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1Ceramics: Crystal Chemistry, Chap 2
Material Science I
http://www.mineralienatlas.de/ http://webmineral.comhttp://www.uniterra.de
Ceramic Materials
F. Filser & L.J. Gauckler
ETH-Zürich, Departement Materials
HS 2007
Chapter 2: Crystal Chemistry
2Ceramics: Crystal Chemistry, Chap 2
Material Science I
Order of the atoms in a solid
• type, strength and direction of the bonds determines the atom‟s
spatial order in a solid.
• the strength of a bond is determined by the potential well.
• The order of the atoms in a solid determines its crystal structure.
• The crystal structure (spatial filling) is determined by
(a) the stoichiometry (chemical composition),
(b) the ratio of radii of the ions and
(c) the type of the bond (its tendency towards covalent bonding).
3Ceramics: Crystal Chemistry, Chap 2
Material Science I
Bond types in Solids
• metallic
• ionic
• covalent
• attraction holds the solid together
• no prefered direction
• charge neutrality of the bond
• ionic bonds unfavorable
charge neutrality of the bonds
• direction of the bond is very important, and
• prevails the principle of achieving max. packing
density
• no preferred spatial direction of the bond
• delocalized electrons and conduction bands ->
charge neutrality of a bond is not required
• maximum coordination, densest packing
• metallic
• ionic
• covalent
Ceramic
5Ceramics: Crystal Chemistry, Chap 2
Material Science I
Mechanism of Bond Formation: Ionic Bonding
electron transferordering of the ions in a
crystal structureRocksalt crystal
electron
reception
electron
donation
6Ceramics: Crystal Chemistry, Chap 2
Material Science I
Equilibrium of Attraction and Repulsion:
Ionic Bonding
Sum of attracting and repelling potential
bringing together a cat-ion and an an-ion
Ion‟s Distance
Potential
Eattraction
E repulsion
r0 = equilibrium distance
attr
acti
ng
rep
elli
ng
Sum
- +r0
7Ceramics: Crystal Chemistry, Chap 2
Material Science I
Equations for the Potentials: Ionic Bond
2
1 2
0
2
1 2
0
4
4
net att rep
att
rep n
net n
E E E
z z eE
r
BE
r
z z e BE
r r
8Ceramics: Crystal Chemistry, Chap 2
Material Science I
Equilibrium Distance and Energy of a Bond:
Ionic Bond
0
2
1 2
2 1
0 0 0
2
1 2
0 0
04
11
4
net
n
r r
bond
dE z z e n B
dr r r
z z eE
r n
What can we do with the knowledge of Ebond ?
9Ceramics: Crystal Chemistry, Chap 2
Material Science I
Lattice Energy: Ionic BondingExample: Structure type AB (NaCl)
NaCl lattice structure (Rocksalt)
10Ceramics: Crystal Chemistry, Chap 2
Material Science I
Lattice Energy: Ionic BondingInteraction of charges within the lattice structure (NaCl)
(Equation is only valid for ions of equal charge)
2
1 2
0 0
2
1 2
0 0
2
1 2
0 0
11
4
11
4
11
4
6 12 8 6 24....
1 2 3 4 5sum
sum
Lattice Av
z z eE
r n
z z eE
r n
z z e
r nE N
2
1 2
0 0 04sum n
z z e BE
r r
11Ceramics: Crystal Chemistry, Chap 2
Material Science I
Madelung Constant
Structure type Stoichiometry
Rocksalt NaCl AB 1.74756
Cesiumchloride CsCl AB 1.76267
Zinc blende ZnS AB 1.63806
Wurtzite ZnS AB 1.64132
Fluorite CaF2 AB2 5.0387
Rutile TiO2 AB2 4.816
Cadmiumiodide CdI2 AB2 4.383
Corundum Al2O3 A2B3 25.031
2.5190
2.4080
4.1719
2.4023
We find big, non-neglible differences in a simple
calculation of the Madelung constant like before
vs its precise calculation !!!
12Ceramics: Crystal Chemistry, Chap 2
Material Science I
Literature on the Calculation of
the Madelung Constant
References for Madelung's Constant:
• M. L. Glasser and I. J. Zucker, Lattice sums, Theoretical Chemistry: Advances and Perspectives, v. 5, ed. D. Henderson, Academic Press, 1980.
