The Lindemann and Grüneisen Laws

Gilvarry, J. J.

doi:10.1103/physrev.102.308

Cited by 402 publications

(192 citation statements)

References 30 publications

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“…The possible reason is still the nonuniform changes of the interatomic distances within the unit cell for RE-123. We have studied the trend of melting temperature of RE-123 by "Lindemann law" [44,45], and found that the vibrations along c-axis are the most important modes to determine the melting temperatures while the isotropic approximation fails to yield correct results [38]. Here, we take another approach to investigate the relation between melting temperatures and formation energies of Schottky defects.…”

Section: +mentioning

confidence: 99%

Strain effects on point defects and chain-oxygen order-disorder transition in 123 cuprate compounds

Welch

Wong‐Ng³

2004

Phys. Rev. B

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The energetics of Schottky defects in 123 cuprate superconductor series, REBa2Cu3O7 (where RE = lanthandies) and YAE2Cu3O7 (AE = alkali-earths), were found to have unusual relations if one considers only the volumetric strain. Our calculations reveal the effect of non-uniform changes of interatomic distances within the RE-123 structures, introduced by doping homovalent elements, on the Schottky defect formation energy. The energy of formation of Frenkel Pair defects, which is an elementary disordering event, in 123 compounds can be substantially altered under both stress and chemical doping. Scaling the oxygen-oxygen short-range repulsive parameter using the calculated formation energy of Frenkel pair defects, the transition temperature between orthorhombic and tetragonal phases is computed by quasi-chemical approximations (QCA). The theoretical results illustrate the same trend as the experimental measurements in that the larger the ionic radius of RE, the lower the orthorhombic/tetragonal phase transition temperature. This study provides strong evidence of the strain effects on order-disorder transition due to oxygens in the CuO chain sites.

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Section: +mentioning

confidence: 99%

Strain effects on point defects and chain-oxygen order-disorder transition in 123 cuprate compounds

Welch

Wong‐Ng³

2004

Phys. Rev. B

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“…The derivation of h 3 (r) is provided in Walzer et al [2004a]. In that paper, we start from a self-consistent theory using the Helmholtz free energy, the Birch -Murnaghan equation of state, the free-volume Grüneisen parameter and Gilvarry's [1956] formulation of Lindemann's law. The viscosity is calculated as a function of melting temperature provided by Lindemann's law.…”

Section: Balance Equationsmentioning

confidence: 99%

Mantle convection and evolution with growing continents

Walzer

Hendel

2008

J. Geophys. Res.

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[1] We present a three-dimensional spherical shell numerical model for chemical differentiation and redistribution of incompatible elements in a convective Earth's mantle heated mostly from within by U, Th, and K and slightly from below. The evolution-model equations guarantee conservation of mass, momentum, energy, angular momentum, and four sums of the number of atoms of the pairs 238 U-206 Pb, 235 U-207 Pb, 232 Th-208 Pb, and 40 K-40 Ar. The pressure-and temperature-dependent viscosity is supplemented by a viscoplastic yield stress, s y . The lithospheric viscosity is partly imposed to mimic its increase by dehydration of oceanic lithosphere and other effects. Also, the asthenosphere is generated not only by the distribution of temperature and melting temperature, but essentially by the profiles of water solubility and water abundance. Therefore we introduced a radial viscosity profile factor describing that behavior. However, the focus of this paper is the episodic growth of continents and oceanic plateaus. As a complement, the differentiation generates the depleted MORB mantle (DMM) which predominates immediately beneath the lithosphere. Our continents are not artificially imposed on the surface of the spherical shell, but instead they evolve by the interplay between chemical differentiation and convection/mixing. No restrictions are imposed regarding number, size, form, and distribution of continents. However, oceanic plateaus that impinge upon a continent have to be united with it. This mimics the accretion of terranes. The numerical results show an episodic growth of the total mass of the continents and display a plausible time history for the laterally averaged surface heat flow, qob, and the Rayleigh number, Ra. We use our model to explore a moderate region of Ra-s y parameter space. We find Earth-like continent distributions in a central part of the Ra-s y space we explored. We identified a Ra-s y region where the calculated total continental volume is very close to the observed value; another Ra-s y region where the Urey number, Ur, is close to the accepted value; a third Ra-s y area where surface heat flow is very close to the present-day observed mean global heat flow using typical abundances of the heat-producing elements. It is remarkable that these different acceptable Ra-s y regions share a common overlap area, where Earth-like behavior is simultaneously fulfilled.Although the convective flow patterns and the chemical differentiation of oceanic plateaus are coupled, the evolution of time-dependent Rayleigh number, Ra t , is relatively well predictable and the stochastic parts of the Ra t (t) curves are small. Regarding the time distribution of juvenile growth rates of the total mass of the continents, predictions are possible only in the first epoch of the evolution, presumed that the initial conditions are given. Later on, the distribution of the continental growth episodes is increasingly stochastic. Independent of the varying individual runs, our model shows that the total mass of the presen...

