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Journal of
AppliedCrystallography
ISSN 0021-8898
Rietveld texture analysis of Dabie Shan eclogite from TOF neutrondiffraction spectra
H.-R. Wenk, L. Cont, Y. Xie, L. Lutterotti, L. Ratschbacher and J. Richardson
Copyright © International Union of Crystallography
Author(s) of this paper may load this reprint on their own web site provided that this cover page is retained. Republication of this article or itsstorage in electronic databases or the like is not permitted without prior permission in writing from the IUCr.
J. Appl. Cryst. (2001). 34, 442–453 H.-R. Wenk et al. � Rietveld texture analysis
research papers
442 H.-R. Wenk et al. � Rietveld texture analysis J. Appl. Cryst. (2001). 34, 442±453
Journal of
AppliedCrystallography
ISSN 0021-8898
Received 19 December 2000
Accepted 30 March 2001
# 2001 International Union of Crystallography
Printed in Great Britain ± all rights reserved
Rietveld texture analysis of Dabie Shan eclogitefrom TOF neutron diffraction spectra
H.-R. Wenk,a*² L. Cont,b Y. Xie,a L. Lutterotti,b L. Ratschbacherc and J. Richardsond
aDepartment of Geology and Geophysics, University of California, 94720 Berkeley, California,
USA, bDipartimento di Ingegneria dei Materiali, UniversitaÁ di Trento, 38050 Trento, Italy, cInstitut
fuÈ r Geologie, Technische UniversitaÈt Bergakademie, 09596 Freiberg, Germany, and dIntense Pulsed
Neutron Source, Argonne National Laboratory, 60439 Argonne, Illinois, USA. Correspondence e-
mail: [email protected]
Orientation distributions of garnet and omphacite in eclogite from the ultra-high
pressure Dabie Shan belt in east-central China were determined from neutron
diffraction data by the Rietveld method. Diffraction spectra were recorded in 16
sample orientations with seven detectors, with a kappa-geometry texture
goniometer at the time-of-¯ight (TOF) neutron facility at the Intense Pulsed
Neutron Source (IPNS). The textures of the two minerals were extracted
simultaneously from 16� 7 = 112 diffraction spectra, covering a large portion of
the pole ®gure. The texture analysis was performed both with the Williams±
Imhof±Matthies±Vinel (WIMV) method and the harmonic method, imple-
mented in the program package MAUD. The incomplete pole-®gure coverage
introduced arti®cial oscillations in the case of the harmonic method. The
discrete WIMV method produced better results, which illustrate a more or less
random orientation distribution for cubic garnet. Apparently elongated grains
turned out to be layers of randomly oriented crystals. Monoclinic omphacite
displays a sharp texture, with [001] parallel to the lineation direction. The
texture data obtained by neutron diffraction were veri®ed with EBSP (electron
backscatter pattern) measurements.
1. Introduction
Most rocks and many man-made materials are composed of
several phases. If such materials are deformed, the different
phases attain characteristic orientation distributions. We still
know very little about polyphase polycrystal plasticity (Wenk,
1994), partly because of the dif®culty of quantitatively char-
acterizing textures. Composite materials often have very
complex diffraction spectra, with many partially or fully
overlapping diffraction peaks. There are only a few examples
of quantitative texture analyses of polymineralic rocks and
most have used neutron diffraction (e.g. Wenk & Pannetier,
1990; Siegesmund et al., 1994; Dornbusch et al., 1994; Leiss et
al., 1999; Ullemeyer & Weber, 1999; Chateigner et al., 1999). In
the study reported here, we investigated an eclogite from the
Bixiling area of the Dabie Shan region of east-central China.
The eclogite contains garnet and omphacite as the major
phases, and phengite, zoisite and rutile as the most common
minor phases. We have been particularly interested in this
eclogite because it shows ductile deformation. Grains of both
garnet and omphacite appear elongated and this study, though
emphasizing methodology, will contribute to a better under-
standing of deformation of those minerals in continental
subduction zones. Garnet is cubic; optical microscopy does not
provide any insight into the texture pattern.
Usually textures are determined by extracting pole ®gures
from single diffraction peaks. This is dif®cult if pole ®gures are
overlapped. During recent years, methods have been devel-
oped that use continuous diffraction spectra and rely on the
Rietveld method (Wenk et al., 1994; Ferrari & Lutterotti, 1994;
Von Dreele, 1997). This report describes the ®rst application
of the method to a polyphase material containing low-
symmetry compounds, which adds considerable complexity.
We will use the example to illustrate some of the possibilities
and limitations of the method. Texture results obtained with
time-of-¯ight (TOF) neutron diffraction will be compared
with EBSP measurements on the same specimens and some of
the advantages and disadvantages of the two methods will be
discussed.
2. Geologic background
The Dabie Shan ultra-high pressure (UHP) belt is part of the
2000 km long Qinling-Dabie-Sulu orogen and is formed by
attempted subduction of the Yangtze (or South China) craton
beneath the Sino-Korean (or North China) craton in the
Triassic (see Fig. 1 and e.g. Hacker et al., 2000). The largest
tract of UHP continental crust, the Dabie-Hong'an area, was² Present address: European Synchrotron Radiation Facility, BP 220, F38043Grenoble CEDEX, France.
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exhumed from >100 km depth as a coherent, >15 km thick
slab between 240 and 230 million years ago. Ma®c or ultra-
ma®c rocks with particularly well preserved ultrahigh-pressure
parageneses constitute only about ®ve volume percent of an
otherwise mostly felsic and chie¯y paragneissic sequence.
