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Texturesand Microstructures, 1989, Vol. 10 , pp. 265-307Reprints available directly from the publisherPhotocopying permitted by license only C 1989 Gordon and Breach Science Publishers Inc.Printed in the United Kingdom

Advantages of NeutronDiffraction in Texture AnalysisH. J. BUNGEDepartment of Physical Metallurgy, Technical University of Clausthal, FRG

Received February, 1989

Neutron diffraction texture analysis is based on pole figure measurement followed bypole figure inversion. Neutron diffraction pole figure measurement is quite similar tothat by X-rays.There are, however, several advantages in detail which are mainlydue to the lower absorption coefficient. Besides these quantitative differences, thereis one principle difference between the two methods. Neutron diffraction allows themagnetic tex ture to be measured which is no t possible by X-rays. The paper gives asurvey on the advantages of neutron diffraction texture analysis which are onlycounteracted by the limited availability and higher costs of neutron diffraction.

K Y WORDS: Pole figure measurement, low absorption coefficient, positionsensitive detector, time-of-flight-method, magnetic texture analysis.

INTRODUCTION

The texture of a polycrystaline material is defined as the orientationdistribution function of its crystallites

dV V g/ g 1

sin tpdtpl, dq, dq 2

dgdg= r

Thereby dV V is the volume fraction of crystallites having acrystallographic orientation g within the limits dg. The orientation gof the crystallographic axes with respect to a sample-fixed coordin-ate system may be described by the Euler angles tpl, , tp2, or bymany other orientation parameters, see e.g. Figure 1.

26 5

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normoldireclion

transversedirection

rolting

//direction

Angle

.90

50

20

Angle (x

Figure 1 The texture is the orientation distribution function of the crystallites. Itdepends on three orientation parameters.

Texture measurements can be carried out with the help ofdifferent kinds of radiation using either imaging or diffractionmethods. These radiations are mainly visible light X rays neu-trons, and electrons.

Imaging methods may be based on light and electrons whereasdiffraction methods may be applied with X rays neutrons andelectrons as is shown in Table 1.

The methods of texture analysis can also be classified according towhether they are individual crystallite methods or polycrystalmethods.

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UTRO DIFFR TION IN T XTUR N LYSIS 26 7

Table 1 Texture measurement with different radiations,using imaging and diffraction methods

Radiation Texture measurement byimaging methods diffraction methods

Light xX-rays xNeutrons xElectrons x x

1) If lateral and vertical resolving power is higher than grain size,then individual orientation measurements can be used. Thereby thecrystallographic orientation of a crystallite may be obtained from a)crystallographicallyoriented features of the crystallite seen in itsimage in direct space imaging method) and b) the diffractionpattern image in reciprocal space ) diffraction method).

2) If the lateral resolving power of the method is much smallerthan grain size then collective diffraction patterns pole figures)ca n be used to obtain information about the orientationdistribution.

In the first group of methods, the discontinuous) individualorientations have to be converted somehow into a statisticallyrelevant continuous orientation distribution function, Figure 2.

In the second method, statistically relevant continuous distribu-tion functions are directly obtained, however, not the completedistribution function depending on all three orientation parameters.The obtained pole figures are only two-dimensional projectionstaken along certain projection paths in the orientation space fromwhich the three-dimensional distribution function has to be con-structed by mathematical methods which are comparable to thewell-known computer tomography. This is shown schematically inFigure 3 see e.g. Bunge, 1969, 1982, 1987).

In the first group of methods statistical relevance can only beimproved by increasing the number of orientation measurementsi.e. by increasing the experimental effort considerably).

In the pole figure method statistical relevance can be increased nearly unlimited)by increasing the size of the sample, compared tograin size, provided the whole sample volume can be made to

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a o

/

c o

ligare 2 Texture determination from individual orientation measurements a Theorientation of an individual grain represented in Euler space b cloud oforientation points c The continuous orientation density distribution.

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UTRO DIFFR TION IN T XTUR N LYSIS 26 9

Figare 3 Texture determination from pole figures

contribute to the measurement at the same time Hence with thepole figure method st tistic lly relevant results can be obtained inreasonable time The virtual disadvantage of this method thenecessity of a mathematical inversion processs is no longer an

essential obstacle since highly performant computer programs forpole figure inversion are now available

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Furthermore pole figure measurement can be nearly completelyautomatized by using computer-operated texture goniometers e.g.

Puch Klein Bunge 1984 . The individual orientation measure-ments on the other hand have only been semiautomatized up tonow Hence the great majority of texture determinations have beencarried ou t by pole figure measurement followed by pole figureinversion.

As was already mentioned pole figure measurement can inprinciple, be carried ou t by three kinds of radiation i.e. by X-rays,neutrons and electrons. It is the purpose of the present paper toprovide an o ver vie w over the advantages and disadvantages of

neutron-diffraction as a means of texture analysis.

