- Email: [email protected]
High resolution powder diffraction at HASYLAB
664
Nuclear Instruments and Methods in Physics Research A266 (1988) 664-667 North-Holland, Amsterdam
HIGH RESOLUTION
POWDER
DIFFRACTION
AT HASYLAB
Thomas WROBLEWSKI HASYLAB, DESY, Notkestrasse 85, 2000 Hamburg 52, FRG
Jorg IHRINGER
and Josef MAICHLE
University Tubingen, Charlottenstrasse 33, 7400 Tubingen, FRG
HASYLAB's beamline F1 was modified for powder diffraction in a triple-axis geometry. The diffractometer consists of two independent circles for 0 and 20 motion on either side of the beam. The 0 circle can be translated along its axis. This makes the instrument highly flexible for the installation of different attachments like a cryostat which was used for low temperature measurements on the new high T~ superconductors. Measurements on zeolites demonstrate the excellent resolution and signal-to-noise ratio. Novel measuring strategies concerning the use of multiple analyzers, the examination of phase transitions and anomalous dispersion are presented.
1. Introduction
2. I n s t r u m e n t a t i o n
In conventional powder diffraction with X-ray tubes or neutron sources focussing geometries are mainly being used. The nearly parallel beam of synchrotron radiation requires parallel beam optics, however. The Debye-Scherrer technique which was applied by Christensen et al. [1] at H A S Y L A B has such a geometry. Capillaries of about 0.1 m m diameter and a position sensitive detector at a distance of 1 m from the sample were used in these experiments. The small amount of material and the large sample to detector distance require a very intense source to collect data within a reasonable time. Therefore, these experiments are now performed with a focussed beam at the wiggler source. Another approach is that of Pardsh et al. [2] who used Soller silts for the collimation of the scattered beam. Best collimation is obtained if a single crystal analyzer is used as "receiving slit" as demonstrated by Cox et al. [3]. This triple-axis geometry consisting of monochromator, sample and analyzer, has dispersion not only between monochromator and sample but also between sample and analyzer, both affecting the peak width. This effect can be used to shift the minimum of the resolution function. We chose the triple-axis geometry for our high resolution powder experiments. Since phase transitions are one of the main objects of powder diffraction, a powder diffractometer has to be constructed in a way that allows easy installation of special sample environments. The design of our instrument at beamline F1 takes this into account.
The b e a m path of the experimental setup is shown in fig. 1. Behind the variable entrance slit system two Ge(111) crystals in nondispersive ( + , - ) setting serve as a monochromator. An ionisation chamber is used to monitor the intensity of the monochromatic beam. These elements, as well as the beam stop for the white beam are separated from the diffractometer by a wall of l e a d - a l u m i n i u m sandwiches. An evacuated beam tube between the monochromator and the sample reduces both absorption and background. The diffraction plane is oriented vertically, parallel to the X circle of an
0168-9002/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
///
\\
//// /
///
/
/~
// /
//
//
-/S I J [ 55 Fig. 1. Beam path of the powder diffractometer: SS = slit system, DCM = double crystal monochromator, IC = ionisation chamber, S = sample, SC = Soller collimator, A = analyzer, and D = detector.
T. Wroblewski et aL / High resolution powder diffraction
Eulerian cradle which works as a 2 O circle carrying the analyzer crystal, the detector and the Soller slits for collimation in the horizontal plane. A goniometer, offset along the 20 axis, is used as the 0 circle carrying the sample. This goniometer is not rigidly connected to the 20 circle but can be translated along the 0 axis simplifying the installation of accessories like a cryostat without having to move the components of the 20 circle. The advantages of this setup are clearly evident. - The time needed for a sample to reach equilibrium conditions inside a special environment can be used to collect data from a second sample mounted on the outside. - Several samples can be interchanged while the position of the analyzer remains fixed, allowing calibration of the diffractometer and correction for instabilities during the measurements (e.g. backlash, shifts in the beam position and drift of the monochromator). - Instead of moving the sample inside a special environment (low or high temperature, vacuum, high pressure, aggressive gases) the whole 0 circle can be rocked to reduce the influence of preferred orientation of crystallites.
