Thermodynamics of volume-collapse transitions in cerium and related compounds

Bustingorry, Sebastián; Jagla, E. A.; Lorenzana, J.

doi:10.1016/j.actamat.2005.07.027

Cited by 24 publications

(33 citation statements)

References 33 publications

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“…This effect becomes dramatic in solid-solid phase transitions, where nucleation may be totally suppressed, even with a nonzero thermodynamic drive δG, whenever δG(T ) < E elastic = ǫ 0 G ∞ [8,9,10,11]. In liquids, however, the stress is always relaxed for long enough times, and eq.…”

mentioning

confidence: 99%

“…The central idea is that on time scales shorter than the structural relaxation time, deeply supercooled liquids exhibit a solid-like response to strains [5]. In particular, the inclusion of a crystalline nucleus in the liquid matrix produces a strain [6,7], and thus a longrange elastic response [8,9,10,11]. Therefore, the thermodynamic drive for crystal nucleation gets depressed by an elastic contribution, which depends on the ratio between the relaxation time τ R and the time scale τ N over which nucleation occurs.…”

mentioning

confidence: 99%

“…When the nucleus of the stable phase forms in an elastic background, there is an extra energetic price that has to be paid [8,9,10,11]. Because of the long-range nature of the elastic strains, the elastic price is proportional to the nucleus volume, and thus it corrects the bare thermodynamic drive δG,…”

mentioning

confidence: 99%

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Viscoelasticity and Metastability Limit in Supercooled Liquids

Cavagna¹,

Attanasi

Lorenzana³

2005

Phys. Rev. Lett.

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A supercooled liquid is said to have a kinetic spinodal if a temperature Tsp exists below which the liquid relaxation time exceeds the crystal nucleation time. We revisit classical nucleation theory taking into account the viscoelastic response of the liquid to the formation of crystal nuclei and find that the kinetic spinodal is strongly influenced by elastic effects. We introduce a dimensionless parameter λ, which is essentially the ratio between the infinite frequency shear modulus and the enthalpy of fusion of the crystal. In systems where λ is larger than a critical value λc the metastability limit is totally suppressed, independently of the surface tension. On the other hand, if λ < λc a kinetic spinodal is present and the time needed to experimentally observe it scales as exp [ω/(λc−λ) 2 ], where ω is roughly the ratio between surface tension and enthalpy of fusion.When a liquid is cooled below its freezing point without forming a crystal, it enters a metastable equilibrium phase known as supercooled [1]. A supercooled liquid is squeezed in an uncomfortable time region: if we are too fast in measuring its properties, the system cannot thermalize and an off-equilibrium glass is formed; on the other hand, if we are too slow, the system has the time to nucleate the solid, and we obtain an off-equilibrium polycrystal, and, eventually, a thermodynamically stable crystal [2,3]. What is the maximum degree of supercooling a metastable equilibrium liquid can reach ?The tricky point about this question is that it mixes aspects of the experimental protocol, with intrinsic properties of the system. If we stick to cooling the system linearly in time, there is a minimum cooling velocity below which the system is bound to crystallize [3]. This velocity is inversely proportional to the minimum nucleation time as a function of temperature [4]: we cannot cool slower than this minimum cooling rate, otherwise crystallization occurs. On the other hand, as we cool, the relaxation time increases steeply, and therefore the system necessarily leaves the supercooled phase, and becomes a glass, at the temperature where the relaxation time becomes too large for this minimum cooling rate.To penetrate deeper in the supercooled region, one can use an ad hoc nonlinear cooling protocol: cool fast close to the temperature where crystallization is a concern [4], and where relaxation time is still small; and slow down at lower temperatures, to cope with the increasing relaxation time, once the nucleation time starts raising again. Therefore, we may think that the unique limitation to the extent of supercooling is given by our capability of cooling slow and fast enough a sample, and that in principle there is no bound to supercooling a metastable equilibrium liquid.In fact, our experimental capability is not the only limitation to supercooling a system. If at a certain temperature the relaxation time of the liquid τ R exceeds the nucleation time of the crystal τ N , no equilibrium measurements can be performed on the liquid sample and the ...

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Viscoelasticity and Metastability Limit in Supercooled Liquids

Cavagna¹,

Attanasi

Lorenzana³

2005

Phys. Rev. Lett.

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“…Nucleation with volume mismatch in an elastic solid has been studied in different contexts [7,8]. In the case of an isotropic systems the elastic cost for nucleation (or for any inhomogeneous configuration) takes a simple form [8]:…”

Section: Introducing Elasticity In the Modelmentioning

confidence: 99%

“…In the case of an isotropic systems the elastic cost for nucleation (or for any inhomogeneous configuration) takes a simple form [8]:…”

Section: Introducing Elasticity In the Modelmentioning

confidence: 99%

Elasticity and metastability limit in supercooled liquids: a lattice model

Attanasi

Cavagna

Lorenzana³

2007

Philosophical Magazine

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We present Monte Carlo simulations on a lattice system that displays a first order phase transition between a disordered phase (liquid) and an ordered phase (crystal). The model is augmented by an interaction that simulates the effect of elasticity in continuum models.The temperature range of stability of the liquid phase is strongly increased in the presence of the elastic interaction. We discuss the consequences of this result for the existence of a kinetic spinodal in real systems.

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Many Faces of Entropy or Bayesian Statistical Mechanics

Starikov

2010

ChemPhysChem

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Some 80-90 years ago, George A. Linhart, unlike A. Einstein, P. Debye, M. Planck and W. Nernst, managed to derive a very simple, but ultimately general mathematical formula for heat capacity versus temperature from fundamental thermodynamic principles, using what we would nowadays dub a "Bayesian approach to probability". Moreover, he successfully applied his result to fit the experimental data for diverse substances in their solid state over a rather broad temperature range. Nevertheless, Linhart's work was undeservedly forgotten, although it represents a valid and fresh standpoint on thermodynamics and statistical physics, which may have a significant implication for academic and applied science.

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Thermodynamics of volume-collapse transitions in cerium and related compounds

Cited by 24 publications

References 33 publications

Viscoelasticity and Metastability Limit in Supercooled Liquids

Viscoelasticity and Metastability Limit in Supercooled Liquids

Elasticity and metastability limit in supercooled liquids: a lattice model

Many Faces of Entropy or Bayesian Statistical Mechanics

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