High temperature structural and thermoelastic behaviour of mantle orthopyroxene: an in situ neutron powder diffraction study

The temperature induced structural evolution and thermoelastic behaviour of a natural (Pbca) orthopyroxene (Opx), with chemical formula ^M2(Mg_0.856Ca_0.025Fe²⁺ _0.119) ^M1(Mg_0.957Fe²⁺ _0.011Fe³⁺ _0.016Cr_0.011Al_0.005)Al_0.032Si_1.968O₆, from a suite of high pressure ultramafic nodules of mantle origin, have been investigated by in-situ neutron powder diffraction at several temperatures starting from 1,200°C down to 150°C. Unit-cell parameter variations as a function of T show no phase transition within this temperature range. The volume thermal expansion coefficient, α = V ⁻¹(∂V/∂T) _P0, varies linearly with T. The axial thermal expansion coefficients, α_j = l _j⁻¹(∂l _j/∂T)_P0, increase non-linearly with T. The principal Lagrangian unit-strain coefficients (ɛ//a, ɛ//b, ɛ//c), increase continuously with T. However, the orientation of the unit-strain ellipsoid appears to change with T. With decreasing T, the values of the unit-strain coefficients along the b and c axes tend to converge. The orientation at ΔT = 1,080°C is maintained down to the lowest temperature (150°C). The two non-equivalent tetrahedral chains, TA _n OA_3n and TB _n OB_3n , are kinked differently. At room-T, the TB _n OB_3n chain is more strongly kinked by about 23° than the TA _n OA_3n chain. With increasing T, the difference decreases by 3° for the TB _n OB_3n chain. The intersite cation exchange reaction between M1 and M2 (Mg²⁺ and Fe²⁺) shows a slight residual order at 1,200°C followed by reordering with decreasing temperature although seemingly not with a definite progressive trend. At the lowest temperature reached (150°C), reordering has occurred with the same value of partitioning coefficient K _D as that before heating. The absence of the expected phase transition is most likely due to the presence of minor amounts of Fe³⁺, Al, Ca and Cr which must play a crucial role on the thermoelastic behaviour and phase stability fields in natural Opx, with consequent important petrologic and geological implications.     

Octahedral cation ordering in olivine at high temperature. II: an in situ neutron powder diffraction study on synthetic MgFeSiO4 (Fa50)

 The partitioning of Fe and Mg between the M1 and M2 octahedral sites of olivine has been investigated by in situ time-of-flight neutron powder diffraction. The degree of M-cation order was determined from direct measurements of site occupancies in a synthetic sample of Fo50Fa50 heated to 1250 °C at the Fe-FeO oxygen buffer. Fe shows slight preference for M1 at temperatures below about 600 °C, progressively disordering on heating to this temperature. Above 630 °C, the temperature at which site preferences cross over (T _cr), Fe preferentially occupies M2, becoming progressively more ordered into M2 on increasing temperature. The cation-ordering behaviour is discussed in relation to the temperature dependence of the M1 and M2 site geometries, and it is suggested that vibrational entropy, crystal field effects and changes in bond characteristics play a part in the cross-over of partitioning behaviour. The temperature dependence of site ordering is modelled using a Landau expansion of the free energy of ordering of the type ΔG = −hQ + gTQ +  (T − T _c)Q ² +  Q ⁴, with a/h = 0.00406 K⁻¹, b/h = 2.3, T _c = 572 K and g/h = 0.00106 K⁻¹. These results suggest that the high-temperature ordering behaviour across the forsterite-fayalite join will have a bearing on the activity-composition relations of this important rock-forming mineral, and indicate that Fe-Mg olivine solid solutions become less ideal as temperature increases. Received: 12 August 1999 / Accepted: 25 April 2000     

Octahedral cation ordering in olivine at high temperature. I: in situ neutron single-crystal diffraction studies on natural mantle olivines (Fa12 and Fa10)

