43 Vol: 301.932 Fract(%): 7.96
Rf-factor : 3.05 ATZ: 6.099 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=5.0357 Å c=13.7488 Å
c/a=2.7303
V=301.93 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35501 -0.00330
O -2 18e 0.2 1.54843 0.32240 0.00000 0.25000 0.10040
Sample Fifteen Percent (15%)
Current global Chi2 (Bragg contrib.) = 1.154
Phase: 1 - BaFe12O19
Bragg R-factor : 1.51 Vol: 698.843 Fract(%): 85.17
Rf-factor : 1.89 ATZ: 45.052 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8946 Å c=23.2242 Å
c/a=3.9399
V=698.84 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 -0.00270
Fe +3 2a -3m. 0.99057 0.00000 0.00000 0.00000 -0.01150
Fe +3 2b -6m2 0.93310 0.00000 0.00000 0.25027 -0.00210
Fe +3 4f 3m. 0.96784 0.33333 0.66667 0.02788 -0.01280
Fe +3 4f 3m. 1.08877 0.33333 0.66667 0.19012 0.00920
Fe +3 12k .m. 0.96598 0.16914 0.33816 0.89180 -0.00970
O -2 4e 3m. 1.03173 0.00000 0.00000 0.14939 0.00990
O -2 4f 3m. 1.09777 0.33333 0.66667 0.94525 0.01800
O -2 6h mm2 1.23928 0.18519 0.37042 0.25000 0.02850
O -2 12k .m. 1.09248 0.15492 0.30968 0.05153 -0.00090
O -2 12k .m. 1.24943 0.50201 1.00404 0.14796 0.02910
Phase: 2 - Fe2O3
Bragg R-factor : 2.31 Vol: 302.1 Fract(%): 14.83
Rf-factor : 1.98 ATZ: 7.157 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=5.0363 Å c=13.7528 Å
c/a=2.7307
V=302.10 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35517 -0.00910
O -2 18e 0.2 1.23563 0.31597 0.00000 0.25000 0.04070
34
Figure (3.4) Fitted XRD pattern using Rietveld method for the sample with Fe:Ba ratio
= 13.97.
Figure (3.5) Fitted XRD pattern using Rietveld method for the sample with Fe:Ba ratio
= 14.99.
35
Sample Twenty Percent (20%)
Current global Chi2 (Bragg contrib.) = 1.183
Phase: 1 - BaFe12O19
Bragg R-factor : 1.83 Vol: 698.091 Fract(%): 80.34
Rf-factor : 2.18 ATZ: 50.271 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8926 Å c=23.2151 Å
c/a=3.9397
V=698.09 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 -0.00170
Fe +3 2a -3m. 1.06749 0.00000 0.00000 0.00000 -0.00190
Fe +3 2b -6m2 0.94403 0.00000 0.00000 0.25027 -0.00700
Fe +3 4f 3m. 0.92099 0.33333 0.66667 0.02696 -0.02320
Fe +3 4f 3m. 1.05597 0.33333 0.66667 0.18997 0.00750
Fe +3 12k .m. 1.01166 0.16919 0.33822 0.89195 -0.00500
O -2 4e 3m. 1.26872 0.00000 0.00000 0.15181 0.05130
O -2 4f 3m. 1.24897 0.33333 0.66667 0.94445 0.03290
O -2 6h mm2 1.10809 0.18162 0.36332 0.25000 0.00730
O -2 12k .m. 1.26145 0.15671 0.31334 0.05194 0.03990
O -2 12k .m. 1.23018 0.50476 1.00954 0.14930 0.02110
Phase: 2 - Fe2O3
Bragg R-factor : 3.3 Vol: 301.82 Fract(%): 19.66
Rf-factor : 2.32 ATZ: 20.074 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=5.0348 Å c=13.7483 Å
c/a=2.7306
V=301.82 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35555 -0.00260
O -2 18e 0.2 1.13611 0.31775 0.00000 0.25000 0.01650
36
Sample Twenty Five Percent (25%)
Current global Chi2 (Bragg contrib.) = 1.225
Phase: 1 - BaFe12O19
Bragg R-factor : 1.89 Vol: 698.37 Fract(%): 74.62
Rf-factor : 2.36 ATZ: 47.87 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8934 Å c=23.2183 Å
c/a=3.9397
V=698.37 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25 0.0023
Fe +3 2a -3m. 1.11471 0 0 0 0.0107
Fe +3 2b -6m2 1.02743 0 0 0.25027 0.0284
Fe +3 4f 3m. 0.92394 0.33333 0.66667 0.02739 -0.0171
Fe +3 4f 3m. 0.97091 0.33333 0.66667 0.19008 -0.0093
Fe +3 12k .m. 0.98351 0.1675 0.33489 0.89174 -0.0063
O -2 4e 3m. 1.31214 0 0 0.15056 0.0729
O -2 4f 3m. 0.84414 0.33333 0.66667 0.94507 -0.0529
O -2 6h mm2 1.02605 0.17826 0.35665 0.25 0.0002
O -2 12k .m. 1.33195 0.15185 0.30357 0.05105 0.0467
O -2 12k .m. 1.0859 0.50385 1.00771 0.15112 0.0059
Phase: 2 - Fe2O3
Bragg R-factor : 2.7 Vol: 301.891 Fract(%): 25.38
Rf-factor : 1.7 ATZ: 9.123 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=5.0354 Å c=13.7483 Å
c/a=2.7303
V=301.89 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35608 0.00110
O -2 18e 0.2 0.88372 0.31022 0.00000 0.25000 -0.03920
37
Figure (3.6) Fitted XRD pattern using Rietveld method for the sample with Fe:Ba ratio
= 16.16.
3.2 XRD Data Refinement Result of Non-Stoichiometric Barium
Hexaferrite Samples with Fe:Ba Ratio = 9
This section presents the Rietveld refinement results of barium iron oxide samples
with Fe:Ba ratio of 9. The structural characteristics for (BaFe2O4 & Ba3Fe2O6) reported
elsewhere [53, 54] were used at the initial stages of the fitting process in order to
shorten the processing time and ease the job.
The patterns of the samples sintered at different temperatures were initially analyzed
using X’Pert High Score Plus software (Figures 3.7-3.11). These figures indicate that the
patterns of the samples sintered at temperatures below 1000° C consisted of BaM
hexaferrite phase in addition to two minor phases, namely, BaFe2O4 barium spinel and α-
Fe2O3. At higher sintering temperatures these phases diminish with increasing sintering
temperature, and a new (Ba3Fe2O6) phase evolves. Table (3.1) shows the phases co-
existing in the patterns of the samples sintered at different temperatures.
38
Figure (3.7) XRD pattern for the sample with Fe:Ba = 9 sintered at 1200° C.
Figure (3.8) XRD pattern for the sample with Fe:Ba = 9 sintered at 1100° C.
39
Figure (3.9) XRD pattern for the sample with Fe:Ba = 9 sintered at 1000° C.
40
Figure (3.10) XRD pattern for the sample with Fe:Ba = 9 sintered at 900° C.
41
Figure (3.11) XRD pattern for the sample with Fe:Ba = 9 sintered at 800° C.
42
Table (3.1) Structural phases existing in the samples with Fe:Ba = 9 sintered at different
temperatures
Sample's Phases in the sample
Cent. Tem. Phase #1 Phase #2 Phase #3
1200° C Ba Fe12 O19 Ba3 Fe2 O6
1100° C Ba Fe12 O19 Ba3 Fe2 O6 Ba Fe2 O4
1000° C Ba Fe12 O19 Ba3 Fe2 O6 Ba Fe2 O4
900° C Ba Fe12 O19 Ba Fe2 O4 Fe2 O3
800° C Ba Fe12 O19 Ba Fe2 O4 Fe2 O3
The main structural information for the various phases in all samples were
obtained from Rietveld refinement of the diffraction patterns. Specifically, the types of
phases, their structural parameters and relative proportion (as weight ratio) in each
sample are presented below.
Sample Sintered at (1200° C)
Current global Chi2 (Bragg contrib.) = 1.34
Phase: 1 - BaFe12O19
Bragg R-factor : 2.31 Vol: 702.056 Fract(%): 93.33
Rf-factor : 2.34 ATZ: 45.59 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.9002 Å c=23.2864 Å
c/a=3.9467
V=702.06 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930
Fe +3 2a -3m. 1.01784 0.00000 0.00000 0.00000 0.00840
Fe +3 2b -6m2 0.87766 0.00000 0.00000 0.25027 0.00520
Fe +3 4f 3m. 0.96304 0.33333 0.66667 0.02757 0.00320
Fe +3 4f 3m. 1.06839 0.33333 0.66667 0.19068 0.00760
Fe +3 12k .m. 1.02251 0.16758 0.33501 0.89240 0.00610
O -2 4e 3m. 0.98003 0.00000 0.00000 0.14883 0.00600
O -2 4f 3m. 0.93670 0.33333 0.66667 0.94346 0.00680
O -2 6h mm2 1.02407 0.17994 0.35994 0.25000 0.00560
O -2 12k .m. 1.19088 0.14689 0.29360 0.04970 0.00630
O -2 12k .m. 1.09544 0.50402 1.00812 0.14942 0.00600
Phase: 2 - Ba3Fe2O6
Bragg R-factor : 5.49 Vol: 4699.994 Fract(%): 6.67
Rf-factor : 7.13 ATZ: 136.703 Brindley: 2.24
Phase data
Space-group P a -3 (205) - cubic
43
Cell a=16.7507 Å
V=4700.00 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270
Ba 4b .-3. 0.73916 0.50000 0.00000 0.00000 0.01270
Ba 8c .3. 1.00129 0.25226 0.25226 0.25226 0.01270
Ba 8c .3. 0.76440 0.37500 0.37500 0.37500 0.01270
Ba 24d 1 0.84110 0.12964 0.37744 0.11673 0.01270
Ba 24d 1 0.83700 0.37372 0.38000 0.11977 0.01270
Fe 24d 1 2.58565 0.26620 -0.00217 0.01797 0.01270
Fe 24d 1 2.83225 0.24765 0.23832 -0.00329 0.01270
O 24d 1 1.69547 0.28115 0.11895 0.01386 0.01270
O 24d 1 1.92632 0.48167 0.12288 0.25036 0.01270
O 24d 1 1.22244 0.24696 0.30480 0.10193 0.01270
O 24d 1 0.21458 0.41001 0.29516 0.01270
O 24d 1 1.96656 0.36943 -0.00574 0.01734 0.01270
O 24d 1 4.63592 0.15068 -0.01144 -0.02054 0.01270
Sample Sintered at (1100° C)
Current global Chi2 (Bragg contrib.) = 1.37
Phase: 1 - BaFe12O19
Bragg R-factor : 3.95 Vol: 699.947 Fract(%): 92.35
Rf-factor : 2.8 ATZ: 45.59 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8962 Å c=23.2481 Å
c/a=3.9429
V=699.95 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930
Fe +3 2a -3m. 0.96584 0.00000 0.00000 0.00000 0.00840
Fe +3 2b -6m2 0.98036 0.00000 0.00000 0.25027 0.00520
Fe +3 4f 3m. 1.04398 0.33333 0.66667 0.02795 0.00320
Fe +3 4f 3m. 1.13920 0.33333 0.66667 0.19125 0.00760
Fe +3 12k .m. 1.04256 0.16737 0.33459 0.89182 0.00610
O -2 4e 3m. 1.04825 0.00000 0.00000 0.15556 0.00600
O -2 4f 3m. 1.11187 0.33333 0.66667 0.94346 0.00680
O -2 6h mm2 1.35753 0.18147 0.36294 0.25000 0.00560
O -2 12k .m. 1.13123 0.16429 0.32834 0.05167 0.00630
O -2 12k .m. 1.33276 0.50224 1.00454 0.14769 0.00600
44
Phase: 2 - Ba3Fe2O6
Bragg R-factor : 3.94 Vol: 4699.897 Fract(%): 6.13
Rf-factor : 4.71 ATZ: 108.207 Brindley: 1.915
Phase data
Space-group P a -3 (205) - cubic
Cell a=16.7506 Å
V=4699.89 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270
Ba 4b .-3. 0.69485 0.50000 0.00000 0.00000 0.01270
Ba 8c .3. 0.53613 0.25126 0.25126 0.25126 0.01270
Ba 8c .3. 0.99923 0.37543 0.37543 0.37543 0.01270
Ba 24d 1 1.09877 0.12767 0.37353 0.12316 0.01270
Ba 24d 1 0.94081 0.37121 0.37647 0.12617 0.01270
Fe 24d 1 1.25109 0.25225 -0.00517 -0.00019 0.01270
Fe 24d 1 1.66013 0.24902 0.24418 -0.00322 0.01270
O 24d 1 1.71791 0.27413 0.11091 0.01235 0.01270
O 24d 1 2.46861 0.48665 0.12833 0.25334 0.01270
O 24d 1 0.61991 0.23381 0.33620 0.13170 0.01270
O 24d 1 0.22811 0.43551 0.28525 0.01270
O 24d 1 2.93889 0.35669 -0.00251 0.01393 0.01270
O 24d 1 2.51819 0.13222 -0.01231 -0.01094 0.01270
Phase: 3 - BaFe2O4
Bragg R-factor : 7.37 Vol: 885.059 Fract(%): 1.52
Rf-factor : 5.12 ATZ: 0.746 Brindley: 1
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=19.3033 Å b=5.4285 Å c=8.4462 Å
a/b=3.5559 b/c=0.6427 c/a=0.4376
V=885.06 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4 0.13070 0.25000 0.00000 0.01270
Ba 4 0.61730 0.22700 0.00000 0.01270
Fe 8 0.50000 0.04240 0.73200 0.27760 0.01270
Fe 8 0.50000 0.20840 0.77400 0.29130 0.01270
O 8 0.50000 0.03700 0.40300 0.24300 0.01270
O 8 0.50000 0.12300 0.91700 0.22500 0.01270
O 8 0.50000 0.20900 0.41700 0.28100 0.01270
O 4 0.45300 0.22600 0.00000 0.01270
O 4 0.28000 0.22600 0.00000 0.01270
45
Figure (3.12) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1200° C
Figure (3.13) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1100° C
46
Sample Sintered at (1000° C)
Current global Chi2 (Bragg contrib.) = 1.29
Phase: 1 - BaFe12O19
Bragg R-factor : 2.64 Vol: 697.834 Fract(%): 92.35
Rf-factor : 2.12 ATZ: 45.59 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8916 Å c=23.2140 Å
c/a=3.9402
V=697.83 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930
Fe +3 2a -3m. 0.96584 0.00000 0.00000 0.00000 0.00840
Fe +3 2b -6m2 0.98036 0.00000 0.00000 0.25027 0.00520
