Standard Test Method for Preparing Quantitative Pole Figures

SCOPE
1.1 This test method covers the use of the X-ray diffractometer to prepare quantitative pole figures.  
1.2 The test method consists of several experimental procedures. Some of the procedures (1-5) permit preparation of a complete pole figure. Others must be used in combination to produce a complete pole figure.  
1.3 Pole figures (6) and inverse pole figures (7-10) are two-dimensional averages of the three-dimensional crystallite ori- entation distribution. Pole figures may be used to construct either inverse pole figures (11-13) or the crystallite orientation distribution (14-21). Development of series expansions of the crystallite orientation distribution from reflection pole figures (22, 23) makes it possible to obtain a series expansion of a complete pole figure from several incomplete pole figures. Pole figures or inverse pole figures derived by such methods shall be termed calculated. These techniques will not be described herein.  
1.4 Provided the orientation is homogeneous through the thickness of the sheet, certain procedures (1-3) may be used to obtain a complete pole figure.  
1.5 Provided the orientation has mirror symmetry with respect to planes perpendicular to the rolling, transverse, and normal directions, certain procedures (4, 5, 24) may be used to obtain a complete pole figure.  
1.6 The test method emphasizes the Schulz reflection technique (25). Other techniques (3, 4, 5, 24) may be considered variants of the Schulz technique and are cited as options, but not described herein.  
1.7 The test method also includes a description of the transmission technique of Decker, et al (26), which may be used in conjunction with the Schulz reflection technique to obtain a complete pole figure.
1.8 This standard does not purport to address all of the safety concerns, if any, 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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Publication Date
31-Dec-2000
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ASTM E81-96(2001) - Standard Test Method for Preparing Quantitative Pole Figures
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NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
Contact ASTM International (www.astm.org) for the latest information
Designation: E 81 – 96 (Reapproved 2001)
Standard Test Method for
1
Preparing Quantitative Pole Figures
ThisstandardisissuedunderthefixeddesignationE81;thenumberimmediatelyfollowingthedesignationindicatestheyearoforiginal
adoptionor,inthecaseofrevision,theyearoflastrevision.Anumberinparenthesesindicatestheyearoflastreapproval.Asuperscript
epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope priate safety and health practices and determine the applica-
bility of regulatory limitations prior to use.
1.1 This test method covers the use of the X-ray diffracto-
meter to prepare quantitative pole figures.
2. Summary of Test Method
1.2 The test method consists of several experimental proce-
2 2.1 The test method consists of characterizing the distribu-
dures. Some of the procedures (1-5) permit preparation of a
tion of orientations of selected lattice planes with respect to
complete pole figure. Others must be used in combination to
sample-fixed coordinates (6). The distribution will usually be
produce a complete pole figure.
obtained by measurement of the intensity of X rays diffracted
1.3 Pole figures (6) and inverse pole figures (7-10) are two
by the sample. In such measurements the detector and associ-
dimensional averages of the three-dimensional crystallite ori-
ated limiting slits are fixed at twice the appropriate Bragg
entation distribution. Pole figures may be used to construct
angle,andthediffractedintensityisrecordedastheorientation
either inverse pole figures (11-13) or the crystallite orientation
of the sample is changed (1-6, 25, 26, 27).After the measured
distribution (14-21). Development of series expansions of the
data have been corrected, as necessary, for background, defo-
crystallite orientation distribution from reflection pole figures
cusing, and absorption, and normalized to have an average
(22, 23) makes it possible to obtain a series expansion of a
value of unity, the results may be plotted in stereographic or
completepolefigurefromseveralincompletepolefigures.Pole
equal-area projection.
figuresorinversepolefiguresderivedbysuchmethodsshallbe
2.2 The geometry of the Schulz (25) reflection method is
termed calculated. These techniques will not be described
illustrated in Fig. 1. Goniometers employing this geometry are
herein.
3
commercially available. The source of X rays is indicated by
1.4 Provided the orientation is homogeneous through the
L.SlitS1limitsdivergenceoftheincidentbeamintheplaneof
thickness of the sheet, certain procedures (1-3) may be used to
projection. Slit S2 limits divergence perpendicular to the plane
obtain a complete pole figure.
of projection. The sample, indicated by crosshatching, may be
1.5 Provided the orientation has mirror symmetry with
tilted about the axis FF8, which is perpendicular to the
respect to planes perpendicular to the rolling, transverse, and
diffractometer axis and lies in the plane of the sample. The tilt
normal directions, certain procedures (4, 5, 24) may be used to
angle was denoted f by Schulz (25). The sample position
obtain a complete pole figure.
shown in Fig. 1 corresponds to f=0 deg, for which approxi-
1.6 The test method emphasizes the Schulz reflection tech-
mateparafocusingconditionsexistatthedetectorslit,S3.With
nique (25). Other techniques (3, 4, 5, 24) may be considered
theapplicationofadefocusingcorrection,thismethodisuseful
variants of the Schulz technique and are cited as options, but
over a range of colatitude f from 0 deg to approximately 75
not described herein.
deg.
1.7 The test method also includes a description of the
2.2.1 Tilting the sample about FF8, so as to reduce the
transmission technique of Decker, et al (26), which may be
distance between L and points in the sample surface above the
used in conjunction with the Schulz reflection technique to
plane of projection, causes X rays diffracted from these points
obtain a complete pole figure.
to be displaced to the left of the center of S3, while X rays
1.8 This standard does not purport to address all of the
diffractedfrompointsinthesamplesurfacebelowtheplaneof
safety concerns, if any, associated with its use. It is the
projection are displaced to the right of the center of S3. The
responsibility of the user of this standard to establish appro-
displacement is equal to 2D tan f cos u, where D is the
distance above or below the plane of projection. The inte-
1
This test method is under the jurisdiction of ASTM Committee E04 on grated, or total, diffracted intensity is influenced only slightly
Metallography and is the direct responsibility of Subcommittee E04.11 on X-Ray
by tilting the sample (28). Insofar as possible, the detector slit
and Electron Metallography.
Current edition approved May 10, 1996. Published July 1996. Originally
published as E81–49T. Last previous edition E81–90.
2 3
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