STRESSES AND ELASTIC CONSTANTS OF CRYSTALLINE SODIUM, FROM MOLECULAR DYNAMICS.

Persistent Link:
http://hdl.handle.net/10150/187840
Title:
STRESSES AND ELASTIC CONSTANTS OF CRYSTALLINE SODIUM, FROM MOLECULAR DYNAMICS.
Author:
SCHIFERL, SHEILA KLEIN.
Issue Date:
1984
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
The stresses and the elastic constants of bcc sodium are calculated by molecular dynamics (MD) for temperatures to T = 340 K. The total adiabatic potential of a system of sodium atoms is represented by a pseudopotential model. The resulting expression has two terms: a large, strictly volume-dependent potential, plus a sum over ion pairs of a small, volume-dependent two-body potential. The stresses and the elastic constants are given as strain derivatives of the Helmholtz free energy. The resulting expressions involve canonical ensemble averages (and fluctuation averages) of the position and volume derivatives of the potential. An ensemble correction relates the results to MD equilibrium averages. Evaluation of the potential and its derivatives requires the calculation of integrals with infinite upper limits of integration, and integrand singularities. Methods for calculating these integrals and estimating the effects of integration errors are developed. A method is given for choosing initial conditions that relax quickly to a desired equilibrium state. Statistical methods developed earlier for MD data are extended to evaluate uncertainties in fluctuation averages, and to test for symmetry. The fluctuation averages make a large contribution to the elastic constants, and the uncertainties in these averages are the dominant uncertainties in the elastic constants. The strictly volume-dependent terms are very large. The ensemble correction is small but significant at higher temperatures. Surprisingly, the volume derivatives of the two-body potential make large contributions to the stresses and the elastic constants. The effects of finite potential range and finite system size are discussed, as well as the effects of quantum corrections and electronic excitations. The agreement of theory and experiment is very good for the magnitudes of C₁₁ and C₁₂. The magnitude of C₄₄ is consistently small by ∼9 kbar for finite temperatures. This discrepancy is most likely due to the neglect of three-body contributions to the potential. The agreement of theory and experiment is excellent for the temperature dependences of all three elastic constants. This result illustrates a definite advantage of MD compared to lattice dynamics for conditions where classical statistics are valid. MD methods involve direct calculations of anharmonic effects; no perturbation treatment is necessary.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Metals -- Thermomechanical properties.; Molecular dynamics.; Sodium.; Physics -- Simulation methods.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Physics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Wangsness, Roald K.

Full metadata record

DC FieldValue Language
dc.language.isoenen_US
dc.titleSTRESSES AND ELASTIC CONSTANTS OF CRYSTALLINE SODIUM, FROM MOLECULAR DYNAMICS.en_US
dc.creatorSCHIFERL, SHEILA KLEIN.en_US
dc.contributor.authorSCHIFERL, SHEILA KLEIN.en_US
dc.date.issued1984en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractThe stresses and the elastic constants of bcc sodium are calculated by molecular dynamics (MD) for temperatures to T = 340 K. The total adiabatic potential of a system of sodium atoms is represented by a pseudopotential model. The resulting expression has two terms: a large, strictly volume-dependent potential, plus a sum over ion pairs of a small, volume-dependent two-body potential. The stresses and the elastic constants are given as strain derivatives of the Helmholtz free energy. The resulting expressions involve canonical ensemble averages (and fluctuation averages) of the position and volume derivatives of the potential. An ensemble correction relates the results to MD equilibrium averages. Evaluation of the potential and its derivatives requires the calculation of integrals with infinite upper limits of integration, and integrand singularities. Methods for calculating these integrals and estimating the effects of integration errors are developed. A method is given for choosing initial conditions that relax quickly to a desired equilibrium state. Statistical methods developed earlier for MD data are extended to evaluate uncertainties in fluctuation averages, and to test for symmetry. The fluctuation averages make a large contribution to the elastic constants, and the uncertainties in these averages are the dominant uncertainties in the elastic constants. The strictly volume-dependent terms are very large. The ensemble correction is small but significant at higher temperatures. Surprisingly, the volume derivatives of the two-body potential make large contributions to the stresses and the elastic constants. The effects of finite potential range and finite system size are discussed, as well as the effects of quantum corrections and electronic excitations. The agreement of theory and experiment is very good for the magnitudes of C₁₁ and C₁₂. The magnitude of C₄₄ is consistently small by ∼9 kbar for finite temperatures. This discrepancy is most likely due to the neglect of three-body contributions to the potential. The agreement of theory and experiment is excellent for the temperature dependences of all three elastic constants. This result illustrates a definite advantage of MD compared to lattice dynamics for conditions where classical statistics are valid. MD methods involve direct calculations of anharmonic effects; no perturbation treatment is necessary.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectMetals -- Thermomechanical properties.en_US
dc.subjectMolecular dynamics.en_US
dc.subjectSodium.en_US
dc.subjectPhysics -- Simulation methods.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplinePhysicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorWangsness, Roald K.en_US
dc.identifier.proquest8504132en_US
dc.identifier.oclc693403924en_US
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