High pressure research with synchrotron radiation

Nuclear Instruments and Methods 208 (1983) 563-568 North-Holland Publishing Company

563

HIGH PRESSURE RESEARCH WITH SYNCHROTRON

RADIATION

B. B U R A S Physics Laboratory 11, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen and Riso National Laboratory, DK-4000 Roskilde, Denmark

1. Introduction The use of high pressure as a parameter for the investigation of solid state phenomena has become increasingly important in recent years for basic and applied solid state physics and geophysics. Modern band calculations enable predictions of the properties of solids under high pressure that can be tested by experiments. In particular, special attention is at present devoted to structural changes, the fluctuating valence in rare earths, actinides and their compounds, and to insulator-metal transitions [1]. The highest attainable static pressure for powder samples [2] equals 1.7 Mbar (170 GPa) and corresponds to the pressure at approximately 3000 km depth in the earth, which is within the earth's core. Laboratory high pressure experiments can thus be used for studies of geophysical problems under conditions simulating those at the core-mantel boundary. High pressure research needs: (1) means of producing and maintaining the high pressure, and (2) a probe to study the sample in the high pressure envrionment. In this paper we restrict ourselves to diamond-anvil high pressure cells and X-rays as a probe for structural studies by means of diffraction techniques. However, parts of the discussion apply to other types of cells as well, and to powder diffraction in general. The aim of the discussion is to illuminate some problems encountered in this type of research when a storage ring is used as a source of X-ray radiation. The quantitative part of the discussion deals with orders of magnitude and thus to simplify it several crude approximations have been made. First we describe very briefly a typical diamond-anvil high pressure cell and indicate the limitations imposed by it on X-ray diffraction studies. Secondly we review briefly the angular-dispersive and energy-dispersive powder diffraction techniques and discuss in some detail the spectral distribution of the beam incident on the sample and the consequences of the limitation in the scattering angle. The requirements for the synchrotron radiation source and the instrumentation are mentioned. The paper ends with a brief summary. 0167-5087/83/0000-0000/$03.00 © 1983 North-Holland

2. The diamond-anvil high pressure cell and the limitations imposed by it on X-ray diffraction studies. In recent years diamond-anvil cells have been developed and used for X-ray diffraction studies in the hundreds kilobar and megabar range of static pressures [1,2]. Fig. 1 shows the principle of such a cell. The sample is placed in a small hole 0.1-0.3 mm in diameter made in an about 0.01-0.1 mm thick metal foil (gasket). The pressure is exerted by the two flat diamond faces pressed against each other. To ensure hydrostatic or semi-hydrostatic conditions an appropriate liquid (e.g. a mixture of 4 : 1 methanol/ethanol by volume) is added and usually a small ruby crystal. The wavelength of the fluorescence line R l (~ = 6942 ,~) of the latter is pressure dependent and enables pressure calibration. The main limitations imposed by the high pressure cell on X-ray diffraction studies are the following. a. the absorption of the incident and diffracted beams by the diamonds, DIFFRACTED BEAM

BEAM

Fig. 1. The principle of a diamond-anvil high pressure cell. Vll. SCATTERING/DIFFRACTION/RELATEDTECHN.

564

B. Buras / High pressure research

b. the limitation in the scattering angle, c. the small cross-section and the small volume of the sample.

angle-dispersive: p ~ . ) = i(Xo)X4oT(Xo) , , si--nO--n-si-n 20-~ Rt"'" ( j l F I 2 ) H '

(2a)

energy -dispersive." 3. Diffraction techniques

p ( . ) = i ( X H ) X 4 H " T(XH) si-~ 0o- s-~n} ~ ° R(e)(jlFIZ)H,

As is well known, there exist two diffraction techniques for powdered samples; they are schematically illustrated in fig. 2. In the angle-dispersive method a monochromatic beam of wavelength X0 is selected from the white SR by means of a crystal monochromator and the intensity of the beam diffracted by the powdered sample is measured as a function of the scattering angle 20. In the energy-dispersive method [3] the scattering angle 200 is fixed and the white SR beam is impinging on the sample. The wavelength (photon energy) composition of the diffracted beam is analysed by means of a solid state detector (SSD). Because of the fixed scattering angle the energy-dispersive method is especially suitable for diffraction studies of samples in special environments and is at present widely used for high pressure research. The Bragg equations for the two methods are angular-dispersive: d n = k o / 2 sin OH,

(la)

energy-dispersive: (lb)

