Crystallographic shear phases

A crystallographic shear (CS) plane is a fault in which a plane of atoms has been (notionally) removed from the crystal. In oxides, this is frequently a plane of oxygen atoms, eliminated as a result of reduction. In the resulting structures, the slab types are all identical and the same as the parent phase. To illustrate this phenomenon, crystallographic shear in reduced tungsten trioxide will be described. 

Continued reduction causes an increase in the density of the CS planes and as the composition approaches WO2.97, they tend to become ordered. In the case where the CS planes are perfectly ordered, defects are no longer present. Each CS plane is equivalent to the removal of a 102 oxygen-only plane, and the composition of a 

The decrease in lattice strain is so great that further reduction, now using 103 CS planes, can take place. 

Like polytypes, crystallographic shear (CS) phases are built from slabs of a single parent 

The CS planes reduce the amount of oxygen in the structure. The composition of a crystal 

The discussion of these diffraction patterns is quite general and not just restricted to CS planes. This means that the polytypes and other phases described above, as well as the long period 

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The literature available and experimental evidence on this subject are not extensive, and much of it concerns the crystallographic shear phases. These of necessity figure prominently in the survey which follows but, in so far as is possible, generalizations to other systems will be made. To some extent, therefore, the present review is a continuation and extension of two earlier review articles which have appeared in this series and which contain much background information to that presented here. 

IR-11.6.1 Introduction Several special problems of nomenclature for non-stoichiometric phases have arisen with the improvements in the precision with which their structures can be determined. Thus, there are references to homologous series, non-commensurate and semi-commensurate structures, Vernier structures, crystallographic shear phases, Wadsley defects, chemical twinned phases, infinitely adaptive phases and modulated structures. Many of the phases that fall into these classes have no observable composition ranges although they have complex structures and formulae an example is Mo17047. These phases, despite their complex formulae, are essentially stoichiometric and possession of a complex formula must not be taken as an indication of a non-stoichiometric compound (cf. Section IR-11.1.2). 

Crystallographic shear plane. Series of discrete shear phases are observed among the oxides of several transition metals. By progressive reduction, series of Ti 02 i, V 02 i phases are obtained from the dioxides, as Me 03 i phases may be related to trioxides such as M0O3 or WO3. An example of a crystallographic shear plane formation is schematically shown in Fig. 7.54. 

One of the simplest oxides is the rhenium trioxide (ReOs) structure shown in figure lA(b). It consists of an incomplete fee host lattice of with Re in one-quarter of the octahedral sites. (Crystallographic shear (CS) phases (discussed in 1.10.5) based on ReOs may be considered as consisting of the cubic MO2 structure.) Many oxides and fluorides adopt the ReOs structure and are used in catalysis. 

Nb02.5 and this was described in detail in elegant papers by Anderson (1970, 1973). Ordered phases are based on shear structures, with parallel CS planes (double crystallographic shear) separating the blocks of the ReOs lattice. Ternary and intergrowth block structures have been discovered by extensive HRTEM... 

Oxygen bacancies are commonly encountered in oxide perovskites. In AB03 unlike in W03, and Ti02 crystallographic shear planes are not found. Instead, a variety of superstructures are seen due to the ordering of vacancies. The brownmillerite phase of... 

Empty perovskite lattices can also form oxygen deficient phases by a process known as Crystallographic Shear, which introduces edge-sharing octahedra in addition to comer sharing. Examples include the reduced molybdenum oxides M08O23, M09O26, and VeOis. The latter is a metallic phase with substantial reversible capacity for electrochemical lithium intercalation between 2.8 and 2.2 V with respect to lithium metal. 

The authors suggested that the M018O52 phase consists of crystallographic shear planes similar to crystalline M018O52, which would be similar in their XANES signature. The shear planes were also suggested by electron microscopy studies... 

Crystallographic Shear (C5) Phases.—The CS phases are the best-known group of materials which appear to be intolerant of point-defect populations. There are three major families those based upon tungsten trioxide, WO3, upon rutile, Ti02, and upon niobium pentoxide, Nb205. These and other less studied systems have been described in some considerable detail in two previous review articles in this series and elsewhere and the fundamental principles underlying their structures will not be repeated here. In this section some of the results found in the tungsten trioxide and rutile-related systems will be outlined. Older results, covered in the earlier reviews, will merely be sketched in where relevant, and emphasis will be upon newer data or else on a re-examination of earlier results from the point of view of this article. 

IR-11.4.5 Defect clusters and use of quasi-chemical equations IR-11.5 Phase nomenclature IR-11.5.1 Introduction IR-11.5.2 Recommended notation IR-11.6 Non-stoichiometric phases IR-11.6.1 Introduction IR-11.6.2 Modulated structures IR-11.6.3 Crystallographic shear structures IR-11.6.4 Unit cell twinning or chemical twinning IR-11.6.5 Infinitely adaptive structures IR-11.6.6 Intercalation compounds IR-11.7 Polymorphism IR-11.7.1 Introduction IR-11.7.2 Use of crystal systems IR-11.8 Final remarks IR-11.9 References... 

This is a structure-building component in which two constituent parts of the structure are twin-related across the interface. The twin plane changes the composition of the host crystal by a definite amount (which may be zero). Ordered, closely spaced arrays of twin planes will lead to homologous series of phases. Disordered twin planes will lead to non-stoichiometric phases in which the twin planes serve as the defects. There is a close parallel between chemical twinning and crystallographic shear (see Section IR-11.6.3). 

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