Influence of Refinement Strategies on Rietveld Phase Composition Determinations

Transcription

1 Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo DENVER X-RAY CONFERENCE ( 1998) nfuence of Refinement Strategies on Rietved Phase Composition Determinations Brian O Connor and Deyu Li Materias Research Group, Department of Appied Physics Cur-tin University of Technoogy GPO Box U1987, Perth, WA, Austraia 6845 Abstract Refinement strategy may profoundy infuence phase composition (PC) resuts due to various parameter correations if the measured data are biased in some way and/or if the refinement mode is inadequate. The principa issues considered in this paper are (i) the infuence of preferred orientation (PO) on the refinement PC resuts and (ii) the need to refine individua-atom therma parameters with particuar reference to parameter correations. The paper examines these questions by examining a powder x-ray diffraction data set for a 4-phase mixture comprising - (i) a-a203 (corundum), ZnO (zincite) and TiOz (r-utie), a with minima preferred orientation; and (ii) CaC03 (cacite) which introduced substantia preferred orientation into the mixture. The quaity of the phase composition resuts is assessed according to their disagreement with the known vaues; the phase composition precision estimates; and the refinement figures-of-merit. ntroduction The authors have more than 10 years experience in obtaining Rietved PC anaysis (PCA) resuts in their own materias research projects, and aso in providing Rietved PCA services to mineras-oriented cients. Additionay, they have extensive experience in teaching Rietved anaysis to undergraduate and postgraduate students some having weak mathematica backgrounds and aso minima crystaography and diffraction science knowedge. t is evident in teaching Rietved principes and practice that practitioners without an adequate appreciation of the underying principes, who adopt a back box approach, are ikey to obtain severey erroneous phase composition resuts. Aspects of the method which must be appreciated by beginners incude parameter correations and the associated infuence of bias on the vaidity of the resuts. The study reported here was designed to consider the extent to which parameters correating with the phase scae factors (notaby the therma and PO parameters) wi infuence PCA resuts. Two specific questions were considered: 1. The infuence of therma parameter refinement strategy on the quaity of the PCA estimates. 2. The extent to which negect of PO biases the PCs.

2 This document was presented at the Denver X-ray Conference (DXC) on Appications of X-ray Anaysis. Sponsored by the nternationa Centre for Diffraction Data (CDD). This document is provided by CDD in cooperation with the authors and presenters of the DXC for the express purpose of educating the scientific community. A copyrights for the document are retained by CDD. Usage is restricted for the purposes of education and scientific research. DXC Website CDD Website -

3 Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Procedures The powders seected to make up the mixture for the study were designed to provide a muti-phase specimen with one component having substantia PO. Three of the four components were regarded as ikey to provide minima PO - a-a203 [corundum], ZnO [zincite]; and TiOz [r-utie]. The fourth component CaC03 [cacite] was incuded to provide PO. The a-a203 was type 1OOOSG suppied by Acoa of America, and the ZnO, TiOz and CaC03 were a Univar grade powders from AJAX Chemicas. The PCs-by-weight in the specimen were 40% for a-a203 and 20 % for each of the other phases. The voumetric median sizes for the four phases were reduced beow 5pm with a micronising mi to reduce microabsorption bias, and reasonabe comminution was then achieved by briefy micronising the components together. Sampes were mounted for XRD by ighty front-pressing to minimise PO. XRD data were measured with a Siemens D500 Bragg-Brentano diffractometer configured as foows - Cu tube [type Fk60-04 CU] operating at 40 kv and 30 ma (Ka waveengths: , A); fixed sit optics with incident beam divergence = o, receiving sit = 0.15, post-diffraction graphite anayser; Na detector with puse discrimination; 28 step size = 0.04, counting time = 1 s/step, 28 range = PCA was performed by the Rietved method using the Rietica-LHPM Microsoft Windows 95 program [] which derives from the Hi-Howard-Hunter LHPM program [2]. Crysta structure data (atom coordinates and unit ce parameters) were taken from the norganic Crysta Structure Data Base (FachnformationsZentrum and Gmein nstitut, Germany) - CSD (see Tabe 1). These structura parameters were fixed during the refinements. The computations invoved adjustment of the scae factors, patternbackground poynomia parameters, 28-scae offset and peak profie functions (pseudo-voig,t with asymmetry). Refinement trias of two types were conducted - the first with random orientation (RO) assumed for a phases, and second with the March-Doase PO mode [3] being empoyed for cacite. Tabe 1. Crysta Structure Modes Used in Rietved Refinements Structura Modes CSD Authors/Data* Number C& Masen et a - ref 4: SC-XRD ZnO Abertson et a - ref 5: SC-XRD TiOz, rutie Howard et a - ref 6: PWD-ND CaC03, cacite Masen et a - ref 7: SC-XRD * Codes: SC = singe crysta, PWD = powder diffraction XRD = x-ray diffraction, ND = neutron diffraction