( d denotes the interplanar spacing, E the photon energy and H the set of reflection indices HKL). The integrated intensities [4] can be expressed in the following way suitable for our discussion:

o-

white be am ~,~., crystal j monochrom~ ' monochrom ),o beam 1

Energy-dispersive e-

©

t white beam

E -I monitor

sample ~

~"etect or )'o = const. 20 = variable 2 d H K L •sin OHK L = )'o

with R (a) = AX0/X 0, and R (e) = cot 00 • A00,

(2c)

where i(X) is the number of p h o t o n s / s , cm 2 and per unit interval of wavelength incident on the sample, T(X) the transmission factor, A00 the the overall divergence of the beam in the energy dispersive method, and C a constant depending on the geometry of the experiment, sample volume and unit cell volume. R (a) and R (e) determine the relative wavelength band widths related to reflections in both methods, respectively. In order to simplify our discussion we assume that R (a) = R (~). For the same reason we neglect the polarization factors and detector efficiences. We are, of course, interested only in the (jIFHDH values, but we measure, as can be seen from eqs. (2), these values "modulated" by factors M~o,= i ( X o ) " # o r ( X o ) si--n0-n- - ~ 2"0H and

d H = XH/2 sin 00 = 6.199 keV. A l E H • sin 00

Angle- dispersive

(2b)

X :variable 20o=const. 2dHK L sin Oo= XHK L .

Fig. 2. X-ray powder diffraction techniques using synchrotron radiation.

M~¢)_ i(XH)X4H " T(XH) sin00-sin200 '

(3)

in the angle-dispersive and energy-dispersive methods, respectively. In the next section we discuss the dependence of the modulation factors on wavelength and angle.

4. Modulation factors We discussed first the dependence of i(X)X4T(X) on wavelength, and in order to simplify the discussion further we do not take into account the absorption in the sample. Fig. 3 shows, as an example, i(X) and i(X)X4 at the position of the sample located at the electron orbit plane 40 m from the bending magnet source point of DORIS (5 GeV, 1 mA, R = 12.12 m, E¢ = 22.88 keV). The figure also shows T(X) for an empty cell composed of two diamonds, each 2.5 mm thick. We notice that i(X)X 4 favours long wavelengths and T(X) the short ones, as expected. As a result i(x)XnT(X) reaches a maximum at about 0.8 A ( - 15 keV) and falls off very rapidly on both sides. The character of the i(X)X4T(X) curve does not change if one uses a multipole wiggler source instead of

565

B. Buras / High pressure research

15

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~

''~:c=11"4/* k e Y - - / Ec=z.,5.75 keY ~ 0.4

0.2

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L 1.4

1.6

Fig. 4. i(X)X4T(X) as function of wavelength for two critical eenrgies, 11.44 keV and 45.75 keV, showing the shift towards shorter wavelengths for higher critical energies.

wavelength for a critical energy % = 22.88 keV (see text).

a bending magnet source of the same critical wavelength, although all values of i(X)X4T(X) increase by a constant factor equal roughly to the number of poles, resulting in a decrease in measuring time. A single-bump wavelength-shifter shifts, however, the curve towards shorter wavelength, as can be seen from the example in fig. 4. Accepting a small decrease at long wavelengths one obtains a large gain at short wavelengths (e.g. at = 0.2 .~ the gain factor is about 20). We discuss now the influence of the modulation factor on the X-ray pattern beginning with the energydispersive method. Fig. 5 shows, as an example, M ~ e) as a function of the interplanar spacing for two scattering angles 10 ° and 20 °. In the region 0.5 ,~ < d < 4 A the modulation factor changes by several orders of magnitude. This has two effects. The accuracy of measurements due to the statistics is very different for different parts of the pattern, decreasing the overall accuracy of the measurements. The obtaining of a large count rate for reflections corresponding to small modulation factors by increasing i(X) (e.g. by using a multipole wiggler) might be prevented by saturation effects in the solid state detector caused by reflections corresponding to large modulation factors. Thus the only remedy might be the use of longer exposure times. In the angle-dispersive method one might tend to use a wavelength corresponding to the maximum of

i(X)X4T(X) curve. However, as can be seen from fig. 6 the limitation in the scattering angle restricts from below the range of measured interplanar spacings. If one is not able to increase 20,1, x by a proper design of the

,

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11 1 2 3 /, INTERPLANAR SPACING (/~)

Fig. 5. The modulation factor for the energy-dispersive method M (e) = i(X)X4T(X)/sin 200.sin O0 as a function of the inter-

planar spacing for two scattering angles l0 ° and 20 °. VII. SCATTERING/DIFFRACTION/RELATED TECHNIQUES

566

B. Buras / High pressure research ,

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Fig. 6. The modulation factor for the angle-dispersive method M (e) = i()~o))~4oT()~o)/Sin 0.sin 20 as a function of the interplanar spacing for three different wavelengths.

pressure cell, then one is forced to use shorter wavelength with a smaller I()%))~40T()~0) value leading to an increase of the measuring time. As can be seen from fig. 6 the m o d u l a t i o n factor changes also rapidly in the angle-dispersive method, however, less rapidly than in the energy-dispersive method.

