Computational study of tetrahedral Al–Si ordering in muscovite

 The nature of Al–Si ordering across the tetrahedral sites in muscovite, K₂Al₄(Si₆Al₂O₂₀)(OH)₄, was investigated using various computational techniques. Values of the atomic exchange interaction parameters J _l were obtained. From these parameters, a two-dimensional Al–Si ordering scheme was deduced. The transition temperature T _c for this two-dimensional ordering is 1900 K. There are several possible ordering schemes in three dimensions, based on different stacking sequences of ordered sheets of tetrahedral sites. Monte Carlo simulations of both two-dimensional and three-dimensional ordering were performed, but in the three-dimensional simulation only the two-dimensional ordering is seen, implying that three-dimensional ordering is too slow to be attained during the timescale of the simulation. The effect of the three-dimensional interactions is to raise the two-dimensional ordering temperature to 2140 K. From the three-dimensional Monte Carlo simulation, the frequency of occurrence of 4Si0Al, 3Si1Al, 2Si2Al and 1Si3Al clusters was determined, which match those inferred by ²⁹Si MAS–NMR measurements reasonably well. In fact, the match suggests that the cation ordering seen in experiments corresponds to a configuration with considerable short-range order but no long-range order, similar to a state that is at a temperature just above an ordering phase transition. Received: 28 August 2000 / Accepted: 12 March 2001     

A statistical-mechanics model of ordering in aluminosilicate solid solutions

A statistical-thermodynamic approximation for order-disorder phase transitions in aluminosilicate solid solutions is presented. The approximation involves estimating the number of configurations with long range order parameter Q and short range order parameter σ, using an approximation to the probability that a configuration with the correct amount of long range order will also have the correct amount of short range order. This estimate is then used to give a free energy F(Q, σ, x, T), where x is the concentration of Al in the structure, and hence quantities such as T _c (x) are estimated. The predictions of the model for T _c (x) and the critical concentration x _c at which T _c falls to zero are shown to be in good agreement with the results of Monte Carlo simulations. Received: 14 May 1997 / Revised, accepted: 2 June 1997     

A computational study of Al/Si ordering in cordierite

The ordering of Al and Si in Mg cordierite Mg₂Al₄Si₅O₁₈ is considered using computer simulation. First the enthalpy of interaction J _ij between sites is derived by computer modelling 101 different Al/Si configurations and analysing their energies. They are compared with similar results for three other minerals and with ab initio calculations to assess the whole approach. Secondly the ordering process is studied using Monte Carlo simulation applied to the J _ij . The ordering phase transition temperature T _c is found as 1800°C in reasonable agreement with the experimental estimate of 1450° C. These are much lower than the estimate T _c(ABW)≈7600°C obtained from Bragg-Williams theory. Strong short-range order sets in below T _c(ABW), and the reasons for much lower temperature T _c of long-range ordering are discussed. Strong short-range also sets in very rapidly in a simulated anneal, in agreement with experiment. Thirdly an attempt is made to compare our calculated enthalpies directly with the results of NMR and calorimetry experiments, not completely successfully. A free energy ΔG≈4.6 eV for the activation barrier for ordering is suggested.     

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     

Computer modelling of Al/Si ordering in sillimanite

Computer simulation is used to investigate the effect of Al/Si disordering over the tetrahedral sites on the lattice energy and the lattice constants of the mineral sillimanite Al₂SiO₅. A methodology for an atomistic assessment of the energy of the reaction 2(Si-O-Al)→(Si-O-Si)+(Al-O-Al) and its various contributions is established. This ordering energy is 0.97 eV for nearest neighbour sites in the ab-plane and 0.56 eV for those separated in the c-direction. The large difference is due to a greater constraint on the atomic relaxation in the ab-plane and shows the structural dependence of the ordering energy. Its magnitude appears to be determined by a complicated balance between Coulomb and short-range repulsive energy involving strain over many bonds, both in the ordered and disordered structures. There is also a significant interaction between second neighbour sites whereas the contribution of more distant neighbours is negligible. The lattice energies of most of the 154 configurations studied show a linear behaviour as a function of short-range order, specified by the number of Al-Al pairs. The ordering temperature T_c, estimated on the basis of a statistical mechanical model of disordering, and the calculated ordering energies are in semi-quantitative agreement with experimental values.     

