The single crystal elastic moduli of neighborite

The adiabatic elastic moduli of a single crystal of Neighborite (NaMgF ₃ perovskite) have been measured at ambient conditions using Brillouin spectroscopy. The adiabatic aggregate (Voight-Reuss-Hill) bulk modulus is K = 75.6 GPa, and shear modulus is = 46.7 GPa. The experimental results show the ratio of linear compressibilities _b / _a = 0.80 for neighborite. These ratios reflect the different amounts of tilting freedom of the octahedral framework along each lattice axis of the perovskite structure. It is understood that the elastic compliance S _ij of the crystal can directly sense the behavior of the octahedral tilting in the structural distortion of NaMgF₃ perovskite. The octahedral tilting angles are considered to be the order parameters of the ferroelastic phase transition in the perovskite structure. Single crystal elasticity data provide a basis for understanding the role of octahedral tilting in the ferroelasticity of perovskite. Together with high pressure compressional data, one can thus elucidate the relationship between crystal structure and physical properties of perovskite. A detailed assessment indicates that the dominant compression mechanism for NaMgF₃ perovskite is shortening of the octahedral [MgF] bond, which is also true for orthorhombically distorted MgSiO₃ perovskite.     

Pressure and temperature dependence of the elastic properties of synthetic MnO

The adiabatic elastic stiffness constants of synthetic single-crystal MnO were measured in this study using pulse superposition interferometry. Data were obtained up to 1.0 GPa in pressure and over the temperature range 273 to 473 K. As a result, we were able to determine the complete set of second-order stiffness moduli (C _ij ^s ) and their pressure and temperature derivatives, as well as higher-order properties for selected modes. Relevant results for the adiabatic bulk modulus are: K ^s=155.1±0.8 GPa; (K^s/P)_T=4.70±0.13; and, (K ^s/T)_P= -0.0203±0.0009 GPa/K. Our results for the second-order moduli are generally consistent with the data from previous studies. However, relative to the estimated uncertainties, small and systematic discrepancies appear to characterize the data set. The available evidence indicates that the differences result from microstructural variations (in particular, microcracks and Mn₃O₄ inclusions) between the synthetic MnO specimens used in different investigations. The pure shear mode C ₄₄ exhibits anomalous soft-mode behavior with both temperature (the ambient derivative is positive) and pressure (the ambient derivative is negative). In both cases the C ₄₄ data trends appear to primarily reflect the influence of Mn-Mn magnetoelastic interactions associated with the onset of a paramagnetic-antiferromagnetic (PM AFM) phase transition.     

The extrapolation of elastic moduli to high pressure and temperature

The elastic constants of a crystal under stress, defined as the second derivative of the crystal free energy with respect to strain, require a correction related to the static pressure at non-zero pressures. The corrections required for the elastic constants calculated by the free energy minimisation code PARAPOCS are described and tested by comparison with the elastic constants calculated numerically by applying small stresses in the appropriate orientations to simulated crystals of fluorite, forsterite, α-quartz and albite. The corrected elastic constants are then used to investigate the extrapolation of the bulk and shear moduli (and hence also the seismic wave velocities V _p and V _s) of β-spinel and forsterite to upper mantle pressures. A Murnaghan equation, thirdorder Eulerian finite strain equation, second order polynomial equation and a logistic equation were all fitted to the simulated bulk and shear moduli between 0 and 3 GPa pressure. The parameters derived for these equations are used to extrapolate the bulk and shear moduli to 14 GPa and the results are compared to the simulated high pressure moduli. Over this pressure range, the second order polynomial provides the best extrapolation of the bulk modulus, but the use of the logistic equation results in the best extrapolation of the shear modulus.     

Pressure dependence of the elastic constants of nonmetamict zircon

The single crystal elastic constants of nonmetamict zircons have been measured as a function of pressure to 12 kb at room temperature and also as a function of temperature between 25 and 300° C at atmospheric pressure. The pressure derivatives of the elastic constants are: C ₁₁=10.78, C ₃₃=5.88, C ₄₄=0.99, C ₆₆=?0.31, C ₁₂=3.24, C ₁₃=6.20. The anomalous negative behaviour of C ₆₆ versus pressure could be associated with a high pressure phase transition. The pressure and temperature derivatives of the isotropic elastic wave velocities and elastic moduli for nonmetamict zircon are calculated from the present single crystal data by the Voigt, Ruess, and Hill approximations and compared with the values of some other oxides and silicates. The pressure derivative of the isotropic adiabatic bulk modulus is relatively high (dK _S/dP=6.50), and the pressure derivative of the shear modulus is relatively low, (dG/dP=0.78), compared to the corresponding values for some other oxides and silicates. The Debye temperature, ?_D, and the high temperature limit of the Grüneisen parameter, γ_Ht, calculated from the elastic constants and their pressure derivatives, agrees well with the Debye temperature and the thermal Grüneisen parameter, γ_th, calculated from the thermal expansion, heat capacity, and compressibility data.     

