Information Capacity of Condensed Systems

Bal’makov, M. D.

doi:10.1016/s0080-8784(04)80003-6

Cited by 4 publications

(10 citation statements)

References 15 publications

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“…Similarly, from expressions (14), (17), and = kT 2 ∂lnZ i /∂T (i = l, s) [7], at the melting temperature T m , we find…”

Section: The Spectrum Corresponding To the Maximum Heat Capacitymentioning

confidence: 66%

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The thermodynamic aspect of melting and softening of nanoparticles

Bal’makov

2008

Glass Phys Chem

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The specific features of the energy spectrum of stationary quantum states responsible for the melting and softening of a polyatomic system are investigated. It follows from the first principles of the quantum mechanics and statistical physics that the melting temperature of small nanoparticles can exceed the melting temperature of a macroscopic sample of the same chemical composition. The dependence of the temperature range of the transition of the polyatomic system to a microscopically labile state on the number of atoms is determined.

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“…Similarly, from expressions (14), (17), and = kT 2 ∂lnZ i /∂T (i = l, s) [7], at the melting temperature T m , we find…”

Section: The Spectrum Corresponding To the Maximum Heat Capacitymentioning

confidence: 66%

“…According to [14], we can write the following asymptotic relationship: (21) where α n is the positive parameter dependent on the chemical composition n of the system under consideration. 5 The numerical values of α n in relationship (21) usually differ from ln2 ≈ 0.69 by smaller than one order of magnitude.…”

Section: On the Diversity Of Structuresmentioning

confidence: 99%

The thermodynamic aspect of melting and softening of nanoparticles

Bal’makov

2008

Glass Phys Chem

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“…In the case where α n ( ) 0, we have s 0. In other words, the decrease in the parameter α n ( ), according to relationship (5), leads to a decrease in the entropy of melting s and, consequently, to an increase in the melting temperature T m in accordance with relationship (6).…”

mentioning

confidence: 76%

“…As a rule, the number J of different minima (equilibrium configurations) increases with an increase in the number of atoms M . According to [6], we can write the following asymptotic relationship: (1) Here, α n is the positive parameter dependent on the chemical composition n of the system under consideration. 1 The numerical values of α n in relationship (1) usually differ from ln2 ≈ 0.69 by smaller than one order of magnitude.…”

mentioning

confidence: 99%

“…Finally, according to relationships (3) and (5), the melting temperature T m can be described by one more expression (6) which coincides with the known expression that relates the latent heat q , the entropy s , and the temperature T m of the transition [7]. Note that, in the case of the macroscopic system, the heat of melting q and the entropy of melting s per atom in relationship (6) are independent of the number M of atoms forming the macroscopic system, whereas the opposite situation is observed for the nanoparticle.…”

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confidence: 99%

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On the melting temperature of nanoparticles

Bal’makov

2008

Glass Phys Chem

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110According to the results obtained Eroshenko [1], clusters consisting of 17 gallium atoms do not undergo melting even at a temperature of 800 K but clusters consisting of 40 atoms are melted at 550 K, whereas the melting temperature of macroscopic gallium samples is only 303 K. This experimental fact has so far defied an appropriate theoretical explanation, because it contradicts the conventional viewpoint based on the commonly accepted interpretation of surface phenomena. According to this viewpoint, microscopic particles of matter, on the contrary, should undergo melting at a lower temperature as compared to macroscopic samples of the same chemical composition. This contradiction stems from the fact that the specificity of the nanostate of matter is determined not only by the surface. In particular, Uvarov and Boldyrev [2, p. 308] noted that there exist strong size effects in the case where the observed radical changes in properties of materials cannot be attributed to usual surface phenomena and that, most frequently, these effects are observed for very small particles whose size does not exceed 10 nm. Even with knowledge of the wave functions, the boundary surface cannot be adequately described on the microscopic level. The boundary surface for nanoparticles consisting of 17 atoms is as conventional as for a hydrogen atom. Note that the complete quantummechanical description of the hydrogen atom ignores the notion of the surface at all.Moreover, as the size of the system decreases, the interpretation of a number of physical quantities, such as the melting temperature T m , the heat of melting Q m , and the entropy of melting S m [3,4], should be refined. Indeed, one molecule, for example, the hydrogen molecule, cannot melt, because its dissociation occurs with an increase in the temperature. Consequently, at some stage of the dispersion of the macroscopic system, the notion of the melting temperature T m losses its physical meaning.The melting is accompanied by structural transformations. The point is that, according to Berry and Smirnov [4, p. 367], the nature of the phase transition is associated with the configurational excitation, which involves a sequence of transitions from one minima of the adiabatic electronic term to other minima. Each of these minima corresponds to one of the equilibrium configurations.There exist a large number of physically nonequivalent minima in the adiabatic electronic term [5]. For example, the adiabatic electronic term approximated with the use of the Lennard-Jones potential for a cluster consisting of 13 atoms involves 1478 minima [4]. As a rule, the number J of different minima (equilibrium configurations) increases with an increase in the number of atoms M . According to [6], we can write the following asymptotic relationship:(1)Here, α n is the positive parameter dependent on the chemical composition n of the system under consideration. 1 The numerical values of α n in relationship (1) usually differ from ln2 ≈ 0.69 by smaller than one order of magnitude. The estimatio...

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