Cation ordering in BaAl2Ge2O8-feldspar: implications for the phase transition in anorthite

BaAl₂Ge₂O₈-Feldspar undergoes an order-disorder phase transition I2/c↔C2/m at T _tr ≈1690 K. The thermodynamics of the Al,Ge cation ordering process is described in terms of the compressible Ising model in mean field approximation. The mean field potential predicts a first order character of the phase transition. This is compared to antiferromagnetic ordering in a two-dimensional square Ising model with NN-pair interactions and four-spin interactions on alternating squares. Calculated order parameters and short range ordering are in good agreement with the corresponding properties observed in BaAl₂Ge₂O₈-feldspar by means of X-ray diffraction, hard mode infrared spectroscopy and TEM. Using known calorimetric data a similar model is postulated for Al,Si ordering in anorthite, CaAl₂Si₂O₈, for which the derived potential describes a transition with slightly stronger first order character at T _tr ≈1928 K. Received: 30 January 1998 / Revised, accepted: 29 August 1998     

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     

NMR-spectroscopy of synthetic potassium-bearing cordierites

Potassic cordierites with the chemical composition K _x Mg₂Al_4+x Si₅–xO₁₈ (x = 0.00, 0.10, 0.20, and 0.25) were synthesized by annealing glasses at 1290° C for different lengths of time. The procedure resulted in cordierites with different states of Al,Si-order for the tetrahedral sites in the structure. The dependence between the potassium-content and the state of order on one side and between annealing time and the state of order on the other side was then studied using ²⁹Si MAS nuclear magnetic resonance (NMR) spectroscopy. The spectra show that the state of order is a continuous function of annealing time for all compositions considered, but the rate of ordering decreases with increasing K-content. Since the substitution K+Al Si leads to higher Al/Si-ratios; the lower rate of ordering is discussed as a consequence of changed statistics for Al, Si site exchanges. The Al atoms replacing silicon in the structure to balance the charge of potassium cations are not located close to the potassium ion but at a maximum distance from it. This is shown to be a consequence of an improvement in coordination of all oxygen atoms in the cordierite framework.     

H T -XRD study of synthetic ferrian magnesian spodumene: the effect of site dimension on the P 21/ c → C 2/ c phase transition

 Ferrian magnesian spodumene was synthesized in the MLFSH system at P=0.4 GPa, T=700 °C, fO₂=NNO+2.3. The space group at room T is P2₁/c [a=9.638(3) ?, b=8.709(2) ?, c=5.258(2) ?, β=109.83(3)^∘, V=415.2 ?³]. The structure is topologically equivalent to that of ferrian spodumene, LiFeSi₂O₆, and has two symmetrically independent tetrahedral chains, A and B, and two independent octahedral sites, M1 and M2. The crystal-chemical composition was determined combining EMP, SIMS and single-crystal XRD analysis, yielding ^M2(Li_0.85Mg_0.09Fe²⁺ _0.06) ^M1(Fe³⁺ _0.85Mg_0.15)Si₂O₆. Li is ordered at the M2 site and Fe³⁺ is ordered at the M1 site, whereas Mg (and Fe²⁺) distribute over both octahedral sites. Structure refinements done at different temperatures (25, 70, 95, 125, 150 and 200 °C) allowed characterization of a reversible displacive P2₁/c→C2/c transition at 106 °C. Previous HT-XRD studies of Li-clinopyroxenes had shown that the transition temperature is inversely related to the size of the M1 cation. For the crystal of this work, the aggregate ionic radius at M1 is longer than that of ferrian spodumene, for which the transition temperature is −44 °C. The higher transition temperature observed can only be explained on the basis of the shorter aggregate radius at the M2 site (due to the presence of Mg substituting after Li), in keeping with the results obtained for ferromagnesian P2₁/c pyroxenes. The effects of all the chemical substitutions must be considered when modelling transition temperatures and thermodynamic behaviour in clinopyroxenes. Received: 7 May 2002 / Accepted: 23 October 2002     

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     

Al,Si ordering on cordierite using “magic angle spinning” NMR

Silicon-29 “magic angle spinning” nuclear magnetic resonance (NMR) spectroscopy has been used to study the changes in local Si environment during Al, Si ordering in synthetic cordierite, Mg₂Al₄Si₅O₁₈. In the most disordered form, crystallized from a glass, eight distinct tetrahedral sites for silicon can be identified and assigned, while there are only two distinguishable Si sites in the well-annealed ordered form. This allows the changes in the Si site environments to be determined as a function of annealing time for the transformation from the disordered to the ordered form. The first crystallized state has a considerable degree of partitioning between T₁ and T₂ sites with the following site occupancies: T₁ ? Al:Si=0.80:0.20, T₂?Al:Si=0.27:0.73 The changes in Si environment are approximately linear with log time. The measured values of ²⁹Si isotropic chemical shift do not fit well to previously determined correlations of shift with various structural parameters.     

