Crystalline solids defined

The three-dimensional synnnetry that is present in the bulk of a crystalline solid is abruptly lost at the surface. In order to minimize the surface energy, the themiodynamically stable surface atomic structures of many materials differ considerably from the structure of the bulk. These materials are still crystalline at the surface, in that one can define a two-dimensional surface unit cell parallel to the surface, but the atomic positions in the unit cell differ from those of the bulk structure. Such a change in the local structure at the surface is called a reconstruction. 

For tire purjDoses of tliis review, a nanocrystal is defined as a crystalline solid, witli feature sizes less tlian 50 nm, recovered as a purified powder from a chemical syntliesis and subsequently dissolved as isolated particles in an appropriate solvent. In many ways, tliis definition shares many features witli tliat of colloids , defined broadly as a particle tliat has some linear dimension between 1 and 1000 nm [1] tire study of nanocrystals may be drought of as a new kind of colloid science [2]. Much of die early work on colloidal metal and semiconductor particles stemmed from die photophysics and applications to electrochemistry. (See, for example, die excellent review by Henglein [3].) However, the definition of a colloid does not include any specification of die internal stmcture of die particle. Therein lies die cmcial distinction in nanocrystals, die interior crystalline stmcture is of overwhelming importance. Nanocrystals must tmly be little solids (figure C2.17.1), widi internal stmctures equivalent (or nearly equivalent) to drat of bulk materials. This is a necessary condition if size-dependent studies of nanometre-sized objects are to offer any insight into die behaviour of bulk solids. 

Cane sugar is generally available ia one of two forms crystalline solid or aqueous solution, and occasionally ia an amorphous or microcrystalline glassy form. Microcrystalline is here defined as crystals too small to show stmcture on x-ray diffraction. The melting poiat of sucrose (anhydrous) is usually stated as 186°C, although, because this property depends on the purity of the sucrose crystal, values up to 192°C have been reported. Sucrose crystallines as an anhydrous, monoclinic crystal, belonging to space group P2 (2). 

Clinoptilolite is microporous crystalline solid with well-defined structure, which have great potential for a number of applications in various fields, such as adsorption, separation, ion-exchange and catalysis. 

Melamine, a non-hygroscopic, white crystalline solid, melts with decomposition above 347°C and sublimes at temperatures below the melting point. It is only slightly soluble in water 100 ml of water dissolve 0.38 g at 20°C and 3.7 g at 90°C. It is weakly basic and forms well-defined salts with acids. 

For a substance to dissolve in a liquid, it must be capable of disrupting the solvent structure and permit the bonding of solvent molecules to the solute or its component ions. The forces binding the ions, atoms or molecules in the lattice oppose the tendency of a crystalline solid to enter solution. The solubility of a solid is thus determined by the resultant of these opposing effects. The solubility of a solute in a given solvent is defined as the concentration of that solute in its saturated solution. A saturated solution is one that is in equilibrium with excess solute present. The solution is still referred to as saturated, even... 

FIGURE 5-16 Crystalline solids have well-defined faces and an orderly internal structure. Each face of the crystal is formed by the top plane of an orderly stack of atoms, molecules, or ions. 

A crystalline solid is a solid in which the atoms, ions, or molecules lie in an orderly array (Fig. 5.16). A crystalline solid has long-range order. An amorphous solid is one in which the atoms, ions, or molecules lie in a random jumble, as in butter, rubber, and glass (Fig. 5.17). An amorphous solid has a structure like that of a frozen instant in the life of a liquid, with only short-range order. Crystalline solids typically have flat, well-defined planar surfaces called crystal faces, which lie at definite angles to one another. These faces are formed by orderly layers of atoms (Box 5.1). Amorphous solids do not have well-defined faces unless they have been molded or cut. 

To answer this question we need to consider the kind of physical techniques that are used to study the solid state. The main ones are based on diffraction, which may be of electrons, neutrons or X-rays (Moore, 1972 Franks, 1983). In all cases exposure of a crystalline solid to a beam of the particular type gives rise to a well-defined diffraction pattern, which by appropriate mathematical techniques can be interpreted to give information about the structure of the solid. When a liquid such as water is exposed to X-rays, electrons or neutrons, diffraction patterns are produced, though they have much less regularity and detail it is also more difficult to interpret them than for solids. Such results are taken to show that liquids do, in fact, have some kind of long-range order which can justifiably be referred to as a structure . 

Crystalline solids are built up of regular arrangements of atoms in three dimensions these arrangements can be represented by a repeat unit or motif called a unit cell. A unit cell is defined as the smallest repeating unit that shows the fuU symmetry of the crystal structure. A perfect crystal may be defined as one in which all the atoms are at rest on their correct lattice positions in the crystal structure. Such a perfect crystal can be obtained, hypothetically, only at absolute zero. At all real temperatures, crystalline solids generally depart from perfect order and contain several types of defects, which are responsible for many important solid-state phenomena, such as diffusion, electrical conduction, electrochemical reactions, and so on. Various schemes have been proposed for the classification of defects. Here the size and shape of the defect are used as a basis for classification. 

Solid solutions are very common in crystalline solids. A solid solution may be defined as a single crystalline phase with variable composition. In general, these... 

