1、Designation: E 81 96 (Reapproved 2007)Standard Test Method forPreparing Quantitative Pole Figures1This standard is issued under the fixed designation E 81; the number immediately following the designation indicates the year of originaladoption or, in the case of revision, the year of last revision.A
2、number 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 use of the X-ray diffracto-meter to prepare quantitative pole figures.1.2 The test method consists of severa
3、l experimental proce-dures. Some of the procedures (1-5)2permit preparation of acomplete pole figure. Others must be used in combination toproduce a complete pole figure.1.3 Pole figures (6) and inverse pole figures (7-10) are twodimensional averages of the three-dimensional crystallite ori-entation
4、 distribution. Pole figures may be used to constructeither inverse pole figures (11-13) or the crystallite orientationdistribution (14-21). Development of series expansions of thecrystallite orientation distribution from reflection pole figures(22, 23) makes it possible to obtain a series expansion
5、of acomplete pole figure from several incomplete pole figures. Polefigures or inverse pole figures 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) m
6、ay be used toobtain a complete pole figure.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 figure.1.6 The test method emphasizes the Schulz reflec
7、tion 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
8、 reflection technique toobtain a complete pole figure.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
9、of regulatory limitations prior to use.2. Summary of Test Method2.1 The test method consists of characterizing the distribu-tion of orientations of selected lattice planes with respect tosample-fixed coordinates (6). The distribution will usually beobtained by measurement of the intensity of X rays
10、diffractedby the sample. In such measurements the detector and associ-ated limiting slits are fixed 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, fo
11、r background, defo-cusing, 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) reflection method isillustrated in Fig. 1. Goniometers employing this geometry arecommercially available
12、. 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 FF8, which is perpendicular to thediffractometer a
13、xis and lies in the plane of the sample. The tiltangle was denoted f by Schulz (25). The sample positionshown in Fig. 1 corresponds to f = 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
14、 range of colatitude f from 0 deg to approximately 75deg.2.2.1 Tilting the sample about FF8, 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 rays1Th
15、is 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 May 1, 2007. Published May 2007. Originallyapproved in 1949. Last previous edition approved in 2001 as E
16、81 96 (2001).2The boldface numbers in parentheses refer to the list of references at the end ofthis test method.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.diffracted from points in the sample surface below the plane ofprojection
17、 are displaced to the right of the center of S3. Thedisplacement is equal to 2D tan f cos u, where D is thedistance above or below the plane of projection. The inte-grated, or total, diffracted intensity is influenced only slightlyby tilting the sample (28). Insofar as possible, the detector slitsha
18、ll be of sufficient width to include the defocused line profilecorresponding to the maximum sample tilt for which measure-ments are to be made. Because of interferences from neigh-boring diffraction peaks and physical limitations on samplesize and detector slit width, it is necessary to limit vertic
19、aldivergence of the incident beam. A widely used pole figuregoniometer with a focal spot to the center of the sampledistance of 172 mm employs a 0.5-mm slit located 30 mm fromthe center of the sample for this purpose. Measured intensitiesmay be corrected for defocusing by comparison with intensities
20、diffracted by a randomly oriented specimen of similar material,or byemploying the theoretically calculated corrections (28).2.3 The geometry of the transmission technique of Decker,et al (26) is shown in Fig. 2. In contrast to the reflectionmethod, X rays diffracted from different points in the samp
21、lediverge, making the resolution of adjacent peaks more difficult.The ratio of the diffracted intensity at a = 5, 10, , 70 deg,to the diffracted intensity at a = 0 deg, calculated in accordancewith the expression given by Decker, et al (26) for linearabsorption thickness product, t, = 1.0, 1.4, , 3.
22、0, and, foru = 5, 10, , 25 deg is given in Table 1. These data may beused as a guide to determine the useful range of a for a givent and u. If, for example, Ia/I0is restricted to values$0.5, onearrives at the series of curves shown in Fig. 3.3. Significance and Use3.1 Pole figures are two-dimensiona
23、l graphic representa-tions, on polar coordinate paper, of the average distribution ofcrystallite orientations in three dimensions. Data for construct-ing pole figures are obtained with X-ray diffractometers, usingreflection and transmission techniques.3.2 Several alternative procedures may be used.
