1、Designation: E 82 91 (Reapproved 2007)Standard Test Method forDetermining the Orientation of a Metal Crystal1This standard is issued under the fixed designation E 82; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the year of last
2、 revision.Anumber in parentheses indicates the year of last reapproval.Asuperscriptepsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the back-reflection Laue proce-dure for determining the orientation of a metal crystal. Theback-refle
3、ction Laue method for determining crystal orienta-tion (1, 2)2may be applied to macrograins (3) (0.5-mmdiameter or larger) within polycrystalline aggregates, as well asto single crystals of any size. The method is described withreference to cubic crystals; it can be applied equally well tohexagonal,
4、 tetragonal, or orthorhombic crystals.1.2 Most natural crystals have well developed externalfaces, and the orientation of such crystals can usually bedetermined from inspection. The orientation of a crystal havingpoorly developed faces, or no faces at all (for example, a metalcrystal prepared in the
5、 laboratory) must be determined by moreelaborate methods. The most convenient and accurate of theseinvolves the use of X-ray diffraction. The “orientation of ametal crystal” is known when the positions in space of thecrystallographic axes of the unit cell have been located withreference to the surfa
6、ce geometry of the crystal specimen. Thisrelation between unit cell position and surface geometry ismost conveniently expressed by stereographic or gnomonicprojection.1.3 The values stated in inch-pound units are to be regardedas the standard.1.4 This standard does not purport to address all of thes
7、afety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenced Documents2.1 ASTM Standards:3E3 Guide for Preparation of M
8、etallographic Specimens2.2 Adjunct:Hyberbolic chart for solving back reflection Laue patterns (1film positive)43. Summary of Test Method3.1 The arrangement of the apparatus is similar to that of thetransmission Laue method for crystal structure determinationexcept that the photographic film is locat
9、ed between the X-raysource and the specimen. The beam of white Xradiation passesthrough a pinhole system and through a hole in the photo-graphic film, strikes the crystal, and is diffracted back onto thefilm. Dark spots, which represent X-ray beams “reflected” bythe atomic planes within the specimen
10、, appear on the devel-oped film. The atomic planes these spots represent are identi-fied by crystallographic procedures and the orientation of themetal crystal is determined.4. Significance and Use4.1 Metals and other materials are not always isotropic intheir physical properties. For example, Young
11、s modulus willvary in different crystallographic directions. Therefore, it isdesirable or necessary to determine the orientation of a singlecrystal undergoing tests in order to ascertain the relation of anyproperty to different directions in the material.4.2 This test method can be used commercially
12、 as a qualitycontrol test in production situations where a desired orienta-tion, within prescribed limits, is required.4.3 With the use of an adjustable fixed holder that can laterbe mounted on a saw, lathe, or other machine, a single crystalmaterial can be moved to a preferred orientation, and subs
13、e-quently sectioned, ground, or processed otherwise.4.4 If grains of a polycrystalline material are large enough,this test method can be used to determine their orientations anddifferences in orientation.5. Apparatus5.1 X-Ray TubeIn order that exposure times be reduced toa minimum, the X-ray tube sh
14、all have a target that gives a highyield of white X-radiation. The tube voltage shall be near 50kVp.5.2 Back-Reflection Laue X-Ray Camera The X-ray cam-era shall have (1) a pinhole system about 6 cm in length with1This test method is under the jurisdiction of ASTM Committee E04 onMetallography and i
15、s the direct responsibility of Subcommittee E04.11 on X-Rayand Electron Metallography.Current edition approved May 1, 2007. Published May 2007. Originallyapproved in 1949. Replaces E82 49 . Last previous edition approved in 2001 asE82 91 (2001).2The boldface numbers in parentheses refer to the list
16、of references at the end ofthis method.3For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.4Plate I is available
17、from ASTM Headquarters. Order Adjunct: ADJE0082.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.openings of14 to 1 mm, (2) a flat, light-tight film holder (thehole in the center of the film should be as small as possible,preferably a
18、bout18 in. (3.2 mm) in diameter), (3) a specimenholder, and ( 4) means for setting the crystal-to-film distance at3.00 cm. These parts may be assembled in various waysdepending upon the type of specimen being studied and uponthe accuracy desired. The main requirement for accurate resultsis that the