High-pressure crystal chemistry of MgSiO3 perovskite

A high-pressure single-crystal x-ray diffraction study of perovskite-type MgSiO₃ has been completed to 12.6 GPa. The compressibility of MgSiO₃ perovskite is anisotropic with b approximately 23% less compressible than a or c which have similar compressibilities. The observed unit cell compression gives a bulk modulus of 254 GPa using a Birch-Murnaghan equation of state with K set equal to 4 and V/V ₀ at room pressure equal to one. Between room pressure and 5 GPa, the primary response of the structure to pressure is compression of the Mg-O and Si-O bonds. Above 5 GPa, the SiO₆ octahedra tilt, particularly in the [bc]-plane. The distortion of the MgO₁₂ site increases under compression. The variation of the O(2)-O(2)-O(2) angles and bondlength distortion of the MgO₁₂ site with pressure in MgSiO₃ perovskite follow trends observed in GdFeO₃type perovskites with increasing distortion. Such trends might be useful for predicting distortions in GdFeO₃-type perovskites as a function of pressure.     

Composition, lattice parameters, and room temperature elastic constants of natural single crystal xenotime from Novo Horizonte

The composition, lattice parameters, and elastic constants of natural single crystal YPO₄ xenotime from Novo Horizonte (Brazil) were determined using EPMA, XRD, and the pulse-echo technique. The composition indicates a 24% substitution of Y sites with other rare-earth elements. The lattice parameters of the studied crystal deviated only slightly from those reported for synthetic YPO₄ and were in a good agreement with trends obeyed by other orthophosphates with the xenotime structure. The measured elastic constants C ₁₁, C ₃₃, C ₄₄, and C ₆₆ were consistent with synthetic crystals when porosity was accounted for. C ₁₂ and C ₁₃ constants were evaluated based on the comparison with other materials with xenotime structure. The elastic constants could be rationalized using interionic force constants and bond energies.

Pressure and temperature dependence of cation distribution in Mg-Mn olivine

Synthetic (Mg_0.51, Mn_0.49)₂SiO₄ olivine samples are heat-treated at three different pressures; 0, 8 and 12 GPa, all at the same temperature (～500° C). X-ray structure analyses on these single crystals are made in order to see the pressure effect on cation distribution. The intersite distribution coefficient of Mg and Mn in M1 and M2 sites, K _D = (Mn/Mg) _M1/(Mn/Mg) _M2, of these samples are 0.192 (0 GPa), 0.246 (8 GPa) and 0.281 (12 GPa), indicating cationic disordering with pressure. The small differences of cell dimensions between these samples are determined by powder X-ray diffraction. Cell dimensions b and c decrease, whereas a increases with pressure of equilibration. Cell volume decreases with pressure as a result of a large contraction of the b cell dimension. The effect of pressure on the free energy of the cation exchange reaction is evaluated by the observed relation between the cell volume and the site occupancy numbers. The magnitude of the pressure effect on cation distribution is only a fifth of that predicted from the observed change in volume combined with thermodynamic theory. This phenomenon is attributed to nonideality in this solid solution, and nonideal parameters are required to describe cation distribution determined in the present and previous experiments. We use a five-parameter equation to specify the cationic equilibrium on the basic of thermodynamic theory. It includes one energy parameter of ideal mixing, two parameters for nonideal effects, one volume parameter, and one thermal parameter originated from the lattice vibrational energy. The present data combined with some of the existing data are used to determine the five parameters, and the cation distribution in Mg-Mn olivine is described as a function of temperature, pressure, and composition. The basic framework of describing the cationic behavior in olivine-type mineral is worked out, although the result is preliminary: each of the determined parameters is not accurate enough to enable us to make a reliable prediction.     