665
against the actual experimental resolution, a germanium powder was chosen as the sample. Test experiments were then performed on germanium powder with a Ge(111) monochromator and a Ge(111) or Ge(511) analyzer. Fig. 2 shows both the theoretical and experimental resolution curves. In general, the experimental resolution is not quite as good as that given by theory. This is probably due to the limited quality of the Ge crystals which have a certain mosaic spread and do not show the ideal Darwin width. The larger discrepancy between theory and experiment for the 511 analyzer supports this assumption: the 111 crystal was cut from the center of a Ge rod while the 511 crystal was cut from its periphery where the concentration of crystal faults is expected to be higher.
4. S o m e r e c e n t e x p e r i m e n t s
A few examples demonstrating the potential of our instrument are given below. They will be reported in detail elsewhere. 4.1. Zeolites
3. R e s o l u t i o n
The peak width was calculated for the combination of several analyzer and monochromator crystals. The convolution of the divergence of the incoming beam and the Darwin widths of monochromator, sample and analyzer crystals was calculated numerically taking the final horizontal divergence behind the sample into account. To allow an easy check of these calculations
FWHM [degrees]
Zeolites containing mainly fight elements have relatively large unit cell constants for powder diffraction work (about 2 nm) and a low density leading to a low integral scattering power. This scattering power is distributed over a large number of peaks making zeolites a very sensitive probe for the resolution and signal-tonoise ratio of the instrument. In a collaboration with Baerlocher and Harvey from ETH, Zurich data were taken from three different beryllium zeolites. Fig. 3, showing a part of the diffraction pattern from zeolite B2, gives an impression of the capabilities of the instrument.
014 012 001 008 006
"=" ~,£~
OOt.
~ - ...... x..... x_~_:-Z . . . . . .
2500,
111
/.~ ~ ~x ~
~"
/~ / /
~/~ ~
-~ /.x / / "/ . / /'
150o
2000
511
y
..../
0.02
Z
0 0
90o 1000 1100 1200
Fig. 2. Experimental and calculated fwhm for Ge(111) and Ge(511) analyzer crystals. Solid line: theoretical fwhm for (111) analyzer. Dashed line and triangles: measured fwhm for (111) analyzer. Dash-double-dotted line: theoretical fwhm for (511) analyzer. Dash-dotted line and crosses: measured fwhm for (511) analyzer.
1000 500
24
25
26
27 28 2- THETA
29
30
Fig. 3. Part of the diffraction pattern of zeolite B2 at 0.14033 nm showing both resolution and signal-to-noise ratio of the instrument. IV(d). SCATTERING/DIFFRACTION
T. Wroblewski et al. / High resolution powder diffraction
666
xlO 3
4.2. Low temperature measurements R o o m temperature measurements o n BaPbo.75Bio.25 0 3 h a d already been performed last year before this substance turned out to b e one of the class of newly discovered high Tc superconductors. The profile was refined with a newly developed version of the Rietveld program which allows simultaneous refinement of several i n d e p e n d e n t data sets [4]. W e o b t a i n e d R values below 5%. This year we installed a cryostat to examine the superconducting phase of BaPb0.vsBi0.2503 below 13 K. We also determined b o t h the high a n d low temperature structure of three samples of Sr~ La = ~CuO 3 with x = 0.1, 0.2 a n d 0.3. While for x = 0.2 and x = 0.3 the structure was tetragonal, the sample with x = 0.1 turned out to be o r t h o r h o m b i c down to 12 K. F u r t h e r more, we collected data on two samples of the 90 K superconductor Ba2YCu309_y where y is approximately 2. O n the pure superconducting phase we measured the group of reflections (110), (103), (013) during cooling and heating. The choice of this group allowed us to follow the change of all three lattice c o n s t a n t s simultaneously. These peaks are located within 0.4 ° in 20. Therefore, scans over 0.8 ° in 20 were sufficient, taking less than 5 m i n per scan. Twenty scans were
A5 z,O 35 30
(c)/ /" //
,/.,
25
?"
<~ 20
(b).°
.."
15 05
./~
/./" *
~'~
"
..o-'~" ° I
50
100
150
200
250
300
T [°K ]
Fig. 5. Change of the lattice constants of Ba~YCu309_ v with temperature, a, b and c refer to the crystal axes.
d o n e d u r i n g cooling. Fig. 4 shows the diffraction pattern at 285 K (a) a n d 14 K (b). The zero shift was calculated from the whole p a t t e r n ( 2 0 ° - 1 3 0 ° ) measured at 14 a n d 300 K. T h e observed change in the lattice c o n s t a n t s is s h o w n in fig. 5. While the a a n d the b axes change only slightly the c axis shows a n unusually strong increase with temperature.
