Al,Ge cation ordering in BaAl2Ge2O8-feldspar: monodomain ordering kinetics

The kinetics of monodomain order-disorder processes in monoclinic (I2/c) BaAl₂Ge₂O₈-feldspar have been investigated by X-ray powder diffraction, Hard Mode IR Spectroscopy, and TEM darkfield imaging on quenched samples. Compared to the behaviour predicted by the TDGL approximation ordering kinetics observed at low temperatures slow down significantly when equilibrium is approached. Such a delay is not observed in disordering experiments starting from essentially ordered cation distributions. The deviation from TDGL behaviour is interpreted in terms of partial order parameter conservation in a non-uniformly ordered phase. Modifications to the uniform TDGL rate equation are tested against the available data. An activation energy of 352 ± 28 kJ/mol is obtained for Al,Ge ordering. The mixing coefficient ξ_c ²/ξ², which describes the degree of order parameter conservation, is obtained as a function of temperature. While this coefficient vanishes in the vicinity of the transformation temperature T _tr, it saturates towards a level of ξ_c ²/ξ²≈0.4 for T→0. ξ _c ²/ξ² determines the kinetic stability of ordered clusters quenched from T≈T _tr. Received: 21 April 1999 / Revised, accepted: 19 July 1999     

Non-convergent ordering and displacive phase transition in pigeonite: in situ HT XRD study

A natural Ca-rich pigeonite (En₄₇Fs₄₃Wo₁₀), free of augite exsolution products, was studied by in situ high-temperature single-crystal X-ray diffraction. The sample, monoclinic P2 ₁ /c (a=9.719(7) Å, b=8.947(9) Å, c=5.251(3) Å, β=108.49(5), V=433.0(6) ų), was annealed up to 1000 °C to induce a phase transition from P2 ₁ /c to C2/c symmetry. Complete single-crystal X-ray diffraction data collections were carried out in situ at 650, 750, 850 and 950 °C after the crystal had reached equilibrium for the Fe–Mg intracrystalline exchange reaction at each temperature. The variation, with increasing temperature, of lattice parameters, of intensity of hkl reflections with h + k=2n + 1 (which vanish at high temperature) and of some geometrical parameters from structure refinement, showed that the displacive phase transition P2 ₁ /c?C2/c was continuous in character. This contrasts with the first-order character for the HT phase transition in pigeonite containing significantly less calcium.     

Phase transition of synthetic zinc ferrite spinel (ZnFe2O4) at high pressure, from synchrotron X-ray powder diffraction

 Synthetic Zn-ferrite (ideally ZnFe₂O₄; mineral name: franklinite) was studied up to 37 GPa, by X-ray powder diffraction at ESRF (Grenoble, France), on the ID9 beamline; high pressure was achieved by means of a DAC. The P-V equation of state of franklinite was investigated using the Birch-Murnaghan function, and the elastic properties thus inferred [K₀ = 166.4(±3.0) GPa K₀ ^′ = 9.3(±0.6) K₀ ^″ = −0.22 GPa⁻¹] are compared with earlier determinations for MgAl-spinel and magnetite. The structural behaviour of Zn-ferrite as a function of pressure was studied by Rietveld refinements, and interpreted in the light of a phase transition from spinel to either CaTi₂O₄- or MnFe₂O₄-like structure; this transformation occurs above 24 GPa. Received: 15 March 1999 / Accepted: 22 April 2000     

Pressure-induced phase transition in synthetic trioctahedral Rb-mica

 The crystal structure of a synthetic Rb analog of tetra-ferri-annite (Rb–TFA) 1M with the composition Rb_0.99Fe²⁺ _3.03(Fe³⁺ _1.04 Si_2.96)O_10.0(OH)_2.0 was determined by the single-crystal X-ray diffraction method. The structure is homooctahedral (space group C2/m) with M1 and M2 occupied by divalent iron. Its unit cell is larger than that of the common potassium trioctahedral mica, and similar lateral dimensions of the tetrahedral and octahedral sheets allow a small tetrahedral rotation angle α=2.23(6)°. Structure refinements at 0.0001, 1.76, 2.81, 4.75, and 7.2 GPa indicate that in some respects the Rb–TFA behaves like all other micas when pressure increases: the octahedra are more compressible than the tetrahedra and the interlayer is four times more compressible than the 2:1 layer. However, there is a peculiar behavior of the tetrahedral rotation angle α: at lower pressures (0.0001, 1.76, 2.81 GPa), it has positive values that increase with pressure [from 2.23(6)° to 6.3(4)°] as in other micas, but negative values −7.5(5)° and −8.5(9)° appear at higher pressures, 4.75 and 7.2 GPa, respectively. This structural evidence, together with electrostatic energy calculations, shows that Rb–TFA has a Franzini A-type 2:1 layer up to at least 2.81 GPa that at higher pressure yields to a Franzini B-type layer, as shown by the refinements at 4.75 and 7.2 GPa. The inversion of the α angle is interpreted as a consequence of an isosymmetric displacive phase transition from A-type to B-type structure between 2.81 and 4.75 GPa. The compressibility of the Rb–TFA was also investigated by single-crystal X-ray diffraction up to a maximum pressure of 10 GPa. The lattice parameters reveal a sharp discontinuity between 3.36 and 3.84 GPa, which was associated with the phase transition from Franzini-A to Franzini-B structure. Received: 21 October 2002 / Accepted: 25 February 2003     

