High-Energy Double-Crystal X-ray Diffraction

Transcription

1 516 J. Appl. Cryst. (1988). 21, High-Energy Double-Crystal X-ray Diffraction BY V. HOL~',* S. CUMMINGS AND M. HART University of Manchester, Manchester M13 9PL, England (Received 4 May 1988; accepted 20 May 1988) Dedicated to Ulrich Bonse on the occasion of his 60th birthday Abstract High-energy double-crystal X-ray diffraction has previously only been demonstrated with radioactive sources. The advantages of very low absorption, no extinction and high resolution have been clearly demonstrated in a wide variety of experiments. The experiments reported here are the first to be performed with a high-energy X-ray tube providing radiation up to 160keV. Mosaic spread has been studied by double-crystal rocking curves in silicon, germanium and calcium flouride in very thick samples. Mosaic spreads from 1" arc to several minutes of arc have been measured in 10 mm thick fluorite, in 25 mm thick germanium and in silicon. Routine non-destructive characterization of bulk crystalline materials is possible and many new opportunities will become available when high-energy storage rings make bright synchrotron radiation available in this part of the electromagnetic spectrum. Introduction X-ray diffraction, scattering and spectroscopy in the 30 to 300 kev energy range will become feasible with high resolution and high intensity at several synchrotron radiation facilities in the next few years (Freund, Hart & Schneider, 1988; Freund, 1988). Throughout this energy range, a 3.5 T magnet on a 6 GeV storage ring would produce intensity gains of much more than 10 6 compared with either conventional electron-excited X-ray sources or radioactive sources. Because of intensity limitations and safety requirements, very few laboratories exist where intense radioactive sources can be used for diffraction and scattering experiments. The experiments which have been published show the great promise of synchrotron radiation sources in this part of the electromagnetic spectrum. We describe here some diffraction experiments using the 160keV white spectrum from a sealed-off microfocus X-ray tube. *Permanent address: J. E. Purkyn6 University, Kotla~skfi 2, Brno, Czechoslovakia. General features of high-energy X-ray diffraction The extremely low absorption cross section allows the study of bulk material, for example 13 mm thick steel (Bechtoldt, Placious, Boettinger & Kuriyama, 1981) and the increased sample scattering volume compensates to some extent for the rapid decrease in integrated intensity compared with diffraction at lower energies. Whereas, on both kinematic and dynamic diffraction theories, the integrated intensity decreases with 23, the absorption length increases rapidly with increasing X-ray energy. In nearly perfect crystals the Darwin width of Bragg reflection becomes very small at high energy so that increased sensitivity to strain over large volumes of material can be achieved compared with conventional crystallographic wavelengths. For example, Schneider, Goncalves, Rollason, Bonse, Lauer & Zulehner (1988) used single-crystal rocking curves at 316.5keV (iridium 7 source, ). = A) to study oxygen and precipitate strain in annealing silicon with a sensitivity of 0.1" arc in 10 mm thick samples. Double-crystal rocking curves with this sensitivity on 30 mm thick silicon at 412 kev using a radioactive gold source were also obtained by Abdul Gani, Clark & Tanner (1981). At somewhat lower energies (up to 60 kev, 0.2 A) Deutsch, Hart & Cummings (1987) used doublecrystal rocking curves to determine strains as small as 10-9 in similar crystals. Splitting of Bragg peaks near phase transitions has been measured with 10" arc resolution at 412 kev by Bastie & Dolino (1985) in quartz. In this lower resolution range 7 diffraction is used for the quantitative determination of mosaic structure in thick crystals such as those used in neutron diffraction (Freund, 1973; Adlhart, Frey & Schneider, 1978; Schneider, 1980, 1981; Schneider & Graf, 1986). Structure factors can be measured with high precision in imperfect crystals because they may be ideally mosaic for high-energy X-rays. At the other extreme, appropriate materials show Pendell6sung fringes with high contrast. Integrated intensities in extinction-free crystals (Graf & Schneider, 1986; Alkire, Yelon & Schneider, 1982; Alkire & Yelon, 1981) have been used to determine structure factors as have Pendell6sung fringes in perfect crystals at 468.1,316.5 and 103 kev International Union of Crystallography

