Solid State

The Solid State

Solids are chemical substances characterized by a defined shape and volume, rigidity, high density, and low compressibility. The constituent particles (atoms, molecules, or ions) in solids are closely packed and held together by strong interparticle forces. Solids surround us and are used more frequently than liquids and gases. For various applications, we require solids with a wide range of properties, which depend on the nature of the constituent particles and the binding forces between them.

Therefore, studying the structure of solids is important. Understanding the correlation between structure and properties aids in discovering new solid materials with desired characteristics. These include high-temperature superconductors, magnetic materials, biodegradable polymers for packaging, and biocompatible solids for surgical implants.

1.0General Characteristics of Solid State

Under specific temperature and pressure conditions, a substance's most stable state depends on the balance between intermolecular forces and thermal energy. Lower temperatures favor intermolecular forces, leading to the solid state, where particles maintain fixed positions but oscillate slightly.

Solids have:

definite mass, volume, and shape,
short intermolecular distances,
strong intermolecular forces,
and are incompressible and rigid.

2.0Amorphous and Crystalline Solids

Amorphous and crystalline solids are two fundamental classifications in solid-state physics and materials science. Let's delve into each:

Amorphous solids lack a regular, repeating atomic structure. Instead, their atoms or molecules are arranged randomly, without any long-range order.. Their lack of a distinct crystalline structure gives them unique properties, such as isotropy (uniform properties in all directions) and a characteristic absence of sharp melting points.
Crystalline solids are characterized by a highly ordered, repeating atomic or molecular structure known as a crystal lattice. This regular arrangement extends over long distances, giving crystalline solids distinct properties like anisotropy (directional dependence of properties) and sharp, well-defined melting points.

Crystalline Solids	Amorphous Solids
Have a highly ordered and repetitive atomic or molecular structure	Lack long-range order in their atomic or molecular arrangement.
Exhibit well-defined geometric shapes.	Have irregular shapes and lack specific geometric patterns.
Possess sharp and distinct melting points	Soften gradually over a range of temperatures rather than having a distinct melting point
Display regular patterns when viewed under a microscope.	Show no regular patterns when observed under a microscope.
When cut with a sharp edged tool, they split into two pieces and the newly generated surfaces are plain and smooth	When cut with a sharp edged tool, they cut into two pieces with irregular surfaces
Anisotropic in nature	Isotropic in nature
True solids	Pseudo solids or super cooled liquids
Examples include salt, sugar, and diamond.	Examples include glass, rubber, and some plastics

3.0Classification of Crystalline Solids

Crystalline solids can be classified on the basis of nature of intermolecular forces operating in them into four categories viz., molecular, ionic, metallic and covalent solids.

Molecular Solids:

Molecular solids are crystalline solids composed of molecules as their constituent particles. They can be categorized into three types:

Non-Polar Molecular Solids:

These molecular solids consist of non-polar covalent bonds between the atoms within the molecules. Examples include H₂, Br₂, etc.

Polar Molecular Solids:

Polar molecular solids are characterized by polar covalent bonds between the atoms within the molecules. In these solids, molecules are held together by dipole-dipole interactions. Examples include HCl, SO₂, etc.

Hydrogen Bonded Molecular Solids:

Hydrogen bonded molecular solids have polar covalent bonds between the atoms within the molecules, and the molecules are held together by hydrogen bonding. An example is water molecules held together by hydrogen bonding.

Ionic Solids:

Ionic solids are crystalline solids where the constituent particles are ions. These solids feature cations and anions bonded together by strong electrostatic forces. Examples include NaCl, ZnS, etc.

Metallic Solids:

Metallic solids consist of positive metal ions and delocalized electrons as constituent particles. In these solids, orderly arranged positive metal ions are held together by free electrons. Examples include Fe, Au, Ag, etc.

Covalent Solids:

Covalent solids are crystalline solids where atoms of non-metals are joined to their adjacent atoms by covalent bonds. Examples include diamonds and graphite. Due to the strength of covalent bonds, these solids are hard and brittle. They are also known as network solids or giant molecules.

4.0Crystal Lattices and Unit Cells

Crystal Lattice

A crystal lattice refers to the geometric arrangement of points in space where the atoms, molecules, ions, or constituent particles of a crystal are situated. It defines the orderly pattern in which these particles are arranged throughout the crystal structure.

Unit cell

The unit cell is the smallest repeating part of a crystal lattice, defining its structure. It encompasses lattice points, positions where particles are most likely to be found, and repeating this unit in three dimensions constructs the entire crystal.

Crystal system	Axial distances	Axial angles	Possible Variations	Examples
Cubic	a = b = c	α = β = γ = 90°	Primitive, Body centered,face centered	Copper , KCl, NaCl, zinc blende, diamond
Tetragonal	a = b ≠ c	α = β = γ = 90°	Primitive, body centered	SnO₂, White tin, TiO₂
Orthorhombic	a ≠ b ≠ c	α = β = γ = 90°	Primitive body centered, face centered, end centered	Rhombic sulphur, KNO₃, CaCO₃
Hexagonal	a = b ≠ c	α = β = 90° γ = 120°	Primitive	Graphite, Mg, ZnO
Trigonal or Rhombohedral	a = b = c	α = β = γ ≠ 90°	Primitive	(CaCO₃) Calcite, HgS(Cinnabar)
Monoclinic	a ≠ b ≠ c	α = β = 90° γ ≠ 90°	Primitive and end centered	Monoclinic sulfur, Na₂SO₄.10H₂O
Triclinic	a ≠ b ≠ c	α ≠ β ≠ γ ≠ 90°	Primitive	K₂Cr₂O₇, CuSO₄.5H₂O

