Chem114-4-Lab-Crystals

INTRODUCTION

  • Crystal Structure: Arrangement of atoms, ions, or molecules in space.

    • Composed of a unit cell: Smallest group of atoms with the crystalline symmetry that repeats to develop the crystal lattice.

    • The collection points in a regular pattern form the crystal lattice.

TYPES OF UNIT CELL

  1. Simple/Primitive (P)

    • Atoms at the corners of the unit cell only.

  2. Body-centered (I)

    • Atoms at corners and an additional atom at the center of the unit cell.

  3. Face-centered (F)

    • Atoms at corners and at the center of each face of the unit cell.

  4. Base-centered (C)

    • Atoms at corners and two opposite faces of the unit cell (typically at the top and bottom).

SIMPLE CUBIC (PRIMITIVE CUBIC) UNIT CELL

  • Atoms are positioned at the corners of a cube.

  • Each corner atom represents 1/8th of an atom per unit cell.

  • The particles touch along the edges but not diagonally on faces or through the center.

BODY-CENTERED CUBIC (BCC) UNIT CELL

  • Atoms positioned at corners and at the center of the cube.

  • Coordination number: 8

FACE-CENTERED CUBIC (FCC) UNIT CELL

  • Atoms positioned at corners and center of each face of the cube.

  • Coordination number: 12

CHARACTERISTICS OF CRYSTAL STRUCTURE

  1. Coordination number (CN): Number of nearest neighbor atoms.

  2. Number of atoms per unit cell: Total number of atoms enclosed in the unit cell.

  3. Edge length (a) and atomic radius (r): Relationship that correlates the lattice constant with atomic radius.

  4. Atomic Packing Factor (APF): Ratio of space filled by spherical atoms to total available volume.

CHARACTERISTICS OF CRYSTAL STRUCTURE

  • Types of Unit Cells:

    Structure

    Atoms per Cell

    Coordination Number

    Edge Length (a)

    Packing Efficiency

    Simple Cubic

    1

    6

    2r

    52%

    Body-Centered Cubic

    2

    8

    4r

    68%

    Face-Centered Cubic

    4

    12

    2√2r

    74%

RELATIONSHIPS IN CRYSTAL STRUCTURE

  • Cubic Relationships:

    • For Simple cubic and Body-centered cubic: C2=A2+B2=2A2.

    • For Face-centered cubic: C2=16r2=2A2.

SAMPLE PROBLEM

Atomic Packing Factor for FCC

  • Calculate PA for FCC structure: it is 0.74.

DENSITY CALCULATION

  • Density Formula: ρ = nA/VcNA

    • Where:

      • n = number of atoms/unit cell

      • A = atomic weight

      • Vc = volume of unit cell

      • NA = Avogadro's number (6.023 x 10²³ atoms/mol)

SAMPLE PROBLEMS

1. Copper

  • Given: Atomic radius = 0.128 nm, FCC structure, Atomic weight = 63.5 g/mol.

  • Task: Compute theoretical density.

2. Aluminum

  • Atomic radius = 143 pm, FCC unit cell.

  • Task: Calculate density of crystalline aluminum in g/cm³.

3. Silver

  • Unit cell edge length = 408.7 pm, FCC structure.

  • Task: Calculate density of silver in g/cm³.

DEFECTS OF CRYSTAL

  1. Point defects: Atoms in irregular positions (lattice vacancies, substitutional and interstitial impurities).

    • Frenkel defect: Pair of cation vacancy and cation interstitial (or anion equivalent).

    • Schottky defect: A pair of cation and anion vacancies.

  2. Linear defects: Groups of atoms in irregular positions (e.g. screw and edge dislocations).

  3. Planar defects: Interfaces between homogeneous regions (grain boundaries, stacking faults, external surfaces).