Properties of bulk solids

The inherent problems associated with the computation of the properties of solids have been reduced by a computational technique called Density Functional Theory. This approach to the calculation of the properties of solids again stems from solid-state physics. In Hartree-Fock equations the N electrons need to be specified by 3/V variables, indicating the position of each electron in space. The density functional theory replaces these with just the electron density at a point, specified by just three variables. In the commonest formalism of the theory, due to Kohn and Sham, called the local density approximation (LDA), noninteracting electrons move in an effective potential that is described in terms of a uniform electron gas. Density functional theory is now widely used for many chemical calculations, including the stabilities and bulk properties of solids, as well as defect formation energies and configurations in materials such as silicon, GaN, and Agl. At present, the excited states of solids are not well treated in this way. 

While mechanical testing of all types provides a general description of the bulk properties of solid propellants, it is difficult to make generalizations or even extrapolations which may be used in a predictive fashion. When the content or type of solid filler is changed, or curative ratios are altered, there is no simple corresponding material property change which can be defined based on mechanical testing experience. If filler content... 

Gupta, M.K. Goldman, D. Bogner, R.H. Tseng, Y.C. Enhanced drug dissolution and bulk properties of solid dispersions granulated with a surface adsorbent. Pharm. Dev. Technol. 2001, 6, 563-572. 

The BFS method has been applied to a variety of problems, ranging from the determination of bulk properties of solid solution fee and bee alloys and the defeet strueture in ordered bee alloys [28] to more speeifie applieations ineluding detailed studies of the strueture and eomposition of alloy surfaees [29], ternary [30] and quaternary alloy surfaees and bulk alloys [31,32], and even the determination of the phase strueture of a 5-element alloy [33]. Previous appheations have foeused on fundamental features in monatomie [26] and alloy surfaces [29] surface energies, reconstructions, surface structure and surface segregation in binary and higher order alloys [34,35] and multilayer relaxations [36,37]. While most of the work deals with metallic systems, the lack of restrictions on the type of system that can be studied translated into the extension of BFS to the study of semiconductors [38]. 

A most significant aspect of the chemistry of niobium and tantalum has been the development of heterogeneous catalysis and its relationship to the surface and bulk properties of the solid supports.668-679 In this concluding section, molecular connections between fundamental coordination chemistry and surface and bulk properties of solids, particularly the oxides, are emphasized. A broad description of Nb compounds and heterogeneous catalysis is available.670... 

IGC is a gas phase technique for characterizing surface and bulk properties of solid materials. The principles of IGC are very simple, being the reverse of a conventional gas chromatographic (GC) experiment. A cylindrical column is uniformly packed with the solid material of interest, typically a powder, fiber, or film. A pulse or constant concentration of gas is then injected down the column at a fixed carrier gas flow rate, and the time taken for the pulse or concentration front to elute down the column is measured by a detector. A series of IGC measurements with different gas phase probe molecules then allows access to a wide range of physicochemical properties of the solid sample. The flow and retention of gas is shown in Figure 3. 

It is apparent that both these acoustic TA techniques examine the fine-structure associated with solid-state thermal events. Thus, these techniques are particularly suitable for a detailed TA of surface and bulk properties of solids, together with lattice imperfections. Microimpurities and the interactions of these with the host are also able to be evaluated by these specialized techniques. In particular, water inclusions in a host lattice can, in principle, be characterized in terms of the degree of bonding involved and the dehydration characteristics of the material under examination can be determined. These techniques have major analytical potential in materials science, mainly in terms of providing refinements to the traditional understanding of solid-state physical phenomena. 

In this section, we describe the applications of the density functional pseudopotential scheme to the bulk properties of solids. Since this is a very active area, only specific prototypical calculations are featured to illustrate major subareas. The results on semiconductors were calculated using the plane wave method whereas results on transition metals and insulators were obtained either using the mixed basis approach or the LCAO approach. 

This book gives an account of the bulk properties of solids and liquids (and, particularly, their response to external forces) and an attempt is made to show how many of these properties can be explained in terms of the intermolecular forces and the internal energy. In this chapter a simple account is given of the most important properties of solids and liquids in terms of intermolecular forces. No detailed account of the origin of these forces is given, but the basic features are described and characterised. 

A useful approximation of B for a conical hopper is B = 22f/a, where a is the bulk density of the stored product. The apparatus for determining the properties of solids has been developed and is offered for sale by the consulting firm of Jenike and Johansen, Winchester, Massachusetts, which also performs these tests on a contract basis. The flow-factor FF tester, a constant-rate-of-strain, direct-shear-type machine, gives the locus of points for the FF cui ve as well as ( ), the... 

The molecular and bulk properties of the halogens, as distinct from their atomic and nuclear properties, were summarized in Table 17.4 and have to some extent already been briefly discussed. The high volatility and relatively low enthalpy of vaporization reflect the diatomic molecular structure of these elements. In the solid state the molecules align to give a layer lattice p2 has two modifications (a low-temperature, a-form and a higher-temperature, yS-form) neither of which resembles the orthorhombic layer lattice of the isostructural CI2, Br2 and I2. The layer lattice is illustrated below for I2 the I-I distance of 271.5 pm is appreciably longer than in gaseous I2 (266.6 pm) and the closest interatomic approach between the molecules is 350 pm within the layer and 427 pm between layers (cf the van der Waals radius of 215 pm). These values are... 

