Crystal Chemistry

the study of the spatial arrangement and chemical bonds of atoms in crystals and of the dependence of the physical and chemical properties of crystalline substances on structure. A branch of chemistry, crystal chemistry is closely related to crystallography. The sources of experimental data on crystal structures are mainly X-ray structural analysis and electron-diffraction and neutron-diffraction studies, by which the absolute values of the interatomic distances and the angles between the chemical bond axes (valence angles) are determined. Crystal chemistry has at its disposal a wide body of knowledge on the crystal structures of several thousand chemical compounds, including proteins and viruses.

The major concerns of crystal chemistry are the systematics of crystal structure, the description of the types of chemical bonds observed in crystals, the interpretation of crystal structures (that is, the elucidation of the determinants of structure in various crystalline substances), the prediction of structure, and the study of the relationship of the physical and chemical properties of crystals to their structure and the nature of their chemical bonds.

Crystal structure displays extraordinary diversity. For example, in the case of diamond, the structure is rather simple, but it is fantastically complex in the case of crystalline boron. As a rule, every crystalline substance has its own characteristic structure. However, rather frequently (for example, in the case of NaCl and KC1, Br₂ and C1₂), different substances have nearly identical structures (isostructural compounds), and often they form mixed crystals. On the other hand, the same substance produced under various conditions may have various structures (polymorphism).

Crystal chemistry divides crystal structure into two basic types: homodesmic, or coordination, and heterodesmic. In the homodesmic structure, all of the atoms are bonded identically, the chemical bonds forming the spatial framework. There are no fragments that might be considered molecules. Homodesmic structure is found in diamond and alkali-metal halides.

Heterodesmic structure is found much more frequently. Its characteristic feature is the presence of structural fragments in which the atoms are bonded by very strong, usually covalent, bonds. The fragments may be finite atomic groups, chains, layers, or frameworks. Crystal structures are accordingly classified as insular, chained, layered, or framework.

Insular structures are found for almost all organic compounds and for such inorganic substances as the halogens, O₂, N₂, CO₂, and N₂O₄. The molecules in this case play the role of “islands,” and substances of this type are called molecular crystals. The islands are also often polyatomic ions—for example, in the case of the sulfates, nitrates, and carbonates.

The chained structure is found (for example) in one of the crystalline modifications of selenium, in which the atoms are bonded in infinite spirals, and in PdCl2 crystals, which contain infinite ribbons in the following form:

The layered structure is found for graphite, BN, and MoS₂. The framework structure is found for CaTiO₃: the titanium and oxygen atoms, covalently bonded, form an open framework in which the calcium atoms occupy the vacancies.

There are also heterodesmic structures that comprise another type of structural fragment. Thus, crystals of the chemical complex [N(CH₃)₄] [MnCl₃] are constructed of islands consisting of [N(CH₃)₄]+ ions and chains of

According to the nature of the bonds between the atoms in the case of homodesmic structures or between the structural fragments in the case of heterodesmic structures, crystals are classified as covalent (for example, SiC and diamond), ionic, metallic (metals and intermetallic compounds), and molecular. Of these, molecular crystals, in which the structural fragments are bonded by intermolecular interaction, are the most heavily represented and include the crystals of the inert gases.

The division of crystals into the groups named is to a large extent arbitrary, since the transitions from one group to another are continuous. However, the typical representatives of the various groups differ significantly in properties—in particular, in structural energy H (the energy required at atmospheric pressure and room temperature to dissociate one mole of a crystalline substance into its separate atoms, ions, or molecules).

A decrease in H corresponds to a decrease in bond strength. The sharp difference in H for Fe and Na is explained by covalent interaction, which contributes substantially to the structural energy of Fe (See Table 1).

Table 1. Values of structural energy H for certain crystals
Crystal type	Substance	H (kcal per mole)1
11 kcal per mole = 4.19 kJ per mole
Covalent ................................	SiC	283
Ionic ................................	NaCl	180
Metallic ................................		94
		26
Molecular ................................	CH4	2.4

The crystallochemical structural analysis of a substance has two aspects: stereochemistry and crystal structure. Stereochemical analysis concerns itself with the shortest interatomic distances and valence angles, using the concepts of the coordination number (that is, the number of nearest neighbors of a given atom) and the coordination polyhedron. Certain coordination numbers and polyhedra are typical for the atoms of many elements inclined to covalent bonding and result in the directedness of the covalent bonds. Thus, the beryllium atom, with rare exceptions, has a coordination number of 4 (a tetrahedron), the cadmium atom usually has its six nearest neighbors arranged in an octahedron, and the divalent palladium atom has its four nearest neighbors occupying the corners of a square (for example, in the structure of PdCl₂). The methods of quantum mechanics are usually used to explain such relationships.

The study of crystal structure involves investigation of the relative spatial arrangement within the crystalline substance of structural fragments and monatomic ions. In the case of molecular crystals, molecular packing is studied. The causes for the formation of a particular crystal structure are determined by the general thermodynamic principle that the most stable structure is that which has the lowest free energy at a given pressure and temperature. At present, approximate calculations of the free energy and prediction of the most favorable structure are possible only for comparatively simple cases, and the accuracy of such calculations is significantly lower than experimental accuracy.

Crystal chemistry shares the investigation of the dependence of the properties of crystals on their structure with the fields of crystal physics and solid-state physics.