Solids: Classification and Crystal Structure | Electrical Engineering

In this article we will discuss about the classification and crystal structure of solids.

Classification of Solids:

The classification of crystals on the basis of symmetry elements and in terms of interrelation of bond length (a, b and c) and bond angles (α, β, and ) between different crystal axes. It is equally useful to classify solids by the units that occupy the lattice sites and in terms of the bond type.

Solids may be distinguished and classified in four different bond types, each representing different type of force between their constituent units in the crystal lattice.

They are:

(a) Ionic solids- Ionic bonding

(b) Metallic solids- Metallic bonding

(c) Covalent solids- Covalent bonding

(d) Molecular solids- Molecular bonding.

These are the main groups in which solids can be broadly classified. Examples of solid substances are, however, known which exhibit properties characteristic of more than one of these groups. This type of intermediate behaviour may be observed either due to the presence of two different types of bonds in these solids or these solids may consist of bonds which are intermediate in character. Some of the physical properties associated with these solids are summarized in Table 2.6.

1. Ionic Solids:

The constituents which make up ionic solids are oppositely charged ions. The force of attraction between constituents which have very large differences in electron attracting power allows complete transfer of electrons from one constituent to another, known as ionic bonding which takes place only between metals and non-metals.

Let us consider the combination of extremely reactive metal sodium (Na) and equally reactive non-metallic gas chlorine (CI) to form sodium chloride (known as table salt). The sodium has single electron in its outer shell, which transfers to join the seven electrons in the outer shell of chlorine atom. This type of atomic attraction, involving the transfer of one electron from one atom to another, leads to formation of ions which are held together by purely electrostatic attractions.

Because of electrostatic nature of the binding force, the bond between atoms is said to be ionic or electrovalent and the solids whose constituents are held together by these electrostatic forces, are known as ionic solids. Examples of ionic solids are- NaCl, CsCl and ZnS. Since these ions are held in fixed positions, therefore, ionic solids do not conduct electricity in the solid state.

They conduct electricity in the fused state. The forces of attraction in ionic solids are very strong and therefore, they exhibit high melting points and cleave only if force is applied along certain directions. All ionic solids are hard and brittle. It may be observed that movement of layers of ions brings ions of the same charge near to each other and this causes strong repulsions which lead to the breakdown of the crystal [Fig. 2.24 (b)].

2. Metallic Solids:

The constituent units of metallic solids are positive ions. This array of positive ions are held together by the free moving electron charge cloud which arises due to the grouping of all the valence electrons, and results into metallic bonding. This type of bonding takes place when each of the atoms of the metal contributes its valence electrons to the formation of an electron cloud or gas that belongs to the entire crystal.

The valence electrons are not bonded directly to an individual atom but they move freely in the sphere of influence of other atoms and are bound to different atoms at different times and that too for a short time. This model for metallic bonding is also consistent with other properties of metals, i.e., malleability and ductility. A malleable metal can be beaten into sheets and a ductile material can be drawn into wires.

For metals to be shaped and drawn without breakup, the atoms in the lattice must be easily displaced with respect to each other. The movement does not produce any repulsive effect due to the presence of electron gas everywhere which provides a buffer between the positive ions. This situation is very different to that in ionic crystals.

They also exhibit lustre, i.e., their surface appears shiny. Since the electrons are free and are not tied to any bond, they can absorb and emit light of all wave lengths. Since electrons can move freely throughout the lattice, the metals exhibit high electrical and thermal conductivity. Examples of metallic solids include Cu, Ag, Au, Na, K etc.

3. Covalent Solids:

The structural unit in covalent solids is the atom. These atoms are bound to other atoms by shared electron pair, rather than by transfer of electrons, known as covalent bond. The solids, whose constituents are held together by strong covalent bonds, are known as covalent solids. This bonding extends throughout the crystal and as covalent bond is directional, it results in a giant interlocking structure.