The Bixiling complex (Fig. 1) is the largest ma®c±ultrama®c
UHP block in Dabie. It consists of banded eclogite and thin
layers of garnet-bearing ultrama®c rocks (e.g. Liou et al.,
1996). The existence of abundant coesite inclusions in eclogitic
omphacite, zoisite, kyanite and garnet, together with Fe±Mg
partitioning of coexisting clinopyroxene±garnet indicate peak
metamorphic conditions at 873±1043 K and�3 GPa (Zhang et
al., 1995). Microstructures indicate a top NW ¯ow along a well
developed foliation and, in particular, lineation. The kine-
matic history began in the garnet±omphacite stability ®eld and
extended at lower temperature to brittle±ductile chlorite-
bearing veins.
The sample that we investigated, D556e, is a typical Bixiling
eclogite with garnet and omphacite as the major phases, and
rutile, zoisite/clinozoisite, phengite, quartz, talc/tremolite and
kyanite as minor phases. Chemical compositions obtained with
the electron microprobe for some main phases are given in
Table 1. The two principal minerals (Fig. 2) are garnet and
omphacite. The cubic garnet, rich in a pyrope component, is
arranged in layers parallel to the regional foliation. Garnet is
slightly zoned with an enrichment of Mg and Ca in the core,
becoming more Fe- and Mn-rich towards the rim. In the
photomicrograph with crossed polars, the analyzer was slightly
rotated to illustrate microstructures within the dark garnet
layer. Monoclinic omphacite occurs as prismatic crystals that
de®ne a lineation.
3. Experimental techniques
Neutron diffraction experiments were performed on the
general purpose powder diffractometer (GPPD) (Jorgensen et
al., 1989) at the IPNS of Argonne National Laboratory. Since
the neutron source is pulsed, detectors measure neutron
scattering as a function of TOF of neutrons, rather than the
scattering angle. At the IPNS, 80 ns bursts of 450 MeV protons
are extracted in a single revolution from a rapid cycling
synchrotron and directed to a depleted-235U target at pulses of
30 Hz. The fast neutrons are slowed down by a liquid-methane
moderator, maintained at a temperature of 100 K, providing a
wide range of wavelengths (0.2±5.7 AÊ ). The moderator-to-
sample distance is 19.96 m and the sample-to-detector
distance is 1.5 m. The beam at the sample was collimated to a
size of 1.2 � 3 cm. The sample consists of a cube, side length
1 cm, with rounded corners and edges, and is therefore fully
immersed in the beam. The time-averaged intensity at the
sample is about 3 � 106 neutrons cmÿ2 sÿ1.
The sample chamber is surrounded by 320 3He gas
proportional detector tubes, collected in 14 banks and
arranged within a horizontal plane (Fig. 3a). Each tube is
1.3 cm in diameter and 38 cm long. We have only used seven
high-angle banks with average positions in 2� of �144, ÿ126,
�108 and �90�. The detector bank number 3 (+126�) was not
used because of the presence of a strong additional peak that
is not observed in any of the other spectra. Subsequent
investigation revealed that the spurious features resulted from
malfunction of an isolated module in the instrument electro-
nics, and were therefore not from the sample. For these banks
the resolution �d/d (full width at half-maximum) is approxi-
J. Appl. Cryst. (2001). 34, 442±453 H.-R. Wenk et al. � Rietveld texture analysis 443
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Figure 1Bixiling eclogite sample location within the Dabie Shan ultrahigh-pressure orogen that is a part of the Triassic collisional orogen in east-central China. [Modi®ed after Ratschbacher et al. (2000).]
Figure 2Photomicrograph of Dabie Shan eclogite with crossed polars, but with theanalyzer slightly rotated. Dark grey regions are garnet. The scale isindicated.
Table 1Chemical microprobe analyses of the major minerals in Bixiling eclogitecalculated based on the assumed number of O atoms.
All iron atoms are assumed to be Fe2+.
Mineral Formula
Garnet (core) (Ca0.938Mg1.237Fe0.875Mn0.013)3.063(Ti0Al2.023)Si2.95O12
Garnet (rim) (Ca0.748Mg1.051Fe1.227Mn0.025)3.055(Ti0Al1.99)Si2.981O12
Omphacite (Na0.531Ca0.469)(Fe0.057Mg0.435Mn0.001Ti0.002Al0.527)Si1.988O6
Clinozoisite Ca1.883Fe0.285Al2.646Si2.904O12(OH)
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444 H.-R. Wenk et al. � Rietveld texture analysis J. Appl. Cryst. (2001). 34, 442±453
mately 0.27% for�144�, 0.32% for 126�, 0.39% for�108�, and
0.49% for �90�, respectively.
To obtain an ef®cient orientation coverage, we used a
locally designed texture goniometer with kappa geometry
(Fig. 4). The angle � is ®xed at 180� and ! is set to 18� (inclined
to the incident beam, Fig. 3a). The sample, mounted on a
vanadium rod perpendicular to the foliation, is rotated about
the ' axis in sixteen 22.5� intervals (Fig. 3b). If the rotation
axis is at this angle, a lattice plane perpendicular to the rota-
tion axis is in Bragg re¯ection geometry for detector bank 2.
