Prabhatasree Goel

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.

Lattice dynamics and Born instability in yttrium aluminum garnet, Y3A15O12

We report lattice dynamics calculations of various microscopic and macroscopic vibrational and thermodynamic properties of yttrium aluminum garnet (YAG), Y3Al5O12, as a function of pressure up to 100 GPa and temperature up to 1500 K. YAG is an important solid-state laser material with several technological applications. Garnet has a complex structure with several interconnected dodecahedra, octahedra and tetrahedra. Unlike other aluminosilicate garnets, there are no distinct features to distinguish between intramolecular and intermolecular vibrations of the crystal. At ambient pressure, low energy phonons involving mainly the vibrations of yttrium atoms play a primary role in the manifestations of elastic and thermodynamic behavior. The aluminum atoms in tetrahedral and octahedral coordination are found to be dynamically distinct. Garnets stability can be discerned from the response of its phonon frequencies to increasing pressure. The dynamics of both octahedral and tetrahedral aluminum atoms undergo radical changes under compression which have an important bearing on their high pressure and temperature properties. At 100 GPa, YAG develops a large phonon bandgap (90-110 meV) and its microscopic and macroscopic physical properties are found to be profoundly different from that at the ambient pressure phase. There are significant changes in the high pressure thermal expansion and specific heat. The mode Grüneisen parameters show significant changes in the low energy range with pressure. Our studies show that the YAG structure becomes mechanically unstable around P = 108 GPa due to the violation of the Born stability criteria. Although this does not rule out thermodynamic crossover to a lower free energy phase at lower pressure, this places an upper bound of P = 110 GPa for the mechanical stability of YAG.

Inelastic neutron scattering studies of phonon spectra, and simulations of pressure-induced amorphization in tungstatesAWO4(A=Ba,Sr,Ca, andPb)

Lattice dynamics and high pressure phase transitions in AWO4 (A = Ba, Sr, Ca and Pb) have been investigated using inelastic neutron scattering experiments, ab-initio density functional theory calculations and extensive molecular dynamics simulations. The vibrational modes that are internal to WO4 tetrahedra occur at the highest energies consistent with the relative stability of WO4 tetrahedra. The neutron data and the ab-initio calculations are found to be in excellent agreement. The neutron and structural data are used to develop and validate an interatomic potential model. The model is used for classical molecular dynamics simulations to study their response to high pressure. We have calculated the enthalpies of the scheelite and fergusonite phases as a function of pressure, which confirms that the scheelite to fergusonite transition is second order in nature. With increase in pressure, there is a gradual change in the AO8 polyhedra, while there is no apparent change in the WO4 tetrahedra. We found that that all the four tungstates amorphize at high pressure. This is in good agreement with available experimental observations which show amorphization at around 45 GPa in BaWO4 and 40 GPa in CaWO4. On amorphization, there is an abrupt increase in the coordination of the W atom while the bisdisphenoids around A atom are considerably distorted. The pair correlation functions of the various atom pairs corroborate these observations. Our observations aid in predicting the pressure of amorphization in SrWO4 and PbWO4, which have not been experimentally reported.

New insights into the compressibility and high-pressure stability of Ni(CN)2: a combined study of neutron diffraction, Raman spectroscopy, and inelastic neutron scattering.

Nickel cyanide is a layered material showing markedly anisotropic behaviour. High-pressure neutron diffraction measurements show that at pressures up to 20.1 kbar, compressibility is much higher in the direction perpendicular to the layers, c, than in the plane of the strongly chemically bonded metal-cyanide sheets. Detailed examination of the behaviour of the tetragonal lattice parameters, a and c, as a function of pressure reveal regions in which large changes in slope occur, for example, in c(P) at 1 kbar. The experimental pressure dependence of the volume data is fitted to a bulk modulus, B0, of 1050 (20) kbar over the pressure range 0-1 kbar, and to 124 (2) kbar over the range 1-20.1 kbar. Raman spectroscopy measurements yield additional information on how the structure and bonding in the Ni(CN)2 layers change with pressure and show that a phase change occurs at about 1 kbar. The new high-pressure phase, (Phase PII), has ordered cyanide groups with sheets of D4h symmetry containing Ni(CN)4 and Ni(NC)4 groups. The Raman spectrum of phase PII closely resembles that of the related layered compound, Cu1/2Ni1/2(CN)2, which has previously been shown to contain ordered C≡N groups. The phase change, PI to PII, is also observed in inelastic neutron scattering studies which show significant changes occurring in the phonon spectra as the pressure is raised from 0.3 to 1.5 kbar. These changes reflect the large reduction in the interlayer spacing which occurs as Phase PI transforms to Phase PII and the consequent increase in difficulty for out-of-plane atomic motions. Unlike other cyanide materials e.g. Zn(CN)2 and Ag3Co(CN)6, which show an amorphization and/or a decomposition at much lower pressures (~100 kbar), Ni(CN)2 can be recovered after pressurising to 200 kbar, albeit in a more ordered form.

Phonons, lithium diffusion and thermodynamics of LiMPO4 (M = Mn, Fe)

We report phonon studies using neutron inelastic scattering experiments, ab initio density functional theory calculations and potential model calculations on LiMPO4 (M = Mn, Fe) at ambient and high temperature to understand the microscopic picture of a Li sub-lattice. The experiments are in good agreement with calculations. Here for the first time we have correlated the diffusion of lithium and dynamical instability in LiMPO4. The lattice dynamics calculations indicate the instability of the zone-centre as well as zone-boundary phonon modes along the [100] direction at unit cell volumes corresponding to elevated temperature. Under ambient conditions, eigen vectors of Li corresponding to these modes exhibit displacement only in the x–y plane. However with initiation of phonon instability Li atoms exhibit displacement along all the three directions with the highest component along the x direction. Molecular dynamics simulations with increasing temperature indicate large mean square displacement of Li as compared to other constituent atoms. The computed pair-correlations between various atom pairs show that there is local disorder occurring in the lithium sub-lattice with increasing temperature, while other pairs show minimal changes.