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“…At the temperature at which the system starts exploring large regions of phase space, the δ function exceeds the value of 0.1 (Lindemman's criterion). 32 From Figure 8 we can see that the icosahedron of Mg + Ar 12 is the most stable cluster. Its transition temperature is about 45 K. The stability of the cluster is further examined by computing distributions of the average distances at different energies.…”

Section: Dynamic Propertiesmentioning

confidence: 99%

Potential Functions and Static and Dynamic Properties of Mg^m⁺Ar_n (m = 1, 2; n = 1−18) Clusters

Fanourgakis

Farantos

1996

J. Phys. Chem.

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Analytical potential functions have been constructed for Mg m+Ar n , m)1, 2, clusters by combining ab initio calculations with the electrostatic model of ion-induced dipole and induced dipole-induced dipole interactions. The most stable structures and dynamic properties are investigated by molecular dynamics techniques. For Mg + Ar 12 an icosahedral geometry is predicted. For Mg + Ar n clusters with n ) 7-12 two series of minima with small differences in energy were found; in one the magnesium ion stays inside the cluster (solvated) and in the other on the surface of the system. For n > 9, clusters with Mg on the surface are slightly more stable and have a distinguishable high vibrational frequency relative to those with the magnesium ion inside. We find no such trends for Mg 2+ Ar n clusters, in which the Mg cation is always solvated. The absolute minimum of Mg 2+ Ar 4 is a regular tetrahedron, and that of Mg 2+ Ar 6 , a regular octahedron. The stability of all these clusters is investigated by studying caloric curves, root mean square bond length fluctuations, radial distributions, and power spectra.

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The Lindemann and Grüneisen Laws

Abstract: fh-rj X.0«n»r>l 1 wil Li nrt-nn Lav

Cited by 402 publications

References 30 publications

Strain effects on point defects and chain-oxygen order-disorder transition in 123 cuprate compounds

Strain effects on point defects and chain-oxygen order-disorder transition in 123 cuprate compounds

Mantle convection and evolution with growing continents

Potential Functions and Static and Dynamic Properties of Mg^m⁺Ar_n (m = 1, 2; n = 1−18) Clusters

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The Lindemann and Grüneisen Laws

Abstract: fh-rj X.0«n»r>l 1 wil Li nrt-nn Lav

Cited by 402 publications

References 30 publications

Strain effects on point defects and chain-oxygen order-disorder transition in 123 cuprate compounds

Strain effects on point defects and chain-oxygen order-disorder transition in 123 cuprate compounds

Mantle convection and evolution with growing continents

Potential Functions and Static and Dynamic Properties of Mgm+Arn (m = 1, 2; n = 1−18) Clusters

Contact Info

Product

Resources

About

Potential Functions and Static and Dynamic Properties of Mg^m⁺Ar_n (m = 1, 2; n = 1−18) Clusters