Elasticity of diopside

The thirteen single-crystal elastic moduli for diopside as determined by the acoustic technique based on Brillouin scattering are: c₁₁=2.23, c₂₂=1.71, c₃₃=2.35, c₄₄=0.74, c₅₅=0.67, c₆₆=0.66, c₁₂=0.77, c₁₃=0.81, c₁₅=0.17, c₂₃=0.57, c₂₅=0.07, c₃₅=0.43, c₄₆=0.073. The Reuss bound of the adiabatic bulk and shear moduli calculated from these data are K _s=1.08 Mbar and G=0.651 Mbar. The room-pressure isothermal bulk modulus, K _T , and the pressure derivative of the bulk modulus, K′ _T have also been determined on a four-circle diffractometer, from a single crystal mounted in a gasketed opposed-anvil diamond cell, giving values of K _T =1.13 Mbar and K′ _T =4.8. The principal axes of the strain ellipsoid, calculated from the elastic moduli and observed in the static compression data, are identical, and the linear compressibilities are in reasonable agreement. The single-crystal elastic moduli can be correlated with the structural features of diopside.     

Elasticity of the olivine and spinel polymorphs of Ni2SiO4

The single-crystal elastic moduli, c _ij x, of the olivine (α) and spinel (γ) polymorphs of nickel orthosilicate have been measured at atmospheric pressure and 20° C by Brillouin spectroscopy. The results are (Mbar), Ni₂SiO₄ olivine: c ₁₁=3.40(2), c ₂₂=2.38(2), c ₃₃=2.53(2), c ₄₄=0.71(1), c ₅₅=0.87(1), c ₆₆=0.78(1), c ₁₂=1.09(2), c ₁₃=1.10(4), c ₂₃=1.13(3), Ni₂SiO₄ spinel: c ₁₁=3.66(3), c ₄₄=1.06(1), c ₁₂=1.55(3). In comparing these results with extant elasticity data for olivine- and spinel-type compounds we find distinctive elastic characteristics related to crystal structure, and systematic trends due only to compositional variation. For silicate olivines, the longitudinal moduli decrease in the order c ₁₁>c ₃₃>c ₂₂, regardless of composition. The moduli c ₅₅ and c ₆₆ are approximately equal, and greater than c ₄₄. The former relationship is related to differences in polyhedral linkages along the crystallographic axes, whereas the latter may result from rotational freedom of SiO₄ tetrahedra in response to different directions of shear. Composition affects elasticity most directly through the relative magnitudes of \(\bar c_{12} > \; = (c_{12} + c_{13} + c_{23} )/3\) and \(\bar c_{44} = (c_{44} + c_{55} + c_{66} )/3\) . When transition-metal cations are six-coordinated by oxygen \(\bar c_{12} > \bar c_{44}\) , and when alkaline-earth cations are six-coordinated \(\bar c_{44} > \bar c_{12}\) . The longitudinal moduli along and normal to the close-packed directions of spinels are similar, reflecting the framework-like arrangement of octahedra. These longitudinal moduli exhibit little compositional dependence upon tetrahedral cations but vary dramatically with octahedral substitution. Our data indicate that tetrahedral cations affect elastic properties more as the oxygen positional parameter, u, decreases. The u parameter is also directly related to elastic anisotropy. While γ-Ni₂SiO₄ (u=0.244) is elastically isotropic, anisotropy increases rapidly as u approaches a limiting value near 0.27, and may be related to mechanical stability of the spinel structure. The longitudinal wave velocities along close-packed directions in α and γ Ni₂SiO₄ are equal. Thus, for an α-γ polymorphic pair, the assumptions of elastic isotropy of the γ phase and equal velocities in close-packed directions of α and γ allows the c _ij's and shear modulus of a spinel-structure silicate to be estimated from c ₁₁ of the corresponding α phase and the bulk modulus of the γ phase.     