Fe +3 4f 3m. 1.04398 0.33333 0.66667 0.02744 0.00320
Fe +3 4f 3m. 1.13920 0.33333 0.66667 0.19146 0.00760
Fe +3 12k .m. 1.04256 0.16667 0.33241 0.89153 0.00610
O -2 4e 3m. 1.04825 0.00000 0.00000 0.15584 0.00600
O -2 4f 3m. 1.11187 0.33333 0.66667 0.94336 0.00680
O -2 6h mm2 1.35753 0.17698 0.35395 0.25000 0.00560
O -2 12k .m. 1.13123 0.15578 0.31132 0.05096 0.00630
O -2 12k .m. 1.33276 0.49863 0.99731 0.14760 0.00600
Phase: 2 - Ba3Fe2O6
Bragg R-factor : 3.11 Vol: 4682.433 Fract(%): 6.12
Rf-factor : 3.85 ATZ: 108.207 Brindley: 1.915
Phase data
Space-group P a -3 (205) - cubic
Cell a=16.7298 Å
V=4682.43 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270
Ba 4b .-3. 0.73111 0.50000 0.00000 0.00000 0.01270
Ba 8c .3. 0.52897 0.25126 0.25126 0.25126 0.01270
Ba 8c .3. 0.82462 0.37543 0.37543 0.37543 0.01270
Ba 24d 1 0.89095 0.12767 0.37353 0.12316 0.01270
Ba 24d 1 0.78915 0.37121 0.37647 0.12617 0.01270
Fe 24d 1 0.89987 0.25225 -0.00517 -0.00019 0.01270
Fe 24d 1 1.27131 0.24902 0.24418 -0.00322 0.01270
O 24d 1 1.29670 0.27413 0.11091 0.01235 0.01270
O 24d 1 2.05405 0.48665 0.12833 0.25334 0.01270
O 24d 1 0.74370 0.23381 0.33620 0.13170 0.01270
O 24d 1 0.22811 0.43551 0.28525 0.01270
47
O 24d 1 2.06623 0.35669 -0.00251 0.01393 0.01270
O 24d 1 2.26942 0.13222 -0.01231 -0.01094 0.01270
Phase: 3 - BaFe2O4
Bragg R-factor : 8.28 Vol: 883.719 Fract(%): 1.53
Rf-factor : 5.49 ATZ: 0.746 Brindley: 1
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=19.2787 Å b=5.4314 Å c=8.4396 Å
a/b=3.5495 b/c=0.6436 c/a=0.4378
V=883.72 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4 0.13070 0.25000 0.00000 0.01270
Ba 4 0.61730 0.22700 0.00000 0.01270
Fe 8 0.50000 0.04240 0.73200 0.27760 0.01270
Fe 8 0.50000 0.20840 0.77400 0.29130 0.01270
O 8 0.50000 0.03700 0.40300 0.24300 0.01270
O 8 0.50000 0.12300 0.91700 0.22500 0.01270
O 8 0.50000 0.20900 0.41700 0.28100 0.01270
O 4 0.45300 0.22600 0.00000 0.01270
O 4 0.28000 0.22600 0.00000 0.01270
Figure (3.14) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 1000° C
48
Sample Sintered at #4 (900° C)
Current global Chi2 (Bragg contrib.) = 1.52
Phase: 1 - BaFe12O19
Bragg R-factor : 2.81 Vol: 697.946 Fract(%): 89.53
Rf-factor : 2.68 ATZ: 47.638 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8927 Å c=23.2097 Å
c/a=3.9388
V=697.95 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930
Fe +3 2a -3m. 1.13704 0.00000 0.00000 0.00000 0.00840
Fe +3 2b -6m2 0.94186 0.00000 0.00000 0.25027 0.00520
Fe +3 4f 3m. 1.01744 0.33333 0.66667 0.02868 0.00320
Fe +3 4f 3m. 1.16653 0.33333 0.66667 0.19152 0.00760
Fe +3 12k .m. 0.93037 0.16877 0.33730 0.89164 0.00610
O -2 4e 3m. 1.17982 0.00000 0.00000 0.15225 0.00600
O -2 4f 3m. 1.01163 0.33333 0.66667 0.94275 0.00680
O -2 6h mm2 1.40670 0.18357 0.36716 0.25000 0.00560
O -2 12k .m. 0.96110 0.16475 0.32925 0.05035 0.00630
O -2 12k .m. 1.06271 0.49655 0.99298 0.14611 0.00600
Phase: 2 - BaFe2O4
Bragg R-factor : 5.84 Vol: 870.27 Fract(%): 9.48
Rf-factor : 5.96 ATZ: 0.729 Brindley: 1
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=19.0096 Å b=5.3973 Å c=8.4821 Å
a/b=3.5221 b/c=0.6363 c/a=0.4462
V=870.27 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba1 4 0.13070 0.25000 0.00000 0.03590
Ba2 4 1.30716 0.61730 0.22700 0.00000 0.03930
Fe1 8 1.96763 0.04240 0.73200 0.27760 0.09300
Fe2 8 1.31198 0.20840 0.77400 0.29130 0.04200
O1 8 1.85124 0.03700 0.40300 0.24300 0.00130
O2 8 0.68871 0.12300 0.91700 0.22500 0.00130
O3 8 1.25689 0.20900 0.41700 0.28100 0.00130
O4 4 0.31543 0.45300 0.22600 0.00000 0.02440
O5 4 3.39807 0.28000 0.22600 0.00000 0.05480
49
Phase: 3 - Fe2O3
Bragg R-factor : 7.15 Vol: 295.448 Fract(%): 1
Rf-factor : 4.43 ATZ: 7.926 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=4.9776(1) Å c=13.7694(0) Å
c/a=2.7663
V=295.45(1) Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35530 0.00110
O -2 18e 0.2 0.81256 0.33032 0.00000 0.25000 -0.03920
Figure (3.15) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 900° C
50
Sample Sintered at #5 (800° C)
Current global Chi2 (Bragg contrib.) = 1.45
Phase: 1 - BaFe12O19
Bragg R-factor : 2.92 Vol: 697.436 Fract(%): 55.59
Rf-factor : 2.7 ATZ: 36.271 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8906 Å c=23.2093 Å
c/a=3.9401
V=697.44 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930
Fe +3 2a -3m. 1.09325 0.00000 0.00000 0.00000 0.00840
Fe +3 2b -6m2 1.17956 0.00000 0.00000 0.25027 0.00520
Fe +3 4f 3m. 1.12302 0.33333 0.66667 0.02872 0.00320
Fe +3 4f 3m. 1.25546 0.33333 0.66667 0.19257 0.00760
Fe +3 12k .m. 1.02133 0.16313 0.32604 0.89065 0.00610
O -2 4e 3m. 1.42708 0.00000 0.00000 0.15777 0.00600
O -2 4f 3m. 1.08383 0.33333 0.66667 0.94588 0.00680
O -2 6h mm2 1.63757 0.18002 0.36003 0.25000 0.00560
O -2 12k .m. 1.00876 0.15616 0.31204 0.04811 0.00630
O -2 12k .m. 1.16204 0.47897 0.95788 0.14526 0.00600
Phase: 2 - BaFe2O4
Bragg R-factor : 6.4 Vol: 866.024 Fract(%): 28.4
Rf-factor : 6.71 ATZ: 0.93 Brindley: 0.346
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=19.0160 Å b=5.3845 Å c=8.4579 Å
a/b=3.5316 b/c=0.6366 c/a=0.4448
V=866.02 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba1 4 0.13070 0.25000 0.00000 0.03590
Ba2 4 1.60329 0.61730 0.22700 0.00000 0.03930
Fe1 8 1.48709 0.04240 0.73200 0.27760 0.09300
Fe2 8 1.08157 0.20840 0.77400 0.29130 0.04200
O1 8 0.55106 0.03700 0.40300 0.24300 0.00130
O2 8 1.09566 0.12300 0.91700 0.22500 0.00130
O3 8 1.52934 0.20900 0.41700 0.28100 0.00130
O4 4 0.20305 0.45300 0.22600 0.00000 0.02440
O5 4 3.23005 0.28000 0.22600 0.00000 0.05480
51
Phase: 3 - Fe2O3
Bragg R-factor : 4.09 Vol: 301.793 Fract(%): 16.02
Rf-factor : 3.31 ATZ: 7.926 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=5.0353 Å c=13.7445 Å
c/a=2.7296
V=301.79 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35530 0.00110
O -2 18e 0.2 0.81256 0.33032 0.00000 0.25000 -0.03920
Figure (3.16) FullProf fitted pattern of the sample with Fe:Ba = 9 sintered at 800° C
52
3.3 XRD Data Refinement Result of Non-Stoichiometric Barium Hexaferrite
Samples with Iron to Barium ratio = 7
This section presents the Rietveld refinement results of barium iron oxide samples
with Fe:Ba = 7 Refinement method. XRD patterns of the samples sintered at different
temperatures (3.17 – 3.21) indicated the existence of the phases observed in the patterns
of the sample with Fe:Ba = 9, which evolve with increasing the sintering temperature in
a similar fashion. Although the stoichiometry of this sample is identical to that oy the T-
type hexaferrite, the Y-type phase was not observed in the range of sintering temperature
up to 1200° C. Table (3.2) summarizes the phases that were formed in the samples
sintered at different temperaturess.
Figure (3.17) XRD pattern for the sample with Fe:Ba = 7 sintered at 1200° C.
53
Figure (3.18) XRD pattern for the sample with Fe:Ba = 7 sintered at 1100° C.
Figure (3.19) XRD pattern for the sample with Fe:Ba = 7 sintered at 1000° C.
54
Figure (3.20) XRD pattern for the sample with Fe:Ba = 7 sintered at 900° C.
55
Figure (3.21) XRD pattern for the sample with Fe:Ba = 7 sintered at 800° C.
56
Table (3.2) Structural phases existing in the samples with Fe:Ba = 7 sintered at different
temperatures
Sample's Phases in the sample
Cent. Tem. Phase #1 Phase #2 Phase #3 Phase #4
1200° C Ba Fe12 O19 Ba3 Fe2 O6
1100° C Ba Fe12 O19 Ba3 Fe2 O6 Ba Fe2 O4
1000° C Ba Fe12 O19 Ba3 Fe2 O6 Ba Fe2 O4
900° C Ba Fe12 O19 Ba3 Fe2 O6 Ba Fe2 O4 Fe2 O3
800° C Ba Fe12 O19 Ba Fe2 O4 Fe2 O3
The main structural information for the various phases in all samples were
obtained from Rietveld refinement of the diffraction patterns. Specifically, the types of
phases, their structural parameters and relative proportion (as weight ratio) in each
sample are presented below.
Sample Sintered at (1200° C)
Current global Chi2 (Bragg contrib.) = 1.52
Phase: 1 - BaFe12O19
Bragg R-factor : 4.15 Vol: 704.121 Fract(%): 87.57
Rf-factor : 3.19 ATZ: 45.59 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.9044(0) Å c=23.3217 Å
c/a=3.9499
V=704.12(0) Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930
Fe +3 2a -3m. 0.92928 0.00000 0.00000 0.00000 0.00840
Fe +3 2b -6m2 0.88158 0.00000 0.00000 0.25027 0.00520
Fe +3 4f 3m. 0.96875 0.33333 0.66667 0.02743 0.00320
Fe +3 4f 3m. 1.15666 0.33333 0.66667 0.19039 0.00760
Fe +3 12k .m. 0.99753 0.16744 0.33475 0.89260 0.00610
O -2 4e 3m. 1.02056 0.00000 0.00000 0.15183 0.00600
O -2 4f 3m. 1.02097 0.33333 0.66667 0.94413 0.00680
O -2 6h mm2 1.18503 0.17905 0.35813 0.25000 0.00560
O -2 12k .m. 1.15159 0.14913 0.29810 0.04955 0.00630
O -2 12k .m. 1.16886 0.50535 1.01076 0.14843 0.00600
Phase: 2 - Ba3Fe2O6
Bragg R-factor : 4.78 Vol: 4703.589 Fract(%): 12.43
57
Rf-factor : 6.17 ATZ: 108.207 Brindley: 1.915
Phase data
Space-group P a -3 (205) - cubic
Cell a=16.7549 Å
V=4703.59 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270
Ba 4b .-3. 1.33436 0.50000 0.00000 0.00000 0.01270
Ba 8c .3. 0.86081 0.25126 0.25126 0.25126 0.01270
Ba 8c .3. 0.87730 0.37543 0.37543 0.37543 0.01270
Ba 24d 1 1.06391 0.12767 0.37353 0.12316 0.01270
Ba 24d 1 0.81046 0.37121 0.37647 0.12617 0.01270
Fe 24d 1 1.60953 0.25225 -0.00517 -0.00019 0.01270
Fe 24d 1 1.93737 0.24902 0.24418 -0.00322 0.01270
O 24d 1 1.51483 0.27413 0.11091 0.01235 0.01270
O 24d 1 2.74642 0.48665 0.12833 0.25334 0.01270
O 24d 1 1.53847 0.23381 0.33620 0.13170 0.01270
O 24d 1 0.22811 0.43551 0.28525 0.01270
O 24d 1 2.81339 0.35669 -0.00251 0.01393 0.01270
O 24d 1 2.86388 0.13222 -0.01231 -0.01094 0.01270
Sample Sintered at (1100° C)
Current global Chi2 (Bragg contrib.) = 1.31
Phase: 1 - BaFe12O19
Bragg R-factor : 2.49 Vol: 702.602 Fract(%): 87.31
Rf-factor : 2.41 ATZ: 35.357 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.9020 Å c=23.2905 Å
c/a=3.9462
V=702.60 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850
Fe +3 2a -3m. 0.94418 0.00000 0.00000 0.00000 0.00640
Fe +3 2b -6m2 0.94797 0.00000 0.00000 0.25027 0.00860
Fe +3 4f 3m. 0.91769 0.33333 0.66667 0.02648 0.00240
Fe +3 4f 3m. 1.03832 0.33333 0.66667 0.18970 0.00970
Fe +3 12k .m. 0.99495 0.17061 0.34131 0.89239 0.00590
O -2 4e 3m. 0.83207 0.00000 0.00000 0.15348 0.01460
O -2 4f 3m. 0.80416 0.33333 0.66667 0.94427 0.00020
O -2 6h mm2 0.99748 0.17085 0.34180 0.25000 0.00830
58
O -2 12k .m. 1.07742 0.15136 0.30269 0.05053 0.00790
O -2 12k .m. 1.04494 0.50146 1.00287 0.15073 0.00490
Phase: 2 - Ba3Fe2O6
Bragg R-factor : 2.68 Vol: 4704.008 Fract(%): 11.59
Rf-factor : 5.07 ATZ: 102.671 Brindley: 1.915
Phase data
Space-group P a -3 (205) - cubic
Cell a=16.7554 Å
V=4704.01 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270
Ba 4b .-3. 1.20223 0.50000 0.00000 0.00000 0.01270
Ba 8c .3. 0.85908 0.25126 0.25126 0.25126 0.01270
Ba 8c .3. 0.91162 0.37543 0.37543 0.37543 0.01270
Ba 24d 1 1.08585 0.12767 0.37353 0.12316 0.01270
