S. L. Chaplot

Inelastic neutron scattering and lattice dynamics of minerals

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 Earths 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 Earths 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.

Relationship between phonons and thermal expansion in Zn(CN)2 and Ni(CN)2 from inelastic neutron scattering and ab initio calculations

Zn(CN)2 and Ni(CN)2 are known for exhibiting anomalous thermal expansion over a wide temperature range. The volume thermal expansion coefficient for the cubic, three dimensionally connected material, Zn(CN)2, is negative (alpha(V) = −51  10(-6) K-1) while for Ni(CN)2, a tetragonal material, the thermal expansion coefficient is negative in the two dimensionally connected sheets (alpha(a) = −7  10(-6) K-1), but the overall thermal expansion coefficient is positive (alpha(V) = 48  10(-6) K-1). We have measured the temperature dependence of phonon spectra in these compounds and analyzed them using ab initio calculations. The spectra of the two compounds show large differences that cannot be explained by simple mass renormalization of the modes involving Zn (65.38 amu) and Ni (58.69 amu) atoms. This reflects the fact that the structure and bonding are quite different in the two compounds. The calculated pressure dependence of the phonon modes and of the thermal expansion coefficient, alpha(V), are used to understand the anomalous behavior in these compounds. Our ab initio calculations indicate that phonon modes of energy approx. 2 meV are major contributors to negative thermal expansion (NTE) in both the compounds. The low-energy modes of approx.8 and 13 meV in Zn(CN)2 also contribute significantly to the NTE in Zn(CN)2 and Ni(CN)2, respectively. The measured temperature dependence of the phonon spectra has been used to estimate the total anharmonicity of both compounds. For Zn(CN)2, the temperature-dependent measurements (total anharmonicity), along with our previously reported pressure dependence of the phonon spectra (quasiharmonic), is used to separate the explicit temperature effect at constant volume (intrinsic anharmonicity).

Phonon density of states and thermodynamic properties in cubic and orthorhombic phases of ZrW2O8

Abstract Lattice dynamical calculations have been carried out in the cubic and orthorhombic phases of the negative thermal expansion compound ZrW 2 O 8 . The phonon density of states, thermal expansion, specific heat and bulk modulus have been calculated. The calculations are in good agreement with the available experimental data.

Free energy and relative stability of the enstatite Mg2Si2O6 polymorphs

Abstract Detailed lattice dynamical studies of the equations of state and the phase diagram of the geophysically important mineral enstatite have been undertaken. There are several enstatite polymorphs: ortho, proto and clinoenstatite, whose structures are characterized by double MgO6 octahedral ribbons and single silicate chains. The computed equations of state are found to be in good agreement with available experimental data and ab initio results. The calculations reveal that the stable phase at ambient conditions is orthoenstatite, which transforms to the protoenstatite phase at high temperatures. The monoclinic C2/c clinoenstatite phase is found to be stable at high pressures. The computed phase diagram is in overall qualitative agreement with the experimental data. These studies have enabled a microscopic understanding of the factors contributing to the relative stability and indicate that while the orthoenstatite to protoenstatite transition is temperature driven, the orthoenstatite to clinoenstatite transition is pressure driven.

The behaviour of alpha -quartz and pressure-induced SiO2 glass under pressure: a molecular dynamical study

The authors have carried out extensive molecular dynamical calculations on alpha -quartz and pressure-induced glass and have related these to the experimental observations under static and shock pressure loading. In the crystalline quartz, densification and amorphization take place sharply around 20 GPa and are related to the changes in the Si coordination. The pressure-induced glass is considerably less compressible than the fused silica, showing a gradual change in the Si coordination, and is unlike the glass studied earlier by Tse, Klug and Le Page (1992). However even this glass shows a densification, similar to that of quartz as well as fused silica. Retrieval of the four-coordinated state, in both cases, requires annealing at high temperatures. Just before amorphization of alpha -quartz, O atoms are still far from the recently proposed BCC packing.