Compressibility and crystal structure of sillimanite, Al2SiO5, at high pressure

The unit-cell dimensions and crystal structure of sillimanite at various pressures up to 5.29 GPa have been refined from single-crystal X-ray diffraction data. As pressure increases, a and b decrease linearly, whereas c decreases nonlinearly with a slightly positive curvature. The axial compression ratios at room pressure are β_a:β_b:β_c=1.22:1.63:1.00. Sillimanite exhibits the least compressibility along c, but the least thermal expansivity along a (Skinner et al. 1961; Winter and Ghose 1979). The bulk modulus of sillimanite is 171(1) GPa with K′=4 (3), larger than that of andalusite (151 GPa), but smaller than that of kyanite (193 GPa). The bulk moduli of the [Al1O₆], [Al2O₄], and [SiO₄] polyhedra are 162(8), 269(33), and 367(89) GPa, respectively. Comparison of high-pressure data for Al₂SiO₅ polymorphs reveals that the [SiO₄] tetrahedra are the most rigid units in all these polymorphic structures, whereas the [AlO₆] octahedra are most compressible. Furthermore, [AlO₆] octahedral compressibilities decrease from kyanite to sillimanite, to andalusite, the same order as their bulk moduli, suggesting that [AlO₆] octahedra control the compression of the Al₂SiO₅ polymorphs. The compression of the [Al1O₆] octahedron in sillimanite is anisotropic with the longest Al1-OD bond shortening by ～1.9% between room pressure and 5.29 GPa and the shortest Al1-OB bond by only 0.3%. The compression anisotropy of sillimanite is primarily a consequence of its topological anisotropy, coupled with the compression anisotropy of the Al-O bonds within the [Al1O₆] octahedron.     

Elasticity of a beryllium silicate (phenacite: Be2SiO4)

The adiabatic single-crystal elastic moduli of a beryllium silicate (phenacite: Be₂SiO₄, trigonal, have been determined at atmospheric pressure and 22° C by Brillouin spectroscopy. The elastic stiffness moduli in gigapascals are: C ₁₁=341.9 C ₃₃=391.0 C ₄₄=91.4 C ₆₆= 96.9 C ₁₂=148.0 C ₁₃=136.0 C ₁₄= 0.1 C ₁₅= 3.5Overall, the elastic stiffness moduli for phenacite parallel and perpendicular to the c axis are comparable (i.e., it is almost cubic in its elastic signature). The elastic moduli can be rationalized in terms of division of the structure into two types of coordination polyhedra (1Si+2Be) with slightly different stiffnesses, which are linked to form a three dimensional framework. Values of the isothermal bulk modulus and the linear compressibilities, as determined from hydrostatic compression experiments of Hazen and Au (1986), are in good agreement with those obtained here. Combining the two studies indicates a low pressure derivative of the bulk modulus for phenacite.     

Petrogenesis of andalusite–kyanite–sillimanite veins and host rocks, Sanandaj-Sirjan metamorphic belt, Hamadan, Iran

Quartz‐rich veins in metapelitic schists of the Sanandaj‐Sirjan belt, Hamadan region, Iran, commonly contain two Al₂SiO₅ polymorphs, and, more rarely, three coexisting Al₂SiO₅ polymorphs. In most andalusite and sillimanite schists, the types of polymorphs in veins correlate with Al₂SiO₅ polymorph(s) in the host rocks, although vein polymorphs are texturally and compositionally distinct from those in adjacent host rocks; e.g. vein andalusite is enriched in Fe₂O₃ relative to host rock andalusite. Low‐grade rocks contain andalusite + quartz veins, medium‐grade rocks contain andalusite + sillimanite + quartz ± plagioclase veins, and high‐grade rocks contain sillimanite + quartz + plagioclase veins/leucosomes. Although most andalusite and sillimanite‐bearing veins occur in host rocks that also contain Al₂SiO₅, kyanite‐quartz veins crosscut rocks that lack Al₂SiO₅ (e.g. staurolite schist, granite). A quartz vein containing andalusite + kyanite + sillimanite + staurolite + muscovite occurs in andalusite–sillimanite host rocks. Textural relationships in this vein indicate the crystallization sequence andalusite to kyanite to sillimanite. This crystallization sequence conflicts with the observation that kyanite‐quartz veins post‐date andalusite–sillimanite veins and at least one intrusive phase of a granite that produced a low‐pressure–high‐temperature contact aureole; these relationships imply a sequence of andalusite to sillimanite to kyanite. Varying crystallization sequences for rocks in a largely coherent metamorphic belt can be explained by P–T paths of different rocks passing near (slightly above, slightly below) the Al₂SiO₅ triple point, and by overprinting of multiple metamorphic events in a terrane that evolved from a continental arc to a collisional orogen.     

