### Abstract

We discuss the effect of elastic fields on the late stages of coarsening during a solid-solid phase transformation in a two-phase binary alloy. The treatment is valid for both isotropic and anisotropic media. We hypothesize that there exist regimes in which coarsening proceeds in a self-similar or scale invariant manner. We show that this hypothesis is self-consistent in the two limiting regimes in which elastic effects are either dominated by, or dominate, capillary effects; when these effects are comparable, no scaling solution exists. For nonvanishing misfits and for domain sizes smaller than a certain crossover length, we recover the classical Lifshitz-Slyozov law that the characteristic length scale l(t) of the system evolves in time as t^{ 1 3}. At intermediate values of l, there is a crossover regime in which no single power law is expected. For large values of l, elastically driven coarsening dominates, leading to a different growth law [l(t) ∼ t^{ 1 2}]. Theoretical work of others suggests that elastically driven coarsening occurs when the domains are elastically harder than the matrix. We estimate the value of l corresponding to the crossover region for the case of idotropic materials.

Original language | English (US) |
---|---|

Pages (from-to) | 1573-1580 |

Number of pages | 8 |

Journal | Acta Metallurgica Et Materialia |

Volume | 38 |

Issue number | 8 |

DOIs | |

State | Published - Aug 1990 |

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*Acta Metallurgica Et Materialia*,

*38*(8), 1573-1580. https://doi.org/10.1016/0956-7151(90)90125-Z

**Effect of elasticity on late stage coarsening.** / Leo, P. H.; Mullins, W. W.; Sekerka, R. F.; Viñals, J.

Research output: Contribution to journal › Article

*Acta Metallurgica Et Materialia*, vol. 38, no. 8, pp. 1573-1580. https://doi.org/10.1016/0956-7151(90)90125-Z

}

TY - JOUR

T1 - Effect of elasticity on late stage coarsening

AU - Leo, P. H.

AU - Mullins, W. W.

AU - Sekerka, R. F.

AU - Viñals, J.

PY - 1990/8

Y1 - 1990/8

N2 - We discuss the effect of elastic fields on the late stages of coarsening during a solid-solid phase transformation in a two-phase binary alloy. The treatment is valid for both isotropic and anisotropic media. We hypothesize that there exist regimes in which coarsening proceeds in a self-similar or scale invariant manner. We show that this hypothesis is self-consistent in the two limiting regimes in which elastic effects are either dominated by, or dominate, capillary effects; when these effects are comparable, no scaling solution exists. For nonvanishing misfits and for domain sizes smaller than a certain crossover length, we recover the classical Lifshitz-Slyozov law that the characteristic length scale l(t) of the system evolves in time as t 1 3. At intermediate values of l, there is a crossover regime in which no single power law is expected. For large values of l, elastically driven coarsening dominates, leading to a different growth law [l(t) ∼ t 1 2]. Theoretical work of others suggests that elastically driven coarsening occurs when the domains are elastically harder than the matrix. We estimate the value of l corresponding to the crossover region for the case of idotropic materials.

AB - We discuss the effect of elastic fields on the late stages of coarsening during a solid-solid phase transformation in a two-phase binary alloy. The treatment is valid for both isotropic and anisotropic media. We hypothesize that there exist regimes in which coarsening proceeds in a self-similar or scale invariant manner. We show that this hypothesis is self-consistent in the two limiting regimes in which elastic effects are either dominated by, or dominate, capillary effects; when these effects are comparable, no scaling solution exists. For nonvanishing misfits and for domain sizes smaller than a certain crossover length, we recover the classical Lifshitz-Slyozov law that the characteristic length scale l(t) of the system evolves in time as t 1 3. At intermediate values of l, there is a crossover regime in which no single power law is expected. For large values of l, elastically driven coarsening dominates, leading to a different growth law [l(t) ∼ t 1 2]. Theoretical work of others suggests that elastically driven coarsening occurs when the domains are elastically harder than the matrix. We estimate the value of l corresponding to the crossover region for the case of idotropic materials.

UR - http://www.scopus.com/inward/record.url?scp=0025474518&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025474518&partnerID=8YFLogxK

U2 - 10.1016/0956-7151(90)90125-Z

DO - 10.1016/0956-7151(90)90125-Z

M3 - Article

AN - SCOPUS:0025474518

VL - 38

SP - 1573

EP - 1580

JO - Acta Materialia

JF - Acta Materialia

SN - 1359-6454

IS - 8

ER -