Podcast
Questions and Answers
If a crystal displays symmetry elements including a three-fold rotational axis and a mirror plane perpendicular to it with additional two-fold axes, which crystal system does it belong to?
If a crystal displays symmetry elements including a three-fold rotational axis and a mirror plane perpendicular to it with additional two-fold axes, which crystal system does it belong to?
- Orthorhombic
- Hexagonal (correct)
- Cubic
- Tetragonal
A crystal is found to have three mutually perpendicular axes of unequal lengths and all angles between these axes are 90 degrees. To which crystal system does it belong?
A crystal is found to have three mutually perpendicular axes of unequal lengths and all angles between these axes are 90 degrees. To which crystal system does it belong?
- Triclinic
- Tetragonal
- Monoclinic
- Orthorhombic (correct)
A crystal's unit cell is defined by three axes of equal length, with all axes intersecting at $90^o$. What crystal system is the crystal?
A crystal's unit cell is defined by three axes of equal length, with all axes intersecting at $90^o$. What crystal system is the crystal?
- Tetragonal
- Isometric (correct)
- Hexagonal
- Orthorhombic
Which of the following is a valid combination of symmetry elements that can exist within a crystal structure, adhering to crystallographic restrictions?
Which of the following is a valid combination of symmetry elements that can exist within a crystal structure, adhering to crystallographic restrictions?
Which statement accurately describes the relationship between crystal systems and Bravais lattices?
Which statement accurately describes the relationship between crystal systems and Bravais lattices?
A crystal is determined to belong to the trigonal crystal system. What specific symmetry element is required for its classification?
A crystal is determined to belong to the trigonal crystal system. What specific symmetry element is required for its classification?
Why is it impossible for a crystal to possess a five-fold rotational symmetry?
Why is it impossible for a crystal to possess a five-fold rotational symmetry?
Within crystallography, what fundamentally defines a 'unit cell'?
Within crystallography, what fundamentally defines a 'unit cell'?
How would you describe a 'crystal lattice'?
How would you describe a 'crystal lattice'?
Based on the arrangement of atoms within their unit cells, what distinguishes different Bravais lattices from one another?
Based on the arrangement of atoms within their unit cells, what distinguishes different Bravais lattices from one another?
What criteria fundamentally determine the subdivision of the 32 point groups into the six crystal systems?
What criteria fundamentally determine the subdivision of the 32 point groups into the six crystal systems?
What is the key characteristic difference between the hexagonal and trigonal crystal subdivisions within the broader hexagonal system?
What is the key characteristic difference between the hexagonal and trigonal crystal subdivisions within the broader hexagonal system?
While studying crystallography, you encounter a mineral sample exhibiting a 'truncated octahedron' shape. Which statement best describes the relationship between this shape and the crystal's internal structure?
While studying crystallography, you encounter a mineral sample exhibiting a 'truncated octahedron' shape. Which statement best describes the relationship between this shape and the crystal's internal structure?
Why do crystal faces form?
Why do crystal faces form?
What is the main reason for defining and studying the different crystal systems?
What is the main reason for defining and studying the different crystal systems?
If you were to cut a crystal, which orientation from the following options would result in a cut that that terminates crystal lattices in a stable way?
If you were to cut a crystal, which orientation from the following options would result in a cut that that terminates crystal lattices in a stable way?
A crystal is observed to have differing hardness values when scratched along different crystallographic axes. What is the underlying reason for this?
A crystal is observed to have differing hardness values when scratched along different crystallographic axes. What is the underlying reason for this?
Why aren't the lattice parameters alone sufficient to identify a specific mineral?
Why aren't the lattice parameters alone sufficient to identify a specific mineral?
How does considering the chemical composition and the crystal structure improve accurate mineral identification?
How does considering the chemical composition and the crystal structure improve accurate mineral identification?
In crystallography, the Miller-Bravais indices are used to describe the orientation of crystal planes in hexagonal crystal systems. What is the key difference between Miller indices and Miller-Bravais indices?
In crystallography, the Miller-Bravais indices are used to describe the orientation of crystal planes in hexagonal crystal systems. What is the key difference between Miller indices and Miller-Bravais indices?
A crystallographer determines that a mineral sample possesses a non-primitive unit cell. Which observation led to this conclusion?
A crystallographer determines that a mineral sample possesses a non-primitive unit cell. Which observation led to this conclusion?
You are analyzing the crystal structure of a newly discovered mineral and determine that it belongs to the monoclinic crystal system. Which set of characteristics must define its crystallographic axes?
You are analyzing the crystal structure of a newly discovered mineral and determine that it belongs to the monoclinic crystal system. Which set of characteristics must define its crystallographic axes?
What distinguishes a crystal structure from an amorphous solid?
What distinguishes a crystal structure from an amorphous solid?
Which of the following statements accurately links the concept of a crystal lattice to the formation of crystal faces?
Which of the following statements accurately links the concept of a crystal lattice to the formation of crystal faces?
Crystal faces tend to...
Crystal faces tend to...
A crystal structure is found to have one four-fold rotation axis. Which of the following crystal systems could it potentially belong to?
A crystal structure is found to have one four-fold rotation axis. Which of the following crystal systems could it potentially belong to?
Why is understanding 'crystal systems' important in mineralogy and materials science?
Why is understanding 'crystal systems' important in mineralogy and materials science?
How can crystal symmetry be used to predict the macroscopic properties of a mineral?
How can crystal symmetry be used to predict the macroscopic properties of a mineral?
Which of the following best describes a 'truncated octahedron' in the context of crystal morphology?
Which of the following best describes a 'truncated octahedron' in the context of crystal morphology?