Suppression of antiferroelectric state in NaNbO3 at high pressure from in situ neutron diffraction

We report direct experimental evidence of antiferroelectric to paraelectric phase transition under pressure in NaNbO3 using neutron diffraction at room temperature. The paraelectric phase is found to stabilize above 8 GPa and its crystal structure has been determined in orthorhombic symmetry with space group Pbnm. The variation of the structural parameters of the both orthorhombic phases as a function of pressure was determined. We have not found evidence for structural phase transition around 2 GPa as previously suggested in the literature based on Raman scattering experiments; however, significant change in Nb-O-Nb bond angles are found around this pressure. The response of the lattice parameters to pressure is strongly anisotropic with a largest contraction along 〈100〉. The structural phase transition around ∼8 GPa is followed by an anomalous increase in the orthorhombic strain and tilt angle associated with the R point (q = ½ ½ ½). Ab-initio calculation of the enthalpy in the various phases of NaNbO3 ...

X-ray diffraction study of anisotropic thermal expansion in ZrMo2O8

Temperature-dependent X-ray diffraction measurements are reported for ZrMo2O8 in the trigonal phase from 80 to 925 K. The measurements reveal highly anisotropic thermal expansion coefficients with average values of −3.9 × 10−6 and 52 × 10−6 K−1 for the a and c cell parameters, respectively.

Phonon Density of States and Specific Heat of Forsterite, Mg2SiO4

The phonon density of states of the geophysically important mineral forsterite has been calculated with a rigid-ion model, which gives good agreement with an experimental measurement by inelastic neutron scattering. The density of states has been used to calculate the specific heat as a function of temperature, the results of which are in excellent agreement with calorimetrically measured values. The rigid-ion model takes account of the interatomic interactions and normal modes of vibration on a detailed microscopic basis, and is therefore more realistic than the Debye and other empirical models used previously.

Magnetic lattice dynamics of the oxygen-free FeAs pnictides: how sensitive are phonons to magnetic ordering?

To shed light on the role of magnetism on the superconducting mechanism of the oxygen-free FeAs pnictides, we investigate the effect of magnetic ordering on phonon dynamics in the low-temperature orthorhombic parent compounds, which present a spin density wave. The study covers both the 122 (AFe(2)As(2); A = Ca, Sr, Ba) and 1111 (AFeAsF; A = Ca, Sr) phases. We extend our recent work on the Ca (122 and 1111) and Ba (122) cases by treating, computationally and experimentally, the 122 and 1111 Sr compounds. The effect of magnetic ordering is investigated through detailed non-magnetic and magnetic lattice dynamical calculations. The comparison of the experimental and calculated phonon spectra shows that the magnetic interactions/ordering have to be included in order to reproduce well the measured density of states. This highlights a spin-correlated phonon behavior which is more pronounced than the apparently weak electron-phonon coupling estimated in these materials. Furthermore, there is no noticeable difference between phonon spectra of the 122 Ba and Sr, whereas there are substantial differences when comparing these to CaFe(2)As(2) originating from different aspects of structure and bonding.

Study of phonon dispersion relations in forsterite, Mg2SiO4 by inelastic neutron scattering

Abstract Phonon dispersion relations in forsterite, Mg2SiO4 (orthorhombic, a = 10.190, b = 5.978, c = 5.753 A , space group PnmaZ = 4) have been determined under ambient conditions using inelastic neutron scattering (INS). Nine acoustic and seventeen optic branches have been measured along the three principal symmetry directions in the Brillouin zone. Seven zone center phonons have been observed with frequencies 104, 144, 184, 192, 200, 258, 315, and 325 cm−1, which are in good agreement with Raman and infra red measurements, except the lowest frequency phonon at 104 cm−1, which is Raman and IR inactive and has been observed for the first time in INS. In order to select suitable wave vector transfers for phonon measurements, the one-phonon neutron structure factors predicted from a lattice-dynamical rigid ion molecular model were used as guides for the INS experiment. The measured dispersion relations agree very well with those predicted from a rigid ‘molecular’ ion model, where the tetrahedral [SiO4] unit is assumed to be a rigid group. The elastic constants determined from the slopes of the acoustic branches show good agreement with those measured by ultrasonic techniques.