• D. Borwein, J. M. Borwein and K. F. Taylor, Convergence of lattice sums and Madelung's constant, J. Math. Phys 26 (1985) 2999-3009; MR 86m:82047.
• J. M. Borwein and P. B. Borwein, Pi and the AGM: A Study in Analytic Number Theory and Computational Complexity, Wiley, 1987; MR 99h:11147.
• I. J. Zucker and M. M. Robertson, Exact values for some two-dimensional lattice sums, J. Phys. A: Math. Gen. 8 (1975) 874-881; MR 54 #9515.
• K. F. Taylor, On Madelung's constant, J. Computat. Chem. 8 (1987) 291-295; MR 88h:82066.
• A. Hautot, A new method for the evaluation of slowly convergent series, J. Math. Phys 15 (1974) 1722-1727; MR 53 #9575.
• R. E. Crandall, New representations for the Madelung constant, Experim. Math. 8 (1999) 367-379.
13Ceramics: Crystal Chemistry, Chap 2
Material Science I
Ionic Bonded Solids
• Ions are modeled as rigid and charged spheres.
• Ions possess an ionic radius which is a function of its atomic number and its
valency.
• Coulomb attraction is effective along the direct connection line of the spheres„
centerpoints.
• No ion overlap because of the high repulsion forces at short inter-ionic
distance.
• cations want to be surrounded by as much anions as possible closest
packed spheres = highest atomic packing density for ionic bonding
• Cationen take a maximum distance from each other, anions will do the same.
• Ionic bonds are isotrop, i.e. they are non-directional.
• The ionic ratio (cations to anions) determines the spatial structure of the ions.
14Ceramics: Crystal Chemistry, Chap 2
Material Science I
Covalent Bonded Solids
• The direction of the bonds are the main factor.
• The atomic orbitals mainly determine the direction of
the bonds.
• Highest atomic packing density is sacrificed for the
direction of the bonds.
• A less dense packing for covalent bonded solids in
comparison to ionic bonded solids.
15Ceramics: Crystal Chemistry, Chap 2
Material Science I
Metallic Bonded Solids
• Free electrons in metals, i.e. valency electrons can„t be allocated to
one atom and they move freely within the solid body. No
limitation because of charge neutrality.
• No limitations because of stoichiometry
• Ions are modeled as spheres, the bond is non-directional. All ions
and electrons possess the same attraction.
• In pure metals all ions are of the same size, therefore ions pack as
dense as possible, i.e. want to achieve highest packing density
• Simlarily for alloys and intermetallic phases. However, in some
cases the different radius of the atoms prevents it from achieving
the closest packing density.
16Ceramics: Crystal Chemistry, Chap 2
Material Science I
Ionic Radius
• Each neutral atom possess a radius which is determined by its outer
electron orbit (Elektronenschale).
• Atomic radius decreases within a period of the periodic system
(horizontal from left to right).
• Ionisation of an atom (electron donation or reception) changes its radius.
• If valence electrons are donated (cation), then the remaining electrons will
be stronger attracted to the nucleus and the ionic radius decreases
Example: neutral charged Na atom: rNa = 1.86 Å, BUT rNa+ = 0.98 Å.
• If more than one electron is donated, then the ionic radius decreases.
• If valence electrons are received (anion), then the ionic radius increases
Example: neutral charged Cl atom, rCl = 1.07 Å, BUT rCl- = 1.81Å.
• If more than one electron is received then the ionic radius increases.
17Ceramics: Crystal Chemistry, Chap 2
Material Science I
Packing Density in Ionic Bonded Solids
stable stable instable
18Ceramics: Crystal Chemistry, Chap 2
Material Science I
rCation/RAnion Coordination
number CN
Name Geometry
0 - 0.155 2 linear
0.155 - 0.225 3 triangular
planar
0.225 - 0.414 4 tetrahedral
0.414 - 0.732 6 octahedral
0.732 - 1.0 8 cubic
1.0 12 12-
coordinated
Ionic Radius and Coordination Number
in Ionic Bonded Solids
19Ceramics: Crystal Chemistry, Chap 2
Material Science I
Packing Density in Covalent Bonded Compounds
The coordination number is determined by:
• number of valence electrons in each atom
• number of valence electrons which participate in the bonding
• hybridisation of the orbitals (sp, sp2, sp3)
Atoms of Group IV A to VII A show number of bonding NB
assuming single bonds:
NB = 8 - NV
NB = number of bondings per atom
NV = number of valence electrons for that atom
20Ceramics: Crystal Chemistry, Chap 2
Material Science I
Packing Density in Covalent Bonded Solids: Carbon
Diamond:
sp3 hybride: single bonds (s), hence the
coordination number is 4
Graphite:
sp2 hybride: single bonds (s), planar,
coordination number is 3
the free “unpaired” electron per C atom is
responsible for a weak bonding between the
platelike layers of the graphite.