24、Someproduce complete pole figures. Others yield partial pole fig-ures, which may be combined to produce a complete figure.4. Apparatus4.1 Source of X RaysA beam of characteristic X rays ofsubstantially constant intensity is required. Characteristic Kal-pha radiation of chromium, iron, cobalt, nickel
25、, copper, mo-lybdenum, and silver have all been used successfully, depend-ing on the chemical composition of the specimen. Insofar aspossible, the radiation selected shall provide sufficient angulardispersion to permit the resolution of peaks to be measured,and shall not produce excessive fluorescen
26、ce in the sample.Linear absorption coefficients (29) for selected elements aregiven in Table 2. Lower energy radiation (Cr, Fe, Co, Ni, Cu)is generally preferred for reflection pole figure measurementsas it provides greater angular dispersion. Higher energy radia-tion (Mo, Ag) is generally preferred
27、 for transmission measure-ments.4.2 SlitsSuitable slits shall be provided to limit horizon-tal (in the plane of projection of Figs. 1 and 2) and vertical(perpendicular to the plane of projection of Figs. 1 and 2)divergence of the incident beam. Horizontal divergences of 1 to3 deg for reflection and
28、0.5 deg for transmission are typical.Vertical divergences of 0.2 deg for reflection and 1 deg fortransmission are typical. Insofar as possible, the receiving slitshall be of sufficient width to include the diffracted peak.Receiving slits corresponding to 1 deg 2theta are typical.4.3 Specimen HolderR
29、eflection Method:4.3.1 The specimen holder for the reflection method shallpreferably employ the Schulz reflection geometry illustrated inFig. 1 and described in 2.2. It is desirable that the specimenholder be equipped with a means for oscillating the sample inthe plane of its surface without changin
30、g the orientation of thesample. It is also desirable that the magnitude of the oscillationbe variable. The specimen holder shall preferably be providedwith automatic means for changing colatitude and longitude ofthe sample.4.3.2 Alternative reflection geometries include those ofBakarian (1), Field a
31、nd Marchant (27), and Jetter and Borie (2).The method of Bakarian requires machining a number ofcylindrical specimens whose axes are perpendicular to thesheet normal direction. Each specimen provides intensity dataalong one parallel of longitude. The method of Jetter and Borieentails the preparation
32、 of a spherical specimen. In the methodsof Bakarian and of Jetter and Borie, the sample shall, insofar aspossible, be prepared from homogeneous material. Thesemethods have the advantage that intensity data need not becorrected for absorption or defocusing. They do not permitFIG. 1 Geometry of Reflec
33、tion Method.FIG. 2 Geometry of Transmission Method.E 81 96 (2007)2oscillation of the sample. Equipment is not currently commer-cially available for these methods.4.3.3 The method of Field and Marchant (27) requires anabsorption correction. If this method is used in conjunctionwith the transmission m
34、ethod of Decker, et al (26),itisnecessary to use either different orders of reflection or differentradiations in order to obtain a complete pole figure.4.4 Specimen HolderTransmission MethodIf the trans-mission method is used, the specimen holder shall employ thegeometry of Decker, et al (26), shown
35、 in Fig. 2 and describedin 2.3. It is desirable that the specimen holder be equipped witha means for oscillating the sample in the plane of its surfacewithout changing the orientation of the sample. The specimenholder shall preferably be providedwith automatic means forchanging colatitude and longit
36、ude of the sample.4.5 DetectorThe detector shall preferably be of anenergy-dispersive type, for example, a solid state, proportional,or scintillation counter, and used in conjunction with a pulseheight selector circuit to discriminate against X rays whoseenergies differ markedly from that of the cha