POLE FIGURE MEASUREMENT

pole figure is defined as the orientation distribution function of anindividual crystal direction h perpendicular to a reflecting latticeplane hkl

dV V y {a, fl}Ph Y 2

dy dy sin ct do lThereby dV V is the volume fraction of crystals the direction h ofwhich is parallel to the sample direction y. In the conventionalmethod of pole figure measurement one incident and one reflectedbeam are being used the bisectrix of which defines the diffractionvector s. Pole figure measurement then requires to bring all sampledirections y---one after the other--into the diffraction direction sand each time to measure the diffracted intensity. This methodrequires a diffractometer in order to fix the Bragg-angle 0 and asample rotation device which is usually a Eulerian cradle shownschematically in Figure 4b. The Eulerian cradle allows to rotate thesample through three angles which are usually denoted by toXtpas isalso shown in Figure 4b. For pole figure measurement the samplehas to be rotated through two angles fl . Hence differentscanning procedures may be applied e.g. by using only the angles and or the angles to and respectively. This corresponds to thereflection and transmission method in X-ray diffraction although theprinciple distinction between these two methods does not apply to

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UTRO DIFFR CTION IN T XTUR N LYSIS 271

b

X

Euleriancradle

diffractometer drive

Figare 4 Principles of pole figure measurement using a Eulerian cradleDiffraction of an incident beam in a polycrystalline sample b The Eulerian

cradle

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neutron diffraction. In the conventional method of pole figuremeasurement the whole angular range 0 -< te -< 90 0 -< -

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UTRO DIFFRACTION IN T XTUR ANALYSIS 273

5

Figure 5

Neutrons

Spectral characteristics of X-rays and neutrons.

tic line spectrum as is seen in Figure 5. Hence, it is then necessaryto use a monochromator. Typical monochromator materials arecopper, aluminium, lead, silicon, germanium and graphite whichselect a wave length according to Bragg s law Eq. 3 . In order tochange the wave length it is thus necessary to change the monochromator or to change the Bragg angle or both. In this case thereflected beam i.e. the incident beam of the texture goniometer)has to pass through the monochromator shielding at different anglesand the position of the goniometer itself has to be changed. Thisrequires a higher technical effort than to work with just one takeoff angle. Hence, the available wavelengths are often restricted toonly a few (notwithstanding the continuous nature of the neutronspectrum).

According to Bragg s law a monochromator may allow a shorterwavelength to pass through an integer fraction /n . For the caseof texture analysis this is, however, not a serious problem. It leadsonly to the superposition of pole figures hkl and nh, nk, nlwhich are identical.

The angular divergence of incident and reflected beam of themonochromator determines the spectral width A3. of the monochro

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matized beam and this, in turn gives rise to a certain linebroadening in the measured diffraction spectrum of the sample. On

the other hand the higher the divergencies and the higher A thehigher is the measured intensity and hence the shorter is therequired measuring time. For texture analysis in most cases a ratherstrong instrumental line broadening can be tolerated at least ifmaterial such as metals with not too linerich spectra are beingstudied . Hence an optimization of the divergencies is used intexture analysis which may be different from the requirements inother diffraction methods e.g. high resolution structure analysis .This must be taken into consideration when multi purpose

diffractometers are being used for texture analysis. Thesediffractometers are mostly optimized for crystal structure analysis.

TEXTURE ANALYSIS BY NEUTRON DIFFRACTION

The three kinds of radiation X-rays, neutrons and electrons havegreatly different penetration depths in matter due to differentabsorption coefficients. At the same time also the lateral resolving

power in the three methods is different as is shown schematically inTable 2. Accordingly the irradiated sample volume may bedifferent by nearly twenty orders of magnitude for electrondiffraction and neutron diffraction.

Even if one takes into account that in X ray diffraction texturemeasurement an additional sample integration may be appliedwhich increases the irradiated sample size without decreasing the

Table 2 Penetration depth lateral resolving power andsample volume for the three kinds of radiation

Penetrationdepth [mm]

Lateralresolvingpower [mm]

Samplevolume[mm

Neutrons

10

10

10

X rays

10 1_10 2

1_10 2

10 1_10 6

Electrons

10 4

10 3_10 6

10 1o_10 6

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NEUTRON DIFFR CTION IN TEXTURE N LYSIS 275

angular resolving power see e.g. Bunge and Puch 1984)then still adifference of about three orders of magnitude in sample size remains

between neutron and X-ray diffraction. This bigger sample sizeconstitutes one of the main advantages of neutron diffractioncompared with X-ray diffraction texture analysis.