Ba 24d 1 0.80188 0.37121 0.37647 0.12617 0.01270
Fe 24d 1 1.59528 0.25225 -0.00517 -0.00019 0.01270
Fe 24d 1 2.05427 0.24902 0.24418 -0.00322 0.01270
O 24d 1 1.48222 0.27413 0.11091 0.01235 0.01270
O 24d 1 2.52070 0.48665 0.12833 0.25334 0.01270
O 24d 1 1.35894 0.23381 0.33620 0.13170 0.01270
O 24d 1 0.22811 0.43551 0.28525 0.01270
O 24d 1 2.87102 0.35669 -0.00251 0.01393 0.01270
O 24d 1 3.08094 0.13222 -0.01231 -0.01094 0.01270
Phase: 3 - BaFe2O4
Bragg R-factor : 9.58 Vol: 867.639 Fract(%): 1.1
Rf-factor : 7.01 ATZ: 0.89 Brindley: 1
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=18.8592 Å b=5.3793 Å c=8.5524 Å
a/b=3.5059 b/c=0.6290 c/a=0.4535
V=867.64 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba1 4 0.13070 0.25000 0.00000 0.03590
Ba2 4 1.61333 0.61730 0.22700 0.00000 0.03930
Fe1 8 1.53576 0.04240 0.73200 0.27760 0.09300
Fe2 8 1.11697 0.20840 0.77400 0.29130 0.04200
O1 8 0.56909 0.03700 0.40300 0.24300 0.00130
O2 8 1.13152 0.12300 0.91700 0.22500 0.00130
O3 8 1.57939 0.20900 0.41700 0.28100 0.00130
O4 4 0.20970 0.45300 0.22600 0.00000 0.02440
O5 4 3.33576 0.28000 0.22600 0.00000 0.05480
59
Figure (3.22) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 1200° C
Figure (3.23) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 1100° C
60
Sample Sintered at (1000° C)
Current global Chi2 (Bragg contrib.) = 1.36
Phase: 1 - BaFe12O19
Bragg R-factor : 3.07 Vol: 699.873 Fract(%): 87.29
Rf-factor : 2.81 ATZ: 35.357 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8974 Å c=23.2364 Å
c/a=3.9401
V=699.87 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850
Fe +3 2a -3m. 1.03977 0.00000 0.00000 0.00000 0.00640
Fe +3 2b -6m2 1.05044 0.00000 0.00000 0.25027 0.00860
Fe +3 4f 3m. 0.91562 0.33333 0.66667 0.02689 0.00240
Fe +3 4f 3m. 1.02764 0.33333 0.66667 0.18981 0.00970
Fe +3 12k .m. 0.98561 0.17127 0.34262 0.89152 0.00590
O -2 4e 3m. 0.93744 0.00000 0.00000 0.15949 0.01460
O -2 4f 3m. 0.89282 0.33333 0.66667 0.94268 0.00020
O -2 6h mm2 1.01164 0.16905 0.33817 0.25000 0.00830
O -2 12k .m. 0.98173 0.14337 0.28669 0.05051 0.00790
O -2 12k .m. 0.88862 0.50519 1.01028 0.14927 0.00490
Phase: 2 - Ba3Fe2O6
Bragg R-factor : 3.51 Vol: 4698.067 Fract(%): 11.62
Rf-factor : 5.53 ATZ: 102.671 Brindley: 1.915
Phase data
Space-group P a -3 (205) - cubic
Cell a=16.7484 Å
V=4698.07 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270
Ba 4b .-3. 1.27461 0.50000 0.00000 0.00000 0.01270
Ba 8c .3. 0.96526 0.25126 0.25126 0.25126 0.01270
Ba 8c .3. 0.90447 0.37543 0.37543 0.37543 0.01270
Ba 24d 1 1.13565 0.12767 0.37353 0.12316 0.01270
Ba 24d 1 0.87055 0.37121 0.37647 0.12617 0.01270
Fe 24d 1 1.50400 0.25225 -0.00517 -0.00019 0.01270
Fe 24d 1 2.28632 0.24902 0.24418 -0.00322 0.01270
O 24d 1 1.66998 0.27413 0.11091 0.01235 0.01270
O 24d 1 2.25407 0.48665 0.12833 0.25334 0.01270
O 24d 1 1.34105 0.23381 0.33620 0.13170 0.01270
61
O 24d 1 0.22811 0.43551 0.28525 0.01270
O 24d 1 3.29267 0.35669 -0.00251 0.01393 0.01270
O 24d 1 3.68900 0.13222 -0.01231 -0.01094 0.01270
Phase: 3 - BaFe2O4
Bragg R-factor : 7.86 Vol: 867.683 Fract(%): 1.09
Rf-factor : 6.48 ATZ: 0.89 Brindley: 1
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=18.8825 Å b=5.3663 Å c=8.5631 Å
a/b=3.5187 b/c=0.6267 c/a=0.4535
V=867.68 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba1 4 0.13070 0.25000 0.00000 0.03590
Ba2 4 1.61333 0.61730 0.22700 0.00000 0.03930
Fe1 8 1.53576 0.04240 0.73200 0.27760 0.09300
Fe2 8 1.11697 0.20840 0.77400 0.29130 0.04200
O1 8 0.56909 0.03700 0.40300 0.24300 0.00130
O2 8 1.13152 0.12300 0.91700 0.22500 0.00130
O3 8 1.57939 0.20900 0.41700 0.28100 0.00130
O4 4 0.20970 0.45300 0.22600 0.00000 0.02440
O5 4 3.33576 0.28000 0.22600 0.00000 0.05480
Figure (3.24) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 1000° C
62
Sample Sintered at (900° C)
Current global Chi2 (Bragg contrib.) = 1.48
Phase: 1 - BaFe12O19
Bragg R-factor : 3.08 Vol: 698.586 Fract(%): 70.14
Rf-factor : 2.83 ATZ: 32.946 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8941 Å c=23.2194 Å
c/a=3.9394
V=698.58 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00850
Fe +3 2a -3m. 1.12500 0.00000 0.00000 0.00000 0.00640
Fe +3 2b -6m2 1.04400 0.00000 0.00000 0.25030 0.00860
Fe +3 4f 3m. 0.93400 0.33333 0.66667 0.02740 0.00240
Fe +3 4f 3m. 1.10600 0.33333 0.66667 0.19010 0.00970
Fe +3 12k .m. 1.03700 0.16880 0.33770 0.89250 0.00590
O -2 4e 3m. 0.96100 0.00000 0.00000 0.16340 0.01460
O -2 4f 3m. 1.10700 0.33333 0.66667 0.94390 0.00020
O -2 6h mm2 0.99900 0.17910 0.35820 0.25000 0.00830
O -2 12k .m. 1.01000 0.15750 0.31510 0.04650 0.00790
O -2 12k .m. 0.93900 0.51240 1.02460 0.14730 0.00490
Phase: 2 - Ba3Fe2O6
Bragg R-factor : 3.08 Vol: 4640.244 Fract(%): 4.32
Rf-factor : 4.29 ATZ: 82.661 Brindley: 1.915
Phase data
Space-group P a -3 (205) - cubic
Cell a=16.6794 Å
V=4640.25 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba 4a .-3. 0.00000 0.00000 0.00000 0.01270
Ba 4b .-3. 2.26600 0.50000 0.00000 0.00000 0.01270
Ba 8c .3. 1.07500 0.25370 0.25370 0.25370 0.01270
Ba 8c .3. 1.07300 0.37700 0.37700 0.37700 0.01270
Ba 24d 1 1.08900 0.12770 0.37350 0.12320 0.01270
Ba 24d 1 1.24000 0.37120 0.37650 0.12620 0.01270
Fe 24d 1 1.60200 0.25220 -0.00520 -0.00020 0.01270
Fe 24d 1 2.77600 0.24900 0.24420 -0.00320 0.01270
O 24d 1 1.09200 0.27410 0.11090 0.01240 0.01270
O 24d 1 1.48700 0.48660 0.12830 0.25330 0.01270
O 24d 1 1.58400 0.23380 0.33620 0.13170 0.01270
63
O 24d 1 0.22810 0.43550 0.28530 0.01270
O 24d 1 3.30300 0.35670 -0.00250 0.01390 0.01270
O 24d 1 4.80100 0.13220 -0.01230 -0.01090 0.01270
Phase: 3 - BaFe2O4
Bragg R-factor : 4.5 Vol: 868.811 Fract(%): 24.69
Rf-factor : 4.46 ATZ: 0.871 Brindley: 0.346
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=18.9739 Å b=5.3879 Å c=8.4986 Å
a/b=3.5216 b/c=0.6340 c/a=0.4479
V=868.81 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba1 4 0.13070 0.25000 0.00000 0.03590
Ba2 4 1.58200 0.61730 0.22700 0.00000 0.03930
Fe1 8 1.94700 0.04240 0.73200 0.27760 0.09300
Fe2 8 1.18800 0.20840 0.77400 0.29130 0.04200
O1 8 0.08400 0.03700 0.40300 0.24300 0.00130
O2 8 1.47700 0.12300 0.91700 0.22500 0.00130
O3 8 1.28000 0.20900 0.41700 0.28100 0.00130
O4 4 0.62100 0.45300 0.22600 0.00000 0.02440
O5 4 3.33900 0.28000 0.22600 0.00000 0.05480
Phase: 4 - Fe2O3
Bragg R-factor : 4.55 Vol: 296.418 Fract(%): 0.85
Rf-factor : 2.64 ATZ: 7.926 Brindley: 0.765
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=4.9790 Å c=13.8068 Å
c/a=2.7730
V=296.42 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35530 0.00110
O -2 18e 0.2 0.81300 0.33030 0.00000 0.25000 -0.03920
64
Figure (3.25) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 900° C
Figure (3.26) FullProf fitted pattern of the sample with Fe:Ba = 7 sintered at 800° C
65
Sample Sintered at (800° C)
Current global Chi2 (Bragg contrib.) = 1.63
Phase: 1 - BaFe12O19
Bragg R-factor : 3.45 Vol: 696.759 Fract(%): 51.16
Rf-factor : 2.76 ATZ: 37.534 Brindley: 1
Phase data
Space-group P 63/m m c (194) - hexagonal
Cell
a=5.8889 Å c=23.1999 Å
c/a=3.9396
V=696.76 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba +2 2d -6m2 0.66667 0.33333 0.25000 0.00930
Fe +3 2a -3m. 1.20140 0.00000 0.00000 0.00000 0.00840
Fe +3 2b -6m2 1.29113 0.00000 0.00000 0.25027 0.00520
Fe +3 4f 3m. 1.15354 0.33333 0.66667 0.03134 0.00320
Fe +3 4f 3m. 1.25823 0.33333 0.66667 0.19511 0.00760
Fe +3 12k .m. 1.01496 0.16420 0.32819 0.89023 0.00610
O -2 4e 3m. 2.15753 0.00000 0.00000 0.15834 0.00600
O -2 4f 3m. 0.93868 0.33333 0.66667 0.95571 0.00680
O -2 6h mm2 1.86075 0.14504 0.29004 0.25000 0.00560
O -2 12k .m. 1.17398 0.14676 0.29331 0.04655 0.00630
O -2 12k .m. 1.12895 0.46730 0.93449 0.13989 0.00600
Phase: 2 - BaFe2O4
Bragg R-factor : 4.98 Vol: 864.837 Fract(%): 39.49
Rf-factor : 6.14 ATZ: 1.063 Brindley: 0.346
Phase data
Space-group B b 21 m (36) - orthorhombic
Cell
a=19.008(2) Å b=5.3822(8) Å c=8.4532(9) Å
a/b=3.5316 b/c=0.6367 c/a=0.4447
V=864.80(18) Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Ba1 4 0.13070 0.25000 0.00000 0.03590
Ba2 4 1.40000 0.61730 0.22700 0.00000 0.03930
Fe1 8 1.33838 0.04240 0.73200 0.27760 0.09300
Fe2 8 1.08378 0.20840 0.77400 0.29130 0.04200
O1 8 0.96162 0.03700 0.40300 0.24300 0.00130
O2 8 0.41405 0.12300 0.91700 0.22500 0.00130
O3 8 1.40000 0.20900 0.41700 0.28100 0.00130
O4 4 0.45300 0.22600 0.00000 0.02440
O5 4 3.11000 0.28000 0.22600 0.00000 0.05480
66
Phase: 3 - Fe2O3
Bragg R-factor : 4.06 Vol: 301.46 Fract(%): 9.35
Rf-factor : 3.17 ATZ: 8.014 Brindley: 0.75
Phase data
Space-group R -3 c (167) - trigonal
Cell
a=5.0336 Å c=13.7384 Å
c/a=2.7293
V=301.46 Å3
Atomic parameters
Atom Ox. Wyck. Site S.O.F. x/a y/b z/c U [Å2]
Fe +3 12c 3.0 0.00000 0.00000 0.35714 0.00110
O -2 18e 0.2 0.84102 0.33333 0.00000 0.25000 -0.03920
67
CHAPTER 4
Analysis and
Discussion
4.1 Non-stoichiometric barium hexaferrite samples
with Fe:Ba ratio ≥ 11.5
4.2 Non-stoichiometric barium hexaferrite samples
with Fe:Ba ratio = 9
4.3 Non-stoichiometric barium hexaferrite samples
with Fe:Ba ratio = 7
68
4.1 Non-stoichiometric barium hexaferrite samples with Fe:Ba ratio
≥ 11.5
In this section the results of the structural refinement for the system with Fe:Ba ratio
ranging from 11.5 – 16.16 are discussed. The relative diffracted intensity for the evolving
α-Fe2O3 (hematite) phase with increasing (Fe:Ba) ratio was used to determine the weight
ratio of the secondary hematite phase in the sample. In addition, a relation between the
weight ratio of the hematite phase and the starting Fe:Ba ratio was established, from
which the optimal ratio required for the synthesis of a pure hexaferrite phase was
determined. A summary of crystallographic information is also included, and the unit cell
of each crystallographic phase is constructed from the refined crystallographic
parameters.
As it has been shown in the previous chapter, the process of Rietveld refinement
revealed full structural information and the relative proportions of iron oxide (α-Fe2O3)
and BaM phases in each sample. Figure (4.1) shows the diffraction patterns of all samples
added with different amounts of α-Fe2O3. The figure demonstrates the evolution of the
structural peaks corresponding to α-Fe2O3 (shaded in yellow) as a function of the weight
ratio of hematite added to the original powder (Fe:Ba = 11.5). The integrated intensities
Iα and IBaM of all structural peaks of α-Fe2O3 and BaFe12O19 phases, respectively, and the
ratio of these intensities for each sample are summarized in Table (4.1).
69
Figure (4.1) XRD patterns of all samples added with different amounts of α-Fe2O3. The
main structural peaks of iron oxide phase are shaded in yellow.
70
Table (4.1) The integrated intensity of all structural peaks of BaM (IBaM) and of
α-Fe2O3 (Iα), and the ratio (Iα/IBaM) for the samples with different Fe:Ba ratio.
