Free-energy derivatives and structure optimization within quasiharmonic lattice dynamics

Taylor, Mark; Barrera, Gustavo D.; Allan, Neil L.; Barron, T. H. K.

doi:10.1103/physrevb.56.14380

Cited by 87 publications

(63 citation statements)

References 12 publications

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“…In principle, it is also possible to account for thermal effects on the structure of each configuration by performing a free energy minimization at each geometry and temperature, using the quasi-harmonic approximation (e.g. Taylor et al, 1997;Gale, 1998;Grau-Crespo et al, 2002). However, considering the large number of configurations treated here and the high computational cost of free energy minimizations, we have optimized the structures only with respect to the lattice energy.…”

Section: Evaluation Of Energies and Free Energies And Geometry Predicmentioning

confidence: 99%

Thermochemistry of strontium incorporation in aragonite from atomistic simulations

Ruiz‐Hernandez

Grau‐Crespo

Ruiz‐Salvador

et al. 2010

Geochimica et Cosmochimica Acta

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We have investigated the thermodynamics of mixing between aragonite (orthorhombic CaCO 3 ) and strontianite (SrCO 3 ). In agreement with experiment, our simulations predict that there is a miscibility gap between the two solids at ambient conditions. All Sr x Ca 1Àx CO 3 solids with compositions 0.12 < x < 0.87 are metastable with respect to separation into a Ca-rich and a Sr-rich phase. The concentration of Sr in coral aragonites (x $ 0.01) lies in the miscibility region of the phase diagram, and therefore formation of separated Sr-rich phases in coral aragonites is not thermodynamically favorable. The miscibility gap disappears at around 380 K. The enthalpy of mixing, which is positive and nearly symmetric with respect to x = 0.5, is the dominant contribution to the excess free energy, while the vibrational and configurational entropic contributions are small and of opposite sign. We provide a detailed comparison of our simulation results with available experimental data.

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Section: Evaluation Of Energies and Free Energies And Geometry Predicmentioning

confidence: 99%

Thermochemistry of strontium incorporation in aragonite from atomistic simulations

Ruiz‐Hernandez

Grau‐Crespo

Ruiz‐Salvador

et al. 2010

Geochimica et Cosmochimica Acta

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“…Some methods have recently been developed to fully minimize G (x; p, T ) with respect to x within the quasiharmonic approximation when simple pair potentials are used in the crystal simulation [2]. However, when a firstprinciples method is used, the full minimization of G (x; p, T ) is currently infeasible.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, the third term, A vib , is the vibrational Helmholtz free energy, which includes both the vibrational contribution to the internal energy and the −T S constant temperature condition term (since we are considering a perfect crystal whose only internal degrees of freedom are vibrations, S = S vib ). The rigorous statistical calculation of A vib requires knowledge of the exact vibrational levels, but it is customary to introduce the quasi-harmonic approximation [1], (2) A vib (x; T ) = ∞ 0 1 2h ω + kT ln(1 − e −hω/ kT ) g(x; ω) dω, where g(x; ω) is the phonon or vibrational density of states. The term quasi-harmonic, as different from the rigid harmonic approximation, remarks that the density of states is allowed to vary with the crystal configuration, thus including anharmonic contributions to a certain extent.…”

Section: Introductionmentioning

confidence: 99%

GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model

Blanco

Francisco

Luaña

2004

Computer Physics Communications

1,746

812

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“…In the static limit, the structure is determined by the condition EaX i 0Y where E is the static contribution to the internal energy, and the X i are the variables that define the structure. These are the three lattice vectors, the atomic positions in the unit cell and, in the case of the shell model, the shell displacements (Taylor et al 1997). The most convenient approach to vacancy and other defect energies is the two-region approach introduced by Lidiard & Norgett (1972) and described in full by Catlow & Mackrodt (1982).…”

Section: Displacement Energy E Dmentioning

confidence: 99%

Sputtering of grains in C-type shocks

May

Forêts

Flower

et al. 2000

Monthly Notices of the Royal Astronomical Society

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113

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A B S T R A C TSputtering yields are reported for the release of Mg, Fe, Si and O under impact of He, C, O, Si and Fe on grain material composed of Mg-and Fe-bearing silicates. The yields were derived using the trim code, which simulates the results of the transport of ions in matter by means of classical Monte Carlo techniques. The energetics of the sputtering process are a key factor in the sputtering calculations, and so detailed determinations have been made of the energy with which atoms are bound to the lattice, using solid-state simulation programs. The probability of ejection of an atom is computed at a given energy, for a number of angles of incidence, and integrated to obtain the mean yield at that energy. These numerical results are then fitted with a simple function of energy for convenience in subsequent applications.A grid of C-type shock models has been computed, using our new sputtering yields, for pre-shock densities in the range 10 4 < n H nH 1 2nH 2 < 10 6 cm 23 and shock speeds 20 < v s < 45 km s 21 X Sputtered fractions can be high, exceeding 50 per cent for shock speeds in excess of approximately 40 km s 21 . The column densities of Si and SiO were also computed, for comparison with observations. Key words: shock waves ± ISM: jets and outflows. I N T R O D U C T I O NIn an earlier work (Field et al. 1997; hereafter FMFF), sputtering yields were reported for amorphous carbon and amorphous SiO 2 targets, for sputtering of C, Si and O from these targets by impact of He, C, O, Si and Fe. The consequences for the chemistry in C-type shocks were very briefly explored with special reference to the production of gas-phase SiO. Our purpose in the present work is twofold. In the first place, we seek to make available values of sputtering yields for targets that mimic more closely the composition of interstellar grains. To this end, the sputtering of grains composed of Mg-and Fe-bearing silicates is studied here. The results are relevant to the oxygen-rich environments in which outflows, associated with star formation, are typically found. In the second place, the new sputtering data are used in a sophisticated C-type shock model to yield a grid of results for a range of shock parameters, notably the shock velocity, pre-shock gas density and magnetic field. These models determine, for example, the budget of refractory material in the gas phase, in particular of SiO. These results may be used in conjunction with observational data (e.g. Dutrey, Guilloteau & Bachiller 1997; Lefloch et al. 1998) as a guide to the shock conditions in any particular region.In Section 2 the technical means for calculating sputtering yields are described, with particular reference to the energetics of the processes involved in sputtering. Sputtering yields are presented in Section 3 for magnesium silicate (Mg 2 SiO 4 ), or forsterite', iron silicate (Fe 2 SiO 4 ), or`fayalite' and an`olivine', MgFeSiO 4 , for a variety of projectile species. In Section 4, the grid of shock models is presented and brief reference is made to...

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Free-energy derivatives and structure optimization within quasiharmonic lattice dynamics

Cited by 87 publications

References 12 publications

Thermochemistry of strontium incorporation in aragonite from atomistic simulations

Thermochemistry of strontium incorporation in aragonite from atomistic simulations

GIBBS: isothermal-isobaric thermodynamics of solids from energy curves using a quasi-harmonic Debye model

Sputtering of grains in C-type shocks

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