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