more ceramic examples: SiC, Si3N4, AlN
21Ceramics: Crystal Chemistry, Chap 2
Material Science I
Packing Density for Metals
pure metals: r/R=1
hence coordination number 12 => closest packed, highest packing density
fcc
22Ceramics: Crystal Chemistry, Chap 2
Material Science I
fcc / cpp - metals
C
B
A
C
B
A
bcc - metals
23Ceramics: Crystal Chemistry, Chap 2
Material Science I
Other Packing Density than the most Dense
Packing in Metalic Bonded Solids
Body-Centered Cubic (BCC)
Coordination number 8
Packing density 68 vol-%
Simple Cubic (SC) =
Coordination number 6
Packing density 52 vol-%
24Ceramics: Crystal Chemistry, Chap 2
Material Science I
Why should metals have also
other packing densities than fcc?
25Ceramics: Crystal Chemistry, Chap 2
Material Science I
Melting temperature: Melting temperature:
Gruppe IA (oC) Gruppe IIA (oC)
Li (181) Be (1290)
Na (98) Mg (650)
K (63) Ca (839)
Rb (39) Sr (769)
Cs (29) Ba (729)
Thermal Expansion Coefficient: Thermal Expansion Coefficient:
Gruppe IA (oC) Gruppe IIA (oC)
(x 10-6 cm/cm) (x 10-6 cm/cm)
Na (70) Be (12)
K (83) Mg (25)
E E
Why should metals have also
other packing densities than fcc?
26Ceramics: Crystal Chemistry, Chap 2
Material Science I
Group VB and VIB, transistion metal (V, Cr, Nb, Mo, Ta, W, Fe)
• These elements possess partial filled d orbitals in their base state.
• The d-electrons are split-up in either bonding or antibonding orbitals.
• This split favors the bcc structure over a closest packed structure (hcp,
fcc)
Why should metals also have
other packing densities than fcc?
27Ceramics: Crystal Chemistry, Chap 2
Material Science I
Atomic and Ionic Radii
From this section you should learn:
the concept of atomic radii
The concept of ionic radii and how they change with:
• the atomic number in the periodic system
• the coordination number
• the oxidation state / oxidation number
• for coordination numbers of CN 6 and 8, respectively
28Ceramics: Crystal Chemistry, Chap 2
Material Science I
Atomic Radii
The periodic system of the elements: http://www.uniterra.de/
29Ceramics: Crystal Chemistry, Chap 2
Material Science I
Ionic Radius = Bond Length
Ionic radius can„t be measured isolated, but it can be
derived from the bond length in elements and compounds. (see - Shannon, Acta Cryst. (1976) A32 751)
Oxygen ion is assumed to: r0 = 1.26 Å
30Ceramics: Crystal Chemistry, Chap 2
Material Science I
Different Ionic Radii:
Ions can be approximated as rigid spheres.
Element or
Compound
Elements or
Compounds, („Alloys“)Pure Ionic bonding
Metals atomic radius = d/2 in the element (metalic radius)
covalent radius = d/2 in simple bonding (s)
Nonmmetals atomic radius = d/2 in the element
covalent radius = d/2 in simple bonding (s)
31Ceramics: Crystal Chemistry, Chap 2
Material Science I
Radius of Anions & Cations in
Periods and Groups of the Periodic System
incre
asin
g ra
diu
s
dec inc
decreasing radius
incre
asin
g ra
diu
s
dec dec inc
32Ceramics: Crystal Chemistry, Chap 2
Material Science I
Ionic Radius
The ionic radius (in pm) of iso-charged ions grew
with increasing nucleus charge (atomic number)
33Ceramics: Crystal Chemistry, Chap 2
Material Science I
Determination of the Ionic Radius
electron density map of NaCl crystals
electron
density
34Ceramics: Crystal Chemistry, Chap 2
Material Science I
Ionic Radius
References:
• Krug et al. Zeit. Phys Chem.
