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. References BECKER, P. J. & COPPENS, P. (1974). Acta Cryst. A30, 129-147. EPPERSON, J. E., CARPENTER, J. M., THIYAGARAJAN, P. & HEUSER, B. (1990). Nucl. Instrum. Methods, A289, 30-34. HAEF~R, K. (1964). Thesis, Univ. of Chicago, USA. HAEFNER, K., STOUT, J. W. & BARRETT, C. S. (1966). J. Appl. Phys. 37, 449-450. JAHN, I. R. (1973). Phys. Status Solidi B, 57, 681--692. JAUCH, W. (1991). Phys. Rev. B, 44, 6864-6869. JAUCH, W., Mclr~T'rRE, G. J. & SCHULTZ,A. J. (1990). Acta Cryst. B46, 739-742. JAUCH, W., SCHULTZ, A. J. & SCHNEIDER,J. R. (1988). J. Appl. Cryst. 21,975-979. JAUCH, W. & STEWART, R. F. (1991). Sagamore X Conference on Spin, Charge and Momentum Densities, Konstanz, Germany. Abstracts, p. 58. PALMER, A. & JAUCH, W. (1991). Solid State Commun. 77, 95- 97. PALMER, A. & JAUCH, W. (1993). Phys. Rev. B, 46. In the press. SEARS, V. F. (1992). International Tables for Crystallography, Vol. C. Dordrecht: Kluwer. WILKINSON, C. (1986). J. Phys. (Paris) Colloq. C5, 47, 35-42. ZACHARIASEN,W. H. (1967). Acta Cryst. 23, 558-564. 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