Elasticity of superhydrous B

The adiabatic single-crystal elastic moduli of superhydrous B, Mg₁₀Si₃O₁₄(OH)₄, have been measured at ambient conditions using Brillouin spectroscopy. This material is the first hydrous phase found to be stable at the extreme conditions of 20 GPa and 1400 °C. The single-crystal moduli, in GPa, are: C ₁₁=280.0±1.5, C ₂₂=307.4±1.6, C ₃₃=293.4±1.4, C ₄₄=90.0±1.1, C ₅₅=99.2±0.8, C ₆₆=89.6±0.6, C ₁₂=66.1±2.2, C ₁₃=105.6±2.6, C ₂₃=81.8±2.6. With aggregate elastic properties of K _VRH =154.0±4.2 and μ _VRH =97.0±0.7 GPa, superhydrous B is approximately 16% suffer than forsterite and 20% softer than magnesium silicate spinel; it is also considerably more elastically isotropic than forsterite. The single-crystal moduli are compared to those of forsterite, magnesium silicate spinel and periclase, materials that are both structurally and compositionally similar to superhydrous B. The longitudinal moduli of superhydrous B and forsterite follow similar trends and appear to be dominated by the incompressibility and rotation of silicon tetrahedra. The shear and off-diagonal moduli more closely resemble those of periclase and spinel and may reflect the properties inherent to layers of magnesium octahedra.     

Electronic structure and electric field gradient calculations of Al2SiO5 polymorphs

 The electronic structure of the three polymorphs of Al₂SiO₅, andalusite, sillimanite, and kyanite, is studied by linearized-augmented-plane-wave (LAPW) calculations using the WIEN code. Total energy calculations verify, in agreement with recent pseudopotential calculations, that andalusite is the most stable phase, followed by sillimanite and kyanite.We determine the electronic charge density distribution and find strong polarizations on all oxygen ions. We identify different polarizations due to Al or Si neighbors which depend on their respective distances to the oxygen atom. The chemical bonding is not purely ionic in nature but has important covalent contributions. Electric field gradients (EFGs) at all sites are calculated and agree well (within 10%) with available experimental data on Al. We identify the origin of the EFGs and demonstrate its relation to the nearest-neighbor coordination and the resulting anisotropy of the electronic charge distribution. Received: 22 March 2000 / Accepted: 3 August 2000     

Potential protonation sites in the Al<Subscript>2</Subscript>SiO<Subscript>5</Subscript> polymorphs based on polarized FTIR spectroscopy and properties of the electron density distribution

Potential protonation sites for, kyanite, sillimanite, and andalusite, located in a mapping of the (3, −3) critical points displayed by their L(r) = −∇²ρ(r) distributions, are compared with polarized single-crystal FTIR spectra of kyanite and sillimanite determined earlier and with andalusite measured in this study. For andalusite, seven peaks were observed when the electric vector, E, is parallel to [100]: four intense ones at 3,440, 3,460, 3,526, and 3,597 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹. Six peaks, three intense ones at 3,440, 3,460, and 3,526 cm⁻¹ and three weaker ones at 3,480, 3,520, and 3,653 cm⁻¹ when E parallels [010]. No peaks were observed when E is parallel to [001]. The concentration of water in andalusite varies between 110 and 168 ppm by weight % H₂O. Polarized FTIR spectra indicate that the OH vector is parallel to (001) in andalusite and sillimanite and in kyanite. Examination of the L(r) (3, −3) critical points in comparison with the polarized FTIR indicates that H prefers to bond to the oxygen atoms O1 and O2 in andalusite and O2 and O4 in sillimanite which correspond to the underbonded oxygen atoms and those with the largest L(r) maxima. In kyanite, comparison of the FTIR spectrum and the critical points indicates that H will preferentially bond to the two 4-coordinated O2 and O6 atoms.     