After n eu tr on diffraction became available with the advent ofnuclear reactors after 1945 it was applied to texture measurementfor the first time by Brockhouse in 1953. t that time one of themajor advantages of neutron diffraction over X-ray diffraction fortexture analysisthe much higher accuracy of the results--couldhowever not yet be exploited. In fact, it could no t even be proven

since quantitative accuracy figures for texture measurements wereno t yet available. Hence the major disadvantage of neutrondiffraction, its much higher experimental effort dominated suchthat virtually no more texture measurements were carried out byneutron diffraction in the following fifteen years.

reliability criterion for pole figures based on the seriesexpansion method Bunge 1966) showed lateron that neutrondiffraction pole figures were much more accurate than thoseobtained by X-rays Schlifer, 1968). Furthermore this higher

accuracy was actually needed forthe calculation

ofO F from

polefigures. Hence Bunge and Tobisch 968) and Bunge Tobisch andSonntag 1971) determined the O F of cold rolled copper fromneutron diffraction pole figures. Textures of a-Brass were deter-mined by Bunge and Tobisch 1972) and Bunge Tobisch andMiicklich 1974)and the rolling and recrystallization textures of lowcarbon steels were investigated this way by Schlifer and Bunge1974 and Bunge Schleusener and Schlifer 1974). The methodicaldetails as well as the advantages of n eu tr on diffraction or texture

analysiswere

reviewed by Szpunar 1976)and

byKleinstiick et al.

1976). From this time on neutron diffraction texture analysis wascontinuously carried out in several neutron diffraction laboratories

including magnetic scattering Szpunar et al., 1968; Stott andHutchinson 1973; Hennig et al., 1981).

Besides metallic materials also non-metallics were studied Wal-ter et al. 1981 Brokmeier 1982) and the method proved to beespecially valuable for geological studies Bunge Wenk Pannetier1982 Bankwitz et al. 1984 Htifler, Schiller, Will 1986 H6fler Will

1986Drechsler et al.

1984).Texture development in steels was

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studied by Schreiber et al. 1978 and by Klimanek et al. 1981 .The high-speed PSD method was applied to dynamic recrystalliza-

tion investigations by Jensen et al. 1981 and a detailed review wasgiven by Welch 1986 . The time-of-flight method was especiallydeveloped by Szpunar et al. 1968 , Nosik et al. 1979 , Feldmann etal. 1981 , Betzl et al. 1984 and a review of this method is containedin the paper by Feldmann in this volume.

LARGE GRAIN SAMPLES

The statistical relevance of pole figure measurement is limited bythe number of grains involved in each pole figure point. Thisnumber depends on the angular resolving power and on the totalnumber of grains in the irradiated sample volume. Comparing X-rayand neutron measurements with the same angular resolving power,it is thus possible to obtain the same statistical relevance in neutrondiffraction samples having bigger grain size by one order ofmagnitude in diameter i e three orders in grain volume .

TEXTURE INHOMOGENEITY AND GLOBAL TEXTURES

The texture of a material is often inhomogeneous, i.e. It is differentin samples taken from different places in the material, as is shownschematically in Figure 6a. It is then necessary to distinguishbetween local textures and the global texture of the whole material.Inhomogeneities may be divided roughly into macro and microin-homogeneities, examples of which are shown in Figure 6b and c

respectively. An important macroinhomogenity is,for

instance,the

variation of the texture of a sheet from surface to the interior,Figure 6b. prominent microinhomogeneity occurs in the shearbands, Figure 6c. In Table 3 it is shown how local and globaltextures in the macro and microscale can be distinguished by thethree kinds of radiation. The global texture on a macroscale isneeded for ins tance when macroscopic properties of the materialare being considered. If E g is any physical property of acrystallite which depends on its orientation g e.g. resistance to

plastic deformationthen the

corresponding macroscopic property is

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UTRO DIFFRACTION IN T XTUR ANALYSIS 277

a Iota[

texture

\ v /gtoba[

texture

b

c

Neu n \\\\ \ \ \ \ \sa p e

X-ray sample

Figure 6 Inhomogenity of textures a Definition of local and global texture.b Macroinhomogeneity. c Microinhomogeneity shear band .

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Table 3 Detection of macro- and microinhomogeneitiesby the three kinds of radiation

Inhomogeneities Neutrons X-rays Electrons

macro global local localmicro global global local

given by

4)

Thereby f g is the orientation distribution of all crystals of the

macroscopic sample i.e. the global texture of the material.In the case of plastic aniostropy as a fundamental property for

deep drawing sheet, thicknesses in the range of several milimetersare often to be considered. The plastic properties of such materialsare correlated with the global texture obtained by the x-raycomposite sample method or directly by neutron diffraction. Thesurface texture measured by the x-ray back-reflection method gives

1.0

0.8

10

composite _

[1.2

0* 10 20 30* 40* 50* 60 70* B0* 90*

Angle roiling direction

Figure 7 Variation of the r-value of plastic anisotropy in the sheet plane of asteel sample measured mechanically circles) and calculated from texture measure-ments in the whole volume composite sample and the surface back-reflection).