Lattice dynamics of lithium oxide

Li2O finds several important technological applications, as it is used in solid-state batteries, can be used as a blanket breeding material in nuclear fusion reactors, etc. Li2O exhibits a fast ion phase, characterized by a thermally induced dynamic disorder in the anionic sub-lattice of Li+, at elevated temperatures around 1200 K. We have carried out lattice-dynamical calculations of Li2O using a shell model in the quasi-harmonic approximation. The calculated phonon frequencies are in excellent agreement with the reported inelastic neutron scattering data. Thermal expansion, specific heat, elastic constants and equation of state have also been calculated which are in good agreement with the available experimental data.

Inelastic Neutron Scattering, Lattice Dynamics and High Pressure Stability of LuVO4

We report here inelastic neutron scattering, lattice dynamics calculations and relative high pressure stability of LuVO4. We have developed transferable interatomic potentials to study the lattice dynamics and model the experimentally obtained phonon density of states in LuVO4. The parameters of the theoretical interatomic potential have been fitted with respect to experimentally available Raman and infrared frequencies and equilibrium structure. We have also studied the stability of the zircon structure at ambient temperature with increasing pressure. We find that zircon phase (I41/amd) goes into a scheelite phase (I41/a) at around 8 GPa which is in excellent agreement with reported value of 7.9 GPa.

Molecular Dynamics Studies On Strontium And Barium Tungstate

Alkaline‐earth tungstates exhibit an interesting phase diagram with respect to increasing pressure. We report molecular dynamics simulation studies on pressure driven transformations of the scheelite phase in SrWO4 and BaWO4. We have studied the behavior of the tungstates up to 100 GPa. Our calculated equation of state is in very good agreement with reported experimental and first principles calculations. Our calculations reproduce the scheelite to fergusonite transformation in SrWO4 and BaWO4 around 10 and 5 GPa respectively. Volume discontinuity is not apparent at this transition. The two tungstates transform to an amorphous phase beyond 45 GPa with significant volume collapse. The pair correlation functions show that there are subtle changes in the arrangement of the AO8 polyhedra with increasing pressure. But the WO4 tetrahedra remain unperturbed with increasing pressure until amorphization occurs. Our calculations indicate that SrWO4 amorphizes at around 50 GPa, which has not been reported experiment...

Phonons and Thermal Expansion Behavior of NiSi and NiGe

We have carried out first principles calculations of the vibrational and thermodynamic behavior in NiSi and isostructural compound NiGe. Phonon density of states has also been measured in NiSi using inelastic neutron scattering techniques. We find that the vibrational spectra of the two compounds are very different, due to the difference in the size and mass of Si and Ge. Interesting anomalous thermal behavior of NiSi due to anharmonic phonons is brought out well in our calculations, particularly the negative thermal expansion (NTE) along the b-axis of the orthorhombic unit cell. Large difference in thermal expansion behavior of NiSi and NiGe is very well reproduced by the calculations. Additionally, calculations enable to identify the phonon modes which lend major contribution to the negative thermal expansion behavior in NiSi, and reasons for negligible NTE in NiGe. Such typical representative modes at the zone-boundary along b-axis involve transverse vibrations of Si/Ge along c-axis. PACS numbers: 78.70.Nx, 63.20.-e, 65.40.–b.

Inelastic neutron scattering investigations of negative thermal expansion behavior in semiconductors and framework solids

Volume 25 • Number 1 • 2014 Neutron News 34 Negative thermal expansion (NTE) is known in simple compounds like ZnSe as well as framework compounds like Zn(CN)2 [1] and Cu2O [2]. In Cu2O, the Cu atoms are linearly coordinated by two oxygen atoms, while oxygen is tetrahedrally coordinated by four Cu atoms. EXAFS data [3] on intranetwork and internetwork Cu-Cu distances suggest different thermal expansion of these bonds above 100 K, which is not possible in the cubic structure; no structural changes have been reported from diffraction experiments too. Zn(CN)2 is reported [4] to have an isotropic NTE coeffi cient (αV = –51 × 10 -6 K-1). The ordered structure of Zn(CN)2 consists of a ZnC4 tetrahedron (at the centre of the cell) linked to four neighbouring ZnN4 tetrahedra (at the corners of the cell) with CN groups along four of the body diagonals. Low energy (large-amplitude) transverse modes have been identifi ed as the principal cause of anomalous thermal expansion in framework compounds. At ambient pressure, ZnSe, Zn(CN)2 as well as Cu2O crystallize in the cubic structure. ZnSe has a transition [5] to a rocksalt phase at about 13.7 GPa. Theoretical studies [6] predicted that ZnSe could transform from zincblende to SC16 (simple cubic with 16-atom basis) phase, and then to rocksalt. But the SC16 phase has not been observed experimentally in this material, upon either pressure increase or decrease. For the semiconductor alloy ZnS1-xSex, infrared and Raman spectra [7] reveal a two-mode behavior (corresponding to ZnSe-like vibrations and ZnS-like ones). Two additional modes were also observed in the region of the ZnS-like modes. In all the four materials, inelastic neutron scattering measurements were carried out to determine the phonon density of states and interpreted with lattice dynamics computations, for the calculation of the phonon frequencies, their pressure dependence, and to estimate their anharmonicity, thus leading to an insight to the phonon modes responsible for the NTE, the phase transitions and the nature of these modes.