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The crystal structure of zektzerite, NaLiZrSi6O15, orthorhombic (space group Cmca), consists of six-tetrahedral-repeat corrugated double silicate chains connected into a three-dimensional framework by edge-sharing Li tetrahedral–Zr octahedral chains. At room temperature, the Na+ ions occur at the Na(1) site located within the cylindrical channels created by the corrugation of the silicate double chains. The second sodium site, Na(2), occurs above and below the Zr octahedron and is nominally vacant at room temperature. Above 773 K, vacancies are created at the Na(1) site due to the migration of Na+ ions from the Na(1) to the Na(2) site. Crystal structure refinements at 300, 773, 973, 1223 and 1323 K indicate a progressive increase in the sodium occupancy at the Na(2) site from 0.04 at 773 K to 0.35 at 1323 K. Induced by increasing Na+-ion migration, a first-order high-temperature phase transition occurs above 1123 K as evidenced by a break in the slopes of the thermal expansion curves of the unit cell dimensions and a substantial increase in the electrical conductivity. The unit cell measurements as a function of temperature show marked hysteresis effects during the heating and cooling cycles.

International audience; We report on the lattice dynamics of MgSiO 3 perovskite (bridgmanite). Phonon spectroscopy was performed employing inelastic X-ray scattering from single crystals, and the results were confronted to ab initio calculations. We observe a remarkable agreement between experiment and theory, and provide accurate results for phonon dispersion relations, the vibrational density of states, and the full elasticity tensor. The present work constitutes an important milestone fully validating the lattice dynamics calculation against precise experimental evidence and marks a starting point to extend this kind of combined studies to the high-pressure and high-temperature conditions directly relevant for the physical properties and chemical composition of Earth's lower mantle.

In efforts to improve the thermal conductivity (TC) of Ultem(TM) 1000, it was compounded with three carbon based nano-fillers. Multiwalled carbon nanotubes (MWCNT), vapor grown carbon nanofibers (CNF) and expanded graphite (EG) were investigated. Ribbons were extruded to form samples in which the nano-fillers were aligned. Samples were also fabricated by compression molding in which the nano-fillers were randomly oriented. The thermal properties were evaluated by DSC and TGA, and the mechanical properties of the aligned samples were determined by tensile testing. The degree of dispersion and alignment of the nanoparticles were investigated with high-resolution scanning electron microscopy. The thermal conductivity of the samples was measured in both the direction of alignment as well as perpendicular to that direction using the Nanoflash technique. The results of this study will be presented.

We have undertaken a detailed analysis of the X-ray photoelectron spectra obtained from the three polymorphs of Al2SiO5; andalusite, sillimanite, and kyanite. Comparison of the spectra was made based on the chemical bonding and structural differences in the Al- and Si-coordination within each polymorph. The spectra for Si(2p) for all three polymorphs are nearly identical, consistent with the fact that all the Si atoms are in 4-fold (tetrahedral) coordination, whereas the binding energies, peak shapes, and peak widths for Al(2p) vary depending on the type of polymorph. The upper-valence band for all three polymorphs is characterized by four main features derived from O(2p), Al(3s), Al(2p), Si(3s), and Si(3p), and the differences in their contributions are observed. The density of state of the Al2SiO5 polymorphs is relatively featureless compared to those observed from α-SiO2 and α-Al2O3, suggesting that the orbital overlaps span a greater range in energy. The observed band gap energy for Al2SiO5 (sillimanite) was ~9.1eV, a value in between those for α-SiO2 (~8.6eV) and α-Al2O3 (~9.6eV). The conduction band feature of Al2SiO5 was experimentally compared to those of α-SiO2 and α-Al2O3, and shown that it is indeed intermediate between the α-SiO2 and α-Al2O3 phases.

This paper reviews the inelastic-neutron-scattering measurements and theoretical lattice-dynamics calculations, which have aimed at providing a microscopic understanding of the vibrational and thermodynamic properties of geophysically important minerals. In the last decade, detailed inelastic-neutron-scattering measurements supported by extensive model calculations have extended our knowledge of the nature of phonon-dispersion relations and density of states of minerals and their variations in various mineral phases in the Earth's mantle. An accurate understanding of these vibrational properties of minerals is crucial for predicting the phase transitions and thermodynamic properties of minerals at the pressures and temperatures prevalent in the Earth's mantle. The mineral studies reviewed here include the olivine end members forsterite and fayalite, the pyroxene end member enstatite, the garnet minerals pyrope, almandine, grossular and spessartine, the silicate perovskite MgSiO3, the mineral zircon, the aluminium-silicate minerals sillimanite, kyanite and andalusite, the layer silicates vermiculite and muscovite, the oxide minerals MgO, FeO, Al2O3 and the SiO2 polymorphs, and the carbonate minerals rhodochrosite and calcite. Inelastic-neutron-scattering measurements using reactors and spallation sources on single crystals and powder samples have provided data of their phonon-dispersion relations and density of states, which have been interpreted using theoretical calculations. While quantum mechanical ab initio calculations have been successfully employed to understand the vibrational properties of minerals like MgO, Al2O3, MgSiO3 perovskite etc ., theoretical studies of structurally more complex minerals have largely employed an atomistic approach involving semi-empirical interatomic potentials. The calculations enabled microscopic interpretations of the experimental data and have been very useful in providing an atomic-level understanding of the vibrational and thermodynamic properties of these minerals.

We report coherent inelastic neutron scattering measurements of the phonon dispersion relations and lattice dynamics shell model calculations of several microscopic and macroscopic properties of andalusite, Al 2 SiO 5 . Andalusite has an orthorhombic structure with 32 atoms/unit cell. The inelastic neutron scattering measurements (up to energy transfers of 45 meV) were carried out using the triple axis spectrometer at Dhruva reactor, India using a single crystal of andalusite and the phonon dispersion relations along the [100] direction have been measured. The shell model calculations have been used to compute the crystal structure, elastic constants, phonon frequencies, dispersion relations, density of states and the specific heat. The calculated results are in good agreement with available experimental data. The computed one-phonon neutron scattering structure factors based on the shell model have been very useful in the planning and analysis of the inelastic neutron scattering experiments.

