β(Mg0.9, Fe0.1)2SiO4: Single crystal structure,cation distribution,and properties of coordination polyhedra

The synthesis boundaries of the phase transformation; ++ in (Mg_0.9, Fe_0.1)SiO₄, have been clarified at temperatures to 2000° C and pressures up to 20 GPa in order to synthesize single crystals of high quality. A single crystal of (Mg_0.9, Fe_0.1)₂SiO₄ was grown successfully to a size of 500 m. The crystal structure has been refined from single-crystal X-ray intensities. The ferrous ions prefer M1 and M3 sites to over the larger M2 site. The volume change of all the occupied polyhedra does not contribute to the decrease of total volume in the transformation; rather it tends to increase the bulk volume through the expansion of occupied tetrahedra. The volume reduction in the phase transformations is accounted for by unoccupied polyhedra, with the octahedra contributory 60% and the tetrahedra 40% to the V of the transition. The volume change in the transformation is caused also partly by the volume decrease of MO ₆ (25%), partly the unoccupied tetrahedra (45%) and octahedra (30%).     

Molecular force constants in dynamical model of α-quartz

Ab initio force constants of structural fragments of -quart, Si-O-Si bridge and SiO₄ tetrahedron, are calculated by the gradient (force) method for molecules accessible to spectroscopic investigation, disiloxane and tetramethoxysilane respectively. The comparison of theoretical frequencies with experimental ones enables the empirical scaling of quantum chemical force constants. A generalized approach to the inverse vibrational problem in spectroscopy of solids is outlined. It consists of a joint treatment of vibrational spectra and properties of a crystal related to its homogeneous deformation, namely compressibility and elastic constants. The importance of analyzing the microscopic structure of compressibility for testing the force field model is emphasized. The scaled molecular force constants complemented by the force constants of nonbonded O...O interactions at shortest distances after slight empirical correction are found to be sufficient to reproduce all mechanical properties of -quartz accessible to experimental determination. A discussion of results in terms of structure and bonding including the analysis of various versions of a force field model is presented. The calculated shapes of normal coordinates and uniform strains are validated by satisfactory reproduction of IR intensities and piezoelectric constants.     

Al-Si ordering in Sr-feldspar SrAl2Si2O8: IR,TEM and single-crystal XRD evidences

Al-Si ordering in Sr-feldspar has been followed by isothermal annealing, starting from a disordered metastable configuration. Ordering could not be followed by changes in the spontaneous strain as cell parameters did not show significant changes with thermal treatment from 0.016 h to 452 h at T=1350° C, while, on the contrary, significant changes in IR spectra are observed. A single crystal obtained from melt (Q _od 0) has been progressively heated up to 678 h at T=1350° C and the relevant structural refinements enabled to monitor changes in degree of Al-Si order up to Q_od = 0.86. In isothermal treatment for Sr-feldspar it is observed a significantly lower Q _od than in anorthite after the same annealing time. TEM observation has shown in Sr-feldspar, also for shortest annealing, b type reflections, while in anorthite, in the same conditions, e type reflections have been observed (Carpenter 1991a). In the first stages of ordering b APDs sized 100 Å (at T=1350° C, 0.33 h) have been observed in Sr-feldspar; APD coarsening occurs with an activation energy of 120±7 kcal mol^-1, not significantly different from anorthite. The ordering process seems to be a slower process in Sr-feldspar than in anorthite, even though data from longer annealing suggest that the Q _od close to the equilibrium is the same in Sr and Ca-feldspar (Q _od = 0.86 at T=1350° C).     

Phase transitions in leucite: X-ray diffraction studies

Lattice parameters, and intensities of selected X-ray reflexions, have been measured as a function of temperature for natural leucite, to characterise the phase transformation behaviour. At low temperatures leucite has a large ferroelastic distortion, but the temperature evolution of lattice parameters cannot be explained in terms of a purely ferroelastic phase transition; in particular, the considerable change in volume with temperature implies an additional transition mechanism, which we correlate with off-centring of K-ions in the low-temperature phase, and a collapse of the 111 structural channels. The transition behavior can therefore be rationalised in terms of two competing mechanisms: (I) Ferroelastic (consistent with the change m3m 4/mmm); (II) Volume-changing (consistent with m3m 4/m). Coupling of the two order parameters Q_I, and Q_II gives rise to the intermediate 4/mmm tetragonal phase.Our results confirm the existence of an I4 ₁/aI4 ₁/acd transition, but the non-disappearance of the 200 reflexion at high temperatures implies that the expected transition from I4₁/acd to Ia3d (cubic) symmetry does not occur. We attribute this to a residual strain field conjugated to the order parameter, due to defects (with possible Al/Si order). Nevertheless, within our experimental resolution, the lattice becomes metrically cubic at 665° C.     