Fig. 15 Cooling curves of crystallinity (solid line) and demixing parameter of comonomers (dashed line). The latter is defined as the mean fraction of neighboring sites occupied by other comonomers around each comonomer. The cooling program is a stepwise increase of Ep/(k T) from zero with a step length of 0.002 and a step period of 300 Monte Carlo cycles, a The slightly alternating copolymer with a comonomer mole fraction 0.36 b the heterogeneous copolymer with a comonomer mole fraction of 0.36 [52]...

When the reaction was attempted with Cl2C=IrCl3(PPh3)2 a crystalline solid, which was a green color typical of osmium carbyne complexes, could be observed at -78°C, but attempts to characterize this solid at room temperature were unsuccessful (39). No well-defined carbyne complexes of iridium have been reported to date. 

For crystalline solids, comparative quantities for second harmonic generation and the linear electrooptic coefficient are given by Miller s delta and the polarization optic coefficient f. The quantity 6 is defined by the relation... 

Unlike the case of diffraction of light by a ruled grating, the diffraction of x-rays by a crystalline solid leads to the observation that constructive interference (i.e., reflection) occurs only at the critical Bragg angles. When reflection does occur, it is stated that the plane in question is reflecting in the nth order, or that one observes nth order diffraction for that particular crystal plane. Therefore, one will observe an x-ray scattering response for every plane defined by a unique Miller index of (h k l). 

The model fundamental to all analyses of vibrational motion requires that the atoms in the system oscillate with small amplitude about some defined set of equilibrium positions. The Hamiltonian describing this motion is customarily taken to be quadratic in the atomic displacements, hence in principle a set of normal modes can be found in terms of these normal modes both the kinetic energy and the potential energy of the system are diagonal. The interaction of the system with electromagnetic radiation, i.e. excitation of specific normal modes of vibration, is then governed by selection rules which depend on features of the microscopic symmetry. It is well known that this model can be worked out in detail for small molecules and for crystalline solids. In some very favorable simple cases the effects of anharmonicity can be accounted for, provided they are not too large. 

Clearly, the most prominent imperfection in a crystalline solid is its surface, since it represents a cutoff of the lattice periodicity. The surface can be defined as constituting one atomic-molecular layer. This definition is sometimes not particularly useful, however. lu certaiu cases the system or property of iuterest requires that additioual layers be cousidered as the surface. ... 

Liquid crystal polymers (LCP) are polymers that exhibit liquid crystal characteristics either in solution (lyotropic liquid crystal) or in the melt (thermotropic liquid crystal) [Ballauf, 1989 Finkelmann, 1987 Morgan et al., 1987]. We need to define the liquid crystal state before proceeding. Crystalline solids have three-dimensional, long-range ordering of molecules. The molecules are said to be ordered or oriented with respect to their centers of mass and their molecular axes. The physical properties (e.g., refractive index, electrical conductivity, coefficient of thermal expansion) of a wide variety of crystalline substances vary in different directions. Such substances are referred to as anisotropic substances. Substances that have the same properties in all directions are referred to as isotropic substances. For example, liquids that possess no long-range molecular order in any dimension are described as isotropic. 

A point group is the symmetry group of art object of finite extent, such as an atom or molecule. (Infinite lattices, occruring in the theory of crystalline solids, have translational symmetry in addition.) Specifying the point group to which a molecule belongs defines its symmetry completely. 

In the diffraction pattern from a crystalline solid, the positions of the diffraction maxima depend on the periodicity of the stmcmre (i.e. the dimensions of the unit cell), whereas the relative intensities of the diffraction maxima depend on the distribution of scattering matter (i.e. the atoms or molecules) within the unit cell. In the case of XRD, the scattering matter is the electron density within the unit cell. Each diffraction maximum is characterized by a unique set of integers h, k and I (Miller indices) and is defined by a scattering vector H in three-dimensional... 

Ultraphosphates are defined as phosphates in which the ratio Me1 is less than unity. The existence of such compounds, e.g. Ag2P60,o, PbP6Oio and Ca2PeOi7, was detected in the corresponding melts some time ago (165) and the compounds CaP4Ou and CasPeOn were described as crystalline solid phases (136). In such compounds P04 tetrahedra must be present which are linked by three of their O atoms with neighboring P atoms (349). 

The specific conductivity of a large number of oxide melts is in excess of 1 ohm-1 cm-1 and the temperature coefficient of conductance is positive. Two types of experiments from which conclusions are drawn regarding the mechanism of conduction are to be found in the literature. In one, the applicability of Faraday s laws is directly tested. In the second case, the conductivity of both the crystalline solid up to the melting point and that of the melt is measured if the change in specific conductivity on fusion is negligible, and if the so-called activation energy EK defined by... 

The state of polarization, and hence the electrical properties, responds to changes in temperature in several ways. Within the Bom-Oppenheimer approximation, the motion of electrons and atoms can be decoupled, and the atomic motions in the crystalline solid treated as thermally activated vibrations. These atomic vibrations give rise to the thermal expansion of the lattice itself, which can be measured independendy. The electronic motions are assumed to be rapidly equilibrated in the state defined by the temperature and electric field. At lower temperatures, the quantization of vibrational states can be significant, as manifested in such properties as thermal expansion and heat capacity. In polymer crystals quantum mechanical effects can be important even at room temperature. For example, the magnitude of the negative axial thermal expansion coefficient in polyethylene is a direct result of the quantum mechanical nature of the heat capacity at room temperature." At still higher temperatures, near a phase transition, e.g., the assumption of stricdy vibrational dynamics of atoms is no... 

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