This produces the pole-®gure coverage shown in Fig. 5. Each
small circle corresponds to a detector bank, with bank 2
recording the central point of the pole ®gure. Spectra were
measured for 2.5 h for each orientation. On Fig. 5, the fabric
coordinates X = l, Y, Z are indicated. The pole to the foliation
s is in the center (Z) and the lineation direction l is at the top
(X). The directions l, Y and Z are also marked on the sample
in Fig. 3(b). All pole ®gures, except Fig. 12, are represented in
this orientation.
In the initial processing of the data, individual spectra for
each detector were transformed to GSAS format (Larson &
Von Dreele, 1986).
The average of spectra over all 16 sample orientations is
illustrated in Fig. 6(a) for the ÿ144� detector bank 2, and in
Fig. 6(b) for the +90� detector bank 7. We only used the range
from 1.75 to 2.95 AÊ . Below the spectrum are indicated all the
diffraction peaks for garnet and omphacite. The strongest
Figure 3(a) Detector arrangement on the GPPD TOF powder diffractometer at the IPNS. Detector banks are numbered and angles are indicated. The rotationaxis of the kappa goniometer (' axis) is indicated. (b) Cube-shaped sample of the eclogite mounted on a vanadium rod. The sample is rotated around therod axis in 15 increments of 22.5�.
Figure 4Kappa texture goniometer at the IPNS. The goniometer is mounted withrods from the top plate. Three motors are visible: ! (on top, vertical axis),� (diagonal axis) and ' (small motor at bottom). The sample is mountedon the horizontal rod. In the texture experiment, ! is set to 18� and thesample is only rotated around '.
Figure 5Pole-®gure coverage with the kappa goniometer. Each detector bankrecords a small circle (numbers). Detector bank 3 was not used. Theeclogite sample is mounted with Z in the ' rotation axis; X, Y and Z aremesoscopic fabric coordinates; X = l is the lineation direction; Z is thenormal to the foliation.
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peaks are labeled in Fig. 6(a). We wanted to avoid the low-d
region with very closely spaced peaks and low signal to noise
ratio. Note that the high-angle ÿ144� bank 2 has a higher
resolution than the 90� bank 7. The high-d region also was not
used because the intensity for that particular neutron energy
was too low to distinguish the peaks from the background
easily. The 16 � 7 = 112 individual spectra served as input for
the Rietveld texture analysis.
4. Rietveld texture analysis
Traditionally, texture analysis has relied on pole-®gure
measurements. Pole ®gures are measured with monochromatic
X-ray or neutron diffraction by positioning a detector on the
center of a diffraction peak and rotating the sample into
various orientations (between 500 and 1000). This is ef®cient if
only a few pole ®gures are required for the orientation
distribution (OD) analysis and if diffraction peaks are
reasonably strong (relative to the background) and well
separated, such as in pure face-centered cubic (f.c.c.) and
body-centered cubic (b.c.c.) metals. The method becomes
increasingly unsatisfactory for complex diffraction patterns of
polyphase materials and low-symmetry compounds with many
closely spaced and partially or completely overlapped peaks.
The amount of texture information is roughly contained in
the product of the number of pole ®gures (hkl) times the
number of sample orientations. In conventional OD analysis,
one relies on a few pole ®gures and many sample orientations.
The objective of this research was to develop a method that
uses many pole ®gures and fewer sample orientations. This is
an obvious advantage for TOF neutron diffraction where
many diffraction peaks are measured in a spectrum, and beam
time is limited, precluding us from measuring a large number
of spectra.
As texture researchers are becoming concerned with
complex diffraction spectra, crystallographers have developed
J. Appl. Cryst. (2001). 34, 442±453 H.-R. Wenk et al. � Rietveld texture analysis 445
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Figure 6TOF diffraction spectra, averaged over 16 sample orientations, recorded using (a) detector bank 2 and (b) detector bank 7. In (a), the peaks used in thetexture analysis for garnet (G) and omphacite (O) are labeled; (b) highlights some unknown diffraction peaks (*) and indicates the ranges that were notused in the analysis. Dotted lines are actual measurements; solid lines are curves ®tted by the Rietveld method. Below spectrum (b) are all the diffractionlines for garnet and omphacite. Two TOF diffraction spectra recorded using detector bank 1 are shown in (c) and (d). The two spectra are in differentsample orientations and show different relative intensities for omphacite as a result of the texture. Four examples of the differences are indicated byarrows. Diffraction intensities for garnet are similar because of weak preferred orientation. The individual spectra (c) and (d) also illustrate the poorcounting statistics.
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446 H.-R. Wenk et al. � Rietveld texture analysis J. Appl. Cryst. (2001). 34, 442±453
a comprehensive new approach to crystal structure analysis.
Rietveld (1969) proposed the use of continuous powder
patterns and his method is implemented in several software
packages [e.g. DBWS (Wiles & Young, 1981), GSAS (Larson
& Von Dreele, 1986) and Fullprof (Rodriguez-Carvajal et al.,
1991)]. Texture analysis can take advantage of these devel-
opments in crystallography and make use of the new expertise
in pro®le analysis.
Figs. 6(c) and 6(d) illustrate two TOF spectra of eclogite for
detector bank 1, measured in different sample orientations. It
is obvious that for omphacite, relative intensities are different
as a result of the preferred orientation (some peaks with
signi®cant differences are indicated by arrows). A detector
only records intensity from those crystallites that have lattice
planes (hkl) in a Bragg re¯ection orientation. In a powder with
a random orientation of crystallites, the intensities remain the
same for all sample orientations and only arise from the crystal
structure. In a textured material, the systematic intensity
deviations from those observed in a powder contain infor-
mation about crystal orientation. Intensities are linked to the
crystal structure by means of the structure factor. They are
also linked to the texture through the orientation distribution
function (ODF). The sum of the weighted intensities over the
whole pole ®gure has to correspond to the structure factor.
