Introduction:

All solids are comprised of atoms which are bonded altogether. The bonding might be of different nature based on the constituent atoms and the common energy states; however all the bonds are meant to give a certain level of attractive force to keep the atoms altogether.

What is a Bond?

A bond is the attachment between multiple atoms due to which a resistance is felt while separating them. Atoms make a bond via exchanging or sharing the electrons between partners.

It is the nature of bond in the solid which finds out the behavior of the material. Strong bonds yield in higher melting temperatures, high hardness, high elastic modulus, low coefficient of thermal expansion and so on. Lower bonding strength outcomes in the whole inferior qualities. This is the reason why we have differently behaving materials around us: a plastic water bottle acts very differently than the steel or glass bottle.

In order to comprehend the bonding in solids, we require understanding what an atom is, what its behavior is and what is the outcome. This is the reason an atom is the fundamental building block in solids.

Concept of an atom:

The atom is considered to be the smallest self adequate entity which forms any matter. It is supposed to be spherical in shape. The atom comprises of a central positively charged nucleus and a few negatively charged electrons orbiting the nucleus. The nucleus is further comprised of positively charged protons and neutrally charged neutrons. We can compare an apricot by an atom where the seed symbolizes the nucleus and the fleshy portion symbolizes the electron orbitals. The attractive force between the opposite charges and the gravitational pull altogether counter the centrifugal force acting on orbiting electrons.

The atom consists of a charge balance between the nucleus and electrons. In common, the number of electrons equivalents the number of protons. Though, the atom has the capability to gain or lose electrons under appropriate conditions and therefore become negatively or positively charged correspondingly. Atoms generally don't exchange protons as they are placed at the core. It is simpler to exchange the electrons which are at the outskirt. Whenever an atom gains or losses electron, a positively charged atom known as an anion and a negatively charged atom known as cation is obtained.

Crystal Planes and Miller Indices:

The crystal planes come from the structures termed as crystal lattices. Such lattices are (3-D) three dimensional patterns that comprise of symmetrically organized atoms intersecting three sets of parallel planes. Such parallel planes are 'crystal planes' and are employed to find out the shape and structure of the unit cell and crystal lattice. The planes intersect with one other and make 3-D shapes which encompass six faces. Such crystal planes define the crystal structure via making axes visible and are the means through which we can compute the Miller Indices.

Calculating Miller Indices:

The orientation of a surface or the crystal plane might be stated by considering how any plane intersects the major crystallographic axes of the solid. The application of a set of rules leads to the assignment of the Miller Indices, (hkl). These are the set of numbers which might be employed to recognize the plane or surface.

To compute the Miller Indices, follow these steps:

Find out the intercepts of the face all along the crystallographic axes, in terms of unit cell dimensions, then:

• Take the reciprocals
• Clear the fractions
• Decrease to lowest terms

For illustration, if x-, y-, and z- intercepts are 3, 1 and 6, the Miller indices are computed as follows:

• Take reciprocals: 1/3, 1/1, 1/6
• Clear the fractions {multiply via 6}: 2, 6, 1
• Decrease to the lowest terms (already there)

General principles to keep in mind regarding Miller Indices:

Whenever a Miller index is zero, the plane is parallel to that axis. If a Miller index is smaller, the plane is more parallel to that axis. If a Miller index is bigger, the plane is more perpendicular to that axis.

Categories of Solids:

=> Solids can be categorized into three categories on the basis of how the particles that form the solid pack.

1) Crystalline solids are the (3-D) three-dimensional analogs of a brick wall. They encompass a regular structure, in which the particles pack in the repeating pattern from one edge of the solid to the other.

2) Amorphous solids (literally, "solids with no form") encompass an arbitrary structure, having little if any long-range order.

3) Polycrystalline solids are the aggregate of a large number of small crystals or grains in which the structure is regular; however the crystals or grains are arranged in an arbitrary fashion.

The extent to which a solid is crystalline consists of significant effects on its physical properties.

Illustrations: The polyethylene utilized to make sandwich bags and garbage packs is an amorphous solid that comprise of more or less arbitrarily oriented chains of (-CH₂-CH₂-) linkages. Milk bottles are made up from a more crystalline form of polyethylene, and they encompass a much more rigid structure.

=> Categories of Solids Based on Bonds that Hold the Solid Together

Solids can be categorized on the basis of the bonds that hold the atoms or molecules altogether. This approach classifies solids as molecular, covalent, ionic and metallic.

Iodine (I₂), sugar (C₁₂H₂₂O₁₁), and polyethylene are illustrations of compounds that are molecular solids at room temperature. Water and bromine are liquids that form the molecular solids whenever cooled slightly; H₂O freezes at 0^oC and Br₂ freezes at -7^oC.

1) Molecular solids are characterized by relatively strong intramolecular bonds between the atoms that form the molecules and much weaker intermolecular bonds between these molecules. Because the intermolecular bonds are relatively weak, molecular solids are often soft substances with low melting points.

