ASTM E82-91(2001)
(Test Method)Standard Test Method for Determining the Orientation of a Metal Crystal
Standard Test Method for Determining the Orientation of a Metal Crystal
SCOPE
1.1 This test method covers the back-reflection Laue procedure for determining the orientation of a metal crystal. The back-reflection Laue method for determining crystal orientation (1, 2) may be applied to macrograins (3) (0.5-mm diameter or larger) within polycrystalline aggregates, as well as to single crystals of any size. The method is described with reference to cubic crystals; it can be applied equally well to hexagonal, tetragonal, or orthorhombic crystals.
1.2 Most natural crystals have well developed external faces, and the orientation of such crystals can usually be determined from inspection. The orientation of a crystal having poorly developed faces, or no faces at all (for example, a metal crystal prepared in the laboratory) must be determined by more elaborate methods. The most convenient and accurate of these involves the use of X-ray diffraction. The "orientation of a metal crystal" is known when the positions in space of the crystallographic axes of the unit cell have been located with reference to the surface geometry of the crystal specimen. This relation between unit cell position and surface geometry is most conveniently expressed by stereographic or gnomonic projection.
1.3 The values stated in inch-pound units are to be regarded as the standard.
1.4 This standard does not purport to address the safety problems associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: E 82 – 91 (Reapproved 2001)
Standard Test Method for
Determining the Orientation of a Metal Crystal
ThisstandardisissuedunderthefixeddesignationE82;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginal
adoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscript
epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope Hyberbolic chart for solving backreflection Laue patterns (1
film positive)
1.1 This test method covers the back-reflection Laue proce-
dure for determining the orientation of a metal crystal. The
3. Summary of Test Method
back-reflection Laue method for determining crystal orienta-
2 3.1 Thearrangementoftheapparatusissimilartothatofthe
tion (1, 2) may be applied to macrograins (3) (0.5-mm
transmission Laue method for crystal structure determination
diameterorlarger)withinpolycrystallineaggregates,aswellas
except that the photographic film is located between the X-ray
to single crystals of any size. The method is described with
sourceandthespecimen.ThebeamofwhiteXradiation passes
reference to cubic crystals; it can be applied equally well to
through a pinhole system and through a hole in the photo-
hexagonal, tetragonal, or orthorhombic crystals.
graphic film, strikes the crystal, and is diffracted back onto the
1.2 Most natural crystals have well developed external
film. Dark spots, which represent X-ray beams “reflected” by
faces, and the orientation of such crystals can usually be
the atomic planes within the specimen, appear on the devel-
determinedfrominspection.Theorientationofacrystalhaving
oped film. The atomic planes these spots represent are identi-
poorlydevelopedfaces,ornofacesatall(forexample,ametal
fied by crystallographic procedures and the orientation of the
crystalpreparedinthelaboratory)mustbedeterminedbymore
metal crystal is determined.
elaborate methods. The most convenient and accurate of these
involves the use of X-ray diffraction. The “orientation of a
4. Significance and Use
metal crystal” is known when the positions in space of the
4.1 Metals and other materials are not always isotropic in
crystallographic axes of the unit cell have been located with
their physical properties. For example, Young’s modulus will
reference to the surface geometry of the crystal specimen.This
vary in different crystallographic directions. Therefore, it is
relation between unit cell position and surface geometry is
desirable or necessary to determine the orientation of a single
most conveniently expressed by stereographic or gnomonic
crystalundergoingtestsinordertoascertaintherelationofany
projection.
property to different directions in the material.
1.3 The values stated in inch-pound units are to be regarded
4.2 This test method can be used commercially as a quality
as the standard.
control test in production situations where a desired orienta-
1.4 This standard does not purport to address all of the
tion, within prescribed limits, is required.
safety concerns, if any, associated with its use. It is the
4.3 With the use of an adjustable fixed holder that can later
responsibility of the user of this standard to establish appro-
be mounted on a saw, lathe, or other machine, a single crystal
priate safety and health practices and determine the applica-
material can be moved to a preferred orientation, and subse-
bility of regulatory limitations prior to use.
quently sectioned, ground, or processed otherwise.
4.4 If grains of a polycrystalline material are large enough,
2. Referenced Documents
thistestmethodcanbeusedtodeterminetheirorientationsand
2.1 ASTM Standards:
3 differences in orientation.
E3 Methods of Preparation of Metallographic Specimens
2.2 Adjunct:
5. Apparatus
5.1 X-Ray Tube—Inorderthatexposuretimesbereducedto
aminimum,theX-raytubeshallhaveatargetthatgivesahigh
This test method is under the jurisdiction of ASTM Committee E04 on
Metallography and is the direct responsibility of Subcommittee E04.11 on X-Ray yield of white X-radiation. The tube voltage shall be near 50
and Electron Metallography.
kVp.