Frankfurt 4 36 (1955)
• Krebs, Fundamentals of Inorganic
Crystal Chemistry, (1968)
35Ceramics: Crystal Chemistry, Chap 2
Material Science I
Coordination Number CN
Bonding CN Length (Å)
C-O 3 1.32
Si-O 4 1.66
Si-O 6 1.80
Ge-O 4 1.79
Ge-O 6 1.94
SnIV
-O 6 2.09
PbIV
-O 6 2.18
PbII-O 6 2.59
The ionic radius of an element increases with increasing CN.
37Ceramics: Crystal Chemistry, Chap 2
Material Science I
Valency
The ionic radius of an element increases with increasing CN.
The ionic radius decreases with increasing valency.
Bonding CN Length (Å)
C-O 3 1.32
Si-O 4 1.66
Si-O 6 1.80
Ge-O 4 1.79
Ge-O 6 1.94
SnIV
-O 6 2.09
PbIV
-O 6 2.18
PbII-O 6 2.59
38Ceramics: Crystal Chemistry, Chap 2
Material Science I
Main Group in the Periodic System
The ionic radius of an element increases with increasing CN.
The ionic radius decreases with increasing valency.
The ionic radius increases within a main group of periodic system from
top to down (increasing atomic number)
Anions are often larger than cations.
Bonding LC-O 3 1.32Si-O 4 1.66Si-O 6 1.80Ge-O 4 1.79Ge-O 6 1.94Sn
IV-O 6 2.09
PbIV
-O 6 2.18Pb
II-O 6 2.59
CN Length (Å)C-O 3 1.32Si-O 4 1.66Si-O 6 1.80Ge-O 4 1.79Ge-O 6 1.94Sn
IV-O 6 2.09
PbIV
-O 6 2.18Pb
II-O 6 2.59
40Ceramics: Crystal Chemistry, Chap 2
Material Science I
Tetrahedral Hole (Interstice)
Spatial space of the tetrahedral interstice.
41Ceramics: Crystal Chemistry, Chap 2
Material Science I
Octahedral Hole (Interstice)
RX
RA
cross section of the octahedral interstice
42Ceramics: Crystal Chemistry, Chap 2
Material Science I
Rules for the Ionic Radii Ratio(Coordination Number CN =6)
Calculation of the ionic radii ratio in case of
octahedral coordination (CN = 6)
R= radius of the large ions
r = radius of the small ions
2
145cos
rR
R
rRR 2
rR )12(
414.0R
r
43Ceramics: Crystal Chemistry, Chap 2
Material Science I
For coordination number CN = 8 :
unit cell length a = 2R
ions are in touch along the room diagonal of the cell:
a3 = 2(R+r)
division: 3 = (R+r)/R
multiplication: 3R = R+r
then: R(3 -1) = r
r/R = 3 -1 = 0.732
Rules for the Ionic Radii Ratio(Coordination Number CN = 8)
44Ceramics: Crystal Chemistry, Chap 2
Material Science I
Radius ratio: Limits of a Coordination Configuration
If r/R < 0.414, then the cation is too small and “wiggles” in the octahedral hole
If r/R > 0.414, then the anions will be moved away from each other
If r/R << or >> 0.414, then the coordination number changes
This simple rules works very often, however … not in all the cases!
Coordination smallest r/R ratio
linear, 2 -
triangular planar, 3 0.155
tetrahedral, 4 0.225
octahedral, 6 0.414
cubic, 8 0.732
closest packing, 12 1.000
45Ceramics: Crystal Chemistry, Chap 2
Material Science I
Additional means for the classification of crystals
1) Maps for crystal structures (structure maps)
e.g. for AxByOz compounds:
draw a diagram showing radius of A ions vs radius of B ions and mark
the limits for the different structures (properties) in that map!
2) Mooser-Pearson Graphs
Focus on the amount of the convalent bond. Draw a graph showing the
difference of electronegativity of the elements versus the principal
quantum number and determine the limits for the different structures.