2 V. HOL~', S. CUMMINGS AND M. HART 517 All of these high-energy X-ray experiments have been done at fixed energies using very narrow nuclear )' lines; in this paper we describe the first exploratory experiments using white ),-radiation from a highvoltage microfocus source. Two sets of experiments, ene in the angle mode and the other in energydispersive mode, are described in this paper. Experimental arrangement The experimental arrangements used are shown in Fig. 1. All three major components, the X-ray source, diffractometer and germanium solid-state detector, are mounted on a robust vibration-isolated optical bench so that their relative positions can easily be changed between the two different modes of operation. All the axes, parallel-slit assemblies and goniometer heads can be operated remotely under microcomputer control. The X-ray source is a shielded but otherwise standard radiographic microfocus tube with either tungsten or molybdenum target. The 600 W of power is focused in an effective source mm in size. While the tungsten target gives the highest X-ray output, the molybdenum target has the advantage of a featureless Bremsstrahlung spectrum from the limit of the molybdenum K spectrum at 20 to 160 kev, which is ideal for energy-dispersive diffraction experiments. Scintillation counters with 5mm thick NaI(Th) crystals are approximately % efficient throughout the available energy range while the 10mm thick germanium solid-state detector's efficiency falls to about 50% at 140 kev, which is the highest energy used in these experiments. The parallel slits PS are made from long bars of molybdenum 5 mm thick separated by 0.4 mm spacers. They provide total attenuation of the direct beam in the forward direction S~ I I l I~v CS 1 Axis1 ta) ~ ( b ) Fig. 1. Experimental arrangements for high-energy diffraction: double-crystal mode; energy-dispersive mode. S microfocus X-ray source, PS parallel slits made from solid molybdenum, CR reference crystal, CS sample crystal, D germanium solid-state detector. even at Bragg angles of 1 and yet produce no fluorescent background in the 20 to 160 kev spectral range. For ease of alignment the long parallel slits can be translated normal to their lengths in the plane of diffraction. Double-crystal diffraction It is not feasible, with presently available X-ray sources, to select narrow energy bands of radiation with, say, A E/E ~ as in the case of X-rays from radioactive sources. Instead, high angular resolution can be obtained with broader energy bands (AE/E ~_ 4 x 10-3 with our molybdenum parallel slits) by working in the non-dispersive double-crystal geometry shown in Fig. 1. In practice, the problem of obtaining an ideally perfect first crystal is not too severe because the main motivation in these experiments is to study mosaic distribution in bulk materials, for example germanium and fluorite up to 25 mm thick or silicon in bulk as-grown samples. Since the reference crystal need be only about one extinction length thick (a few tenths of a millimetre), in all practical cases the rocking curve profiles will be dominated by features from the sample on the second axis. Beam size on the sample is approximately 0.4 x 4 mm high. Three different specimens were chosen to cover a wide range of typical problems. Float-zoned dislocation-free silicon is almost ideally perfect and has quite low X-ray absorption, permitting sample thicknesses of up to ram to be studied nondestructively. Bulk high-quality germanium cannot be studied in transmission at low energies and has a mosaic spread of about 1" arc, while synthetic fluorite grown by the Stockbarger method has a distinct mosaic subgrain structure covering a range of about " arc. This is typical of a wide range of materials such as the alkali halides and worked metals. Silicon rocking curves To explore the variation of intensity with energy two high-quality (111) wafers were prepared. They were 0-8 mm thick and oriented and cut for symmetric 2_20 Laue case in transmission. Fig. 2 shows the comparison between theory and experiment as a function of energy. In each case the theoretical doublecrystal rocking curve has been normalized to the same peak intensity as the experimental curve. The spectral band pass is determined by the collimation system and was about 160 ev at 40 kev, increasing to 560 ev at 140 kev which was the highest energy used in these experiments. The angular resolution is clearly much better than 1" arc and the intensity, between 200 and 1400 s-1, is very high compared with the intensities available in experiments with radioactive sources. For example, in double-crystal 111 Bragg reflections from silicon wafers approximately 30 mm thick, a

