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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

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J. Appl. Cryst. (2001). 34, 442–453 H.-R. Wenk et al. � Rietveld texture analysis

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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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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


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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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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


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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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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


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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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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.


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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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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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