Ferroelastic phase transition in cryolite,Na3AlF6, a mixed fluoride perovskite: High temperature single crystal X-ray diffraction study and symmetry analysis of the transition mechanism

Cryolite, Na₃AlF₆[ = 2Na⁺(Na_0.5 ⁺Al_0.5 ³⁺)F₃] is a mixed fluoride perovskite, in which the corner-sharing octahedral framework is formed by alternating [NaF₆] and [AlF₆] octahedra and the cavities are occupied by Na⁺ ions. At 295 K, it is monoclinic (α phase), space group P2 ₁/n with a = 5.4139 (7), b = 5.6012 (5) and c = 7.7769 (8) Å and β = 90.183 (3)°, Z = 2. A high temperature single crystal X-ray diffraction study in the range 295–900 K indicates a fluctuation-induced first-order phase transition from monoclinic to orthorhombic symmetry at T ₀ ～ 885 K, in contrast to a previous report that it becomes cubic at ～823 K. The space group of the high temperature β phase is Immm with a = 5.632 (4), b = 5.627 (3) and c = 7.958 (4) Å, Z = 2 at 890 K. Above T ₀, the coordination number of the Na⁺ ion in the cavity increases from eight to twelve and the zigzag Na1 — Al octahedral chains parallel to c become straight with the Na1-F-Al angle = 180 °. The phase transition is driven by two coupled primary order parameters. The first corresponds to the rotation of the nearly rigid [AlF₆] group and transforms according to the Γ ₄ ⁺ irreducible representation of Immm. Coupled to the [AlF₆] rotation is a second primary order parameter corresponding to the displacement of the Na2⁺ ion in the cavity from its equilibrium position. This order parameter transforms according to the X ₃ ⁺ irreducible representation of Immm. Following Immm → P2 ₁ /n phase transition, four equivalent domains of P2 ₁/n are determined relative to Immm, which are in an antiphase and/or twin relationship. The abrupt shortening of the octahedral Al-F and Na-F bonds and a sudden change in orientations of the atomic thermal vibration ellipsoids above T ₀ indicate a crossover from displacive to an order-disorder mechanism near the transition temperature. The β phase is interpreted as a dynamic average of four micro-twin and -antiphase domains of the a phase. This view is consistent with the entropy of phase transition, ΔS_trans (11.43 JK^?1 mol^?1) calculated from heat capacity measurements (Anovitz et al. 1987), which corresponds closely to R ln4 (11.53 JK^?1 mol^?1), where 4 is the number of domains formed during the phase transition. The dynamic nature of the β phase is independently confirmed from a considerable narrowing of the ²⁷Al nuclear magnetic resonance (NMR) line-shape above T ₀ (Stebbins et al. 1992).     

Computational model of the structural and elastic properties of the ilmenite and perovskite phases of MgSiO3

The structural and elastic properties of the ilmenite and perovskite phases of MgSiO₃ are investigated with a computational model based on energy minimization. The potential energies of these two crystals are approximated by the sum of Coulomb, van der Waals, and repulsion terms between atoms. Required energy parameters are derived by fitting the parameters to the observed crystal structures of these two phases as well as to the measured elastic constants of the ilmenite phase. The resulting potential model is applied to predicting the elastic constants of the perovskite phase. The calculated bulk modulus of the perovskite phase compares favorably with the data obtained from volume-compression experiments as well as the values estimated from empirical elasticity systematics of perovskite type compounds. The predicted shear modulus of the perovskite phase is also in reasonable agreement with the values proposed from similar empirical elasticity systematics. Subsequently, the model is used to simulate the high pressure behaviors of the crystal structures and elastic constants of these two phases.     

High temperature creep of single crystal gadolinium gallium garnet

High temperature creep of single crystal gadolinium gallium garnet (GGG) was studied in the temperature range of 1723–1853 K (0.86–0.94 T_m, T_m: melting temperature) and strain rate from 9 · 10^?7 s^?1 to 2 · 10^?5 s^?1. The compression tests were made along the 〈100〉 and 〈111〉 orientations. We have performed both constant strain-rate and stress-dip tests. For the 〈100〉 orientation, deformation occurs via the 〈111〉 slip systems. For the 〈111〉 orientation, both the 〈100〉 {010} and the 〈111〉 slip systems can be activated. GGG garnet is very strong under these conditions: σ/μ=(1–3)×10^?3 (σ: creep strength, μ: shear modulus). The creep behavior is characterized by a power law with stress exponent n=2.9–3.3 and high activation energies E^*=612–743 kJ/mol (E^*～45×RT_m, at zero stress which decrease with the increase of stress). Stress-dip tests suggest a small internal stress (σ_i/σ～0.62; σ_i: internal stress, σ: applied stress) compared to other materials. These results suggest that the high creep strength of GGG is mainly due to difficulty of dislocation glide rather than dislocation climb.     

