STRUCTURES OF SOLIDS

Structure of Solids - A H- H dipolar coupling NMR study of the water molecule in magnetically H dilute crystalline hydrates has been reported. High resolution F MAS and F- Cd REDOR NMR spectroscopy has been used to study oxygen/fluorine ordering in oxyfluorides. Solid-state N NMR spectroscopy has been used to investigate nitrosoarene-metal interactions in model systems and in haem proteins. Phase-alternated composite pulses have 

1344 Yamada, Y. Kuranaga, K. Ueda, S. Goto, T. Okuda, and Y. Furukawa, Bull. 

1354 J Grabias andN. Pislewski, Solid State Nucl Magn. Reson., 1998,12, 37. 

Spaniol, andT. Terao, J. Magn. Reson., 1998,133, 330. 

1 Group 1. - The Li and C MAS NMR spectra of [MeLi (EtO)2CH2 i.5]co have been reported. Li and C NMR spectroscopy has been used to investigate LixCeo, and lithium insertion into carbon. Lithium doping of multi- 

Kaiser, B. Pongs, G. Fischer and E. Dormann, Phys. Lett. A, 2001, 282,125. 

Jozkow, W. Medycki, J. Zaleski, R. Jakubas, G. Bator and Z. Ciunik, P/iys. Chem. Chem. Phys., 2001,3, 3222. 

Matsumoto, Los Alamos Natl. Lab., Prepr. Arch., Condens. Matter, 2001, 1, arXivxond-mat/0011257. Los Alamos National Laboratory. Avail. URL http //xxx.lanl.gov/pdf/cond-mat/0011257. 

Walfort, L. Lameyer, W. Weiss, R. Herbst-Irmer, R. Bertermann, J. Rocha and D. Stalke, Chem.-Eur. J., 2001, 7, 1417. 

The word solid will be applied only to crystalline solids, since it is always possible to distinguish between a crystalline solid and noncrystalline phases such as liquid and amorphous solids. Structurally, the constituent particles—atoms, molecules, or ions— of a crystalline solid are arranged in an orderly, repetitive pattern in three dimensions. If we observe this pattern in some small region of the crystal, we can predict accurately the positions of particles in any region of the crystal however far they may be removed from the region of observation. The crystal has long-range order. 

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As we have outlined, a very wide variety of methods are available to calculate the electronic structure of solids. Empirical TB methods (such as discussed in section B3.2.2) are the least expensive, affordmg the... 

It can be readily confirmed thaf by decreases as the number of bonds N increases and/or llieir length (r ) decreases. This relationship between the bond strength and the number of neighbours provides a useful way to rationalise the structure of solids. Thus the high coordination of metals suggests that it is more effective for them to form more bonds, even though each individual bond is weakened as a consequence. Materials such as silicon achieve the balance for an infermediate number of neighbours and molecular solids have the smallest atomic coordination numbers. 

Gillan M J1989. Ah Initio Calculation of the Energy and Structure of Solids. Journal of the Chemical Society Faraday Transactions 2 85 521-536. 

Crystal structure of solids. The a-crystal form of TiCla is an excellent catalyst and has been investigated extensively. In this particular crystal form of TiCla, the titanium ions are located in an octahedral environment of chloride ions. It is believed that the stereoactive titanium ions in this crystal are located at the edges of the crystal, where chloride ion vacancies in the coordination sphere allow coordination with the monomer molecules. 

In the last chapter we examined data for the yield strengths exhibited by materials. But what would we expect From our understanding of the structure of solids and the stiffness of the bonds between the atoms, can we estimate what the yield strength should be A simple calculation (given in the next section) overestimates it grossly. This is because real crystals contain defects, dislocations, which move easily. When they move, the crystal deforms the stress needed to move them is the yield strength. Dislocations are the carriers of deformation, much as electrons are the carriers of charge. 

Below a temperature of Toi 260 K, the Ceo molecules completely lose two of their three degrees of rotational freedom, and the residual degree of freedom is a ratcheting rotational motion for each of the four molecules within the unit cell about a different (111) axis [43, 45, 46, 47]. The structure of solid Ceo below Tqi becomes simple cubic (space group Tji or PaS) with a lattice constant ao = 14.17A and four Ceo molecules per unit cell, as the four oriented molecules within the fee structure become inequivalent [see Fig. 2(a)] [43, 45]. Supporting evidence for the phase transition at Tqi 260 K is... 

Slater, J. C., Handbuch der Physik, Springer, Berlin, 1956, Band XIX, Elektrische Leitungsphanomene I, p. 1. The electronic structure of solids. ... 

T.L. Boggs et al, AIAA J 8 (2), 370-72 (1970) CA 72, 113371 (1970) Scanning electron microscopy is used to study the surface structure of solid proplnts, prepd from AP (1) and polyurethane or caiboxylated polybutadiene. Polyurethane proplnts are self-extinguish-ing at high pressure due to the flow of molten binder over I crystals. I crystals formed a thin surface melt with gas liberation in the molten phase... 

The arrangement of atoms, ions, and molecules within a crystal is determined by x-ray diffraction (Major Technique 3, which follows this chapter), one of the most useful techniques for determining the structures of solids. 

Predict the likely structure of solid sodium chloride. 