Crystallographic determinations on natural olivine single crystals of mantle composition and origin, carried out by in situ neutron diffraction at high temperature, show that the octahedrally co-ordinated Fe²⁺ and Mg cations undergo two successive trends of cation ordering with increasing temperature. An initial slight preference of Fe²⁺ for site M1, up to a temperature of about 850?°C, is followed by a reverse-ordering reaction with a site preference exchange between the two cations. The cross-over between the two regimes of ordering, corresponding to a situation of complete disorder, occurs at about 900?°C. Above this temperature Fe²⁺ progressively and strongly segregates into site M2 up to 1300?°C, the practical limit of the experimental setup utilized in the experiments. Care was taken to ensure that no chemical changes occurred in the crystals (i.e. oxidation), as testified by Mössbauer spectroscopy determinations carried out before and after the heat treatment. The cation-ordering behaviour is reflected in temperature-dependent changes of geometrical and atomic displacement parameters occurring in the octahedral sites M1 and M2. A thermodynamical explanation of this behaviour is proposed in terms of a prevailing vibrational contribution to entropy.     

Cation partitioning versus temperature in (Mg0.70Fe0.23)Al1.97O4 synthetic spinel by in situ neutron powder diffraction

Neutron powder diffraction experiments in the temperature range 300–1770 K were performed at BENSC, Berlin, Germany, on synthetic (Mg_0.70Fe_0.23) Al_1.97O₄. The cation partitioning over the crystallographic tetrahedral and octahedral sites was determined as a function of temperature through joint Rietveld refinements and advanced minimization techniques. The thermal expansion coefficients of the lattice parameter and inter-atomic bond lengths were also obtained from the full-profile structure refinements. The behaviour of the polyhedral bond-lengths, especially the T−O distances, and of the cell constant upon heating, clearly indicate that the interdiffusion of tetrahedral and octahedral Mg/Al cations starts at about 950 K. This result is straightforwardly supported by the direct analysis of the neutron site scattering factors: Fe always retains tetrahedral coordination at all temperatures, and the cation rearrangement is entirely due to Mg and Al diffusion. Received: 18 November 1997 / Revised, accepted: 23 August 1998     

In situ neutron diffraction study of deuterated portlandite Ca(OD)2 at high pressure and temperature

The structure of deuterated portlandite, Ca(OD)₂, has been investigated using time-of-flight neutron diffraction at pressures up to ∼4.5 GPa and temperatures up to ∼823 K. Rietveld analysis of the data reveals that with increasing pressure, unit-cell parameter c decreases at a rate about 4.5 times larger than that for a, which is largely due to rapid contraction of the interlayer spacing in this pressure range. Fitting of the determined cell volumes to the third-order Birch–Murnaghan equation of state yields a bulk modulus (K ₀) of 32.2 ± 1.0 GPa and its first derivative (K ₀′) of 4.4 ± 0.6. Moreover, on compression, hydrogen-mediated interatomic interactions within the interlayer become strengthened, as reflected by decreases in interlayer D···O and D···D distances with increasing pressure. Correspondingly, D–D, the distance between the three equivalent sites over which D is disordered, increases, suggesting a pressure-induced hydrogen disorder. This behavior is similar to that reported in brucite at elevated pressure. On heating at ∼2.1 GPa, cell parameter c increases more rapidly than a, as expected. However, because of the pressure effect, the thermal expansion coefficients, particularly along c, are much smaller than those at ambient pressure. With increasing temperature, the three partially occupied D sites become further apart, and the D-mediated interactions, mainly the interlayer D···D repulsion, become weakened.     

Structural changes and oxidation of ferroan phlogopite with increasing temperature: in situ neutron powder diffraction and Fourier transform infrared spectroscopy

The thermal response of the natural ferroan phlogopite-1M, K₂(Mg_4.46Fe_0.83Al_{0. 34}Ti_0.22)(Si_5.51Al_{2. 49})O₂₀[OH_3.59F_0.41] from Quebec, Canada, was studied with an in situ neutron powder diffraction. The in situ temperature conditions were set up at ?263, 25, 100°C and thereafter at a 100°C intervals up to 900°C. The crystal structure was refined by the Rietveld method (R _p=2.35–2.78%, R _wp=3.01–3.52%). The orientation of the O–H vector of the sample was determined by the refinement of the diffraction pattern. With increasing temperature, the angle of the OH bond to the (001) plane decreased from 87.3 to 72.5°. At room temperature, a = 5.13 Å, b = 9.20 Å, c = 10.21 Å, β = 100.06° and V(volume) = 491.69 ų. The expansion rate of the unit cell dimensions varied discontinuously with a break at 500°C. The shape of the M-octahedron underwent some significant changes such as flattening at 500°C. At temperatures above 500°C, the octahedral thickness and mean distance was decreased, while the octahedral flattening angle increased. Those results were attributed to the Fe oxidation and dehydroxylation processes. The dehydroxylation mechanism of the ferroan phlogopite was studied by the Fourier transform infrared spectroscopy (FTIR) after heated at temperatures ranging from 25 to 800°C with an electric furnace in a vacuum. In the OH stretching region, the intensity of the OH band associated with Fe²⁺(N _B-band) begun to decrease outstandingly at 500°C. The changes of the IR spectra confirmed that dehydroxylation was closely related to the oxidation in the vacuum of the ferrous iron in the M-octahedron. The decrease in the angle of the OH bond to the (001) plane, with increasing temperature, might be related to the imbalance of charge in the M-octahedra due to Fe oxidation.     

