Crystal structure of transition metals

The crystal structures of transition metal compounds and minerals have either cubic or lower symmetries. The cations may occur in regular octahedral (or tetrahedral) sites or be present in distorted coordination polyhedra in the crystal structures. When cations are located in low-symmetry coordination environments in non-cubic minerals, different absorption spectrum profiles may result when linearly polarized light is transmitted through single crystals of the anisotropic phases. Such polarization dependence of absorption bands is illustrated by the spectra ofFe2+ in gillespite (fig. 3.3) and of Fe3+in yellow sapphire (fig. 3.16). 

An extensive compilation of the crystal structures of transition metal carbides is found in Pearson s Handbook. Ward has discussed the structures of carbides extensively. Epicier and de Novion have suimnarized the results of investigations on ordering in transition metal carbides. Lengauer recently reviewed the knowledge on transition metal carbides and carbonitrides. For a comparison of close-packed transition metal carbides with close-packed transition nitrides, see Nitrides Transition Metal Solid-state Chem istry. 

D.G. Pettifor "Theory of the Crystal Structures of Transition Metals at Absolute Zero", in Metallurgical Chemistry, ed. by 0. Kubaschewsky (HMS0, London 1972) Calphad. 1, 305 (1977)... 

Molecular and crystal structures of transition metal carbonyls... 

TABLE 5.1 Crystal Structures of Transition Metals, and Structure Progression in Nitrides and Carbides... 

Analysis of the valence-band spectrum of NiO helped to understand the electronic structure of transition-metal compounds. It is to be noted that th.e crystal-field theory cannot explain the features over the entire valence-band region of NiO. It therefore becomes necessary to explicitly take into account the ligand(02p)-metal (Ni3d) hybridization and the intra-atomic Coulomb interaction, 11, in order to satisfactorily explain the spectral features. This has been done by approximating bulk NiO by a cluster (NiOg) ". The ground-state wave function Tg of this cluster is given by,... 

As noted in Section 9.1, there are three closely related theories of the electronic structures of transition metal complexes, all making quite explicit use of the symmetry aspects of the problem but employing different physical models of the interaction of the ion with its surroundings as a basis for computations. These three theories, it will be recalled, are the crystal field, ligand field, and MO theories. There is also the valence bond theory, which makes less explicit use of symmetry but is nevertheless in accord with the essential symmetry requirements of the problem. We shall now briefly outline the crystal field and ligand field treatments and comment on their relationship to the MO theory. 

Historically the first non-empirical calculation of entire multiplet structures of transition metal (TM) ions in crystals was performed by Watanabe and Kamimura based on the combination of a local density approximation (LDA) calculation and the ligand field theory (Watanabe and... 

Measurements of electronic absorption spectra in the visible region not only lead to the evaluation of CFSE s, but they also provide useful information about the crystal chemistry of transition metal ions in the crystal structures and causes of colour and pleochroism of minerals. In this chapter, techniques for measuring absorption spectra of minerals are briefly described and some general applications of the optical spectra to basic crystal chemical properties, such as colour and pleochroism, are discussed. These examples also amplify many of the features of crystal field spectra outlined in chapter 3. 

Considerable interest centres on the Mantle constituting, as it does, more than half of the Earth by volume and by weight. Attention has been focussed on several problems, including the chemical composition, mineralogy, phase transitions and element partitioning in the Mantle, and the geophysical properties of seismicity, heat transfer by radiation, electrical conductivity and magnetism in the Earth. Many of these properties of the Earth s interior are influenced by the electronic structures of transition metal ions in Mantle minerals at elevated temperatures and pressures. Such effects are amenable to interpretation by crystal field theory based on optical spectral data for minerals measured at elevated temperatures and pressures. 

CONTENTS Introduction, Thom H. Dunning, Jr. Electronic Structure Theory and Atomistic Computer Simulations of Materials, Richard P. Messmer, General Electric Corporate Research and Development and the University of Pennsylvania. Calculation of the Electronic Structure of Transition Metals in Ionic Crystals, Nicholas W. Winter, Livermore National Laboratory, David K. Temple, University of California, Victor Luana, Universidad de Oviedo and Russell M. Pitzer, The Ohio State University. Ab Initio Studies of Molecular Models of Zeolitic Catalysts, Joachim Sauer, Central Institute of Physical Chemistry, Germany. Ab Inito Methods in Geochemistry and Mineralogy, Anthony C. Hess, Battelle, Pacific Northwest Laboratories and Paul F. McMillan, Arizona State University. 

The Effect of Crystal Structure in Transition Metal Sulfide... 

Molecular symmetry and ways of specifying it with mathematical precision are important for several reasons. The most basic reason is that all molecular wave functions—those governing electron distribution as well as those for vibrations, nmr spectra, etc.—must conform, rigorously, to certain requirements based on the symmetry of the equilibrium nuclear framework of the molecule. When the symmetry is high these restrictions can be very severe. Thus, from a knowledge of symmetry alone it is often possible to reach useful qualitative conclusions about molecular electronic structure and to draw inferences from spectra as to molecular structures. The qualitative application of symmetry restrictions is most impressively illustrated by the crystal-field and ligand-field theories of the electronic structures of transition-metal complexes, as described in Chapter 20, and by numerous examples of the use of infrared and Raman spectra to deduce molecular symmetry. Illustrations of the latter occur throughout the book, but particularly with respect to some metal carbonyl compounds in Chapter 22. 

The first problem to address is that of the experimental and theoretical tools . Single-crystal X-ray crystallography has, of course, been the method of choice for the determination of the solid-state structures of transition metal clusters. Their structural variability, complexity, and even, at times, unpredictability preceded, in terms of experimental challenge, that of large biomolecules and proteins. New scientific challenges such as, on the one hand, the advent of area detector techniques and powerful X-ray radiation sources and, on the other hand, the use of variable temperature techniques, combined with spectroscopic solid-state methods enables in depth investigation of the temperature-dependence of solid-state molecular and crystal structures and the study of their phase transitional behavior. 

Structures of transition metal ion complexes Measurements performed on single crystals, powders and frozen solutions give information about the geometric and electronic structure by analysis of the strengths and symmetries of the g-, zero-field- (S > V2) and hyperfine interactions. The field is summarised in a modern treatise [15]. 

Crystal field theory a model of the electronic structure of transition-metal complexes that considers how the energies of the d orbitals of a metal ion are affected by the electric field of the ligands. (23.7)... 

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