The percentage ratio associated with the Fe:Ba ratio represents the wt% of α-
Fe2O3 added to the original powder
Fe:Ba => 16.158
(25%)
14.993
(20%)
13.966
(15%)
13.053
(10%)
12.236
(5%)
11.500
(0%)
IBaM 1234.7 1368.9 1408.9 1727.3 1626.3 1661.8
Iα 265.8 209.2 146 80.7 37.1 0
Iα/IBaM (%) 21.53 15.28 10.36 4.67 2.28 0
Figure (4.2) A plot of Iα/IBaM (%) vs Fe:Ba ratio for all samples
Figure 4.2 demonstrates a linear variation of the relative integrated intensity of α-Fe2O3
with increasing Fe:Ba ratio. The linear fit to the data gave a slope of 5.208 and an
intercept of 62.701. These values can be used to determine an approximate value (based
on integrated intensity) of the optimal Fe:Ba ratio for fabricating single BaM phase with
71
no additional iron oxide phase. The results indicates that the optimal value of Fe:Ba ratio
is 12.039.
The ratio of the secondary iron oxide phase in each sample can also be determined by
investigating the integrated intensities of the main peaks of the phases. Table (4.2) shows
the integrated intensity of the main peak of BaM at 34.1° (IMB) and that of α-Fe2O3 located
at 33.15° (IMα), as well as the ratio of the intensities of these peaks. Figure 4.3 shows the
relative intensity of the main peak of α-Fe2O3 as a function of Fe:Ba ratio. Linear fit to
the data gave a slope of 9.0535 and an intercept of 109.565. From these values the optimal
Fe:Ba ratio for a single BaM phase was found to be 12.102. This value is close to that
obtained from the whole-pattern integrated intensity analysis, and to the stoichiometric
composition of 12.0 for M-type hexaferrite. Further, Figure 4.3 can be used to determine
the weight ratio of α-Fe2O3 phase in any hexaferrite sample by evaluating the relative
intensity of the main peak and determining the corresponding Fe:Ba ratio, which can be
subsequently converted into wt% of the α-Fe2O3 phase using the molecular weights of the
phases and standard calculations.
Table (4.2) The integrated intensities of the main peaks of BaM (IMB), α-Fe2O3 (IMα), and
the peak ratios of the two phases for all samples. The percentage ratio associated with the
Fe:Ba ratio represents the wt% of α-Fe2O3 added to the original powder
angle
Fe:Ba ratio
16.158 14.993 13.966 13.053 12.236 11.5
-25% -20% -15% -10% -5% 0%
IMB 34.1 187.1 208.9 212 266.2 248.6 267.9
IMα 33.15 69.2 53.5 37.1 21 4 0
IMα/ IMB (%) 37 25.6 17.5 7.9 1.6 0
72
Figure (4.3) A plot of IMα/IMB (%) vs Fe:Ba ratio for all samples
The weight ratios of the different structural phases in a given sample can be
evaluated using Reitveld fitting of the corresponding diffraction pattern. The wt% of α-
Fe2O3 phase for each sample as determined by the fitting routine is listed in Table 4.3.
These values are generally lower than the wt% of α-Fe2O3 added to the original powder
(with Fe:Ba = 11.5), which indicates that the Fe:Ba ratio required for the synthesis of a
single BaM phase is higer than 11.5, a result consistent with the optimal ratio determined
by the analyses associated with Figure 4.2. Figure 4.4 shows the variation of the relative
main peak intensity of α-Fe2O3 with the weight ratio of this phase in each sample as
determined from Reitveld refinement of the corresponding diffraction pattern. The wt%
of α-Fe2O3
73
Table (4.3) α-Fe2O3 α-Fe2O3 wt% determined from Rietveld refinement of the
diffraction patterns and the corresponding relative main peak integrated intensity.
Sample 25% 20% 15% 10% 5% 0%
α-Fe2O3 wt% 25.01 19.53 14.59 7.50 3.53 0.00
IMα/ IMB (%) 37.00 25.60 17.50 7.90 1.60 0.00
The quantitative analysis parameters belonging to the impurity α-Fe2O3 phase were left
to be generated automatically in the refinement process of the sample added with 5 wt%
α-Fe2O3 to get better results. This is because the phase peaks are weak, approaching the
background fluctuations, so that the X-Ray absorption contrast cannot play a proper role
in this calculation. J. Berar [55] and R. Hill [56] for Standard deviations multiplication
factor (correlated residuals) during the fitting process.
Figure (4.4) A plot of IMα/IMB (%) as a function of α-Fe2O3 wt% evaluated from
the refinement of the patterns of all samples
74
The optimum ratio for synthesizing pure sample of barium hexaferrite (BaFe12O19)
can be obtained from the experimental result by linearly fitting the Fe:Ba ratio of the
prepared samples with the α-Fe2O3 wt% obtained from Rietveld refinement (Figure 4.6).
The best straight line representing the data intercepts the Fe:Ba ratio axis at 11.6, which
is the refined optimum ratio for a single barium hexaferrite phase. This value is somewhat
higher than 11.5 as predicted in the above discussion, but is lower than the value obtaind
from analysis of the integrated intensities.
Figure (4.5) Linear fit of Fe:Ba ratio vs α-Fe2O3 wt% obtained from the refinement of
the diffraction patterns.
Our refined patterns with rather low Chi-squared values gave valuable information
on the crystal structure and relative proportions of α-Fe2O3 α-Fe2O3 secondary phase.
Figure (4.6) shows the calculated pattern of our hexaferrite sample with Fe:Ba = 11.5,
together with standard patterns available in the ICDD library [57 , 58].
75
Figure (4.6) the calculated XRD stick pattern for BaFe12O19 phase compared with other
standard patterns in ICDD library.
All the data needed to build up the structural model of the unit cell is now available.
Since there is no difference in the crystallographic structure of the phases in samples
prepared with different stoichiometries as can be clearly seen from the results of the
refinement, the structural data of the sample with Fe:Ba = 11.5 was used to construct the
unit cell. Figures 4.7 and 4.8 show the unit cell from different angles as can be noted from
the direction of the unit cell vectors in each snapshot.
76
Figure (4.7) the crystal structure of BaFe12O19 unit cell in 3D.
Figure (4.8) the crystal structure of Fe2O3 unit cell in a 3D.
77
Figure (4.9) shows a two-dimensional cross-section of the barium hexaferrite unit
cell of the samples with Fe:Ba = 11.5 and 16.158 (in yellow and red colors), overlapped
over each other to check if there are structural differences in the two extreme samples. It
is obvious from this figure that no structure structural differences are apparent in the two
samples.
Figure (4.9) Compression of tow barium hexaferrite structures, samples zero and
twenty-five percent.
The chemical composition for our barium hexaferrite phase was determined by
XRD quantitative analysis using Rietveld refinement, and was found to be
BaFe11.896O19.812 which is very close to the theoretical composition. In addition, our
refined composition is in good agreement with the formula BaFe11.80O19.46 reported by
Sozeriet et al. [37].
78
4.2 Non-stoichiometric barium hexaferrite samples with Fe:Ba ratio
= 9
This section is concerned with the results of the structural analysis of samples of non-
stoichiometric ferrites with Fe:Ba 9 sintered at different temperatures. The phases
present in each sample were identified, and their evolution with temperature was
investigated. The crystallographic information derived from the structural refinement
was used to construct the unit cell for each phase.
A preliminary look at the XRD patterns of the samples of this system indicated the
evolution trends of the impurity phases with sintering temperature. Barium spinel
(BaFe2O4) and α-Fe2O3 were observed at T ≤ 900°C. At higher temperatures, these phases
disappear almost completely, and a new high-temperature phase (Ba3Fe2O6) evolves. The
appearance of barium spinel phase was expected in barium rich sample [36], and the
coexistence of this phase with α-Fe2O3 phase at low sintering temperatures indicated that
these are intermediate phases resulting from incomplete reaction at such low
temperatures. Figure 4.10 shows a highlight of the main peaks for each phase and their
evolution with the sintering temperature. In this figure the main peaks of each phase were
highlighted in a unique color, the iron oxide (α-Fe2O3) was highlighted in yellow, the
barium spinel (BaFe2O4) in blue, and the barium iron oxide (Ba3Fe2O6) in green.
79
Figure (4.10) XRD patterns samples with Fe:Ba of 9 sintered at different temperatures.
α-Fe2O3 was highlighted in yellow, the barium spinel (BaFe2O4) in blue, and the barium
iron oxide (Ba3Fe2O6) in green.
80
Quantitative analysis of the patterns of the samples sintered at different
temperatures was performed to obtain the relative proportions of the different phases in
each sample, and to establish some sort of a phase diagram for barium iron oxide with
Fe:Ba = 9. Table (4.4) shows the wt% of each phase in each sample, and the Figure (4.11)
shows the phases and their relative proportions as a function of sintering temperature.
This figure demonstrates that the barium iron oxide phase (Ba3Fe2O6) is a high-
temperature phase, which appears in barium rich samples (Fe:Ba < 12). On the other hand,
the barium spinel (BaFe2O4) is a low-temperature phase. This phase appears in large
quantities in samples sintered at temperatures below 900° C, and diminishes with
increasing sintering temperature until it disappears completely at 1200° C. Our results
indicate that the reaction of α-Fe2O3 to form other barium-iron oxides is completed at
sintering temperature of 1000° C, beyond which the relative abundances of BaFe12O19
and Ba3Fe2O6 seem to stabilize. The unit cell and other structural information on each
phase are summarized in Table 4.5.
Table (4.4) the calculated ratios for each phase according to the sintering temperature.
Ba:Fe ratio = 1:9
Sintering T° BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3
1200 C° 93.79% 0.00% 6.21% 0.00%
1100 C° 92.35% 1.52% 6.13% 0.00%
1000 C° 92.35% 1.53% 6.12% 0.00%
900 C° 90.43% 9.57% 0.00% 1.00%
800 C° 55.59% 28.39% 0.00% 16.02%
81
Figure (4.11) a schematic representation for each phase calculated ratios according to
the sintering temperature, Fe:Ba ratio =9.
Table (4.5) the total sites multiplicity and the unit cell volume of each phase at 1000° C
sintering temperature.
Unit Cell Number
Phase volume (Å3) tot. mult. of Sites
BaFe12O19 698.6 64 11
BaFe2O4 868.8 56 9
Ba3Fe2O6 4640.2 272 14
α-Fe2O3 296.4 30 2
Figure (4.12) shows the calculated pattern of the barium iron oxide (Ba3Fe2O6)
phase which appeared. Also Figure (4.13) shows the comparison between this pattern and
another one indexed in the ICDD library [59]. Figure (4.2.5) also shows the calculated
barium spinel pattern compared to other indexed ICDD patterns [60 – 61].
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
800 900 1000 1100 1200
System 2 – Ba:Fe ratio = 1:9
BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3
82
Figure (4.12) the XRD stick pattern of barium iron oxide (Ba3Fe2O6) phase.
Figure (4.13) the calculated XRD stick pattern for Ba3Fe2O6 phase compared with other
standard pattern in ICDD library.
That the barium iron oxide (Ba3Fe2O6) is a complicated structure as it became clear
during the data refinement. Refinement of this pattern is time-consuming, where a
refinement step for this structure takes about five seconds of calculation, whereas the rest
of the phases combined take about just one second of calculation in each step.
The data also show that the unit cell volume is temperature dependent, where in
general, increasing the sintering temperature leads to an increase in the unit cell volume.
Table (4.6) shows the cell volume of the barium hexaferrite and barium iron oxide
(Ba3Fe2O6) at different sintering temperatures.
83
Figure (4.14) the calculated XRD stick pattern for BaFe2O4 phase compared with
other standard patterns in ICDD library.
Table (4.6) the unit cell volume at each sintering degree.
Sintering Temp. => 1200 C° 1100 C° 1000 C° 900 C° 800 C°
BaFe12O19 volume (Å3) 702.056 699.947 697.834 697.946 697.436
Ba3Fe2O6 volume (Å3) 4699.908 4699.897 4682.433 4640.244
From Table (4.9), the barium hexaferrite formed at low temperature with unit cell
volume about (697 Å3). Increasing the sintering temperature above 1000° C seems to
result in an increase of the unit cell volume. On the other hand, the unit cell volume of
Ba3Fe2O6 seems to stabilize at the maximum value of 4699 Å3 in samples sintered at
temperatures T ≥ 1100° C. This value is only about 0.1% higher than that (4694.37 Å3)
reported by Montorsi et al. [59]. At lower sintering temperatures, the cell volume is
smaller, and seems to decrease with decreasing sintering temperature.
Figure (4.15) and (4.16) shows he barium spinel (BaFe2O4) and the barium iron
oxide (Ba3Fe2O6),derived from the refinement output.
84
Figure (4.15) the crystal structure of Ba3Fe2O6 unit cell in 3D.
Figure (4.16) the crystal structure of BaFe2O4 unit cell in 3D.
It was hard to notice significant difference between the atomic positions in the
barium hexaferrite lattice of samples sintered at different temperatures. However, there is
a slight noticeable difference (a slight cell deformation) when comparing the samples
sintered at 800° C and 1200° C. Figure (4.17) shows overlapped cross sections of the
barium hexaferrite unit cell for the samples sintered at 800° C (yellow) and 1200° C
(green).
85
Figure (4.17) Compression of tow barium hexaferrite structures sintered at 800° &
1200° C.
4.3 Non-stoichiometric barium hexaferrite samples samples with
Fe:Ba ratio = 7
This section is concerned with the results of the structural analysis of samples of
non-stoichiometric ferrites with iron to barium ratio of 7 sintered at different
temperatures. The phases present in each sample were identified, and their evolution with
temperature was investigated.
Five discs of the powder sample were prepared and sintered at different
temperatures ranging from 800° to 1200° C. The XRD paterns (Figure 4.18) show the
presence of the phases observed in the previous sample with Fe:Ba = 9. The main peaks
for each phase were highlighted in diffirent color, the iron oxide (α-Fe2O3) in yellow, the
barium spinel (BaFe2O4) in blue and the barium iron oxide (Ba3Fe2O6) in green. The phase
evolution with temperature is similar to that observed in the previous sample. However,
the high-temperature equilibrium ratio of the BaM phase is lower than that observed in
the previous sampe due to the the lower concentration of Fe in this sample. This is obvious
86
since by noticing the Fe:Ba ratio in the two phases, where it is clear that while the
formation of the BaM phase require a high Fe:Ba ratio ( of 12), the formation of the
Ba3Fe2O6 requires a ratio as low as 0.67. Table (4.7) summarizes the wt% of the different
phases in samples sinterd at different temperatures. Also, Figure (4.19) illestrates the
evolution of the different phases with increasing sintering temperature.
Figure (4.18) XRD patterns samples with Fe:Ba of 7 sintered at different temperatures.
α-Fe2O3 was highlighted in yellow, the barium spinel (BaFe2O4) in blue, and the barium
iron oxide (Ba3Fe2O6) in green.
87
Table (4.7) the calculated ratios for each phase according to the sintering temperature.
