A geometrical model of the pre-melting properties

Alvarado, Fray De Landa Castillo; Puente, G. Contreras; Ławrynowicz, Julian; Wojtczak, L.; Rutkowski, Jerzy H.

doi:10.1063/1.51120

Cited by 1 publication

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“…This idea, introduced by analogy with the considerations reported by Ruppeiner [38] in order to describe the thermodynamical curvature in terms of the pseudoriemannian geometry, was preliminarily applied to the model of the surface melting description [36]. In the present paper, we outline a self-consistent approach determining the surface energy characteristics.…”

Section: Geometrical Model Of the Surface Melting Effectmentioning

confidence: 92%

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Basic properties and applications of graded fractal bundles related to Clifford structures: An introduction

2008

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The idea of fractal modeling of crystals dates back to Bethe [1], who observed its convenience when coming to first, second, and third nearest neighbors of an atom. Taking into account that it is a neighbor of two or more other atoms, even in the case of one layer with a lattice formed by squares, one naturally comes to the notion of cluster [2,3]. It is then natural to cut the plane of the lattice correspondingly to the cluster involved and construct a Riemann surface or a Bethe lattice-a fractal set of the branch type [4,5]. The construction is parallel to that related to the holomorphic function f (z) = exp z 2 in C (Fig. 1). The example already shows the importance of the corresponding group Γ of cover symmetry transformations (Decktransformationengruppe), inoculation (of the branch corresponding to no. 1 on the branch corresponding to no. 4), and gradation related to the points , •, , and •.The next important step was done by Kikuchi [6], who-within his theory of cooperative phenomenadeveloped a method of approximation for order-disorder phenomena.In this context, Sukiennicki, Wojtczak, Zasada, and Castillo Alvarado [7] investigated an infinite thin film of an AB 3 alloy. As examples we may take Ni 3 Fe or Cu 3 Au. They assumed the (111) orientation of the alloy. Let z(j) denote the concentration of A-atoms in the layer j = 0, 1, . . . , where j = 0 corresponds to the surface. Then the concentration of B-atoms in that layer is 1 − z(j). If U is the energy of interaction of the system, T is the absolute temperature, and g is the number of possible configurations, then the entropy S and the free energy F of the system are given byrespectively, where k is the Boltzmann constant, and the conditions for thermodynamic equilibrium at a given temperature T are ∂ ∂τ F τ =τ (j) = 0, ∂ ∂z F z=z(j) = 0 for each j, λ = const. Thus, 1 T ∂ ∂τ U τ =τ (j) = ∂ ∂z S τ =τ (j).

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Section: Geometrical Model Of the Surface Melting Effectmentioning

confidence: 92%

“…A good example of physical application of Theorem 2 is provided by the geometrical model of the surface melting effect [8,[34][35][36] related to formulas (13).…”

Section: Geometrical Model Of the Surface Melting Effectmentioning

confidence: 99%