TY - JOUR

T1 - Non-equilibrium growth of a binary alloy

AU - Fowler, A. C.

N1 - Publisher Copyright:
© 2022 The Author(s). Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications.

PY - 2022/6/1

Y1 - 2022/6/1

N2 - We present an interpretation of the phase diagram for a binary alloy from the point of view of reaction dynamics. We consider a model system in which the two-component liquid phase is an ideal solution, but the solid phase can be non-ideal, with its non-ideality increasing with reducing temperature. We show how a 'batch' model for the evolution of the two-component solid-liquid system, in which the interfacial growth rates are proportional to free energy differences, leads to a set of four differential equations, whose equilibria correspond to the familiar solidus and liquidus curves. In addition, we explain how the transitions between them depend on the bifurcation structure of the solutions. We show that locally stable mixed-phase solutions can exist below the eutectic temperature, thus providing an alternative explanation for the observation of super-cooled liquids, and we also explain why complete solidification 'normally' occurs below the eutectic temperature, despite the fact that this temperature has no intrinsic dynamic significance, being simply a value at which two completely different equilibrium states happen to share a common liquid concentration.

AB - We present an interpretation of the phase diagram for a binary alloy from the point of view of reaction dynamics. We consider a model system in which the two-component liquid phase is an ideal solution, but the solid phase can be non-ideal, with its non-ideality increasing with reducing temperature. We show how a 'batch' model for the evolution of the two-component solid-liquid system, in which the interfacial growth rates are proportional to free energy differences, leads to a set of four differential equations, whose equilibria correspond to the familiar solidus and liquidus curves. In addition, we explain how the transitions between them depend on the bifurcation structure of the solutions. We show that locally stable mixed-phase solutions can exist below the eutectic temperature, thus providing an alternative explanation for the observation of super-cooled liquids, and we also explain why complete solidification 'normally' occurs below the eutectic temperature, despite the fact that this temperature has no intrinsic dynamic significance, being simply a value at which two completely different equilibrium states happen to share a common liquid concentration.

KW - binary alloy

KW - non-equilibrium growth

KW - phase diagram

UR - http://www.scopus.com/inward/record.url?scp=85136277007&partnerID=8YFLogxK

U2 - 10.1093/imamat/hxac009

DO - 10.1093/imamat/hxac009

M3 - Article

AN - SCOPUS:85136277007

SN - 0272-4960

VL - 87

SP - 354

EP - 379

JO - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

JF - IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

IS - 3

ER -