Ba:Fe ratio = 1:7
Sintering T° BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3
1200° C 87.57% 0.00% 12.43% 0.00%
1100° C 87.31% 1.10% 11.59% 0.00%
1000° C 87.29% 1.09% 11.62% 0.00%
900° C 70.14% 24.69% 4.32% 0.85%
800° C 51.52% 39.06% 0.00% 9.42%
Due to the increease of barium relative concentration in the sample with Fe:Ba = 7,
the Ba3Fe2O6 wt% was found to be 12.4% (at 1200° C), to be compared with 6.2%
observed in the sample of Fe:Ba ratio of 9. The extra barium ratio gives the opportunity
to form more barium iron oxide (Ba3Fe2O6) phase which requires more barium than BaM
phase.
88
Figure (4.19) a schematic representation for each phase calculated ratios according to
the sintering temperature, Fe:Ba ratio = 7.
The barium spinel (BaFe2O4) and the iron oxide (α-Fe2O3) phases, almost
disapeared at 1000° C, and the barium iron oxide (Ba3Fe2O6) phase was formed at 900°
C. Also, the proportions of the different phases changed with the increase in barium to
iron ratio. The data show an increase of barium spinel weight ratio, which reached (39%)
compared with (28.4%) observed in the previous sample with Fe:Ba = 9 sintered at 800°
C. This can also be directly attributed to the additional quantity of barium in the sample
with Fe:Ba = 7, since barium spinel phase requires more relative Ba content thanbaM
phase.
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
100.00%
800 900 1000 1100 1200
System 3 - Ba:Fe ratio = (1:7)
BaFe12O19 BaFe2O4 Ba3Fe2O6 α-Fe2O3
89
The previous study shows that the sintering temperature of (1000° C), is the
transformational sintering tempreture, below which the high tempreture phases will tend
to disapear, and above it the intermediate phases will do the same.
In conclusion, the use of low Fe:Ba ratio (lower than 11.5) in preparing M-type
barium hexaferrites results in the development of barium spinel intermediate phase, and
the presence of unreacted α-Fe2O3 at low sintering temperatures. Our results are in good
agreement with the experimental results of Topal et al. [40] who reported the presence of
the intermediate phases in samples with low Fe/Ba ratio.
The barium hexaferrite phase (BaFe12O19) prepared from powders with different
Fe:Ba ratios ranging from 7 to 16.16) was found to have the same structural
characteristics, which are not affected by the presence of other phases in the sample. This
result is in disagreement with the results of Suastiyant et al. who reported a shift in phase
peak positions (and a cchnage in cell parameters) due to the different Fe:Ba ratio that was
used for preparing the precursor material. The only parameter which seems to affect the
charactristics of the structural phases is the sintering temperature, a result which is in full
agreement with the results of Guo et al. [62].
90
CHAPTER 5
Conclusions and
Recommendations
91
Conclusions
The structural analysis of the samples consisting of a mixture of M-type barium
hexaferrit (with Fe/Ba ratio of 11.5) and α-Fe2O3 iron oxide revealed the presnece of pure
M-type phase and α-Fe2O3 phase, with no other secondary phases. Also, the structural
properties of the M-type barium hexaferrite phase were found to be independent of the α-
Fe2O3 mass ratio in the mixture. The quantitative analysis using Rietveld refinement for
these samples had shown that the optimum iron-to-barium ratio require to prepare a pure
M-type barium hexaferrite phase is in the range of 11.6 – 12. This work established a
reference scheme for the determination of the mass ratio of iron oxide (α-Fe2O3) impurity
phase in non-stoichiometric hexaferrite compounds.
The structural analyses of non-stoiciometric hexaferrites with Fe:Ba ratio of 9 and
7 prepared by sintering at temperatures ranging between 800° to 1200° C revealed the
presence of different phases, the proportion of which was found to depend critically on
the sintering temperature. Specifically, barium spinel phase (BaFe2O4) and α-Fe2O3
phases were detected at sintering temperatures ≤ 900° C due to incomplete reaction
between these intermediate phases in this temperature regime. At higher temperatures,
these intermediate phases disappear as they fully react, resulting in the appearance of a
new barium ferrite phase (Ba3Fe2O6) due to the excessive amounts of Ba in the samples.
It was shown that the M-type barium hexaferrite structure differed slightly with the
temperature variation. The structural deformation was however slight when the structural
parameters of samples sintered at 800° C and 1200° C were compared. Also, the unit cell
volume of Ba3Fe2O6 Ba3Fe2O6 was found to increase with increasing the sintering
temperature.
92
The particle absorption contrast factor represented by Brindley's coefficient, was
determined for each phase in the barium hexaferrite samples. The refined powder
diffraction pattern for each phase was calculated and the relative abundance of each
structural phase in each sampe was determined.
The structural characteristics of the barium iron oxide (Ba3Fe2O6) phase appearing
in the samples with Fe:Ba = 7 and 9 were fully investigated using Rietveld refinement,
and its whole crystalline information was determined; the cell parameter, Wyckoff
positions, space group, atomic sites, multiplicity...etc. Up to our knowledge, these
structural charcteristics were not previously reported in the literature.
Recommendations for Future Work
In order to determine the exact temperature required for the complete reaction of
intermediate spinel and iron oxide phases and appearance of the new barium ferrite phase
(Ba3Fe2O6), we suggest the preparation and careful structural characterization of samples
with iron to barium ratio of 9 and sintering temperatures in the range 900° C – 1000° C.
Further, the present approach of the structural analyses of non-stoichiometric
barium hexaferrites can be applied to other systems with different impurity phases and
structural properties. The impurity phases and their relative abundances can be
determined quantitatively by following the steps developed in this thesis.
93
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[52] S. Mitra, S. Das, S. Basu, P. Sahu, K. Mandal (2009), Shape- and field-dependent
Morin transitions in structured α-Fe2O3, Journal of Magnetism and Magnetic
Materials, 321 (18), 2925-2931.
[53] C. Tenailleau, M. Allix, J.B. Claridge, M. Hervieu, M.F. Thomas, J.P. Hirst, M.J.
Rosseinsky (2008), Modular Construction of Oxide Structures-Compositional Control of
Transition Metal Coordination Environments, Journal of the American Chemical
Society, 130 , 7570-7583
[54] P. Mondal, J. W. Jeffery (1975), The crystal structure of tricalcium aluminate,
Ca3Al2O6, Acta Crystallographica, Section B, 31, 689-697.
99
[55] J.F.Berar, P.Lelann (1991), Journal of Applied Crystallography, 24, 1-5. And
J.F.Berar (1992), Accuracy in Powder Diffraction II, NIST Special Publication, 846, 63.
[56] R.J. Hill, C.J. Howard (1987), Journal of Applied Crystallography, 20, 467-476.
[57] Paretzkin (1955), Polytechnic Inst. of Brooklyn, Brooklyn, NY, USA., Private
Communication.
[58] Shin, H., Kwon, S.-J. (1992), Powder Diffraction, 7, 212.
[59] Montorsi, Brisi. (1972), Annales de chimie et de physique (Rome), 62, 641.
[60] Mitsuda, Mori, Okazaki (1967), Matsushita Electric Industrial Company, Ltd.,
Osaka, Japan., Private Communication.
[61] Grier, D., McCarthy, G. (1993), North Dakota State University, Fargo, ND, USA.,
ICDD Grant-in-Aid.
[62] L. Guo, M. Huang, X. Zhang (2003), Effects of sintering temperature on structure of
hydroxyapatite studied with Rietveld method, Journal of Materials Science: Materials
in Medicine, 9, 817-22.
100
تحليل التركيب البلوري لمركبات الفرايت السداسي
إعداد
يزن مسودة
المشرف
األستاذ الدكتور سامي محمود
ملخــــــــص
الجوهر الرئيسيييييه للدر ال ياضييييي لتحيييييلب اه التركيا اللحدئه للردلدي الر ل السييييي اضيييييي
بحدًء عكى مالئل أنلدط حيود االشيييييس السييييييحي وبدألخص مردلدي الر ل السييييي اضيييييي م اللديلو
بدضييييت ا رييييلا يلتنيك ومب و دياضيييي وجركيا الحتدئل اللحيول لكلردلدي الته جو جرحيييييرهد اه
ظروف م لرل م تكن اه مردول لنلو ديني جشيييييها هدر اللردلدي وأاحيييييا الهر، لت يييييحيسلد
بحي هدر اللردلدي.بدإلضدا الى جأ ير ديج الرراية والشوائب عكى
م 19O12BaFeب ال ً جو جرحيييييير مواد جللي ل للردب الر ل السييييي اضيييييه مب نو
1.11.11 وحتى 1.11.1مراعدة جس لا نسييييييل اللديلو الى الر ل اه هدر السيحدي ابت اًء مب
مردب دي انبدلت يلل عكى خلس عيحدي وجرت ننس الظروف الل لرل . جليب مب جركيا هدر السيح
الر ل السييييي اضيييييه مب نو لو لتأ ر بحدئيد او دليد وددنت الملددة اه دلي أدسيييييي الر ل جظلر
دلرحك شييدئل محن ييك اه هدر السيحدي جمداد دليتلد بدددلدد نسييل الر ل الى اللديلو اه اللواد
نسيييل لهلي مردلدي الر ل التللي ل وجو علا م هط مرجسه لليدس دلي شيييوائب أدسيييي الر ل
الس اضي م اللديلو جلسد لحسل مسدح الللو الرئيسي بيب اللردليب.
101
ول ياض هدر السيحدي بدختالف نسل اللديلو الى الر ل اه اللواد التللي ل عكى م ى أوض
دا نسيييل وجكلي خلس عيحدي مب1.1 و 1.1جو جرحيييير مواد جللي ل بحسيييل بديلو الى ح ل
ديج مئول .1088 1188 1888 188 088دا عكى ديج حراية م تكن
جليب مب جركيا السيحدي السيييدبل جشيييها أيب مردلدي م تكن جتراوس اه نسيييللد جلسد الختالف
ديج حراية التكل وجو وض م هط لليب جهوي جشها اللراحا اه هدر السيحدي جلسد الددلدد ديج
حسييييدط نلط لليب حلو حيود االشييييس السيييييحي اللبدله لها مردب ويضييييو نلو ال ه الرراية و
االبسدد لها مردب م بيدن االختالادي الته طرأي عكى الليها اللحيوي لها مردب جلسد الختالف
ديج حراية التكل .
FullProf output file. Example: sample (10%),
Full pattern refinement. Number of phases = 2. Chi squared value = 1.135
**********************************************************
** PROGRAM FullProf.2k (Version 4.60 - Mar2009-ILL JRC) **
**********************************************************
M U L T I -- P A T T E R N
Rietveld, Profile Matching & Integrated Intensity
Refinement of X-ray and/or Neutron Data
Date: 12/08/2013 Time: 18:42:46.759
=> PCR file code: 10 per
=> DAT file code: 10 per.dat -> Relative contribution: 1.0000
==> CONDITIONS OF THIS RUN FOR PATTERN No.: 1
=> Global Refinement of X-ray powder diffraction data
=> Global Refinement of X-ray powder diffraction data
Bragg-Brentano or Debye-Scherrer geometry
=> Title: 10 per
=> Number of phases: 2
=> Number of excluded regions: 0
=> Number of scattering factors supplied: 0
=> Conventional weights: w=1.0/Variance(yobs)
=> Asymmetry correction as in J.Appl.Cryst. 26,128(1993)
=> Background linearly interpolated between the 52 points given
=> The 5th default profile function was selected
=> Pseudo-Voigt function (ETA variable)
X-parameter correspond to: ETA=ETA0+X*2theta
pV(x)= ETA*L(x)+(1-ETA)*G(x)
==> INPUT/OUTPUT OPTIONS:
=> Generate file *.PRF for plot
=> Output Integrated Intensities
=> Generate new input file *.PCR
=> Data supplied in free format for pattern: 1
=> Plot pattern at each cycle
=> Wavelengths: 1.54056 1.54439
=> Alpha2/Alpha1 ratio: 0.5000
=> Cos(Monochromator angle)= 0.9100
=> Asymmetry correction for angles lower than 0.000 degrees
=> Absorption correction (AC), muR-eff = 0.0000
=> Base of peaks: 2.0*HW* 8.00
=> Number of cycles: 1
=> Relaxation factors ==> for coordinates: 1.00
=> for anisotropic temperature factors: 1.00
=> for halfwidth/strain/size parameters: 1.00
=> for lattice constants and propagation vectors: 1.00
=> EPS-value for convergence: 0.1
=> Background ==>
Position Intensity
20.32 28.91 0.00
20.87 26.14 0.00
21.48 26.65 0.00
22.30 26.16 0.00
23.56 21.90 0.00
23.72 21.47 0.00
24.72 21.57 0.00
25.63 22.54 0.00
26.54 21.21 0.00
27.34 22.87 0.00
28.71 22.32 0.00
30.08 15.49 0.00
31.73 7.97 0.00
32.84 0.44 0.00
32.96 8.40 0.00
33.62 6.83 0.00
34.90 6.62 0.00
36.36 17.12 0.00
36.56 12.72 0.00
38.12 14.61 0.00
38.88 17.99 0.00
39.63 14.09 0.00
41.42 13.65 0.00
41.66 14.41 0.00
42.15 16.77 0.00
43.38 13.69 0.00
44.47 17.94 0.00
45.12 16.08 0.00
47.02 16.30 0.00
48.23 14.23 0.00
49.05 15.65 0.00
49.34 15.43 0.00
51.64 17.56 0.00
52.67 18.50 0.00
52.87 19.05 0.00
53.74 19.52 0.00
55.71 17.75 0.00
55.92 18.50 0.00
57.11 17.55 0.00
58.14 19.83 0.00
59.59 17.93 0.00
60.60 18.69 0.00
60.86 18.09 0.00
61.75 18.27 0.00
62.15 17.51 0.00
63.96 19.47 0.00
65.08 19.17 0.00
66.43 15.60 0.00
67.84 20.76 0.00
68.53 11.46 0.00
69.00 16.97 0.00
69.62 16.47 0.00
=> Number of Least-Squares parameters varied: 0
=>--------------------------->
=>-------> PATTERN number: 1
=>--------------------------->
=> Global parameters and codes ==>
=> Zero-point: 0.1368 0.0000
=> Displacement peak-shift parameter and code: 0.00 0.00
=> Transparency peak-shift parameter and code: 0.01 0.00
=> Reading Intensity data =>>
==> Angular range, step and number of points:
2Thmin: 20.000000 2Thmax: 70.000000 Step: 0.010000 No. of points: 5001
--------------------------------------------------------------------------------
=> Phase No. 1
BaFe12O19
--------------------------------------------------------------------------------
=>-------> Pattern# 1
=> Crystal Structure Refinement
=> Preferred orientation vector: 0.0000 0.0000 1.0000
=>-------> Data for PHASE: 1