For example, in diamond each carbon atom is attached to four other carbon atoms by covalent bonds. Since every atom is held rigidly in its position by four strong covalent bonds, therefore, it results in a very hard solid; diamond is the hardest substance known. We may also have two or more different elements linked together by these forces which result in building the entire lattice. In the example of quartz, the arrangement of silicon and oxygen atoms forms such a three dimensional network.

Silicon carbide (SiC) has a structure which is very similar to that of diamond except that in this solid alternate carbon atom positions are occupied by silicon atoms. In these solids the bonds are covalent and generally, are quite strong. Covalent solids usually have high melting points, are quite hard and are bad conductors of electricity. They have high latent heat of fusion and low coefficient of expansion.

4. Molecular Solids:

The constituent units of molecular solids are molecules (either polar or non-polar) rather than atoms or ions, except in solidified noble gases where the units are atoms. For the same reason these solids have relatively high coefficients of expansion. They melt at low temperatures and have low heats of fusion.

The bonding within the molecule is covalent and strong whereas the forces which operate between different molecules of the crystal lattice are the weak Van der Waals forces. These forces are due to the electrostatic interaction between the nucleus of one atom and the electrons of the other. This is largely but not completely neutralized by the electrostatic repulsion of the nucleus of one atom by the nucleus of the other.

The resultant weak attraction between the two atoms is called Van der Waals force. As a result of these weak forces, the molecular solids are soft and vaporize very readily. These solids do not conduct electricity. The electrons are localized in the bonds in each molecule. They are, therefore, unable to move from one molecule to another on the application of electric field. Examples of such solids are iodine, sulphur, phosphorus (non-polar), water, sugar (polar) etc.

Crystal Structure of Solids:

The atomic order in crystalline solids indicates that the small groups of atoms form a repetitive pattern. Thus, in describing crystal structures, it is often convenient to subdivide the structure into small repeat entities called unit cells, which when repeated in space indefinitely, will generate the space lattice. Unit cells for most crystals are parallelepiped or cubes having three sets of parallel faces.

A unit cell is chosen to represent the symmetry of the crystal structure, wherein all the atom positions in the crystal may be generated by translations of the unit cell integral distances along each of its edges. Thus, the unit cell is the basic structural unit or building block of the crystal structure by virtue of its geometry and atomic positions within. Furthermore, more than a single unit cell may be chosen for a particular crystal structure; however, we generally use the unit cell having the highest geometrical symmetry.

The unit cell is so chosen as to fulfill the following conditions:

(i) It should possess the same symmetry as the crystal structure.

(ii) If there is a choice between more than one repeating arrangements, the one which has the minimum number of atoms (i.e., smallest volume) is chosen as the unit cell. Such a unit cell is often labelled as the primitive or simple unit cell representation.

Fig. 2.5 shows a unit cell of a three-dimensional crystal lattice. The lattice is made-up of a repetition of unit cells, and a unit cell can be completely described by the three vectors a⃗, b⃗, c⃗ when the length of the vectors and the angles between them (α, β, ) are specified.

Taking any lattice point as the origin, all other points on the lattice can be obtained by a repeated operation of the lattice vectors a⃗, b⃗, c⃗. These lattice vectors and the above said interfacial angles constitute the lattice parameters of the unit cell. It is thus obvious that if the values of these intercepts and interfacial angles are known, we can easily determine the form and actual size of the unit cell.

The vectors a⃗, b⃗, c⃗ may or may not be equal. Also, the angles a, P and y may or may not be right-angles. Based on these conditions, there are seven different crystal systems. If atoms are existing only at the corners of the unit cells, the seven crystal will yield seven types of lattices.

More space lattices can be constructed by placing atoms (or particles) at the body centres of unit cells or at the centres of the faces. Bravais showed that the total number of different space lattice types (obeying the condition that every point has identical surroundings) is only fourteen, hence the term is Bravais Lattice.

Unit Cells versus Primitive Cells:

Primitive cell may be defined as a geometrical shape which, when repeated indefinitely in three dimensions, will fill all space and is the equivalent to one lattice point i.e., the unit cell that contains a lattice point only at the corners is known as primitive cell. The unit cell differs from the primitive cell in that it is not restricted to being the equivalent to one lattice point, in some cases, the two coincide, thus, unit cells may be primitive cells, but all the primitive cells need not be unit cells.