5.0Number of Atoms in a Unit Cell

In a crystal lattice, each lattice point holds one constituent particle (atom, molecule, or ion), and these points are arranged in unit cells. Here's the fraction of particles per unit cell for three types of cubic unit cells, assuming atoms:

Primitive Cubic Unit Cell: Each corner atom contributes 1/8 of an atom to the unit cell. With 8 corner atoms, the total is 1 atom per unit cell.
Body-Centered Cubic (bcc) Unit Cell: In addition to atoms at each corner, there's an atom at the body center belonging wholly to the unit cell. Hence, 2 atoms per unit cell.
Face-Centered Cubic (fcc) Unit Cell: Each corner atom contributes 18 of an atom, totaling 1 atom. Additionally, each face-centered atom is shared between two unit cells, contributing 12 of an atom. With 6 face-centered atoms, the total is 3 atoms per unit cell, making 4 atoms in total.

6.0Close Packed Structures

Close-packed structures in solids are highly dense, with minimal void space. They can be one-dimensional, where particles are tightly arranged along a line; two-dimensional, forming closely packed patterns; or three-dimensional, exhibiting even denser packing with less void space between particles.

7.0Packing Efficiency

The packing efficiency of a solid refers to the percentage of total space filled by the constituent particles within its crystal structure. It is a quantitative measure that helps understand the arrangement of particles in a solid.

Mathematically, packing efficiency is calculated using the following formula:

Packing Efficiency = ((Volume occupied by particles) / (Total volume of the unit cell ))x 100%

Type of unit cell	Number of atoms in a unit cell	Packing efficiency	Void space	Coordination number
Primitive cubic unit cell	1	52.4%	47.6%	6
Body centered cubic unit cell	2	68%	32%	8
Face centered cubic unit cell (hcp and ccp)	4	74%	26%	12

8.0Imperfections in Solids

Defects in solids are imperfections that disrupt the regular patterns in crystalline structures. They include point defects, line defects, and planar defects. Frenkel defects, a type of point defect, occur when some units of a crystal have fewer atoms than ideal units.

9.0Properties Of Solids

Physical Properties

Solids have a definite shape and volume due to strong intermolecular forces.
They're rigid and incompressible because of tightly packed molecules.
Solids are denser than other states, with negligible diffusion.
High energy is needed to distort their structure, resulting in high melting and boiling points.

These properties stem from close intermolecular distances and strong attractions between particles, ensuring solidity and stability.

Electrical Properties

Solids can be classified into three types based on their electrical conductivity:

Metals (conductors): These materials allow a significant portion of the applied electric field to flow through them. They exhibit high conductivities typically ranging from 10⁶ to 10⁸ ohm⁻¹.
Insulators: Insulators have very low conductivities, practically preventing the flow of electric current through them. Their electrical conductivity is typically in the range of 10^-10 to 10^-20 ohm⁻¹.
Semiconductors: These materials have intermediate conductivities at room temperature. Semiconductors behave as perfect insulators at absolute zero but can conduct electric current at higher temperatures.

Magnetic Properties

Magnetic properties in solids arise from the magnetic moments associated with the atomic or molecular structure of the material. Solids can exhibit various magnetic behaviors, including:

Diamagnetism: Occurs in materials where all the magnetic moments of individual atoms cancel out, resulting in a no repulsion in a magnetic field. Most materials exhibit diamagnetism to some extent.
Paramagnetism: Arises from unpaired electron spins in atoms or molecules, which align with an external magnetic field, causing the material to be weakly attracted to the magnetic field.
Ferromagnetism: Exhibited by materials with permanent magnetic moments that spontaneously align parallel to each other, resulting in a strong attraction to an external magnetic field. Ferromagnetic materials can retain their magnetization even after the external field is removed.
Antiferromagnetism: Similar to ferromagnetism, but with adjacent magnetic moments aligned in opposite directions, resulting in zero net magnetization. Antiferromagnetic materials can exhibit strong magnetic ordering at low temperatures.
Ferrimagnetism: Similar to ferromagnetism, but with unequal magnetic moments aligned in opposite directions, resulting in a net magnetization. Ferrimagnetic materials often have permanent magnetization, such as in magnets and magnetic recording media.

10.0Solved Examples

Ques.1 If an element crystallizes separately in both hcp and ccp structures, will these two structures exhibit the same density? Provide a justification for your answer.

Ans. The two structures (hcp and ccp) of the same element will have the same density because the packing fraction and the mass of atoms per unit cell are the same for both structures, leading to the same density calculation.

Ques.2 Describe the distribution of atoms within a cubic unit cell, including the number of atoms found at the corner, body center, face center, and edge center positions.

Ans. The distribution is as follows:

In a cubic unit cell, eight neighboring unit cells share the same atom located at the corner. Consequently, each unit cell represents 1/8th of the atom.
Within a cubic unit cell, each unit cell possesses its own atom positioned at the body center, which is not shared with adjacent unit cells. Therefore, the contribution of an atom to the unit cell is one due to its exclusive presence in a single unit cell.
Six neighboring unit cells situated on the faces of a cubic unit cell share the same atom. As a result, each unit cell represents one-half of an atom.
The edge of a cubic unit cell is shared by four unit cells simultaneously. Consequently, each unit cell will receive 1/4th of an atom at the edge center.

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