Simulation of structural phase transition in NaNO3 and CaCO3

 The order-disorder phase transitions in NaNO₃ and CaCO₃ are simulated by molecular dynamics. The simulations are based on the potentials calculated from the Gordon–Kim modified electron gas formalism extended to molecular ions. We successfully reproduced the transition temperature T _c and the abnormally large c axis thermal expansion observed in experiment. The phase transitions in NaNO₃ and CaCO₃ were found to be initiated by ±60 and ±180° reorientation of the NO₃ and CO₃ ions about the c axis. The orientations of NO₃ and CO₃ ions are continuous with six preferred calcite-type orientations above the phase-transition temperature. Received: 30 January 2001 / Accepted: 11 May 2001     

Monte Carlo simulation of mixing in Ca3Fe2Ge3O12–Ca4Ge4O12 garnets and implications for the thermodynamic stability of pyrope–majorite solid solution

Static lattice energy calculations, based on empirical pair potentials, were performed for a large set of structures differing in the arrangement of octahedral cations within the garnet 2 × 2 × 2 supercell. The compositions of these structures varied between Ca₃Fe₂Ge₃O₁₂ and Ca₄Ge₄O₁₂. The energies were cluster expanded using pair and quaternary terms. The derived ordering constants were used to constrain Monte Carlo simulations of temperature-dependent mixing properties in the ranges of 1,073–3,673 K and 0–10 GPa. The free energies of mixing were calculated using the method of thermodynamic integration. The calculations predict a wide miscibility gap between Fe-rich (cubic) and Fe-pure (tetragonal) garnets consistent with recent experimental observations of Iezzi et al. (Phys Chem Miner 32:197–207, 2005). It is shown that the miscibility gap arises due to a very strong cation ordering at the Fe-pure composition, driven by the charge difference between Ca²⁺ and Ge⁴⁺ cations. The structural and thermodynamic analogies between Ca–Ge and Mg–Si systems suggest that a similar miscibility gap should exist between pyrope and Mg–Si-majorite.     

High-pressure phase transformations in the MgFe2O4 and Fe2O3–MgSiO3 systems

 The crystal structure of MgFe₂O₄ was investigated by in situ X-ray diffraction at high pressure, using YAG laser annealing in a diamond anvil cell. Magnesioferrite undergoes a phase transformation at about 25 GPa, which leads to a CaMn₂O₄-type polymorph about 8% denser, as determined using Rietveld analysis. The consequences of the occurrence of this dense MgFe₂O₄ form on the high-pressure phase transformations in the (MgSi)_0.75(Fe^III)_0.5O₃ system were investigated. After laser annealing at about 20 GPa, we observe decomposition to two phases: stishovite and a spinel-derived structure with orthorhombic symmetry and probably intermediate composition between MgFe₂O₄ and Mg₂SiO₄. At pressures above 35 GPa, we observe recombination of these products to a single phase with Pbnm perovskite structure. We thus conclude for the formation of Mg₃Fe₂Si₃O₁₂ perovskite. Received: 27 March 2000 / Accepted: 1 October 2000     

Enthalpy of formation of CaSi2O5, a quenched high-pressure phase with pentacoordinate silicon

 The monoclinic titanite-like high-pressure form of calcium disilicate has been synthesized and quenched to ambient conditions to form the triclinic low-pressure phase containing silicon in four-, five- and sixfold coordination. The enthalpy of formation of the quench product has been measured by high-temperature oxide melt calorimetry. The value obtained from samples from a series of several synthesis experiments is ΔH _f = (−26.32 ± 4.27) kJ mol⁻¹ for the formation from the component oxides, or ΔH _f  = (−2482.81 ± 4.59) kJ mol⁻¹ for the formation from the elements. The result is identical within experimental error to available estimates, although the previously predicted energy difference between the monoclinic and triclinic phases could not be verified. Received: 16 February 2000 / Accepted: 14 July 2000     