Temperature coefficients of elastic constants of single crystal MgO between 80 and 1,300 K

Elastic constants of single crystal MgO have been measured by the rectangular parallelepiped resonance (RPR) method at temperatures between 80 and 1,300 K. Elastic constants C _ij (Mbar=10³ kbar) and their temperature coefficients (kbar/K) are: $$\begin{gathered} {\text{ }}C_{{\text{11}}} {\text{ }}C_{{\text{12}}} {\text{ }}C_{{\text{44}}} {\text{ }}K_s {\text{ }}C_s \hfill \\ C_{ij} {\text{ 300 K 2}}{\text{.966 0}}{\text{.959 1}}{\text{.562 1}}{\text{.628 1}}{\text{.004}} \hfill \\ \partial C_{ij} {\text{/}}\partial T{\text{100 K }} - {\text{0}}{\text{.259 0}}{\text{.013 }} - {\text{0}}{\text{.072 }} - {\text{0}}{\text{.078 }} - {\text{0}}{\text{.136}} \hfill \\ {\text{ 300K }} - {\text{0}}{\text{.596 0}}{\text{.068 }} - {\text{0}}{\text{.122 }} - {\text{0}}{\text{.153 }} - {\text{0}}{\text{.332}} \hfill \\ {\text{ 800 K }} - {\text{0}}{\text{.619 0}}{\text{.009 }} - {\text{0}}{\text{.152 }} - {\text{0}}{\text{.200 }} - {\text{0}}{\text{.314}} \hfill \\ {\text{ 1,300 K }} - {\text{0}}{\text{.598 0}}{\text{.036 }} - {\text{0}}{\text{.130 }} - {\text{0}}{\text{.223 }} - {\text{0}}{\text{.218}} \hfill \\ \end{gathered} $$ By combining the present results with the previous data on the thermal expansivity and specific heat, the thermodynamic properties of magnesium oxide are presented and discussed. The elastic parameters of MgO at very high temperatures in the earth's lower mantle are also clarified.     

The pressure and temperature dependence of the elastic properties of single-crystal fayalite Fe2SiO4

The nine adiabatic elastic stiffness constants of synthetic single-crystal fayalite, Fe₂SiO₄, were measured as functions of pressure (range, 0 to 1.0 GPa) and temperature (range, 0 to 40° C) using the pulse superposition ultrasonic method. Summary calculated results for a dense fayalite polycrystalline aggregate, based on the HS average of our single-crystal data, are as follows: V_p = 6.67 km/s; V_s = 3.39km/s; K= 127.9 GPa; μ = 50.3 GPa; (?K/?P)_T = 5.2; (?μ/?P)_T=1.5;(?K/?T)_P= ?0.030 GPa/K;and,(?/?T)_P =-0.013 GPa/K (the pressure and temperature data are referred to 25° C and 1 atm, respectively). Accuracy of the single-crystal results was maintained by numerous cross and redundancy checks. Compared to the single-crystal elastic properties of forsterite, Mg₂SiO₄, the fayalite stiffness constants, as well as their pressure derivatives, are lower for each of the on-diagonal (C _ij for which i=j) values, and generally higher for the off-diagonal (C _ij for which i≠j) data. As a result, the bulk moduli (K) and dK/dP for forsterite and fayalite are very similar, but the rigidity modulus (μ) and dμ/dP for polycrystalline fayalite are much lower than their forsterite counterparts. The bulk compression properties derived from this study are very consistent with the static-compression x-ray results of Yagi et al. (1975). The temperature dependence of the bulk modulus of fayalite is somewhat greater (in a negative sense) than that of forsterite. The rigidity dependencies are almost equivalent. Over the temperature range relevant to this study, the elastic property results are generally consistent with the data of Sumino (1978), which were obtained using the RPR technique. However, some of the compressional modes are clearly discrepant. The elastic constants of fayalite appear to be less consistent with a theoretical HCP model (Leibfried 1955) than forsterite, reflecting the more covalent character of the Fe-O bonding in the former.     

