Volume 113A, number 1 PHYSICS LETTERS 25 November 1985 THE LIQUID-LIQUID PHASE TRANSITION A.C. MITUS I, A.Z. PATASHINSKII and B.I. SHUMILO Institute of Nuclear Physics, 630090 Novosibirsk, USSR Received 23 August 1985; accepted for publication 24 September 1985 It is shown that a change in the local structure of a liquid may lead to a first-order liquid-liquid phase transition. A simple phenomenological model describing this phenomenon is proposed. 1. The experimental data and the results of com- puter simulations confirm indirectly the existence of local crystal ordering in liquids [1]. Nevertheless, a direct observation of the local structure of the matter is difficult and, to the best of our knowledge, has not been performed yet. Important evidence in favour of the existence of a local structure in the liquid phase might be the revealing of the liquid-liquid phase tran- sition (PT) - an abrupt change of the local structure of the matter. The theory of the liquid state based on the hy- pothesis of local crystal ordering of the matter has recently been proposed by us (A.P. and B.Sh.) [2]. According to it, the configurations of atoms, statis- tically probable in the liquid, are of the following type: the greater part of the atoms belongs to a mul- tiply connected region of the "perfect matter", and the rest of the atoms belongs to pointlike and linear defects which are the complement of the "perfect matter" region with respect to the whole space. The local structure of the "perfect matter" is supposed to be similar to that of the crystal. More precisely, a local mapping of atoms onto the sites of some ideal lattice is assumed to be possible. The mapping preserves the neighbourhood relations, i.e. the lattice images of the nearest neighbours of an atom are the nearest neighbours of the image of this atom. The space orientation of this tangent lattice and its posi- tion as a whole is determined with the help of a 1 On leave of absence from Phys~ Dept. of Technical Univer- sity, Wybrzeze Wyspianskiego 27, 50-370 Wroclaw, Poland. 0.375-9601/85/$ 03.30 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) suitable minimization (over an element of the mat- ter under consideration) of displacements of atoms with respect to the corresponding lattice sites. Every configuration of atoms in the condensed state can be represented as some realization of the fields of ro- tations of the tangent lattice and of its relatively small deformations. The type of the lattice and its param- eters are timed by the minimization of, say, the elas- tic energy integrated over the whole body. In contrast to the crystal, in the liquid relative rotation of the tangent lattices of distant elements can be arbitrary because of the existence of a finite density of linear defects. These linear defects are locally equivalent to dislocations. The Burgers vector of such a defect is not constant along its line but rotates together with the tangent lattice. The grain-boundary like structures are of small probability in the liquid phase. A section of the liquid by an arbitrary plain is a surface struc- turally "perfect" everywhere except for isolated patches of intersections with the lines of defects. The described configurations of atoms are of dominant statistical weight in the liquid. (For a detailed discus- sion of the point see ref. [2] .) Very often the structure of a particular substance is determined by the number of competing interac- tions. This may lead to transformations of the local structure - the polymorphic phase transitions (PPT). The phenomenon is well known for the crystal. Since the long-range ordering is not of decisive importance one can imagine a similar phase transition to take place in the locally ordered liquid. Let us call it the PPT of the tangent lattice. This PT must be of first order 41