19、pinhole system shall be precisely perpendicular tothe film holder and thus to the film.An aluminum sheet may beplaced between the specimen and the film, preferably in closecontact with the film, in order to filter much of the secondaryX-radiation emitted by the crystal.NOTE 1Fig. 1 illustrates a bac
20、k-reflection Laue camera constructedfor use with metallic sheet specimens having grains with a diameter of 0.5mm or larger. The specimen-to-film distance is fixed at 3 cm and thespecimen surface is maintained perpendicular to the incident beam andparallel to the film.NOTE 2Fig. 2 illustrates a unive
21、rsal 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 rotatingthe specimen to an angle for which a prominent pole is perpendicular tothe film, so that a pattern of recognized symmetr
22、y is obtained.6. Test Specimen6.1 The test specimen may be of any convenient size orshape. Normally, the orientation will be determined withreference to a prepared surface and a line on this surface.Surfaces on metal crystals may be prepared by methodsordinarily used in preparing metallographic spec
23、imens (Note3). After final polishing, the specimen shall be etched deeplyenough to remove all polishing distortion. This surface shall beexamined microscopically to make sure that the etch hasremoved all scratches or distorted metal. Strain-free surfaces ofaluminum, iron, copper, brass, tungsten, ni
24、ckel, etc., are easilyprepared. Great care is needed in preparing surfaces on cystalsof metals such as tin and zinc (or their solid solutions), whichtwin readily on being plastically deformed.NOTE 3Reference may be made to Methods E3, for procedures forpolishing specimens.PROCEDURE7. Orientation of
25、Specimen and Film7.1 It is necessary that the orientation relationships betweenthe specimen and film be fixed at the outset (a sketch of thisrelationship should be made) and be preserved throughout thedeterminations. For example, this relationship is fixed if (1) theexposed specimen surface is paral
26、lel to the plane of the film,(2) a vertical line inscribed on the specimen surface is parallelto a vertical line on the film, (3) the “top” of the filmcorresponds with the “top” of the specimen, and ( 4) theexposed surface of the film facing the specimen is definitelymarked.8. Back-Reflection Laue P
27、attern8.1 The back-reflection Laue pattern, properly prepared,will contain a hundred or more diffraction spots. These spotsrepresent “reflections” of the X-ray beam from all importantlattice planes of the crystal that are in position for diffraction.With the crystal-to-film distance of 3 cm and a ph
28、otographicfilm 5 in. (127 mm) in diameter or 4 by 5 in. (102 by 127 mm),this will include all important lattice planes that make an angleof less than about 35 with the film; the reflections from allother planes in the crystal will not be intercepted by the film.The diffraction spots form a pattern c
29、onsisting of manyhyperbolic curves; these curves represent crystallographiczones (1, 2). Some of these hyperbolic curves are moreprominent (more thickly populated with spots) than others, asthey represent crystallographic zones having a higher popula-tion of low-indices planes.FIG. 1 Back-Reflection
30、 Laue Camera for Metallic SheetSpecimensFIG. 2 Universal Camera With Goniometer Head for Back-Reflection Laue StudiesE 82 91 (2007)29. Hyperbolic and Polar Coordinate Charts9.1 The hyperbolic chart, Fig. 3 (Plate I),4and the polarchart, Fig. 4, are used in the solution of back-reflection Lauepattern
31、s. Use the hyperbolic chart (reproduced as a positive onphotographic film or plate) on the back-reflection Laue patternin much the same way that a gnomonic (or stereographic) netis used on gnomonic (or stereographic) projections. Locateboth horizontal and vertical curves 2 apart in terms of angleswi
32、thin the crystal. The horizontal curves are meridians, thuscorresponding to crystallographic zones; the vertical curves areparallels. The series of meridian curves shown on the chartrepresents all possible curvatures that a crystallographic zoneof a back-reflection Laue pattern may have; the zone is
33、 astraight line only when it passes through the origin.9.2 The vertical curves are parallels and are used to measureangles along meridian curves. Thus, the angle between twocrystal planes that produce two spots on the film may be readdirectly from the chart. To measure this angle, superimpose thecha
34、rt on the film with centers coinciding and rotate the plate (orfilm) until a hyperbolic meridian coincides with the zonal curveconnecting the two spots in question; then read the anglebetween the two planes directly from the set of parallels. Readthe angle of inclination of the zone axis to the film