The crystal and magnetic structure of Li-aegirine LiFe3+Si2O6: a temperature-dependent study

Single crystals of Li-aegirine LiFe³⁺Si₂O₆ were synthesized at 1573?K and 3?GPa, and a polycrystalline sample suitable for neutron diffraction was produced by ceramic sintering at 1223?K. LiFe³⁺Si₂O₆ is monoclinic, space group C2/c, a=9.6641(2)?Å, b= 8.6612(3)?Å, c=5.2924(2)?Å, β=110.12(1)^° at 300?K as refined from powder neutron data. At 229?K Li-aegirine undergoes a phase transition from C2/c to P2₁ /c. This is indicated by strong discontinuities in the temperature variation of the lattice parameters, especially for the monoclinic angle β and by the appearance of Bragg reflections (hkl) with h+k≠2n. In the low-temperature form two non-equivalent Si-sites with 〈SiA–O〉=1.622?Å and 〈SiB–O〉=1.624?Å at 100?K are present. The bridging angles of the SiO₄ tetrahedra O3–O3–O3 are 192.55(8)° and 160.02(9)° at 100?K in the two independent tetrahedral chains in space group P2₁ /c, whereas it is 180.83(9)° at 300?K in the high-temperature C2/c phase, i.e. the chains are nearly fully expanded. Upon the phase transition the Li-coordination changes from six to five. At 100?K four Li–O bond lengths lie within 2.072(4)–2.172(3)?Å, the fifth Li–O bond length is 2.356(4)?Å, whereas the Li–O3?A bond lengths amount to 2.796(4)?Å. From ⁵⁷Fe Mössbauer spectroscopic measurements between 80 and 500?K the structural phase transition is characterized by a small discontinuity of the quadrupole splitting. Temperature-dependent neutron powder diffraction experiments show first occurrence of magnetic reflections at 16.5?K in good agreement with the point of inflection in the temperature-dependent magnetization of LiFe³⁺Si₂O₆. Distinct preordering phenomena can be observed up to 35?K. At the magnetic phase transition the unit cell parameters exhibit a pronounced magneto-striction of the lattice. Below T _N Li-aegirine shows a collinear antiferromagnetic structure. From our neutron powder diffraction experiments we extract a collinear antiferromagnetic spin arrangement within the a–c plane.     

LiFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> and NaFeSi<Subscript>2</Subscript>O<Subscript>6</Subscript> at low temperatures: an infrared spectroscopic study

 Synthetic aegirine LiFeSi₂O₆ and NaFeSi₂O₆ were characterized using infrared spectroscopy in the frequency range 50–2000 cm⁻¹, and at temperatures between 20 and 300 K. For the C2/c phase of LiFeSi₂O₆, 25 of the 27 predicted infrared bands and 26 of 30 predicted Raman bands are recorded at room temperature. NaFeSi₂O₆ (with symmetry C2/c) shows 25 infrared and 26 Raman bands. On cooling, the C2/c–P2₁/c structural phase transition of LiFeSi₂O₆ is characterized by the appearance of 13 additional recorded peaks. This observation indicates the enlargement of the unit cell at the transition point. The appearance of an extra band near 688 cm⁻¹ in the monoclinic P2₁/c phase, which is due to the Si–O–Si vibration in the Si₂O₆ chains, indicates that there are two non-equivalent Si sites with different Si–O bond lengths. Most significant spectral changes appear in the far-infrared region, where Li–O and Fe–O vibrations are mainly located. Infrared bands between 300 and 330 cm⁻¹ show unusually dramatic changes at temperatures far below the transition. Compared with the infrared data of NaFeSi₂O₆ measured at low temperatures, the change in LiFeSi₂O₆ is interpreted as the consequence of mode crossing in the frequency region. A generalized Landau theory was used to analyze the order parameter of the C2/c–P2₁/c phase transition, and the results suggest that the transition is close to tricritical. Received: 21 January 2002 / Accepted: 22 July 2002     

Molecular dynamics simulations of the phase transition between low-temperature and high-temperature clinoenstatites