Cr and Al diffusion in chromite spinel: experimental determination and its implication for diffusion creep

Diffusion coefficients of Cr and Al in chromite spinel have been determined at pressures ranging from 3 to 7 GPa and temperatures ranging from 1,400 to 1,700°C by using the diffusion couple of natural single crystals of MgAl₂O₄ spinel and chromite. The interdiffusion coefficient of Cr–Al as a function of Cr# (=Cr/(Cr + Al)) was determined as D _Cr–Al = D ₀ exp {−(Q′ + PV*)/RT}, where D ₀ = exp{(10.3 ± 0.08) × Cr#^0.54±0.02} + (1170 ± 31.2) cm²/s, Q′ = 520 ± 81 kJ/mol at 3 GPa, and V* = 1.36 ± 0.25 cm³/mol at 1,600°C, which is applicable up to Cr# = 0.8. The estimation of the self-diffusion coefficients of Cr and Al from Cr–Al interdiffusion shows that the diffusivity of Cr is more than one order of magnitude smaller than that of Al. These results are in agreement with patterns of multipolar Cr–Al zoning observed in natural chromite spinel samples deformed by diffusion creep.     

The effect of oxygen vacancies and aluminium substitution on the high-pressure properties of brownmillerite-structured Ca2Fe2?xAlxO5

The structural evolution with pressure and the equations of state of three members of the brownmillerite solid solution, Ca₂(Fe_2−x Al _x )O₅, have been determined by single-crystal X-ray diffraction up to a maximum pressure of 9.73 GPa. The compositions of the samples were x = 0.00 and x = 0.37 (with Pnma symmetry) and x = 0.55 (with I2mb symmetry). No phase transitions were observed in the experiments. The equation of state parameters determined from the pressure-volume data are K _0T = 128.0 (7) GPa, K′₀ = 5.8 (3) for the sample with x = 0.00, K _0T = 131 (2) GPa, K′₀ = 5.5 (4) for x = 0.37, and K _0T = 137.5 (6) GPa, K′₀ = 4 for x = 0.55. The bulk modulus therefore increases with Al content, being 11% higher in the x = 0.55 sample than in the Al-free sample. The unit-cell compression is anisotropic, with the c-axis being stiffer than a or b, and the anisotropy increases with increasing Al content of the structure. The structural response to pressure of all samples is similar. The (Al,Fe)O₄ tetrahedra and the (Al,Fe)O₆ octahedra undergo approximately isotropic compression. There is an increase in the twists of the chains of corner-sharing (Al,Fe)O₄ tetrahedra, and an increase in the tilts of the (Al,Fe)O₆ octahedra, because these framework polyhedra are stiffer than the Ca–O bonds to the extra-framework Ca site. The alignment of the two shortest Ca–O bonds sub-parallel to [001] accounts for the relative stiffness of the c-axis and thus the elastic anisotropy. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Thermal expansion and structural transformations of stuffed derivatives of quartz along the LiAlSiO4–SiO2 join: a variable-temperature powder synchrotron XRD study

 The structural behavior of stuffed derivatives of quartz within the Li_{1− x} Al_{1− x} Si_{1+ x} O₄ system (0 ≤ x ≤ 1) has been studied in the temperature range 20 to 873 K using high-resolution powder synchrotron X-ray diffraction (XRD). Rietveld analysis reveals three distinct regimes whose boundaries are defined by an Al/Si order-disorder transition at x=∼0.3 and a β–α displacive transformation at x=∼0.65. Compounds that are topologically identical to β-quartz (0 ≤ x < ∼0.65) expand within the (0 0 1) plane and contract along c with increasing temperature; however, this thermal anisotropy is significantly higher for structures within the regime 0 ≤ x < ∼0.3 than for those with compositions ∼0.3 ≤ x < ∼0.65. We attribute this disparity to a tetrahedral tilting mechanism that occurs only in the ordered structures (0 ≤ x < ∼0.3). The phases with ∼0.65 ≤ x ≤ 1 adopt the α-quartz structure at room temperature, and they display positive thermal expansion along both a and c from 20 K to their α–β transition temperatures. This behavior arises mainly from a rotation of rigid Si(Al)-tetrahedra about the <100> axes. Landau analysis provides quantitative evidence that the charge-coupled substitution of Li+Al for Si in quartz dampens the α–β transition. With increasing Li+Al content, the low-temperature modifications exhibit a marked decrease in spontaneous strain; this behavior reflects a weakening of the first-order character of the transition. In addition, we observe a linear decrease in the α–β critical temperature from 846 K to near 0 K as the Li+Al content increases from x=0 to x=∼0.5. Received: 26 June 2000 / Accepted: 1 December 2000     