5. Future developments 1200
A new p o w d e r diffractometer is p l a n n e d at the b e a m l i n e C1 h a v i n g a toroidal focussing mirror with a cutoff energy of a b o u t 13 keV. Based o n the experience with the present i n s t r u m e n t it will also consist of two goniometers for O a n d 2 0 m o t i o n located o n either side of the beam. Both goniometers can b e m o v e d i n d e p e n dently along their r o t a t i o n axes allowing easy installation of different sample a n d detector arrangements, This m u l t i p u r p o s e i n s t r u m e n t will also allow time resolved studies [5]. F o r high resolution m e a s u r e m e n t s it
al
1000 80O
~ 600 Z
200 0 29.2
29 3
29.4
295 296 29.7 2 - THETA
298
29.9
30
1600 1400 1200
-/
',S,
-----7
w 1000
-~PSD
m 800 Z
D 600 O o 400 20o 0 29.2 29.3 294
/ 295 29.6 29,7 29.8
, 29.9 30
2 - T HETA
Fig. 4. Reflection group (110), (103), (013) of Ba2YCu3Og_yat 285 K (a) and at 14 K (b). The wavelength is 0.14033 nm.
Fig. 6. Arrangement of a group of identical analyzer crystals and a position sensitive detector (PSD). After a wavelength change only the circles carrying the assembly of analyzers and the PSD have to be rotated.
T. Wroblewski et al. / High resolution powder diffraction A
Fig. 7. Setup that uses the full horizontal divergence of an unfocussed beam. Monochromatization in the horizontal plane creates a wavelength gradient that can be used for anomalous dispersion measurements (the diffraction plane defined by sample and analyzer remains vertical). Monochromatization in the vertical plane does not create such a gradient but would allow simultaneous measurement of rays from different areas along the sample. (Symbols are the same as in fig. 1.)
offers the possibility of installing several analyzer-detector combinations simultaneously, allowing one to scan different 20 regions with different analyzer crystals, each of them having the minimum of the resolution function in the scanned region. A further reduction of measuring time can be achieved by combining sets of identical analyzers with a position sensitive detector, PSD (fig. 6). The crystals have to be arranged in a Guinier-like geometry along the circumference of a circle. The PSD will be placed on the rim of a goniometer whose axis coincides with that of the other circle. After alignment, the only requirement is to rotate these two circles through 0 and 2 0, respectively, if the wavelength of the incident beam is changed. In addition to this new instrument at beamline C1, we will continue to use beamline F1 for powder diffraction. F1 is an unfocussed beamline. To make full use of the 2 mrad horizontal divergence the detector will be replaced by a PSD which analyzes the horizontal distribution of the scattered radiation (fig. 7). This allows simultaneous measurements of different areas of the sample. Phase transitions can be followed within one
667
scan if a (thermal) gradient is put across the sample such that different phases are separated along the sample. In addition, data from different compounds can be taken at the same time. Monochromatization in the horizontal plane creates a gradient in the horizontal wavelength distribution. This allows simultaneous measurements around an absorption edge (fig. 7). Using a G e ( l l l ) monochromator the energy spread will be about 70 eV at 0.15 nm. This has to be compared with the typical range of absorption edges which is about 15 eV. The wavelength spread will cause only small zero point corrections in the order of the horizontal divergence of the primary beam. Corrections due to deviations from the mean Bragg angle in the horizontal plane are of second order and therefore negligible.
Acknowledgement We wish to thank K. Eichhoru for critically reading the manuscript. The support of the H A S Y L A B staff is gratefully acknowledged.
References [1] A.N. Christensen, M.S. Lehmann and M. Nielsen, Austral. J. Phys. 38 (1985) 497. [2] W. Panfish, M. Hart and T.C. Huang, J. Appl. Crystallog. 19 (1986) 92. [3] D.E. Cox, J.B. Hastings, T. Thomlinson and C.T. Prewitt, Nucl. Instr. and Meth. 208 (1983) 573. [4] J. Maichle and J. Ihringer, submitted to J. Appl. Crystallogr. [5] H. Arnold, High Resolution Powder Diffraction, ed., C.R.A. Catlow (Material Science Forum, 1986) Vol. 9, pp. 47-56.