5. The incident spectrum As can be seen from formula (2b), for energy-dispersive diffraction one needs to know i ( h ) in order to derive the structure factors from the measured integrated intensities. In this respect SR sources have a great advantage over X-ray tubes because the spectrum is smooth * a n d calculable [5,6]. However, it is necessary for the calculations to know precisely the position of the sample relative to the electron orbit plane. Fig. 7 shows a family of spectral distributions as seen by a slit 0.2 m m of height located 40 m from the source p o i n t at different vertical distances from the electron orbit plane. The calculations were m a d e for D O R I S working at 5 G e V and 1 m A ( R = 12.12 m, E c = 22.88 keV). One sees from the figure that in the wavelength region of interest, an elevation of 1 m m at a distance of 40 m from the source point causes already an appreciable change in * It was pointed out [7] that the spectrum from a multipole wiggler might show some wiggles for )~ > ~c, in particular when seen by a small sample, which is the case in high pressure experiments. This point needs clarification.

w

U3ZE

gE

SE

-rr ! o_(:3

7 0

50 100 PHOTON ENERGY (keY)

Fig. 7. The spectral distribution of the incident beam as seen by a slit 0.2 mm of height located 40 m from the source point at different distances h from the electron orbit plane.

the spectrum (and a smaller change in polarization). This points to the necessity of a precise positioning of the high pressure cell. It requires also appropriate position and angular stability of the source. The above quoted calculations were m a d e for a point source. A real extended source will cause some smearing.

6. The small cross-section and small volume of the sample In order to avoid diffraction lines from the gasket, obscuring the X-ray pattern, a n d in order to keep the b a c k g r o u n d as low as possible, it is m a n d a t o r y that the X-ray b e a m hits the sample only. In recent experiments at H A S Y L A B [8] at pressures up to 300 k b a r the b e a m cross-section was typically 0.1 × 0.1 m m 2. In the megab a r region these dimensions must be even smaller. This points to b o t h (1) the necessity to use a very good collimated incident beam, a n d (2) a high precision of the m o v e m e n t s of the high pressure cell in the vertical a n d horizontal planes. As concerns the latter, for example, in the diffractometer at H A S Y L A B [9] these movem e n t s can be done in steps of 1 / 6 of a micrometer. The collimation of the incident b e a m is defined by (1) the source dimensions, (2) the sample dimensions, a n d (3) the distance between the source and the sample. F o r ox = % = 1 mm, typical for most of the present

B. Buras / High pressure research

machines, a 0.1 x 0 . 1 m m 2 slit in front of the high pressure cell and a 30 m source-sample distance, the collimation in the horizontal and vertical plane amounts to about 0.03 mrad or 7 seconds of arc, It is a sufficient collimation which indicates that - at least at present high pressure energy-dispersive diffraction experiments do not need smaller size sources. It indicates also that for collimation reasons the horizontal and vertical scattering planes are equivalent. They differ, however, as concerns polarization and, as it is well known, a vertical scattering plane is preferable. For angle-dispersive diffraction one might focus the beam on the sample and then a small source size is important. The volume of the sample, as already mentioned, is very small ( 1 0 - 3 - 1 0 5 mm3), which especially in powder diffraction results in a very small intensity of the diffracted beams and thus increases the measuring times. For example, recently reported measurements with - 5 X 10 -4 mm 3 powdered samples performed with an X-ray tube using monochromatic radiation and a film recording technique required an exposure of 4 - 1 6 days [10]. This points to both the necessity of using more intense X-ray sources and less time consuming measuring techniques. A synchrotron radiation source and the energydispersive method has proved to be a good solution to this problem. In recent experiments at H A S Y L A B [5] using a diamond anvil cell and a sample of the same volume of 5 x 10 -4 mm 3 X-ray energy-dispersive patterns with 10 4 counts peak height were obtained in 500 s (fig. 8). Assuming the same absorption in the cell one could reduce the several days exposure time, mentioned above, by a factor of hundreds with a probably better peak to background ratio. It follows from the discussion above that small samples require for energy-dispersive diffraction a source of high brightness (number of photons per second and unit solid angle) and for angle-dispersive diffraction a source of high brilliance (number of p h o t o n s / s - m m 2 of the source and unit solid angle). The small volume of the sample does not only affect