4 Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo The fina Rietved scae factors were converted to PCs-by-weight ZMV expressions, Reative Phase Compositions: [s (ZMv) anayte phase wt % (anayte phase) = [ (zmv) a phases using the (1) Absoute Phase Compositions with nterna Standard (a-azo,) : anayte phase wt % (anayte phase) = x wt % (anayte phase) (2) [S (ZMv) int std where s, Z, M and V signify the phase scae factors; number of formua units/ce; formua weights and unit ce voumes, respectivey. These two measures of PC were examined in view of the authors experience that constraining the aggregate of the PCs to 100 % may substantiay bias the fina resuts. The a-a203 component was designated the interna standard for absoute determination with equation (2). Four refinement trias were conducted, as summarised in Tabe 2. Tria 1 was intended to examine the impact of ignoring preferred orientation. n this initia tria, therma parameters were set using a guideine generay foowed by the authors in setting initia therma vaues for inorganic phases - we have itte confidence in pubished therma parameters, particuary those from XRD studies. Tabe 2. Rietved Refinement Trias Tria # #2 #3 #4 Mode No preferred orientation Therma parameters fixed: B = 0.5 A2 for first atom, 1.0 for second atom, 1.5 for third atom, eg CaC03: 0.5 for Ca, 1.0 for C, 1.5 for 0. Preferred orientation for CaCOs Therma parameters fixed at tria 1 vaues. Preferred orientation for CaC03 Phase therma parameters refined. Preferred orientation for CaC03 Atom therma parameters refined. n the second tria, PO was introduced for cacite and therma parameters remained fixed at their assigned vaues. Next, in tria 3, the phase therma parameters were refined. Then, finay, the individua atom isotropic therma parameters were reaxed in tria 4.

5 Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Resuts and Discussion The resuts were examined in terms of (1) comparison of the PCA resuts with the known vaues - Figures 1 and 2; (2) the refinement figures-of-merit - Tabe 3; (3) the PC esds; and (4) the refinement correation coefficients - see Tabe 4 for seected coefficients cross-inking the scae factors, the atom therma parameters and the cacite PO parameter. These correation coefficients provide indications of ikey bias in the PC resuts. Other coefficients inked to the scae factors were a sma, the argest of these being < 0.2. t is noted aso that the inter-phase correations are very sma, and therefore bias in the scae factor for one phase wi not transate to bias in the scae factors of other phases. Tabe 3. Figures-of-merit for the Refinements <exp RP RW: Bragg R-factors (Rn) Tabe 4. Seected Correation Coefficients for Refinement 4 Correations inking the four scae factors and the PO parameter for cacite with the therma parameters. Parameter f&o3 scae factor: ZnO scae factor: Ti02 scae factor: CaC03 scae factor: CaC03 PO parameter: Coefficients A1203 parameters BA = 0.79, Bo = 0.61 ZnO parameters Bz,, = 0.81, Bo = 0.16 TiO2 parameters BTi = 0.76, Bo = 0.44 CaCO3 parameters Bca = 0.70, Bc = -0.01, B. = 0.65 CaCO3 parameters Bca = 0.56, Bc = -0.06, B. = 0.56, scae factor = 0.95 The Refinement 1 resuts in Figures 1 and 2 show severe bias due to the negect of PO. The absoute PCs give a vaue of 35.2 (0.7)* for the cacite eve compared with * Vaue in parentheses is the PC esd derived from the Rietved scae factor esds.

6 . Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo (0.7) T 3 h --==T--- 1g-?.2) 38.2(M) , ZnO 22.8(0.3) 23.0(0.5) 22.4(0.5) T - O i (0.4) 22.9(0.4) 22.5(0.6). TO 21.8(0.6) T w m O -* 1 Refine-2 Refine-3 Refine-4 Figure 1. Pots of reative Rietved phase composition resuts for each of the four refinement procedures. The numbers aongside each point give the PC vaue and, in parentheses, the PC esd. Error bars represent ti esds. The broken ines indicate the known vaues of PC.

7 Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo x- A,O, 40,,,,,,, * 30 1 ZnO 21.4(0.4) TiO,, CaCO, Refine-3 Refine-4 Figure 2. Pots of absoute Rietved phase composition resuts for each of the four refinement procedures. The numbers aongside each point give the PC vaue and, in parentheses, the PC esd. Error bars represent &.2 esds. The broken ines indicate the known vaues of PC. The PC vaue for A&O3 was fixed.

