A self-consistent thermodynamic model of metallic systems. Application for the description of gold

Balcerzak, T.; Szałowski, K.; Jaščur, M.

doi:10.1063/1.4891251

Cited by 7 publications

(12 citation statements)

References 55 publications

(95 reference statements)

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“…Anderson et al, 1989;Shim et al, 2002;Tsuchiya, 2003;Yokoo et al, 2009); a remarkably good agreement between calculated and experimental values is observed even at the highest temperatures. However, Balcerzak et al (2014) report calculated specific heat values that are different by up to 3% from the experimental results, where for T near T m , the calculated specific heat is slightly higher than the experimental one. The same tendency has been observed by Yokoo et al (2009).…”

Section: Thermal Expansion and Heat Capacity Of Goldmentioning

confidence: 64%

“…In our analysis we did not include the electronic contribution to the specific heat as it is small and did not improve the fit at high temperatures. Balcerzak et al (2014) reported that the electronic contribution amounts to 0.3% and up to 3.5% of the total specific heat at 100 and 1300 K, respectively, but according to Cordoba & Brooks (1971) the electronic contribution is only 0.1% at 1330 K.…”

Section: Thermal Expansion and Heat Capacity Of Goldmentioning

confidence: 99%

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The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal

et al. 2018

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Section: Thermal Expansion and Heat Capacity Of Goldmentioning

confidence: 64%

Section: Thermal Expansion and Heat Capacity Of Goldmentioning

confidence: 99%

The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal

et al. 2018

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“…(14) and (15) can be calculated for T > T D /(2π) by the approximate method (as in Ref. [40]) using Bernoulli series. On the other hand, for the whole temperature range the integral can be calculated either by the direct numerical integration, or by the exact method as, for instance, presented in Ref.…”

Section: Lattice Subsystemmentioning

confidence: 99%

“…The vibrational energy is taken in the Debye approximation and its form can appear in two variants: for low temperatures only, and in the whole temperature range. In the low temperature limit the free energy is given by the formula [40]:…”

Section: Lattice Subsystemmentioning

confidence: 99%

Self-consistent model of a solid for the description of lattice and magnetic properties

Balcerzak

Szałowski

Jaščur

2017

Journal of Magnetism and Magnetic Materials

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In the paper a self-consistent theoretical description of the lattice and magnetic properties of a model system with magnetoelastic interaction is presented. The dependence of magnetic exchange integrals on the distance between interacting spins is assumed, which couples the magnetic and the lattice subsystem. The framework is based on summation of the Gibbs free energies for the lattice subsystem and magnetic subsystem. On the basis of minimization principle for the Gibbs energy, a set of equations of state for the system is derived. These equations of state combine the parameters describing the elastic properties (relative volume deformation) and the magnetic properties (magnetization changes).The formalism is extensively illustrated with the numerical calculations performed for a system of ferromagnetically coupled spins S =1/2 localized at the sites of simple cubic lattice. In particular, the significant influence of the magnetic subsystem on the elastic properties is demonstrated. It manifests itself in significant modification of such quantities as the relative volume deformation, thermal expansion coefficient or isothermal compressibility, in particular, in the vicinity of the magnetic phase transition. On the other hand, the influence of lattice subsystem on the magnetic one is also evident. It takes, for example, the form of dependence of the critical (Curie) temperature and magnetization itself on the external pressure, which is thoroughly investigated.V, considered at some temperature T (see for example Ref. [2]). Therefore, the magnetic equation of state involves three variables: h, m and T .In majority of cases both the subsystems of solid state (magnetic and lattice one) are described separately, with no coupling between them. In such situation, the lattice-related properties of the magnetic solid are considered as fully independent on magnetic properties, leading to another equation of state interrelating p, V and T . However, this approach neglects the magnetoelastic interactions which occur between these subsystems. The simplest source of this kind of coupling is the fact that the magnetic exchange integral between magnetic moments depends on their mutual distance, thus is a volume-dependent quantity. The magnetoelastic interactions are basis for such effects as the magnetostriction and piezomagnetism, which are important from the point of view of possible applications. They are also responsible for sensitivity of any magnetic properties (for example, the critical temperature) to external pressure.Among the literature concerning the studies of magneto-elastic interactions, many particular contributions can be mentioned. One of the subjects of intensive studies was compressible Ising model of various dimensionalities [3][4][5][6][7][8][9][10][11][12], including the diluted case [13,14] and the quantum versions [15]. The studies involved also Heisenberg model [16][17][18] or spin glasses [19] or highly interesting frustrated magnetic systems [20][21][22]. Some of the results also incorporate magnet...

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“…In the paper the total grand potential has been constructed for the dimer system, in which the magnetic, elastic and thermal vibration energies play important roles. The similar attempts at the total Gibbs energy construction, i.e., consisting in summation of various energy contributions, have been undertaken, so far, for the bulk materials [61,[63][64][65][66]. According to our knowledge, for the Hubbard dimer such method has not been presented previously.…”

Section: Discussionmentioning

confidence: 99%

Hubbard pair cluster with elastic interactions. Studies of thermal expansion, magnetostriction and electrostriction

Balcerzak

Szałowski

2019

Physica A: Statistical Mechanics and its Applications

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The pair cluster (dimer) is studied within the framework of the extended Hubbard model and the grand canonical ensemble. The elastic interatomic interactions and thermal vibrational energy of the atoms are taken into account. The total grand potential is constructed, from which the equation of state is derived. In equilibrium state, the deformation of cluster size, as well as its derivatives, are studied as a function of the temperature and the external magnetic and electric fields. In particular, the thermal expansion, magnetostriction and electrostriction effects are examined for arbitrary temperature, in a wide range of Hamiltonian parameters.

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A self-consistent thermodynamic model of metallic systems. Application for the description of gold

Abstract: A self-consistent thermodynamic model of metallic system is presented. The expression for the Gibbs energy is derived, which incorporates elastic (static) energy,

Cited by 7 publications

References 55 publications

The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal

The thermal expansion of gold: point defect concentrations and pre-melting in a face-centred cubic metal

Self-consistent model of a solid for the description of lattice and magnetic properties

Hubbard pair cluster with elastic interactions. Studies of thermal expansion, magnetostriction and electrostriction

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