 Phase transition between low-temperature clinoenstatite (LT-CEn) and high-temperature clinoenstatite (HT-CEn) was studied by using molecular dynamics (MD) simulations, based on empirical potential parameters. Starting from LT-CEn, the MD calculations were carried out at atmospheric pressure and at elevated pressures (1–6 GPa). At elevated temperatures the transformation from the starting LT-CEn to HT-CEn occurred at any pressure. It was confirmed that the HT-CEn has the same space group C2/c as diopside but the M2 site is six-coordinated, unlike diopside. A significant difference in the MD-simulated cell volumes between LT-CEn and HT-CEn was also observed, showing a first-order transition. In addition, there were some temperature ranges where LT-CEN and HT-CEn would be coexistent and very small thermal hystereses between increasing and decreasing temperatures during the transition. These behaviors are consistent with the characteristic of a thermoelastic-martensitic transformation. The phase boundary between LT-CEn and HT-CEn was determined for the first time. Its positive dT/dP slope strongly shows that the high-pressure clinoenstatite is a significantly distinct phase from HT-CEn although the both phases have the same space group, C2/c. Received: 8 November 2000 / Accepted: 28 April 2001     

A dynamical model for the P1 — I1 phase transition in anorthite,CaAl2Si2O8

Electron diffraction and electron microscopic evidence is presented for a dynamical and reversible phase transition in anorthite at T _c=516 K. Antiphase boundaries with a displacement vector, R=1/2[111] become unstable at T _c, while other antiphase boundary loops with the same displacement vector are formed. These interfaces are very mobile and vibrate with a frequency which increases strongly with temperature. At temperatures considerably above T _c, a shimmering effect is observed on imaging in dark field using diffuse c reflections. These observations are in agreement with the interpretation of the high temperature body-centered phase as a statistical dynamical average of very small c type antiphase domains of primitive anorthite. We propose that the c type antiphase domains in primitive anorthite originate from ordered and anti-ordered configurations around Ca²⁺ ions at (ooo) and (oio) [likewise (zoo) and (zio)] positions. The dynamical model for the transition involves a two-stage mechanism: a softmode mechanism causing the aluminosilicate framework to approach body-centered symmetry, followed by an orderdisorder of the Ca²⁺ ion configurations. Close to T _c, statistical fluctuations set in and breathing motion type lattice vibrations of the aluminosilicate framework cause the configurations around Ca (ooo) and Ca(oio) [likewise Ca(zoo) and Ca(zio)] in the configuration to dynamically interchange through an intermediate configuration. The dynamical nature of the phase transition in anorthite is comparable to the — phase transition in quartz.     

Displacive phase transitions in C-centred clinopyroxenes: spodumene, LiScSi2O6 and ZnSiO3

The clinopyroxenes spodumene (LiAlSi₂O₆), LiScSi₂O₆ and ZnSiO₃, all with space group C2/c at ambient conditions, were studied under high pressures by single-crystal X-ray diffraction in a diamond-anvil cell. Changes in the evolution of the unit-cell parameters, optical properties and the appearance of h + k odd reflections characteristic of a primitive lattice, indicate that all three pyroxenes undergo phase transitions. The transitions are mostly displacive in character, and are non-quenchable. Transition pressures are 3.19 GPa in spodumene, ∼0.6 GPa in LiScSi₂O₆ and 1.92 GPa in ZnSiO₃. The space group of all three high-pressure phases was determined to be P2₁/c by structure refinement to single-crystal X-ray intensity data collected in the DAC. In the ZnSiO₃ clinopyroxene the intermediate P2₁/c phase further transforms to a second C2/c phase (HP-C2/c) at 4.9 GPa (confirmed by structure refinement). The volume change at this transition is about 2.6%, three times larger than in the first phase transition, and typical of the P2₁/c→ HP-C2/c phase transitions found previously in MgSiO₃, FeSiO₃, etc. These results therefore provide the first direct evidence that the HP-C2/c and the HT-C2/c structures of pyroxenes are distinct polymorphs with the same space group. The phase transition from C2/c to P2₁/c symmetry in spodumene and LiScSi₂O₆ therefore occurs because the polymorphs stable at ambient conditions are isotypic to the high-temperature C2/c phases of clinopyroxenes such as pigeonite and clinoenstatite. Received: 22 December 1999 / Accepted: 7 June 2000     

Phase transition and mixing behaviour of the cummingtonite–grunerite solid solution