The texture correlations are quantitatively described by the
ODF.
There are various ways to implement texture effects in the
Rietveld method. One way is to expand the ODF with
generalized spherical harmonics (Bunge, 1969) and then
determine the ®nite number of coef®cients, in a similar way as
crystallographic parameters are re®ned with a non-linear
least-squares procedure (Popa, 1992; Ferrari & Lutterotti,
1994; Von Dreele, 1997). Another approach is to use discrete
methods that directly relate the ODF to pole-density values in
the pole ®gures. In this case, it is more ef®cient to separate
crystal structure and texture, and proceed in iterations.
Intensity deviations can be extracted as arbitrary weights, e.g.
with the Le Bail algorithm (Le Bail et al., 1988). They can then
be used to calculate the ODF using texture correlations
between pole densities within a single pole ®gure, and between
different pole ®gures. Reconstructed pole ®gures from the
ODF are then used to compute the texture deviations of the
intensities for ®tting in the (crystal structure) re®nement
procedure. This procedure for texture computation does not
require detailed knowledge of the crystal structure, but only
the space group and cell parameters. In principle, it can be
applied at the early stages of ab initio methods to solve the
crystal structure, not only for the re®nement, as has been
demonstrated by Wessels et al. (1999).
In the analysis of the eclogite sample, we used both
methods. We applied ®rst the harmonic apparatus [in GSAS
and MAUD (Materials Analysis Using Diffraction; Lutterotti
et al., 1999)] and then the Williams±Imhof±Matthies±Vinel
(WIMV) algorithm [in MAUD and BEARTEX (Wenk et al.,
1998)]. The analysis with GSAS was not successful, in part
because the program is unable to handle more than 99 spectra
simultaneously, and we will not report further details. Using
only 99 spectra in GSAS, the pole-®gure coverage was not
suf®cient to assure a unique solution for the ODF and resulted
in the appearance of artifacts in the harmonic functions. This is
particularly severe for weak textures.
For most of our work, we relied on the Rietveld code
MAUD, which is designed for the characterization of bulk and
layered materials. The program is written in Java and bene®ts
from an object-oriented implementation for easy modi®cation
and extensibility. The core of the package is a Rietveld ®tting
routine (least squares) of multiple spectra extended to analyze
texture, phase quantities, crystallite size and microstrain,
residual stresses and re¯ectivity. Since Java is platform inde-
pendent, the program runs on a variety of systems, such as
Windows, Mac OS, Unix and Linux. The program is driven by
a graphical interface and it has an automatic mode, mainly for
routine structure re®nements from powders, and a manual
mode. The automatic procedure requires the user to input
only the spectra, the instrument used, the phases present in
the sample and the choice of which models to use for texture,
microstructure, etc. The program will choose automatically the
re®nement strategies, iterations and parameters to re®ne
throughout the analysis. In manual mode, the re®nement
strategy is instead decided by the user step by step; obviously
it requires more experience of both the Rietveld method and
texture analysis. We found that for analyzing the eclogite
texture, manual operation was required at all stages because of
the complexity of the analysis. Secondary factors affecting the
failure of the automatic procedure were the overall weak
intensity and counting statistics, as well as grain statistics, even
if neutrons were used to obtain a large sample volume.
Complicating factors for the eclogite sample are the
presence of two major phases with unknown volume ratios.
Furthermore, secondary phases are present and several peaks
(some marked by asterisks in Fig. 6b) could not be identi®ed.
Such complications are quite typical for rocks and require a
rather laborious and stepwise procedure.
The ®rst step is to calculate average spectra over all 16
sample orientations for each of the seven detectors (two are
shown in Figs. 6a and 6b). In these average spectra, texture
effects are reduced but not absent since they only average
over a ring in the pole-®gure coverage (Fig. 5), not over the
whole pole ®gure. These average spectra show excellent
counting statistics (corresponding to a counting time of 40 h),
and are more suitable for the re®nement of instrumental
parameters, background and crystal structure.
Some unrecognized peaks were ®tted with arbitrary Gaus-
sian functions, the height, half-width and intensity (constant
for all spectra) of which were re®ned independently. Some
peaks could not be ®tted easily because their intensity was not
constant for all spectra and we excluded them from the
computation in two regions, from 1.848 to 1.864 AÊ and from
2.375 to 2.410 AÊ .
Instrumental parameters (one set for each detector) include
a bulk scaling intensity, a peak width function [de®ned by
three Caglioti parameters (Caglioti et al., 1958)], and a zero
offset. After the re®nement of instrumental parameters, we
proceeded to re®ne the background as a second-degree
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polynomial. This was dif®cult
because of the presence of
unidenti®ed peaks and manual
adjustments were necessary to
obtain a good ®t. Next, lattice
parameters were re®ned, for
each phase in a row, beginning
with the most abundant
omphacite. Table 2 presents the
results for garnet and omphacite
for all the detectors, docu-
menting good resolution.
Finally, crystal structure para-
meters, such as atomic coordi-
nates and temperature factors,
were re®ned, though shifts from
published values were insignif-
icant. This procedure was repe-
ated several times.
The ®nal step was to re®ne
the texture. At that stage, some
instrumental and structural
parameters were kept ®xed.