High-resolution single-crystal X-ray diffraction intensities recorded with a charge-coupled device detector at low temperature (100 K) were used to derive the electron density distribution in three Al2SiO5 polymorphs: andalusite, sillimanite, and kyanite. The 27Al nuclear quadrupole coupling tensors were estimated from both the internal polarization contribution of the Al electron density and that of the lattice with electronic multipoles up to octupoles for oxygen atoms and hexadecapoles for Si and Al. Based on new estimations of the 27Al Sternheimer shielding factor, R and the antishielding factor, γ, a close agreement was achieved between the quadrupole coupling tensors at the various Al-sites derived from the X-ray diffraction data for all three polymorphs of Al2SiO5 with those determined previously from single-crystal 27Al NMR spectra.

Enstatite ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{6}$ is an important rock-forming silicate of the pyroxene group. It exists in several polymorphs, the structures of which are characterized by double $[{\mathrm{MgO}}_{6}]$ octahedral bands and single silicate chains. This paper reports lattice-dynamical rigid-ion model calculations and polarized Raman and inelastic-neutron-scattering measurements of orthoenstatite ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{6},$ which is orthorhombic $(\mathrm{Pbca})$ with 80 atoms in the unit cell. The calculated elastic constants, phonon frequencies, density of states, and specific heat are in good agreement with the experimental data. The optical-phonon branches along the \ensuremath{\Sigma} and \ensuremath{\Delta} directions are relatively flat without significant dispersion, but have moderate dispersion along the \ensuremath{\Lambda} direction, reflecting the strong structural anisotropy in orthoenstatite. Orthoenstatite undergoes a displacive-reconstructive phase transformation at $\ensuremath{\sim}1360\mathrm{K}$ to protoenstatite ${\mathrm{Mg}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{6},$ which is also orthorhombic $(\mathrm{Pbcn})$ with 40 atoms in the unit cell and the $a$ dimension half that of orthoenstatite. However, the computed phonon-dispersion relations in orthoenstatite do not exhibit any lattice instability in the entire Brillouin zone. The calculations predict that at the \ensuremath{\Gamma} point the lowest optic ${A}_{g}$ mode involving translations of ${\mathrm{Mg}}^{2+}$ ions and translations and rotations of the tetrahedral silicate groups softens from $104{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in protoenstatite to $82{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ in orthoenstatite, which is consistent with the single-crystal polarized Raman-scattering measurements. The phonon spectra obtained from inelastic-neutron-scattering measurements have been interpreted on the basis of model calculations. The broad peak in the 20--80-meV range in orthoenstatite is mainly due to Mg translations and the librations of the nearly rigid tetrahedral $[{\mathrm{SiO}}_{4}]$ groups, whereas the internal Si-O bond stretching vibrations of the $[{\mathrm{SiO}}_{4}]$ groups contribute mainly above 80 meV. The bridging oxygens in the silicate chains are vibrationally distinct from the nonbridging oxygens, leading to significant differences in the vibrational spectra of orthoenstatite and protoenstatite with tetrahedral silicate chains from those in forsterite ${\mathrm{Mg}}_{2}{\mathrm{SiO}}_{4}$ with isolated silicate tetrahedra. The band gaps found in the phonon density of states of forsterite are filled by the vibrations of the bridging oxygens in the silicate chains in the phonon densities of states of orthoenstatite and protoenstatite.

The crystal structure of the high temperature phase of KAlSi 2 O 6 at 700 dgC has been refined to R (%) = 5.4 by the least-squares method using 309 reflections. The thermal oscillation of K atom is great and the equivalent temperature factor B eq = 15.871(27) A 2 . One of the principal axes of the thermal ellipsoids in K atom is close to the [111] direction and the magnitude of rms amplitude in this axis is larger than in other axes.

ABSTRACf From in-situ structure and site occupancy refinements of a synthetic orthopyroxene, (Mm and (2) the In KD values (where KD = FeM1MgM2/ FeM2MgM1) vary linearly with liT (K) between 1000 and 1200 K, but nonlinearly between 1200 and 1300 K. The drastic straightening of the silicate chains at 1300 K is accompanied by the attainment of very similar configurations of the SiO. tetrahedra, SiA and SiB, in shapes, sizes, and out-of-plane tiltings. The rigid-body thermal vibration analysis suggests that the librational motion of the SiA tetrahedron (8.1°2) is slightly larger than that of SiB (5.2°2) at 296 K but becomes considerably smaller (48.0°2) than that of SiB (77.3°2) at 1300 K. The M I octahedron remains nearly regular from 296 to 1300 K, whereas the M2 coordination changes from sixfold (296 K) to sevenfold (1200 K) and to sixfold (1300 K) because of the bridging 03B moving out and 03B' moving into the coordination sphere (r ~ 3.0 A) at elevated temperatures. At 1300 K, the highly distorted M2 octahedron shares two edges with SiA and SiB, rather than one with SiA at 296 K, and the structure has all features of the high-temperature orthopyroxene phase predicted by Pannhorst (1979), which, in fact, is a transitional structural state between orthopyroxene and the so-called protoenstatite. On the basis of the configurations of the silicate chains in Mg- and Fe-rich orthopyroxenes at high temperature, an explanation is given as to why Mg-rich orthopyroxenes tend to transform to the protoenstatite structure with increasing temperature, whereas Fe-rich ones tend to transform to a clinopyroxene with space group C2/c. The anomalous behavior of the Fe-Mg order-disorder above 1200 K is attributed to the existence of the transitional state, particularly the changing charge distribution around the M2 site.

Thermal expansion properties of synthetic orthopyroxenes (Fe0.20Mg0.80)SiO3, (Fe0.40Mg0.60)SiO3, (Fe0.50Mg0.50)SiO3, (Fe0.75Mg0.25)SiO3 and (Fe0.83Mg0.17)SiO3 were systematically studied by means of single-crystal x-ray diffraction in the temperature range from 296 to 1300 K. The measurements of unit cell dimensions as a function of temperature reveal that the a and c dimensions and the unit cell volume V increase nonlinearly with a positive curvature with rising temperature, whereas the b dimension behaves differently, depending on the total Fe content. For Mg-rich orthopyroxenes (Fe/(Fe+Mg) 30%. Together with the high temperature neutron diffraction data on enstatite (MgSiO3) (McMullan, Haga and Ghose, unpublished) and x-ray diffraction data on ferrosilite (FeSiO3) (Sueno et al. 1976), the measured unit cell dimensions were analyzed in terms of the Gruneisen theory of thermal expansion. The linear thermal expansion coefficients α a and α c both increase as temperature is elevated, with α c increasing faster, while α b changes gradually from increasing for Mg-rich orthopyroxenes to decreasing for Fe-rich orthopyroxenes. The relative magnitudes of linear thermal expansion coefficients are always in the order α b >α c >α a between 300 and 500 K, but at higher temperatures, the order changes to α c >α b >α a for Mg-rich orthopyroxenes and α c >α a >α b for Fe-rich ones. The linear thermal expansion behavior is interpreted on the basis of the structural mechanical model of Weidner and Vaughan (1982). The anomalous behavior of α b is mainly attributed to the changes in the Fe2+ population at the M2 site and the relative stiffness of the M2(Fe2+)-O bonds compared to the M2(Mg2+)-O bonds. The volume thermal expansion coefficients are nonlinear functions of temperature and lie between 23 and 49×10−6/K. The previously reported results of mean volume thermal expansion coefficients appear to represent the α V values characteristic of higher temperatures compared to our results. The thermal Debye temperatures are composition-dependent, decreasing linearly from 812 (MgSiO3) to 561 K (FeSiO3), and are systematically higher than the corresponding acoustic Debye temperatures. The Gruneisen parameters range from 0.85 to 0.89 and do not seem to vary with composition. The linear compressibilities derived from thermal expansion and elastic moduli data agree very well. The pressure derivatives of the isothermal bulk modulus (dK0/dP) are also composition-dependent and decrease from 11.2 (MgSiO3) to 8.77 (FeSiO3). Such large values indicate possible anomalous elastic behavior of orthopyroxenes at high pressures in the Earth's upper mantle.