IV(d). SCATTERING/DIFFRACTION
Nuclear Instruments and Methods in Physics Research A266 (1988) 664-667 North-Holland, Amsterdam
HIGH RESOLUTION
POWDER
DIFFRACTION
AT HASYLAB
Thomas WROBLEWSKI HASYLAB, DESY, Notkestrasse 85, 2000 Hamburg 52, FRG
Jorg IHRINGER
and Josef MAICHLE
University Tubingen, Charlottenstrasse 33, 7400 Tubingen, FRG
HASYLAB's beamline F1 was modified for powder diffraction in a triple-axis geometry. The diffractometer consists of two independent circles for 0 and 20 motion on either side of the beam. The 0 circle can be translated along its axis. This makes the instrument highly flexible for the installation of different attachments like a cryostat which was used for low temperature measurements on the new high T~ superconductors. Measurements on zeolites demonstrate the excellent resolution and signal-to-noise ratio. Novel measuring strategies concerning the use of multiple analyzers, the examination of phase transitions and anomalous dispersion are presented.
1. Introduction
2. I n s t r u m e n t a t i o n
In conventional powder diffraction with X-ray tubes or neutron sources focussing geometries are mainly being used. The nearly parallel beam of synchrotron radiation requires parallel beam optics, however. The Debye-Scherrer technique which was applied by Christensen et al. [1] at H A S Y L A B has such a geometry. Capillaries of about 0.1 m m diameter and a position sensitive detector at a distance of 1 m from the sample were used in these experiments. The small amount of material and the large sample to detector distance require a very intense source to collect data within a reasonable time. Therefore, these experiments are now performed with a focussed beam at the wiggler source. Another approach is that of Pardsh et al. [2] who used Soller silts for the collimation of the scattered beam. Best collimation is obtained if a single crystal analyzer is used as "receiving slit" as demonstrated by Cox et al. [3]. This triple-axis geometry consisting of monochromator, sample and analyzer, has dispersion not only between monochromator and sample but also between sample and analyzer, both affecting the peak width. This effect can be used to shift the minimum of the resolution function. We chose the triple-axis geometry for our high resolution powder experiments. Since phase transitions are one of the main objects of powder diffraction, a powder diffractometer has to be constructed in a way that allows easy installation of special sample environments. The design of our instrument at beamline F1 takes this into account.
The b e a m path of the experimental setup is shown in fig. 1. Behind the variable entrance slit system two Ge(111) crystals in nondispersive ( + , - ) setting serve as a monochromator. An ionisation chamber is used to monitor the intensity of the monochromatic beam. These elements, as well as the beam stop for the white beam are separated from the diffractometer by a wall of l e a d - a l u m i n i u m sandwiches. An evacuated beam tube between the monochromator and the sample reduces both absorption and background. The diffraction plane is oriented vertically, parallel to the X circle of an
0168-9002/88/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)
///
\\
//// /
///
/
/~
// /
//
//
-/S I J [ 55 Fig. 1. Beam path of the powder diffractometer: SS = slit system, DCM = double crystal monochromator, IC = ionisation chamber, S = sample, SC = Soller collimator, A = analyzer, and D = detector.
T. Wroblewski et aL / High resolution powder diffraction
Eulerian cradle which works as a 2 O circle carrying the analyzer crystal, the detector and the Soller slits for collimation in the horizontal plane. A goniometer, offset along the 20 axis, is used as the 0 circle carrying the sample. This goniometer is not rigidly connected to the 20 circle but can be translated along the 0 axis simplifying the installation of accessories like a cryostat without having to move the components of the 20 circle. The advantages of this setup are clearly evident. - The time needed for a sample to reach equilibrium conditions inside a special environment can be used to collect data from a second sample mounted on the outside. - Several samples can be interchanged while the position of the analyzer remains fixed, allowing calibration of the diffractometer and correction for instabilities during the measurements (e.g. backlash, shifts in the beam position and drift of the monochromator). - Instead of moving the sample inside a special environment (low or high temperature, vacuum, high pressure, aggressive gases) the whole 0 circle can be rocked to reduce the influence of preferred orientation of crystallites.
