29, 71-80. RSCU-SOS- a rapid searching and centering utility routine for single-crystal X-ray diffraction studies at simultaneous high pressures and temperatures.
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PROGRAMS
J. Appl. Cryst. (1996). 29, 71-80
R S C U - S O S - a rapid searching and centering utility routine for single-crystal X-ray diffraction
studies at simultaneous high pressures and temperatures YUSHENG ZHAO, DAVID SCHIFERL AND J. M. ZAUG at Los Alamos National Laboratory, Los Alamos, NM 87545, USA
(Received 20 January 1995; accepted 26 April 1995)
Abstract
Single-crystal diffraction studies conducted in a diamond-anvil cell (DAC) under high pressure (P) and temperature (T) conditions often have the annoying problem that the sample orientation changes when P and/or T is changed. It is essential to quickly find and recenter the diffraction peaks in order to refine a new orientation matrix and further collect diffraction data from the single crystal at the changed P-T conditions. This paper presents a rapid searching and centering utility (RSCU) routine to deal with the orientation-shifting problem in highP-T DAC single-crystal diffraction studies. The RSCU routine starts with a refined reflection list from previous P-T conditions and conducts a search in the pattern of a spiral of open square (SOS) for diffraction peaks in the X--9 plane. Following the peak search, it conducts 20, to and X scans to center the diffraction peaks and then performs a least-squares curve fit to refine the true diffraction positions in 20, to, X and ~0space. The RSCU routine incorporates the Hamilton method to eliminate errors due to sample misalignment. Reflections are sorted to minimize the driving time between successive peaks. The algorithm of the routine is given in symbolic logic so that it can be translated and inserted into other crystallographic software packages.
1. Introduction
The study of physics and chemistry of materials under highpressure (P) and temperature (T) conditions demands accurate structural information on the sample substance. Under truly hydrostatic pressures, single-crystal diffraction provides the most accurate structural refinement among various X-ray crystallographic techniques (lOng & Finger, 1979); however, when single-crystal diffraction experiments are conducted at simultaneous high pressure and temperature (high P-T), several problems become critical, including: (i) modification of the orientation matrix of the crystal owing to compression or expansion of the unit cell; (ii) changes in crystal alignment during variation of pressure and temperature; (iii) drills in sample orientation over time, usually over periods of many hours. In all cases, it is important to find a new orientation matrix very quickly so that all measurements are made under the same P-T and orientation conditions. It is difficult to hold a crystal firmly in place in a high-P-T DAC while maintaining hydrostatic pressure conditions. In order to avoid permanent deformation of the sample crystal, it is © 1996 Intemational Union of Crystallography Printed in Great Britain - all rights reserved
necessary to use a pressure medium, such as argon, neon or helium, which is chemically inert and hydrostatic or very nearly so for the experimental range of pressures and temperatures. The sample crystal is usually fixed to one diamond anvil with a small amount of very-high-viscosity silicone fluid or surrounded by several smaller crystals of much sorer substances to restrict its motion in the sample chamber without the introduction of nonhydrostatic stresses. These procedures are only moderately successful in controlling the orientation of the crystal. On the one hand, we have found that the orientation of a crystal in the DAC is maintained nearly perfectly for at least 8 h, during the diffraction measurements, while the diffractometer angles X and ~o are driven 'randomly' through essentially theft full ranges of motion (throughout this paper, we follow the angle conventions for four-circle diffractometers developed by Busing & Levy, 1967). However, the X and tp angles of a diffraction peak can still drift as much as 3-5 ° while the DAC sits overnight. The simplest way to reduce the overnight crystal drift is to park the DAC so that the crystal rests on the horizontal surface of the diamond anvil. However, this does not completely solve the sample-drifting problem. Furthermore, the time required for measurements in a high-P-T DAC single-crystal diffraction study must be as short as possible to minimize pressure and temperature drift during the experiment. The conventional netsearching and steep-slope centering routines most frequently used in crystallographic studies (Busing, 1970) are not well suited to high-P-T DAC single-crystal diffraction studies. It is difficult