Parameters related to intensity
(scaling, phase quantity,
temperature factors) and peak
positions (cell parameters and
zero offsets) were re®ned with
the texture.
The Rietveld texture analysis
can be performed either in
Fourier space with the harmonic
approximation or in direct space with the WIMV method. At a
®rst glance, the former seems more elegant and attractive in
the Rietveld procedure (Ferrari & Lutterotti, 1994) because a
small number of harmonic coef®cients fully characterize the
ODF. Such parameters are re®ned directly, together with the
structural and instrumental parameters. By contrast, the
WIMV method requires the extraction of the experimental
pole ®gures and the subsequent processing by its algorithm to
obtain the texture, which can then be used to compute the
pattern. Consequently, the extraction and texture computation
has to be performed externally to the least-squares routine of
the Rietveld analysis. This does not preclude fast convergence
between the texture and structure iterations because of the
very small correlation between the two (Matthies et al., 1997).
In the case of the eclogite, the texture analysis with the
harmonic method was not successful and only the results
obtained by the WIMV method will be discussed in detail. The
primary de®ciencies of the harmonic method are highlighted
in Fig. 7(b), where some pole ®gures for garnet have been
reconstructed by re®ning harmonic texture coef®cients. Since
the experiment does not cover the outer part of the pole
®gures (see Fig. 5), the problem is not suf®ciently de®ned to
obtain a unique solution by the harmonic method. The
harmonic method, as implemented in the Rietveld method,
does not impose the positivity condition on the ODF (Dahms
& Bunge, 1988) and unreal solutions are possible. In the least-
squares framework of the Rietveld method, corrections for
positivity are cumbersome because they would require intro-
duction of odd coef®cients. In principle, the harmonic method
can handle an arbitrary and incomplete coverage, but the
blind peripheral area and larger regions with no data intro-
duce severe artifacts. Unacceptable oscillations occur in the
outer part that is not covered by experimental points. Even
with a low harmonic expansion to a maximum order Lmax = 4
this problem persists [the pole ®gures in Fig. 7(b) correspond
to this case], and using a higher expansion makes it worse. No
one has analyzed the in¯uence of coverage on results, but
clearly it is not a simple relationship and ought to be explored.
The harmonic method is very sensitive to an uneven coverage
of the pole ®gure and thus de®es in some sense the advantages
of the Rietveld scheme, i.e. many (hkl) and few sample
J. Appl. Cryst. (2001). 34, 442±453 H.-R. Wenk et al. � Rietveld texture analysis 447
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Table 2Re®ned lattice parameters and phase proportions of omphacite andgarnet.
Volume fractions are normalized to 100, neglecting minor phases.
Phase a (AÊ ) b (AÊ ) c (AÊ ) � (�) % vol.
Omphacite 9.6197 (6) 8.7913 (3) 5.2457 (4) 106.58 (1) 57Garnet 11.5970 (1) ± ± ± 43 (1)
Figure 7Selected pole ®gures for garnet in equal-area projection and linear scale. The pole-density scale is shown onthe right-hand side. Grey shades indicate the pole density in multiples of a uniform distribution. (a) Pole-density distribution from the Le Bail intensity extraction. (b) Pole ®gures obtained with the harmonicmethod and Lmax = 4. (c) Pole ®gures obtained from the WIMV ODF in MAUD. (d) Pole ®gures obtainedwith the WIMV from seven pole ®gures, using BEARTEX. For the sample orientation see Fig. 5.
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448 H.-R. Wenk et al. � Rietveld texture analysis J. Appl. Cryst. (2001). 34, 442±453
orientations. In the harmonic functions that are re®ned,
sample and crystal space enter separately and both need to be
constrained by suf®cient data. Compared with this de®ciency,
other disadvantages, such as the dif®culty of obtaining odd
coef®cients (Matthies et al., 1988; Dahms & Bunge, 1988), or
the poor angular resolution (around 90� for Lmax = 4) are of
secondary importance.
For most of the texture calculations, we used the WIMV
algorithm, which is a discrete method based on tomographic
principles (Matthies & Vinel, 1982). Each pole-®gure value
corresponds to a projection path of the OD. OD values are
obtained as the intersection of at least three projection paths.
In our case, with 112 sample directions, seven crystal vectors
[(hkl) pole ®gures] for garnet, and 26 (only 13 in BEARTEX)
for omphacite, the system is highly determined. The number of
intersections in OD cells ranges from 52 to 61 for garnet and
from 5 to 20 for omphacite (for the reduced set of 13 pole
®gures, see below).
All 112 individual spectra were used simultaneously, and by
the Le Bail procedure (Le Bail et al., 1988; Matthies et al.,
1997) intensity weights were extracted for all hkl in each
spectrum. After the intensity extraction, pole ®gures on a 5 �5� grid were generated by linear interpolation between all
points that lie within a selectable limiting angular distance
from the grid point to be determined (in our case a distance of
20� was chosen). If fewer than three points describe a polygon
that contains the grid point, the interpolation was rejected.
The effect of the interpolation is twofold. Firstly, it increases
arti®cially the resolution in the pole-®gure coverage, gener-
ating suf®cient data to ensure a better coverage of the ODF
and a unique solution. Secondly, it smoothes the experimental
pole ®gures to obtain a better de®ned ODF and reduce
statistical errors, noise and possible grain effects. The inter-
polated pole ®gures are subsequently analyzed by the WIMV
method to obtain the ODF in a 5 � 5 � 5� angular grid.