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NEUTRON DIFFRACTION IN TEXTURE ANALYSIS 27 9

quite different results. This is illustrated in Figure 7. Hence,neutron diffraction is especially advantageous for technological

samples.

ACCURACYOF THE MEASUREMENT

Pole figure measurement is based on intensity measurements of thereflected beam. The intensity depends on the volume fraction ofcrystallites in reflection position the pole density value which is tobe measured and the absorption of incident and reflected beam in

the sample. This has to be taken into account by an absorptioncorrection factorA e - x 5

where is the linear absorption coefficient, and x is the total path ofincident and reflected beam in the sample. The absorption factor Amay be calculated and used as a correction factor if the shape of thesample and hence the path x is correctly known. If the shape ofthe sample is only incorrectly known, then the absorption factor andhence the resulting pole density values are falsified. Differentiating

0

Neutrons

Figure 8 The accuracies dx/x required for a neutron and an X-ray sample in orderto obtain a resulting accuracy of in the correction factor and hence in the poledensity values.

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28 0 H J UNGE

Eq. 5 with respect to x gives

dA dx x 6x

Hence the relative error dA A of the correction factor depends on

Figure 9 The spherical sample method in neutron diffraction texture analysis.a The absorption coefficient is independent of the pole figure angles a 3 b a spherical sample may have an approximate form.

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NEUTRON DIFFRACTION IN TEXTURE ANALYSIS 281

the relative error dx/x of the sample shape bu t it also increases with x. In the case of neutron samples usually much lower/ x values

are being used than in the case of X-raysand

also the sample sizex is much higher for neutrons than for X rays. Hence the possibletolerance dx of the sample size is much higher for neutrons than forX rays. Two typical examples are compared in Figure 8 wheredA A 5 is assumed. Hence the accuracy of neutron texturemeasurements can easily be made better by an order of magnitudecompared to X-ray measurements

Figure 10 A spherical sample for neutron texture analysis.

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282 H.J. UNGE

The highest accuracy can be obtained when a spherical sample isbeing used Tobisch, Bunge 1972 .Then the absorption factor is

independent of the pole figure angles fl as is shown in Figure9a. Because of the low/ x-value in Eq. 6 a sphere may havethe shape of Figure 9b or it may even be a cylinder as in Figure 10.

The resulting accuracy is shown in Figure 11 where errorcoefficients AF are drawn as a function of the order A. It is seenthat neutron diffraction with the spherical sample method givesmuch better results than X-ray diffraction. Especially, the strongincrease of these coefficients at low A-values does not occur. It hasbeen shown that the increase is due to systematic errors, Figure 12

0.12

0.10

008

006

00/,

0.02

\ Bockreflecti0n\/Iransnission

Spherical/Sample

X X X

SphericalJ o oSampte

o

Neutrons

8 12 16 ZO

Order

ligare 11 Error coefficients AF for pole figure measurements: X-ray transmission-reflection method; X-ray spherical sample method; neutron spherical samplemethod.

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NEUTRON DIFFRACTION IN TEXTURE ANALYSIS 283

0 10

0 08

0 06

0 04

0 02

error

statist=cal error

4 8 12 16

x

Order h

Figure 12 Statistical and systematical errors of pole figures expressed in the errorcoefficients IAFI

which are particularly detrimental when O F are to be calculatedfrom pole figure measurements .

MULTIPHASE MATERIALS

particularly strong influence of the absorption factor on X-raytexture measurements occurs in the case of multiphase materials, ifthe shape and arrangement of the phases is anisotropic. In Figure 13the absorption factor of a directionally solidified Pb Sn eutectic isshown as a function of the angle of the diffraction plane relative tothe lamellae plane (Bunge, Liu, Hanneforth, 1987 . It is seen thatin this case the influence of absorption is so strong that texturemeasurements by X-ray diffraction become

virtuallyimpossible.

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18 O

ROTATIONkJI6LE Y

Figure 13 Anisotropic absorption of X rays in lamellar structures a Metallographic section of a directionally solidified Pb Sn eutectic b Absorption factor as afunction of the angle between lamellar plane and diffraction plane

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UTRO DIFFRACTION IN TEXTURE ANALYSIS 285

Figure 14 Metallographic section of a 90 extruded AI Pb composite.

The situation is similar in highly deformed two-phase materials e g90 extruded A1 Pb composites as shown in Figure 14 Brokmeier,B6cker and Bunge, 1988 Also in this case the X-ray absorptionfactor varies by as much as 25 . Hence, X-ray texture measure-ments are falsified by this amount. In neutron diffraction thisinfluence is in the range of 0.1 . Figure 15 shows inverse polefigures of AI and Pb of a highly extruded AI Pb composite obtained

byneutron diffraction. These measurements are free of errors due

to anisotropic absorption.

SMALL VOLUME FRACTIONS OF SECOND PHASES

It is interesting to study the texture of a phase which is present in amultiphase material only in small volume fractions e g below 1 .