3 518 HIGH-ENERGY DOUBLE-CRYSTAL X-RAY DIFFRACTION ' I I -8 :8 _J-, I. +,k I.I sec arc Jf 4.,t ' 4, j, sec arc,i 41 't,,,,,,,,,m secarc (c) 250 Ci 198Au source at 412 kev gave about s-a and a peak width of 1" arc (Abdul Gani, Clark & Tanner, 1981) while 220 Bragg reflections from silicon wafers 4mm thick, using a 200Ci 192Ir source at 316"5 kev, gave about 5 s-1 in the same peak width and similar intensities were obtained from a wide range of mosaic samples including beryllium, aluminium and gold (Schneider, 1981), niobium, vanadium, pyrite and copper (Schneider & Graf, 1986). In all those experiments the beam was about 5-10mm 2 compared with 2 mm 2 in our experiments. Singlecrystal reflections, with a beam divergence of about 10" arc, yield intensities similar to those obtained at to 140 kev in double-crystal diffraction from the microfocus X-ray tube, i.e. approximately 0 s- 1. A major advantage of the white radiation source is that intensity can be gained at the expense of energy bandwidth in some experiments. Over the 40 to 140 kev energy range the Bragg width is proportional to the X-ray wavelength giving full widths at half maximum intensity (FWHM) ranging from 1.75 to 0"5" arc. The experimental rocking curve FWHM's are typically 0.2" arc wider than the theoretical curves, indicating a mosaic spread of about that amount. Germanium rocking curves Bulk germanium is opaque to X-rays at 10 kev. In Fig. 3 we have obtained double-crystal 2_20 rocking curves at 140keV from wafers 1.9 (Fig. 3a) and 26.5 mm thick (Fig. 3b). The crystal growth axis was [111]. It is clear that the mosaic spread increases from about 1" arc in the thin sample to 5" arc in the thick S-1 50 i,..,..., sec. arc. (d) S-l:.ii" " i' 't:.... ;.,' sec.arc "1":- 5. / "" sec. arc. (e) Fig. 2. Double-crystal rocking curves from thin high quality silicon at: 40; 75; (c) 90; (d) 120; and (e) 140keV. 220 Bragg reflection. #'~ 7".at sec orc Fig. 3. Double-crystal rocking curves at 140 key energy from: thin and thick germanium. 220 Bragg reflection.

4 V. HOLY, S. CUMMINGS AND M. HART 519 one; this is not unexpected, since in the thicker crystal the beam samples a greater length along the growth axis. In both experiments the first crystal was cut from the same boule and was only 0-9 mm thick. Thus, most of the information in the rocking curves relates to the second crystal. Calcium fluoride rocking curves Fluorite is chosen as a typical example of a strongly scattering mosaic crystal. As in the germanium example, the first crystal is thin (0"3 mm) while the sample crystal is thick (7-4 mm) so that the doublecrystal rocking curves are expected to be dominated by the sample characteristics. Two representative rocking curves indicating ten or so subgrains over an angular range of 120" arc are shown in Fig. 4. The instrumental angle resolution is 2" arc FWHM and the intensity is sufficiently high for mapping the reflectivity of large samples with a spatial resolution of 1 mm at the rate of one complete rocking curve per hour. lattice parameter variations Ad/d ~-10-4 can be detected. We have confirmed that result but note that modern microfocus X-ray generators offer a considerable gain in brightness over previous industrial radiography units. Whereas Bechtoldt et al. used 2 kw of power on a source effectively 4 x 4 mm in size, the present source is 30 times brighter. Thus, the three energy-dispersive spectra were obtained in 20 min from a specimen area 0.4 x 2 mm in size and a three-dimensional stress map imaging about pixels of millimetre scale size could be obtained in a day. However, with a synchrotron radiation source about one million times more flux is available and therefore large-area high-resolution imaging could be achieved. Fig. 5 shows very clearly that the normalized intensities from different regions vary considerably. This is a result of the strong preferred orientation which occurs in a recrystallized and highly stressed region and is being explored as a possible technique Energy-dispersive diffraction The apparatus can also be rearranged for energydispersive diffraction, as shown in Fig. l. Information about stress in bulk steel samples is of considerable industrial interest. As Bechtoldt, Placious, Boettinger & Kuriyama (1981) have shown, X-rays in the 60 to 160 kev energy range easily penetrate 10 mm thick steel samples and with present intrinsic germanium solid-state detectors 0 N 0 ~ 0 o ~, 0 ~ e..,:.j' lo0 kev S-1 1,50 ~ o 50 5'0 160 sec.or'c kev (b S--1 I 50".J 5'0 sec.arc. Fig. 4. Double-crystal rocking curves from two different regions of fluorite (CaF2) kev ( ) Fig. 5. Energy-dispersive diffraction patterns from 13 mm thick steel showing shifts due to strain and intensity variations due to preferred orientation: annealed steel; in a melted weld region; (c) within the heat-affected zone at the edge of the weld.