to preset the scan range and grid size for net searching and it takes too long to finish the scan of a whole net frame in 20, to, X and ~ospace. The steep-slope centering routine is slow and often confused by polycrystalline diffraction rings from the gasket. For these reasons, we found it necessary to develop a rapid searching and centering routine to follow and to maximize the intensity of single-crystal diffraction peaks. We present here a novel routine for rapid peak searching and centering for either weak or strong peaks in the presence of powder diffraction tings and other uneven backgrounds, starting with an orientation matrix that is accurate to within about 10° in ) and ~o. The rapid searching and centering utility (RSCU) routine involves the following steps: (i) the initial peak search is conducted using the efficient spiral-search approach often used in aft-sea rescue missions, where the scanning grid is automatically resized according to whether or not the peak is found and no time is wasted on finishing the search once there is evidence of the peak; (ii) the peaks are closely centered in a constant self-learning mode, which successively adjusts the sizes of the centering regions as well as the scan steps for the angles 20, to and Z,
Journal of Applied Crystallography ISSN 0021-8898 © 1996
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distinguishes the peak from background and maximizes the peak intensity in the shortest time; (iii) the final set of scans of the 20, tO and X angles are stored and have an auto-adjustable sampling time and peak-width scaling to give satisfactory counting statistics and to cover an optimum angular range for curve fitting. The RSCU routine incorporates a number of other important features: (i) For each peak, the Koq-Kot 2 doublet is fitted with the known dispersion and fixed relative intensity, using the approach of Finger (1992). The d spacings (and hence the lattice constants) are based on the fitted 20 values for 2(Kcrl) and thus implicitly on 2(Kt~2) , as well. (ii) Errors due to sample miscentering are eliminated by the use of the eight-position or four-position Hamilton (1974) technique. (iii) The list of reflections and Hamilton settings for each reflection are sorted to minimize the driving time between peaks for the final scans during curve fitting. (iv) At the end of a set of measurements, the centering of the first peak is repeated to ensure that the sample orientation in the DAC has not changed; if it has, the entire set of reflections will be discarded. (v) Temperatures determined from thermocouples are constantly monitored and automatically recorded before and after each peak position is measured. The RSCU routine has been developed for simultaneous high-pressure and temperature single-crystal X-ray diffraction experiments with a Huber four-circle diffractometer. It is much more successful than the conventional procedure in quickly, automatically and accurately finding, centering and fitting diffraction peaks. We have successfully applied the RSCU routine to the collection of single-crystal diffraction data of MgSiO3 orthoenstatite at pressures up to 4.6 GPa and temperatures as high as 1001 (1) K using a special high-P-T DAC (Schiferl & Zhao, 1995; Zhao, Schiferl & Shankland, 1995). A crystal of NaC1 in the sample chamber serves as an in situ high-temperature pressure standard (Decker, 1971). Data from orthoenstatite at 1.51 ( 2 ) G P a and 1001 ( 2 ) K are provided to illustrate the implementation of the RSCU routine.
PROGRAMS
Peak Search on Chi-Phi (wide open slits) -
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Peak Search on Chi-Phi Plane (Wide Open Slit~ 1200 ....
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2. RSCU routine 2.1. Peak searching - SOS (spiral open square) The diffraction peak of a single-crystal at an angular position of (200, tOo, Xo, ~o0)may move to a new angular position of (201, o9], Xl, tp]) because of changes in pressure and temperature or due to the overnight drift of the crystal in the high-P-T DAC. It has been observed that such angular movement is most severe for X and 9, which can change as much as 3-5 °. The angular positions of 20 and to are relatively stable with perturbations typically less than 0.3-0.5 ° . For these reasons, peak searching should concentrate on the X--9 plane. The RSCU routine fixes the angles of 20 and to at 200 and to = 0, respectively, since to [the deviation of the angle 0 from its bisecting position of 20, i.e. tO = ( 0 - 20/2)] is very close to zero in most practical cases. From inspiration by the search patterns practiced in airsea rescue missions, the peak search is performed in the X--9 plane in the fashion of a spiral open square (SOS) (Fig. la). The slits behind the detector collimator should be kept wide open.