Current edition approved Feb. 22, 1991. Published May 1991. Originally
5.2 Back-Reflection Laue X-Ray Camera—The X-ray cam-
published as E82–49. Replaces E82– 49T. Last previous edition E82–63(1984)
era shall have (1) a pinhole system about 6 cm in length with
e1
Theboldfacenumbersinparenthesesrefertothelistofreferencesattheendof
this method.
3 4
Annual Book of ASTM Standards, Vol 03.01. Plate I is available from ASTM Headquarters. Order Adjunct: ADJE0082.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
E 82 – 91 (2001)
openings of ⁄4 to 1 mm, (2) a flat, light-tight film holder (the
hole in the center of the film should be as small as possible,
preferably about ⁄8 in. (3.2 mm) in diameter), (3) a specimen
holder,and( 4)meansforsettingthecrystal-to-filmdistanceat
3.00 cm. These parts may be assembled in various ways
depending upon the type of specimen being studied and upon
theaccuracydesired.Themainrequirementforaccurateresults
is that the pinhole system shall be precisely perpendicular to
thefilmholderandthustothefilm.Analuminumsheetmaybe
placed between the specimen and the film, preferably in close
contact with the film, in order to filter much of the secondary
X-radiation emitted by the crystal.
NOTE 1—Fig. 1 illustrates a back-reflection Laue camera constructed
forusewithmetallicsheetspecimenshavinggrainswithadiameterof0.5
mm or larger. The specimen-to-film distance is fixed at 3 cm and the
specimen surface is maintained perpendicular to the incident beam and
parallel to the film.
NOTE 2—Fig. 2 illustrates a universal camera with a goniometer head,
as adapted for back-reflection Laue studies. With this camera the inter-
pretation of an unsymmetrical pattern may be verified rapidly by rotating
the specimen to an angle for which a prominent pole is perpendicular to
the film, so that a pattern of recognized symmetry is obtained. FIG. 2 Universal Camera With Goniometer Head for Back-
Reflection Laue Studies
6. Test Specimen
6.1 The test specimen may be of any convenient size or
of metals such as tin and zinc (or their solid solutions), which
shape. Normally, the orientation will be determined with
twin readily on being plastically deformed.
reference to a prepared surface and a line on this surface.
NOTE 3—Reference may be made to Methods E3, for procedures for
Surfaces on metal crystals may be prepared by methods
polishing specimens.
ordinarily used in preparing metallographic specimens (Note
3). After final polishing, the specimen shall be etched deeply
PROCEDURE
enoughtoremoveallpolishingdistortion.Thissurfaceshallbe
examined microscopically to make sure that the etch has
7. Orientation of Specimen and Film
removedallscratchesordistortedmetal.Strain-freesurfacesof
7.1 It is necessary that the orientation relationships between
aluminum, iron, copper, brass, tungsten, nickel, etc., are easily
the specimen and film be fixed at the outset (a sketch of this
prepared. Great care is needed in preparing surfaces on cystals
relationship should be made) and be preserved throughout the
determinations.Forexample,thisrelationshipisfixedif(1)the
exposed specimen surface is parallel to the plane of the film,
(2) a vertical line inscribed on the specimen surface is parallel
to a vertical line on the film, (3) the “top” of the film
corresponds with the “top” of the specimen, and ( 4) the
exposed surface of the film facing the specimen is definitely
marked.
8. Back-Reflection Laue Pattern
8.1 The back-reflection Laue pattern, properly prepared,
will contain a hundred or more diffraction spots. These spots
represent “reflections” of the X-ray beam from all important
lattice planes of the crystal that are in position for diffraction.
With the crystal-to-film distance of 3 cm and a photographic
film5in.(127mm)indiameteror4by5in.(102by127mm),
this will include all important lattice planes that make an angle
of less than about 35° with the film; the reflections from all
other planes in the crystal will not be intercepted by the film.
The diffraction spots form a pattern consisting of many
hyperbolic curves; these curves represent crystallographic
zones (1, 2). Some of these hyperbolic curves are more
prominent (more thickly populated with spots) than others, as
they represent crystallographic zones having a higher popula-
FIG. 1 Back-Reflection Laue Camera for Metallic Sheet
Specimens tion of low-indices planes.
