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Statistical Thermodynamics: From First Principles Computations to Macroscopic Properties of...
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Statistical Thermodynamics: From First Principles Computations to Macroscopic Properties of Matter

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Thermodynamics".

Deadline for manuscript submissions: closed (20 March 2022) | Viewed by 9515

Special Issue Editor

Prof. Dr. Mauro Prencipe

E-Mail Website
Guest Editor
Department of Earth Sciences, University of Turin, 10125 Torino, Italy
Interests: quantum-mechanical simulation; equation of state; IR and Raman spectroscopy; thermodynamic; chemical bond in minerals

Special Issue Information

Dear Colleagues,

Statistical thermodynamics is the bridge from the microscopic to the macroscopic worlds. Together with its conceptual framework, it provides the tools for the computation of all the thermodynamic properties of matter in whatever state, temperature, and pressure, as averages of properties evaluated from first principles at the atomic and molecular level, or at the scale of a unit cell of a crystal. For instance, in the last decade, statistical thermodynamics has been effectively used to predict thermodynamic properties of minerals at the thermobaric conditions of the Earth mantle, thus providing a thermodynamic basis to new ideas and models of the Earth mantle at conditions not easily accessible to experimental investigation. The focus of this Special Issue is on (i) applications to specific problems; (ii) development of models for effective computations; and (iii) their possible implementations in computer programs.

Prof. Dr. Mauro Prencipe
Guest Editor

Manuscript Submission Information

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Keywords

  • statistical thermodynamics
  • first principles computation
  • physics
  • chemistry
  • solid state physics
  • Earth sciences
  • modeling
  • algorithms and computer programs

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Published Papers (3 papers)

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Research

16 pages, 1209 KiB  
Article
Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements
by Yang Huang and Michael Widom
Entropy 2022, 24(5), 618; https://doi.org/10.3390/e24050618 - 28 Apr 2022
Cited by 7 | Viewed by 3851
Abstract
The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, [...] Read more.
The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρN. We calculate the information-theoretic entropy from the expectation value of lnρN. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye–Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures, we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti. Full article
(This article belongs to the Special Issue Statistical Thermodynamics: From First Principles Computations to Macroscopic Properties of Matter)
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19 pages, 3883 KiB  
Article
Exploration of Entropy Pair Functional Theory
by Clifton C. Sluss, Jace Pittman, Donald M. Nicholson and David J. Keffer
Entropy 2022, 24(5), 603; https://doi.org/10.3390/e24050603 - 26 Apr 2022
Cited by 2 | Viewed by 2302
Abstract
Evaluation of the entropy from molecular dynamics (MD) simulation remains an outstanding challenge. The standard approach requires thermodynamic integration across a series of simulations. Recent work Nicholson et al. demonstrated the ability to construct a functional that returns excess entropy, based on the [...] Read more.
Evaluation of the entropy from molecular dynamics (MD) simulation remains an outstanding challenge. The standard approach requires thermodynamic integration across a series of simulations. Recent work Nicholson et al. demonstrated the ability to construct a functional that returns excess entropy, based on the pair correlation function (PCF); it was capable of providing, with acceptable accuracy, the absolute excess entropy of iron simulated with a pair potential in both fluid and crystalline states. In this work, the general applicability of the Entropy Pair Functional Theory (EPFT) approach is explored by applying it to three many-body interaction potentials. These potentials are state of the art for large scale models for the three materials in this study: Fe modelled with a modified embedded atom method (MEAM) potential, Cu modelled with an MEAM and Si modelled with a Tersoff potential. We demonstrate the robust nature of EPFT in determining excess entropy for diverse systems with many-body interactions. These are steps toward a universal Entropy Pair Functional, EPF, that can be applied with confidence to determine the entropy associated with sophisticated optimized potentials and first principles simulations of liquids, crystals, engineered structures, and defects. Full article
(This article belongs to the Special Issue Statistical Thermodynamics: From First Principles Computations to Macroscopic Properties of Matter)
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9 pages, 1817 KiB  
Article
Anharmonic Effects on the Thermodynamic Properties of Quartz from First Principles Calculations
by Mara Murri and Mauro Prencipe
Entropy 2021, 23(10), 1366; https://doi.org/10.3390/e23101366 - 19 Oct 2021
Cited by 2 | Viewed by 2306
Abstract
The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been [...] Read more.
The simple chemistry and structure of quartz together with its abundance in nature and its piezoelectric properties make convenient its employment for several applications, from engineering to Earth sciences. For these purposes, the quartz equations of state, thermoelastic and thermodynamic properties have been studied since decades. Alpha quartz is stable up to 2.5 GPa at room temperature where it converts to coesite, and at ambient pressure up to 847 K where it transforms to the beta phase. In particular, the displacive phase transition at 847 K at ambient pressure is driven by intrinsic anharmonicity effects (soft-mode phase transition) and its precise mechanism is difficult to be investigated experimentally. Therefore, we studied these anharmonic effects by means of ab initio calculations in the framework of the statistical thermodynamics approach. We determined the principal thermodynamic quantities accounting for the intrinsic anharmonicity and compared them against experimental data. Our results up to 700 K show a very good agreement with experiments. The same procedures and algorithms illustrated here can also be applied to determine the thermodynamic properties of other crystalline phases possibly affected by intrinsic anharmonic effects, that could partially invalidate the standard quasi-harmonic approach. Full article
(This article belongs to the Special Issue Statistical Thermodynamics: From First Principles Computations to Macroscopic Properties of Matter)
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