We have to refine our atomic and molecular model of matter to see how bulk properties can be interpreted in terms of the properties of individual molecules, such as their size, shape, and polarity. We begin by exploring intermolecular forces, the forces between molecules, as distinct from the forces responsible for the formation of chemical bonds between atoms. Then we consider how intermolecular forces determine the physical properties of liquids and the structures and physical properties of solids. 

Praliaud, H., Mikhailenko, S., Chajar, Z. et al. (1998) Surface and bulk properties of Cu—ZSM-5 and Cu/A1203 solids during redox treatments. Correlation with the selective reduction of nitric oxide by hydrocarbons, Appl. Catal. B, 16, 359. 

In the Introduction the problem of construction of a theoretical model of the metal surface was briefly discussed. If a model that would permit the theoretical description of the chemisorption complex is to be constructed, one must decide which type of the theoretical description of the metal should be used. Two basic approaches exist in the theory of transition metals (48). The first one is based on the assumption that the d-elec-trons are localized either on atoms or in bonds (which is particularly attractive for the discussion of the surface problems). The other is the itinerant approach, based on the collective model of metals (which was particularly successful in explaining the bulk properties of metals). The choice between these two is not easy. Even in contemporary solid state literature the possibility of d-electron localization is still being discussed (49-51). Examples can be found in the literature that discuss the following problems high cohesion energy of transition metals (52), their crystallographic structure (53), magnetic moments of the constituent atoms in alloys (54), optical and photoemission properties (48, 49), and plasma oscillation losses (55). 

Every example of a vibration we have introduced so far has dealt with a localized set of atoms, either as a gas-phase molecule or a molecule adsorbed on a surface. Hopefully, you have come to appreciate from the earlier chapters that one of the strengths of plane-wave DFT calculations is that they apply in a natural way to spatially extended materials such as bulk solids. The vibrational states that characterize bulk materials are called phonons. Like the normal modes of localized systems, phonons can be thought of as special solutions to the classical description of a vibrating set of atoms that can be used in linear combinations with other phonons to describe the vibrations resulting from any possible initial state of the atoms. Unlike normal modes in molecules, phonons are spatially delocalized and involve simultaneous vibrations in an infinite collection of atoms with well-defined spatial periodicity. While a molecule s normal modes are defined by a discrete set of vibrations, the phonons of a material are defined by a continuous spectrum of phonons with a continuous range of frequencies. A central quantity of interest when describing phonons is the number of phonons with a specified vibrational frequency, that is, the vibrational density of states. Just as molecular vibrations play a central role in describing molecular structure and properties, the phonon density of states is central to many physical properties of solids. This topic is covered in essentially all textbooks on solid-state physics—some of which are listed at the end of the chapter. 

More recently, Yang and Thompson implemented this type of sensor in FI manifolds, which they consider ideal environments for relating the sensor s hydrodynamic response to the analyte s concentration-time profile produced by the dispersion behaviour of sample zones. Network analysis of the sensor generates multi-dimensional information on the bulk properties of the liquid sample and surface properties at the liquid/solid interface. The relationship between acoustic energy transmission and the interfacial structure, viscosity, density and dielectric constant of the analyte have been thoroughly studied by using this type of assembly [171]. 

In surface studies, one is confronted with the difficulty of detecting a small number of surface atoms in the presence of a large number of bulk atoms a typical solid surface has 10 atoms/cm as compared with 10 atoms/cm in the bulk. In order to be able to probe the properties of solid surfaces using conventional methods, one needs the use of powders with very high surface-to-volume ratio so that surface effects become dominant. However, this technique suffers from the distinct disadvantage of an entirely uncontrolled surface structure and composition which are known to play an important role in surface chemical reactions. It is thus desirable to use specimens with well-defined surfaces which generally means small surface area, of the order of 1 cm, and examine them with tools that are surface sensitive. 

Considering the method of preparation of these ZnO samples, these results correspond to what one would expect on the basis of the adsorption model. The samples were sintered or evaporated at some high temperature, and then cooled to room temperature in air. As discussed in Section IV, 1, adsorption will occur until the rate of electrons crossing the surface barrier is pinched off to zero at room temperature. If the temperature is now lowered below room temperature, no electron transfer will be possible between the surface level and the bulk of the solid due to this high surface barrier. Thus the surface levels will be isolated and unable to affect the conductivity, which will therefore reflect bulk properties of the zinc oxide. 

The familiar bulk properties of a solid, liquid, and gas. (a) The submicroscopic particles of the solid phase vibrate about fixed positions, (b) The submicroscopic particles of the liquid phase slip past one another. 

In this section, these influences will be described. Besides the acidic properties, the absorption properties of solid heteropolyacids for polar molecules are often critical in determining the catalytic function in pseudoliquid phase behavior. This is a new concept in heterogeneous catalysis by inorganic materials and is described separately in Section VI. With this behavior, reactions catalyzed by solid heteropoly compounds can be classified into three types surface type, bulk type I, and bulk type II (Sections VII and IX). Softness of the heteropolyanion is important for high catalytic activity, although the concept has not yet been sufficiently clarified. 

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