E 82 – 91 (2001)
9. Hyperbolic and Polar Coordinate Charts 9.3 A second, though not often needed, operation that may
be performed with the aid of the hyperbolic and polar charts is
9.1 The hyperbolic chart, Fig. 3 (Plate I), and the polar
the measurement of the angle between two zone axes (which
chart, Fig. 4, are used in the solution of back-reflection Laue
arerepresentedonthepatternastwointersectingzonalcurves).
patterns. Use the hyperbolic chart (reproduced as a positive on
If the point of intersection is located not more than about 10°
photographic film or plate) on the back-reflection Laue pattern
from the origin, the following procedure is used: Place the
in much the same way that a gnomonic (or stereographic) net
chart over the film with centers coinciding so that a meridian
is used on gnomonic (or stereographic) projections. Locate
coincides with one of the zonal curves. Then rotate the chart
both horizontal and vertical curves 2° apart in terms of angles
about the origin until another meridian coincides with the
within the crystal. The horizontal curves are meridians, thus
second zonal curve. The angle or rotation of the chart,
correspondingtocrystallographiczones;theverticalcurvesare
measured by means of the polar net, gives the angle between
parallels. The series of meridian curves shown on the chart
the zone axes producing the two zonal curves. A procedure
represents all possible curvatures that a crystallographic zone
whichmaybeusedfor anytwozonalcurvesinvolvesarotation
of a back-reflection Laue pattern may have; the zone is a
of a few spots of the back-reflection Laue pattern as follows:
straight line only when it passes through the origin.
Superimpose the hyperbolic chart and the film so that the
9.2 Theverticalcurvesareparallelsandareusedtomeasure
angles along meridian curves. Thus, the angle between two straight-line parallel (the vertical line through the center of the
chart)containsthepointofintersectionofthetwozonalcurves
crystal planes that produce two spots on the film may be read
directlyfromthechart.Tomeasurethisangle,superimposethe in question. Then rotate this point of intersection to the origin,
and move a (any) point on each of the two zonal curves the
chartonthefilmwithcenterscoincidingandrotatetheplate(or
film)untilahyperbolicmeridiancoincideswiththezonalcurve same number of degrees (along parallels, of course) in the
connecting the two spots in question; then read the angle same direction. Since both zonal curves now pass through the
between the two planes directly from the set of parallels. Read origintheyappearasstraightlines,andtheanglebetweenthese
the angle of inclination of the zone axis to the film directly radial lines is then the angle between the two zone axes in
from the scale of meridian angles. question (6 ⁄2 °, if the rotation has been carefully carried out).
FIG. 3 Hyperbolic Chart for Solution of Laue-Back-Reflection Patterns
E 82 – 91 (2001)
FIG. 4 Polar Chart for Solution of Laue Back-Reflection Patterns
Thisoperationisthesameastheoperationrequiredtomeasure central spot and parallel to a prominent direction in the
the angle between any two intersecting great circles on a specimen, and measure all azimuth angles with respect to this
stereographic projection. line. Methods for plotting the projections are described by
Barrett (4). Methods for identifying prominent spots and zones
10. Interpretation of Unsymmetrical Back-Reflection
are summarized in 10.2 to 10.6, inclusive.
Laue Patterns
10.2 After some experience has been gained, it will be
10.1 The most rigorous method for solving an unsymmetri- found that back-reflection Laue patterns may be solved by
cal pattern is by preparing a stereographic projection with its inspection alone. The following remarks should be of assis-
plane parallel to the plane of the film. Read the film from the tanceinthedevelopmentofasystematicapproach:Atleastone
side opposite that of incident radiation, so that the projection standard stereographic projection (5) of the lattice being
corresponds to viewing the crystal from the position of the studied shall be prepared. This projection shall include ^100&,
X-ray tube. Inscribe a reference line on the film through the ^110&,and ^111&zones,andifthecrystalisface-centeredcubic,
E 82 – 91 (2001)
the projection shall include all the poles of the forms {100}, solution of a pattern it is necessary only to identify two
{110}, {111}, and {113}; if body-centered cubic, the projec- important diffraction spots, or one important spot and a zonal
tion shall include {100}, {110}, {111}, and {112}. This curve.Animportantspotonaback-reflectionLauepatternmay
standard projection shall be studied until one has become be recognized easily because (1) it is (comparatively) isolated
familiar with the relative positions of poles and their angular from its neighbors, (2) it is a point of intersection of a large
separations, the symmetry characteristics of each pole, the number of zonal curves, and (3) it is of rather high intensity.A
important zonal curves passing through each pole, etc. spot is identified by the angles between the important zonal
10.3 In Figs. 5-8 are reproduced standard stereographic curvesthatintersectatthespotinquestion,orbyitspositionin
projections of a cubic crystal with the {100}, {111}, {110}, relation to that of some other important spot. The indexing of
and {112} poles at the center. These projections illustrate theseparatepointsisalsomuchsimplifiedbyusingatabulated
orientations having four-fold, three-fold, and two-fold axes of summary of the possible angular separations for the crystal
symmetry and a plane of symmetry, respectively. Note that the form investigated. Such a summary made by Stahlein and
standard cubic, or {100}, projection is made of 24 identical Schlechtinig (6) for the body-centered cubic lattice is repro-
triangular areas. duced in Fig. 9. Data for the face-centered cubic lattice are
10.4 Crystallographic zones are of great importance in the given in Table 1 (7). Peavler and Lenusky (8) calculated the
solutionofback-reflectionLau
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