Single-crystal elastic properties of alunite, KAl3(SO4)2(OH)6

The single-crystal elastic constants of natural alunite (ideally KAl₃(SO₄)₂(OH)₆) were determined by Brillouin spectroscopy. Chemical analysis by electron microprobe gave a formula KAl₃(SO₄)₂(OH)₆. Single crystal X-ray diffraction refinement with R ₁ = 0.0299 for the unique observed reflections (|F _o| > 4σ _F) and wR ₂ = 0.0698 for all data gave a = 6.9741(3) Å, c = 17.190(2) Å, fractional positions and thermal factors for all atoms. The elastic constants (in GPa), obtained by fitting the spectroscopic data, are C ₁₁ = 181.9 ± 0.3, C ₃₃ = 66.8 ± 0.8, C ₄₄ = 42.8 ± 0.2, C ₁₂ = 48.2 ± 0.5, C ₁₃ = 27.1 ± 1.0, C ₁₄ = 5.4 ± 0.5, and C ₆₆ = ½(C ₁₁–C ₁₂) = 66.9 ± 0.3 GPa. The VRH averages of bulk and shear modulus are 63 and 49 GPa, respectively. The aggregate Poisson ratio is 0.19. The high value of the ratio C ₁₁/C ₃₃ = 2.7 and of the ratio C ₆₆/C ₄₄ = 1.6 are characteristic of an anisotropic structure with very weak interlayer interactions along the c-axis. The basal plane (001) is characterized by 0.1% longitudinal acoustic anisotropy and 0.9–1.1% shear acoustic anisotropy, which gives alunite a characteristic pseudo-hexagonal elastic behavior, and is related to the pseudo-hexagonal arrangement of the Al(O,OH)₆ octahedra in the basal layer. The elastic Debye temperature of alunite is 654 K. The large discrepancy between the elastic and heat capacity Debye temperature is also a consequence of the layered structure.     

Elasticity of an upper mantle clinopyroxene

The ambient pressure elastic properties of a natural clinopyroxene (C2/c symmetry) from Kilbourne Hole, NM have been determined. In terms of end-members, diopside (CaMgSi₂O₆), hedenbergite (CaFeSi₂O₆), jadeite (NaAlSi₂O₆), cosmochlor (NaCrSi₂O₆), and Mg-Tschermak (MgAl(AlSi)O₆), its composition is Di₇₂He₉Jd₃Cr₃Ts₁₂. The analytic density, based on chemistry and cell parameters is 3.327 (0.003) g/cm³. The elastic constants [c₁₁, c₁₂, c₁₃, c₁₅, c₂₂, c₂₃, c₂₅, c₃₃, c₃₅, c₄₄, c₄₆, c₅₅, c₆₆] are [273.8 (0.9), 83.5 (1.3), 80.0 (1.1), 9.0 (0.6), 183.6 (0.9), 59.9 (1.6), 9.5 (1.0), 229.5 (0.9), 48.1 (0.6), 76.5 (0.9), 8.4 (0.8), 73.0 (0.4), 81.6 (1.0)] GPa where uncertainties are reported at the 95% confidence level. The aggregate (mean of Hashin-Strikman bounds) adiabatic bulk modulus is 117.2 (0.7) GPa, and the shear modulus is 72.2 (0.2) GPa. Although measured moduli are broadly consistent with trends in elasticity versus atomic volume, deviations from the systematics would produce significant (percent level) changes in calculated velocities for candidate mantle mineral assemblages. The compositional dependence of elasticity for several clinopyroxenes is explored on the basis of just the Di+He and Jd+Ts mole fractions. The bulk modulus lies within experimental uncertainties of the linear mixture of end-member properties while the shear modulus deviates by 3%. Received: 29 September 1997 / Revised, accepted: 4 March 1998     