35、 directlyfrom the scale of meridian angles.9.3 A second, though not often needed, operation that maybe performed with the aid of the hyperbolic and polar charts isthe measurement of the angle between two zone axes (whichare represented on the pattern as two intersecting zonal curves).If the point of
36、 intersection is located not more than about 10from the origin, the following procedure is used: Place thechart over the film with centers coinciding so that a meridiancoincides with one of the zonal curves. Then rotate the chartabout the origin until another meridian coincides with thesecond zonal
37、curve. The angle or rotation of the chart,measured by means of the polar net, gives the angle betweenthe zone axes producing the two zonal curves. A procedurewhich may be used for any two zonal curves involves a rotationof a few spots of the back-reflection Laue pattern as follows:Superimpose the hy
38、perbolic chart and the film so that thestraight-line parallel (the vertical line through the center of thechart) contains the point of intersection of the two zonal curvesin question. Then rotate this point of intersection to the origin,and move a (any) point on each of the two zonal curves thesame
39、number of degrees (along parallels, of course) in thesame direction. Since both zonal curves now pass through theorigin they appear as straight lines, and the angle between theseradial lines is then the angle between the two zone axes inquestion (612 , if the rotation has been carefully carried out)
40、.FIG. 3 Hyperbolic Chart for Solution of Laue-Back-Reflection PatternsE 82 91 (2007)3This operation is the same as the operation required to measurethe angle between any two intersecting great circles on astereographic projection.10. Interpretation of Unsymmetrical Back-ReflectionLaue Patterns10.1 T
41、he most rigorous method for solving an unsymmetri-cal pattern is by preparing a stereographic projection with itsplane parallel to the plane of the film. Read the film from theside opposite that of incident radiation, so that the projectioncorresponds to viewing the crystal from the position of theX
42、-ray tube. Inscribe a reference line on the film through thecentral spot and parallel to a prominent direction in thespecimen, and measure all azimuth angles with respect to thisline. Methods for plotting the projections are described byBarrett (4). Methods for identifying prominent spots and zonesa
43、re summarized in 10.2 to 10.6, inclusive.10.2 After some experience has been gained, it will befound that back-reflection Laue patterns may be solved byinspection alone. The following remarks should be of assis-tance in the development of a systematic approach:At least onestandard stereographic proj
44、ection (5) of the lattice beingstudied shall be prepared. This projection shall include 100 if body-centered cubic, the projec-tion shall include 100, 110, 111, and 112. Thisstandard projection shall be studied until one has becomefamiliar with the relative positions of poles and their angularsepara
45、tions, the symmetry characteristics of each pole, theimportant zonal curves passing through each pole, etc.10.3 In Figs. 5-8 are reproduced standard stereographicprojections of a cubic crystal with the 100, 111, 110,and 112 poles at the center. These projections illustrateorientations having four-fo
46、ld, three-fold, and two-fold axes ofsymmetry and a plane of symmetry, respectively. Note that thestandard cubic, or 100, projection is made of 24 identicaltriangular areas.10.4 Crystallographic zones are of great importance in thesolution of back-reflection Laue patterns. For the face-centeredcubic
47、lattice, the important zones, arranged in order of impor-tance, are 110 for the body-centered cubic latticethese are 111 likewise, every face-centered-cubic patternwill contain at least one of these; likewise, every face-centered-cubic pattern will contain at least one (usually two) 110 Fig. 12 is a
48、 tracing ofthe obviously important zones and spots of Fig. 10. A measurement ofangles between the spots of Fig. 12 gives the following:ab = 45ac =3512 bc = 30The fact that angle ab measures 45 means that one of these spots maybe 100 and the other 110. Now, in as much as 110:112 = 30 and100:112 = 351
49、4 , the following must be true: a = 100, b = 110,and c = 112. This solution may be checked in various ways. Forexample, note that four important zonal curves pass through spot a, andthat these zones are at angles of 45 with each other. This is possible onlywhen the symmetry about the point is four-fold; hence spot a must be100.The tracing of important zones and spots in Fig. 11 is shown in Fig. 13.The pattern symmetry about spot a is obviously four-fold; angle abmeasures 35+. In as much as 100:112 = 3514 , a =