The interpolated pole ®gures were used both internally in
the Rietveld procedure in MAUD in the iterative process to
re®ne structural phase parameters and the texture, as well as
externally in the program BEARTEX (Wenk et al., 1998) at
the end of the re®nement, selecting only a few experimental/
interpolated pole ®gures generated by MAUD. In BEARTEX,
the pole ®gures were again analyzed with WIMV, but
excluding those pole ®gures that showed poor correspondence
between observed and recalculated values, generally because
of peak overlap or weak re¯ections.
The main computer we used for the calculations had a
Pentium III 700 Mhz processor with 1 Gbyte RAM on board.
Windows NT was the operating system. The most demanding
part of the computing was the texture analysis. The WIMV
algorithm took 30 min and about 45 Mbyte of memory to
re®ne all spectra simultaneously. By comparison, texture
computation by means of the harmonic method was much
slower, requiring about 38 h of CPU time and a vary large
amount of memory (516 Mbyte). Other re®nements, such as
background, scale factors, basic phase parameters (cell para-
meters, temperature factors and quantities) and micro-
structure, were faster, with computing times in the range of a
few minutes. In particular, the harmonic texture analysis in
MAUD is slower than in GSAS during the least-squares
minimization step. This is because of the program structure of
MAUD, by which derivatives are computed numerically
instead of analytically. On the other hand, the employment of
numerical derivatives does not impose limitations on the
methodologies implemented in the program, speci®cally when
an analytical derivative cannot be computed. Mixing numer-
ical and analytical derivatives in the least-squares procedure is
highly discouraged.
5. Results
Fig. 7 shows pole ®gures for selected lattice planes of garnet in
equal-area projection (not all the pole ®gures used in the
computation are shown in the picture). Fig. 7(a) represents
normalized intensities extracted with the Le Bail algorithm
and illustrates the coverage. Fig. 7(b) shows pole ®gures
recalculated from the ODF that was obtained with the
harmonic method. As has been noted above, the harmonic
pole ®gures for Lmax = 4 show unrealistic oscillations in the
peripheral region. Fig. 7(c) shows pole ®gures recalculated
from the ODF obtained by the WIMV algorithm of MAUD,
based on the pole ®gures in Fig. 7(a). These pole ®gures for
garnet document the absence of signi®cant preferred orien-
tation. Weak maxima are considered to be caused by poor
grain statistics. Fig. 7(d) again shows pole ®gures calculated
with WIMV, but this time using BEARTEX. The solutions by
MAUD and BEARTEX are similar because the same set of
seven experimental pole ®gures was used.
From the WIMV ODF of BEARTEX, we also calculated
pole ®gures in the principal directions of this cubic mineral
(Fig. 8). They all document a more or less random orientation
distribution.
Figs. 9 and 10 illustrate corresponding results for omphacite.
Fig. 9(a) shows four incomplete intensity distributions
obtained with the Le Bail algorithm. A total of 26 were
extracted and used in the MAUD WIMV ODF analysis (Fig.
9b, only six reported). Selecting only 13 of the more reliable
experimental pole ®gures (the choice was based on the Rp
values of the pole ®gures), a second WIMV solution was
obtained with BEARTEX. Both distributions are again
similar, demonstrating that the method is not very sensitive to
occasional faulty data and noise, as long as the ODF solution is
well de®ned. In the case of omphacite, a strong texture is
observed with asymmetric girdle distributions around the
lineation direction for most pole ®gures. This becomes parti-
cularly obvious in the recalculated pole ®gures for principal
crystallographic directions of this monoclinic mineral (hkl are
labeled in the setting where y is the twofold symmetry axis)
(Fig. 10). (100) and (010) show girdle distributions, with poles
to (010) having a slight preference to be oriented perpendi-
cular to the foliation plane. (001), which is at an angle of 16� to
the z axis, [001], has a strong maximum in the lineation
direction.
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6. Discussion
The discussion is divided into three parts. First we comment on
the advantages and limitations of the MAUD Rietveld tech-
nique for complex polyphase materials. Then we introduce
texture data on the same specimens, obtained with the scan-
ning electron microscope electron backscatter patterns (SEM-
EBSP), and compare them with the neutron TOF results.
Finally we will explore brie¯y some geological implications.
The example of neutron TOF analysis of eclogite shows that
complex geological materials are amenable to quantitative
Rietveld texture analysis. But the analysis also showed us that
procedures are far from routine and, at this stage, cannot be
automated, which is contrary to our previous experience with
simple monomineralic calcite (Lutterotti et al., 1997) and two-
phase cubic metals (Lutterotti et al., work in progress). In the
case of eclogite, the procedure required manual intervention
at every step. One reason is the high complexity of the pattern
J. Appl. Cryst. (2001). 34, 442±453 H.-R. Wenk et al. � Rietveld texture analysis 449
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Figure 8Recalculated pole ®gures for garnet and principal crystallographic directions, using the WIMV ODF of BEARTEX. The same conventions as in Fig. 7 areadopted.
Figure 9Selected pole ®gures for omphacite in equal-area projection and linear scale. The pole-density scale is shown on the right-hand side. (a) Pole-densitydistribution from the Le Bail intensity extraction. (b) Pole ®gures obtained from the WIMV ODF of MAUD, based on 26 experimental incomplete pole®gures. (c) Pole ®gures obtained with the WIMV from 13 incomplete pole ®gures, using BEARTEX. The same conventions as in Fig. 7 are adopted.
Figure 10Recalculated pole ®gures for omphacite and principal crystallographic directions, using the WIMV ODF of BEARTEX. The same conventions as in Fig.7 are adopted.