Self-Test 5.6A Predict the likely structure of solid ammonium chloride. Assume that the ammonium ion can be approximated as a sphere with a radius of 151 pm. 

I. V. Tomov, D. A. Oulianov, P. Chen, and P. M. Rentzepis, Ultrafast time-resolved transient structures of solids and liquids studied by means of X-ray diffraction and EXAFS. J. Phys. Chem. B 103(34), 7081-7091 (1999). 

There stiU is one aspect of phase chemistry that we have not yet addressed. That is the case where more than one solid phase exists. The basic properties of a solid include two factors, namely composition and structure. We will address structures of solids in the next chapter. The composition of solids is one where the individual constituents will vary if the solid is heterogenous. That is, the two types of inorganic solids vary according to whether they are homogeneous or heterogeneous. This is shown in the following ... 

This chapter will present more advanced topics than those of the first chapter in terms of determining the structure of solids. Consequently, you will gain some knowledge of how one goes about determining the structure of a solid, even if you never have to do it. 

In this section, we will present the basis developed to explain the structure of solids. That is, the concepts that were perfected in order to accurately describe how atoms or ions fit together to form a solid phase. This work was accomplished by many prior workers who established the rationale used to define the structure of a symmetrical solid. As you will recall, we said that the basic difference between a gas, liquid and that of a solid lay in the orderliness of the solid, compared to the other phases of the same material. 

We have already indicated that solids can have several forms or symmetries. To elucidate the structure of solids in more detail, at least three postulates apply ... 

This completes our discussion of the beisis and factors developed by past investigators to describe and conceptulize the structure of solids. You will note that we have not yet fully described the s)unmetry factor of solids. The reason for this is that we use symmetry factors to characterize solid structure without resorting to the theoretical basis of structure determination. That is, we have a standard method for categorizing solid structures. We say that salt, NaCl, is cubic. That is, the Na" ion and the Cl ion are alternately arranged in a close-packed cubic structure. The next section now investigates these structure protocols. 

We have already dlsussed structure factors and symmetry as they relate to the problem of defining a cubic unit-cell and find that still another factor exists if one is to completely define crystal structure of solids. This turns out to be that of the individual arrangement of atoms within the unit-cell. This then gives us a total of three (3) factors are needed to define a given lattice. These can be stipulated as follows ... 

In Point Groups, one point of the lattice remains invarient under symmetry operations, i.e.- there is no translation involved. Space Groups are so-named because in each group all three- dimensional space remains invarient under operations of the group. That is, they contain translation components as well as the three symmetiy operations. We will not dwell upon the 231 Space Groups since these relate to determining the exact structure of the solid. However, we will show how the 32 Point Groups relate to crystal structure of solids. 

The result is that Factor III of 2.2.6. given above imposes further symmetry restrictions on the 32 point groups and we obtain a total of 231 space groups. We do not intend to delve further into this aspect of lattice contributions to crystal structure of solids, and the factors which cause them to vary in form. It is sufficient to know that they exist. Having covered the essential parts of lattice structure, we will elucidate how one goes about determining the structure for a given solid. 

In the first chapter, we defined the nature of a solid in terms of its building blocks plus its structure and symmetry. In the second chapter, we defined how structures of solids are determined. In this chapter, we will examine how the solid actually occurs in Nature. Consider that a solid is made up of atoms or ions that are held together by covalent/ionic forces. It is axiomatic that atoms cannot be piled together and forced to form a periodic structure without mistakes being made. The 2nd Law of Thermodynamics demands this. Such mistakes seriously affect the overall properties of the solid. Thus, defeets in the lattice are probably the most important aspect of the solid state since it is impossible to avoid defects at the atomistic level. Two factors are involved ... 

We have Investigated the structure of solids In the second chapter and the nature of point defects of the solid in the third chapter. We are now ready to describe how solids react. This will Include the mechanisms Involved when solids form by reaction from constituent compounds. We will also describe some methods of measurement and how one determines extent and rate of the soUd state reaction actually taking place. We will also show how the presence and/or formation of point defects affect reactivity In solid state reactions. They do so, but not In the memner that you might suspect. We will also show how solid state reactions progress, particularly those involving silicates where several different phases appear as a function of both time and relative ratios of reacting components. 

Newnham, R. E. Roy, R. In Treatise on Solid State Chemistry The Chemical Structure of Solids Hannay, Bruce, Ed. Structural Characterization of Solids Plenum New York, 1974, Vol. 3, pp 437-529N. 

Perdew, J. P., 1991, Unified Theory of Exchange and Correlation Beyond the Local Density Approximation , in Electronic Structure of Solids, P. Ziesche, H. Eschrig (eds.), Akademie Verlag, Berlin. 

As was shown in various previous chapters, many structures of solids can be regarded as derivatives of simple, high-symmetry structure types. Let us recall some examples ... 

With this imaging system it is possible to study virtually all metals and alloys, many semiconductors and some ceramic materials. The image contrast from alloys and two-phase materials is difficult to predict quantitatively, as the effects of variations in chemistry on local field ion emission characteristics are not fully understood. However, in general, more refractory phases image more brightly in the FIM. Information regarding the structure of solid solutions, ordered alloys, and precipitates in alloys has been obtained by FIM. 

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