Smectic-A--C transition in three dimensions

Journal Article · Fri Oct 01 00:00:00 EDT 1982 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.26.2196· OSTI ID:6526025

Grinstein, G; Pelcovits, R A

A theory of the smectic-A--C transition in which fluctuations in both the elastic and director degrees of freedom are treated is developed. It is argued that in zero magnetic field the asymptotic critical behavior belongs in the universality class of the three-dimensional XY model, in agreement with earlier studies which did not treat fully both elastic and director fluctuations. For most experimental situations the true critical region is unobservably narrow whereupon a simple-harmonic approximation adequately describes the transition; in this approximation the static structure factor exhibits a crossover from algebraic decay charaterized by a nonuniversal exponent eta/sub A/ in the A phase to algebraic decay characterized by a different nonuniversal exponent eta/sub A/C at the critical temperature T/sub c/. The splay elastic constant K/sub 1/ is decays algebraically; schematically, approx.x/sup() -2+eta/ at T/sub c/ in th harmonic theory, while m(x) vanishes like t/sup ..beta../, where t is the reduced temperature. The exponent beta/ and eta, though nonuniversal, satisfy the scaling law 4/beta/ = 2+eta. These finite-field results are modified at large distances (say x> or approx. =15/sup 5/ A) by the inclusion of anharmonic terms. We find approx.x/sup() -2+etavertical-barlnk/ at T/sub c/, while approx.t/sup beta-tildevertical-barlnt/ as t/right arrow/0.

• Research Organization: IBM Thomas J. Watson Research Center, P. O. Box 218, Yorktown Heights, New York 10598
• OSTI ID: 6526025
• Journal Information: Phys. Rev. A; (United States), Vol. 26:4
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
LIQUID CRYSTALS
CRYSTAL-PHASE TRANSFORMATIONS
CRITICAL TEMPERATURE
LANDAU FLUCTUATIONS
MAGNETIC FIELDS
MAGNETO-THERMAL EFFECTS
THREE-DIMENSIONAL CALCULATIONS
CRYSTALS
FLUCTUATIONS
FLUIDS
LIQUIDS
PHASE TRANSFORMATIONS
PHYSICAL PROPERTIES
TEMPERATURE EFFECTS
THERMODYNAMIC PROPERTIES
TRANSITION TEMPERATURE
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360602* - Other Materials- Structure & Phase Studies