Structures of Some Crystalline Solids

We have described the structure of crystals in a general way. Now we want to look in detail at the structure of several crystalline solids that represent the different types molecular, metallic, ionic, and covalent network. 

Liquid-crystal displays use nematic hquid crystals. The molecular order in a nematic hquid crystal, which results from weak intermolecular forces, is easily disrupted. For this reason, the hquid crystals flow like a hquid. Because of the weakness of the intermolecular forces, the molecules in a nematic phase are easily reahgned along new directions. 

A liquid-crystal display uses this ease of molecular reorientation to change areas of the display from light to dark. 

The rodlike molecules are aligned in the same direction, although the positions of the molecules are random. 

The simplest molecular solids are the frozen noble gases—for example, solid neon. In this case, the molecules are single atoms and the intermolecular interactions are London forces. These forces are nondirectional (in contrast to covalent bonding, which is directional), and the maximal attraction is obtained when each atom is surrounded by the largest possible number of other atoms. The problem, then, is simply to find how identical spheres can be packed as tightly as possible into a given space. 

---

The forward search starts from the name of a chemical compound, proceeds to finding its molecular structure, and then its physical and chemical properties, such as the boiling point, melting point, density, etcetera, in a handbook. Many databases for single compounds are also organized by classes and families of similar structures. Fluid solutions represent the next level of complexity. For the most important fluids, such as water, air, and some refrigerants, we can find extensive tables for the thermal properties of mixtures. For complex fluids, such as paint and emulsion, which are difficult to characterize and to reproduce, specialized books and journals should be consulted. The properties of some crystalline solids can be found, but usually not for multicrystal composite and amorphous solids. 

To specify the complete structure of a crystalline solid it is only necessary to show one unit cell, but interpreting these pictures requires practice. Figure 1 shows some views of the cesium chloride structure (CsCl, depicted as MX). 

Solids cannot be understood as well as the much simpler units of matter, the atoms and molecules. There are some simplifying features of solids, however, which allow considerable insight into their nature. One of these features is the regularity in the structure of all crystalline solids, as a consequence of which an entire macrocrystal consists of a three-dimensional replication of a basic unit of atoms, ions, or molecules arranged in a fixed way. 

The simplest diamine, hydrazine N2H4 (Table 3), is normally available as the monohydrate. An X-ray structure of the crystalline solid has been determined (there is some doubt as to the correct space group ) as well as an electron diffraction study of the vapor.The structxues of the di(hydrogen fluoride), di(hydrogen chloride) and monoperchlorate crown ether salts are also known. The N—N distance in hydrazine (1.499 A) is an important parameter, as one half this distance is used for the covalent radius of the single-bonded nitrogen atom. 

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 . 

Kflvankova, I., Marcisinova, M. and Sohnel, 0. Solubility of itaconic and kojic acids, J. Chem. Eng. Data, 37(l) 23-24,1992. Kronberger, H. and Weiss, J. Formation and structure of some organic molecular compounds. III. The dielectric polarization of some solid crystalline molecular compounds, J. Chem. Soc. (London), pp. 464-469, 1944. 

Hydroxycarboxylate compounds of Mn111 are known for salicylates and various aliphatic acids.299 Some crystalline solids have been isolated, including bis-chelate species of the salicylates M[Mn(X-sal)2L2] (L = H20, py) but the only tris-chelate compound isolated is the black Cs3[Mn (CF2)2C(0)COO 3]. Various red or green crystalline solids also are known with tartrate ligands and they are reasonably robust, but no structural data are available. 

Since our surroundings are three-dimensional, we tend to assume that crystals are formed by periodic arrangements of atoms or molecules in three dimensions. However, many crystals are periodic only in two, or even in one dimension, and some do not have periodic structure at all, e.g. solids with incommensurately modulated structures, certain polymers, and quasicrystals. Materials may assume states that are intermediate between those of a crystalline solid and a liquid, and they are called liquid crystals. Hence, in real crystals, periodicity and/or order extends over a shorter or longer range, which is a function of the nature of the material and conditions under which it was crystallized. Structures of real crystals, e.g. imperfections, distortions, defects and impurities, are subjects of separate disciplines, and symmetry concepts considered below assume an ideal crystal with perfect periodicity. ... 

Upon release of supersaUiration, the initially dissolved compound will be separated from the solution and form a secondary phase, which could be either oil, amorphous solid, or crystalline solid. Crystalline materials are solids in which molecules are arranged in a periodical three-dimensional pattern. Amorphous materials are solids in which molecules do not have a periodical three-dimensional pattern. Under some circumstances with very high supersaturation, the initial secondary phase could be a liquid phase, i.e., oil, in which molecules could be randomly arranged in three-dimensional patterns and have much higher mobility than solids. Generally, the oil phase is unstable and will convert to amorphous material and/or a crystalline solid over time. At a lower degree of supersaturation, an amorphous solid can be generated. Like the oil, the amorphous solid is unstable and can transform into a crystalline solid over time. Even as a crystalline solid, there could be different solid states with different crystal structures and stability. The formation of different crystalline solid states is the key subject of polymorphism, which will be mentioned below and... 

There is, in principle, nothing which limits the self-consistent field method to any particular form of the exchange-correlation potential, and the procedure outlined above has been used in connection with several approximations for exchange and correlation. Most notable in this respect is SLATER S Xa method [1.4] which has been applied to all atoms in the periodic table, to some molecules, and in the majority of the existing electronic-structure calculations for crystalline solids. 

An implicit assumption made in deriving the Debye equations is that of a single relaxation time. In other words, the heights of the barriers are identical for all sites. And while this may be true for some crystalline solids, it is less likely to be so for an amorphous solid such as a glass, where the random nature of the structure will likely lead to a distribution of relaxation times. 

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. 

In the case of a crystalline solid it is possible to determine, by diffraction methods, the equilibrium positions and vibrational amplitudes of all the atoms involved and this information specifies the structure of the crystal. A liquid, by its very nature, cannot have a structure in this sense. The environment of each atom or molecule is continually changing and we must usually be satisfied with some sort of time-averaged specification of the environment or, which is essentially the same thing in this case, a space average over the environments of many different molecules. 

Interpretation of mechanical measurements in terms of molecular structure was until fairly recently confined essentially to identification of the temperatures of the major viscoelastic relaxations through extensional or torsional dynamic mechanical studies. Now, however, investigations of the elastic constants and their temperature dependence—allied with dynamic mechanical, creep and both wide and small angle X-ray diffraction— are yielding fairly detailed pictures of the interrelation of the crystalline and less well ordered regions of some oriented solid polymers. 

---