3.1 Introduction to Crystallography

Crystallography is the secret decoder ring of minerals. It reveals how atoms stack up in crystals, unlocking the mysteries of their properties. By understanding crystal structures, we can predict how minerals will behave and why they look the way they do.

This topic sets the stage for exploring symmetry in crystals. We'll dive into the different crystal systems, from cubic to triclinic, and see how their unique arrangements impact everything from cleavage to optical properties.

Crystallography in Mineralogy

Fundamentals of Crystallography

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• Crystallography studies arrangement of atoms in crystalline solids and geometric structure of crystals
• Employs techniques (X-ray diffraction, neutron diffraction, electron microscopy) to determine atomic and molecular structure of crystals
• Provides insights into internal order of minerals influencing optical properties, cleavage, hardness, and other diagnostic features
• Essential for mineral identification, classification, and development of new materials with specific properties
• Fundamental in fields (materials science, solid-state physics, structural chemistry)

Importance in Mineralogy

• Crucial for understanding physical and chemical properties of minerals
• Explains mineral formation processes and behavior under different conditions
• Vital for predicting and explaining mineral behavior in geological processes (metamorphism, weathering, ore formation)
• Influences optical properties, cleavage, hardness, and other diagnostic features used in mineral identification
• Aids in understanding relationships between mineral structure and properties

Crystal Structure and Lattices

Basic Concepts

• Crystal structure represents highly ordered, three-dimensional arrangement of atoms, ions, or molecules in crystalline material
• Unit cell contains full symmetry of crystal lattice as smallest repeating unit of crystal structure
• Crystal lattice describes periodic arrangement of atoms or molecules, represented by set of translation vectors
• Lattice points indicate positions of atoms or molecules in crystal structure
• Bravais lattices encompass 14 unique three-dimensional lattice types describing all possible crystal structures

Advanced Concepts

• Miller indices define planes and directions within crystal lattice
• Coordination number indicates number of nearest neighbors surrounding atom or ion, influencing bonding and physical properties
• Crystal structures exhibit various symmetry elements (rotation axes, mirror planes, inversion centers)
• Polymorphism occurs when a substance can crystallize in multiple crystal structures
• Isomorphism describes different substances crystallizing in similar crystal structures

Crystal Systems and Characteristics

Cubic and Tetragonal Systems

• Cubic system features three equal axes at right angles, highest symmetry, four 3-fold rotation axes
• Examples of cubic minerals (halite, pyrite, garnet)
• Tetragonal system has two equal axes and one unique axis, all at right angles, one 4-fold rotation axis
• Examples of tetragonal minerals (zircon, rutile, chalcopyrite)

Orthorhombic and Hexagonal Systems

• Orthorhombic system comprises three unequal axes at right angles, three 2-fold rotation axes or mirror planes
• Examples of orthorhombic minerals (olivine, topaz, barite)
• Hexagonal system includes three equal coplanar axes at 120° and fourth axis perpendicular to this plane, one 6-fold rotation axis
• Examples of hexagonal minerals (quartz, beryl, apatite)

Trigonal, Monoclinic, and Triclinic Systems

• Trigonal system described using rhombohedral or hexagonal unit cell, one 3-fold rotation axis
• Examples of trigonal minerals (calcite, corundum, tourmaline)
• Monoclinic system has three unequal axes with one oblique angle (typically β), one 2-fold rotation axis or mirror plane
• Examples of monoclinic minerals (gypsum, orthoclase, hornblende)
• Triclinic system consists of three unequal axes with three oblique angles, lowest symmetry, only center of inversion
• Examples of triclinic minerals (plagioclase, kyanite, rhodonite)

Crystal Structure vs Mineral Properties

Physical Properties

• Crystal structure directly influences mineral's physical properties (hardness, cleavage, fracture, tenacity)
• Arrangement of atoms determines chemical composition and bonding characteristics, affecting stability and reactivity
• Cleavage planes relate to weak bonding directions within crystal structure, often corresponding to specific crystallographic planes
• Symmetry of crystal structure influences mineral's external morphology (crystal habit, development of crystal faces)

Optical and Thermal Properties

• Optical properties (refractive index, birefringence, pleochroism) result from interaction between light and crystal structure
• Thermal properties (thermal expansion, conductivity) affected by strength and nature of bonds within crystal structure
• Crystal structure's ability to accommodate impurities or substitutions influences formation of solid solutions and occurrence of color in minerals

Electrical and Magnetic Properties

• Electrical and magnetic properties determined by distribution and movement of electrons within crystal structure
• Piezoelectricity occurs in certain crystal structures when mechanical stress generates electrical charge
• Ferromagnetism, paramagnetism, and diamagnetism depend on arrangement of magnetic moments within crystal structure