This paper reports single-crystal inelastic neutron scattering measurements of the phonon-dispersion relations of the aluminium silicate minerals andalusite and sillimanite, Al2SiO5. The measurements were undertaken using the triple-axis spectrometer at the Dhruva reactor, Trombay for andalusite and at the Oak Ridge National Laboratory, USA for sillimanite. The phonon-dispersion relations (up to 50 meV) along various high-symmetry directions have been measured and have been analyzed on the basis of lattice dynamics shell model calculations. The calculated structure factors based on the model calculations were used as guides for planning these single-crystal measurements and have been used to identify regions in reciprocal space with large cross sections. The calculated phonon-dispersion relations are in good agreement with the measured data. The model has been successfully used to derive the high pressure–temperature thermodynamic properties like the specific heat and the equation of state.

Electron- and ion-microprobe and Mossbauer analyses combined with X-ray structure refinement of a straw-yellow Mn-bearing alkali amphibole from Tirodi, Maharashtra, India, with no evidence of exsolution or inclusions, indicate a composition (Na 0.30 K 0.03 )(Na 0.87 Ca 0.39 Mn 0.57 Mg 0.17 )(Mg 3.84 Fe 3+ 0.72 Mn 0.38 Li 0.06 )(Si 7.88 Al 0.12 ) O 22 F 0.40 (OH) 1.60 , nearly half-way between (Ca-Na) and (Fe-Mg-Mn) amphiboles. The unit-cell dimensions are: a = 9.704 (7), b = 17.990 (12), c = 5.297 (3) A, β = 103.51 (5)°; space group C2/m and Z = 2. The single-crystal X-ray structure refinement (1363 reflections, R all = 0.039) was done to characterize the crystal-chemical features that might act as indicators of incipient exsolution phenomena due to immiscibility between (Ca-Na) and (Fe-Mg-Mn) amphibole compositions. An 57 Fe Mossbauer spectrum shows all iron to be in the trivalent state. All manganese is in the divalent state, and preferentially occurs at the split M4' site. The value of the β angle is related to the cation content at M4, and is consistent with the intermediate composition. C Mn 2+ is distributed almost equally over the three octahedral sites M1, M2, M3. A small amount of Li (detected by ion-microprobe) is ordered at the M3 site with concomitant substitution of Fe 3+ at the M2 site for charge balance

Inelastic neutron scattering measurements of phonon spectra from a powder sample of fayalite at various temperatures is reported. The measured spectra have been satisfactorily analyzed on the basis of a lattice dynamical model. The phonon density of states is used to derive the specific heat, which are found to be in good agreement with experimental data.

Inelastic neutron scattering measurements and rigid-ion model calculations of phonon dispersion relation in the geophysically important mineral fayalite is reported. The measured Σ 4 TA branch is found to be softer in fayalite as compared to that in forsterite Mg 2 SiO 4 . The rigid-ion model calculations are in satisfactory agreement with the experimental data.

Ilvaite, Ca(Fe2+, Fe3+)Fe2+Si2O7O(OH) with double octahedral chains of Fe2+(A) and Fe3+(A) ions with Fe2+(B) octahedra occurring above and below shows electron delocalization at the A sites and a semiconductor-insulator transition (∼370K) followed by a crystallographic transition (346 K). In addition, it shows two magnetic transitions at 123 and 50 K. The magnetic structure derived from powder neutron diffraction consists of A site ribbons composed of two single ferromagnetic (Fe2+−Fe3+−Fe2+−Fe3+…) chains, whose spins are aligned antiparallel to each other below 123 K; the Fe2+(B) spins are weakly coupled to their A site neighbors and are mostly ordered below 50 K. Both A and B site spins are nearly parallel and antiparallel to b. Below 123 K, the Fe2+(A) and Fe3+(A) moments increase rapidly with decreasing temperature, showing a sharp increase at 50 K indicating the second transition, whereas Fe2+(B) moment increases very slowly below 123 with a substantial increase at 50 K indicating considerable spin fluctuation between 123 and 50 K. The moments extrapolated to 0 K are 3.6, 4.6, and 3.6 μB for Fe2+(A), Fe3+(A) and Fe2+(B) sites respectively. The difference in the thermal evolution of the magnetic moments at A and B sites is due to the frustration of Fe2+(B) spins, which occurs at the apex of a square pyramid, a corner common between two triangles with respect to two sets of Fe2+(A)-Fe3+(A) pairs with opposite spin directions.

The longitudinal acoustic and optical phonon branches along the Gamma-X direction of MgO at 35 GPa have been determined by inelastic x-ray scattering using synchrotron radiation and a diamond-anvil cell. The experimentally observed phonon branches are in remarkable agreement with ab initio lattice dynamics results. The derived thermodynamic properties, such as the specific heat CV and the entropy S are in very good accord with values obtained from a thermodynamically assessed data set involving measured data on molar volume, heat capacity at constant pressure, bulk modulus and thermal expansion.