=> Number of atoms: 11
=> Number of distance constraints: 0
=> Number of angle constraints: 0
=> Symmetry information on space group: P 63/M M C
-> The multiplicity of the general position is: 24
-> The space group is Centric (-1 at origin)
-> Lattice type P: { 000 }
-> Reduced set of symmetry operators:
No. IT Symmetry symbol Rotation part Associated Translation
1: ( 1) 1 --> ( x , y, z) + { 0.0000 0.0000 0.0000}
2: ( 6) 6+ ( 0, 0, z) --> ( x-y, x , z) + { 0.0000 0.0000 0.5000}
3: ( 2) 3+ ( 0, 0, z) --> ( -y, x-y, z) + { 0.0000 0.0000 0.0000}
4: ( 4) 2 ( 0, 0, z) --> (-x , -y, z) + { 0.0000 0.0000 0.5000}
5: ( 3) 3- ( 0, 0, z) --> (-x+y,-x , z) + { 0.0000 0.0000 0.0000}
6: ( 5) 6- ( 0, 0, z) --> ( y,-x+y, z) + { 0.0000 0.0000 0.5000}
7: ( 7) 2 ( x, x, 0) --> ( y, x ,-z) + { 0.0000 0.0000 0.0000}
8: (12) 2 (2x, x, 0) --> ( x , x-y,-z) + { 0.0000 0.0000 0.5000}
9: ( 8) 2 ( x, 0, 0) --> ( x-y, -y,-z) + { 0.0000 0.0000 0.0000}
10: (10) 2 ( x,-x, 0) --> ( -y,-x ,-z) + { 0.0000 0.0000 0.5000}
11: ( 9) 2 ( 0, y, 0) --> (-x ,-x+y,-z) + { 0.0000 0.0000 0.0000}
12: (11) 2 ( x,2x, 0) --> (-x+y, y,-z) + { 0.0000 0.0000 0.5000}
Information on Space Group:
---------------------------
=> Number of Space group: 194
=> Hermann-Mauguin Symbol: P 63/m m c
=> Hall Symbol: -P 6c 2c
=> Table Setting Choice:
=> Setting Type: IT (Generated from Hermann-Mauguin symbol)
=> Crystal System: Hexagonal
=> Laue Class: 6/mmm
=> Point Group: 6/mmm
=> Bravais Lattice: P
=> Lattice Symbol: hP
=> Reduced Number of S.O.: 12
=> General multiplicity: 24
=> Centrosymmetry: Centric (-1 at origin)
=> Generators (exc. -1&L): 2
=> Asymmetric unit: 0.000 <= x <= 0.667
0.000 <= y <= 0.667
0.000 <= z <= 0.250
=> List of S.O. without inversion and lattice centring translations
=> SYMM( 1): x,y,z => SYMM( 2): x-y,x,z+1/2
=> SYMM( 3): -y,x-y,z => SYMM( 4): -x,-y,z+1/2
=> SYMM( 5): -x+y,-x,z => SYMM( 6): y,-x+y,z+1/2
=> SYMM( 7): -y,-x,z => SYMM( 8): -x,-x+y,z+1/2
=> SYMM( 9): -x+y,y,z => SYMM(10): y,x,z+1/2
=> SYMM(11): x,x-y,z => SYMM(12): x-y,-y,z+1/2
=> Initial parameters ==>
Atom Ntyp X Y Z B occ. in fin Spc Mult
B11 B22 B33 B12 B13 B23
Ba Ba 0.66667 0.33333 0.25000 -0.22808 0.01164 0 0 0 2
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
Fe Fe 0.00000 0.00000 0.00000 -0.69165 0.01193 0 0 0 2
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
Fe Fe 0.00000 0.00000 0.25027 -0.24119 0.01057 0 0 0 2
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
Fe Fe 0.33333 0.66666 0.02734 -0.63383 0.02252 0 0 0 4
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
Fe Fe 0.33333 0.66666 0.19063 1.25653 0.02535 0 0 0 4
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
Fe Fe 0.16928 0.33841 0.89179 -0.03360 0.07117 0 0 0 12
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
O O 0.00000 0.00000 0.15076 -1.30999 0.02267 0 0 0 4
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
O O 0.33333 0.66667 0.94475 3.46959 0.02700 0 0 0 4
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
O O 0.17995 0.35989 0.25000 1.43085 0.03962 0 0 0 6
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
O O 0.15524 0.31029 0.05176 1.76383 0.08287 0 0 0 12
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
O O 0.50398 1.00803 0.14867 2.30019 0.08497 0 0 0 12
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
=> IT IS ASSUMED THAT THE FIRST GIVEN SITE IS FULLY OCCUPIED
(If this is not the case, change the order of atoms to obtain correct values for the content of the unit cell)
The phase contains sites partially occupied
-> Atom: Ba , Chemical element: BA Atomic Mass: 137.3400
-> Atom: Fe , Chemical element: FE Atomic Mass: 55.8470
-> Atom: Fe , Chemical element: FE Atomic Mass: 55.8470
-> Atom: Fe , Chemical element: FE Atomic Mass: 55.8470
-> Atom: Fe , Chemical element: FE Atomic Mass: 55.8470
-> Atom: Fe , Chemical element: FE Atomic Mass: 55.8470
-> Atom: O , Chemical element: O Atomic Mass: 15.9994
-> Atom: O , Chemical element: O Atomic Mass: 15.9994
-> Atom: O , Chemical element: O Atomic Mass: 15.9994
-> Atom: O , Chemical element: O Atomic Mass: 15.9994
-> Atom: O , Chemical element: O Atomic Mass: 15.9994
=> The given value of ATZ is 45.65 the program has calculated: 45.65
The value of ATZ given in the input PCR file will be used for quantitative analysis
=> The chemical content of the unit cell is:
2.0000 Ba + 2.0498 Fe + 1.8162 Fe + 3.8694 Fe + 4.3557 Fe + 12.2285 Fe + 3.8952 O + 4.6392 O + 6.8076 O + 14.2388 O +
14.5997 O
=> The normalized site occupation numbers in % are:
100.0000 Ba : 102.4914 Fe : 90.8076 Fe : 96.7354 Fe : 108.8917 Fe : 101.9044 Fe : 97.3797 O : 115.9794 O : 113.4593 O : 118.6569 O :
121.6638 O
=>-------> PROFILE PARAMETERS FOR PATTERN: 1
=> Overall scale factor: 0.133890E-02
=> ETA (p-Voigt) OR M (Pearson VII): 0.5868
=> Overall temperature factor: 0.00000
=> Halfwidth U,V,W: 0.02994 -0.03141 0.04166
=> X and Y parameters: 0.0014 0.0000
=> Direct cell parameters: 5.8933 5.8933 23.2186 90.0000 90.0000 120.0000
=> Preferred orientation parameters: 0.0186 0.0000
=> Asymmetry parameters : 0.00000 0.00000 0.00000 0.00000
=> Strain parameters : 0.00000 0.00000 0.00000
=> Size parameters : 0.00000 0.00000
==> CODEWORDS FOR PROFILE PARAMETERS of PATTERN# 1
=> Overall scale factor: 0.000
=> ETA (p-Voigt) OR M (Pearson VII): 0.000
=> Overall temperature factor: 0.000
=> Halfwidth U,V,W: 0.000 0.000 0.000
=> X and Y parameters: 0.000 0.000
=> Direct cell parameters: 0.000 0.000 0.000 0.000 0.000 0.000
=> Preferred orientation parameters: 0.000 0.000
=> Asymmetry parameters : 0.000 0.000 0.000 0.000
=> Strain parameters : 0.000 0.000 0.000
=> Size parameters : 0.000 0.000
=> Cell constraints according to Laue symmetry: 6/mmm
Metric information:
-------------------
=> Direct cell parameters:
a = 5.8933 b = 5.8933 c = 23.2186
alpha = 90.000 beta = 90.000 gamma = 120.000
Direct Cell Volume = 698.3628
=> Reciprocal cell parameters:
a*= 0.195935 b*= 0.195935 c*= 0.043069
alpha*= 90.000 beta*= 90.000 gamma*= 60.000
Reciprocal Cell Volume = 0.00143192
=> Direct and Reciprocal Metric Tensors:
GD GR
34.7308 -17.3654 0.0000 0.038391 0.019195 0.000000
-17.3654 34.7308 0.0000 0.019195 0.038391 0.000000
0.0000 0.0000 539.1033 0.000000 0.000000 0.001855
=> Cartesian frame: x // a; y is in the ab-plane; z is x ^ y
Crystal_to_Orthonormal_Matrix Orthonormal_to_Crystal Matrix
Cr_Orth_cel Orth_Cr_cel
5.8933 -2.9466 0.0000 0.169685 0.097968 0.000000
0.0000 5.1037 0.0000 0.000000 0.195935 0.000000
0.0000 0.0000 23.2186 0.000000 0.000000 0.043069
=> Number of propagation vectors [K] = 0
=> Laue symmetry 6/mmm will be used to generate HKL for pattern# 1
=> Reflections generated between S(1/d)min: 0.2249 A-1 and S(1/d)max: 0.7721 A-1
=> dmax: 4.4469 A and dmin: 1.2952 A
=> The number of reflections generated is: 85
=> The max. scatt. variable (gen.ref.) is: 72.9821
=> Scattering coefficients from internal table
=> X-ray scattering coeff. (A1, B1, A2,...C, f(0), Z, Dfp,Dfpp)
BA 20.3361 3.2160 19.2970 0.2756 10.8880 20.2073 2.6959 167.2020 2.7731 55.9901 56.0000 -1.3340 8.4600
FE 11.7695 4.7611 7.3573 0.3072 3.5222 15.3535 2.3045 76.8805 1.0369 25.9904 26.0000 -1.1790 3.2040
O 3.0485 13.2771 2.2868 5.7011 1.5463 0.3239 0.8670 32.9089 0.2508 7.9994 8.0000 0.0470 0.0320
--------------------------------------------------------------------------------
=> Phase No. 2
Fe2O3
--------------------------------------------------------------------------------
=>-------> Pattern# 1
=> Crystal Structure Refinement
=> Preferred orientation vector: 0.0000 0.0000 1.0000
=>-------> Data for PHASE: 2
=> Number of atoms: 2
=> Number of distance constraints: 0
=> Number of angle constraints: 0
=> Symmetry information on space group: R -3 c
-> The multiplicity of the general position is: 36
-> The space group is Centric (-1 at origin)
-> Lattice type R: { 000; 2/3 1/3 1/3; 1/3 2/3 2/3 }+
-> Reduced set of symmetry operators:
No. IT Symmetry symbol Rotation part Associated Translation
1: ( 1) 1 --> ( x , y, z) + { 0.0000 0.0000 0.0000}
2: ( 2) 3+ ( 0, 0, z) --> ( -y, x-y, z) + { 0.0000 0.0000 0.0000}
3: ( 3) 3- ( 0, 0, z) --> (-x+y,-x , z) + { 0.0000 0.0000 0.0000}
4: ( 7) 2 ( x, x, 0) --> ( y, x ,-z) + { 0.0000 0.0000 0.5000}
5: ( 8) 2 ( x, 0, 0) --> ( x-y, -y,-z) + { 0.0000 0.0000 0.5000}
6: ( 9) 2 ( 0, y, 0) --> (-x ,-x+y,-z) + { 0.0000 0.0000 0.5000}
Information on Space Group:
---------------------------
=> Number of Space group: 167
=> Hermann-Mauguin Symbol: R -3 c
=> Hall Symbol: -R 3 2"c
=> Table Setting Choice: H
=> Setting Type: IT (Generated from Hermann-Mauguin symbol)
=> Crystal System: Rhombohedral
=> Laue Class: -3m1
=> Point Group: -3m
=> Bravais Lattice: R
=> Lattice Symbol: hR
=> Reduced Number of S.O.: 6
=> General multiplicity: 36
=> Centrosymmetry: Centric (-1 at origin)
=> Generators (exc. -1&L): 2
=> Asymmetric unit: 0.000 <= x <= 0.667
0.000 <= y <= 0.667
0.000 <= z <= 0.083
=> List of S.O. without inversion and lattice centring translations
=> SYMM( 1): x,y,z => SYMM( 2): -y,x-y,z
=> SYMM( 3): -x+y,-x,z => SYMM( 4): -y,-x,z+1/2
=> SYMM( 5): -x+y,y,z+1/2 => SYMM( 6): x,x-y,z+1/2
=> Initial parameters ==>
Atom Ntyp X Y Z B occ. in fin Spc Mult
B11 B22 B33 B12 B13 B23
Fe Fe 0.00000 0.00000 0.35571 0.01865 0.02352 0 0 0 12
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
O O 0.31546 0.00000 0.25000 4.90012 0.04681 0 0 0 18
Codes: 0.00000 0.00000 0.00000 0.00000 0.00000
=> IT IS ASSUMED THAT THE FIRST GIVEN SITE IS FULLY OCCUPIED
(If this is not the case, change the order of atoms to obtain correct values for the content of the unit cell)
The phase contains sites partially occupied
-> Atom: Fe , Chemical element: FE Atomic Mass: 55.8470
-> Atom: O , Chemical element: O Atomic Mass: 15.9994
=> The given value of ATZ is 5.24 the program has calculated: 5.24
The value of ATZ given in the input PCR file will be used for quantitative analysis
=> The chemical content of the unit cell is:
12.0000 Fe + 23.8827 O
=> The normalized site occupation numbers in % are:
100.0000 Fe : 132.6814 O
=>-------> PROFILE PARAMETERS FOR PATTERN: 1
=> Overall scale factor: 0.167490E-02
=> ETA (p-Voigt) OR M (Pearson VII): 0.8496
=> Overall temperature factor: 0.00000
=> Halfwidth U,V,W: -0.31472 0.25684 -0.01466
=> X and Y parameters: -0.0078 0.0000
=> Direct cell parameters: 5.0357 5.0357 13.7488 90.0000 90.0000 120.0000
=> Preferred orientation parameters: 0.0454 0.0000
=> Asymmetry parameters : 0.00000 0.00000 0.00000 0.00000
=> Strain parameters : 0.00000 0.00000 0.00000
=> Size parameters : 0.00000 0.00000
==> CODEWORDS FOR PROFILE PARAMETERS of PATTERN# 1
=> Overall scale factor: 0.000
=> ETA (p-Voigt) OR M (Pearson VII): 0.000
=> Overall temperature factor: 0.000
=> Halfwidth U,V,W: 0.000 0.000 0.000
=> X and Y parameters: 0.000 0.000
=> Direct cell parameters: 0.000 0.000 0.000 0.000 0.000 0.000
=> Preferred orientation parameters: 0.000 0.000
=> Asymmetry parameters : 0.000 0.000 0.000 0.000
=> Strain parameters : 0.000 0.000 0.000
=> Size parameters : 0.000 0.000
=> Cell constraints according to Laue symmetry: -3m1
Metric information:
-------------------
=> Direct cell parameters:
a = 5.0357 b = 5.0357 c = 13.7488
alpha = 90.000 beta = 90.000 gamma = 120.000
Direct Cell Volume = 301.9332
=> Reciprocal cell parameters:
a*= 0.229304 b*= 0.229304 c*= 0.072734
alpha*= 90.000 beta*= 90.000 gamma*= 60.000
Reciprocal Cell Volume = 0.00331199
=> Direct and Reciprocal Metric Tensors:
GD GR
25.3581 -12.6790 0.0000 0.052580 0.026290 0.000000
-12.6790 25.3581 0.0000 0.026290 0.052580 0.000000
0.0000 0.0000 189.0288 0.000000 0.000000 0.005290
=> Cartesian frame: x // a; y is in the ab-plane; z is x ^ y
Crystal_to_Orthonormal_Matrix Orthonormal_to_Crystal Matrix
Cr_Orth_cel Orth_Cr_cel
5.0357 -2.5178 0.0000 0.198583 0.114652 0.000000
0.0000 4.3610 0.0000 0.000000 0.229304 0.000000
0.0000 0.0000 13.7488 0.000000 0.000000 0.072734
=> Number of propagation vectors [K] = 0
=> Laue symmetry -3m1 will be used to generate HKL for pattern# 1
=> Reflections generated between S(1/d)min: 0.2249 A-1 and S(1/d)max: 0.7722 A-1
=> dmax: 4.4469 A and dmin: 1.2951 A
=> The number of reflections generated is: 17
=> The max. scatt. variable (gen.ref.) is: 72.9950
=> Scattering coefficients from internal table
=> X-ray scattering coeff. (A1, B1, A2,...C, f(0), Z, Dfp,Dfpp)
=> No optimization for routine tasks
Standard deviations have to be multiplied by: 1.2583
(correlated residuals) See references:
-J.F.Berar & P.Lelann, J. Appl. Cryst. 24, 1-5 (1991)
-J.F.Berar, Acc. in Pow. Diff. II,NIST Sp.Pub. 846, 63(1992)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
=> CYCLE No.: 1
---------------------------------------------------------------------------------------
=> Phase 1 Name: BaFe12O19
---------------------------------------------------------------------------------------
=> New parameters, shifts, and standard deviations
Atom x dx sx y dy sy z dz sz B dB sB occ. docc. socc.
