The thermodynamics of melting of simple substances

Стишов, С. М.

doi:10.1070/pu1975v017n05abeh004361

Cited by 161 publications

(83 citation statements)

References 1 publication

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“…There are several theoretical and experimental works pointing in these directions. [68][69][70][71][72][73] For instance, the reduced-unit static structure factor of liquid iron measured by x-ray scattering is invariant along the melting curve for pressures up to 58 GPa. 74 Finally, note that the Hansen-Verlet 75 criterion, according to which melting takes place when the liquid structure factor peak is 2.85, due to the invariance of the structure factor in reduced coordinates, is also consistent with the melting curve being an isomorph for strongly correlating liquids.…”

Section: A Phenomenological Melting Rulesmentioning

confidence: 99%

Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams

Gnan

Schrøder

Pedersen

et al. 2009

The Journal of Chemical Physics

339

847

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This paper is the fourth in a series devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids where virial and potential energy correlate better than 90% in their thermal equilibrium fluctuations in the NVT ensemble. For such liquids we here introduce the concept of "isomorphic" curves in the phase diagram. A number of thermodynamic, static, and dynamic isomorph invariants are identified. These include the excess entropy, the isochoric specific heat, reduced-unit static and dynamic correlation functions, as well as reduced-unit transport coefficients. The dynamic invariants apply for both Newtonian and Brownian dynamics. It is shown that after a jump between isomorphic state points the system is instantaneously in thermal equilibrium; consequences of this for generic aging experiments are discussed. Selected isomorph predictions are validated by computer simulations of the Kob-Andersen binary Lennard-Jones mixture, which is a strongly correlating liquid. The final section of the paper relates the isomorph concept to phenomenological melting rules, Rosenfeld's excess entropy scaling, Young and Andersen's approximate scaling principle, and the two-order parameter maps of Debenedetti and co-workers. This section also shows how the existence of isomorphs implies an "isomorph filter" for theories for the non-Arrhenius temperature dependence of viscous liquids' relaxation time, and it explains isochronal superposition for strongly correlating viscous liquids.

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Section: A Phenomenological Melting Rulesmentioning

confidence: 99%

Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams

Gnan

Schrøder

Pedersen

et al. 2009

The Journal of Chemical Physics

339

847

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show abstract

“…• Different IPL systems' close similarities with respect to structure and dynamics, similarities that extend to all other Roskilde-simple liquids [47][48][49][50][51][52][53][54][55][56][57][58][59][60].…”

Section: A Quasiuniversality Of Simple Systemsmentioning

confidence: 99%

Isomorphs, hidden scale invariance, and quasiuniversality

Dyre

2013

Phys. Rev. E

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This paper first establishes an approximate scaling property of the potential-energy function of a classical liquid with good isomorphs (a Roskilde-simple liquid). This "pseudohomogeneous" property makes explicit that -and in which sense -such a system has a hidden scale invariance. The second part gives a potential-energy formulation of the quasiuniversality of monatomic Roskilde-simple liquids, which was recently rationalized in terms of the existence of a quasiuniversal single-parameter family of reduced-coordinate constant-potential-energy hypersurfaces [J. C. Dyre, Phys. Rev. E 87, 022106 (2013)]. The new formulation involves a quasiuniversal reduced-coordinate potential-energy function. A few consequences of this are discussed.

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“…Because one may consider T g -curve on P-T plane as isochronous curve where the relaxation time is constant, so one may naturally expect a scaling relation for it which is a consequence of Eq. (3) 17,18,20,64 :…”

Section: Discussion and Conclusive Remarksmentioning

confidence: 99%

“…The latter may be a good approximation of interactions that take place in liquid PC, since this potential is quite typical of molecular systems. Thermodynamic properties of the soft-sphere model can be derived using the Klein theorem [16][17][18] , but the solution for the kinetic properties will be more complicated. Taking into account a direct analogy 10,19 sometimes supported by deeper theoretical consideration 17,18,20,21 , one may write a scaling relationship for the characteristic time of the structural relaxation (also known as α-relaxation) τ in the form:…”

Section: Introductionmentioning

confidence: 99%

Dielectric spectroscopy and ultrasonic study of propylene carbonate under ultra-high pressures

Kondrin

Gromnitskaya²,

Pronin³

et al. 2012

The Journal of Chemical Physics

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We present the high pressure dielectric spectroscopy (up to 4.2 GPa) and ultrasonic study (up to 1.7 GPa) of liquid and glassy propylene carbonate (PC). Both of the methods provide complementary pictures of the glass transition in PC under pressure. No other relaxation processes except α-relaxation have been found in the studied pressure interval. The propylene carbonate liquid is a glassformer where simple relaxation and the absence of β-relaxation are registered in the record-breaking ranges of pressures and densities. The equation of state of liquid PC was extended up to 1 GPa from ultrasonic measurements of bulk modulus and is in good accordance with the previous equations developed from volumetric data. We measured the bulk and shear moduli and Poisson's ratio of glassy PC up to 1.7 GPa. Many relaxation and elastic properties of PC can be qualitatively described by the soft-sphere or Lennard-Jones model. However, for the quantitative description of entire set of the experimental data, these models are insufficient. Moreover, the Poisson coefficient value for glassy PC indicates a significant contribution of non-central forces to the intermolecular potential. The well-known correlation between Poisson's ratio and fragility index (obtained from dielectric relaxation) is confirmed for PC at ambient pressure, but it is violated with pressure increase. This indicates that different features of the potential energy landscape are responsible for the evolution of dielectric response and elasticity with pressure increase.

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The thermodynamics of melting of simple substances

Cited by 161 publications

References 1 publication

Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams

Pressure-energy correlations in liquids. IV. “Isomorphs” in liquid phase diagrams

Isomorphs, hidden scale invariance, and quasiuniversality

Dielectric spectroscopy and ultrasonic study of propylene carbonate under ultra-high pressures

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