Orthopyroxenes, ${\mathrm{Fe}}_{x}{\mathrm{Mg}}_{1\ensuremath{-}x}{\mathrm{SiO}}_{3},$ ranging in composition between the Fe and Mg end members, represent an interesting system from the physical point of view because of the strong site preference of ${\mathrm{Fe}}^{2+}$ for one of the two octahedral sites in the crystal structure. For Mg-rich samples with $xl0.5,$ a major portion of the ${\mathrm{Fe}}^{2+}$ ions reside in the distorted octahedral $M2$ site and the magnetic susceptibility and optical absorption spectra are dominated by the effects of ${\mathrm{Fe}}^{2+}$ in this site. Two natural orthopyroxenes with $x=0.12$ and 0.20 have been investigated by magnetic susceptibility measurements and M\"ossbauer spectroscopy. The thermal characteristics of the observed mean magnetic susceptibility $\overline{\ensuremath{\chi}}$ and the quadrupole splitting $\ensuremath{\Delta}{E}_{Q}$ were analyzed using ligand-field theory. A minimum number of approximations were made to modify the Hamiltonian for ${\mathrm{Fe}}^{2+}$ in the distorted octahedral $M2$ site. The electronic energy-level pattern and the corresponding wave functions were obtained from a best fitting of the experimental results with the corresponding theoretical values. These results were used to calculate the thermal characteristics of the crystalline magnetic susceptibilities ${\ensuremath{\chi}}_{a},$ ${\ensuremath{\chi}}_{b},$ and ${\ensuremath{\chi}}_{c},$ arising from ${\mathrm{Fe}}^{2+}$ in the $M1$ and $M2$ sites in the ratio of their occupancies. The directional magnetic susceptibilities ${\ensuremath{\chi}}_{b}g{\ensuremath{\chi}}_{c}g{\ensuremath{\chi}}_{a}$ are in agreement with the corresponding values in orthopyroxenes with higher concentration of ${\mathrm{Fe}}^{2+}.$ The energy-level diagram of ${\mathrm{Fe}}^{2+}$ at the $M2$ site agrees well with the optical absorption spectra resulting mainly from ${\mathrm{Fe}}^{2+}$ at the $M2$ site. There is very little variation in $\ensuremath{\Delta}{E}_{Q}$ for ${\mathrm{Fe}}^{2+}$ at the $M2$ site as a function of temperature compared with that in the regular octahedral $M1$ site which shows a large variation. The $\ensuremath{\Delta}{E}_{Q}$ of ${\mathrm{Fe}}^{2+}$ at the $M2$ site and the magnetic susceptibility show very little variation with chemical composition. Our analysis also suggests considerable overlap of the molecular orbitals of the ligand electrons with those of the ${\mathrm{Fe}}^{2+}$ ions.

A high temperature single-crystal X-ray diffraction study of enstatite, Mg2Si2O6 was undertaken at 296, 900, 1200, 1360 and 1400 K. During the X-ray data collection at 1360 K (T0), orthoenstatite (Pbca) transformed to protoenstatite (Pbcn). The unit cell parameters measured at T0 are a=18.456(4), b=8.960(2) and c=5.270(1) A for ortho and a=9.306(1), b=8.886(1) and c=5.360(1) A for proto. The discontinuous increase in c and decrease in b due to the ortho to proto transformation are associated with the drastic unkinking of the silicate chains, whereas the abrupt increase in a results from the large expansion of the M2 — O distances along a coupled with the increase in the out-of-plane tilting of the silicate tetrahedra. Stacking faults form in ortho prior to the phase transition, as well as in proto between 1360 and 1400 K. With increasing temperature, the silicate B chain in ortho straightens faster than the A chain as the configurations of the SiA and SiB tetrahedra tend to become similar. At T0, the A and B chains with the O3-O3-O3 angles (O3 being the bridging oxygen atom) of 163.0° and 149.5° in ortho, respectively, attain an identical angle of 168.4° in proto. The configuration of the silicate chain in proto resembles that of the A chain in ortho. Rigid-body thermal vibration analysis suggests that between 1200 and 1400 K the largest, the second largest and the smallest thermal librational motions of the [SiO4] tetrahedra in both ortho and proto are approximately around a, c and b, respectively. Below 1200 K, the largest thermal librational amplitudes of the SiA and SiB tetrahedra in ortho are quite different, but become nearly equivalent at T0. In contrast to the results reported for all iron-bearing orthopyroxenes at high temperature, switching of the O3B atoms coordinated with the M2 cation occurs during the ortho to proto transformation, but not in ortho below T0. The ortho-proto transition does not affect the configuration of the M1 octahedron significantly, but results in a decrease of the mean M2 — O bond distance by 0.043 A and a highly distorted M2 octahedron in proto.

Despite their crystallographic differences, the mechanisms of the α-β phase transitions in the cristobalite phases of SiO2 and AlPO4 are very similar. The β→α transition in AlPO4 cristobalite is from cubic (\(\left( {F\bar 43m} \right)\)) to orthorhombic (C2221), whereas that in SiO2 cristobalite is from cubic (\(\left( {Fd\bar 3m} \right)\)) to tetragonal (P43212 or P41212). These crystallographic differences stem from the fact that there are two distinct cation positions in AlPO4 cristobalite as opposed to one in SiO2 cristobalite and the ordered (Al,P) distribution is retained through the phase transition. As a result, there are significant differences in their crystal structures, domain configurations resulting from the phase transition and Landau free energy expressions. A symmetry analysis of the “improper ferroelastic” transition from \(F\bar 43m \to C222_1\)in AlPO4 cristobalite has been carried out based on the Landau formalism and the projection operator methods. The six-component order parameter, η driving the phase transition transforms as the X5 representation of \(F\bar 43m\)and corresponds to the simultaneous translation and rotation of the [AlO4] and [PO4] tetrahedra coupled along 110. The Landau free energy expression contains a third order invariant, the minimization of which requires a first-order transition, consistent with experimental results. The tetrahedral configurations of twelve α phase domains resulting from the β→α transition in AlPO4 cristobalite are of two types: (1) transformation twins from a loss of the 3-fold axis, and (2) antiphase domains from the loss of the translation vectors 1/2[101] and 1/2[011] (F→C). In contrast to α-SiO2 cristobalite, the α-AlPO4 cristobalite (C2221) does not have chiral elements (43, 41) and hence, enantiomorphous domains are absent. These transformation domains are essentially macroscopic and static in the α phase and microscopic and dynamic in the β phase. The order parameter, η couples with the strain components, which initiates the structural fluctuations causing the domain configurations to dynamically interchange in the β phase. An analysis of the MAS NMR data (29Si, 17O, 27Al) on the α α-β transitions in SiO2 and AlPO4 cristobalites (Spearing et al. 1992, Phillips et al. 1993) essentially confirms the dynamical model proposed earlier for SiO2 cristobalite (Hatch and Ghose 1991) and yields a detailed picture of the transition dynamics. In both cases, small atomic clusters with the configuration of the low temperature α phase persist considerably above the transition temperature, T0. The NMR data on the β phases above T0 cannot be explained by a softening of the tetrahedral rotational and translational modes alone, but require the onset of an order-disorder mechanism resulting in a dynamic averaging due to rapidly changing domain configurations considerably below T0.