Computational study of tetrahedral Al–Si and octahedral Al–Mg ordering in phengite

 As part of a wider study of the nature and origins of cation order–disorder in micas, a variety of computational techniques have been used to investigate the nature of tetrahedral and octahedral ordering in phengite, K₂ ^[6](Al₃Mg)^[4](Si₇Al)O₂₀(OH)₄. Values of the atomic exchange interaction parameters J _n used to model the energies of order–disorder were calculated. Both tetrahedral Al–Si and octahedral Al–Mg ordering were studied and hence three types of interaction parameter were necessary: for T–T, O–O and T–O interactions (where T denotes tetrahedral sites and O denotes octahedral sites). Values for the T–T and O–O interactions were taken from results on other systems, whilst we calculated new values for the T–O interactions. We have demonstrated that modelling the octahedral and tetrahedral sheets alone and independently produces different results from modelling a whole T–O–T layer, hence justifying the inclusion of the T–O interactions. Simulations of a whole T–O–T layer of phengite indicated the presence of short-range order, but no long-range order was observed. Received: 8 August 2002 / Accepted: 14 February 2003 Acknowledgements The authors are grateful to EPSRC (EJP) and the Royal Society (CIS) for financial support. Monte Carlo simulations were performed on the Mineral Physics Group's Beowulf cluster and the University of Cambridge's High Performance Computing Facility.     

Al hematites prepared by homogeneous precipitation of oxinates: material characterization and determination of the Morin transition

A novel method for synthesis of aluminium hematites, based upon the homogeneous precipitation of Fe and Al oxinates in various proportions, is presented. The precursor precipitates are heated in air at 700?°C. X-ray diffraction, thermal analyses, BET, FTIR, optical reflection analysis, TEM and Mössbauer spectroscopy at room temperature and 80?K of the resulting products indicate that single-phase hematites are formed with structural Al substitution of up to 10 at%. Interestingly, the particle size (>100?nm) is not substantially reduced by the Al content. Although it remains difficult to obtain a homogeneously distributed Al substitution in the final hematite, this processing line offers a unique opportunity to separate the effects of grain size and Al substitution on the Morin transition temperature (T _M) of Al hematite. From the comparison between the present hematites and a series of Al-substituted hematites with lepidocrocite as precursor, it could be shown that the effect on T _M, associated with a change of a factor 10 in grain size, is about 1/3 of the effect caused by a change of 10 in the degree of substitution. Finally, it is suggested that proper thermal treatments under different conditions of the same precursors are likely to produce spinel phases.     

Thermodynamics of mixing in diopside–jadeite,CaMgSi<Subscript>2</Subscript>O<Subscript>6</Subscript>–NaAlSi<Subscript>2</Subscript>O<Subscript>6</Subscript>, solid solution from static lattice energy calculations

Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have been performed for a set of 800 different structures in a 2 × 2 × 4 supercell of C2/c diopside with compositions between diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273–2,023 K and to calculate a temperature–composition phase diagram. The simulations predict the order–disorder transition in omphacite at 1,150 ± 20°C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433–440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1–M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral 83:419–433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600°C.     

