Acta Cryst. (1993). B49, 387-392 Lattice Parameters, Spontaneous Strain and Phase Transitions in Pb3(PO4)2 BY E. K. H. SALJE, A. GRAEME-BARBERAND M. A. CARPENTER Department of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, England AND U. BISMAYER lnstitut fffr Mineralogie, Welfengarten 1, D3 Hanover, Germany (Received 29 May 1992; accepted 29 July 1992) 387 Abstract The temperature evolution of the lattice parameters of lead phosphate, Pb3(PO4)2, indicates three lattice instabilities with anomalies near 530, 453 and ca 430 K. Only the phase transition at 453 K is ferro- elastic with a spontaneous strain e = (el -el 0 0 e5 0). Volume anomalies occur near 530 and ca 430 K that can be related to the multicomponent behaviour of the structural order parameter. 1. Introduction Lead phosphate, Pb3(PO4)2, is an improper ferro- elastic material that became well known as a proto- type for a whole class of ferroelastics (Von Hodenberg & Salje, 1977; Smirnov, Strukov, Gorelik & Dudnik, 1979; Vagin, Dudnik & Sinyakov, 1979; Dudnik & Nepochatenko, 1980; Torres, Roucau, Ayroles & Taliana, 1980; Benoit, Hennoin, & Lam- bert, 1981; Bismayer & Salje, 1981; Bismayer, Salje & Joffrin, 1982; Darlington, 1983; Roucau, Ayroles & Torres, 1983; Salje, Devarajan, Bismayer & Gui- maraes, 1983; Salje & Wruck, 1983; Bismayer, Salje, ( () () --b o /o ) c Fig. 1. Sketch of the crystal structure of lead phosphate in the ferroelastic phase. The three possible displacements of Pb are indicated by arrows. Glazer & Cosier, 1986; Salje, 1990). It was the first material in which the ferroelastic hysteresis was measured (Salje & Hoppman, 1976). Its spontaneous strain (Guimaraes, 1979; Bismayer & Salje, 1981) and morphic birefringence (Bismayer, Salje & Jof- frin, 1982) are rather large (el = ell = 2%, 2e5 = el3 = 0.7%, Anb¢ = 1.9 x 10 -2 at room temperature) for a phase transition with second-order coupling between the strain and order parameters. The transi- tion mechanism is related to the shift of Pb atoms from the triad and a correlated tilt of the PO4 tetra- hedra (Fig. 1). The global symmetry reduction is R3m-C2/c. The transition is slightly first order and can be made tricritical or second order by appro- priate chemical replacement of P by V or As (Von Hodenberg & Salje, 1977; Bismayer, Salje, Glazer & Cozier, 1986). The principal transition mechanism between the paraelastic and ferroelastic state is apparently not affected by these chemical exchanges (Salje & Wruck, 1983; Bismayer, Salje, Glazer & Cosier, 1986). In detail, the paraelastic-ferroelastic transition mechanism of Pb3(PO4)2 displays two distinct features. Firstly, strong short-range order exists at T > Tc (Bismayer, Salje & Joffrin, 1982; Salje, Devara- jan, Bismayer & Guimaraes, 1983; Salje & Wruck, 1983; Salje, Bismayer, Wruck & Hensler, 1991) lead- ing to domains with mobile walls in crystals of high chemical purity. Impurities (such as Ba, V, As), even in small quantities, pin the walls and these only disappear with the disappearance of the short-range order itself. Due to the high wall density, self- organization could be expected and, indeed, specific heat anomalies in doped material indicate the exist- ence of an intermediate paraelastic phase between 453 and 530 K (Salje & Wruck, 1983). Previous careful X-ray studies (Bismayer, Salje & Joffrin, 1982) have not revealed an expected incommensurate phase in clean crystals so that we must expect the wall configurations to be substantially disordered in pure lead phosphate. Below the ferroelastic transition point at 453 K, a second anomaly exists at 433 K (Smirnov, Strukov, 0108-7681/93/030387-06506.00 © 1993 International Union of Crystallography