8 Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo the expected Ceary, constraining the reative concentration sum to 100% biases the estimates of PC for other three phases - note especiay, the pronounced bias in the a-a203 vaue, 33.8 (0.8) rather then Aso, constraining the PCs has biased the ZnO and TiOz concentrations beow their actua vaues. Reaxation of the March r-parameter in Refinement 2, with non-optimum therma parameters sti in use, resuts in the cacite concentration being biased ow, due presumaby to the infuence of bias in the decared therma parameters. t is noted for this refinement that the esd estimates are substantiay ower than those obtained when therma parameters were reaxed (ower than the Refinement 4 esds by more than x 0.5). The generation of diminished PC esds for Refinement 2 shows the serious underestimates in the esds caused by negecting parameters which correate with the phase scae factors. The cacite PC estimates improve in Refinement 3 through the adjustment of phase therma parameters, and again in Refinement 4 when atom therma parameters are reaxed. The best resuts (Refinement 4, Figure 2) give a cacite PC which agrees with the expected 20.0 vaue within 1.6 cr. t is evident from these resuts that it is important to refine the individua therma parameters for PCA. The corresponding fina PCs for ZnO and TiOz [23.5 (0.5) and 22.8 (0.6), respectivey] both deviate from the true vaue by more than 30. Examination of the mass attenuation coefficients for the phases (30.4, 47.3, and 69.8 cm /g for A203, ZnO, TiO2 and CaC03, respectivey) indicate that the ZnO and TiO2 PCs may be biased ow by microabsorption. t is instructive to examine the atom therma parameters obtained in Refinement 4 (Tabe 5). First, the atom therma parameters for A203, ZnO and TiO2 a satisfy Bcation > Be and, second, the therma parameters for CaC03 appear to be suffer from serious bias. The atter observation may be attributed to inadequacies in the March mode for CaC03 (ref. 8). Tabe 5. sotropic Therma Parameters from Refinement 4 Phase A1203 ZnO TiO2 CaC03 Vaues (A2) BA = 0.34(16), B. = -0.09(20) Bz,, = 0.97(12), Bo = O.o(39) hi = 0.78(16), Bo = 0.49(3 1) &a = 3.56(31), Bc = -3.15(39), B. = 2.24(42) Concusions The specific concusions drawn from this study are: The study has underined the importance of refining individua therma parameters in Rietved PCA.

9 Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Copyright(C)JCPDS-nternationa Centre for Diffraction Data 2000, Advances in X-ray Anaysis, Vo Negect of PO may seriousy bias the PC vaue for that phase due to the substantia scae-po correation coefficient. nter-phase correations are sufficienty sma that an error in the scae factor of one phase wi have minima infuence on the PC estimates of other phases. Constraining the sum of the PCs to 100% by weight tends to mask the presence of systematic errors in the PCs. The PC esds are artificiay reduced when the mode is inadequate. Acknowedgement The authors wish to acknowedge the suppy of the Rietved program Rietica- LHPM by Dr Brett Hunter of the Austraian Nucear Science and Technoogy Organisation. References B.A. Hunter, Rietica - a Visua Rietved Program, nternationa Union of Crystaography, Commission on Powder Diffraction - Newsetter 20, ~21,199s. 2R. J. Hi, C. J. Howard and B.A. Hunter, A Computer Program for Rietved Anaysis of Fixed Waveength x-ray and Neutron Powder Diffraction Patterns, Austraian Atomic Energy Commission (now ANSTO). Rept. No. M112, Lucas Heights Research Laboratories, New South Waes, Austraia, W.A. Doase, Correction of ntensities for Preferred Orientation in Powder Diffractometry: Appication of the March Mode, Journa of Appied Crystaography 19, (1986). 4E.N. Masen, V.A. Stretsov, N.R. Stretsova, N. shizawa and Y. Satow, Synchrotron X-ray Study of the Eectron Density in u-&03, Acta Crystaographica B49, (1993). 5J. Abertson, S.C. Abrahams and A. Kvick, Atomic Dispacement, Anharmonic Therma Vibration, Expansivity and Pyroeectric Coefficient Therma Dependencies in ZnO, Acta Crystaographica B45, (1989). 6C.J. Howard, T.M. Sabine and F. Dickson, Structura and Therma Parameters for Rutie and Anatase, Acta Crystaographica B47, (199 1). 7E.N. Masen, V.A. Stretsov and N.R. Stretsova, X-ray Study of the Eectron Density in Cacite, CaCO3, Acta Crystaographica B49, (1993). ah. Sitepu, March-type Modes for the Description of Texture in Granuar Materias, PhD Thesis - to be submitted, fie: pcdvsm.doc