Cryolite, Na3AlF6[ = 2Na+(Na0.5 +Al0.5 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) A 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) A, 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, ΔStrans (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).

An important objective of the earth sciences is to develop the capability of predicting the thermodynamic properties of minerals and their phase relations under various pressure-temperature conditions in the earth, moon and the terrestrial planets. Experimentally, thermodynamic properties such as specific heat can be measured by adiabatic and differential scanning calorimetry. However, there are cases, in which the determination of the low temperature specific heat by adiabatic calorimetry is not feasible due to the paucity of materials. Such is the case for the high-pressure and high-temperature magnesium silicate phases: Mg2SiO4 (β- and γ-spinel) and MgSiO3 (ilmenite, perovskite and garnet) considered to be stable in the earth’s mantle. These phases are synthesized in cubic-anvil and split-sphere apparati in 10 to 20 mg quantities, that are barely adequate for the specific heat measurement by differential scanning calorimetry (DSC), usually in the range 300 to 900 K. Hence, the ability to correctly predict the low temperature specific heat of these phases would be extremely useful. Such a theoretical treatment should at the same time provide an understanding of the thermodynamic properties of minerals at the atomistic level. This was the goal aimed at the Mineralogical Society of America Short Course organized by S.W. Kieffer and A. Navrotsky on “Macroscopic to microscopic: Atomic environments to mineral thermodynamics” held at Washington College, Chestertown, Maryland in spring, 1985.

The paraelectric to antiferroelectric phase transition in titanite at ∼500 K involves a displacement of the titanium atom from the center of the [TiO6] octahedron in the paraelectric phase (A2/a) to an off-center position in the antiferroelectric (P2 1/a) phase. We have carried out a detailed single crystal high temperature x-ray diffraction study of the phase transition including structure refinements at 294, 350, 400, 430, 440, 450, 500, 600, and 700 K. The unit cell dimensions show a pronounced hysteresis effect in the 450–500 K range on heating and cooling during the first cycle along with a reduction of the transition temperature, T c from 495 ± 5 K on heating to 445 ± 5 K on cooling. The hysteresis effect disappears on further heating and the superstructure reflections show residual intensities above T c (445 K). An order parameter treatment of the phase transition is presented in terms of Landau theory and induced representation theory. The Ti-displacements parallel and antiparallel to a are taken as the primary order parameter η, which transforms as the Y 2 + representation. A coupling of Y 2 + with T 1 + results in the linear-quadratic coupling of the spontaneous strain components, ɛ ij with η. The Ti-displacements are coupled linearly to the Cadisplacements. Both sets of displacements predicted from induced representation theory are observed experimentally. The phase transition is initially driven by the soft mode at the zone boundary point Y 2 + ; near T c critical fluctuations set in and an order-disorder mechanism finally drives the phase transition, whereby parallel and antiparallel Ti-displacements related by [0, 1/2, 1/2] in adjacent domains are dynamically interchanged. Immediately above T c , the high temperature (A2/a) phase is a statistical average of small dynamic antiphase domains of the low temperature (P2 1/a) phase. Vacancies and defects pinning the domain boundaries may drastically alter the transition behavior and affect the domain mobility.

Cristobalite, a high temperature phase of silica, SiO2, undergoes a (metastable) first-order phase transition from a cubic, \(Fd\bar 3m\), to a tetragonal, P43212 (or P41212), structure at around 220° C. The cubic C9-type structure for β-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 A, whereas the corresponding values in tetragonal α-cristobalite are ∼146° and 1.609 A respectively. The structure of the β-phase is still controversial. To resolve this problem, a symmetry analysis of the \(Fd\bar 3m \to P4_3 2_1 2\) (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 (\(Fd\bar 3m\)) C9-type structure with the unit cell dimension a (7.432 A) slightly larger than the known a dimension (7.195 A at 205° C) of β-cristobalite, such that the Si-O-Si angle is still 180°, but the Si-O bond length is 1.609 A. 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 α-cristobalite from the β→α 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〉 (F→P). These domains are macroscopic and static in α-cristobalite, and microscopic and dynamic in β-cristobalite. The order parameter η, couples with the strain components as ɛη2, which initiates the structural fluctuations, thereby causing the domain configurations to dynamically interchange in the β-phase. Hence, the α-β cristobalite transition is a fluctuation-induced first-order transition and the β-phase is a dynamic average of α-type domains.

The crystal structure of akermanite, Ca2Mg-Si2O7, consists of mixed tetrahedral sheets formed by [MgO4] tetrahedra and [Si2O7] groups interleaved along the c axis with Ca2+ ions in eight-fold coordination. Above 358 K, the structure is tetragonal \((P\bar 42_1 {\text{ }}m)\), and below it is incommensurate with modulations parallel to [110] and \([1\bar 10]\). The elastic stiffness moduli, Cij of the incommensurate phase at room temperature were measured from wave velocities in the 20–75 MHz carrier frequency range by the ultrasonic phase comparison method using optically clear synthetic single crystal plates (3×3×2 mm) oriented parallel to (100), (001), (110) and (101) planes. The Cij values (GPa) are: C11 159.40, C33 149.43, C44 30.26, C66 58.10, C12 76.58 and C13 57.80. In (010) and (001) planes, the compressional modulus, ρV2(L) from the longitudinal wave, L is considerably larger than the shear moduli, ρV2(T1, T2) both from the in-plane and perpendicular-to-plane shear waves, T1 and T2. The relatively small values of the shear moduli indicate the ease of tetrahedral rotations in response to in-plane and perpendicular-to-plane shears and may provide preconditions for structural changes involving shear-type atomic movements.

An order parameter treatment of the phase transitions in leucite, KAlSi2O6, at approximately 950 and 920 K: $$Ia\overline 3 d$$ (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 Γ 3 + and Γ 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.

