Theory of Phase Transition in Squaric Acid

Abstract

Phase transition in squaric acid is discussed on the basis of a pscudospin model for the hydrogen bond system. A strong coupling between the lattice distortion and proton system is introduced in order to account for the twin structure and improper ferroelastic behaviour in the low temperature phase. Anomalous elastic constant and electric susceptibility are calculated and compared with experiments. Isotope effect in the transition temperature is discussed by taking account of the tunneling motion of proton. § I. IntroductionSquaric acid H 2 C40 4 C3, 4-dihydroxy-3-cyclobutane-1, 2-dions, abbreviated as HzSQ) is an unusually strong organic acid. This crystal undergoes a second order antiferrodistortive phase transition at Tc = 97.TC from a tetragonal (high temperature phase) to a monoclinic structure (low temperature phase) confirmed by a birefringence experiment. 1 > From the structural studies by means of X-ray'> and neutron diffraction, 3 J. 4 ) informations on the crystal structure, both above and below T" have been obtained. The structure consists of the layers of planar nwlecules HzC40 1 perpendicular to the b-axis as shown in Fig. 1. Above T,, the protons move in the symmetric double well potential of 0-H-0 bonds, and on the average locate in the midpoints of the bonds. Below T" however, the protons are arranged in an ordered pattern such that each C10 4 is linked by four asymmetric hydrogen bonds with two protons nearer to and other two protons apart from a C40 4 radical. Thus the crystal in the low temperature phase consists of planar ferroelectric layers with the layers antiferroelectrically stacked along the unique monoclinic b-axis. The proton arrangement within each layer is uniform but has two different configurations forming a twin structure accompanied by spontaneous distortions with opposite directions. The twin structure in the monoclinic phase was first reported by Semmingsen. 2 ) Ferroelasticity in H 2SQ has been directly confirmed by observations of Okada.') effect in elastic hysteresis loop under the polarizing microscope by Suzuki and Furthermore, H 2SQ and deuteratecl crystal D 2SQ exhibit a large isotope the transition temperature as T, (H) = 371K and T, (D) = 516K. This factsuggests that the hydrogen bonds play an important role in the phase transition mechanism, and an order-disorder pseudospin model for the proton system such as used for KH2P0 4 will be suitable for this substance. Tncleecl a few theories at Michigan State University on June 27, 2015 http://ptp.oxfordjournals.org/ Downloaded from

Microscopic theories of order-disorder structural phase transitions in crystals

“…10, а, являются конфигурации (1) -(4) рис.6 или четвертой строки рис. 3, а, вырожденные вследствие тетрагональной сим-метрии (в связи с чем параметр асимметрии, который в работах 89~91 также обозначался буквой е, следует, видимо, полагать равным нулю 92 . 93 ).…”

Cluster Theory of Phase Transition in Squaric Acid. I: Formulation and General Discussion

“…This condition is fulfilled for KH2P04 with (3)(4)(5)(6) below certain T e , while in the present case of H2SQ with (3-3) it is not always satisfied. By the definition, L>O, and K>l when 8=0.…”

“…where Tc is determined from the condition (3)(4)(5)(6)(7)(8) For this case the long range order parameter <0> turns out to be …”

“…(] 1-K (3)(4)(5)(6)(7)(8)(9) At this stage a crucial difference becomes apparent between two cases of H2SQ and KH2P04: In order that a finite value solution for x is present, it must hold from (3-7)that 1-K>2L. This condition is fulfilled for KH2P04 with (3)(4)(5)(6) below certain T e , while in the present case of H2SQ with (3-3) it is not always satisfied.…”

“…For definiteness, let us take four spins 6i(i = 1,2,3,4) belonging to one particular molecule C40 4. Equation (2·1) will generate a two dimensional net·work through the interaction {Iij} on the plane.…”