Thermal expansion and crystal structure of FeSi between 4 and 1173 K determined by time-of-flight neutron powder diffraction

The thermal expansion and crystal structure of FeSi has been determined by neutron powder diffraction between 4 and 1173?K. No evidence was seen of any structural or magnetic transitions at low temperatures. The average volumetric thermal expansion coefficient above room temperature was found to be 4.85(5)?×?10^?5?K^?1. The cell volume was fitted over the complete temperature range using Grüneisen approximations to the zero pressure equation of state, with the internal energy calculated via a Debye model; a Grüneisen second-order approximation gave the following parameters: θ_D=445(11)?K, V ₀=89.596(8)?ų, K ₀′=4.4(4) and γ′=2.33(3), where θ_D is the Debye temperature, V ₀ is V at T=0?K, K ₀′ is the first derivative with respect to pressure of the incompressibility and γ′ is a Grüneisen parameter. The thermodynamic Grüneisen parameter, γ_th, has been calculated from experimental data in the range 4–400?K. The crystal structure was found to be almost invariant with temperature. The thermal vibrations of the Fe atoms are almost isotropic at all temperatures; those of the Si atoms become more anisotropic as the temperature increases.     

Structural and magnetic properties of Co2Al4Si5O18 and Mn2Al4Si5O18 cordierite

The crystal structures, lattice dynamics and magnetic properties of synthetic Co-cordierite, Co₂Al₄Si₅O₁₈, and Mn-cordierite, Mn₂Al₄Si₅O₁₈ have been studied by neutron powder diffraction, infrared spectroscopy and magnetisation measurements. Due to different synthesis conditions, the Co-cordierite used here crystallised in the hexagonal α-cordierite structure with a disordered Si/Al distribution in the framework, while for the Mn-cordierite the orthorhombic β-structure has been determined. The experimentally determined paramagnetic moments, _exp (Mn) = 5.47(6) _B and _exp (Co) = 3.88(4) _B , are in good agreement with theoretical predictions for octahedrally coordinated Mn²⁺ and Co²⁺, respectively. In both compounds there is no magnetic long-range order down to at least 1.5 K. However, the onset of an anti-ferromagnetic short-range correlation of magnetic moments along [001] has been observed for Mn-cordierite by magnetisation and neutron diffraction measurements. This short-range magnetic correlation becomes evident from diffuse scattering observed at 2 K. The diffuse scattering has been interpreted in terms of a Blech-Averbach function. Received: 30 June 1998 / Revised, accepted: 3 March 1999     

The role of iron in tetrahedrite and tennantite determined by Rietveld refinement of neutron powder diffraction data

Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12?xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12?xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I $ \ifmmode\expandafter\bar\else\expandafter\=\fi{4} Rietveld refinement of neutron powder diffraction data on four samples of synthetic, iron-bearing tetrahedrite (Cu_12−xFe_xSb₄S₁₃) with x = 0.28, 0.69, 0.91, 2.19 and four samples of synthetic tennantite (Cu_12−xFe_xAs₄S₁₃) with x = 0.33, 0.38, 0.86, 1.5 indicate unambiguously that iron is incorporated into tetrahedral M1 (12d) sites and not into triangular M2 (12e) sites in the cubic crystal structure (space group I 3 m). The refinement results also confirm that M2 is a split (24g), flat-pyramidal site situated statistically on both sides of the S1−S1–S2 triangle. In tetrahedrite, this split is about 0.6 ?, in tennantite about 0.7 ?. Trends in bond lengths and magnitude of the M2 split were evaluated by means of linear regression with Fe concentration as the independent variable.     