Pressure solution in sandstones: influence of clays and dependence on temperature and stress

The enhancement of dissolution of quartz under the influence of clays has been recognized in sandstones for many years. It is well known that a grain of quartz in contact with a clay flake dissolves faster than when in contact with another grain of quartz. This phenomenon promotes silica transfer during the diagenesis of sandstones and is responsible of deformation and porosity variations. Here we make an attempt to explain the process of this rock deformation using a pressure solution mechanism.

The model of water film diffusion assumes that matter is dissolved inside the contact between two grains. The resulting solutes are transported to the pore fluid through diffusion along an adsorbed water film. Between two micas, this trapped film is thicker than between two grains of quartz. As a consequence diffusion is easier and the rate of pressure solution faster.

Experiments on pressure solution show that diffusion controls the mechanism at great depth whereas a model based on natural mica indentation indicates that kinetics is the limiting process through the precipitation rate of quartz at low depth, thus temperature is a crucial parameter. There should be a transition between thermally controlled rate and diffusion limited evolution.     

CdGeO3-phase transformations at high pressure and temperature and structural refinement of the perovskite polymorph

Four polymorphs of CdGeO₃ were synthesized at high temperatures (600 ～ 1200° C) and high pressures up to 12 GPa. The pyroxenoid phase synthesized under ambient pressure transforms to garnet, ilmenite and perovskite phases with increasing pressure. The phase boundary of ilmenite-perovskite had a slightly negative P-T slope in contrast to the positive P-T slopes of the pyroxenoid-garnet and garnet-ilmenite transition boundaries. CdGeO₃III has the ilmenite structure with hexagonal lattice parameters, a=5.098 Å and c =14.883 Å. The c/a ratio of 2.919 is greater than that of any other ilmenite. CdGeO₃IV has a distorted perovskite structure with orthorhombic lattice parameters a = 5.209 Å, b = 5.253 Å and c = 7.434 Å. Synthesis of a CdGeO₃IV single crystal was successful and structural refinement revealed that the structure is isomorphic to GdFeO₃ with the space group Pbnm. The increase of density with the CdGeO₃III→CdGeO₃IV transformation is the largest (9.8%) for any ilmenite-perovskite transition studied so far.     

Modelling of the thermal dependence of structural and elastic properties of calcite, CaCO3

A computational method, based on the quasiharmonic approximation, has been computer-coded to calculate the temperature dependence of elastic constants and structural features of crystals. The model is applied to calcite, CaCO₃; an interatomic potential based on a C-O Morse function and Ca-O and O-O Borntype interactions, including a shell model for O, has been used. Equilibrations in the range 300–800 K reproduce the experimental unit-cell edges and bond lengths within 1%. The simulated thermal expansion coefficients are 22.3 (//c) and 2.6 (⊥ c), against 25.5 and-3.7×10^?6K^?1 experimental values, respectively. The thermal coefficients of elastic constants tend to be underestimated; for the bulk modulus, -2.3 against-3.7×10^?4K^?1 is obtained.     

Single crystal X-ray diffraction study of MgSiO3 perovskite from 77 to 400 K

Single crystal X-ray diffraction study of MgSiO₃ perovskite has been completed from 77 to 400 K. The thermal expansion coefficient between 298 and 381 K is 2.2(8) × 10^-5 K^-1. Above 400 K, the single crystal becomes so multiply twinned that the cell parameters can no longer be determined.From 77 to 298 K, MgSiO₃ perovskite has an average thermal expansion coefficient of 1.45(9) × 10^-5 K^-1, which is consistent with theoretical models and perovskite systematics. The thermal expansion is anisotropic; the a axis shows the most expansion in this temperature range (_a = 8.4(9) × 10^-6 K^-1) followed by c(_c = 5.9(5) × 10^-6 K^-1) and then by b, which shows no significant change in this temperature range. In addition, the distortion (i.e., the tilting of the [SiO₆] octahedra) decreases with increasing temperature. We conclude that the behavior of MgSiO₃ perovskite with temperature mirrors its behavior under compression.     