Dislocation strain energy in the Al2SiO5 polymorphs

Molar elastic strain energy arising from dislocations in andalusite and sillimanite were calculated using equations derived from a non-core, linear elasticity model. For perfect (unit) c screw dislocations in these polymorphs, minimum dislocation densities of about 10¹⁰/cm² are necessary to significantly perturb the andalusite=sillimanite equilibrium boundary in P-T space. Compared to unit c dislocations, smaller energy perturbations arise from dissociated c screw dislocations, which are commonly observed in kyanite and sillimanite. A low computed value of stacking fault energy (～30 ergs/cm²) in these polymorphs is compatible with the large separations of dissociated dislocations in these phases. Dislocation densities in naturally occurring Al₂SiO₅ polymorphs are typically <10⁸/cm². Assuming that these densities are representative of those existing during metamorphism, as is supported by the lack of microtextures indicative of strong recovery, it is concluded that molar strain energies corresponding to observed dislocation densities (<10⁸/cm²) result in insignificant perturbation of P-T phase equilibrium boundaries of the Al₂SiO₅ polymorphs.     

Interpreting prograde-growth histories of Al2SiO5 triple-point rocks using oxygen-isotope thermometry: an example from the Truchas Mountains, USA

Oxygen‐isotope compositions of kyanite, andalusite, prismatic sillimanite and fibrolite from the Proterozoic terrane in the Truchas Mountains, New Mexico differ from one another, suggesting that these minerals did not grow in equilibrium at the Al₂SiO₅ (AS) polymorph‐invariant point as previously suggested. Instead, oxygen‐isotope temperature estimates indicate that growth of kyanite, andalusite and prismatic sillimanite occurred at c. 575, 615 and 640 °C respectively. Temperature estimates reported in this paper are interpreted as those of growth for the different AS polymorphs, which are not necessarily the same as peak metamorphic temperatures for this terrane. Two distinct temperature estimates of c. 580 °C and c. 700 °C are calculated for most fibrolite samples, with two samples yielding clear evidence of quartz‐fibrolite oxygen‐isotope disequilibrium. These data indicate that locally, and potentially regionally, oxygen‐isotope disequilibrium between quartz and fibrolite may have resulted from rapid fibrolite nucleation. Pressures of mineral growth that were extrapolated from oxygen‐isotope thermometry results and calculated using petrological constraints suggest that kyanite and one generation of fibrolite grew during M1 at 5 kbar, and that andalusite, prismatic sillimanite and a second generation of fibrolite grew during M2 at 3.5 kbar. M1 and M2 therefore represent two distinct metamorphic events that occurred at different crustal levels. The ability of the AS polymorphs to retain δ¹⁸O values of crystallization make these minerals ideal to model prograde‐growth histories of mineral assemblages in metamorphic terranes and to understand more clearly the pressure–temperature histories of multiple metamorphic events.     

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.     

Elasticity of monticellite

The adiabatic single-crystal elastic moduli of a natural sample of monticellite (CaMgSiO₄), with the olivine crystal structure, have been measured under ambient conditions using Brillouin spectroscopy. From the single-crystal moduli the aggregate bulk and shear moduli are calculated to be K _s=106±1 and = 55.2±0.4 GPa, respectively. These results are consistent with a systematic decrease in bulk modulus with increasing molar volume among the olivine-structured silicates. The longitudinal moduli decrease in the order c ₁₁>c ₃₃>c₂₂, indicating that the structure is stiffest along the a axis and most compliant along the b axis. This relationship among the longitudinal moduli holds for all silicate and germanate olivines, and is thus inferred to result from the topology of the olivine crystal structure. However, the moduli obtained in this study are at variance with previous conclusions concerning deviations from the Cauchy relations (e.g. c ₁₂=c ₄₄). For monticellite, off-diagonal shear moduli of the c ₁₂-type are uniformly greater than pure shear moduli such as c ₄₄. Similar behavior is found in pyroxenes such as diopside. The relative magnitudes of shear and off-diagonal moduli are not, therefore, a diagnostic chemical signature in minerals with complex crystal structures.Department of Applied Physics, Stanford University, Stanford CA, USA     

The phase equilibrium between sillimanite and andalusite as determined from lattice vibrations

The thermodynamic equilibrium between sillimanite and andalusite has been determined from the measured phonon spectra. The corresponding aluminium silicate triple point is found to be in the range T=420° C-440° C and P=3.0–3.2 kbars. From the comparison of calorimetrically determined specific heat functions with those calculated from lattice vibrations additional effects of lattice faults of sillimanite are found to increase the temperature and pressure of the triple point considerably. The thermodynamic functions G(T), S(T) and H(T) are given for both structures.     

