Crystal Systems PDF

# Crystal Systems ## System | a | b | c | α | β | γ | Examples ------- | -------- | -------- | -------- | -------- | -------- | -------- | -------- Cubic | a = b = c | α = β = γ = 90° | NaCl, Cu Trigonal | a = b = c | α = β = 90°, γ < 120° | CaCO₃ Monoclinic | a ≠ b ≠ c | α = γ = 90°, β...

# Crystal Systems ## System | a | b | c | α | β | γ | Examples ------- | -------- | -------- | -------- | -------- | -------- | -------- | -------- Cubic | a = b = c | α = β = γ = 90° | NaCl, Cu Trigonal | a = b = c | α = β = 90°, γ < 120° | CaCO₃ Monoclinic | a ≠ b ≠ c | α = γ = 90°, β ≠ 90° | PtCl₄ Triclinic | a ≠ b ≠ c | α ≠ β ≠ γ ≠ 90° | CuSO₄ Tetragonal | a = b ≠ c | α = β = γ = 90° | TiO₂ Orthorhombic | a ≠ b ≠ c | α = β = γ = 90° | CaSO₄, BaSO₄ Hexagonal | a = b ≠ c | α = β = 90°, γ = 120° | graphite # Type of Unit Cell ### 1. Primitive - Lattice - Found in all systems. - Points: * On corner * Two faces ### 2. Non-Primitive - Body Center - b, I - Face Center - f, more than 2 - Side (base) Center - A, C # Number of Atoms in the Unit Cell - Braavias → 14 Way # Elements of Symmetry - Plane, alxis, center # X-ray - The X-ray technique is used to determine the structure of crystals. - E.ic: - λ = 2d sin θ Where: * λ - wavelength of X-ray * d - spacing between planes * θ - Bragg angle * C = 3 x10⁸ m/s - speed of light * 1m = 10² cm= 10⁹ nm= 10¹⁰ Å = 10¹² pm # Rein force Ampli Poel - **Amplitude:** The vertical distance from the midline to the crest or trough of a wave. - **Wavelength:** The horizontal distance between two consecutive crests or troughs of a wave. - **Wave Number:** The number of waves in a given distance or interval. - **Constructive Interference:** When two waves interfere, resulting in a larger amplitude of the resultant wave. Occurs when crests of waves overlap. - **Destructive Interference:** When two waves interfere, resulting in a smaller amplitude of the resultant wave. Occurs when crests of waves overlap with troughs or vice versa.