High-temperature creep and kinetic decomposition of Ni2SiO4

To investigate high-temperature creep and kinetic decomposition of nickel orthosilicate (Ni₂SiO₄), aggregates containing 3 vol% amorphous SiO₂ have been deformed in uniaxial compression at a total pressure of one atomsphere. Twenty-three samples with grain sizes (d) from 9 to 30 m were deformed at temperatures (T) from 1573 to 1813 K, differential stresses () from 3 to 20 MPa, and oxygen fugacities (f o ₂) from 10^-1 to 10⁵ Pa. At temperatures up to 1773 K, the steady-state creep rate () can be described by the flow law

Strain analysis in Jurassic argillites of the Monte Sirino area (Lagonegro Zone,southern Apennines,Italy) and implications for deformation paths in pelitic rocks

Analysis of strain in Jurassic argillites forming part of the folded and thrusted sedimentary succession of the Lagonegro basin (southern Italian Apennines) has been carried out using ellipsoid-shaped reduction spots as strain markers. Most of the determined finite strain ellipsoids are of oblate type and show a peculiar distribution of the maximum extension direction (X), with maxima either subparallel or subperpendicular to the local fold axes. Using the strain matrix method, two different deformation histories have been considered to assist the interpretation of the observed finite strain pattern. A first deformation history involved vertical compaction followed by horizontal shortening (occurring by a combination of true tectonic strain and volume loss), whereby all strain is coaxial and there is no change in the intermediate axis of the strain ellipsoid. By this type of deformation sequence, which produces a deformation path where total strain moves from the oblate to the prolate strain field and back to the oblate field, prolate strain ellipsoids can be generated and may be recorded where tectonic deformation has not been large enough to reverse pretectonic compaction. This type of deformation history may be of local importance within the study area (i.e. it may characterize some fold hinge regions) and, more generally, is probably of limited occurrence in deformed pelitic rocks. A second deformation sequence considered the superposition of pre-tectonic compaction and tectonic strain consisting of initial layer-parallel shortening followed by layer-parallel shear (related to flexural folding). Also in this instance, volume change during tectonic deformation and tectonic plane strain have been assumed. For geologically reasonable amounts of volume loss due to compaction and of initial layer-parallel shortening, this type of deformation history is capable of producing a deformation path entirely lying within the oblate strain field, but still characterized by a changeover, during deformation, of the maximum extension axis (X) from a position parallel to the fold axis to one perpendicular to it. This type of deformation sequence may explain the main strain features observed in the study area, where most of the measured finite strain ellipsoids, determined from the limb regions of flexural folds, display an oblate shape, irrespective of the orientation of their maximum extension direction (X) with respect to the local structural trends. More generally, this type of deformation history provides a mechanism to account for the predominance of oblate strains in deformed pelitic rocks.     

Phase transitions in leucite,KAISi2O6

An order parameter treatment of the phase transitions in leucite, KAlSi₂O₆, at approximately 950 and 920 K: (cubic) I4₁ acd(tetragonal) I4₁ a(tetragonal) is presented in terms of Landau theory and induced representation theory. The Al-Si order with decreasing temperature is taken as the primary order parameter to which other distortions (K⁺ ion displacements, strain components, etc.) couple linearly. The expected Al-Si ordering behavior and the associated K⁺ ion displacements for both transitions are derived and the resulting twin domain orientations are listed. The sequence of phase transitions results from a coupling of ₃ ⁺ and ₄ ⁺ representations. The Landau free energy for the five-dimensional reducible representation has been simplified to two components resulting in a linearquadratic coupling of the components. Possible phase diagrams are derived by free energy minimization. The cubic tetragonal transition is first-order, whereas the tetragonal-tetragonal transition may be second order. A tricritical point exists at which the first-order transition changes to second-order.     

