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.