 Natural amphiboles with composition close to the binary join cummingtonite–grunerite and crystals of the same samples annealed at 700 °C for 55.5 h, in order to obtain different degrees of non-convergent cation order, have been characterised by means of X-ray single-crystal diffraction and IR spectroscopy. Long-range order parameters describing the non-convergent order of Mg/Fe among the different octahedral sites have been calculated from the site occupancies of the investigated samples. Values of the O6-O5-O6 angles and of the 〈M4-O〉 mean bond distances depend on the C2/m → P2₁/m phase transition for a given degree of order. In the IR spectra, only two phonon lines dominated by the bending of the tetrahedral chains are sensitive to the displacive phase transition and to the different degree of cation order; all the other wavenumber shifts are correlated with compositional changes only. The local strains arising from the cation substitution, ordering and phase transition have been quantified by means of the autocorrelation function. Very small local heterogeneities are associated with the Mg/Fe substitution and disordering in samples at intermediate composition. The displacive phase transition seems to occur in order to reduce local distortions and the P2₁/m samples are as homogeneous as orthorhombic anthophyllites. The orthorhombic structure, however, appears less flexible than the monoclinic in accommodating cations larger than Mg at the octahedral sites. Received: 9 February 2000 / Accepted: 30 September 2000     

The orientation and vibrational states of H2O in synthetic alkali-free beryl

 The polarized single-crystal Raman spectra of synthetic H₂O-containing alkali-free beryl were recorded at room and low temperatures, and the polarized single-crystal IR spectra at room temperature. The H₂O molecule in the channel cavities is characterized by a Raman-active symmetric stretching vibration (ν₁) at 3607 cm⁻¹ and an IR-active asymmetric stretch (ν₃) at 3700 cm⁻¹ at room temperature. At low temperatures this ν₃ mode is observed in the Raman. Weak ν₁ and ν₃ modes of a second type of H₂O are also observed in the Raman spectra but only at 5 K. The H⋯&middot;H vector of the most abundant type of H₂O is parallel to the channel axis of beryl along [0 0 0 1]. The components of the polarizability tensor of the ν₁ mode of H₂O are similar to, but not exactly the same as, those of a free H₂O molecule. The Raman measurements indicate that the H₂O molecule is rotationally disordered around [0 0 0 1]. External translation and librational modes of H₂O could be observed as overtones with the internal H₂O-stretching modes. In the case of the librational motions, normal modes could also be observed directly in the Raman spectra at ∼200 cm⁻¹. The energies of the translational modes can be determined from an analysis of the overtones and are about 9 cm⁻¹ in energy (i.e., T_z). The energies of the librational modes are about 210 cm⁻¹ for R_x and 190 cm⁻¹ for R_y. Received: 8 April 1999 / Accepted: 5 April 2000     

Structural changes in sodium tetrasilicate glass around the liquid-glass transition: a neutron diffraction study

The structure of sodium tetrasilicate (Na₂Si₄O₉) glass and melt was studied in the range from 300 to 950?K by neutron diffraction. Increasing temperature leads to gradual decrease of the peak intensities in the static structure factors possibly with a change in the slope at the glass transition temperature (T _g?773?K), but no shift and broadening of the peaks is observed. Especially, the position of the first sharp diffraction peak (FSDP) at 1.6?Å^–1 remains constant in the whole temperature range studied. The corresponding pair correlation functions g(r) are very similar at all temperatures. Only a slight broadening of the Si-O and O-O first nearest-neighbour peaks with temperature is observed, which can be attributed to temperature enhanced dynamic distortions of the SiO₄ tetrahedra. All these results suggest that there is little change not only in the short- but also in the medium-range order of the sodium tetrasilicate glass and melt around the glass-liquid transition.     

High-pressure stability, structure and compressibility of Cmcm -MgAl2O4: an ab initio study

 Quantum-mechanical solid-state calculations have been performed on the highest-pressure polymorph of magnesium aluminate (CaTi₂O₄-type structure, Cmcm space group), as well as on the low-pressure (Fd3ˉm) spinel phase and on MgO and Al₂O₃. An ab initio all-electron periodic scheme with localized basis functions (Gaussian-type atomic orbitals) has been used, employing density-functional-theory Hamiltonians based on LDA and B3LYP functionals. Least-enthalpy structure optimizations in the pressure range 0 to 60 GPa have allowed us to predict: (1) the full crystal structure, the pV equation of state and the compressibility of Cmcm-MgAl₂O₄ as a function of pressure; (2) the phase diagram of the MgO–Al₂O₃–MgAl₂O₄ system (with exclusion of CaFe₂O₄-type Pmcn-MgAl₂O₄), and the equilibrium pressures for the reactions of formation/decomposition of the Fd3ˉm and Cmcm polymorphs of MgAl₂O₄ from the MgO + Al₂O₃ assemblage. Cmcm-MgAl₂O₄ is predicted to form at 39 and 57 GPa by LDA and B3LYP calculations, with K ₀=248 (K′=3.3) and 222 GPa (K′=3.8), respectively. Results are compared to experimental data, where available, and the performance of different DFT functionals is discussed. Received: 31 January 2001 / Accepted: 16 May 2001     