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3 9

Hgare 15 Inverse pole figures of the AI and Pb phase of pure metals andcomposites extruded 90 measured by neutron diffractiotL

penetration

depth

increased correct reduced

volume fraction

Figure 16 Possible influences of sample preparation on small particles of a secondphase in the sample surface

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NEUTRON DIFFRACTION IN TEXTURE ANALYSIS 28 7

Figure 17

CU {llll

0 15 30 5 60 75 90

RLPHRPole figure of the copper phase of an extruded AI Cu composite with

1 Cu .

In this case X ray texture analysis must assume that the area

fraction of the phase in the investigated surface is the same as thevolume fraction. With a small volume fraction this may not be thecase simply because of poor statistics Furthermore because ofdifferent properties of the phases the surface of the particles maynot be flat as is shown schematically in Figure 16 Hence X raytexture measurements in phases of less than a bo ut 2 or becomevirtually impossible. In neutron diffraction on the other hand thewhole sample volume contributes to the measurement and artefactsat the surface do not play any important role Hence neutron

texture measurementscan be carried ou t with

reasonable accuracywell below 1 Vol. . Figure 17 shows for instance the pole figure ofthe copper phase of an A1 Cu composite with 1 Cu. Recentlymeasurement with 0.1 of copper have also been carried out.

SAMPLE PROTECTION

Another advantage of the high penetration depth of neutrons

comparedwith X rays is that it is easily possible to provide a

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28 8 H J UNG

neutron sample with a protective coating. This may be interestingwhen studying textures in oxygen sensitive or hygroscopic materials.

Similarly, different kinds of environments may be easily applied to atexture sample e.g. high temperatures. In this case, the Euleriancradle can be easily shielded from the heating device with shieldsthe thicknesses of which are in the millimeter range.

INFLUENCE OF THE TOMIC NUMBER

It was already mentioned that the absorption coefficient of neutr

ons is smaller than that of X rays by two or three orders ofmagnitude. This allows much bigger samples to be used. On theother hand also the scattering factors are much smaller. Hence it isno t only possible but in most cases, also necessary to us e biggersamples.

Absorption coefficient and scattering factor are shown in Figure18 and 19 respectively see e.g. Bacon 1975; Squires 1978 . Theyare no t only smaller than those for X-rays. Also the variation ofthese quantities with atomic numbers is quite different in the two

cases. Both quantities show a systematic strong increase withatomic number for X rays which is no t the case for neutrons. Thishas some consequences for neutron texture analysis. In neutrondiffraction, neighbouring elements may have quite different scattering factors. Hence it is easily possible to study ordering effects insolid solutions of such elements. s far as texture measurements areconcerned this may be an important advantage when directionalordering in polycrystallinematerials is to be studied for instance iniron nickel alloys. Directional ordering is strongly related to the

texture of thematerial. The situation is also

quitedifferent for

thelight elements. Hence texture studies of light element phases especially in the presence of other phases containing heavyelements will be much easier with neutrons than with X-rays.

s a consequence of different scattering factors of the atoms alsothe structure factors of a crystalline phase may be strongly differentin X ray and neutron diffraction. In texture analysis this may beimportant for instance if a particular structure factor is zero in oneof the methods. The corresponding pole figure cannot be measured

in thiscase.

n exampleis the

important 0001 pole figure of

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NEUTRON DIFFRACTION IN TEXTURE ANALYSIS 28 9

0

00

0 0 0

0 0

0o

00

C 0 0 00

0

0 0

00

0

Ooo Neutrons oNe C Zn Z Sn N:I Yb Hg

0 10 20 30 40 50 60 70 80Atomic number Z

Figure 18 The absorption factor for X-rays and neutrons as a function of atomic

number.

A1203 ceramics. Its X-ray intensity is lower than 1 of 11.3which has the highest intensity. Hence, this pole figure cannot bemeasured by X-rays. The corresponding neutron diffraction inten-sity is, however, in the order of magnitude of about 10 of themaximum value. Hence it can well be measured by neutrondiffraction. This is of great interest since A1203 substrates sometimes have a strong 0001 fibre texture which is well expressed inthe

0001pole figure.

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290 H.J. BUNGE

x-roys

x lO-Z3cm2O

18

16

Neutrons

x lOZ6cm22OO

o Co

Cu

x to

MO AuC

180Hg,,,

10

140

120

100

8O

6O

o 44]O o o ono o2G--,., c 20 0 000n o .. 0

I0 20 30 40 50 60 70 80Atomic Number Z

Figure 19 The scattering cross section of X rays and neutrons as a function of theatomic number.

