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Physical Review B - Condensed Matter and Materials Physics
Volumn 59, Issue 13, 1999, Pages 8646-8659
Large-scale simulations of phase separation of elastically coherent binary alloy systems
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EID: 10844232219     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.8646     Document Type: Article
Times cited : (56)
References (72)
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    • It may be argued that contrasting these quenches with a model B system does not represent a fair comparison. Model B is strictly a symmetric system, so that the precipitates that form always represent the minority phase. However, the elastic fields break this symmetry allowing for the formation of precipitates of the majority phase. Strictly speaking, a comparison between the systems with elastic fields and an asymmetric model B that allows for the formation of majority phase precipitates is needed. Presumably such an asymmetric model B would also display an enhanced rate of coarsening and display some coalesence phenomena. However, we know of no such model that allows for an easy comparison
    • It may be argued that contrasting these quenches with a model B system does not represent a fair comparison. Model B is strictly a symmetric system, so that the precipitates that form always represent the minority phase. However, the elastic fields break this symmetry allowing for the formation of precipitates of the majority phase. Strictly speaking, a comparison between the systems with elastic fields and an asymmetric model B that allows for the formation of majority phase precipitates is needed. Presumably such an asymmetric model B would also display an enhanced rate of coarsening and display some coalesence phenomena. However, we know of no such model that allows for an easy comparison.
  • 67
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    • Note that our calculations make use of the circularly averaged structure factors and correlation functions, despite the fact that individual domains may be highly anisotropic. This has the following reasons. First, for cases with, elastic parameters, the domains obtained are cuboidal with approximately equal aspect ratios (see, for example, Fig. 22). An examination of the data shows that it is therefore appropriate to use the circularly averaged functions, although one can perhaps expect finer details to emerge if a very much large set of runs was averaged. We do not expect these to change our results in any important way. Second, the domains are most anisotropic for systems with, elastic parameters. However, it is still appropriate to use the circularly averaged functions because these measure the properties of the entire configuration as opposed to those of an individual domain. For example, consider a system with axial symmetry. In this case, there will be an approximately equal number of domains pointing in the axial directions, which will give rise to peaks distributed within a circle (sphere in 3D). Note that this situation changes if a majority of the domains point in the same direction, as exemplified by a phase separating fluid under shear. In this case, a highly anisotropic and ellipsoidal structure factor is obtained
    • Note that our calculations make use of the circularly averaged structure factors and correlation functions, despite the fact that individual domains may be highly anisotropic. This has the following reasons. First, for cases with inhomogeneous elastic parameters, the domains obtained are cuboidal with approximately equal aspect ratios (see, for example, Fig. 22). An examination of the data shows that it is therefore appropriate to use the circularly averaged functions, although one can perhaps expect finer details to emerge if a very much large set of runs was averaged. We do not expect these to change our results in any important way. Second, the domains are most anisotropic for systems with homogeneous elastic parameters. However, it is still appropriate to use the circularly averaged functions because these measure the properties of the entire configuration as opposed to those of an individual domain. For example, consider a system with axial symmetry. In this case, there will be an approximately equal number of domains pointing in the axial directions, which will give rise to peaks distributed within a circle (sphere in 3D). Note that this situation changes if a majority of the domains point in the same direction, as exemplified by a phase separating fluid under shear. In this case, a highly anisotropic and ellipsoidal structure factor is obtained.

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