Dry ice, or solid carbon-dioxide, is a perfect illustration of a molecular solid. The van der Waals forces holding the CO₂ molecules altogether are weak adequate that dry ice sublimes--it passes directly from the solid to the gas phase at 78^oC.

2) Covalent solids, like diamond, form crystals that can be assumed as a single giant molecule made up of an almost endless number of covalent bonds. Each and every carbon atom in diamond is covalently bound to four other carbon atoms oriented in the direction of the corners of a tetrahedron. As all of the bonds in this structure are uniformly strong, covalent solids are often very hard and they are notoriously hard to melt. Diamond is the hardest natural substance and it melts at around 3550^oC.

3) Ionic solids are the salts, like NaCl, which are held altogether by the strong force of attraction between the ions of opposite charge.

F = (q₁ x q₂)/r²

Due to this force of attraction based on the square of the distance between the positive and negative charges, the strength of an ionic bond based on the radii of the ions which form the solid. As such ions become larger, the bond becomes weaker. However the ionic bond is still strong adequate to make sure that salts encompass relatively high melting points and boiling points.

4) To understand metallic solids we have to clear up a general misconception regarding chemical bonds. Ionic and covalent bonds are often assumed as if they were opposite ends of a two-dimensional model of bonding in which the compounds that consists of polar bonds fall somewhere among these extremes.

Ionic........ Polar........Covalent

In actuality, there are three types of bonds between the adjacent atoms: ionic, covalent and metallic. The force of attraction between the atoms in metals, like copper and aluminum, or alloys like bronze and brass are the metallic bonds.

Types of bonding in Solids:

There are mainly three kinds of bonds:

• Ionic bond
• Covalent bond
• Metallic bond

1) Ionic Bonding:

Ionic crystals are such compounds in which the valence electrons are fully transferred from one atom to the other; the final outcome being a crystal which is comprised of negatively and positively charged ions. The atom whose outermost shell consists of only a few electrons given up these electrons in such a way that it is left by completely filled outermost shell. This method is known as ionization. On the other hand if the outermost shell is slightly short of (8-electrons) eight electrons, then the atom consists of a tendency to get the electrons and become an ion.

The atom of sodium metal consists of one electron in its outermost shell and it can be simply liberated by a sodium positive ion left with. This electron can be simply added to the outermost shell of chlorine having already seven electrons. This chlorine atom becomes the negative ion. Due to the mutual attraction between negative and positive ions, a bond is developed between such two ions of opposite charges. The outermost electron of sodium is eliminated via supplying 495 x 10³ kJ/kmol (known ad first ionization potential of sodium).

Na + E₁ → Na⁺ + e^-1

This liberated electron will now move to engage the outermost shell of chlorine (with already 7 electrons) and generate a negatively charged ion.

Cl + e^-1 → Cl^-

The electron affinity of chlorine is around 370 x 10³ kJ/kmol. Therefore total increase in potential energy for transferring an electron from sodium to chlorine is 125 x 10³ kJ/kmol. The chemical reactions in the formation of NaCl at equilibrium spacing are illustrated below:

Fig: Formation of ionic molecule of sodium chloride

Na + Cl → Na⁺ + Cl^- → NaCl

As chlorine as exists as molecules, the chemical reaction should be represented as:

2Na + Cl₂ → 2Na⁺ + 2Cl^- → 2NaCl

2) The Covalent bond:

The existence of compounds like H₂, N₂ and O₂ and also bonds in atomic crystals like diamond can't be accounted for via ionic bonds as atoms of only one type can't produce ions of opposite type by transfer of electrons. The bonds which exist between atoms of the similar type are termed as covalent bonds. In a covalent bond, the electrons from the outermost shell are shared through both the atoms. This might happen among the two atoms of same kind or different types. It might as well be noted in this bond, the shared outer electrons belong to both the atoms and not to this one or the other. Thus, both the atoms are neutral even after the formation of bond. This is due to this reason that solids made by such bond are generally termed as non-polar substances.

The balance between the attractive and repulsive forces in hydrogen molecule takes place at a separation of 0.074 nm. Therefore some energy should be spent to break the covalent bond in a hydrogen molecule into hydrogen atoms. Around 4.5 eV energy is needed to break one bond between the hydrogen atoms, that is,

H₂ + 4.5 eV → H + H

The covalent bond among the two hydrogen atoms in a hydrogen molecule is symbolized as:

H : H

3) Metallic Bond:

Metallic elements encompass low ionization energies and therefore, in this bonding, atoms of the similar element or different elements provide their valence electrons to form an electron cloud or state 'electron gases' all through the space occupied by the atoms. Having given up their valence electrons, the atoms are actually positive ions. These are held altogether through forces which are identical to those of ionic bond in that they are mainly electrostatic, however are between the ions and the electrons. Most of the atoms in metals encompass one or two valence electrons.

Such electrons are loosely held by their atoms and thus can be simply released to the common pool to form an electron cloud. The electrostatic interaction among the positive ions and the electron gas holds the metal altogether. The high electrical and thermal conductivities of metals follow from the capability of the free electrons to migrate via their crystal lattices whereas all of the electrons in ionic and covalent crystals are bound to specific atoms.

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