ASTM E81-96
(Test Method)Standard Test Method for Preparing Quantitative Pole Figures
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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Designation: E 81 – 96
AMERICAN SOCIETY FOR TESTING AND MATERIALS
100 Barr Harbor Dr., West Conshohocken, PA 19428
Reprinted from the Annual Book of ASTM Standards. Copyright ASTM
Standard Test Method for
Preparing Quantitative Pole Figures
This standard is issued under the fixed designation E 81; the number immediately following the designation indicates the year of original
adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A superscript
epsilon (e) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Summary of Test Method
1.1 This test method covers the use of the X-ray diffracto- 2.1 The test method consists of characterizing the distribu-
meter to prepare quantitative pole figures. tion of orientations of selected lattice planes with respect to
1.2 The test method consists of several experimental proce- sample-fixed coordinates (6). The distribution will usually be
dures. Some of the procedures (1-5) permit preparation of a obtained by measurement of the intensity of X rays diffracted
complete pole figure. Others must be used in combination to by the sample. In such measurements the detector and associ-
produce a complete pole figure. ated limiting slits are fixed at twice the appropriate Bragg
1.3 Pole figures (6) and inverse pole figures (7-10) are two angle, and the diffracted intensity is recorded as the orientation
dimensional averages of the three-dimensional crystallite ori- of the sample is changed (1-6, 25, 26, 27). After the measured
entation distribution. Pole figures may be used to construct data have been corrected, as necessary, for background, defo-
either inverse pole figures (11-13) or the crystallite orientation cusing, and absorption, and normalized to have an average
distribution (14-21). Development of series expansions of the value of unity, the results may be plotted in stereographic or
crystallite orientation distribution from reflection pole figures equal-area projection.
(22, 23) makes it possible to obtain a series expansion of a 2.2 The geometry of the Schulz (25) reflection method is
complete pole figure from several incomplete pole figures. Pole illustrated in Fig. 1. Goniometers employing this geometry are
figures or inverse pole figures derived by such methods shall be commercially available. The source of X rays is indicated by
termed calculated. These techniques will not be described L. Slit S1 limits divergence of the incident beam in the plane of
herein. projection. Slit S2 limits divergence perpendicular to the plane
1.4 Provided the orientation is homogeneous through the of projection. The sample, indicated by crosshatching, may be
thickness of the sheet, certain procedures (1-3) may be used to tilted about the axis FF8, which is perpendicular to the
obtain a complete pole figure. diffractometer axis and lies in the plane of the sample. The tilt
1.5 Provided the orientation has mirror symmetry with angle was denoted f by Schulz (25). The sample position
respect to planes perpendicular to the rolling, transverse, and shown in Fig. 1 corresponds to f5 0 deg, for which approxi-
normal directions, certain procedures (4, 5, 24) may be used to mate parafocusing conditions exist at the detector slit, S3. With
obtain a complete pole figure. the application of a defocusing correction, this method is useful
1.6 The test method emphasizes the Schulz reflection tech- over a range of colatitude f from 0 deg to approximately 75
nique (25). Other techniques (3, 4, 5, 24) may be considered deg.
variants of the Schulz technique and are cited as options, but 2.2.1 Tilting the sample about FF8, so as to reduce the
not described herein. distance between L and points in the sample surface above the
1.7 The test method also includes a description of the plane of projection, causes X rays diffracted from these points
transmission technique of Decker, et al (26), which may be to be displaced to the left of the center of S3, while X rays
used in conjunction with the Schulz reflection technique to diffracted from points in the sample surface below the plane of
obtain a complete pole figure. projection are displaced to the right of the center of S3. The
1.8 This standard does not purport to address all of the displacement is equal to 2D tan f cos u, where D is the
safety concerns, if any, associated with its use. It is the distance above or below the plane of projection. The inte-
responsibility of the user of this standard to establish appro- grated, or total, diffracted intensity is influenced only slightly
priate safety and health practices and determine the applica- by tilting the sample (28). Insofar as possible, the detector slit
bility of regulatory limitations prior to use. shall be of sufficient width to include the defocused line profile
corresponding to the maximum sample tilt for which measure-
ments are to be made. Because of interferences from neigh-
This test method is under the jurisdiction of ASTM Committee E-4 on
boring diffraction peaks and physical limitations on sample
Metallography and is the direct responsibility of Subcommittee E04.11 on X-Ray
size and detector slit width, it is necessary to limit vertical
and Electron Metallography.
Current edition approved May 10, 1996. Published July 1996. Originally
published as E 81 – 49 T. Last previous edition E 81 – 90.