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450 H.-R. Wenk et al. � Rietveld texture analysis J. Appl. Cryst. (2001). 34, 442±453
with few diffraction peaks that are not partially or completely
overlapped. Particularly in the low-d region, it is very dif®cult
to de®ne a background. An additional complication is the
diffraction contribution from minor components that could
not be identi®ed. We have marked some peaks in the spectrum
in Fig. 6(b) and on the basis of this we excluded two d ranges
from the analysis, but these minor phases also contribute to
other parts of the spectrum and therefore may falsify the
analysis.
In the case of the eclogite sample described in this paper,
the Rietveld texture analysis was rendered dif®cult because of
the poor counting statistics. In the automatic mode, weak
diffraction peaks were ill-de®ned. Nevertheless, with manual
intervention we succeeded to extract the texture both for a
phase with a random distribution and one with a strong
texture. We used the discrete and direct WIMV method, in an
iterative procedure, making use of only a small portion of the
data in the center of the pole ®gure (out to 60�). An attempt to
use the harmonic method, re®ning directly the even harmonic
coef®cients in the least-squares cycle, failed because of the
incomplete pole-®gure coverage.
To obtain some con®dence in the neutron texture data, we
analyzed the same specimen by EBSP. A polished thin section
was prepared ®rst by mechanical polishing, followed by silane
polishing for 24 h. The thin section was cut perpendicular to
the foliation and parallel to the lineation. Texture data were
subsequently rotated to conform to the neutron pole ®gures.
The sample was not carbon coated but investigated at low
voltage (10 kV) and moderate beam current (3.0 A) in the
LEO 430 SEM at Berkeley. This facility utilizes a locally
designed fully digital imaging system and microscope control
with Windows-based software. The imaging includes ®ber
optic image transfer and a 14 bit Peltier-cooled 1 megapixel
CCD camera (Wenk et al., 1999). Diffraction patterns were
collected, digitally processed and then indexed with the
commercial Channel3+ indexing software (Schmidt & Olesen,
1989).
Three measurements were performed: an automatic stage
scan, covering and analyzing an area of 6 � 4 mm for garnet
with 5050 data points, and two manual measurements, one of
31 grains for garnet, mapping a contiguous area, and another
of 105 grains for omphacite, picked randomly throughout the
thin section.
The automatic orientation data for garnet illustrate a
random orientation distribution (Fig. 11), just like the neutron
diffraction data. To explore further the orientation relations
within elongated grains in garnet layers, we manually
measured the orientations of 31 garnets in domains, separated
by fractures (Fig. 12). It became immediately obvious that
those domains were separated by high-angle boundaries and
that domains represented individual grains. Even within a
small region of a layer, the orientation distribution was fairly
random (Fig. 12b) (symbol size increases with increasing
number to help in identifying orientations).
The 105 omphacite grains were measured manually because
we noticed that, unlike for cubic garnet, the automatic crys-
tallographic indexing of monoclinic omphacite was often not
reliable. In fact, even some manually indexed orientations
were incorrect. Fig. 13 illustrates pole ®gures for omphacite
derived from the EBSP ODF (with orientation data processed
by BEARTEX). Fig. 13(a) reports all 105 orientations, Fig.
13(b) shows a subset of 24 orientations with a good pattern-
matching parameter (MAD in Channel3+ < 1). As can be seen,
the pattern becomes considerably more regular and compares
very well with the neutron diffraction data (Fig. 10), but pole
densities are much higher for EBSP data, even after
smoothing the ODF with 7.5� Gaussians.
The example highlights advantages and differences between
neutron diffraction and EBSP texture analysis. Neutron
diffraction provides statistical information about bulk
samples. Large sample volumes are analyzed. However, long
counting times or a high-¯ux beam are required to obtain
suf®cient counting statistics. At most TOF neutron sources,
data collection for one spectrum exceeds 1 h, and in our case
should have been 10 h. Subsequent data processing with
Rietveld codes is slow and requires considerable skill. Yet
neutron diffraction texture data are advantageous for calcu-
lating average anisotropic physical properties that are repre-
sentative of rocks.
EBSP is obviously the technique of choice to establish local
orientation relationships. Unless the grain size is very small,
grain statistics are generally poor, even if many points are
measured. Engler et al. (1999) demonstrated that the texture
strength depends on the number of orientations that are
measured. For EBSP data, the number is generally not suf®-
cient and apparent textures are far too strong. Kunze et al.
(1994) obtained a good ®t between EBSP and neutron texture
data, but only after smoothing the EBSP ODF with an arbi-
trary 15� ®lter. With EBSP, a certain number of orientations
are wrongly indexed, or cannot be indexed, which leads to a
Figure 11Pole ®gures for garnet obtained with an automatic scan by SEM-EBSP. Compare these pole ®gures with the neutron data of Fig. 8. The same conventionsas in Fig. 7 are adopted, but note that orientation data for this ®gure have been rotated from the original measurements to conform with the conventionof Fig. 8.
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distortion of the texture pattern. A good test is to see if the
texture changes with pattern matching quality (MAD). We
have noted that in our case the texture becomes stronger with
decreasing MAD (Fig. 13). This illustrates the danger of
quantitative interpretation. MAD and the success of indexing
are both to some degree correlated with orientation. EBSP is
fast and provides easily digestible texture infor-
mation. It can be performed in individual
research laboratories and does not require access
to large national facilities. However, for quanti-
tative texture analysis, methods that rely on bulk
characterization, such as neutron diffraction, are
more reliable than EBSP.