Thermodynamics of the xanthoconite-proustite and pyrostilpnite-pyrargyrite phase transition as determined by abrasive stripping voltammetry

The electrochemical reduction of xanthoconite, proustite, pyrostilpnite, and pyrargyrite was studied by abrasive stripping voltammetry, a technique which is based upon a preliminary mechanical transfer of trace amounts of the mineral onto the surface of a paraffin impregnated graphite electrode. Because the electrochemical reduction proceeds near to reversibility and is very similar for each pair of minerals, the peak potentials in differential pulse voltammetry can be used to calculate the standard enthalpy of phase transformation of xanthoconite to proustite and of pyrostilpnite to pyrargyrite: _T H _{(xanth proust)} ^O = 35.46 ± 14.15 kJ/mol and _T H _{(pyrostilp pyrarg)} ^O = 38.85 ± 6.60 kJ/mol. These values are not accessible otherwise until now.     

A comparison of intracrystalline deformation in naturally and experimentally deformed quartzites

A relatively undeformed quartzite sample from the Weverton formation was experimentally deformed in plane strain at a temperature of 700° C, a confining pressure of 15 kb and a constant strain rate of 10⁻⁶/sec, in a modified Griggs apparatus. A comparison of the known experimental strain for the sample with that measured from deformed rutile needles within the quartz grains shows fairly close agreement between the two values. This confirms the validity of using the needles as intracrystalline strain markers. A comparison has been made of the microstructures and preferred orientations in the experimentally deformed sample and a naturally deformed sample of the same quartzite which has undergone the same strain. The experimentally deformed sample exhibits more inhomogeneous intragranular deformation and a “double funnel” pattern of c axes, while the naturally deformed sample exhibits more homogeneous intragranular deformation and a broad great circle girdle of c axes normal to the foliation and lineation.     

Theoretical and natural strain patterns in ductile simple shear zones

A simple empirical model representing the variation of shear strain throughout a simple shear zone allows us to determine the evolution of finite strain as well as the progressive shape changes of passive markers. Theoretical strain patterns (intensity and orientation of finite strain trajectories, deformed shapes of initially planar, equidimensional and non-equidimensional passive markers) compare remarkably well with patterns observed in natural and experimental zones of ductile simple shear (intensity and orientation of schistosity, shape changes of markers, foliation developed by deformation of markers).The deformed shapes of initially equidimensional and non-equidimensional passive markers is controlled by a coefficient P, the product of

1. (1) the ratio between marker size and shear zone thickness

2. (2) the shear gradient across the zone.

For small values of P (approximately P < 2), the original markers change nearly into ellipses, while large values of P lead to “ retort” shaped markers.This theoretical study also allows us to predict, throughout a simple shear zone, various relationships between the principal finite strain trajectory, planar passive markers and foliations developed by deformation of initially equidimensional passive markers.     

Mechanisms of the transformations between the α, β and γ polymorphs of Mg2SiO4 at 15 GPa

Data on the mechanisms of mantle phase transformations have come primarily from studies of analogue systems reacted experimentally at low pressures. In order to study transformation mechanisms in Mg₂SiO₄ at mantle pressures, forsterite () has been reacted in the stability field of -phase, at 15 GPa and temperatures up to 900° C, using a multianvil split-sphere apparatus. Transmission electron microscope studies of samples reacted for times ranging from 0.25–5.0 h show that forsterite transforms to -phase by an incoherent nucleation and growth mechanism involving nucleation on olivine grain boundaries. This mechanism and the resultant microstructures are very similar to those observed at much lower pressures in analogue systems (Mg₂GeO₄ and Ni₂SiO₄) as the result of the olivine to spinel () transformation. Metastable spinel () also forms from Mg₂SiO₄ olivine at 15 GPa, in addition to -phase, by the incoherent nucleation and growth mechanism. With time, the spinel progressively transforms to the stable -phase. After 1 h, spinels exhibit a highly striated microstructure along {110} and electron diffraction patterns show streaking parallel to [110] which indicates a high degree of structural disorder. High resolution imaging shows that the streaking results from thin lamellae of -phase intergrown with the spinel. The two phases have the orientation relationship [001]//[001] and [010]//[110] so that the quasi cubic-close-packed oxygen sublattices are continuous between both phases. These microstructures are similar to those observed in shocked meteorites and show that spinel transforms to -phase by a martensitic (shear) mechanism. There is also evidence that the mechanism changes to one involving diffusion-controlled growth at conditions close to equilibrium.     