The temperature dependence of the crystal structure of berlinite, a quartz-type form of AlPO4

The temperature dependence of atomic positions, mean-square displacements and probability density functions in a synthetic specimen of berlinite was analyzed using X-ray single crystal data measured at fourteen values of temperature. The characteristic features and the temperature dependence of the structure of berlinite were found to be quite similar to those of quartz, in detail. With increasing temperature, the equilibrium position of an atom, if expressed in fractional coordinates, appears to move steadily toward its β-position along a straight line, and finally attain the β-phase positions after abrupt displacements in a narrow temperature range around 583?°C. The temperature dependence of the displacements of atoms from the corresponding high-symmetry β-positions, in α-berlinite, is well fitted with a classical Landau type expression of first-order phase transitions. The highly anisotropic mean square displacements, 〈u ²〉, of O atoms increase with increasing temperature, especially in a narrow range just below the α–β transition, in the directions nearly perpendicular to the librating Al-O-P bonds, attaining a local maximum of 0.115–0.117 Ų just above the transition point. With varying temperature, the principal axes for the O atoms change their directions smoothly toward those of the high temperature phase, while the axis with the largest 〈u ²〉 of the Al or P thermal ellipsoid remains in 〈100〉. These diffraction results are interpreted in terms of displacive structure transition involving both the ordered α- and β-forms. The Al–O and P–O bond distances are nearly constant around 1.73 and 1.53 Å, respectively, through the experimental range of temperature.     

Influence of stress-dependent elastic moduli on stresses and strains around axisymmetric boreholes

Summary Porous or clastic rocks often have elastic moduli which are not constant but increase with increasing minor principal stress. The use of classical constant modulus linear elasticity in these cases can lead to erroneous predictions of the deformations and of the initiation and extent of failure around underground excavations. To illustrate these effects, solutions are developed for axisymmetric excavations in infinite media having power law and exponential variations of elastic modulus with minor principal stress. The maximum stress concentrations do not occur at the excavation boundaries and are less than the constant value of 2.0 given by constant modulus elasticity. When modified slightly to allow for test boundary conditions, the theory gives predictions that are consistent with aspects of the results obtained in hydrostatic compression tests on thick walled cylinders of three sedimentary rocks.     

Calculation of the equation of state and elastic moduli of MgO using molecular orbital theory

The success of molecular orbital theory in calculating crystal properties such as bond lengths and atomic force constants has been well documented in the literature. Calculations can be extended to crystals under simulated compression and strain to determine elastic moduli and their pressure derivatives. Comparison of the molecular orbital results with both experimental values and results obtained by calculations such as the potential induced breathing model provides insight into the nature of chemical bonding in MgO. In this study, several molecular clusters were investigated as possible models for MgO; the cluster Mg₄O₄H₂₄ was chosen as the best model. Molecular energies were calculated with respect to bond length for both compression and expansion based on clusters that had been optimized for minimum energy. The resulting energy-volume curve was fitted to a recently derived equation of state (Brown, in preparation) to derive the values of K ₀ and dK₀/dP and the individual elastic moduli and their pressure derivatives were calculated by applying strain to the molecular cluster at both zero and elevated pressures. Agreement between theory and experiment varies between parameters, but the overall trend is encouraging. Since the molecular orbital model includes only short range interactions, its ability to approximating model the elastic moduli of MgO suggests a strong contribution to the elastic energy from short range interactions.     

Study on Al2O3 content and phase stability of aluminous-CaSiO3 perovskite at high pressure and temperature

 In order to clarify Al₂O₃ content and phase stability of aluminous CaSiO₃-perovskite, high-pressure and high-temperature transformations of Ca₃Al₂Si₃O₁₂ garnet (grossular) were studied using a MA8-type high-pressure apparatus combined with synchrotron radiation. Recovered samples were examined by analytical transmission electron microscopy. At pressures of 23–25 GPa and temperatures of 1000–1600 K, grossular garnet decomposed into a mixture of aluminum-bearing Ca-perovskite and corundum, although a metastable perovskite with grossular composition was formed when the heating duration was not long enough at 1000 K. On release of pressure, this aluminum-bearing CaSiO₃-perovskite transformed to the “LiNbO₃-type phase” and/or amorphous phase depending on its Al₂O₃ content. The structure of this LiNbO₃-type phase is very similar to that of LiNbO₃ but is not identical. CaSiO₃-perovskite with 8 to 25 mol% Al₂O₃ was quenched to alternating lamellae of amorphous layer and LiNbO₃-type phase. On the other hand, a quenched product from CaSiO₃-perovskite with less than 6 mol% consisted only of amorphous phase. Most of the inconsistencies amongst previous studies could be explained by the formation of perovskite with grossular composition, amorphous phase, and the LiNbO₃-type phase. Received: 11 April 2001 / Accepted: 5 July 2002