3) “Structure - Property - Maps”
e.g. for Perovskites ABO3
draw a graph using the polarisation of A ion vs the polarization of B
ion and mark the limits of a property of the compound.
48Ceramics: Crystal Chemistry, Chap 2
Material Science I
ABO3 “Structure – Property - Map”
LaMnO3
Perovskiktes: ABO3
LaCoO3
Kamata, K.,Nakamura, T., Sata, T.(1974):“ On the State of d-
electrons in perovskite-tape compounds ABO3“, Bulletin of Tokyo
Institute of Technology 120:73
Doshi, R., et al. (1999):“Development of Solid Oxide Fuel Cells
that operate at 500°C“ Journal of the Electrochemical Society:
146(4):1273
T
T
T
49Ceramics: Crystal Chemistry, Chap 2
Material Science I
Ionic Radius: Summary
The ionic radius of an element increases with increasing
coordination number and decreasing valency.
The ionic radius increases with increasing atomic
number within the main groups in the periodic system
The ionic radius ratio can be calculated and in lots of
cases to predict the ionic coordination with its help.
50Ceramics: Crystal Chemistry, Chap 2
Material Science I
Principles of coordination I
Coordination-scheme polyhedron examples
cubic close
packing ccp
(Cu, Ne, etc)
hexagonal
close packing
hcp
(Mg, He, etc)
52Ceramics: Crystal Chemistry, Chap 2
Material Science I
Propensity towards Tetrahedric Coordination
Many compounds show a tetrahedric coordination despite their ionic
radius ratio (rc/rA).
For example, many compounds with ionic radius ratio of rc/rA=0.414
crystalize in a tetrahedric coordination like zinc blende or wurtzite. This
is due if the covalent character of the bonds is pronounced, for example,
if :
1) cations with a high polarizing ability, i.e. Cu2+, Al3+, Zn2+, Hg2+ are
combined with anions which are readily to polarize, i.e. I-, S2-, Se2-.
and:
2) atoms are used which are likely to become sp3 -hybridized orbitals, i.e. Si, C
and Ge.
53Ceramics: Crystal Chemistry, Chap 2
Material Science I
Ionic Bonded Solids
radius ratio rC/rX0.3 0.4 0.5 0.6 0.7 0.8 0.9
stoichiometry
AX ZnS NaCl CsCl
AX2SiO2 TiO2 CaF2
A2X3
Corundum
(-Al2O3)
ABX3CaCO3 and Perovskites
A3X4
AB2X4
Spinels
54Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX: Compilation of possible Structures
Compound ZnS NaCl CsCl
rCation/RAnion 0.40 0.53 0.92
Coordination Number 4 6 8
Zin
c b
lende
Wurt
zite
Rocksalt
55Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX: Zinc blende
Representative Ionic Radius Ratio ZnS
ZnS, -SiC, GaAs 0.40
Cation Zn2+
Coordination Number C.-Polyhedron Ionic Radius [Å]
4 Tetrahedron 0.74
Anion S2-
Coordination number C.-Polyhedron Ionic Radius [Å]
4 Tetrahedron 1.84
57Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX: Wurtzite
Representative Ionic Radius Ratio ZnS
ZnS, AlN, BeO, ZnO 0.40
Cation Zn+
Coordination Number C.-Polyhedron Ionic Radius [Å]
4 Tetrahedron 0.74
Anion S-
Coordination Number C.-Polyhedron Ionic Radius [Å]
4 Tetraedron 1.84
58Ceramics: Crystal Chemistry, Chap 2
Material Science I
AB: Wurtzite
Wurtzit
59Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX: NaCl
Representative Ionic Radius Ratio NaCl
NaCl, CaO, MgO, FeO 0.54
Cation Na+
Coordination Number C.-Polyhedron Ionic Radius [Å]
6 Octahedron 0.97
Anion Cl-
Koordinationszahl C.-Polyhedron Ionic Radius [Å]
6 Octahedron 1.81
60Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX: NaCl
Structure of Rocksalt
61Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX2: Compilation of Structures