INFLUENCE OF THE ISOTOPE

The neutron scattering factors for various isotopes of the sameelement are usually quite different till to opposite sign of thescattering factor . A particularly striking example of this effect isobserved in hydrogen. Hydrogen itself ha s a low coherent scatteringfactor but shows strong incoherent scattering whereas the oppositeis true for deuterium. As a consequence of this neutron diffractiontexture analysis in natural salt samples may be strongly complicatedby the often observed presence of moisture in these materials. Onthe other hand texture studies in ice for instance are facilitated ifit is possible to use deuterated ice.

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NEUTRON DIFFRACTION IN TEXTURE ANALYSIS 291

Figure 20

1 2

1 0 Neutrons

X toys

0.2 0 4 0.6 0 8 1 0 1 2sin a

The scattering factor for X rays and neutrons as a function of sin

ANGULAR DEPENDENCE OF THE SCATTERING FACTOR

X ray scattering takes place in the whole volume of an atomwhereas the most important part of neutron scattering comes from

the nucleus the dimension of which is neglegible compared with thewavelength of the neutrons. Hence the X ray scattering depends onsin whereas neutron scattering is independent of this parameter Figure 20. This difference is important for texture analysis

especiallywhen pole

figuresare to be converted into ODF In this

case the resolving power is the better the more pole figures can beused. Neutron diffraction then allows to measure also high indexpole figures with a satisfactory accuracy. This is especially importantfor materials with low crystal symmetries.

POSITION SENSITIVE DETECTORS

In the conventional method of pole figure measurement thedetector is placed at the Bragg angle with respect to the incident

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292 H. J, UNG

beam and an apperture is being used which allows the total integrated intensity of the diffraction peak to be measured. This

way one pole figure is obtained at a time. Then the position of thedetector is changed to the next Bragg-position. Hence the neces-sary pole figures are being measured sequentially. With the help of aposition sensitive detector the whole O-spectrum can be measuredat the same time. Figure 21 shows the instrument D at Grenobleequipped with a position sensitive detector Allemand et al., 1975 .It is thus possible to measure all required pole figuressimultaneously at the same time. This method provides twoadvantages:

1 the measuring time is greatly reduced2 Overlapping pole figures can be separated

This latter point is especially important if materials with line-richdiffraction spectra are to be investiaged. Such spectra may be dueto:

a low symmetry

reactor

beomshutterfiltermonochromator

monitor

collimator

detectorshietding

detector

diffractometerm-drive

sample

Eulerioncradle

Figure 21 The instrument D at Grenoble used as a texture goniometer withposition sensitive detector.

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UTRO DIFFRACTION IN TEXTURE ANALYSIS 29 3

b) high lattice constantsc) multiphase materials

Hence this method is particularly suited to the study of :

a) intermetallic phasesb) ceramicsc) mineralsd) rockse) composites

Figure 22a shows for instance a felspare spectrum measured this

way Bunge Wenk Pannetier 1982). An enlarged part of thespectrum is shown in Figure 22b. It is seen that line separation ispossible by line profile analysis. It is also seen that a completeprofile analysis improves the determinat ion of background scatter-ing and hence improves the accuracy of the measured integrated

a) 5 104

I0 20 30 t,O 50Brogg ongle

Figure 22 Diffraction spectrum of a felspare sample a) the whole spectrum.

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294 H.J. UNG

b)

22-

OZO O01

10 12

Brogg angle

c)

5 5 01i0il

200

0 30

120i) 11i

15 18 19 ZO Z18ragg angle 0

Figure 22 Continued b) partially overlapped peaks, c) totally overlapped peaks.

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N UTRON DIFFR CTION IN TEXTURE N LYSIS 295

intensity Jansen, Schiifer and Will, 1986).Figure 22 c finally showsanother part of the spectrum. Here the overlapping of different

diffraction peaks is total. These peaks cannot be separated ex-perimentally by line profile analysis. They can however beseparated theoretically in the process of O F analysis using thespecial methods of overlapping pole figures. This is possible for intraphase overlapping Dahms and Bunge, 1987)as well as for interphase overlapping Dahms, Brokmeier, Seute and Bunge,1988).

When a position sensitive detector is being used the plane of theEulerian cradle plane of the ;t-rotation) can only be in symmetry

position for one specific Bragg angle e.g. the angle 0,, in Figure23. Only for this angle, the x-circlepasses through north and southpole of the pole sphere. For all other O-angles ;t and t rotationgives a pole figure with a blind area in the vincinity of north- andsouth pole as is shown in Figure 24. Hence, in order to obtaincomplete pole figures an additional scan is necessary in order fill inthe blind area and a coordinate transformation is necessary bywhich the angles to;t of the Eulerian cradle are transformed intothe pole figure angles rfl Bunge, Wenk Pannetier, 1982).Some of

\\m:

Eulerian

raddle 0

,J.

,.>

incident] beam

Figttre 23 Adjustment of the Eulerian cradle in symmetry position for one of theBragg angles 0,.

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Figure 24 Pole figure scan for off symmetry Bragg angles showing blind areas.