The texture analysis of this Dabie Shan eclo-
gite illustrates that omphacite has a strong
preferred orientation with c axes aligned parallel
to the lineation. Garnet, on the other hand, even
though arranged in layers and showing elongated
grain shape in thin section, has no preferred
orientation.
Clinopyroxene aggregates were studied experi-
mentally by Ave Lallemant (1978), Kirby &
Kronenberg (1984) and Boland & Tullis (1986),
which indicates deformation by dislocation creep
at temperatures as low as 773 K. Godard & Roer-
mond (1995) described lattice preferred orienta-
tion of omphacite in naturally deformed eclogites,
with [001] parallel to the lineation, and (010) in the
foliation plane. They also identi®ed active slip
systems (100)[001] and (110)[001]. In addition to
plastic deformation on slip systems, a main contri-
buting factor for preferred orientation is likely
rotations of the elongated prismatic crystals.
Garnet is commonly assumed to be very strong
and often forms rigid clasts in a deformed matrix,
as in eclogites from the Western Alps (Van der
Klauw et al., 1997). On the other hand, Ji &
Martignole (1994) described ¯attened garnets in
quartzites of the contact aureole of the Quebec
anorthosites and suggest that at very high
temperatures garnet may be weaker than quartz
and deform plastically. Kleinschrodt & McGrew
(2000) also observed elongated garnets with
weak preferred orientation in granulites from Sri
Lanka. Indeed dislocations have been observed
in garnets from eclogites (e.g. Ando et al., 1993)
and experiments by Karato et al. (1995) suggest
that the ¯ow strength of garnet may be similar to
that of wet pyroxenite (Boland & Tullis, 1986).
While we ®rst thought that the layered garnet
domains were suggestive of ductile deformation,
the texture analysis convinced us that dislocation
activity was not signi®cant and mechanisms such
as grain boundary sliding and preferential disso-
lution (Den Brok & Kruhl, 1996) may be
responsible for the arrangement of small garnet
grains in layers.
J. Appl. Cryst. (2001). 34, 442±453 H.-R. Wenk et al. � Rietveld texture analysis 451
research papers
Figure 12Local orientation mapping of a portion of a layer of garnet by EBSP. (a) Microstructurewith 31 grains. The trace of the foliation plane is indicated. The lineation is in the planeof the section. (b) {100} pole ®gure with orientations of grains 1±15; equal-areaprojection. The symbol size increases with grain number. Fabric coordinates areindicated and conform with (a). This is a different orientation from all other pole ®guresbut corresponds with the thin section in Fig. 2. (c) Same as (b) but for grains 16±31.
Figure 13Pole ®gures for omphacite, measured by EBSP on 105 grains: (a) all individualmeasurements, (b) only using 25 data with good pattern matching (MAD < 1). TheODF was smoothed with 7.5� Gaussians. Compare with Fig. 10. The slight asymmetrymay arise from the dif®culty of de®ning the foliation plane. The same conventions as inFig. 7 are adopted, except for the scale which is logarithmic and suggests much higherpole densities than the neutron analysis.
7. Conclusions
With the availability of multidetector TOF neutron diffract-
ometers such as GPPD at IPNS, HIPPO at LANSCE, SKATat
Dubna and GEM at ISIS, quantitative characterization of bulk
materials with the Rietveld method will become increasingly
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452 H.-R. Wenk et al. � Rietveld texture analysis J. Appl. Cryst. (2001). 34, 442±453
important. With this approach, a ®nite number of d spectra are
measured in different sample orientations. Spectra are then
processed with standard crystallographic methods developed
for powder diffraction. Data are re®ned, relying on crystal
structure (structure factor) and texture. We have found that it
is more ef®cient and reliable to use an iterative combination of
algorithms for structure determination (Rietveld method) and
ODF calculation (WIMV).
The method offers possibilities for quantitative texture
analysis of polyphase materials that presently elude any
quantitative analysis if partially overlapped diffraction peaks
are present. Also, since whole diffraction spectra are available
for different sample orientations, d spacings in different
directions can be re®ned, leading to simultaneous determi-
nation of residual stresses in textured materials, which is
becoming increasingly important for technological applica-
tions (Hutchings & Krawitz, 1993). Finally, the method
provides an automatic texture correction for the Rietveld
re®nement, which has long been one of its main de®ciencies.
Simple one-dimensional correction approaches, based on the
March (1932) model of platy or ®brous particles (e.g. Dollase,
1986), are often inadequate, as has been demonstrated by
Choi et al. (1993).
This new Rietveld approach to neutron diffraction texture
measurements and ODF analysis is expected to (a) improve
quantitative texture analysis of low-symmetry compounds and
polyphase materials, (b) reduce beam time to obtain full
texture information for a given resolution, (c) allow for
quantitative correction of powder data for texture in crystal
structure re®nements, and (d) provide a basis for the corre-
lation of texture and residual elastic strain.
We are thankful for constructive comments by two
reviewers, to Chris Murphy for help during the TOF experi-
ments, and for the expertise of Art Schultz in designing the
kappa texture goniometer. This work has bene®ted from the
use of the Intense Pulsed Neutron Source at Argonne
National Laboratory. The facility is funded by the US
Department of Energy under contract W-31-109-ENG-38. We
further acknowledge ®nancial support by NSF (EAR 99-
02866), IGPP-LANL and DFG (grant Ra442/14-2).
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