Lecture_4-Crystallography

Basics of Crystallography

  • Course: EACS 223: Earth Materials

  • Topic: Wulfenite

Crystallography

  • Definition: Arrangement of atoms in minerals.

  • Key Concept: Relationship between crystal symmetry and building block (unit cell) symmetry is central to crystallography.

    • Symmetry of Crystals: Describes the order and arrangement of crystal structures, which can be complicated.

    • Example: Fluorite (CaF2)

      • Atomic arrangement: Truncated octahedron

      • Location: Erongo Region, Namibia

Historical Context

  • Early 1800s: Researchers discovered that crystals with similar but slightly different chemical compositions could have identical shapes.

    • Examples of compositions: CaCO3, MgCO3, MnCO3, FeCO3

Case Study: Fluorine (CaF2)

  • Components:

    • Calcium (Ca): Metal from Group 2 with 2 valence electrons.

    • Fluorine (F): Non-metal from Group 17 with 7 valence electrons.

  • Chemical Nature: Combined to form an ionic compound.

    • Fluorine seeks an octet of 8 electrons while Calcium loses 2 electrons.

  • Lewis Structure: Illustrates the ionic nature - presents Ca2+ and F- ions.

Key Concepts in Crystallography

  • All crystals have basic building blocks known as unit cells.

    • Fundamental Shapes: There are 7 unique shapes for unit cells.

    • Unit cells arrange in one of 14 different ways to form crystals.

    • The inferred shapes of the unit cells and lattice types are determined by crystal habit and symmetry.

    • Atomic Structure Symmetry: 230 possible symmetries accessible only through X-ray techniques.

  • Crystal Faces: Crystals can consist of different crystal faces, which are differentiated based on their orientations concerning a coordinate system based on unit cell edges.

Symmetry in Crystallography

  • Definition of Symmetry:

    • Refers to the relationship and order between parts of an entity.

    • Example: Hexagon has 6-fold symmetry being rotatable in increments of 60°.

  • Importance: Symmetry relates to the arrangement and orientation of atoms in minerals, which subsequently influences mineral properties.

Types of Symmetry

  • Translational Symmetry: Describes when an object can be moved in a direction without altering its shape.

  • Lines of Symmetry: Examples include shapes like equilateral triangles, kites, rectangles, and squares.

Lattice Structure in Crystals

  • Definition: The symmetry in crystals arises from the orderly arrangement of atoms in the crystal structure (lattice).

  • 2D Lattice: Comprised of an orderly array of points, defined by spacing and angles between points.

  • 3D Lattice: Crystals feature a three-dimensional atomic array.

Crystal Faces and Development

  1. Crystal faces are formed along planes defined by lattice points.

    • Crystal faces intersect atoms/molecules that constitute those points.

    • More developed faces intersect a greater number of lattice points (Bravais Law).

  2. Angles Between Faces: Controlled by spacing between lattice points.

  3. Steno’s Law of Interfacial Angles: Angles between lined crystal faces remain constant and characteristically define the species.

  4. Lattice Symmetry: Determines angular relationships between crystal faces.

Classification of Crystal Systems

  • Basic forms consist of nodes, planes, and unit meshes with examples including:

    • Plane Lattices: Square, Rectangular, Hexagonal, Oblique

    • Unit Meshes: Various lattice types with unique properties.

Crystal Shapes

  • Definition: A crystal manifests as a solid material with orderly arrangement of constituents (atoms, molecules).

  • External Shape: Results from the stacking of unit cells, defined by cell edges: a, b, c

    • Angles Between Edges: Consist of alpha (α), beta (β), and gamma (γ) which vary by system.

Seven Primitive Crystal Systems

  1. Cubic (Isometric): All axes equal and perpendicular.

  2. Tetragonal: Two axes equal; all perpendicular.

  3. Orthorhombic: All axes unequal and perpendicular.

  4. Hexagonal: Three axes equal in a plane and fourth axis perpendicular.

  5. Monoclinic: All axes unequal; two are perpendicular.

  6. Triclinic: All axes unequal and none are perpendicular.

  7. Rhombohedral (Trigonal): Equal axes; none at right angles.

Symmetry and Axes of a Crystal

  • Lines of Symmetry: Formed when an object can duplicate itself across specific lines (mirror images).

  • Rotational Symmetry: Involves rotating an object around a point and checking for repetitive appearances.

    • Order of Rotational Symmetry: Count of rotations returning object to original position.

    • Examples: 2-fold, 3-fold, 4-fold, and 6-fold rotations relate to symmetry in structures.

Summary of Symmetry Operations

  • Reflection across a line combining translation along that line is defined as glide symmetry.

  • Screw Axis: Involves translations and rotations that produce helical structures, as observed in quartz.

Crystal Identification and Morphology

  • Examination of crystal forms can aid in identification of mineral species.

  • Distinguishing characteristics of crystallization habits include elongation, thickness, and overall form.

    • Examples: Euhedral, Subhedral, Anhedral forms characterize crystal morphology.