The weight of a phase in a mixture is proportional to the product of the scale factor, as derived in a multicomponent Rietveld analysis of the powder diffraction pattern, with the mass and volume of the unit cell. If all phases are identified and crystalline, the weight fraction W of phase p is given by Wp = Sp( Z M IO p/~ S,( Z M IO,, iwhere S, Z, M and V are, respectively, the Rietveld scale factor, the number of formula units per unit cell, the mass of the formula unit and the unit-cell volume. This is the basis of a method providing accurate phase analyses without the need for standards or for laborious experimental calibration procedures. The method is demonstrated by measurements on binary mixtures of rutile, corundum, silicon and quartz.

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The crystal structures of monoclinic ZrO2 [P21/c, a=5.1505 (1) [Fm3m, a=5.0858(1)./k, V= 131.55(1),/k 3, Z=4, Rwp= 0.083] have been refined by Rietveld analysis of 1.377 A neutron powder diffraction data collected at 295 K. In both tetragonal and cubic ZrO2, the stabilizer atoms randomly occupy the Zr site and charge balance is achieved by an appropriate number of vacancies on the O site. In cubic ZrO 2, the anions are displaced from their ideal fluorite positions by 0.025a in the [111] direction and there is evidence for the presence of either a small quantity of a tetragonal impurity phase, or a slight tetragonal distortion. IntroductionPure zirconia, ZrO2, is monoclinic at room temperature, tetragonal between ~ 1440 and ~2640 K, and cubic up to the melting point at ~2950K. The monoclinic phase is a distortion of the fluorite (CaF 2) structure with the Zr atom in seven coordination. In both high-temperature phases, the Zr atom assumes eight coordination, as in fluorite, but in the tetragonal form the O atom is substantially displaced from its ideal fluorite 1 1 ~ position. The tetragonal and cubic phases ~,~,~ of pure zirconia can be stabilized at room temperature by the addition of suitable oxides, namely MgO, CaO, 0108-7681/88/020116-05503.00Sc203, Y203 and certain rare-earth oxides. An orthorhombic form has also been prepared by quenching from high pressure and temperature (Suyama, Ashida & Kume, 1985) but this phase will not be considered further here.The crystal structures of, and mechanisms of the transformations between, the monoclinic, tetragonal and cubic phases are of considerable technical interest since they can be manipulated to provide optimized physical and chemical properties of the materials fabricated from the stabilized zirconia (Garvie, Hannink & Pascoe, 1975;Roth, 1975;Claussen, Ruhle & Heuer, 1984;Fisher, 1986). The so-called partially stabilized zirconias (PSZ), which are typically twophase cubic and tetragonal or single-phase tetragonal, are of importance for mechanical and structural applications. The fully stabilized zirconias (FSZ), which are normally single-phase cubic, are of interest for heating elements, oxygen sensors and fuel-cell applications.Crystal structure determinations have been performed on tetragonal ZrO 2 using X-ray powder diffraction intensities collected at 1470 to 2230 K by Teufer (1962). Monoclinic ZrO 2 (baddeleyite) has been studied at room temperature using X-ray single-crystal methods by McCullough & Trueblood (1959) and Smith & Newkirk (1965). Cubic Zr(Ca,Y)O2_ x solid solutions have been analyzed at various temperatures from both X-ray and neutron data by Carter & Roth (1968), Steele & Fender (1974), Faber, Mueller & Cooper (1978, Morinaga, Cohen & Faber (1979) and Horiuchi, Schultz, Leung & Williams (1984).© 1988 International Union of Crystallography C. J. HOWARD, R. J. HILL AND B. E. REICHERT 117The present study gives new refinements of the crystal structures and compositions of the three ZrO 2 polymorphs from high-resolution neutron pow...

A weighted form of the Durbin-Watson d statistic [Durbin & Watson (1971). Biometrika, 58,[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] has been used to quantify the serial correlation between adjacent least-squares residuals in Rietveld refinements of step-scan powder diffraction data. Analyses of X-ray and neutron data from a range of materials have shown that the d statistic: provides a sensitive measure of the progress of a refinement and remains discriminating when other agreement indices fail, for example, when comparing results at different step widths; provides quantitative information about the significance of serial correlation present in the residuals; provides a convenient means of assessing the reliability of the estimates of the parameter variances; and provides a basis for the selection of values of step width and intensity corresponding to optimum and/or minimum use of experimental beam time.

A neutron powder diffraction investigation confirms that, in tough magnesiapartially‐stabilized zirconia cooled to 30 K, most of the tetragonal zirconia transforms to an orthorhombic phase. This phase is retained on heating to room temperature; the lattice parameters at 295 K are a = 0.5068, b = 0.5260, and c = 0.5077 nm. The room‐temperature crystal structure (space group Pbc21) is determined by multiphase Rietveld refinement from the neutron diffraction pattern. This orthorhombic structure is compared with the parent tetragonal structure and with the structure of monoclinic zirconia, which it closely resembles.