A cluster model for the transition state and its study by means of electron diffraction I. Theoretical model

Abstract

A system which exhibits substitutional disorder is said to be in the "transition state" if the diffuse intensity is confined to the vicinity of a geometric locus in reciprocal space. A model is proposed which allows to describe the ordering in the transition state in terms of predominant clusters. According to the model tho transition state is considered as being built from clusters of a typical polyhedral type, which satisfy a linear relation for the occui pation operators of the cluster sites. This ordering relation is directly derived from the analytical equation of the geometric locus.Ein System mit Substitutionsfehlordnung befindet sich im ,,mergangszustand", wenn die diffuse Intensitiit auf die Umgebung einea geometrischen Punktes im reziproken Raum beschrinkt ist. Es wird ein Modell vorgeschlagen, das es erlaubt, die Ordnung im l h e rgangmustand mit dem vberwiegen von Clustern zu erkliiren. In ffbereinstiaaung mit dem Modell wird angeno-en, da8 der Vbergangszustand aus Clustern mit bestimmtem Polyedertyp aufgebaut ist, die eine lineare Beziehung fiir die Besetzungsoperatoren der Clusterpliitze erfiillen. Diese Ordnungsbeziehung wird direkt aus der analytischen Gleichung des geometrischen Ortes abgeleitet.

Complex Polymorphic Behavior and Dielectric Properties of Perovskite-Related Sr(Sr1/3Nb2/3)O3

“…[1] have been observed in some transition metal carbides (VC \V , TiC \V , NbC \V ), nitrides (TiN \V ) (22,24) and oxides (LiFeO ) (23) having an NaCl-type structure. Di!use scattering in these systems was attributed to ordering of species sharing the same fcc sublattice (i.e., carbon atoms and vacancies in carbides, or Li and Fe in LiFeO ), accompanied by formation of octahedral and cubic clusters of these species in real space (21,22). Octahedral and cubic clusters give rise to di!use intensity surfaces described by Eqs.…”

“…A so-called &&cluster model'' was developed (21,22) which describes a &&transition state'' built of atomic clusters of a speci"c polyhedral type, satisfying a linear relationship between the occupational operators on the cluster sites; for ionic compounds, this model is a direct extension of the Pauling electrostatic valence rule (23). Surfaces of di!use intensity similar to that described by Eq.…”

Ordering and Magnetic Susceptibility of Non-Stoichiometric Hafnium Carbide

“…Apparently, HfC 0.80 carbide corresponds to the boundary of the existence regions of ordered phases Hf 3 C 2 and Hf 6 C 5 and does not undergo any noticeable ordering. To produce short-range or long-range order the HfC 0.80 carbide was additionally annealed at a temperature of 750 K for 20 h. Electron diffuse scattering is very sensitive to substitutional ordering or to a so-called``transition stateº which is intermediate between short-range order and long-range order [30,31]. Annealed powder of HfC 0.80 carbide was studied with the use of transmission electron microscope JEM-200C.…”

Heat capacity anomalies at incommensurate-normal transition of �kermanite solid solution (Ca, Sr)2(Mg, Co, Zn, Fe)Si2O7

“…They found that the circular diffuse scatterings are caused by microdomains, in which the modulation is seen to be only in the [110] direction in some area or only in the [710] direction in another area, sometimes intermittently disordered, and in some areas not seen at all. The diffuse intensity implies short range order (De Ridder et al 1976).…”