Determination of cation distribution in (Co,Ni,Zn)2SiO4 olivine by synchrotron X-ray diffraction

 The cation distribution of Co, Ni, and Zn between the M1 and M2 sites of a synthetic olivine was determined with a single-crystal diffraction method. The crystal data are (Co_0.377Ni_0.396Zn_0.227)₂SiO₄, M _r  = 212.692, orthorhombic, Pbnm, a = 475.64(3), b = 1022.83(8), and c = 596.96(6) pm, V = 0.2904(1) nm³, Z = 4, D _x  = 4.864 g cm⁻³, and F(0 0 0) = 408.62. Lattice, positional, and thermal parameters were determined with MoKα radiation; R = 0.025 for 1487 symmetry-independent reflections with F > 4σ(F). The site occupancies of Co, Ni, and Zn were determined with synchrotron radiation employing the anomalous dispersion effect of Co and Ni. The synchrotron radiation data include two sets of intensity data collected at 161.57 and 149.81 pm, which are about 1 pm longer than Co and Ni absorption edges, respectively. The R value was 0.022 for Co K edge data with 174 independent reflections, and 0.034 for Ni K edge data with 169 reflections. The occupancies are 0.334Co + 0.539Ni + 0.127Zn in the M1 sites, and 0.420Co + 0.253Ni + 0.327Zn in the M2 sites. The compilation of the cation distributions in olivines shows that the distributions depend on ionic radii and electronegativities of constituent cations, and that the partition coefficient can be estimated from the equation: ln [(A/B)_M1/(A/B)_M2] = −0.272 (IR _A -IR _B ) + 3.65 (EN _A −EN _B ), where IR (pm) and EN are ionic radius and electronegativity, respectively. Received: 8 April 1999 / Revised, accepted: 7 September 1999     

Iron-water reaction at high pressure and temperature, and hydrogen transport into the core

We observed a direct reaction of metallic iron with water to form iron hydride and iron oxide, 3Fe + H₂O–>2FeH_x + FeO, at pressures from 6 GPa to 84 GPa and temperatures above 1,000 K in diamond anvil cell (DAC). Iron hydride is dhcpFeH_x or -FeH_x, and iron oxide has the rhombohedral or B1 structure at pressures at least up to 37 GPa. The formation of an assembly composed of dhcpFeH_x and FeO with the B8 structure was observed at 84 GPa. In primordial Earth, water formed by dehydration of the low temperature primitive materials reacts with metallic iron in the high temperature component to form iron hydride FeH_x and iron oxide FeO. The former would be incorporated in the iron forming the core. Thus hydrogen could be an important element of the Earths core. This reaction would be essential for transport of hydrogen into the core in the accretion stage of the Earth.     

The phase boundary between wadsleyite and ringwoodite in Mg2SiO4 determined by in situ X-ray diffraction

The phase boundary between wadsleyite and ringwoodite in Mg₂SiO₄ has been determined in situ using a multi-anvil apparatus and synchrotron X-rays radiation at SPring-8. In spite of the similar X-ray diffraction profiles of these high-pressure phases with closely related structures, we were able to identify the occurrence of the mutual phase transformations based on the change in the difference profile by utilizing a newly introduced press-oscillation system. The boundary was located at ~18.9 GPa and 1,400°C when we used Shim’s gold pressure scale (Shim et al. in Earth Planet Sci Lett 203:729–739, 2002), which was slightly (~0.8 GPa) lower than the pressure as determined from the quench experiments of Katsura and Ito (J Geophys Res 94:15663–15670, 1989). Although it was difficult to constrain the Clapeyron slope based solely on the present data due to the kinetic problem, the phase boundary [P (GPa)=13.1+4.11×10⁻³×T (K)] calculated by a combination of a P–T position well constrained by the present experiment and the calorimetric data of Akaogi et al. (J Geophys Res 94:15671–15685, 1989) reasonably explains all the present data within the experimental error. When we used Anderson’s gold pressure scale (Anderson et al. in J Appl Phys 65:1535–1543, 1989), our phase boundary was located in ~18.1 GPa and 1,400°C, and the extrapolation boundary was consistent with that of Kuroda et al. (Phys Chem Miner 27:523–532, 2000), which was determined at high temperature (1,800–2,000°C) using a calibration based on the same pressure scale. Our new phase boundary is marginally consistent with that of Suzuki et al. (Geophys Res Lett 27:803–806, 2000) based on in situ X-ray experiments at lower temperatures (<1,000°C) using Brown’s and Decker’s NaCl pressure scales.     

