Designation: E81 − 96 (Reapproved 2017)Standard Test Method forPreparing Quantitative Pole Figures 1This standard is issued under the f i xed designation E81; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.Asuperscriptepsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers the use of the X-ray diffracto-meter to prepare quantitative pole f i gures.1.2 The test method consists of several experimental proce-dures. Some of the procedures (1-5) 2 permit preparation of acomplete pole f i gure. Others must be used in combination toproduce a complete pole f i gure.1.3 Pole f i gures (6) and inverse pole f i gures (7-10) are twodimensional averages of the three-dimensional crystallite ori-entation distribution. Pole f i gures may be used to constructeither inverse pole f i gures (11-13) or the crystallite orientationdistribution (14-21). Development of series expansions of thecrystallite orientation distribution from ref l ection pole f i gures(22, 23) makes it possible to obtain a series expansion of acomplete pole f i gure from several incomplete pole f i gures. Polef i gures or inverse pole f i gures derived by such methods shall betermed calculated. These techniques will not be describedherein.1.4 Provided the orientation is homogeneous through thethickness of the sheet, certain procedures (1-3) may be used toobtain a complete pole f i gure.1.5 Provided the orientation has mirror symmetry withrespect to planes perpendicular to the rolling, transverse, andnormal directions, certain procedures (4, 5, 24) may be used toobtain a complete pole f i gure.1.6 The test method emphasizes the Schulz ref l ection tech-nique (25). Other techniques (3, 4, 5, 24) may be consideredvariants of the Schulz technique and are cited as options, butnot described herein.1.7 The test method also includes a description of thetransmission technique of Decker, et al (26), which may beused in conjunction with the Schulz ref l ection technique toobtain a complete pole f i gure.1.8 This standard does not purport to address all of thesafety 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.1.9 This international standard was developed in accor-dance with internationally recognized principles on standard-ization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recom-mendations issued by the World Trade Organization TechnicalBarriers to Trade (TBT) Committee.2. Summary of Test Method2.1 The test method consists of characterizing the distribu-tion of orientations of selected lattice planes with respect tosample-f i xed coordinates (6). The distribution will usually beobtained by measurement of the intensity of X rays diffractedby the sample. In such measurements the detector and associ-ated limiting slits are f i xed at twice the appropriate Braggangle, and the diffracted intensity is recorded as the orientationof the sample is changed (1-6, 25, 26, 27). After the measureddata have been corrected, as necessary, for background,defocusing, and absorption, and normalized to have an averagevalue of unity, the results may be plotted in stereographic orequal-area projection.2.2 The geometry of the Schulz (25) ref l ection method isillustrated in Fig. 1. Goniometers employing this geometry arecommercially available. The source of X rays is indicated by L.Slit S1 limits divergence of the incident beam in the plane ofprojection. Slit S2 limits divergence perpendicular to the planeof projection. The sample, indicated by crosshatching, may betilted about the axis FF', which is perpendicular to thediffractometer axis and lies in the plane of the sample. The tiltangle was denoted φ by Schulz (25). The sample positionshown in Fig. 1 corresponds to φ = 0 deg, for which approxi-mate parafocusing conditions exist at the detector slit, S3. Withthe application of a defocusing correction, this method is usefulover a range of colatitude φ from 0 deg to approximately 75deg.2.2.1 Tilting the sample about FF ', so as to reduce thedistance between L and points in the sample surface above theplane of projection, causes X rays diffracted from these pointsto be displaced to the left of the center of S3, while X raysdiffracted from points in the sample surface below the plane of1 This test method is under the jurisdiction of ASTM Committee E04 onMetallography and is the direct responsibility of Subcommittee E04.11 on X-Rayand Electron Metallography.Current edition approved June 1, 2017. Published June 2017. Originallyapproved in 1949. Last previous edition approved in 2011 as E81 – 96 (2011). DOI:10.1520/E0081-96R17.2 The boldface numbers in parentheses refer to the list of references at the end ofthis test method.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United StatesThis international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for theDevelopment of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.1 Copyright by ASTM Int'l (all rights reserved); Fri Oct 6 22:04:09 EDT 2017Downloaded/printed byUniversity of Edinburgh (University of Edinburgh) pursuant to License Agreement. No further reproductions authorized.