Low-temperature thermodynamic properties of disordered zeolites of the natrolite group

 The heat capacity of paranatrolite and tetranatrolite with a disordered distribution of Al and Si atoms has been measured in the temperature range of 6–309 K using the adiabatic calorimetry technique. The composition of the samples is represented with the formula (Na_1.90K_0.22Ca_0.06)[Al_2.24Si_2.76O₁₀]·nH₂O, where n=3.10 for paranatrolite and n=2.31 for tetranatrolite. For both zeolites, thermodynamic functions (vibrational entropy, enthalpy, and free energy function) have been calculated. At T=298.15 K, the values of the heat capacity and entropy are 425.1 ± 0.8 and 419.1 ±0.8 J K⁻¹ mol⁻¹ for paranatrolite and 381.0 ± 0.7 and 383.2 ± 0.7 J K⁻¹ mol⁻¹ for tetranatrolite. Thermodynamic functions for tetranatrolite and paranatrolite with compositions corrected for the amount of extraframework cations and water molecules have also been calculated. The calculation for tetranatrolite with two water molecules and two extraframework cations per formula yields: C _p (298.15)=359.1 J K⁻¹ mol⁻¹, S(298.15) −S(0)=362.8 J K⁻¹ mol⁻¹. Comparing these values with the literature data for the (Al,Si)-ordered natrolite, we can conclude that the order in tetrahedral atoms does not affect the heat capacity. The analysis of derivatives dC/dT for natrolite, paranatrolite, and tetranatrolite has indicated that the water- cations subsystem within the highly hydrated zeolite may become unstable at temperatures above 200 K. Received: 30 July 2001 / Accepted: 15 November 2001     

Microsommite: crystal chemistry, phase transitions, Ising model and Monte Carlo simulations

Microsommite, ideal formula [Na₄K₂(SO₄)] [Ca₂Cl₂][Si₆Al₆O₂₄], is a rare feldspathoid that occurs in volcanic products of Vesuvius. It belongs to the cancrinite–davyne group of minerals, presenting an ABAB… stacking sequence of layers that contain six-membered rings of tetrahedra, with Si and Al cations regularly alternating in the tetrahedral sites. The structure was refined in space group P6₃ to R=0.053 by means of single-crystal X-ray diffraction data. The cell parameters are a=22.161?Å=√3a _dav, c=5.358?Å=c _dav; Z=3. The superstructure arises due to the long-range ordering of extra-framework ions within the channels of the structure. This ordering progressively decreases with rising temperature until it is completely lost and microsommite transforms into davyne. The order–disorder transformation has been monitored in several crystals by means of X-ray superstructure reflections and the critical parameters T _c?≈?750?°C and β?≈?0.12 were obtained. The kinetics of the ordering process were followed at different temperatures and the activation energy was determined to be about 125?kJ?mol^?1. The continuous order–disorder phase transition in microsommite has been discussed on the basis of a two-dimensional Ising model in a triangular lattice with nn (nearest neighbours) and nnn (next-nearest neighbours) interactions. Such a model was simulated using a Monte Carlo technique. The theoretical model well matches the experimental data; two phase transitions were indicated by the simulated runs: at low temperature only one of the three sublattices begins to disorder, whereas the second transition involves all three sublattices.     

Magnetic phase diagrams of Mg-, Fe-, (Cu + Ti)- and Cu-substituted braunite Mn<Superscript>2+</Superscript>Mn<Subscript>6</Subscript><Superscript>3+</Superscript>SiO<Subscript>12</Subscript>

 The magnetic behavior of the Jahn-Teller structure braunite, (Mn²⁺ _1−yM _y )(Mn³⁺ _{6− x} M_x)SiO₁₂, is strongly influenced by the incorporation of elements substituting manganese. Magnetic properties of well-defined synthetic samples were investigated in dependence on the composition. The final results are presented in magnetic phase diagrams. To derive the necessary data, ac susceptibility and magnetization of braunites with the substitutional elements M = Mg, Fe, (Cu+Ti) and Cu were measured. Whereas the antiferromagnetic ordering temperature, T _N , of pure braunite is hardly affected by the substitution of nonmagnetic Mg, it is rapidly suppressed by the substitution of magnetic atoms at the Mn positions. Typically for a concentration (x, y) ≥ 0.7 of the substituted elements, a spin glass phase occurs in the magnetic phase diagrams. Additionally, for the braunite system with Fe³⁺ substitutions, we observe in the concentration range 0.2 < x< 0.7 a double transition from the paramagnetic state, first to the antiferromagnetic state, followed by a transition to a spin glass state at lower temperatures. The unusual change of the magnetic properties with magnetic substitution at the Mn positions is attributed to the peculiar antiferromagnetic structure of braunite, which has been resolved recently. Received: 19 April 2001 / Accepted: 6 September 2001