Figure 25 Four pole figur s of af lsp r sample.

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N UTRON DIFFRACTION IN TEXTURE ANALYSIS 29 7

the felspare pole figures measured this way are shown in Figure 25 Wenk, Bunge, Jansen and Pannetier, 1986).

In Figure 21 the position sensitive detector was used in Braggangle orientation . In this orientation it measures one pole figurepoint of several Bragg angles at the same time. It can, however,also be used in pole figure orientation as is shown in Figure 26a Juul-Jensenand Kjems, 1983). In this case the wavelength must be

a) Oebye-Scherrer b)Kegel 90

Reflexions-

KPrimir-

Zhler rfat erBereich Potfigur

Figure 26 position sensitive detector used in pole figure orientation .

a) Positioning of the detector at =9 b) Scanned line in the pole figure, c)Complete pole figure scan.

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298 H.J. BUNGE

chosen such that 90 The detector then measures a whole lineof pole figure points but only in one pole figure as is shown in

Figure 26b. In order to scan a whole pole figure completely agreatly reduced number of steps is then sufficient, as is shown inFigure 26d. This method has especially been applied for rapid polefigure measurment, e.g. real-time recystallization and phase trans-formation stuides e.g. Juul-Jensen, 1986 .

W VE LENGTH DISPERSIVE METHOD

Beside the normal angular dispersive measurement also a wavelength dispersive method can be used. In this case, white radiationis being used. The reflection at different lattice planes is thenobtained with different wavelengths but at the same Bragg angle

n i kl 2d hkl sin 7The wavelength of neutrons is correlated with their velocity

h 8

m u

Hence, wavelength measurement can be obtained by time-of-flightmeasurement and this, in turn, requires to fix the starting time of aneutron. Time of flight measurement requires narrow pulses ofneutrons fol lowing each other in rather long t ime intervals.

pulsed beam can be obtained mainly in two ways:

a a continuous beam can be chopped into short pulses using achopper

b The neutrons can be directly produced in pulses e.g. in a pulsereactor or by a pulsed spallation source.

It is thus necessary to measure the time of each incoming neutronregistered in the detector. The time spectrum obtained with oneneutron pulse thus corresponds with the wavelength spectrum andhence with the d-value spectrum. Such spectra are then to be added

up in a multi -channel analyzer for a sufficient number of neutronpulses. Finally a time-of-flight spectrum is obtained as shown forinstance in Figure 27 Feldmann,

1986 .Such spectra have to be

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N UTRON DIFFRACTION IN TEXTURE ANALYSIS 29 9

2 3 4 5 8 7 8 gO

N

Figure 27 Time-of-Flight spectrum of copper.

measured for all necessary sample orientations in order to obtain allpole figures at the same time. Thus far, this method is similar to themethod using a position sensitive detector. In contrast to the latter

one however all pole figures are measured with the sameBragg-angle i.e. in symmetry position as in the sequentialangular dispersive method. Hence a blind area does no t occur inthis method and no transformation from to;t to l is necessary.

COMBINATION OF PSD AND TOF METHOD

The three methods mentioned above may be combined into one

method i.e.

a PSD in Bragg-angle directionb PSD in pole figure directionc TOF method

This requires a pulsed neutron source and a two-dimensionalposition sensitive detector which is at the same time also time-sensitive. This method shown in Figure 28 has been used byVergamini and Wenk

1988 .It gives---at the same t ime--a

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300 H J BUNGE

O T TOR COLLIMAI OR

10 BEAMSTOP

Figure 28 Texture measurement with a two-dimensional TOF method

two-dimensional area of a large number of pole figures. Hence, this

method is the most economic one.

MAGNETIC TEXTURE ANALYSIS

second part of neutron scattering is due to magnetic interactionof the neutron s magnetic dipole moment with the distribution ofthe magnetic moment of the electrons in the atom. Hence, this partof n eu tr on scattering depends on sin t in a similar way as X-ray

scattering, Figure 29 see e.g. Bacon, 1975). In the case ofnon-polarized n eu trons the magnetic part of the reflected intensityis proportional to

q2sin 2 a 9)where a is the angle between magnetization direction and thediffraction vector s i.e. the normal direction to the reflecting latticeplane as is seen in Figure 30. Magnetic neutron scattering is relatedto the magnetic crystal structure of the material which may bedifferent from the c hemica l crystal structure. The most important

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NEUTRON DIFFR CTION IN TEXTURE N LYSIS 301

0 0 0 I 0.2 0 : 0.4

sinO.)l, I 0 cm-*)

X-rays

Neutrons

0 5

Figure 29 The magnetic scattering factor of neutrons depends on sin

cases of magnetic structures are the ferromagnetic and antifer-romagnetic case. In the first case all magnetic moments of theatoms are parallel to a certain crystal direction m in the secondcase they are mutually antiparallel. This means that in the first casethe unit cell is the same as the chemical unit cell but crystalsymmetry is different and in the second case unit cell and symmetryboth are changed. From the view point of texture analysis theferromagnetic case is most important. With an applied magnetic

diffraction

vector

rnognefizofion

Figure 341 The magnetic scattering of unpolarized neutrons depends on the angle trbetween magnetization direction and normal direction to the reflecting lattice plane.

