4.1 Seven Crystal Systems
5 min read•july 31, 2024
Crystal systems are the backbone of mineral structure, defining how atoms arrange themselves in space. There are seven systems, each with unique and axial relationships. Understanding these systems is crucial for identifying minerals and predicting their physical properties.
From the highly symmetric system to the least symmetric , each crystal system has distinct characteristics. These differences in symmetry and atomic arrangement influence everything from crystal shape to optical properties, making crystal systems a fundamental concept in mineralogy.
Crystal System Characteristics
Defining Features of Crystal Systems
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- Seven crystal systems define mineral structures cubic, , , , , , and triclinic
- Each system possesses specific symmetry elements and axial relationships
- Cubic system features three equal axes at right angles with four threefold rotational axes along body diagonals
- Tetragonal system comprises three axes at right angles two equal horizontal axes and distinct vertical axis
- Orthorhombic system consists of three unequal axes all intersecting at right angles
- Hexagonal system defined by four axes three equal coplanar axes at 120° angles and fourth axis perpendicular to this plane
- Trigonal system described using rhombohedral or hexagonal axis system with unique threefold rotational axis
- Monoclinic system has three unequal axes two intersecting at right angles and third inclined to plane of other two
- Triclinic system least symmetrical with three unequal axes intersecting at oblique angles
Symmetry Elements and Axial Relationships
- Cubic system exhibits highest symmetry nine mirror planes, thirteen rotation axes, and center of symmetry
- Tetragonal system characterized by five rotation axes (one fourfold and four twofold) and five mirror planes
- Orthorhombic system contains three twofold rotation axes and three mirror planes all perpendicular to each other
- Hexagonal system defined by sixfold rotation axis perpendicular to six mirror planes and six twofold rotation axes
- Trigonal system possesses single threefold rotation axis may be accompanied by mirror planes or twofold rotation axes
- Monoclinic system has only one twofold rotation axis or one mirror plane
- Triclinic system lacks rotational symmetry higher than onefold and has no mirror planes
- Axial relationships vary between systems
- Cubic: a = b = c, α = β = γ = 90°
- Tetragonal: a = b ≠ c, α = β = γ = 90°
- Orthorhombic: a ≠ b ≠ c, α = β = γ = 90°
- Hexagonal: a = b ≠ c, α = β = 90°, γ = 120°
- Trigonal: a = b = c, α = β = γ ≠ 90° (rhombohedral setting)
- Monoclinic: a ≠ b ≠ c, α = γ = 90° ≠ β
- Triclinic: a ≠ b ≠ c, α ≠ β ≠ γ ≠ 90°
Crystal System Identification
Symmetry-Based Classification
- Symmetry elements used to classify minerals into crystal systems include rotation axes, mirror planes, and centers of symmetry
- Cubic system highest symmetry nine mirror planes, thirteen rotation axes, and center of symmetry
- Tetragonal system five rotation axes (one fourfold and four twofold) and five mirror planes
- Orthorhombic system three twofold rotation axes and three mirror planes all perpendicular to each other
- Hexagonal system sixfold rotation axis perpendicular to six mirror planes and six twofold rotation axes
- Trigonal system single threefold rotation axis may be accompanied by mirror planes or twofold rotation axes
- Monoclinic system one twofold rotation axis or one mirror plane
- Triclinic system lacks rotational symmetry higher than onefold and has no mirror planes
Identification Techniques and Examples
- Visual inspection of crystal faces and angles aids in system identification (cube for cubic, prism for hexagonal)
- provides precise determination of crystal structure and system
- Optical properties like birefringence help identify non-cubic systems (calcite for trigonal)
- Cleavage patterns offer clues to crystal system (octahedral cleavage in cubic system minerals like fluorite)
- Symmetry can be observed through crystal habits (tetragonal prisms in rutile)
- Polarized light microscopy reveals optical characteristics specific to each system
- Electron backscatter diffraction (EBSD) enables identification of crystal systems in complex materials
Crystal Systems and Atomic Arrangement
Atomic Structure and Crystal Systems
- Crystal systems reflect underlying atomic arrangement and bonding patterns within minerals determining overall structure and properties
- Symmetry elements of crystal system result from repetitive, three-dimensional arrangement of atoms, ions, or molecules in crystal lattice
- smallest repeating unit of crystal structure determines crystal system and influences mineral's physical and chemical properties
- Atomic packing efficiency varies among crystal systems cubic typically highest and triclinic lowest packing density
- Coordination number of atoms in mineral often related to crystal system influencing properties such as hardness and cleavage (cubic close-packed structures have higher coordination numbers)
- Polymorphism occurs when mineral can crystallize in different crystal systems resulting in distinct physical properties despite identical chemical compositions (carbon as diamond (cubic) and graphite (hexagonal))
Factors Influencing Crystal Formation
- Stability of particular crystal system for given mineral depends on factors such as temperature, pressure, and chemical environment during formation