Thermal behaviour and kinetics of dehydration of gypsum in air from in situ real-time laboratory parallel-beam X-ray powder diffraction

Thermal behaviour and kinetics of dehydration of gypsum in air have been investigated using in situ real-time laboratory parallel-beam X-ray powder diffraction data evaluated by the Rietveld method. Thermal expansion has been analysed from 298 to 373 K. The high-temperature limits for the cell edges and for the cell volume, calculated using the Einstein equation, are 4.29 × 10⁻⁶, 4.94 × 10⁻⁵, 2.97 × 10⁻⁵, and 8.21 × 10⁻⁵. Thermal expansion of gypsum is strongly anisotropic being larger along the b axis mainly due to the weakening of hydrogen bond. Dehydration of gypsum has been investigated in isothermal conditions within the 348–403 K range with a temperature increase of 5 K. Dehydration proceeds through the CaSO₄·2H₂O → CaSO₄·0.5H₂O → γ-CaSO₄ steps. Experimental data have been fitted with the Avrami equation to calculate the empirical activation energy of the process. No change in transformation mechanism has been observed within the analysed temperature range and the corresponding E _a is 109(12) kJ/mol.     

In situ X-ray observations of the decomposition of brucite and the graphite–diamond conversion in aqueous fluid at high pressure and temperature

 An experimental technique to make real-time observations at high pressure and temperature of the diamond-forming process in candidate material of mantle fluids as a catalyst has been established for the first time. In situ X-ray diffraction experiments using synchrotron radiation have been performed upon a mixture of brucite [Mg(OH)₂] and graphite as starting material. Brucite decomposes into periclase (MgO) and H₂O at 3.6 GPa and 1050 °C while no periclase is formed after the decomposition of brucite at 6.2 GPa and 1150 °C, indicating that the solubility of the MgO component in H₂O greatly increases with increasing pressure. The conversion of graphite to diamond in aqueous fluid has been observed at 7.7 GPa and 1835 °C. Time-dependent X-ray diffraction profiles for this transformation have been successfully obtained. Received: 17 July 2001 / Accepted: 18 February 2002     

Pressure–volume–temperature equation of state of andradite and grossular, by high-pressure and -temperature powder diffraction

 The thermoelastic parameters of natural andradite and grossular have been investigated by high-pressure and -temperature synchrotron X-ray powder diffraction, at ESRF, on the ID30 beamline. The P–V–T data have been fitted by Birch-Murnaghan-like EOSs, using both the approximated and the general form. We have obtained for andradite K ₀=158.0(±1.5) GPa, (dK/dT )₀=−0.020(3) GPa K⁻¹ and α₀=31.6(2) 10⁻⁶ K⁻¹, and for grossular K ₀=168.2(±1.7) GPa, (dK/dT)₀=−0.016(3) GPa K⁻¹ and α₀=27.8(2) 10⁻⁶ K⁻¹. Comparisons between the present issues and thermoelastic properties of garnets earlier determined are carried out. Received: 7 July 2000 / Accepted: 20 October 2000     

Determination of the phase boundary between ilmenite and perovskite in MgSiO3 by in situ X-ray diffraction and quench experiments

Determination of the phase boundary between ilmenite and perovskite structures in MgSiO₃ has been made at pressures between 18 and 24 GPa and temperatures up to 2000 °C by in situ X-ray diffraction measurements using synchrotron radiation and quench experiments. It was difficult to precisely define the phase boundary by the present in situ X-ray observations, because the grain growth of ilmenite hindered the estimation of relative abundances of these phases. Moreover, the slow reaction kinetics between these two phases made it difficult to determine the phase boundary by changing pressure and temperature conditions during in situ X-ray diffraction measurements. Nevertheless, the phase boundary was well constrained by quench method with a pressure calibration based on the spinel-postspinel boundary of Mg₂SiO₄ determined by in situ X-ray experiments. This yielded the ilmenite-perovskite phase boundary of P (GPa) = 25.0 (±0.2) – 0.003 T (°C) for a temperature range of 1200–1800 °C, which is generally consistent with the results of the present in situ X-ray diffraction measurements within the uncertainty of ∼±0.5 GPa. The phase boundary thus determined between ilmenite and perovskite phases in MgSiO₃ is slightly (∼0.5 GPa) lower than that of the spinel-postspinel transformation in Mg₂SiO₄. Received: 19 May 1999 / Accepted: 21 March 2000     