In this article we will discuss about:- 1. Characteristics of Crystalline Materials 2. Solidification and Crystallization (Crystal Growth) of Materials 3. General Feature of Non-Crystalline Structure.

Characteristics of Crystalline Materials:

The main characteristics of crystalline substances are:

(i) Orderly arrangement.

(ii) Crystals are always bounded by plane faces.

(iii) The faces of the crystals always meet at some fixed angle.

(iv) Crystalline solids exhibit anisotropy in many of their properties.

(v) The transition from the solid to liquid for crystalline solids is sharp and distinct. The absence of sharp melting point suggests that most of the amorphous solids may be best thought of as liquids.

(vi) Crystalline solids exhibit definite heats of fusion.

Solidification and Crystallization (Crystal Growth) of Materials:

In order to understand the crystalline state and its difference from the amorphous state, it is important to consider the process of solidification. Solidification is the transformation of materials from liquid to the solid state on cooling. When the liquid solidifies, the energy of each atom is reduced.

This energy is given out as latent heat during the solidification process, which for a pure metal occurs at a fixed temperature, T_s (Fig. 2.2). During solidification, the disordered structure of the liquid (constituents of material in liquid state have more velocity, more collisions and hence have random position) transforms to the orderly arrangement depending upon the time of solidification.

If the growth process is slow, the constituents take definite positions during growth. There is a tendency for the constituents to settle down in positions where the potential energy of the configuration is minimum. This leads to an ordered arrangement of the constituents which are arranged in a pattern that repeats itself in all the three dimensions.

Under these conditions a long range order exists in the solid and it is this order that characterizes the crystalline state. Various stages in the solidification of a polycrystalline specimen are represented schematically in Fig. 2.3. However, in certain extreme cases when the growth process or the phase change takes place rather quickly and the constituents do not have sufficient mobility, the constituents do not get sufficient time to obtain the configuration of minimum energy.

Consequently, a long range order, where a perfect periodicity, is maintained over much larger distances as compared to lattice periodicity, is not achieved. However, a short range order persists in local regions is still present. Solids characterized by this short range order represent the amorphous state or non-crystalline state. Sometimes such materials are called super cooled liquids in as much as their atomic structure resembles that of a liquid.

Whether a crystalline or amorphous solid form depends on the ease with which a random atomic structure in the liquid can transform to an ordered state during solidification. Amorphous materials, therefore, are characterized by atomic or are molecular structures that relatively complex and become ordered only with some difficulty. Furthermore, rapidly cooling through the freezing temperature favours the formation of a non-crystalline solid, since little time is allowed for the ordering process.

Metals normally form crystalline solids; but some ceramic materials are crystalline, whereas, the inorganic glasses are amorphous. Polymers may be completely crystalline, entirely non-crystalline, or a mixture of the two.

General Feature of Non-Crystalline Structure:

Non-crystalline materials do not have a solidification temperature as crystalline materials do; they gradually become more viscous over a range of temperature. This may be considered to be a solidification process associated with a range of energies for the bonds between sub-units.

Since all sub-units do not have identical surroundings, they do not have identical bond energies, even though the difference may be small. As a material with this type of structure cools, the lowest energy (most negative) bonds form first and begin to “stick” the sub-units together locally; then as the temperature is lowered further, the weaker bonds gradually form until the material is completely hard.

The temperature at which this solidifying material first seems to become a rigid mass is called the glass transition temperature, T_g, because at much lower temperature it tends to flow like a very viscous liquid.

Besides their common response to temperature, many non-crystalline materials are transparent, both in the liquid and solid states. Their transparency arises because they have no inclusions, holes, or internal surfaces with the right properties to scatter light, and they have no free electrons or ions which can absorb and emit light by changing their energy states. In addition to some similarities in physical properties like transparency, many non-crystalline materials also have similar mechanical properties.