Solids and Crystal Structures

Introduction to Solids

• Solids are a state of matter characterized by:

  • Structural rigidity

  • Resistance to deformation

Characteristics of Solids

• Fixed Shape and Volume: Solids maintain a distinct shape and do not conform to the shape of their container.

• Strong Intermolecular Forces: Atoms are tightly packed, leading to strong forces between them.

• Low Compressibility: Solids cannot be easily compressed due to their tightly packed structure.

• High Density: Generally, solids are denser than liquids and gases.

• Thermal Conductivity: Many solids can conduct heat, though the efficiency varies by material.

• Elasticity and Rigidity: Solids can return to their original shape after stress (elasticity) or can resist deformation (rigidity).

Types of Solids

• Examples of Solids Include:

  • Metals

  • Plastics

  • Ceramics

  • Composites

• Classification of solids is based on the arrangement of atoms.

Atomic Arrangement in Solids

• Crystalline vs. Amorphous:

  • Crystalline: Atoms/molecules are arranged in geometric patterns.

  • Amorphous: No definite pattern in atom/molecule arrangement.

Types of Crystalline Solids

• Ionic Solids: Formed from ionic bonds.

• Molecular Solids: Formed from molecular bonds.

• Metallic Solids: Atoms share a "sea" of electrons.

• Covalent Networks: Atoms connected by covalent bonds in a rigid structure.

Properties of Crystalline Solids

• Anisotropy: Physical properties vary with direction.

• Definite Melting Point: A specific temperature at which a solid becomes liquid.

• High Stability Under Stress: Typically more stable compared to amorphous solids.

Properties of Amorphous Solids

• Isotropy: Physical properties are the same in all directions.

• Gradual Softening: Amorphous solids do not have a sharp melting point.

• Brittleness: Often shatter rather than deform when under stress.

Crystallography

• Definition: Study of crystals, their internal structures, and external shapes.

• Characteristic Elements of Crystals:

  • Crystal faces

  • Angles between faces

  • Symmetry: Identical halves of the crystal that can be studied through various symmetry elements.

Crystal Systems

• Major Crystal Systems: Classified by crystallographic axes:

  • Cubic

  • Tetragonal

  • Orthorhombic

  • Hexagonal

  • Monoclinic

  • Triclinic

  • Variations in these systems are based on the number, length, and angles of their axes.

Key Terminologies in Crystallography

• Crystal: A periodic arrangement of atoms.

• Lattice: Arrangement of particles forming a crystal.

• Unit Cell: The smallest repetitive part of a crystal.

• Atomic Radius: The radius of participating atoms in a crystalline structure.

• Unit Cell Length: Length of one edge of the unit cell.

• Atomic Packing Factor (APF): Percentage of volume occupied by atoms in a structure.

Density Calculations of Crystals

• Density Formula:

  • ( \rho = \frac{n \times A_W}{V_C \times N_A} )

  • Where:

    • ( \rho ): Density in g/cm³

    • ( n ): Number of atoms per unit cell

    • ( A_W ): Molar mass in g/mol

    • ( V_C ): Volume of the unit cell in cm³

    • ( N_A ): Avogadro's number (6.022 x 10²³)

Examples of Cubic Crystal Structures

• Simple Cubic: Lattice points at the corners of the unit cell.

• Body-Centered Cubic: 8 atoms at corners plus one at the center.

• Face-Centered Cubic: Atoms at the corners and in the center of each face.

• Hexagonal Close-Packed: Consists of spheres close-packed in hexagonal symmetry.

Challenges in Density Calculation

• Example Calculations:

  • Determine unit cell lengths and atomic radii from given density and atomic weights using density formulas, performing calculations for Barium, Molybdenum, Polonium, Aluminum, and Magnesium.

Note: This provides a comprehensive summary of the properties, types, and calculations related to solids and crystals in materials science.