37、racteristic K-alpharadiation being used. Reduction of the characteristic K-betaradiation requires the use of a monochromator or appropriatebeta filter. Pd, Zr, Ni, Co, Fe, Mn, and V are appropriate betafilters for Ag, Mo, Cu, Ni, Co, Fe, and Cr, respectively.5. Test Specimens5.1 For the reflection m
38、ethod, the sample shall be ofsufficient thickness that loss of intensity due to transmissionthrough the sample may be ignored. If a maximum loss of 1 %the incident beam is acceptable, the specimen must have alinear absorption thickness product equal to or greater than 2.3sin u. For an iron sample wi
39、th molybdenum K-alpha radiation,this requires that t 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 thereflection method. Calculations due to Borie (30), who as-sumed a sawtooth surface of spacing a on
40、 a material with linearabsorption coefficient , indicate that the product a should beless than 0.5 if significant intensity losses are to be avoided.For an iron sample with cobalt K-alpha radiation, = 416cm1, corresponding to a # 12 m.5.2 For the transmission method, maximum intensity isobtained for
41、 a linear absorption thickness product equal to cosu. For an iron sample with molybdenum K-alpha, this corre-sponds to t equal to 0.98, 0.97, and 0.95 for the (110), (200),TABLE 1 (Ia/I0) 3 1000uat 5 10 15 20253035404550556065705 1.0 992 984 976 966 954 939 918 890 851 796 703 617 480 3131.4 991 978
42、 962 941 915 882 840 786 719 636 533 412 277 1461.8 989 972 948 917 878 828 768 695 608 508 395 276 162 0702.2 988 966 935 893 842 778 702 614 515 406 294 186 095 0342.6 986 960 922 871 807 731 643 544 436 326 219 126 057 0173.0 985 954 909 849 775 687 589 481 370 261 164 086 034 00910 1.0 984 969 9
43、52 934 912 887 855 815 762 694 603 486 344 1911.4 983 962 938 908 873 831 779 716 640 548 440 320 198 0941.8 981 956 924 884 836 779 710 630 538 435 325 215 119 0492.2 980 950 911 861 801 730 649 556 455 348 242 147 074 0272.6 978 944 898 839 768 686 593 492 385 280 183 103 047 0163.0 977 938 885 81
44、7 737 644 543 436 328 226 139 073 030 00915 1.0 976 952 927 900 868 832 789 735 668 583 477 349 209 0851.4 975 946 912 874 829 776 714 640 553 453 342 227 123 0461.8 973 939 898 850 792 725 648 560 462 358 252 155 078 0272.2 972 933 885 826 758 678 590 492 389 286 190 110 052 0172.6 970 927 872 804
45、725 636 538 435 331 232 146 080 036 0113.0 968 921 859 783 695 597 493 386 283 190 115 060 025 00720 1.0 968 935 901 863 822 774 718 649 566 465 345 214 093 0001.4 966 928 885 836 781 717 643 557 460 354 243 140 058 0001.8 964 921 870 811 743 666 579 484 381 278 180 099 039 0002.2 963 915 857 788 70
46、9 621 525 424 321 224 139 074 028 0002.6 961 909 843 766 678 582 479 375 274 185 111 057 020 0003.0 960 903 831 746 650 547 440 335 238 155 090 044 015 00025 1.0 959 917 872 824 771 710 639 555 455 339 214 096 0001.4 957 909 856 796 728 651 565 468 362 253 151 065 0001.8 955 902 840 770 690 602 505
47、402 298 200 115 048 0002.2 953 895 826 746 657 560 456 352 253 164 092 038 0002.6 952 889 812 724 627 523 417 314 219 139 076 031 0003.0 950 883 800 705 601 493 384 283 194 121 065 025 000FIG. 3 a versus t for Ia/I0= 0.5, u = 5, 10, , 25 deg.E 81 96 (2007)3and (211) reflections, respectively. Thus,
48、a suitable transmis-sion sample can also be used for reflection measurements.5.3 Ordinarily test specimens are obtained from thickersections by reducing them mechanically so far as possible andthen etching to final thickness. The sample must not beoverheated or plastically deformed during the thinni
49、ng process.The etchant used must remove material uniformly withoutpitting. The finished specimen may have a “matte” appearance,but surfaces shall be flat and parallel.5.3.1 For an iron sample with molybdenum K-alpha radia-tion, the linear absorption coefficient is 303 cm1, and optimumspecimen thickness for transmission is approximately 0.03 mm(0.001 in.). It is extremely difficult to prepare specimens thisthin, and in practice iron specimens 0.05 to 0.1 mm (0.002 to0.004 in.) are normally used in transmission with molybdenumK-alpha radiation.5.4 A
