Abstract
We have calculated the interfacial free energy for the hard-sphere system, as a function of crystal interface orientation, using a method that examines the fluctuations in the height of the interface during molecular dynamics simulations. The approach is particularly sensitive for the anisotropy of the interfacial free energy. We find an average interfacial free energy of gamma=0.56+/-0.02k(B)Tsigma(-2). This value is lower than earlier results based upon direct calculations of the free energy [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 85, 4751 (2000)]. However, both the average value and the anisotropy agree with the recent values obtained by extrapolation from direct calculations for a series of the inverse-power potentials [R. L. Davidchack and B. B. Laird, Phys. Rev. Lett. 94, 086102 (2005)].
Highlights
The crystal-melt interfacial free energy ␥ has been the focus of numerous studies[1–16] due primarily to its importance in crystal nucleation and growth.[17–22] Its anisotropyi.e., the dependence of ␥ on the orientation of the crystal with respect to the interfaceis of particular interest for pattern formation in solidification; for example, the anisotropy can determine the dendrite growth direction in directional solidification.[23]
The indirect estimates of this quantity are obtained from the nucleation rate measurements, using theapproximaterelationship between ␥ and the nucleation rate from the classical nucleation theoryor variants thereof
A comparison of values for the interfacial free energy of hard-sphere crystal-melt interface obtained by different computational techniques is shown in Table III: thermodynamic integrationRefs. 7 and 15͒, capillary fluctuationRef. 16 and this work, and homogeneous nucleationRef. 21͒
Summary
The crystal-melt interfacial free energy ␥ has been the focus of numerous studies[1–16] due primarily to its importance in crystal nucleation and growth.[17–22] Its anisotropyi.e., the dependence of ␥ on the orientation of the crystal with respect to the interfaceis of particular interest for pattern formation in solidification; for example, the anisotropy can determine the dendrite growth direction in directional solidification.[23]. Tude of the fluctuation modes, one can use Eq ͑1͒ to determine␥ from the simulations and Eq ͑2͒ to extract the anisotropic interfacial free energy This approach has been initially applied to an interatomic potential of NiRef. 8͒ and has since been extended to a number of metal and alloy systems.[9,14]. This approach is useful for finding the anisotropy, as the interfacial stiffness is much more sensitive to the small anisotropy in ␥ Both the thermodynamic integration and the capillary fluctuation approaches were used[12,13] to calculate the anisotropic free energy of a truncated Lennard-Jones potential. In a recent paper[15] using the thermodynamic integration method the average interfacial free energy was found to be 0.573͑5͒kBT−2, where the numbersin parentheses represent the estimated error in the last digitsshown This value has been obtained by extrapolation from thermodynamic integration results for a series of inverse-power potentials. We obtain a precise estimate of the anisotropy of the interfacial free energy
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