Experimental Establishment of Mother–Daughter Orientation Relationships and Twinning Effects in Phase Transitions: A Great Legacy from Jack Gougoutas and Peggy Etter

Abstract

A simple procedure, with an available program, may readily be used to establish the three-dimensional relationships between a mother and daughter phase, where mother and daughter are either two different phases of a material or a reactant and product in a solid-state transformation. The only requirements are that (i) the process involves a crystal-to-crystal transformation, and (ii) the experiment must be carried out without changing the alignment of the mother crystal. Application of the method supports the inferred alignment of mother and daughter phases in the published structures of two polymorphs of 4-cyanopyridinium perchlorate monohydrate 1. A new low-temperature, monoclinic polymorph of ferrocenium tetrafluoroborate 2 is produced when the known orthorhombic polymorph is cooled from 173 to 120 K. The major features of the transformation include "conservative twinning" and a modulation of the structure along the crystallographic b direction upon cooling. Redetermination of the structure of the low-temperature polymorph of ferrocenium hexafluorophosphate 3 reveals that the phase change is accompanied by reproducible four-component twinning, providing a proper explanation for the previously reported, very high R-factor of 12.4%. Included tutorial information on the process will assist the reader in obtaining topotactic relationships, as well as in preparing figures and animations describing phase transitions or reactions.

Snapshots of a solid-state transformation: coexistence of three phases trapped in one crystal

“…The program TOPO 37 was employed to understand the relationships between the coexisting unit cells, applying the methodology of Etter and Gougoutas. 38 , 39 This program uses the orientation matrices of the samples in order to compare unit cell vectors, and allows determining relationships between the successive phases.…”

Superior thermoelasticity and shape-memory nanopores in a porous supramolecular organic framework

“…Furthermore, the framework of compound 1o gradually breathed with increasing temperature and, at temperatures greater than 438 K, underwent a phase transition via pyridyl ring-flipping from an orthorhombic phase (compound 1o , space group Ccca ) to a tetragonal phase (compound 1t , space group P 4 2 / nbc ). The orientation relationship between the tetragonal phase and the orthorhombic phase can be described as (refs 21 , 22 ) where a o , b o and c o are the lattice axes for the orthorhombic phase, and a t , b t and c t are those for the tetragonal phase. In the following description, all the structures will be presented in the lattice of the orthorhombic phase.…”

Use of Topotactic Phase Transformations To Obtain Solutions of the Crystal Structures of Highly Disordered Materials

“…We then decided to explore whether a set of coordinates could be generated for 1_1 using the methods of topotaxy. As suggested in the Introduction, in any crystal-to-crystal process, reaction, or phase transition, one has the opportunity, if the process is observed during a single diffractometer session, to obtain the exact orientation relationship between the pair of unit cells observed . The procedure, using the current version (4.40) of our available program TOPO, involves reading in a pair of .p4p or .cif files that contain the orientation matrices for Phase 1 and Phase 2, R 1 , and R 2 , respectively.…”

“…The present contribution reports a different approach to the use of phase transitions: to predict , in optimal cases, the structure of a material which has remained elusive at the atomic coordinate level. Topotactic crystal-to-crystal phase transformations, including those processes involving either molecular reorientation or a chemical reaction, have been an important focus of our research for over four decades. − “In topotaxy, a single crystal of a starting material is converted into a pseudomorph containing one or more products in a definite crystallographic orientation; the conversion takes place throughout the entire volume of the crystal.” The topotactic solid-state reaction of bis­( p- methoxy)- trans -stilbene, first described in a 1984 paper by Theocharis, Jones and Rao, served as an opportunity for B.M.F. to write to Professor Bill Jones with some questions about the paper .…”

“…A transformation matrix, the topotactic transformation matrix, which relates the mother and daughter unit cells, is included in the output of TOPO. Our recent paper includes a tutorial-style approach and applications to the phase transitions in cyanopyridinium perchlorate, ferrocenium tetrafluoroborate, and ferrocenium hexafluorophosphate.…”