Comprehensive Study Notes on Crystallography and Crystal Systems
Fundamentals of Crystallography
Definition of Crystallography: Crystallography is defined as a branch of mineralogy that deals specifically with the study of the arrangement and bonding of atoms within crystalline solids. It also explores the geometric structure of the crystal lattice.
Crystalline vs. Amorphous States: * Most minerals are classified as crystalline. * A minority of minerals are classified as amorphous, which refers to substances that are non-crystalline.
Importance of the Field: The primary purpose of studying crystallography is to determine how atoms in a material are arranged. This knowledge allows scientists and gemologists to understand the fundamental relationship between a material's atomic structure and its physical and optical properties.
Introductory Scope: While the field of scientific crystallography is complex and rigorous, this introductory material focuses on the basics necessary for gemology. This is because the majority of gemstones are crystalline, and their specific crystalline structures directly influence their outward form, physical characteristics, and optical behavior.
The Scientific Nature of Crystals
Scientific Definition: The definition of a "crystal" is strictly based on the microscopic arrangement of atoms contained within it, referred to as the "crystal structure."
Periodic Arrangement: A crystal is a solid material where the atoms form a periodic, repeating arrangement.
Visual Characteristics: Crystals are commonly identified by their physical shape, which typically consists of flat faces meeting at sharp angles.
Evolution of the Term: Historically, the word "crystal" referred exclusively to quartz crystals. Over time, the definition broadened to encompass all minerals that possess well-expressed crystal shapes.
Formation and The Law of Constancy of Interfacial Angles
Change of State: Crystals normally form during the phase transition of matter from a liquid or gaseous state into a solid state.
Atomic Forces: In both liquid and gaseous states of a compound, the atomic forces that bind the mass together into a solid are not present. Consequently, a compound must be crystallized before its geometry can be studied.
Geometric Regularity: While liquids and gases conform to the shape of their container, solids take on one of several regular geometric forms.
Nicholas Steno’s Discovery (1669): * In 1669, Nicholas Steno, a Danish physician and natural scientist, discovered a fundamental law governing crystal formation. * Through the examination of various specimens of the same mineral, he determined that the angles between similar crystal faces remain constant regardless of the size or shape of the crystal, provided they are measured at the same temperature. * Implication: Whether a crystal grew under ideal conditions or not, the angles between corresponding faces of the same mineral species will always be identical.
Crystallization and Mineral Habits
Environmental Factors: During crystallization, crystals assume various geometric shapes. These shapes are dependent on both the ordering of the internal atomic structure and the specific physical and chemical conditions present during growth.
Predominant Growth Directions: If there is a dominant direction or plane in which a mineral forms, different habits (external shapes) will prevail.
Examples of Shape Tendencies: * Galena: Often forms equate shapes, such as cubes or octahedrons. * Quartz: Typically exhibits a prismatic habit. * Barite: Typically exhibits a tabular habit. * Pyrite (Iron Sulfide): Known as "fool's gold" with the chemical formula , it belongs to the cubic crystal system.
The Seven Crystal Systems
All mineral crystals are built upon seven basic plans known as the "crystal systems." Each system features a unique architecture determined by the lengths and angles of intersection of the "axes" (imaginary planes through the crystal) and the degrees of symmetry present.
1. Cubic (Isometric): Characterized by three equal axes intersecting at right angles ().
2. Tetragonal: Characterized by three axes at right angles, where one axis is of unequal length compared to the other two.
3. Hexagonal: Characterized by three equal axes intersecting at angles, with a fourth axis set at a right angle to the other three, exhibiting sixfold symmetry.
4. Trigonal (or Rhombohedral): Similar to the hexagonal system (axes-wise), but characterized by threefold symmetry.
5. Orthorhombic: Characterized by three unequal axes, all of which intersect at right angles ().
6. Monoclinic: Characterized by three unequal axes, two of which are at right angles, while the third axis is not.
7. Triclinic: Characterized by three axes, none of which are at right angles to each other.
Unit Cells and Microscopic Architecture
Definition: The innermost structure of every crystal is composed of atomic-scale building blocks called "unit cells."
Symmetry and Shape: These unit cells exhibit the specific symmetries found in the axes of their respective crystal systems: * The unit cell for the Cubic system is a cube. * The unit cell for the Tetragonal system is shaped like a "brick."
Assembly: As a crystal grows, these tiny unit cell structures assemble themselves, building the crystal up to its final finished size and external shape.
Crystal Habit vs. Crystal Form
Definitions: * Crystal Habit: The visible, external shape and geometric appearance of a crystal. It is determined by the length, width, and number of crystal faces. * Crystal Form: While habit is the external shape of an individual or an aggregate, "habit names" are often adjectives that describe the shape.
Why Habits Change: Different habits can be produced when the environment of a growing crystal affects its external morphology without altering its underlying internal atomic structure.
Common Crystal Habits: * Acicular: Needle-like. Examples include golden rutile crystals in quartz or "puffball-like" mesolite specimens consisting of radiating needles. * Prismatic: Pencil-like. Examples include Tourmaline crystals and Red beryl crystals in matrix. * Dendritic: Shaped like tree branches. Examples include quartz with black manganese dioxide inclusions, iron oxide crystals on sandstone surfaces, and native copper crystals. * Drusy: Appearing like a coating of sugar or powdery snow on a surface (e.g., Pyrite crystals on matrix). * Botryoidal: Found in aggregate gems only; resembles a bunch of grapes or bubbles (e.g., blue chalcedony). * Tabular: Plate-like or table-like. * Striated: Marked by parallel grooves or lines.
Case Study: Diamond
Crystal System: Diamonds belong to the Cubic (Isometric) system, which is the most symmetrical of all the crystal systems.
Primary Habit: The basic crystal shape or habit of a diamond is the octahedron.
Morphology: An octahedron consists of eight equal triangular sides, appearing visually like two pyramids joined at their bases.