- Temperature affects atomic vibrations and bond strengths influencing preferred crystal structure ( transitions between trigonal and hexagonal forms at different temperatures)
- Pressure can cause phase transitions between crystal systems (graphite to diamond transition under high pressure)
- Chemical impurities or substitutions can stabilize certain crystal systems or cause distortions in lattice (doping in semiconductors)
- Growth rate and conditions influence final crystal system and habit (rapid cooling may lead to less symmetrical systems)
- Presence of water or other volatiles during crystallization can affect final crystal structure (hydrous vs. anhydrous minerals)
Crystal Systems: Symmetry vs Properties
Symmetry and Physical Properties
- Symmetry decreases progressively from cubic (highest) to triclinic (lowest) affecting properties such as , cleavage, and optical characteristics
- Cubic minerals often exhibit behavior in physical properties while minerals in other systems may show varying degrees of anisotropy
- Presence of unique axis in tetragonal, hexagonal, and trigonal systems can lead to elongated or prismatic crystal habits distinct from more equidimensional habits common in cubic systems
- Orthorhombic, monoclinic, and triclinic systems often display more complex crystal forms and variable physical properties due to lower symmetry
- Cleavage patterns directly related to crystal symmetry cubic minerals potentially showing up to three directions of perfect cleavage (halite) while triclinic minerals may have more complex or less well-defined cleavage
- Optical properties such as birefringence and pleochroism influenced by crystal symmetry cubic minerals being optically isotropic and lower symmetry systems showing more complex optical behavior
Influence on Material Properties
- Crystal system affects mineral's response to external forces influencing properties such as piezoelectricity, pyroelectricity, and ferroelectricity
- Thermal expansion can be isotropic in cubic systems but in lower symmetry systems (quartz exhibits different thermal expansion along different crystallographic directions)
- Electrical conductivity varies with crystal direction in non-cubic systems (graphite highly conductive in basal plane, poorly conductive perpendicular to it)
- Magnetic properties depend on crystal system and atomic arrangement (magnetite (cubic) vs hematite (trigonal) have different magnetic behaviors)
- Mechanical properties like elasticity and plasticity affected by crystal system (mica (monoclinic) shows perfect basal cleavage due to sheet structure)
- Optical activity and birefringence increase with decreasing crystal symmetry (calcite (trigonal) shows strong birefringence)
- Crystal system influences growth rates in different crystallographic directions affecting final crystal morphology and properties
Key Terms to Review (21)
Anisotropic: Anisotropic refers to materials that exhibit different physical properties when measured along different directions. In the context of minerals, this means that their optical, mechanical, or thermal behaviors can vary based on the orientation of the crystal lattice. Understanding anisotropy is essential for interpreting how crystals interact with light and other forces, as well as their classification into various crystal systems based on symmetry.
Bravais lattices: Bravais lattices are a set of distinct lattice structures in three-dimensional space that describe the arrangement of points representing atoms, ions, or molecules in a crystal. Each lattice is defined by its unit cell dimensions and angles, allowing the entire crystal structure to be derived from its repeating unit. These lattices provide a framework for understanding the symmetry and properties of crystalline materials, connecting deeply with the foundational concepts in crystallography and the classification of crystal systems.
Crystal Habit: Crystal habit refers to the characteristic external shape or form that a mineral crystal exhibits. This term encompasses the overall appearance and arrangement of crystal faces, which are influenced by the internal structure and arrangement of atoms within the mineral. Understanding crystal habit is crucial for identifying minerals, as it can vary widely even among crystals of the same mineral species, providing insights into their formation conditions and environmental influences.
Crystallization process: The crystallization process is the method by which atoms or molecules arrange themselves into a structured pattern to form a solid crystal. This process can occur through various mechanisms, including cooling of a molten substance, evaporation of a solution, or changes in pressure and temperature, leading to the formation of distinct crystal shapes and properties. The resulting crystals belong to specific crystal systems that classify them based on their symmetry and geometry.
Cubic: Cubic refers to a geometric shape characterized by having three equal dimensions, forming a regular three-dimensional structure. This term is essential in understanding the arrangement of atoms in certain minerals and how these arrangements influence their properties, classifications, and behaviors in different contexts.
Electron Microscopy: Electron microscopy is a powerful imaging technique that uses electrons instead of light to create highly detailed images of materials at the micro and nanoscale. This method is crucial for studying the structure and composition of minerals, providing insights that are essential for understanding their properties and behaviors in various contexts.
