- Email: [email protected]
On the double structure of the crystal-melt transition layer: Density functional analysis of a (111) fcc crystal-melt interface
A586 Surface Science 223 (1989) 299-314 North-Holland, Amsterdam
299
O N THE D O U B L E STRUCTURE OF THE C R Y S T A L - M E L T TRANSITION LAYER: D E N S I T Y F U N C T I O N A L ANALYSIS OF A (111) fee CRYSTAL-MELT
INTERFACE
L. M I K H E E V
Institute of Crystallography, USSR Academy of Sciences, Leninsky prosp. 59, Moscow, 117333, USSR and A. TRAYANOV
Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia 1040, Bulgaria Received 20 October 1988; accepted for publication 6 July 1989 A density functional theory for a (111) fcc crystal-melt interface is proposed. Two order parameters, ~/.L and ~ll' characterizing the ordering in directions normal and parallel to the interface are used to describe the density wave oscillations. The density waves are parameterized in three different ways: in the crystalline region they are approximated by a superposition of Gaussians, in the liquid-like region a wave representation is used and in the intermediate region, where ~/11is small compared to */±, a mixed Gaussian-wave representation is chosen. As a result of the minimization of the free energy with respect to the order parameters, the double-soliton structure of the interface is revealed. The profiles of the order parameters clearly demonstrate that the lateral ordering decreases much faster than the decay of the density oscillations normal to the interface. Using the calculated surface free energy values, y± and 3,11, 0.609T and 0.433T respectively, we estimated that the crystal-melt interface is rough. The present results are in good agreement with the Lennard-Jones computer simulation data.
Surface Science 223 (1989) 315-325 North-Holland, Amsterdam
315
ENERGY OF THE bee ( l l 0 ) / f c c ( 1 1 1 ) I N T E R F A C E AND ENERGY D E P E N D E N C E O N ITS SIZE
INTERFACIAL Y. GOTOH
and H. FUKUDA
Department of Materials Science and Technology, Science University of Tokyo, Noda, Chiba 278, Japan Received 8 April 1989; accepted for publication 10 July 1989 The interfacial energy of the b c c ( l l 0 ) / f c c ( l l l ) interface is calculated using a simple form of interaction energy. The calculation is carried out for the Nishiyama-Wassermann ([ll0]fcc JI [001]be~), Kurdjumov-Sachs ([110]tccll[lll]bcc) and R30 ° ([2il]fccll[001]bcc) orientation relationships by changing the number of atoms and the atomic diameter ratios of bcc to fcc, a. The energy minima appear at specific values of a in each orientation relationship. As the number of atoms decreases, the minimum value of the interfacial energy versus et curve decreases and the half-width between the maximum and the minimum values increases. This indicates that the interfacial energy depends on the size of the interface if the number of atoms is small, as in the early stage of nucleation on a substrate.
299
O N THE D O U B L E STRUCTURE OF THE C R Y S T A L - M E L T TRANSITION LAYER: D E N S I T Y F U N C T I O N A L ANALYSIS OF A (111) fee CRYSTAL-MELT
INTERFACE
L. M I K H E E V
Institute of Crystallography, USSR Academy of Sciences, Leninsky prosp. 59, Moscow, 117333, USSR and A. TRAYANOV
Institute of Physical Chemistry, Bulgarian Academy of Sciences, Sofia 1040, Bulgaria Received 20 October 1988; accepted for publication 6 July 1989 A density functional theory for a (111) fcc crystal-melt interface is proposed. Two order parameters, ~/.L and ~ll' characterizing the ordering in directions normal and parallel to the interface are used to describe the density wave oscillations. The density waves are parameterized in three different ways: in the crystalline region they are approximated by a superposition of Gaussians, in the liquid-like region a wave representation is used and in the intermediate region, where ~/11is small compared to */±, a mixed Gaussian-wave representation is chosen. As a result of the minimization of the free energy with respect to the order parameters, the double-soliton structure of the interface is revealed. The profiles of the order parameters clearly demonstrate that the lateral ordering decreases much faster than the decay of the density oscillations normal to the interface. Using the calculated surface free energy values, y± and 3,11, 0.609T and 0.433T respectively, we estimated that the crystal-melt interface is rough. The present results are in good agreement with the Lennard-Jones computer simulation data.
Surface Science 223 (1989) 315-325 North-Holland, Amsterdam
315
ENERGY OF THE bee ( l l 0 ) / f c c ( 1 1 1 ) I N T E R F A C E AND ENERGY D E P E N D E N C E O N ITS SIZE
INTERFACIAL Y. GOTOH
and H. FUKUDA
Department of Materials Science and Technology, Science University of Tokyo, Noda, Chiba 278, Japan Received 8 April 1989; accepted for publication 10 July 1989 The interfacial energy of the b c c ( l l 0 ) / f c c ( l l l ) interface is calculated using a simple form of interaction energy. The calculation is carried out for the Nishiyama-Wassermann ([ll0]fcc JI [001]be~), Kurdjumov-Sachs ([110]tccll[lll]bcc) and R30 ° ([2il]fccll[001]bcc) orientation relationships by changing the number of atoms and the atomic diameter ratios of bcc to fcc, a. The energy minima appear at specific values of a in each orientation relationship. As the number of atoms decreases, the minimum value of the interfacial energy versus et curve decreases and the half-width between the maximum and the minimum values increases. This indicates that the interfacial energy depends on the size of the interface if the number of atoms is small, as in the early stage of nucleation on a substrate.