The α-β phase transition in cristobalite,SiO2

Cristobalite, a high temperature phase of silica, SiO₂, undergoes a (metastable) first-order phase transition from a cubic, , to a tetragonal, P4₃2₁2 (or P4₁2₁2), structure at around 220° C. The cubic C9-type structure for -cristobalite (Wyckoff 1925) is improbable because of two stereochemically unfavorable features: a 180° Si-O-Si angle and an Si-O bond length of 1.54 Å, whereas the corresponding values in tetragonal -cristobalite are 146° and 1.609 Å respectively. The structure of the -phase is still controversial. To resolve this problem, a symmetry analysis of the (or P4₁2₁2) transition in cristobalite has been carried out based on the Landau formalism and projection operator methods. The starting point is the ideal cubic ( ) C9-type structure with the unit cell dimension a (7.432 Å) slightly larger than the known a dimension (7.195 Å at 205° C) of -cristobalite, such that the Si-O-Si angle is still 180°, but the Si-O bond length is 1.609 Å. The six-component order parameter driving the phase transition transforms according to the X₄ representation. The transition mechanism essentially involves a simultaneous translation and rotation of the silicate tetrahedra coupled along 110. A Landau free-energy expression is given as well as a listing of the three types of domains expected in -cristobalite from the transition. These domains are: (i) transformation twins from a loss of 3-fold axes, (ii) enantiomorphous twins from a loss of the inversion center, and (iii) antiphase domains from a loss of translation vectors 1/2 110 (FP). These domains are macroscopic and static in -cristobalite, and microscopic and dynamic in -cristobalite. The order parameter , couples with the strain components as ², which initiates the structural fluctuations, thereby causing the domain configurations to dynamically interchange in the -phase. Hence, the - cristobalite transition is a fluctuation-induced first-order transition and the -phase is a dynamic average of -type domains.     

Thermal expansion,heat capacity,and entropy of MgO at mantle pressures

The pressure dependence of the Raman spectrum of forsterite was measured over its entire frequency range to over 200 kbar. The shifts of the Raman modes were used to calculate the pressure dependence of the heat capacity, C _v, and entropy, S, by using statistical thermodynamics of the lattice vibrations. Using the pressure dependence of C _v and other previously measured thermodynamic parameters, the thermal expansion coefficient, , at room temperature was calculated from = K _S (T/P) _S C _V/TVK _T, which yields a constant value of ( ln / ln V)_T= 6.1(5) for forsterite to 10% compression. This value is in agreement with ( ln / ln V)_T for a large variety of materials.At 91 kbar, the compression mechanism of the forsterite lattice abruptly changes causing a strong decrease of the pressure derivative of 6 Raman modes accompanied by large reductions in the intensities of all of the modes. This observation is in agreement with single crystal x-ray diffraction studies to 150 kbar and is interpreted as a second order phase transition.     

A materials failure relation of accelerating creep as empirical description of damage accumulation

A general materials failure relation, , describes accelerating creep of materials with rate coefficients andA, by relating rates of deformation, , to changes in deformation rate, (Voight, 1988). Time of failure can be extrapolated from inverse rate versus time data, and andA may be derived to permit one to calculate the failure time. The method is of value for quantitative hazard assessments.Mechanisms leading to damage accumulation during accelerating creep include creep fracture by stress corrosion and power law lattice deformation. These mechanisms are examined here as phenomenologically related to the materials failure relation. Apparently, both mechanisms favour , where is the parameter of the materials failure relation controlling the sensitivity to accelerating activity. For pure shear governed by power law creep of powerp, under constant load, =2.0 andA=p. Stress corrosion is widely described by Charles' equation, relating crack velocity to stress intensity during subcritical crack growth by the stress corrosion indexn. The relationship betweenn and is given by =(2n–2)/n.     

Neutron diffraction study of the tricritical orientational order/disorder phase transition in calcite at 1260 K

Neutron powder diffraction measurements of the temperature dependence of superlattice reflections in calcite have shown that there is a continuous phase transition at 1260 K. The change in space group symmetry and the halving of the unit cell size on heating indicate that this transition is an orientational order/disorder transition. The intensities of the superlattice reflections show that the temperature dependence of the order parameter, Q, is of the form (T _c –T), where is 0.25, indicating that the transition is tricritical. The transition is accompanied by a large contraction along the c axis on cooling, defining a spontaneous strain e₃ which is related to the order parameter (and hence temperature) via e₃ Q ². No evidence for critical lowering of the value of was found. These measurements confirm that, apart from the detailed critical behaviour, the phase transition in calcite is similar to that observed in NaNO₃.     