5 520 HIGH-ENERGY DOUBLE-CRYSTAL X-RAY DIFFRACTION for the non-destructive imaging of welds in field experiments. This approach, while less quantitative than lattice strain measurements, does not require a multichannel analyser and should therefore be much faster to use. Concluding remarks These preliminary experiments have shown that results previously obtainable only with 7-radiation from radioactive sources can be obtained equally well, but with greater speed and experimental convenience, using high-energy sealed-off X-ray tube sources. In addition energy-dispersive diffraction experiments can be mounted on the same source giving a greater dynamic range and higher material penetration than conventional sources or existing low-energy synchrotron radiation facilities. The relative advantages of 7-radiation sources in the to 400 kev range have been extensively debated in the literature cited. We have not yet explored any problems in crystallography which require radiation more penetrating than 140 kev. However, it is worth noting that sealed-off microfocus tubes are available in ratings up to 320 kev. One of us (VH) is grateful to the British Council and his home university for arranging the visit to Manchester University where this work was done. References ABDUL GANI, S. M., CLARK, G. F. & TANNER, B. K. (1981). Inst. Phys. Conf. Set'. No. 60, ADLHART, W., FREY, F. & SCHNEIDER, J. (1978). J. Phys. E, 1 l, ALKIRE, R. W. & YELON, Y. B. (1981). J. Appl. Cryst. 14, ALK1RE, R. W., YELON, Y. B. & SCHNEIDER, J. R. (1982). Phys. Rev. B, 26, BASTIE, D. & DOLINO, G. (1985). Phys. Rev. B, 31, BECHTOLDT, C. J., PLACIOUS, R. C., BOETTINGER, W. J. & KURIYAMA, M. (1981). Adv. X-ray Anal. 25, DEUTSCH, M., HART, M. & CUMMINGS, S. (1987). Appl. Phys. Lett. 51, FREUND, A. K. (1973). Dr rer nat thesis. Mfinchen Univ., Federal Republic of Germany and ILL, Grenoble, France. FREUND, A. K. (1988). Proc. Workshop Applications of High- Energy X-ray Scattering. ESRF, Grenoble, February, FREUND, A. K., HART, M. & SCHNEIDER, J. R. (1988). Nucl. Instrum. Methods, A266, GRAE, H. A. & SCHNEIDER. J. R. (1986). Phys. Ret'. B, 34, SCHNEIDER, J. R. (1980). Characterization of Crystal Growth Defects by X-ray Methods, edited by B. K. TANNER & D. K. BOWEN, pp New York: Plenum Press. SCHNEIDER, J. R. (1981). Nucl. Sin. Appl. I, SCHNEIDER, J. R., GONCALVES, O. D., ROLLASON, A. J., BONSE, U., LAUER, J. & ZULEHNER, W. (1988). Nucl. lnstrum. Methods. In the press. SCHNEIDER, J. R. & GRAF, H. A. (1986). J. Cryst. Growth, 7,