On the elastic mismatch in the order-disorder transformation and solid state amorphization of intermetallic compounds-I. Estimation of the elastic mismatch energy during order-disorder transition

D. Beke, P. I. Loeff, H. Bakker

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Abstract

Using a method similar to the thermodynamic theory of almost completely ordered alloys an expression for the elastic mismatch energy of an ordered alloy as a function of the long-range order parameter, η, is derived from the continuum elastic theory. It is shown that, similarly to the chemical ordering energy in Bragg-Williams approximation, this has a simple (1 - η2)-type dependence. It is illustrated by detailed calculations that the relation obtained can also be derived requiring that the slope of the elastic mismatch energy at η = 0 should be equal to zero. Is is also shown that the expression proposed for the elastic mismatch energy of a (disordered) solid solution in the Miedema-model contains the interactions between the image elastic fields as well and can be considered to be on the same level of approximation as our result. The maximum elastic energy which can be stored during a disordering process is compared to the elastic mismatch energy of the solid solution (at the same atomic fraction). It is concluded that the differences between the above values are comparable to the differences obtained by using uncorrected volumes for the atoms and holes or using corrected values of them according to the Miedema-model.

Original languageEnglish
Pages (from-to)1259-1266
Number of pages8
JournalActa Metallurgica et Materialia
Volume39
Issue number6
DOIs
Publication statusPublished - 1991

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Order disorder transitions
Amorphization
Intermetallics
Solid solutions
Thermodynamics
Atoms

ASJC Scopus subject areas

  • Engineering(all)

Cite this

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title = "On the elastic mismatch in the order-disorder transformation and solid state amorphization of intermetallic compounds-I. Estimation of the elastic mismatch energy during order-disorder transition",
abstract = "Using a method similar to the thermodynamic theory of almost completely ordered alloys an expression for the elastic mismatch energy of an ordered alloy as a function of the long-range order parameter, η, is derived from the continuum elastic theory. It is shown that, similarly to the chemical ordering energy in Bragg-Williams approximation, this has a simple (1 - η2)-type dependence. It is illustrated by detailed calculations that the relation obtained can also be derived requiring that the slope of the elastic mismatch energy at η = 0 should be equal to zero. Is is also shown that the expression proposed for the elastic mismatch energy of a (disordered) solid solution in the Miedema-model contains the interactions between the image elastic fields as well and can be considered to be on the same level of approximation as our result. The maximum elastic energy which can be stored during a disordering process is compared to the elastic mismatch energy of the solid solution (at the same atomic fraction). It is concluded that the differences between the above values are comparable to the differences obtained by using uncorrected volumes for the atoms and holes or using corrected values of them according to the Miedema-model.",
author = "D. Beke and Loeff, {P. I.} and H. Bakker",
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T1 - On the elastic mismatch in the order-disorder transformation and solid state amorphization of intermetallic compounds-I. Estimation of the elastic mismatch energy during order-disorder transition

AU - Beke, D.

AU - Loeff, P. I.

AU - Bakker, H.

PY - 1991

Y1 - 1991

N2 - Using a method similar to the thermodynamic theory of almost completely ordered alloys an expression for the elastic mismatch energy of an ordered alloy as a function of the long-range order parameter, η, is derived from the continuum elastic theory. It is shown that, similarly to the chemical ordering energy in Bragg-Williams approximation, this has a simple (1 - η2)-type dependence. It is illustrated by detailed calculations that the relation obtained can also be derived requiring that the slope of the elastic mismatch energy at η = 0 should be equal to zero. Is is also shown that the expression proposed for the elastic mismatch energy of a (disordered) solid solution in the Miedema-model contains the interactions between the image elastic fields as well and can be considered to be on the same level of approximation as our result. The maximum elastic energy which can be stored during a disordering process is compared to the elastic mismatch energy of the solid solution (at the same atomic fraction). It is concluded that the differences between the above values are comparable to the differences obtained by using uncorrected volumes for the atoms and holes or using corrected values of them according to the Miedema-model.

AB - Using a method similar to the thermodynamic theory of almost completely ordered alloys an expression for the elastic mismatch energy of an ordered alloy as a function of the long-range order parameter, η, is derived from the continuum elastic theory. It is shown that, similarly to the chemical ordering energy in Bragg-Williams approximation, this has a simple (1 - η2)-type dependence. It is illustrated by detailed calculations that the relation obtained can also be derived requiring that the slope of the elastic mismatch energy at η = 0 should be equal to zero. Is is also shown that the expression proposed for the elastic mismatch energy of a (disordered) solid solution in the Miedema-model contains the interactions between the image elastic fields as well and can be considered to be on the same level of approximation as our result. The maximum elastic energy which can be stored during a disordering process is compared to the elastic mismatch energy of the solid solution (at the same atomic fraction). It is concluded that the differences between the above values are comparable to the differences obtained by using uncorrected volumes for the atoms and holes or using corrected values of them according to the Miedema-model.

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