Enstatites (Mg2Si2O6) are important rock forming silicates of the pyroxene group whose structures are characterised by double MgO6 octahedral bands and single silicate chains. Orthoenstatite transforms to protoenstatite above 1273 K with a doubling of the a axis and a rearrangement of the silicate chains with respect to the Mg2+ ions. Lattice dynamical calculations based on a rigid-ion model in the quasi-harmonic approximation provide theoretical estimates of elastic constants, long wavelength phonon modes, phonon dispersion relations, total and partial density of states and inelastic neutron scattering cross-sections of protoenstatite. The computed elastic constants are in good agreement with experimental data. The computed density of states of a chain silicate such as protoenstatite is distinct from that of olivines (forsterite, Mg2SiO4 and fayalite, Fe2-SiO4) with isolated silicate tetrahedra. The band gaps in the density of states in forsterite are largely due to the separation in the frequency ranges of the external and internal vibrations of the isolated silicate group, whereas in protoenstatite these gaps are filled by the vibrations of the bridging oxygens of the silicate chain. The computed density of states is used to calculate the specific heat, the mean square atomic displacements and temperature factors. Validity of these calculations are supported by Raman scattering measurements. Polarised and unpolarised Raman spectra are obtained from small single crystals of protoenstatite (Li,Sc)0.6Mg1.4Si2O6 stable at room temperature using the 488 nm or 514.5 nm lines of an Ar+ ion laser and a micro-Raman spectrometer with backscattering geometry. The Raman spectra were analysed and interpreted based on the lattice dynamical model. The experimental Raman frequencies and mode assignments (based on polarised single crystal spectra) are in good agreement with those obtained from lattice dynamical calculations.

The non-ferroic triclinic to triclinic $$I\bar 1 - P\bar 1$$ phase transition in anorthite is described in terms of the spontaneous onset of an order parameter η. A triclinic to triclinic phase transition can be driven by order parameters (representations) arising from the Γ, Z, X, U, V, R, Y, and T points of symmetry of the Brillouin zone. Each point leads to a set of two inequivalent representations and thus there is a total of sixteen inequivalent order parameters. However, only the R 1 + representation is consistent with the change from the body-centered to primitive cell (increase of primitive cell size of two) and also with the origin of the two space groups (inversion center) being at the same position. The R 1 + order parameter of the high symmetry triclinic phase $$P\bar 1_0$$ (or equivalently $$I\bar 1$$ ) causes a reciprocal lattice change and, in terms of the lower symmetry reciprocal lattice, the order parameter corresponds to the b* point. This is consistent with experimentally observed x-ray diffuse scattering. Using induced representation theory, microscopic distortions compatible with the R 1 + order parameter are obtained. Assuming a distortion in an arbitrary direction at the general 2(i) Wyckoff position (x0,y0,z0) of $$P\bar 1_0$$ (the higher symmetry phase) induced representation theory demands an opposite displacement at the position (x0, y0, z0), an opposite displacement at (x0+1,y0+1,z0+1), and the same displacement at ( $$\bar x$$ 0+1, $$\bar y$$ 0+1, $$\bar z$$ 0+1) of $$P\bar 1_0$$ . This is also consistent with experiment. The presence of the weak c-type reflections above the transition is attributed to the fluctuating lower symmetry antiphase domains related by the translation (1/2, 1/2, 1/2).

Blanfordite (I), winchite (II), and juddite (III), all showing vivid colors and pleochroism, from highly oxidized parageneses of Indian gondites were studied by microprobe, Mossbauer, and microscope-spectrophotometric techniques and by X-ray structure refinements. The compositions of the Mn-bearing minerals were close to diopsideacmite (I) and magnesio-arfvedsonite to magnesio-riebeckite (II and III). Transition metal ions are located inM(1)-octahedra (I) or predominantlyM(2)-octahedra (II, III).

The crystal structure of the natural zeolite bikitaite, Li2Al2Si4O12·2H2O from Bikita, Zimbabwe, has been determined by neutron diffraction at 295 and 13 K. Space group P1, Z = 1, a = 8.6071(9), b = 4.9540(5), c = 7.5972(7) A, α = 89.900(7), β = 114.437(8), γ = 89.988(8)°, V = 294.9(1) A3 at 295 K, and a = 8.5971(8), b = 4.9395(4), c = 7.6121(7) A, α = 89.850(7), β = 114.520(7), γ = 90.004(7)°, V = 294.10(4) A3 at 13 K. λ = 1.0505(1) A, μ = 0.650 cm−1, Dx = 2.28 g/cm3. Final R(F) = 0.027 and 0.026 for 1845 and 2083 unique reflections at 295 and 13 K, respectively. Refined values of Si Al site occupancies show a high degree of ordering, which results in a triclinic distortion from the monoclinic symmetry reported by X-ray studies. The H2O molecules are hydrogen bonded only to each other, H···O = 1.949(3) and 1.955(3) A, and with H···O (framework) distances in the range 2.544(4)-2.946(4) A. The infinite water chains, parallel to b, are linked to the zeolite framework by Li+···Ow coordination only. The Li+ ions are each tetrahedrally coordinated by one water and three SiOAl oxygens. The Li coordination causes a strong decrease in the SiOAl angles. The significant structural changes when going from 295 to 13 K are stronger hydrogen bonding and a general decrease in the SiO Si Al angles.