Compound SiO2 TiO2 CaF2
rCation/RAnion 0.32 0.52 0.74
Coordination Number 4 6 8
Quart
z T
ype
Rutile
Type
Flu
ori
te T
ype
62Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX2: Quartz
Representative Ionic Radius Ratio SiO2
SiO2 0.32
Cation Si4+
Coordination Number C.-Polyhedron Ionic Radius [Å]
4 Tetrahedron 0.42
Anion O2-
Coordination Number C.-Polyhedron Ionic Radius [Å]
2 linear Coord. 1.32
64Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX2: Rutile
Representative Ionic Radius Ratio TiO2
TiO2, PbO2, GeO2 0.52
Cation Ti4+
Coordination Number C.-Polyhedron Ionic Radius [Å]
6 Octahedron 0.68
Anion O2-
Coordination Number C.-Polyhedron Ionic Radius [Å]
3 planar 3-coord. 1.32
66Ceramics: Crystal Chemistry, Chap 2
Material Science I
AX2: Fluorite
Representative Ionic Radius Ratio CaF2
CaF2, ZrO2, CeO2 0.74
Cation Ca2+
Coordination number C.-Polyhedron Ionic Radius [Å]
8 Cube 0.99
Anion F-
Coordination Number C.-Polyhedron Ionic Radius [Å]
4 Tetrahedron 1.33
68Ceramics: Crystal Chemistry, Chap 2
Material Science I
A2X3: Corundum
Representative Ionic Radius Ratio Al2O3
Al2O3, Fe2O3, Cr2O3, B2O3 0.39
Cation Al3+
Coordination number C.-Polyhedron Ionic Radius [Å]
6 Octahedron 0.51
Anion O2-
Coordination number C.-Polyhedron Ionic Radius [Å]
4 Octahedron with 2
empty vertices
1.32
69Ceramics: Crystal Chemistry, Chap 2
Material Science I
A2X3: Corundum
Corundum
- the large circles represent the oxygen ions- and
- the small circles represent the alumium ions.
C
B
A
C
B
A
70Ceramics: Crystal Chemistry, Chap 2
Material Science I
ABX3: Calcite
Representative Ionic Radius Ratio CaCO3
CaCO3 Ca2+: [CO3]2- = 0.36
Cation Ca2+
Coordination number C.-Polyhedron Ionic Radius [Å]
6 Octahedron 0.99
Anion [CO3]2-
Coordination number C.-Polyhedron Ionic Radius [Å]a
6 Octahedron 2.72
a The bond length C-O in CO3-complex is 1.36 Å.
75Ceramics: Crystal Chemistry, Chap 2
Material Science I
ABX3: Perovskite
Representative Ionic Radius Ratio CaTiO3
CaTiO3, BaTiO3 Ca2+:O2-=0.75; Ti4+:O2-=0.52
Cation Ca2+
Coordination Number C.-Polyhedron Ionic Radius [Å]
12 cuboctahedron 0.99
Anion O2-
Coordination number C.-Polyhedron Ionic Radius [Å]
4 Planare 4-Coordination 1.32
Cation Ti4+
Coordination number C.-Polyhedron Ionic Radius [Å]
6 Octahedron 0.68
77Ceramics: Crystal Chemistry, Chap 2
Material Science I
ABX3: Perovskite
Perowskite
- TiO6 – octahedron
- CaO12 – cuboctahedron
(Ca2+ and O2- possesses a
cubic close packing)
mainly ferroelectrika, superconductors,
etc.
78Ceramics: Crystal Chemistry, Chap 2
Material Science I
A2BX4: Spinel
Representative Ionic Radius Ratio MgFe2O4
Fe2MgO4, Mg2TiO4 Mg2+:O2-=0.50; Fe3+:O2-=0.48
Cation Mg2+
Coordination Number C.-Polyhedron Ionic Radius [Å]
4 Tetrahedron 0.66
Anion O2-
Coordination Number K.-Polyhedron Ionic Radius [Å]
6 Octahedron 1.32
Cation Fe3+
Coordination Number C.-Polyhedron Ionic Radius [Å]
6 Octahedron 0.64
86Ceramics: Crystal Chemistry, Chap 2
Material Science I
Spinel
B2AX4: Spinel
O2-
Mg2+
Fe3+
Example: MgO x Fe2O3 = MgFe2O4
87Ceramics: Crystal Chemistry, Chap 2
Material Science I
Summary
Factors determining the crystal structure:
Three major factors influence the crystal structure in
solid compounds:
1.) the stoichiometry,
2.) the ratio of cation radius and anion radius
and
3.) the propensity for the convalent bond type (sp3-
hybridized bonding).