Crystal System Identifier

Precise Crystallographic Analysis

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Crystal System Identifier

Identify crystal system from lattice parameters.

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Symmetry Elements Calculator

Calculate symmetry elements and point groups.

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Miller Indices Calculator

Calculate plane spacing and angles.

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Understanding Crystal Systems

Basic Principles

Key concepts include:

  • Unit cell parameters
  • Symmetry operations
  • Bravais lattices
  • Point groups
  • Space groups

Crystal Systems

Classification:

  • High Symmetry:
    • Cubic
    • Tetragonal
  • Low Symmetry:
    • Monoclinic
    • Triclinic

Applications

Common uses:

  • Material science
  • Mineralogy
  • Solid state chemistry
  • Drug design
  • Semiconductor physics

Advanced Concepts

Additional topics:

  • Wyckoff positions
  • Systematic absences
  • Reciprocal lattice
  • Crystal morphology
  • Phase transitions

Essential Crystal System Formulas

Lattice Parameters

V = abc(1-cos²α-cos²β-cos²γ+2cosαcosβcosγ)½

d = a/√(h²+k²+l²) [cubic]

cos φ = hh'+kk'+ll'/√[(h²+k²+l²)(h'²+k'²+l'²)]

Symmetry Operations

Rotation: Cn

Reflection: m

Inversion: i

Metric Tensors

gᵢⱼ = aᵢ·aⱼ

|g| = V²

d* = 2π/d