Kinetic control of staurolite–Al2SiO5 mineral assemblages: Implications for Barrovian and Buchan metamorphism

The distribution and textural features of staurolite–Al₂SiO₅ mineral assemblages do not agree with predictions of current equilibrium phase diagrams. In contrast to abundant examples of Barrovian staurolite–kyanite–sillimanite sequences and Buchan‐type staurolite–andalusite–sillimanite sequences, there are few examples of staurolite–sillimanite sequences with neither kyanite nor andalusite anywhere in the sequence, despite the wide (~2.5 kbar) pressure interval in which they are predicted. Textural features of staurolite–kyanite or staurolite–andalusite mineral assemblages commonly imply no reaction relationship between the two minerals, at odds with the predicted first development (in a prograde sense) of kyanite or andalusite at the expense of staurolite in current phase diagrams. In a number of prograde sequences, the incoming of staurolite and either kyanite, in Barrovian sequences, or andalusite, in Buchan‐type sequences, is coincident or nearly so, rather than kyanite or andalusite developing upgrade of a significant staurolite zone as predicted. The width of zones of coexisting staurolite and either kyanite, in Barrovian sequences, or andalusite, in Buchan‐type sequences, is much wider than predicted in equilibrium phase diagrams, and staurolite commonly persists upgrade until its demise in the sillimanite zone. We argue that disequilibrium processes provide the best explanation for these mismatches. We suggest that kyanite (or andalusite) may develop independently and approximately contemporaneously with staurolite by metastable chlorite‐consuming reactions that occur at lower P–T conditions than the thermodynamically predicted staurolite‐to‐kyanite/andalusite reaction, a process that involves only modest overstepping (<15°C) of the stable chlorite‐to‐staurolite reaction and which is favoured, in the case of kyanite, by advantageous nucleation kinetics. If so, the pressure difference between Barrovian kyanite‐bearing sequences and Buchan andalusite‐bearing sequences could be ~1 kbar or less, in better agreement with the natural record. The unusual width of coexistence of staurolite and Al₂SiO₅ minerals, in particular kyanite and andalusite, can be accounted for by a combination of lack of thermodynamic driving force for conversion of staurolite to kyanite or andalusite, sluggish dissolution of staurolite, and possibly the absence of a fluid phase to catalyse reaction. This study represents an example of how kinetic controls on metamorphic mineral assemblage development have to be considered in regional as well as contact metamorphism.     

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.     

Elasticity of single-crystal aragonite by Brillouin spectroscopy

The elastic constants of natural single-crystal aragonite (CaCO₃) have been measured by Brillouin spectroscopy at ambient conditions. The elastic constants C₁₁, C₂₂, C₃₃, C₄₄, C₅₅, C₆₆, C₁₂, C₁₃ and C₂₃ are 171.1±1.0, 110.1±0.9, 98.4±1.2, 39.3±0.6, 24.2±0.4, 40.2±0.6, 60.3±1.0, 27.8±1.6 and 41.9±2.0 GPa, respectively, for aragonite. The linear compressibilities of the a-, b- and c-axis for aragonite at ambient conditions were derived from our measured data to be 3.0±0.2, 4.2±0.2 and 7.3±0.6×10^–3 GPa^–1, respectively. The aggregate bulk and shear moduli for aragonite using the Voigt-Reuss-Hill (VRH) scheme are thus calculated to be 68.9±1.4 and 35.8±0.2 GPa, respectively. The value of bulk modulus is in remarkable contrast to the literature value of 46.9 GPa measured almost a century ago. Our new datum, however, is closer to that derived from recent atomistic simulation and static compression studies.