An isometric crystal will be composed of ______ unit cells.
An isometric crystal will be composed of ______ unit cells.
What is the relationship between Miller indices (hkl) and the crystal lattice?
What is the relationship between Miller indices (hkl) and the crystal lattice?
What does the term “parallelepiped” describe for unit cells mean?
What does the term “parallelepiped” describe for unit cells mean?
Which is TRUE about the triclinic crystal system?
Which is TRUE about the triclinic crystal system?
A mineral crystallizes in the isometric system. Predict the relationship between its unit cell dimensions.
A mineral crystallizes in the isometric system. Predict the relationship between its unit cell dimensions.
What statement best characterizes the classification system shown in the image associated with point groups?
What statement best characterizes the classification system shown in the image associated with point groups?
Why do crystals possess symmetry?
Why do crystals possess symmetry?
What does crystal lattice mean?
What does crystal lattice mean?
Flashcards
Symmetry elements
Symmetry elements
Describing symmetry of a crystal requires naming these elements and associated operations.
Crystallography
Crystallography
The study of crystals and their formation
Crystal
Crystal
A solid with atoms arranged in a repeating pattern.
Point Groups / Crystal Classes
Point Groups / Crystal Classes
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Number of Point Groups
Number of Point Groups
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Crystal Systems
Crystal Systems
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Crystal Systems
Crystal Systems
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Unit Cell
Unit Cell
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Name this mineral?
Name this mineral?
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Crystal Lattice
Crystal Lattice
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Unit Cell Shape
Unit Cell Shape
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Bravais Lattices
Bravais Lattices
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Bravais Lattice Types
Bravais Lattice Types
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Crystal system determination
Crystal system determination
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Crystal Faces
Crystal Faces
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Crystallographic Axis
Crystallographic Axis
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Classification Basis
Classification Basis
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Miller-Bravais indices
Miller-Bravais indices
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Hexagonal Division
Hexagonal Division
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Trigonal Division
Trigonal Division
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Crystals Divided
Crystals Divided
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Point Groups Divided
Point Groups Divided
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Crystal Division Number
Crystal Division Number
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Crystal Structure with a₁=a2≠c; α=β=γ=90°.
Crystal Structure with a₁=a2≠c; α=β=γ=90°.
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Crystal Structure with a1=a2=a3 all axis at 90°.
Crystal Structure with a1=a2=a3 all axis at 90°.
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Crystal Structure with a ≠ b≠ c; α ≠ β ≠ γ ≠ 90°.
Crystal Structure with a ≠ b≠ c; α ≠ β ≠ γ ≠ 90°.
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Crystal Structure with a1=a2=a3≠c; β=90° γ=120°.
Crystal Structure with a1=a2=a3≠c; β=90° γ=120°.
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Study Notes
- Crystallography is the study of crystals
- Knowing the systems and the common symmetry elements is important
- The 32 point groups are subdivided into six crystal systems
Point Groups and Crystal Classes
- The possible combinations that can be made with the different symmetry elements amounts to 32
- They are called the 32 point groups or crystal classes
Unit Cell
- The unit cell is the smallest possible unit of a crystal that contains all the chemical components, structural features, and symmetry of the crystal as a whole
Crystal Lattice
- Units cells can be stacked in three dimensions to form a crystal lattice
- A crystal lattice is an infinitely repeating pattern of atoms, ions, or groups of atoms (molecules), to form a crystal
Unit Cell Shapes
- There are 14 possible shapes of unit cells
- All minerals will fall into one of the 14 basic shapes called Bravais lattices
- Unit cells are parallelepiped, a six-faced figure with each pair of opposite faces parallel and of equal size
Crystal Faces
- Crystals are made of building blocks called unit cells that contain all the structural and chemical components and symmetry of the crystal as a whole
- There are 14 types of unit cells called Bravais lattices, that can be subdivided into trigonal, monoclinic, orthorhombic, tetragonal, hexagonal, rhombohedral, and cubic
- Stacking these unit cells creates a crystal lattice
- Depending on the exact type of unit cell, the crystal that forms will fall into one of the seven crystal systems
- Stacking occurs in a regular way to ensure a uniform charge distribution
- To ensure a uniform charge distribution, crystals tend to develop flat faces
- These flat faces usually arise along planes with the greatest density of atoms in the crystal lattice
- As a crystal grows, new atoms attach easily to the rougher and less stable parts of the surface, but less easily to the flat, stable surfaces
- Flat surfaces tend to grow larger and smoother, until the crystal surface consists of these plane surfaces
Crystallographic Systems
- A crystallographic axis is an imaginary line that passes through the center of a crystal
- There are three axes, the c-axis, which is upright, and two or three horizontal axes, a and b
Determining to Which Crystal System a Crystal Belongs
- Imagine to which shape of parallelepipe it will fit
- Sketch in the three crystallographic axis
- Classify according to length of axis and angle between axis
Orthorhombic Crystal System
- a≠b≠c
- α=β=γ=90°
Tetragonal Crystal System
- a1=a2≠c
- α=β=γ=90°
The Miller-Bravais Indices
- The Miller-Bravais indices use four axes
Hexagonal Crystal System
- a1=a2=a3≠c
- β=90°
- γ=120°
- Hexagonal system is subdivided into two subdivisions, Trigonal and Hexagonal
- Crystals in the hexagonal division have one 6-fold axis, while in the trigonal division it has one 3-fold axis
Isometric System
- a1=a2=a3
- All axis at 90° to each other
Monoclinic
- a ≠ b ≠ c
- β > 90°; α = γ = 90°
Triclinic
- a≠ b≠ c
- α ≠ β ≠ γ ≠ 90°
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