X I0 ~

COUNTS

2.5

10.1 t

YbH~ ~ 8 . 2 GPa 20 = 14,5 ° DORIS/HASYLAB 4 GeV 30 m A

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21-2

20.0 11-2 20.2

21.1 10.4

YbK --~-

0.0 10

20

30

40 50 E(PHOT) key

60

Fig. 8. X-ray diffraction pattern of YbH 2 at 28.2 OPa in a diamond anvil cell obtained in 500 s using synchrotron radiation from the DORIS storage ring at HASYLAB, Hamburg [8].

567

the intensity of the diffracted beams but makes also the measured integrated intensities not very reliable. Such a sample contains a small number of grains which together with the very good collimation of synchrotron radiation leads to a small number of crystallographic planes in the reflection position. Thus the measured integrated intensities depend rather accidentally on the spatial orietation of a very limited number of grains. The obvious remedies are: (1) relaxation of the collimation but this leads to broadening of the peaks, (2) small grain size but this leads also to peak broadening, (3) c o l l e c t i o n of the i n t e n s i t y f r o m the w h o l e Debye-Scherrer ring, and (4) rotation of the cell around the indident beam.

7. Summa~ For energy-dispersive diffraction from samples at high pressure it is important that the source is of high brightness and the emitted radiation has a smooth spectrum, which can be calculated providing that some precautions are taken as concerns the positioning of the sample at the orbit plane. Single-bump wavelength shifters and multipole wigglers shifting the spectrum a n d / o r increasing the brightness make these devices a flexible tool which can produce the required spectrum for a given experiment. However, regardless of the source the X-ray pattern is strongly modulated by the factor i()~))dT(X) which decreases the accuracy of measurements. For angle-dispersive diffraction it is important that the source is of high brilliance and the smoothness of the spectrum of the emitted radiation is of lesser importance. The possibility of using any wavelength within a large interval enables to choose the most suitable wavelength for a given experiment, which is especially important in high pressure research because of the limitations in the scattering angle. This amplifies also the usefulness of multipole wigglers as a first optical element. The X-ray pattern is modulated by the factor (sin 0. sin 2 0 ) - 1 in the usual way, but this modulation is not so strong as in the energy-dispersive case, and can be calculated with high accuracy. The resolution problem was not discussed in this paper, however, it might be in place to recall the known fact that the angular-dispersive method can achieve a better resolution than the energy-dispersive one. The latter produces, however, simultaneously the whole Xray pattern and not reflection-by-reflection as the angle-dispersive method does. In this connection the use of position sensitive detectors and the angular-dispersive method for fast X-ray diffraction by samples at high pressures might be considered [11].

VII. SCATTERING/DIFFRACTION/RELATED TECHNIQUES

568 The author is H A S Y L A B ) for financial support search Council is

B. Buras / High pressure research

indebted to Dr B. SchOnfeld (DESYhelp in computer calculations. The of the Danish Natural Sciences Regreatly appreciated.

References [1] See, for example, Physics of solids under pressure, eds., J.S. Schilling and R.N. Shelton, (North-Holland, Amsterdam, 1981) and references therein. [2] H.K. Mao and P.M. Bell, Science 200 (1978) 1145. [3] E. Laine and I. L~ihteenmaki, J. Mat. Sci. 15 (1980) 269.

[4] B. Buras and L. Gerward, Acta Cryst. A31 (1975) 372. [5] C. Kunz (ed.), Synchrotron radiation techniques and applications (Springer, Berlin, 1979). [6] B. Buras, L. Gerward, A.M. Glazer, M. Hidaka and J. Staun Olsen, J. Appl. Cryst. 12 (1979) 531. [7] R. Coisson, S. Guiducci and M.A. Preger, Nucl. Instr. and Meth. 201 (1982) 3. [8] J. Staun Olsen, B. Buras, L. Gerward, B. Johansson, B. Lebech, H. Skriver and S. Steenstrup, in ref. 1, p. 305. [9] J. Staun Olsen, B. Buras, L. Gerward and S. Steenstrup, J. Phys. El4 (1981) 1154. [10] K. Mao, P.M. Bell, J.W. Shaner and D.J. Steinberg, J. Appl. Phys. 49 (6) (1978) 3276. [11] H. G6bel, Adv. X-ray Anal. 24 (1981) 187.