Facets: Facets refer to the flat surfaces on a crystal that form as a result of its growth process. These surfaces play a vital role in defining the crystal's overall shape and appearance, significantly influencing its optical properties and how it interacts with light. The arrangement and orientation of facets are determined by the underlying atomic structure of the crystal, which is categorized into different crystal systems based on their geometric properties.
Hexagonal: Hexagonal refers to a crystal system characterized by a six-fold symmetry and having unit cells with a hexagonal shape. This system is important in mineralogy as it encompasses several minerals and influences their physical properties, such as crystal habits and growth patterns.
Interfacial angles: Interfacial angles refer to the angles formed between the faces of a crystal, which are a result of the internal arrangement of atoms within the crystal lattice. These angles are crucial for understanding the symmetry and properties of different crystal systems, as they are consistent within each specific type of crystal. By measuring these angles, mineralogists can identify and categorize minerals based on their geometric characteristics.
Isotropic: Isotropic refers to materials that have identical properties in all directions, meaning their physical and mechanical characteristics are uniform regardless of the orientation of the material. This concept is important when analyzing crystal structures and their behavior under various conditions, particularly in how they interact with light and exhibit optical properties.
Lattice parameters: Lattice parameters are the physical dimensions that describe the unit cell of a crystal lattice, including the lengths of its edges and the angles between them. These parameters are essential for understanding the geometric arrangement of atoms in a crystal structure, as they directly influence the properties of the mineral. By defining how a crystal is organized in three-dimensional space, lattice parameters help in categorizing crystals into distinct crystal systems.
Monoclinic: Monoclinic refers to one of the seven crystal systems characterized by three unequal axes, where two axes intersect at an angle other than 90 degrees while the third axis is perpendicular to the plane formed by the other two. This unique arrangement plays a critical role in determining the symmetry and physical properties of minerals, contributing to their classification and identification.
Orthorhombic: Orthorhombic refers to one of the seven crystal systems characterized by three mutually perpendicular axes that are all of different lengths. This distinct arrangement leads to unique crystallographic properties and influences the overall symmetry and structure of minerals within this system.
Quartz: Quartz is a common and abundant mineral composed of silicon dioxide (SiO₂) that forms in a variety of geological environments. Known for its hardness and resistance to weathering, quartz plays a significant role in the classification of minerals and is essential for understanding various geological processes.
Sodium chloride: Sodium chloride, commonly known as table salt, is a chemical compound made up of sodium (Na) and chlorine (Cl) ions. It crystallizes in a cubic structure and is an important mineral found in nature, influencing the properties of minerals and their formations. Its presence in various geological environments connects it to the study of crystal systems, particularly the arrangement and symmetry of crystals in the seven crystal systems.
Symmetry: Symmetry refers to the balanced and proportional arrangement of parts in a mineral's crystal structure, where one half is a mirror image of the other. This concept is essential for understanding the geometric properties of crystals, influencing their physical characteristics, how they grow, and how they are classified into different systems. Symmetry plays a vital role in determining mineral habits, crystal forms, twinning, and the overall atomic arrangement within the crystal lattice.
Tetragonal: Tetragonal refers to one of the seven crystal systems in crystallography characterized by three mutually perpendicular axes, where two of the axes are of equal length, and the third axis is of a different length. This unique arrangement gives rise to distinctive geometric shapes and symmetry properties in the minerals that crystallize in this system, allowing for classification based on their structural features and behaviors.
Triclinic: Triclinic is a crystal system characterized by three unequal axes that are not perpendicular to each other. This unique arrangement means that triclinic crystals lack symmetry, making them distinct from other crystal systems. Their irregular structure influences properties such as cleavage, which is important in understanding the classification and identification of earth materials.
Trigonal: Trigonal refers to a crystal system characterized by a threefold rotational symmetry about a single axis. This symmetry results in a unique arrangement of atoms that can influence the physical properties and classification of minerals. It plays a crucial role in understanding crystal structures, bonding, and mineral identification in various geological contexts.
Unit cell: A unit cell is the smallest repeating unit in a crystal lattice that defines the structure and symmetry of a crystal. It acts as a building block for the entire crystal, containing all the necessary information about the arrangement of atoms, ions, or molecules within the mineral. Understanding the unit cell helps in analyzing the overall properties of a mineral and its behavior during processes like diffraction and optical examination.
X-Ray Diffraction: X-ray diffraction is a powerful analytical technique used to study the structure of crystalline materials by measuring the angles and intensities of X-rays scattered by the crystals. This method is crucial for understanding mineral structures, identifying minerals, and determining their properties, linking it closely to various aspects of mineralogy and crystallography.