2 3
The boldface numbers in parentheses refer to the list of references at the end of Available from Philips Electronics Instruments, Inc., 85 McKee Drive, Mah-
this test method. wah, NJ 07430, and Siemens Corp., 186 Wood Ave. So., Iselin, NJ 08830.
E81
4. Apparatus
4.1 Source of X Rays—A beam of characteristic X rays of
substantially constant intensity is required. Characteristic Kal-
pha radiation of chromium, iron, cobalt, nickel, copper, mo-
lybdenum, and silver have all been used successfully, depend-
ing on the chemical composition of the specimen. Insofar as
possible, the radiation selected shall provide sufficient angular
dispersion to permit the resolution of peaks to be measured,
and shall not produce excessive fluorescence in the sample.
Linear absorption coefficients (29) for selected elements are
given in Table 2. Lower energy radiation (Cr, Fe, Co, Ni, Cu)
is generally preferred for reflection pole figure measurements
as it provides greater angular dispersion. Higher energy radia-
tion (Mo, Ag) is generally preferred for transmission measure-
FIG. 1 Geometry of Reflection Method.
ments.
4.2 Slits—Suitable slits shall be provided to limit horizon-
divergence of the incident beam. A widely used pole figure
tal (in the plane of projection of Figs. 1 and 2) and vertical
goniometer with a focal spot to the center of the sample
(perpendicular to the plane of projection of Figs. 1 and 2)
distance of 172 mm employs a 0.5-mm slit located 30 mm from
divergence of the incident beam. Horizontal divergences of 1 to
the center of the sample for this purpose. Measured intensities
3 deg for reflection and 0.5 deg for transmission are typical.
may be corrected for defocusing by comparison with intensities
Vertical divergences of 0.2 deg for reflection and 1 deg for
diffracted by a randomly oriented specimen of similar material,
transmission are typical. Insofar as possible, the receiving slit
or byemploying the theoretically calculated corrections (28).
shall be of sufficient width to include the diffracted peak.
2.3 The geometry of the transmission technique of Decker,
Receiving slits corresponding to 1 deg 2−theta are typical.
et al (26) is shown in Fig. 2. In contrast to the reflection
method, X rays diffracted from different points in the sample 4.3 Specimen Holder—Reflection Method:
diverge, making the resolution of adjacent peaks more difficult.
4.3.1 The specimen holder for the reflection method shall
The ratio of the diffracted intensity at a5 −5, −10,··· , −70 preferably employ the Schulz reflection geometry illustrated in
deg, to the diffracted intensity at a5 0 deg, calculated in
Fig. 1 and described in 2.2. It is desirable that the specimen
accordance with the expression given by Decker, et al (26) for holder be equipped with a means for oscillating the sample in
linear absorption thickness product, μt, 5 1.0, 1.4, ···, 3.0, and,
the plane of its surface without changing the orientation of the
foru5 5, 10,··· , 25 deg is given in Table 1. These data may be sample. It is also desirable that the magnitude of the oscillation
used as a guide to determine the useful range of a for a given
be variable. The specimen holder shall preferably be provided
μt and u. If, for example, I /I is restricted to values $ 0.5, one with automatic means for changing colatitude and longitude of
a 0
arrives at the series of curves shown in Fig. 3.
the sample.
4.3.2 Alternative reflection geometries include those of
3. Significance and Use
Bakarian (1), Field and Marchant (27), and Jetter and Borie (2).
3.1 Pole figures are two-dimensional graphic representa-
The method of Bakarian requires machining a number of
tions, on polar coordinate paper, of the average distribution of
cylindrical specimens whose axes are perpendicular to the
crystallite orientations in three dimensions. Data for construct-
sheet normal direction. Each specimen provides intensity data
ing pole figures are obtained with X-ray diffractometers, using
along one parallel of longitude. The method of Jetter and Borie
reflection and transmission techniques.
entails the preparation of a spherical specimen. In the methods
3.2 Several alternative procedures may be used. Some
of Bakarian and of Jetter and Borie, the sample shall, insofar as
produce complete pole figures. Others yield partial pole fig-
possible, be prepared from homogeneous material. These
ures, which may be combined to produce a complete figure.
methods have the advantage that intensity data need not be
corrected for absorption or defocusing. They do not permit
oscillation of the sample. Equipment is not currently commer-
cially available for these methods.
4.3.3 The method of Field and Marchant (27) requires an
absorption correction. If this method is used in conjunction
with the transmission method of Decker, et al (26),itis
necessary to use either different orders of reflection or different
radiations in order to obtain a complete pole figure.
