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American Journal of Physics -- May 1986 -- Volume 54, Issue 5, pp. 403
Simple electrostatic model of the structural phase transition
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Add to FacebookA purely classical system of four equal point charges q which are free to move over the surface of a sphere is considered. In the equilibrium configuration all charges are located at the vertices of the regular tetrahedron inscribed into the sphere. If a weak uniform electric field E is directed along the z axis, one charge q will move to the position (0,0,R), while three others will form an equilateral inscribed triangle with the plane perpendicular to the field. An increase of the field will distort the tetrahedron [three charges uniformly shift towards the charge at (0,0,R)], keeping the field (z axis) as a C3‐symmetry axis. However, when E reaches the ‘‘critical’’ value E0=0.732q/R2, the system abruptly changes its symmetry: For E>E0 the equilibrium (least energy) configuration corresponds to all four charges located symmetrically at the corners of the inscribed square whose plane is perpendicular to E. Consequently, the field will now form a C4‐symmetry axis. This jumpwise C3→C4 symmetry change provides a simple classical model for the structural phase transitions when the spontaneous discontinuity arises during a continuous change of one of the intensive variables (in this model the electric field E). Several related open problems which may appear attractive for the modeling on personal computers are also outlined.
EDITORIALLY RELATED
- Comment on ``Simple electrostatic model of the structural phase transition'' [Am. J. Phys. 54, 403 (1986)]: Not that simple
B. W. van de Waal
Am. J. Phys. 56, 750 (1988)AJPIAS000056000008000750000001
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History
Received Mar 1985
Accepted Apr 1985
Accepted Apr 1985
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0002-9505 (print)
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