Diamagnetic anisotropies of oxide minerals

The diamagnetic anisotropy of oxide minerals is analyzed in terms of a new model, in which the anisotropy is assigned to the individual chemical bond in the [MO₆] octahedral unit of the crystal. The diamagnetic principal axis of the individual M-O bond is assumed to be parallel to the direction of the bond. The calculated anisotropy based on this model shows a good correlation with the measured diamagnetic anisotropy, , for various minerals such as talc, sericite, kaolinite of the sheetsilicate group, forsterite of the orthosilicate group, and corundum of the hematite group. The values of many diamagnetic minerals are still unknown since the measurement is difficult to perform by means of conventional methods. The magnetic grain orientation recently observed in the mineral suspensions is effective for estimating the value, when the single crystal of the mineral cannot be obtained. The observation of fieldinduced crystal oscillation in the high magnetic fields can be applied for measuring the minerals with small values of less than 5 × 10^–10 emu/cc. The chemical bond model on the diamagnetic anisotropy can be confirmed, when the compiling of data on various mineral is made by means of the above two methods.     

Field-induced oscillation and rotation of diamagnetic oxide crystals

The harmonic oscillations of large diamagnetic mineral samples induced by a magnetic field is reported, for single crystals of quartz, corundum, and calcite. It was seen for the first time that the period of oscillation, , was proportional to the reciprocal of the magnetic field, H, where the restoring force of the string suspending the crystal became negligible in the high magnetic field. Accordingly, the value of diamagnetic anisotropy, , could be measured from the — H curve with a sensitivity of 5 × 10^–10 emu/cc. The values were 5.50 × 10^–9 emu/cc for quartz, 4.20 × 10^–9 emu/cc for corundum, 9.9 × 10^–8 emu/cc for calcite, and 8.8 × 10^–8 emu/cc for polycrystalline talc piled with the (001) planes aligned parallel. Significant field-induced rotations were observed for the suspended crystals. When the field was applied along the direction of the diamagnetic hard axis of the stationary crystal, the crystal gradually rotated with increasing field, so that the direction of the hard-axis was perpendicular to the applied field. The field-induced energy has a the maximum value when the field is applied along the diamagnetic hard axis. This reorientation of the crystal occurs because the torque due to the field-induced anisotropic energy exceeds that of the restoring force in high magnetic fields.     

Deformation-induced polymorphic transformation: experimental deformation of kyanite, andalusite, and sillimanite

Torsion experiments were performed on the Al₂SiO₅ polymorphs in the sillimanite stability field to determine basic rheological characteristics and the effect of deformation on polymorphic transformation. The experiments resulted in extensive transformation of andalusite and kyanite to sillimanite. No transformation occurred during the hot-press (no deformation) stage of sample preparation, which was carried out at similar P–T conditions and duration as the torsion experiments. Experiments were conducted on fine-grained (< 15 µm) aggregates of natural andalusite, kyanite and sillimanite at 1250 °C, 300 MPa, and a constant shear strain rate of 2 × 10^− 4/s to a maximum shear strain of 400%. Electron back-scattered diffraction (EBSD) analysis of the experiments revealed development of lattice-preferred orientations, with alignment of sillimanite and andalusite [001] slightly oblique to the shear plane. The kyanite experiment could not be analyzed using EBSD because of near complete transformation to sillimanite. Very little strain ( 30%) is required to produce widespread transformation in kyanite and andalusite. Polymorphic transformation in andalusite and kyanite experiments occurred primarily along 500 µm wide shear bands oriented slightly oblique and antithetic to the shear plane and dominated by sub-µm (100–150 nm) fibrolitic sillimanite. Shear bands are observed across the entire strain field preserved in the torsion samples. Scanning transmission electron microscope imaging shows evidence for transformation away from shear bands; e.g. fibrolitic rims on relict andalusite or kyanite. Relict grains typically have an asymmetry that is consistent with shear direction. These experimental results show that sillimanite is by far the weakest of the polymorphs, but no distinction can yet be made on the relative strengths of kyanite and andalusite. These observations also suggest that attaining high bulk strain energy in strong materials such as the Al₂SiO₅ polymorphs is not necessary for triggering transformation. Strain energy is concentrated along grain boundaries, and transformation occurs by a dynamic recrystallization type process. These experiments also illustrate the importance of grain-size sensitive creep at high strains in a system with simultaneous reaction and deformation.