Kinetic roughening and step free energy in the solid-on-solid model and on naphthalene crystals

The authors describe a method to estimate the critical supersaturation sigma c above which a growing crystal face becomes kinetically rough. They discuss the relation of sigma c with the step free energy kT gamma . The method is tested with computer simulations of the growth of the (001) face of a simple cubic crystal in the solid-on-solid (SOS) model. Near TR, the roughening transition temperature, the results are in good agreement with other estimates of gamma . The method is then applied to growth of (110) faces of naphthalene for melt and solution. They find that gamma does not depend on the temperature, in contrast to gamma found for the SOS model. The (110) face of naphthalene hence does not behave according to the infinite-order roughening transition of Kosterlitz-Thouless type. The classical method to model crystal growth from solution with SOS models turns out to be fundamentally incapable to describe surface roughening in the naphthalene case.

[1]  J. P. Eerden,et al.  Nucleation growth processes: A Monte Carlo simulation , 1977 .

[2]  J. P. van der Eerden.  Roughening transition in mean-field and pair approximation of Ising models , 1976 .

[3]  A. Pavlovska.  Experimentelle untersuchungen der rauigkeit der grenzfläche kristall—Dampf von adamantan , 1979 .

[4]  H. Beijeren,et al.  Exactly solvable model for the roughening transition of a crystal surface , 1977 .

[5]  Donald E. Williams.  Nonbonded Potential Parameters Derived from Crystalline Aromatic Hydrocarbons , 1966 .

[6]  G. H. Gilmer,et al.  Simulation of Crystal Growth with Surface Diffusion , 1972 .

[7]  J. P. Eerden,et al.  On the roughening transition of biphenyl: Transition of faceted to non-faceted growth of biphenyl for growth from different organic solvents and the melt , 1981 .

[8]  S. Rice,et al.  A comment on the consistency of truncated nonlinear integral equation based theories of freezing , 1985 .

[9]  S.W.H. de Haan,et al.  Simulation of crystal growth with a special purpose computer , 1974 .

[10]  D. Cruickshank,et al.  A detailed refinement of the crystal and molecular structure of naphthalene , 1957 .

[11]  P. Bennema,et al.  Crystal growth: A comparison of Monte Carlo simulation nucleation and normal growth theories , 1977 .

[12]  V. V. Podolinsky,et al.  Surface structure change of a crystal in solution , 1983 .

[13]  A. Pavlovska,et al.  Les surfaces non-singulires sur la forme d'quilibre du naphtalne , 1972 .

[14]  G. Gilmer,et al.  Computer simulation of crystal surface structure and growth kinetics , 1972 .

[15]  M. Elwenspoek.  Kinetics of a rough crystal face: Temperature dependence of the growth rate , 1986 .

[16]  P. Hartman,et al.  Crystal growth : an introduction , 1973 .

[17]  W. K. Burton,et al.  The growth of crystals and the equilibrium structure of their surfaces , 1951, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[18]  R. Swendsen.  Monte Carlo studies of the interface roughening transition , 1977 .

[19]  Correlations in the XY model and screw dislocations in the solid-on-solid model , 1978 .

[20]  Jorge V. José,et al.  Renormalization, vortices, and symmetry-breaking perturbations in the two-dimensional planar model , 1977 .

[21]  P. Wolf,et al.  Crystal growth and crystal curvature near roughening transitions in hcp 4He , 1985 .

[22]  P. Bennema,et al.  On the observation of the roughening transition of organic crystals, growing from solution , 1984 .

[23]  D. Thouless,et al.  Ordering, metastability and phase transitions in two-dimensional systems , 1973 .

[24]  G. Jacucci,et al.  Free energies of surface steps in the solid on solid model of interfaces: The large system limit , 1984 .