W. JAUCH, A. PALMER AND A. J. SCHULTZ 987
steady-state source of background which could poss-
ibly offset the gain in flux by reducing the accuracy
of the intensity measurements. In the case of NiF2,
an LT data set was collected under each of the two
conditions. From Table 2, it is obvious that the
results are hardly affected and certainly not conta-
minated by the increase in the delayed neutron back-
ground.
We wish to thank Dr I. R. Jahn for the loan of the
samples. The work at Argonne was supported by the
Office of Basic Energy Sciences Division of Materials
Sciences, US Department of Energy, under contract
W-31-109-Eng-38.
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Acta Cryst. (1993). B49, 987-996
Multistage Diffusionless Pathways for Reconstructive Phase Transitions: Application
to Binary Compounds and Calcium Carbonate
BY ANDREW G. CHRISTY
Department of Chemistry, University of Leicester, Leicester LE1 7RH, England
(Received 26 May 1993; accepted 3 August 1993)
Abstract
The distinction between 'displacive' and 'recon-
structive' phase transformations is subjective, but
rigorous classification into three types is possible
using symmetry criteria. Type I shows a group-
subgroup relationship between phase symmetries
corresponding to a unique irreducible representation
of the higher symmetry. Type II transitions are those
in which continuous change of a structural param-
eter relates stable phases through a shared subgroup
or supergroup intermediate. Any other transition
(type III) can be effected through a chain of type I
or II steps. There is experimental evidence that some
'reconstructive' transitions use transformation paths
involving only a small number (3-4) of steps, without
descent in symmetry to an amorphous intermediate.
Such short pathways may be particularly important
at high pressure. However, longer routes and less
symmetrical transition states may be favoured kine-
tically. The shortest pathways between structures are
readily derived by considering structural similarities
and available lattice modes. The probable utilization
of such routes provides a rationale for understanding
observed stable and metastable behaviour, as shown
by examples from MX and MX2 systems and CaCO3.
© 1993 International Union of Crystallography
Printed in Great Britain - all rights reserved
The predictions of this approach are readily tested
using molecular dynamics simulations.
1. Introduction
Buerger (1951) classified structural phase transitions
as reconstructive or displacive, depending on whether
or not breakage of primary interatomic bonds was
required in order to interconvert the crystal struc-
tures. There is a correlation with transformation
mechanism in that reconstructive transitions are
likely to involve heterogeneous nucleation, whereas
new phases may nucleate homogeneously in a displa-
cive transition. Thermodynamically, reconstructive
transitions show discontinuities in first-order free-
energy derivatives (entropy and volume) due to the
significant change in atomic environments at the
transition, whereas displacive transitions may be
second-order in character. Even when a displacive
transition is thermodynamically first order, the close
relationship between the structures of the two phases
makes it easy to visualize transformation occurring
continuously, by variation of a few structural param-
eters. The first-order character then arises because
these intermediate states are higher in energy at the
transition than the structures of either stable phase.
Acta Crystallographica Section B
ISSN 0108-7681 ©1993