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302 H.J. UNG

field H the magnetization direction rn may be parallel to any crystaldirection h. Two limiting cases may be particularly considered. In

the case of zero magnetic field the magnetization direction is parallel toone of several crystallographically equivalent directions hg. In thecase of saturation it is parallel to the field direction

rn hg H 0 10

rn II /-/- oo

In the second case the magnetization direction is uniquely fixed ineach crystal. It is parallel to the same sample direction but todifferent crystal directions which are however uniquely determinedby crystal orientation g. In the first case the distribution ofmagnetization directions over the crystal directions hg will generallydepend on the magnetic history of the material. Different directionshg may occur in one and the same crystallite which is then dividedinto magnetic domains. In this case the magnetic texture can beeasily defined as the orientation distribution function of thedomains. We specify a crystal coordinate sytem K, the xa-axis ofwhich is parallel to the magnetization direction hg of the considereddomaine. The orientation of this coordinate system with respect tothe sample coordinate system K, is described by the rotation gM.The magnetic texture is then the volume fraction of domains havingan orientation gMwithin the angular range dg

fM gdV gm)/V

dg 11

This definition of the magnetic texture is completely analogous toEq. 1 , only the symmetry of the magnetic texture function is

different from that of the crystallographic texture. As an example,in cubic ferromagnets the magnetization direction is often parallelto the cubic axes

h 100 12The magnetic crystal symmetry is then tetragonal instead of cubic.Also the sample symmetry may be different from the conventionalsample symmetry due to the distribution of magnetization directionsover the various h-directions. Also the pole figures of this magnetictexture are defined in the same way as in the crystallographic

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N UTRON DIFFRACTION IN TEXTURE ANALYSIS 30 3

texture see e.g. Miicklich, Hennig, Bouillot and Matthies, 1984dV/V

P y 13dy

with the only difference that now h is the normal direc tion to thereflecting lattice plane hkl indexed in the magnetic coordinatesystem i.e. with the lower magnetic crystal symmetry e.g.tetragonal . The pole figure P y can, however, no t be measureddirectly by neutron diffraction. Rather all those pole figures aresystematically superposed which belong to crystallographically equiv-alent directions h

Ph} Y q2 p, y) 14i= 1

The superposition factors q2 are known according to Eq. 9 . Polefigure inversion, i.e. the calculation of the O F fVt g from polefigures P y can be carried ou t with superposed pole figuresPh} Y instead of the no-superposed ones see e.g. Dahms andBunge 1987 . Hence, information about the magnetic texture can beobtained from the magnetic part of neutron diffraction pole figures see also Bunge in print , 1989 .

CONCLUSIONS

Texture measurements can be carried ou by neutron diffractionmuch in the same way as by X-ray diffraction, i.e. by pole figuremeasurement followed by pole figure inversion. Because of thespecific properties of the two radiations there are, however, somedifferences between the two method as far as the quantitativerelations are considered. These differences are mainly in favour ofneutron diffraction, whereas the main drawback of this radiation compared to X-rays) is its limited availability and high cost ofneutron diffraction equipment and especially of the neutron source.The advantages of neutron diffraction are, first of all, due to thelower absorption coefficient. As a consequence of this, much bigger

samplescan be used.

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30 4 H J BUNGE

--This in turn leads to a much better grain statistics. Hence,samples with one order of magnitude bigger grain sizes can be

succesfullystudied by neutrons.raThe remaining absorption correction is usually much smaller

with neutrons and can be calculated with a much higer precission.Hence, the experimental errors of neutron diffraction pole figuresmay be an order of magnitude lower than those of X-ray diffraction.This is particularly valuable for high precision ODF calculations.

The lower error allows texture analyses of second phases whichare present with only very low volume fractions.

raThe high penetrat ion depth allows the global texture oftechnologically interesting work pieces to be measured directly.

--There is virtually no anisotropic absorption effect in anisotropicpolyphase materials as is the case in X-ray diffraction.

A further advantage of neutron diffraction is due to a scatteringfactor independent of sin This allows high-index pole figures tobe easily measured.

Neutron diffractometers are often equipped with position sensitive

detectors which have no t yet become standard equipment in X-raydiffraction. A PSD in O-direction allows the measurement of manypole figures at the same time. Furthermore, it allows the seperationof overlapping peaks which is particularly valuable for materialswith big unit cells and low symmetries as well as multiphasematerias. Finally, neutron scattering contains a magnetic part whichallows magnetic textures to be measured which is by no meanspossible using X-ray diffraction.

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