4.4 Specimen Holder—Transmission Method—If the trans-
mission method is used, the specimen holder shall employ the
geometry of Decker, et al (26), shown in Fig. 2 and described
in 2.3. It is desirable that the specimen holder be equipped with
a means for oscillating the sample in the plane of its surface
FIG. 2 Geometry of Transmission Method. without changing the orientation of the sample. The specimen
E81
TABLE 1 (I /I ) 3 1000
a 0
−a
u
μt 5 10 15 20 25303540455055606570
5 1.0 992 984 976 966 954 939 918 890 851 796 703 617 480 313
1.4 991 978 962 941 915 882 840 786 719 636 533 412 277 146
1.8 989 972 948 917 878 828 768 695 608 508 395 276 162 070
2.2 988 966 935 893 842 778 702 614 515 406 294 186 095 034
2.6 986 960 922 871 807 731 643 544 436 326 219 126 057 017
3.0 985 954 909 849 775 687 589 481 370 261 164 086 034 009
10 1.0 984 969 952 934 912 887 855 815 762 694 603 486 344 191
1.4 983 962 938 908 873 831 779 716 640 548 440 320 198 094
1.8 981 956 924 884 836 779 710 630 538 435 325 215 119 049
2.2 980 950 911 861 801 730 649 556 455 348 242 147 074 027
2.6 978 944 898 839 768 686 593 492 385 280 183 103 047 016
3.0 977 938 885 817 737 644 543 436 328 226 139 073 030 009
15 1.0 976 952 927 900 868 832 789 735 668 583 477 349 209 085
1.4 975 946 912 874 829 776 714 640 553 453 342 227 123 046
1.8 973 939 898 850 792 725 648 560 462 358 252 155 078 027
2.2 972 933 885 826 758 678 590 492 389 286 190 110 052 017
2.6 970 927 872 804 725 636 538 435 331 232 146 080 036 011
3.0 968 921 859 783 695 597 493 386 283 190 115 060 025 007
20 1.0 968 935 901 863 822 774 718 649 566 465 345 214 093 000
1.4 966 928 885 836 781 717 643 557 460 354 243 140 058 000
1.8 964 921 870 811 743 666 579 484 381 278 180 099 039 000
2.2 963 915 857 788 709 621 525 424 321 224 139 074 028 000
2.6 961 909 843 766 678 582 479 375 274 185 111 057 020 000
3.0 960 903 831 746 650 547 440 335 238 155 090 044 015 000
25 1.0 959 917 872 824 771 710 639 555 455 339 214 096 000
1.4 957 909 856 796 728 651 565 468 362 253 151 065 000
1.8 955 902 840 770 690 602 505 402 298 200 115 048 000
2.2 953 895 826 746 657 560 456 352 253 164 092 038 000
2.6 952 889 812 724 627 523 417 314 219 139 076 031 000
3.0 950 883 800 705 601 493 384 283 194 121 065 025 000
the incident beam is acceptable, the specimen must have a
linear absorption thickness product equal to or greater than 2.3
sin u. For an iron sample with molybdenum K-alpha radiation,
this requires that μt be greater than 0.4, 0.6, and 0.7 for the
(110), (200), and (211) reflections, respectively.
5.1.1 Surface preparation is particularly important in the
reflection method. Calculations due to Borie (30), who as-
sumed a sawtooth surface of spacing a on a material with linear
absorption coefficient μ, indicate that the product μa should be
less than 0.5 if significant intensity losses are to be avoided.
For an iron sample with cobalt K-alpha radiation, μ 5 416
−1
cm , corresponding to a # 12 μm.
5.2 For the transmission method, maximum intensity is
FIG. 3 a versus μt for I /I 5 0.5, u 5 5, 10, ···, 25 deg.
a 0
obtained for a linear absorption thickness product equal to cos
u. For an iron sample with molybdenum K-alpha, this corre-
holder shall preferably be providedwith automatic means for
sponds to μt equal to 0.98, 0.97, and 0.95 for the (110), (200),
changing colatitude and longitude of the sample.
and (211) reflections, respectively. Thus, a suitable transmis-
4.5 Detector—The detector shall preferably be of an
sion sample can also be used for reflection measurements.
energy-dispersive type, for example, a solid state, proportional,
5.3 Ordinarily test specimens are obtained from thicker
or scintillation counter, and used in conjunction with a pulse
sections by reducing them mechanically so far as possible and
height selector circuit to discriminate against X rays whose
then etching to final thickness. The sample must not be
energies differ markedly from that of the characteristic K-alpha
overheated or plastically deformed during the thinning process.
radiation being used. Reduction of the characteristic K-beta
The etchant used must remove material uniformly without
radiation requires the use of a monochromator or appropriate
pitting. The finished specimen may have a “matte” appearance,
beta filter. Pd, Zr, Ni, Co, Fe, Mn, and V are appropriate beta
but surfaces shall be flat and parallel.
filt
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