Low-temperature behaviour of ammonium ion in buddingtonite [N(D/H)<Subscript>4</Subscript>AlSi<Subscript>3</Subscript>O<Subscript>8</Subscript>] from neutron powder diffraction

The structural response of buddingtonite [N(D/H)₄AlSi₃O₈] on cooling has been studied by neutron diffraction. Data have been collected from 280 K down to 11 K, and the crystal structure refined using the Rietveld method. Rigid-body constraints were applied to the ammonium ion to explore the structural properties of ammonium in the M-site cavities at low-temperature. Low-temperature saturation is observed for almost all the lattice parameters. From the present in situ low-temperature neutron diffraction studies, there is no strong evidence of orientational order–disorder of the ammonium ions in buddingtonite.     

Transport properties of low-sanidine single-crystals, glasses and melts at high temperature

Thermal diffusivity (D) was measured using laser-flash analysis from oriented single-crystal low-sanidine (K_0.92Na_0.08Al_0.99Fe³⁺ _0.005Si_2.95O₈), and three glasses near KAlSi₃O₈. Viscosity measurements of the three supercooled liquids, in the range 10^6.8 to 10^12.3 Pa s, confirm near-Arrhenian behavior, varying subtly with composition. For crystal and glass, D decreases with T, approaching a constant near 1,000 K: D _sat ∼ 0.65 ± 0.3 mm² s⁻¹ for bulk crystal and ∼0.53 ± 0.03 mm² s⁻¹ for the glass. A rapid decrease near 1,400 K is consistent with crossing the glass transition. Melt behavior is approximated by D = 0.475 ± 0.01 mm² s⁻¹. Thermal conductivity (k _lat) of glass, calculated using previous heat capacity (C _P) and new density data, increases with T because C _P strongly increases with T. For melt, k _lat reaches a plateau near 1.45 W m⁻¹ K⁻¹, and is always below k _lat of the crystal. Melting of potassium feldspars impedes heat transport, providing positive thermal feedback that may promote further melting in continental crust.     

Crystal structures and cation distributions in simple spinels from powder XRD structural refinements: MgCr2O4, ZnCr2O4, Fe3O4 and the temperature dependence of the cation distribution in ZnAl2O4

The crystal structure and cation distributions in the spinels MgCr₂O₄, ZnCr₂O₄, Fe₃O₄ and a suite of ZnAl₂O₄ samples annealed at 900 to 1400° C and then rapidly quenched, have been determined by powder X-ray diffraction, using several different X-ray procedures and both conventional structure-factor refinement and whole-pattern (or Rietveld) refinement methods. The chromite spinels are expected from crystal chemical considerations to have an almost completely normal cation distribution (inversion parameter, x, equal to zero). In agreement with this expectation, three samples of MgCr₂O₄ annealed at 900, 1100 and 1300° C, and ZnCr₂O₄ were all found to have x=0 within two estimated standard deviations (esd), suggesting that the accuracy with which cation distributions in spinels may be determined by powder XRD is close to the estimated precision. Slightly better results are obtained assuming neutral-atom scattering curves rather than half-ionized or fully ionized, but the differences are small (within the esd). The results from the Rietveld refinements are similarly in good agreement with those using the conventional structure factor refinement approach (agreement within the combined esd's), although in detail the Rietveld procedure sometimes produces small systematic differences in refined parameters. The suite of ZnAl₂O₄ spinels show a smooth increase in x from 0.01 at 900° C to 0.05 at 1300° C, and this behaviour is well described by the simple thermodynamic model for disordering in spinels with α_Zn-Al=89 kJ/mol, assuming β=?20 kJ/mol. The oxygen positional parameters for Fe₃O₄ are similar to those from published single crystal studies, indicating that the powder method also yields accurate interatomic distances in spinels.