Size effects in a thin ferroelastic rod

ABSTRACT

The system of differential equations is derived on the base of the classical theory of elasticity and the phenomenological Landau theory, describing the phase transition in a long thin rod of the rectangular profile. The solution of this system by the Fourier method allowed determining the phase transition temperature in the ferroelastic state as a function of a size l, a profile shape and an extrapolation length. The presence of a maximum in the dependence of on l at the ultra-small size of the profile is revealed. It was found that the value of the maximum increases with increasing in the extrapolation length and shifts to smaller sizes. The critical dimensions of the profile, below which a transition to ferroelastic phase is impossible, are calculated depending on the extrapolation length.

KEYWORDS:

• Thin ferroelastic rod
• size effect
• spontaneous deformation
• free energy
• phase transition temperature
• extrapolation length