High-pressure phase transition and behavior of protons in brucite Mg(OH)2: a high-pressure–temperature study using IR synchrotron radiation

 Infrared absorption spectra of brucite Mg (OH)₂ were measured under high pressure and high temperature from 0.1 MPa 25 °C to 16 GPa 360 °C using infrared synchrotron radiation at BL43IR of Spring-8 and a high-temperature diamond-anvil cell. Brucite originally has an absorption peak at 3700 cm⁻¹, which is due to the OH dipole at ambient pressure. Over 3 GPa, brucite shows a pressure-induced absorption peak at 3650 cm⁻¹. The pressure-induced peak can be assigned to a new OH dipole under pressure. The new peak indicates that brucite has a new proton site under pressure and undergoes a high-pressure phase transition. From observations of the pressure-induced peak under various P–T condition, a stable region of the high-pressure phase was determined. The original peak shifts to lower wavenumber at −0.25 cm⁻¹ GPa⁻¹, while the pressure-induced peak shifts at −5.1 cm⁻¹ GPa⁻¹. These negative dependences of original and pressure-induced peak shifts against pressure result from enhanced hydrogen bond by shortened O–H···O distance, and the two dependences must result from the differences of hydrogen bond types of the original and pressure-induced peaks, most likely from trifurcated and bent types, respectively. Under high pressure and high temperature, the pressure-induced peak disappears, but a broad absorption band between 3300 and 3500 cm⁻¹ was observed. The broad absorption band may suggest free proton, and the possibility of proton conduction in brucite under high pressure and temperature. Received: 16 July 2001 / Accepted: 25 December 2001     

Determination of the mechanism of cation ordering in magnesioferrite (MgFe2O4) from the time- and temperature-dependence of magnetic susceptibility

The kinetics of non-convergent cation ordering in MgFe₂O₄ have been studied by measuring the Curie temperature (T _c) of synthetic samples as a function of isothermal annealing time. The starting material was a synthetic sample of near-stoichiometric MgFe₂O₄, synthesised from the oxides in air and quenched from 900 °C in water. Ordering experiments were performed using small chips of this material and annealing them at temperatures between 450 °C and 600 °C. The chips were periodically removed from the furnace, and their Curie temperatures were determined from measurements of alternating-field magnetic susceptibility (χ) as a function of temperature (T) to 400 °C. The Curie temperature of MgFe₂O₄ is very sensitive to the intracrystalline distribution of Fe³⁺ and Mg cations between tetrahedral and octahedral sites of the spinel crystal structure, and hence provides a very sensitive probe of the cation ordering process. The χ-T curve for the starting material displays a single sharp magnetic transition at a temperature of 303 °C. During isothermal annealing, the χ-T curve develops two distinct magnetic transitions; the first at a temperature corresponding to T _c for the disordered starting material and the second at a higher temperature corresponding to T _c for the equilibrium ordered phase. The size of the magnetic signal from the ordered phase increases smoothly as a function of time, until equilibrium is approached and the shape of the χ-T curve corresponds to a single sharp magnetic transition for the homogeneous ordered phase. These observations demonstrate that cation ordering in MgFe₂O₄ proceeds via a heterogeneous mechanism, involving the nucleation and growth of fine-scale domains of the ordered phase within a matrix of disordered material. Disordering experiments were performed by taking material equilibrated at 558 °C and annealing it at 695 °C. The mechanism of isothermal disordering is shown to involve nucleation and growth of disordered domains within an ordered matrix, combined with continuous disordering of the ordered matrix. This mixed mechanism of disordering may provide an explanation for the difference between the rates of ordering and disordering observed in MgFe₂O₄ using X-ray diffraction. The origin of the heterogeneous ordering/disordering mechanism is discussed in terms of the Ginzburg-Landau rate law. It is argued that heterogeneous mechanisms are likely to occur in kinetic experiments performed far from equilibrium, whereas a homogeneous mechanism may operate under slow equilibrium cooling. The implications of these observations for geospeedometry are discussed. Received: 12 May 1998 / Accepted: 25 June 1998