Ba 0.66667 0.00000 0.00000 0.33333 0.00000 0.00000 0.25000 0.00000 0.00000 -0.22808 0.00000 0.00000 0.01164 0.00000 0.00000
Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.69165 0.00000 0.00000 0.01193 0.00000 0.00000
Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.25027 0.00000 0.00000 -0.24119 0.00000 0.00000 0.01057 0.00000 0.00000
Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.02734 0.00000 0.00000 -0.63383 0.00000 0.00000 0.02252 0.00000 0.00000
Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.19063 0.00000 0.00000 1.25653 0.00000 0.00000 0.02535 0.00000 0.00000
Fe 0.16928 0.00000 0.00000 0.33841 0.00000 0.00000 0.89179 0.00000 0.00000 -0.03360 0.00000 0.00000 0.07117 0.00000 0.00000
O 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.15076 0.00000 0.00000 -1.30999 0.00000 0.00000 0.02267 0.00000 0.00000
O 0.33333 0.00000 0.00000 0.66667 0.00000 0.00000 0.94475 0.00000 0.00000 3.46959 0.00000 0.00000 0.02700 0.00000 0.00000
O 0.17995 0.00000 0.00000 0.35989 0.00000 0.00000 0.25000 0.00000 0.00000 1.43085 0.00000 0.00000 0.03962 0.00000 0.00000
O 0.15524 0.00000 0.00000 0.31029 0.00000 0.00000 0.05176 0.00000 0.00000 1.76383 0.00000 0.00000 0.08287 0.00000 0.00000
O 0.50398 0.00000 0.00000 1.00803 0.00000 0.00000 0.14867 0.00000 0.00000 2.30019 0.00000 0.00000 0.08497 0.00000 0.00000
==> PROFILE PARAMETERS FOR PATTERN# 1
=> Overall scale factor: 0.001338900 0.000000000 0.000000000
=> Eta(p-Voigt) or m(Pearson VII): 0.586780 0.000000 0.000000
=> Overall tem. factor: 0.000000 0.000000 0.000000
=> Halfwidth parameters:
0.029938 0.000000 0.000000
-0.031407 0.000000 0.000000
0.041664 0.000000 0.000000
=> Cell parameters:
5.893282 0.000000 0.000000
5.893282 0.000000 0.000000
23.218599 0.000000 0.000000
90.000000 0.000000 0.000000
90.000000 0.000000 0.000000
120.000000 0.000000 0.000000
=> Preferred orientation:
0.018610 0.000000 0.000000
0.000000 0.000000 0.000000
=> Asymmetry parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> X and Y parameters:
0.001372 0.000000 0.000000
0.000000 0.000000 0.000000
=> Strain parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> Size parameters (G,L):
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
---------------------------------------------------------------------------------------
=> Phase 2 Name: Fe2O3
---------------------------------------------------------------------------------------
=> New parameters, shifts, and standard deviations
Atom x dx sx y dy sy z dz sz B dB sB occ. docc. socc.
Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.35571 0.00000 0.00000 0.01865 0.00000 0.00000 0.02352 0.00000 0.00000
O 0.31546 0.00000 0.00000 0.00000 0.00000 0.00000 0.25000 0.00000 0.00000 4.90012 0.00000 0.00000 0.04681 0.00000 0.00000
==> PROFILE PARAMETERS FOR PATTERN# 1
=> Overall scale factor: 0.001674900 0.000000000 0.000000000
=> Eta(p-Voigt) or m(Pearson VII): 0.849630 0.000000 0.000000
=> Overall tem. factor: 0.000000 0.000000 0.000000
=> Halfwidth parameters:
-0.314717 0.000000 0.000000
0.256845 0.000000 0.000000
-0.014657 0.000000 0.000000
=> Cell parameters:
5.035680 0.000000 0.000000
5.035680 0.000000 0.000000
13.748774 0.000000 0.000000
90.000000 0.000000 0.000000
90.000000 0.000000 0.000000
120.000000 0.000000 0.000000
=> Preferred orientation:
0.045350 0.000000 0.000000
0.000000 0.000000 0.000000
=> Asymmetry parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> X and Y parameters:
-0.007842 0.000000 0.000000
0.000000 0.000000 0.000000
=> Strain parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> Size parameters (G,L):
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
==> GLOBAL PARAMETERS FOR PATTERN# 1
=> Zero-point: 0.1368 0.0000 0.0000
=> Cos( theta)-shift parameter : -0.0005 0.0000 0.0000
=> Sin(2theta)-shift parameter : 0.0126 0.0000 0.0000
==> RELIABILITY FACTORS WITH ALL NON-EXCLUDED POINTS FOR PATTERN: 1
=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#: 1
=> Expected : 11.8 1.9122
=> Deviance :0.571E+04 Dev*: 1.136
=> GoF-index: 1.1 Sqrt(Residual/N)
=> N-P+C: 5001
=> SumYdif SumYobs SumYcal SumwYobsSQ Residual Condition
0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000
=> Conventional Rietveld Rp,Rwp,Re and Chi2: 11.0 15.2 14.3 1.135
=> (Values obtained using Ynet, but true sigma(y))
=> SumYnet, Sum(w Ynet**2): 0.2760E+06 0.2441E+06
=> N-sigma of the GoF: 6.740
==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS FOR PATTERN: 1
=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#:
=> Expected : 11.8 1.9122
=> Deviance :0.571E+04 Dev*: 1.136
=> GoF-index: 1.1 Sqrt(Residual/N)
=> N-P+C: 5001
=> SumYdif SumYobs SumYcal SumwYobsSQ Residual Condition
0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000
=> Conventional Rietveld Rp,Rwp,Re and Chi2: 11.0 15.2 14.3 1.135
=> (Values obtained using Ynet, but true sigma(y))
=> SumYnet, Sum(w Ynet**2): 0.2760E+06 0.2441E+06
=> N-sigma of the GoF: 6.740
=> Global user-weigthed Chi2 (Bragg contrib.): 1.13
=> ---------> Pattern# 1
=> Phase: 1
=> Bragg R-factor: 1.65
=> RF-factor : 1.87
=> Phase: 2
=> Bragg R-factor: 3.19
=> RF-factor : 3.02
Standard deviations have to be multiplied by: 1.2583
(correlated residuals) See references:
-J.F.Berar & P.Lelann, J. Appl. Cryst. 24, 1-5 (1991)
-J.F.Berar, Acc. in Pow. Diff. II,NIST Sp.Pub. 846, 63(1992)
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
=> CYCLE No.: 1
=> Convergence reached at this CYCLE !!!!
=> Parameter shifts set to zero
---------------------------------------------------------------------------------------
=> Phase 1 Name: BaFe12O19
---------------------------------------------------------------------------------------
=> New parameters, shifts, and standard deviations
Atom x dx sx y dy sy z dz sz B dB sB occ. docc. socc.
Ba 0.66667 0.00000 0.00000 0.33333 0.00000 0.00000 0.25000 0.00000 0.00000 -0.22808 0.00000 0.00000 0.01164 0.00000 0.00000
Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 -0.69165 0.00000 0.00000 0.01193 0.00000 0.00000
Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.25027 0.00000 0.00000 -0.24119 0.00000 0.00000 0.01057 0.00000 0.00000
Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.02734 0.00000 0.00000 -0.63383 0.00000 0.00000 0.02252 0.00000 0.00000
Fe 0.33333 0.00000 0.00000 0.66666 0.00000 0.00000 0.19063 0.00000 0.00000 1.25653 0.00000 0.00000 0.02535 0.00000 0.00000
Fe 0.16928 0.00000 0.00000 0.33841 0.00000 0.00000 0.89179 0.00000 0.00000 -0.03360 0.00000 0.00000 0.07117 0.00000 0.00000
O 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.15076 0.00000 0.00000 -1.30999 0.00000 0.00000 0.02267 0.00000 0.00000
O 0.33333 0.00000 0.00000 0.66667 0.00000 0.00000 0.94475 0.00000 0.00000 3.46959 0.00000 0.00000 0.02700 0.00000 0.00000
O 0.17995 0.00000 0.00000 0.35989 0.00000 0.00000 0.25000 0.00000 0.00000 1.43085 0.00000 0.00000 0.03962 0.00000 0.00000
O 0.15524 0.00000 0.00000 0.31029 0.00000 0.00000 0.05176 0.00000 0.00000 1.76383 0.00000 0.00000 0.08287 0.00000 0.00000
O 0.50398 0.00000 0.00000 1.00803 0.00000 0.00000 0.14867 0.00000 0.00000 2.30019 0.00000 0.00000 0.08497 0.00000 0.00000
==> PROFILE PARAMETERS FOR PATTERN# 1
=> Overall scale factor: 0.001338900 0.000000000 0.000000000
=> Eta(p-Voigt) or m(Pearson VII): 0.586780 0.000000 0.000000
=> Overall tem. factor: 0.000000 0.000000 0.000000
=> Halfwidth parameters:
0.029938 0.000000 0.000000
-0.031407 0.000000 0.000000
0.041664 0.000000 0.000000
=> Cell parameters:
5.893282 0.000000 0.000000
5.893282 0.000000 0.000000
23.218599 0.000000 0.000000
90.000000 0.000000 0.000000
90.000000 0.000000 0.000000
120.000000 0.000000 0.000000
=> Preferred orientation:
0.018610 0.000000 0.000000
0.000000 0.000000 0.000000
=> Asymmetry parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> X and Y parameters:
0.001372 0.000000 0.000000
0.000000 0.000000 0.000000
=> Strain parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> Size parameters (G,L):
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
---------------------------------------------------------------------------------------
=> Phase 2 Name: Fe2O3
---------------------------------------------------------------------------------------
=> New parameters, shifts, and standard deviations
Atom x dx sx y dy sy z dz sz B dB sB occ. docc. socc.
