Tension and Stiffness of the Hard Sphere Crystal-Fluid Interface

Abstract

A combination of fundamental measure density functional theory and Monte Carlo computer simulation is used to determine the orientation-resolved interfacial tension and stiffness for the equilibrium hard-sphere crystal-fluid interface. Microscopic density functional theory is in quantitative agreement with simulations and predicts a tension of 0.66 kBT /σ 2 with a small anisotropy of about 0.025 kBT and stiffnesses with e.g. 0.53 kBT /σ 2 for the (001) orientation and 1.03 kBT /σ 2 for the (111) orientation. Here kBT is denoting the thermal energy and σ the hard sphere diameter. We compare our results with existing experimental findings.PACS numbers: 68.08. De, 05.20.Jj, 82.70.Dd Solidification and melting processes involve crystal-fluid interfaces that separate the disordered from the ordered phase. Understanding the properties of such interfaces on a microscopic scale is pivotal to control and optimize crystal nucleation and the emerging microstructure of the material. Important applications include the fabrication of defect-free metallic alloys [1] and of photonic [2], phononic [3] and protein [4] crystals. In equilibrium, i.e. between a coexisting crystal and fluid phase, creating a crystal-fluid interface results in a free energy penalty per area that is called interfacial tension. Unlike the liquid-gas or fluid-fluid interface, the structure of the solid-fluid interface depends on its orientation [5]. This anisotropy is associated with a difference between the interfacial tension and the interfacial stiffness of a crystalline surface.Predicting crystal-fluid interfacial tensions by a molecular theory is a very challenging task. Classical density functional theory of freezing provides a unifying framework to describe the solid and liquid on the same footing and is therefore in principle a promising tool. In this respect, the simple athermal hard sphere system which exhibits a freezing transition from a fluid into a face-centered-cubic (fcc) crystal, is an important reference system. The accuracy of previous density functional calculations of the hard sphere solid-fluid interface [6-9], however, was hampered by the lack of knowledge of a reliable functional and severe restrictions in the parametrization of the trial density profile.In this letter, interfacial tensions and stiffnesses of the equilibrium hard sphere crystal-fluid interface are predicted using fundamental measure density functional theory [10] which has been shown to predict accurate bulk freezing data [11]. The interfacial tension and stiffness for five different orientations are obtained, namely along the (001), (011), (111), (012) and (112) orientations (see Fig. 1). A small orientational anisotropy for the tensions is found and the average tension is about 0.66 k B T /σ 2 with k B T denoting the thermal energy and σ the hard sphere diameter. For the stiffnesses the data are spread in a much wider range between 0.28 k B T /σ 2 for the (011) orientation with lateral direction [100] and 1.03 k B T /σ 2 for the (111) orientation. We have als...

Bcc crystal-fluid interfacial free energy in Yukawa systems

“…8 This drastic reduction of the interfacial free energy agrees with the Spaepen-Meyer theory, 47,48 and is consistent with the Alexander-McTague theory, 49 which predicts that the bcc-crystal is structurally closer to the liquid than the fcc-crystal.…”

“…Recently, simulation schemes have been developed to access the interfacial free energy by studying the capillary wave fluctuations. [2][3][4][5][6][7][8] Even more challenging is a molecular theory predicting interfacial free energies. A necessary requirement to such theory is that it has to describe the crystal and the fluid phase in a unifying way.…”

“…There have been many approximation schemes and studies for the hard-sphere system including the interfacial free energy of the hard sphere facecentered-cubic (fcc) crystal-fluid interface. 8,[13][14][15][16] However, beyond hard-sphere perturbation theory, 14,[17][18][19][20] systems with a softer pair interaction V (r) are much less studied. [21][22][23] In the latter case, the Ramakrishnan-Yussouff perturbative density functional theory 24 or some mean-field variants 23 can be applied in principle, which yield acceptable results for freezing of Yukawa systems, 23 for more sophisticated functionals (see Ref.…”

Determination of the Origin and Magnitude of Logarithmic Finite-Size Effects on Interfacial Tension: Role of Interfacial Fluctuations and Domain Breathing

“…[15,[23][24][25][26][27][28][29][30][31][32][33][34][35]). However, often different variants of these methods yield estimates disagreeing with each other far beyond statistical errors, e.g., for the hard sphere liquid-solid interface tension discrepancies of about 10% occur [33][34][35][36].Finite size effects are a possible source of systematic errors, but often are disregarded due to a lack of a generally accepted theoretical framework. But finite size effects on interfacial tensions are expected [37][38][39][40][41][42][43] and also of physical interest for capillary condensation, nanoparticles, etc.…”

“…[15,[23][24][25][26][27][28][29][30][31][32][33][34][35]). However, often different variants of these methods yield estimates disagreeing with each other far beyond statistical errors, e.g., for the hard sphere liquid-solid interface tension discrepancies of about 10% occur [33][34][35][36].…”