In this paper, recent progress in three areas of the crystal chemistry of rock -forming silicates have been reviewed, where significant progress has been made in the last five years. These areas are : (1) electronic structure and chemical bond in silicates. (2) structural response of silicates under high temperature and pressure and (3) fine structure in chain silicates (biopyriboles). (1) A self-consistent pseudopotential calculation of the electron band structure of α-quartz shows good agreement with spectroscopic measurements. An ab initio calculation on H₄SiO₄ and H₆Si₂O₇ indicates considerable d-p π bonding in the Si — O bond. The theoretically calculated electron density distribution within the bridging and non bridging Si — O bonds in H₆Si₂O₇ is in agreement with the experimentally observed distribution in a silicate chain in enstatite. Electron density measurements of alpha-quartz by X-ray diffraction indicate bent bonds, oxygen-lone pair densities and residual electron density maxima near the midpoints of the Si — O bonds. Similar maxima have been observed in the Si — O bonds in a number of olivines and pyroxenes. These theoretical and experimental advances provide us with a fundamental understanding of the chemical bond in silicates. (2) Recent improvements in the diamond anvil high pressure cell and laser heating now make it possible to reproduce the pressure temperature conditions prevailing at the core-mantle boundary of the earth. Determination of a large number of oxide and silicate structures as a function of high temperature and pressure allows us to derive the thermal expansion and compressibility of cation-oxygen polyhedra, which seem to be independent of the structure type. These relationships will lead to models of the structural behavior of rock forming silicates and their phase transitions in the earth's mantle. (3) Discovery of new minerals, chemically and structurally intermediate between anthophyllite and talc with triple, and alternating double and triple silicate chains, and the observation of the intercalation of n-tuple chains in amphiboles, and their associated order-disorder and defects give us a detailed insight into the details of the chemical reactions involved in the phase transformations within biopyriboles during geologic processes., Cet article passe en revue les récents développements dans trois domaines de la cristallochimie des silicates formant les roches pour lesquels des progrès récents ont été faits ces cinq dernières années. Il s'agit : (1) De la structure électronique et de la liaison chimique dans les silicates, (2) du comportement structural des silicates sous haute température et haute pression, et (3) de la structure exacte des silicates, en particulier biopyriboles. (1) Le calcul de la structure de la bande du quartz α, déterminée par la méthode du pseudo potentiel self-consistant, montre un bon accord avec les résultats obtenus par des mesures de spectroscopic. Un calcul quantique ab initio sur H₄SiO₄ et H₆Si₂O₇ montre pour les liaisons Si — O une notable proportion d'orbitales de type (d-p)π. Dans le composé H₆Si₂O₇ les densités électroniques théoriques calculées pour les liaisons Si — O « bridging » et « non-bridging » sont en bon accord avec celles observées expérimentalement dans les chaînes de l'enstatite. Les mesures de la densité électronique sur le quartz α par diffraction des rayons X montrent l'existence de liaisons courbées, de paires non liées sur l'oxygène, et d'une densité électronique résiduelle maximum près des milieux de liaisons Si — O. De semblables maxima ont été observés pour les liaisons Si — O dans quelques olivines et pyroxènes. Ces améliorations théoriques et expérimentales nous fournissent une connaissance fondamentale de la liaison chimique dans les silicates. (2) De récents perfectionnements dans la cellule haute pression à enclume de diamant et dans le chauffage de l'échantillon par rayon laser, permettent de reproduire maintenant les conditions de température et de pression régnant à la frontière noyau˗manteau dans la terre. La détermination d'un grand nombre de structure d'oxydes et de silicates en fonction de la température et de la pression nous permettent d'en déduire la dilatation thermique et la compressibilité des polyèdres d'oxygènes autour des cations. Ces grandeurs semblent être indépendantes du type de structure considéré et devraient nous conduire à des modèles du comportement structural des silicates et ainsi d'interpréter les transitions de phases se produisant dans le manteau terrestre. (3) La découverte de nouveaux minéraux chimiquement et structuralement intermédiaires entre anthophyllite et talc, avec des triples chaînes silicate et des alternances double chaîne — triple chaîne, la mise en évidence de l'intercalation de n-tuple chaînes, ainsi que leurs défauts structuraux ou bien leur ordre-désordre, nous conduisent à une compréhension exacte des réactions chimiques mises en jeu dans les transformations de phases des biopyriboles lors de leurs développements géologiques., Ghose Subrata. Recent trends in the crystal chemistry of rock forming silicates. In: Bulletin de Minéralogie, volume 104, 2-3, 1981. 12e assemblée générale de l'I.M.A. - Orléans – Juillet 1980. Première partie : croissance cristalline / Physique des minéraux / Microscopie électronique.

Magnetization and neutron diffraction measurements have been made on grunerite, Fe7Si8O22(OH)2, a monoclinic double-chain silicate with Fe2+ octahedral bands. The mineral orders antiferromagnetically at 47K into a collinear structure with a second transition at 8K to a canted arrangement. The magnetic susceptibility follows a Curie-Weiss Law above 120K, with a paramagnetic Curie temeprature ϑp=67K. Magnetization measurements below 47K indicate a spin-flop or metamagnetic transition in an applied field of about 12KOe. Powder neutron diffraction measurements between 8–45K reveal that all the Fe2+ spins within an octahedral band are ferromagnetically coupled parallel to the b axis, with each band antiferromagnetically coupled to neighboring bands. Below 8K Fe2+ spins at the M1 and M4 sites are canted away from the b axis, whereas those at the M2 and M3 sites are not significantly affected. The ordered Fe2+ moment on the M4 site is substantially lower than those on the other sites, most likely indicating strong covalency effects, i.e. considerable spin transfer to neighboring oxygen atoms.

The measurement of the ac conductivity in NaLiZrSi6O15 single crystals under controlle oxygen fugacity conditions indicate conductivity of about 0.003 Siemens/meter at 900°C. The conductivity is highest along [001], intermediate along [010], and least along [100]. A changing conduction mechanism is indicated by a change in activation energy at 524°C. Below this temperature, the conduction presumably takes place thorugh the migration of ionic and electronic defects. The ionic conduction above this temperature is facilitated by the partial migration of Na+ ions from the Na(1) site to the Na(2) site, which is vacant at RT. At high temperature, the Na(1)-Na(1) conduction path along [001] is favored over the Na(1)-Na(2) conduction path along [010] due to a difference in the bottlenecks along these paths. The long Na(1)-Na(1) nearest distance along [100] hinders Na+ migration along this direction.

Amelia albite annealed at > 1080 °C for 3200 hrs by Duba and Piwinskii (1974) shows very fine twin lamellae (∼1 μm) after the albite law, suggesting that it once underwent transformation into monalbite. A fragment of this specimen was investigated at 27 °C, 300 °C, 550 °C, 800 °C and 930 °C using the high-temperature precession technique. As the temperature increases, the splitting angle of c*-axes (likewise c*-axes) of two twin individuals continues to decrease. The photographs taken at 930 °C show that these two splitting angles have converged to 0o, indicating completion of the transformation into monalbite. The transition point we observe supports the results of MacKenzie (1952) (920±20 °C) and Grundy et al. (1967) (930 °C) rather than those of Sueno et al. (1973) and Prewitt et al. (1974) (> 1080 °C); the discrepancy is most likely due to the differences in the degree of Al-Si disorder of the samples used in the experiments.

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

A lattice dynamical study of the geophysically important mineral MgSiO3 in its orthorhombic perovskite phase, with space group Pnma (D 2 16 ) has been carried out using a rigid ion model, with the potential consisting of Coulombic and short-ranged interactions. With the help of program DISPR, the ionic charges and radii were optimized using the equilibrium conditions. The resulting potential model is employed to predict the elastic constants and the phonon dispersion relations. The computed long wavelength optic modes are in good agreement with the corresponding experimental Raman and infrared active bands. The phonon density of states has been obtained and is used to evaluate the specific heat, the mean square displacements and thermal parameters of atoms.