665
against the actual experimental resolution, a germanium powder was chosen as the sample. Test experiments were then performed on germanium powder with a Ge(111) monochromator and a Ge(111) or Ge(511) analyzer. Fig. 2 shows both the theoretical and experimental resolution curves. In general, the experimental resolution is not quite as good as that given by theory. This is probably due to the limited quality of the Ge crystals which have a certain mosaic spread and do not show the ideal Darwin width. The larger discrepancy between theory and experiment for the 511 analyzer supports this assumption: the 111 crystal was cut from the center of a Ge rod while the 511 crystal was cut from its periphery where the concentration of crystal faults is expected to be higher.
4. S o m e r e c e n t e x p e r i m e n t s
A few examples demonstrating the potential of our instrument are given below. They will be reported in detail elsewhere. 4.1. Zeolites
3. R e s o l u t i o n
The peak width was calculated for the combination of several analyzer and monochromator crystals. The convolution of the divergence of the incoming beam and the Darwin widths of monochromator, sample and analyzer crystals was calculated numerically taking the final horizontal divergence behind the sample into account. To allow an easy check of these calculations
FWHM [degrees]
Zeolites containing mainly fight elements have relatively large unit cell constants for powder diffraction work (about 2 nm) and a low density leading to a low integral scattering power. This scattering power is distributed over a large number of peaks making zeolites a very sensitive probe for the resolution and signal-tonoise ratio of the instrument. In a collaboration with Baerlocher and Harvey from ETH, Zurich data were taken from three different beryllium zeolites. Fig. 3, showing a part of the diffraction pattern from zeolite B2, gives an impression of the capabilities of the instrument.
014 012 001 008 006
"=" ~,£~
OOt.
~ - ...... x..... x_~_:-Z . . . . . .
2500,
111
/.~ ~ ~x ~
~"
/~ / /
~/~ ~
-~ /.x / / "/ . / /'
150o
2000
511
y
..../
0.02
Z
0 0
90o 1000 1100 1200
Fig. 2. Experimental and calculated fwhm for Ge(111) and Ge(511) analyzer crystals. Solid line: theoretical fwhm for (111) analyzer. Dashed line and triangles: measured fwhm for (111) analyzer. Dash-double-dotted line: theoretical fwhm for (511) analyzer. Dash-dotted line and crosses: measured fwhm for (511) analyzer.
1000 500
24
25
26
27 28 2- THETA
29
30
Fig. 3. Part of the diffraction pattern of zeolite B2 at 0.14033 nm showing both resolution and signal-to-noise ratio of the instrument. IV(d). SCATTERING/DIFFRACTION
T. Wroblewski et al. / High resolution powder diffraction
666
xlO 3
4.2. Low temperature measurements R o o m temperature measurements o n BaPbo.75Bio.25 0 3 h a d already been performed last year before this substance turned out to b e one of the class of newly discovered high Tc superconductors. The profile was refined with a newly developed version of the Rietveld program which allows simultaneous refinement of several i n d e p e n d e n t data sets [4]. W e o b t a i n e d R values below 5%. This year we installed a cryostat to examine the superconducting phase of BaPb0.vsBi0.2503 below 13 K. We also determined b o t h the high a n d low temperature structure of three samples of Sr~ La = ~CuO 3 with x = 0.1, 0.2 a n d 0.3. While for x = 0.2 and x = 0.3 the structure was tetragonal, the sample with x = 0.1 turned out to be o r t h o r h o m b i c down to 12 K. F u r t h e r more, we collected data on two samples of the 90 K superconductor Ba2YCu309_y where y is approximately 2. O n the pure superconducting phase we measured the group of reflections (110), (103), (013) during cooling and heating. The choice of this group allowed us to follow the change of all three lattice c o n s t a n t s simultaneously. These peaks are located within 0.4 ° in 20. Therefore, scans over 0.8 ° in 20 were sufficient, taking less than 5 m i n per scan. Twenty scans were
A5 z,O 35 30
(c)/ /" //
,/.,
25
?"
<~ 20
(b).°
.."
15 05
./~
/./" *
~'~
"
..o-'~" ° I
50
100
150
200
250
300
T [°K ]
Fig. 5. Change of the lattice constants of Ba~YCu309_ v with temperature, a, b and c refer to the crystal axes.
d o n e d u r i n g cooling. Fig. 4 shows the diffraction pattern at 285 K (a) a n d 14 K (b). The zero shift was calculated from the whole p a t t e r n ( 2 0 ° - 1 3 0 ° ) measured at 14 a n d 300 K. T h e observed change in the lattice c o n s t a n t s is s h o w n in fig. 5. While the a a n d the b axes change only slightly the c axis shows a n unusually strong increase with temperature.