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(b) Fig 1. The spiral open square (SOS) search for the single-crystal diffraction peak. The starting point of the SOS search is the peak position (200, O9o,Xo, ~Oo) of previous P-T conditions. The initial grid of the search is 0.5 ° per step. The new search with the reduced (to half) step size begins at the shifted (by half of the new step size) position of the maximum intensity of the old search. Subsequent searches have higher (by a factor of 2N, up to N = 4) step resolutions and will eventually catch the diffraction peak. The peak (200, o~0, X01, ~001) can be resolved with a step resolution of 0.03-0.04 ° in the X-9 plane. (a) The path of the SOS search on the X--9 plane. Notice the reduction of the step size and the shift of the starting point of the new X--9 scans. (b) The diffraction intensity of the SOS search on the X--9 plane. Notice that the new SOS search with redueed (to half) step size starts after no higher intensity is found in the last loop of the X-9 SCanS,
COMPUTER PROGRAMS The collimator has a hole with diameter 0.3 m m and length 60 m m in our system (with distance to the sample 140 mm), which serves as a scatter shield to block X-rays scattered from other components of the high-P-T DAC. The SOS starts from X0 and ~00 with a preset rough scanning grid of 0.3-0.5 ° in the X-IrZrMAXf0THEN VIJMAX=VIJ
CHMAX(I)--CH(VI) n,rrMAX 0)=ncrP(vI) END IF NEXT VI
A2. Codes S U B RSCU-SOS
OPEN "REFLST.SAV" FOR INPUT AS #1 FOR I=1 TO N INPUT #I, I-IKL0),HAM(1) INPUT #1, TT(I),OM(I),CH(I),PH(I) INPUT #1, INTMAX(I) NEXT I CLOSE #I
* Conducts spiral open square (SOS) search on the X--~ plane
* Read in reflections from file
TOBS=I.0
Z(1)--CINT(TTNEW) Z(E)=Cn~r(OMNSW)+0.5 Z(3)=CINT(CHNEW) z(4)=Clrcr(am,rEW) CALL DRVMOT(Z()) CALL INTENSCrOBS,CPS)
* Scan ~0angle VMOT=4 PHMAX(I)=PHNEW FORVJ=I TO NSTP PH(VJ)=PHNEW+STPSZ*VJ ANGSCN=PH(VJ) CALL SCNMOT(VMOT, ANGSCN) * Intensity measureCALL INTENS(TOBS,CPS) ment INTP(VJ)--CPS IF INTP(VJ)>INTMAX(I) THEN
VIJMAX=VI J PHMAX(I)=PH(VJ) INTMAX(1)=INTP(VJ) END IF NEXT VJ
FOR I=1 TO N
TTNEW=TT0) OMNEW=OM(I) CHNEM=CH(I) PHNEW=PH(I)
CALL RDANGLCrT,OM,CH,PH) * Set starting angular position
CHNEW=CH PHNEW=PH
* Reset maximum intensity
* Read angles at INTMAX of last scan; reset the new start at the current angles
* Counting time for background
STPSZ=-STPSZ
* X--9 scan loop turnaround
* Make sure away from peak
IF VIJ>VLIMAX+2 THEN
* A whole scan loop after VJPMAX * If all INPT< INTMAX then ... * Reduce X--~ grids to haiti * Shift to avoid overlap scan * Reset X - ~ maximums + shiR as start position of new scan
IF INTMAX(I)>THRSHLD THEN * Drive diffractometer to BG target * Measure background intensity
STPSZ=~S(STPSZ)/2 SmrT=~a3S(S~SZ)/2
INTBG=CPS CHNEW=CHMAX(I)+SHIFT THRSHLD= 100 IF 3*INTBG>100 THEN THRSHLD=3*INTBG ENDIF
* Reset maximum intensity
PHNEW=PHMAX(I)+SHIFT * It may be 5*INTBG or so
IF STPSZINTMAX THEN IJKMAX=IJK INTMAX=INTP(IJK) IF VMOT=3 THEN CHMAX=CH(HKMAX) IF VMOT=2 THEN OMMAX=OM(IJKMAX) IF VMOT= 1 THEN TTMAX=TI'(LIKMAX) END IF NEXT IJK IF INTMAX2 THEN EXIT FOR to next peak GOTO 100 END IF FOR IJK=I TO IJKMAX OK1HF=INTP(tIK) IF INTP(IJK)>0.5*INTMAX THEN EXIT FOR NEXT IJK FOR IJK=IJKMAX TO NSTP
trK2i-iF=nvrP(IJK) * Make sure away from peak * Drive diffractometer to BG target * Measure background intensity
INTBG--CPS TOBS=0.2
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* Counting time (s) for centering
IF INTP(IJK)