Orthopyroxene has two tetrahedral sites, designated A and B, and two octahedral sites, M1 and M2. Crystallographic studies of synthetic and natural orthopyroxenes (opx) suggest that the tetrahedral Al is ordered nearly completely in the B site, but the octahedral Al disorders between M1 and M2 sites with a preference for M1. If the ‘aluminum avoidance’ principle is obeyed, then the tetrahedral Si-Al ordering limits the Al substitution in opx to 25 mol%, thus leading to an end-member stoichiometry of Mg3Al2Si3O12 instead of MgAl2SiO6. The enthalpy of formation of these two components has been deduced from the available phase equilibrium data. The thermodynamic properties of the opx solid solution approximates ideal solution behavior more closely when treated in terms of the components Mg4Si4O12(QEn)-Mg3Al2Si3O12(Py) than when expressed in terms of the components Mg2Si2O6-MgAl2SiO6. A model has been developed for the octahedral disordering of Al as function of temperature and composition. These data enable calculation of the configurational entropy and molar entropy of Al-opx; distinction has been made between the cases of completely random mixing of Al and Si in the tetrahedral B site, and of random mixing without violation of the ‘aluminum avoidance’ principle. The second model yields entropy of the Mg3Al2Si3O12 end member which agrees almost exactly with the value derived from phase equilibrium data. The partial molal entropies of the Orthopyroxene components ‘QEn’ and ‘Py’ can be derived from these data; their implications with respect to the P-T slopes of Al2O3 isopleths for the equilibrium of Orthopyroxene with forsterite and spinel/garnet have been discussed.

Synthetic enstatite, MgzSiz06, is orthorhombic, space group Pbca, with eight formula units per cell and lattice parameters a = 18.235(3), b = 8.818(1), c = 5.179(1) A at 230 C. A least-squares structure refinement based on 1790neutron intensity data convergedwith an agreement factor R(FZ) = 0.032, yielding Mg-O and Si-O bond lengths with standard deviationsof 0.0007 and 0.0008 A, respectively. The variations observed in theSi-O bond lengths within the silicate tetrahedra A and B are caused bythe differences in primary coordination of the oxygen atoms and the proximityof the magnesium ions to the silicon atoms. The latter effect is mostpronounced for the bridging bonds of tetrahedron A. The smallest 0- Si- 0 angle is the result of edge-sharing by the Mg(2) octahedron and theA tetrahedron. An analysis of rigid-body thermal vibrations of the two crystallographically independent (Si04J tetrahedra indicates considerable librationalmotion, leading to a thermal correction of apparent Si - 0 bond lengths as large as + 0.002 A at room temperature.

The crystal and magnetic structures of ilvaite Ca(Fe2+, Fe3+)Fe2+Si2O7O(OH) have been obtained by profile refinement of high resolution neutron powder data from a natural sample from Seriphos, Greece. Below about 400 K an electronic transition from an itinerant to an ordered state is expected, with the structure changing from orthorhombic to monoclinic. The structure remains monoclinic P2 1/a down to 5 K, with Fe2+ almost completely ordered on one of the A-sites and Fe3+ on the other: the ordering may increase with decreasing temperature. The B-site contains Fe2+ plus a small amount of Mn2+ impurity. There are two magnetic transitions, at 116 K and 40 K: at 80 K the Fe2+ and Fe3+ spins on the A-sites along one infinite c-axis chain are parallel, and antiparallel to those along the adjoined edge-sharing centrosymmetrically related chain. The spin vectors are all perpendicular to the plane of these chains, i.e. almost parallel to the crystallographic b-axis. At 5 K, this order is maintained, but the Fe2+ spins on the B-sites order antiferromagnetically as well, again almost along the b-axis. These results explain the earlier Mossbauer and magnetisation measurements.

Plagioclase in cataclastic anorthosite 67075 occurs as angular matrix grains and as recrystallized clasts of micro-anorthosite. Olivines are Fe-rich and fall into two compositional groupings. Large grains of pyroxene show exceptionally well-developed exsolution lamellae analogous to those observed in pyroxenes from layered complexes. The low-Ca component in both pigeonites and augites shows varying degrees of inversion to orthopyroxene. The lattices of host and lamellae may deviate slightly (up to 2°) from the ideal orientation. Very slow cooling from magmatic temperatures is required to produce the coarse exsolution textures and inversion features. Augite macrocrystals are distinctly subcalcic indicating crystallization at temperatures around 1100 ± 50°C while host-lamellae pairs and small grains in lithic clasts and matrix indicate reequilibration on a micron scale to temperatures less than 800°C. Pyroxene compositions tend to cluster into two groups both of which are among the most Fe-rich reported for highland pyroxenes. Ti and Al contents of pyroxenes are very low and Ti, Cr, and Mn follow well-established magmatic differentiation trends. The high Cr content may reflect low ƒO 2 conditions and/or early crystallization of olivine and plagioclase. The 87 Sr/ 86 Sr ratios in lunar anorthosites are the lowest reported for any lunar rock. It is likely that anorthosites formed as cumulates during the major differentiation episode which occurred prior to ∼4.3AE . Recrystallization features are common and 39 Ar/ 40 Ar ages cluster around 4.0 AE. This may be the result of the intense bombardment prior to 4.0 AE which caused repeated cycles of in-situ fracturing and granulation followed by recrystallization. The low siderophile element content and the inferred slow cooling indicate a plutonic source region ( 10km ) not frequently plumbed by impact events. The Fe-rich silicates indicate crystallization from a melt at an advanced stage of fractionation. However, the low REE abundances are not consistent with late-stage crystallization. Plagioclase apparently crystallized relatively early and was concentrated by flotation and/or convection currents while the mafic minerals crystallized from a fractionated trapped liquid. The chemical, isotopic, and mineralogical data place stringent constraints on the nature of genetically related rocks and the relationship of anorthosites to other members of the ANT suite does not appear to be one of simple fractionation. The data presented in this paper are consistent with the Taylor-Jakesmodel of lunar evolution.

Two types of nuclear electric quadrupole tensors have been observed for 27Al in epidote. The quadrupole coupling constant C and asymmetry parameter η are AlI |C|=11.9 MHz, η=0.3; AlII, |C|=4.6 MHz, η=0.34. They correspond to the Al1 and Al2 sites, respectively, of the epidote crystal structure. The electric field gradient tensors, with principal contributions from its nearest neighbors in the highly distorted AlO6 tetrahedra, are consistent with the epidote structure and with other aluminosilicate minerals.