5. Future developments 1200
A new p o w d e r diffractometer is p l a n n e d at the b e a m l i n e C1 h a v i n g a toroidal focussing mirror with a cutoff energy of a b o u t 13 keV. Based o n the experience with the present i n s t r u m e n t it will also consist of two goniometers for O a n d 2 0 m o t i o n located o n either side of the beam. Both goniometers can b e m o v e d i n d e p e n dently along their r o t a t i o n axes allowing easy installation of different sample a n d detector arrangements, This m u l t i p u r p o s e i n s t r u m e n t will also allow time resolved studies [5]. F o r high resolution m e a s u r e m e n t s it
al
1000 80O
~ 600 Z
200 0 29.2
29 3
29.4
295 296 29.7 2 - THETA
298
29.9
30
1600 1400 1200
-/
',S,
-----7
w 1000
-~PSD
m 800 Z
D 600 O o 400 20o 0 29.2 29.3 294
/ 295 29.6 29,7 29.8
, 29.9 30
2 - T HETA
Fig. 4. Reflection group (110), (103), (013) of Ba2YCu3Og_yat 285 K (a) and at 14 K (b). The wavelength is 0.14033 nm.
Fig. 6. Arrangement of a group of identical analyzer crystals and a position sensitive detector (PSD). After a wavelength change only the circles carrying the assembly of analyzers and the PSD have to be rotated.
T. Wroblewski et al. / High resolution powder diffraction A
Fig. 7. Setup that uses the full horizontal divergence of an unfocussed beam. Monochromatization in the horizontal plane creates a wavelength gradient that can be used for anomalous dispersion measurements (the diffraction plane defined by sample and analyzer remains vertical). Monochromatization in the vertical plane does not create such a gradient but would allow simultaneous measurement of rays from different areas along the sample. (Symbols are the same as in fig. 1.)
offers the possibility of installing several analyzer-detector combinations simultaneously, allowing one to scan different 20 regions with different analyzer crystals, each of them having the minimum of the resolution function in the scanned region. A further reduction of measuring time can be achieved by combining sets of identical analyzers with a position sensitive detector, PSD (fig. 6). The crystals have to be arranged in a Guinier-like geometry along the circumference of a circle. The PSD will be placed on the rim of a goniometer whose axis coincides with that of the other circle. After alignment, the only requirement is to rotate these two circles through 0 and 2 0, respectively, if the wavelength of the incident beam is changed. In addition to this new instrument at beamline C1, we will continue to use beamline F1 for powder diffraction. F1 is an unfocussed beamline. To make full use of the 2 mrad horizontal divergence the detector will be replaced by a PSD which analyzes the horizontal distribution of the scattered radiation (fig. 7). This allows simultaneous measurements of different areas of the sample. Phase transitions can be followed within one
667
scan if a (thermal) gradient is put across the sample such that different phases are separated along the sample. In addition, data from different compounds can be taken at the same time. Monochromatization in the horizontal plane creates a gradient in the horizontal wavelength distribution. This allows simultaneous measurements around an absorption edge (fig. 7). Using a G e ( l l l ) monochromator the energy spread will be about 70 eV at 0.15 nm. This has to be compared with the typical range of absorption edges which is about 15 eV. The wavelength spread will cause only small zero point corrections in the order of the horizontal divergence of the primary beam. Corrections due to deviations from the mean Bragg angle in the horizontal plane are of second order and therefore negligible.
Acknowledgement We wish to thank K. Eichhoru for critically reading the manuscript. The support of the H A S Y L A B staff is gratefully acknowledged.
References [1] A.N. Christensen, M.S. Lehmann and M. Nielsen, Austral. J. Phys. 38 (1985) 497. [2] W. Panfish, M. Hart and T.C. Huang, J. Appl. Crystallog. 19 (1986) 92. [3] D.E. Cox, J.B. Hastings, T. Thomlinson and C.T. Prewitt, Nucl. Instr. and Meth. 208 (1983) 573. [4] J. Maichle and J. Ihringer, submitted to J. Appl. Crystallogr. [5] H. Arnold, High Resolution Powder Diffraction, ed., C.R.A. Catlow (Material Science Forum, 1986) Vol. 9, pp. 47-56.
IV(d). SCATTERING/DIFFRACTION