Fe 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.35571 0.00000 0.00000 0.01865 0.00000 0.00000 0.02352 0.00000 0.00000
O 0.31546 0.00000 0.00000 0.00000 0.00000 0.00000 0.25000 0.00000 0.00000 4.90012 0.00000 0.00000 0.04681 0.00000 0.00000
==> PROFILE PARAMETERS FOR PATTERN# 1
=> Overall scale factor: 0.001674900 0.000000000 0.000000000
=> Eta(p-Voigt) or m(Pearson VII): 0.849630 0.000000 0.000000
=> Overall tem. factor: 0.000000 0.000000 0.000000
=> Halfwidth parameters:
-0.314717 0.000000 0.000000
0.256845 0.000000 0.000000
-0.014657 0.000000 0.000000
=> Cell parameters:
5.035680 0.000000 0.000000
5.035680 0.000000 0.000000
13.748774 0.000000 0.000000
90.000000 0.000000 0.000000
90.000000 0.000000 0.000000
120.000000 0.000000 0.000000
=> Preferred orientation:
0.045350 0.000000 0.000000
0.000000 0.000000 0.000000
=> Asymmetry parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> X and Y parameters:
-0.007842 0.000000 0.000000
0.000000 0.000000 0.000000
=> Strain parameters:
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
=> Size parameters (G,L):
0.000000 0.000000 0.000000
0.000000 0.000000 0.000000
==> GLOBAL PARAMETERS FOR PATTERN# 1
=> Zero-point: 0.1368 0.0000 0.0000
=> Cos( theta)-shift parameter : -0.0005 0.0000 0.0000
=> Sin(2theta)-shift parameter : 0.0126 0.0000 0.0000
==> RELIABILITY FACTORS WITH ALL NON-EXCLUDED POINTS FOR PATTERN: 1
=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#: 1
=> Expected : 11.8 1.9122
=> Deviance :0.571E+04 Dev*: 1.136
=> GoF-index: 1.1 Sqrt(Residual/N)
=> N-P+C: 5001
=> SumYdif SumYobs SumYcal SumwYobsSQ Residual Condition
0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000
=> Conventional Rietveld Rp,Rwp,Re and Chi2: 11.0 15.2 14.3 1.135
=> (Values obtained using Ynet, but true sigma(y))
=> SumYnet, Sum(w Ynet**2): 0.2760E+06 0.2441E+06
=> N-sigma of the GoF: 6.740
==> RELIABILITY FACTORS FOR POINTS WITH BRAGG CONTRIBUTIONS FOR PATTERN: 1
=> R-Factors: 8.42 12.5 Chi2: 1.13 DW-Stat.: 1.9223 Patt#:
=> Expected : 11.8 1.9122
=> Deviance :0.571E+04 Dev*: 1.136
=> GoF-index: 1.1 Sqrt(Residual/N)
=> N-P+C: 5001
=> SumYdif SumYobs SumYcal SumwYobsSQ Residual Condition
0.3046E+05 0.3616E+06 0.3563E+06 0.3616E+06 5675. 0.000
=> Conventional Rietveld Rp,Rwp,Re and Chi2: 11.0 15.2 14.3 1.135
=> (Values obtained using Ynet, but true sigma(y))
=> SumYnet, Sum(w Ynet**2): 0.2760E+06 0.2441E+06
=> N-sigma of the GoF: 6.740
=> Global user-weigthed Chi2 (Bragg contrib.): 1.13
=> ---------> Pattern# 1
=> Phase: 1
=> Bragg R-factor: 1.65
=> RF-factor : 1.87
=> Phase: 2
=> Bragg R-factor: 3.19
=> RF-factor : 3.02
--------------------------------------------------------------------------------------------------------------
Pattern# 1 Phase No: 1 Phase name: BaFe12O19
--------------------------------------------------------------------------------------------------------------
No. Code H K L Mult Hw ETA/M 2theta/TOF Icalc Iobs Sigma StrFactor^2 d-hkl CORR
1 1 1 0 3 12 0.192100 0.615360 20.831 0.6 0.8 0.473 1.2943 4.260726 1.018325
2 1 0 0 6 2 0.191102 0.618285 22.963 24.8 26.7 2.090 416.6114 3.869767 1.000000
3 1 1 0 4 12 0.190999 0.618593 23.187 4.4 4.6 0.307 12.3454 3.832868 1.013523
4 1 1 0 5 12 0.189794 0.622341 25.919 1.5 2.1 1.007 5.2692 3.434747 1.010194
5 1 1 0 6 12 0.188558 0.626474 28.931 2.3 2.5 0.370 10.5098 3.083600 1.007863
6 1 1 1 0 6 0.188027 0.628362 30.307 115.2 116.5 1.582 1103.9879 2.946641 1.046989
7 1 0 0 8 2 0.187849 0.629012 30.782 39.1 39.1 0.471 1216.9846 2.902325 1.000000
8 1 1 1 2 12 0.187659 0.629714 31.293 23.9 24.3 0.530 124.4419 2.856078 1.033071
9 1 1 0 7 12 0.187346 0.630901 32.158 239.7 240.7 1.586 1357.1069 2.781190 1.006200
10 1 1 1 4 12 0.186677 0.633558 34.095 266.2 267.2 1.661 1681.4869 2.627483 1.022818
11 1 2 0 0 6 0.186336 0.634989 35.137 26.0 26.2 0.431 342.3931 2.551866 1.046989
12 1 2 0 1 12 0.186266 0.635288 35.356 13.9 14.0 0.237 93.3158 2.536592 1.040542
13 1 1 0 8 12 0.186204 0.635560 35.554 17.8 17.8 0.239 125.5349 2.522919 1.004988
14 1 2 0 2 12 0.186063 0.636178 36.005 2.8 3.0 0.257 19.7391 2.492364 1.034729
15 1 2 0 3 12 0.185742 0.637632 37.064 125.7 127.6 2.104 945.6779 2.423528 1.029615
16 1 1 1 6 12 0.185368 0.639415 38.364 7.9 8.1 0.386 64.6778 2.344363 1.015876
17 1 2 0 4 12 0.185329 0.639609 38.505 0.6 0.7 0.059 5.2376 2.336085 1.025208
18 1 0 0 10 2 0.185261 0.639945 38.750 1.3 1.4 0.195 64.3379 2.321860 1.000000
19 1 1 0 9 12 0.185168 0.640413 39.091 6.0 6.4 0.444 52.2035 2.302412 1.004085
20 1 2 0 5 12 0.184854 0.642062 40.293 84.1 85.4 1.537 765.9689 2.236429 1.021467
21 1 2 0 6 12 0.184355 0.644944 42.394 56.3 56.9 0.968 575.4030 2.130363 1.018325
22 1 1 0 10 12 0.184276 0.645433 42.750 3.3 3.4 0.210 34.4981 2.113434 1.003398
23 1 1 1 8 12 0.184067 0.646795 43.742 2.5 2.7 0.299 28.0185 2.067744 1.011323
24 1 2 0 7 12 0.183867 0.648207 44.772 1.4 1.9 0.619 16.5458 2.022561 1.015704
25 1 1 0 11 12 0.183563 0.650605 46.520 14.9 15.8 1.000 190.6987 1.950547 1.002866
26 1 0 0 12 2 0.183501 0.651153 46.919 0.3 0.4 0.071 24.8150 1.934883 1.000000
27 1 2 1 0 12 0.183478 0.651360 47.070 0.0 0.0 0.006 0.2195 1.929029 1.046989
28 1 2 1 1 24 0.183452 0.651596 47.242 2.9 3.2 0.316 18.6834 1.922406 1.042060
29 1 2 0 8 12 0.183429 0.651810 47.398 1.5 1.6 0.203 19.1567 1.916434 1.013523
30 1 2 1 2 24 0.183378 0.652300 47.755 2.8 2.9 0.252 18.4861 1.902938 1.037482
31 1 2 1 3 24 0.183266 0.653461 48.601 2.0 2.5 0.653 13.9138 1.871766 1.033290
32 1 2 1 4 24 0.183132 0.655062 49.768 2.8 2.9 0.170 20.5378 1.830591 1.029503
33 1 1 1 10 12 0.183111 0.655336 49.968 8.3 8.6 0.392 124.0588 1.823722 1.008323
34 1 2 0 9 12 0.183083 0.655719 50.247 21.4 22.4 1.076 322.3138 1.814253 1.011708
35 1 1 0 12 12 0.183069 0.655924 50.396 2.1 2.2 0.119 31.5208 1.809230 1.002447
36 1 2 1 5 24 0.182996 0.657080 51.239 1.0 1.3 0.385 7.7858 1.781439 1.026120
37 1 2 1 6 24 0.182886 0.659491 52.997 0.9 1.2 0.440 7.2142 1.726420 1.023125
38 1 2 0 10 12 0.182873 0.659905 53.298 8.7 8.8 0.384 148.6288 1.717373 1.010194
39 1 3 0 0 6 0.182853 0.660654 53.844 22.0 22.1 0.483 744.5333 1.701244 1.046989
40 1 3 0 1 12 0.182849 0.660868 54.000 0.0 0.0 0.000 0.0451 1.696696 1.042625
41 1 1 0 13 12 0.182840 0.661386 54.377 1.6 1.5 0.058 28.1489 1.685801 1.002111
42 1 3 0 2 12 0.182838 0.661507 54.466 4.9 5.2 0.351 85.8677 1.683266 1.038529
43 1 2 1 7 24 0.182832 0.662272 55.023 104.8 105.9 1.412 956.2604 1.667534 1.020492
44 1 3 0 3 12 0.182831 0.662565 55.237 0.9 0.9 0.010 16.5028 1.661576 1.034729
45 1 0 0 14 2 0.182830 0.662719 55.349 17.5 17.4 0.301 1985.9094 1.658471 1.000000
46 1 3 0 4 12 0.182840 0.664030 56.305 60.5 61.6 1.200 1150.8531 1.632571 1.031241
47 1 2 0 11 12 0.182845 0.664346 56.535 121.1 121.7 1.029 2373.4250 1.626481 1.008928
48 1 1 1 12 12 0.182854 0.664823 56.882 12.9 13.3 0.389 257.7462 1.617365 1.006302
49 1 2 1 8 24 0.182869 0.665397 57.301 14.8 15.2 0.598 147.6992 1.606543 1.018190
50 1 3 0 5 12 0.182885 0.665888 57.659 0.1 0.1 0.004 1.0948 1.597419 1.028069
51 1 1 0 14 12 0.182931 0.666995 58.465 2.2 3.3 1.675 47.2806 1.577285 1.001839
52 1 3 0 6 12 0.182993 0.668121 59.286 1.8 2.0 0.324 39.6205 1.557390 1.025208
53 1 2 1 9 24 0.183040 0.668845 59.814 3.2 3.6 0.498 35.5924 1.544904 1.016182
54 1 2 0 12 12 0.183053 0.669027 59.947 8.2 8.6 0.560 182.3922 1.541800 1.007863
55 1 3 0 7 12 0.183193 0.670712 61.175 0.0 0.0 0.026 0.4430 1.513751 1.022643
56 1 2 1 10 24 0.183392 0.672598 62.549 4.2 4.2 0.110 51.0758 1.483760 1.014435
57 1 1 0 15 12 0.183411 0.672758 62.666 5.5 5.6 0.171 136.8466 1.481278 1.001615
58 1 2 2 0 6 0.183475 0.673275 63.043 126.1 126.7 1.168 6049.6938 1.473320 1.046989
59 1 3 0 8 12 0.183523 0.673646 63.313 1.7 1.7 0.030 41.1813 1.467686 1.020357
60 1 2 0 13 12 0.183562 0.673939 63.527 6.7 6.9 0.298 169.3220 1.463256 1.006964
No. Code H K L Mult Hw ETA/M 2theta/TOF Icalc Iobs Sigma StrFactor^2 d-hkl CORR
61 1 2 2 2 12 0.183577 0.674050 63.608 0.1 0.1 0.006 2.3224 1.461597 1.039599
62 1 0 0 16 2 0.183677 0.674752 64.119 1.6 1.6 0.074 253.7202 1.451162 1.000000
63 1 1 1 14 12 0.183737 0.675153 64.412 3.7 3.6 0.231 96.2901 1.445276 1.004903
64 1 2 2 4 12 0.183930 0.676351 65.285 0.1 0.1 0.030 1.7636 1.428039 1.033071
65 1 2 1 11 24 0.183979 0.676640 65.496 11.7 12.8 1.274 157.6939 1.423957 1.012914
66 1 3 0 9 12 0.184026 0.676905 65.689 0.1 0.1 0.006 1.6466 1.420242 1.018325
67 1 3 1 0 12 0.184087 0.677244 65.936 0.0 0.0 0.002 0.1181 1.415521 1.046989
68 1 3 1 1 24 0.184121 0.677433 66.074 2.4 2.8 0.480 32.3982 1.412897 1.043340
69 1 3 1 2 24 0.184229 0.678000 66.487 2.2 2.2 0.206 29.6998 1.405114 1.039873
70 1 1 0 16 12 0.184365 0.678686 66.987 0.3 0.3 0.065 7.1565 1.395835 1.001429
71 1 3 1 3 24 0.184417 0.678941 67.173 0.3 0.4 0.036 4.8257 1.392423 1.036605
72 1 2 0 14 12 0.184446 0.679078 67.273 32.4 33.9 1.654 927.2337 1.390595 1.006200
73 1 2 2 6 12 0.184673 0.680121 68.033 7.0 7.2 0.373 199.7649 1.376904 1.027484
74 1 3 1 4 24 0.184702 0.680251 68.127 1.0 1.0 0.061 14.1806 1.375221 1.033549
75 1 3 0 10 12 0.184754 0.680477 68.292 3.9 4.0 0.194 112.5767 1.372301 1.016525
76 1 2 1 12 24 0.184868 0.680962 68.646 2.4 3.0 0.682 36.0887 1.366095 1.011591
77 1 3 1 5 24 0.185105 0.681922 69.345 0.5 1.0 1.039 6.9699 1.354012 1.030711
--------------------------------------------------------------------------------------------------------------
Pattern# 1 Phase No: 2 Phase name: Fe2O3
--------------------------------------------------------------------------------------------------------------
No. Code H K L Mult Hw ETA/M 2theta/TOF Icalc Iobs Sigma StrFactor^2 d-hkl CORR
1 1 0 1 2 6 0.160883 0.660264 24.148 5.3 5.9 0.725 25.3785 3.682522 1.046915
2 1 1 0 4 6 0.184160 0.589602 33.158 21.0 20.9 0.389 200.2004 2.699516 1.020410
3 1 1 1 0 6 0.188095 0.570234 35.628 15.2 15.2 0.218 153.7020 2.517840 1.118397
4 1 0 0 6 2 0.192156 0.541555 39.285 0.3 0.3 0.049 12.7175 2.291462 1.000000
5 1 1 1 3 12 0.193258 0.529210 40.860 4.7 5.0 0.300 34.3266 2.206734 1.053131
6 1 2 0 2 6 0.194219 0.508461 43.505 0.5 0.7 0.278 8.1953 2.078460 1.075101
7 1 0 2 4 6 0.192037 0.461764 49.460 7.8 8.2 0.509 173.9207 1.841261 1.046915
8 1 1 1 6 12 0.185629 0.425625 54.068 9.2 9.6 0.441 126.9143 1.694701 1.025032
9 1 2 1 1 12 0.181106 0.409268 56.154 0.0 0.0 0.001 0.5522 1.636594 1.100256
10 1 1 2 2 12 0.177721 0.399154 57.444 0.6 0.6 0.019 8.7935 1.602880 1.084241
11 1 0 1 8 6 0.177280 0.397934 57.600 1.8 1.9 0.122 59.0510 1.598920 1.006411
12 1 2 1 4 12 0.159419 0.360034 62.433 6.9 7.1 0.330 125.9719 1.486252 1.058928
13 1 3 0 0 6 0.151527 0.347779 63.995 6.6 6.5 0.306 241.3243 1.453676 1.118397
14 1 1 2 5 12 0.139147 0.331840 66.028 0.0 0.0 0.004 0.2995 1.413766 1.049365
15 1 2 0 8 6 0.108820 0.303863 69.595 0.8 0.8 0.208 39.3914 1.349758 1.020410
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BRAGG R-Factors and weight fractions for Pattern # 1
-----------------------------------------------------
=> Phase: 1
=> Bragg R-factor: 1.65 Vol: 698.363( 0.000) Fract(%): 92.36( 0.00)
=> Rf-factor= 1.87 ATZ: 45.649 Brindley: 1.0000
=> Phase: 2
=> Bragg R-factor: 3.19 Vol: 301.933( 0.000) Fract(%): 7.64( 0.00)
=> Rf-factor= 3.02 ATZ: 5.239 Brindley: 0.7500
-----------------------------------------------------------------
SYMBOLIC NAMES AND FINAL VALUES AND SIGMA OF REFINED PARAMETERS:
-----------------------------------------------------------------
------------------------------------------------------------------
=> Dimensions of dynamic allocated arrays in this run of FullProf:
------------------------------------------------------------------
=> Total approximate array memory (dynamic + static): 22050920 bytes
MaxPOINT= 60000 Max.num. of points(+int. Inten.)/diffraction pattern
MaxREFLT= 20000 Max.num. of reflections/diffraction pattern
MaxPARAM= 300 Max.num. of refinable parameters
MaxOVERL= 2096 Max.num. of overlapping reflections
----------------------------------------------------------
=> Dimensions of fixed arrays in this release of FullProf:
----------------------------------------------------------
NPATT = 50 Max.num. of powder diffraction patterns
NATS = 830 Max.num. of atoms (all kind) in asymmetric unit
MPAR = 350 Max.num. of non atomic parameters/phase
IEXCL = 30 Max.num. of excluded regions
IBACP = 200 Max.num. of background points for interpolation
NPHT = 16 Max.num. of phases
NMAGM = 8 Max.num. of rotation-matrices sets for magnetic structure
NBASIS = 12 Max.num. of basis functions associated to a single atom
NIREPS = 9 Max.num. of irreducible representations to be combined
N_EQ = 48 Max.num. of user-supplied symmetry operators/propagation vectors
NGL = 222 Max.num. of global parameters/diffraction pattern
N_LINC = 30 Max.num. of global linear restraints
NAT_P = 64 Max.num. of atomic parameters per atom
NCONST = 500 Max.num. of slack constraints per phase
N_SPE = 16 Max.num. of different chemical species
N_FORM = 60 Max.num. of scattering factor values in a table
NPR = 150 Max.num. of points defining a numerical profile
INPR = 25 Max.num. of different numerical peak shapes
NPRC = 150 Max.num. of terms in the table for correcting intensities
NSOL = 10 Max.num. of solutions to be stored in Montecarlo searchs
CPU Time: 0.858 seconds
0.014 minutes
=> Run finished at: Date: 12/08/2013 Time: 18:42:47.670