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Questions and Answers
Planes of symmetry are defined as the plane that divides a crystal into two equal halves.
Planes of symmetry are defined as the plane that divides a crystal into two equal halves.
True
The axis of symmetry refers exclusively to the rotation axis of symmetry.
The axis of symmetry refers exclusively to the rotation axis of symmetry.
False
Crystal symmetry center is one of the elements of symmetry in crystals.
Crystal symmetry center is one of the elements of symmetry in crystals.
True
Symmetry only involves the repetition of patterns without any specific rules.
Symmetry only involves the repetition of patterns without any specific rules.
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Rotation inversion symmetry axis is a type of axis of symmetry.
Rotation inversion symmetry axis is a type of axis of symmetry.
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Every crystal face on one side of the center has a corresponding face on the opposite side.
Every crystal face on one side of the center has a corresponding face on the opposite side.
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The distance of the crystal face from the center is not important for correspondence.
The distance of the crystal face from the center is not important for correspondence.
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Crystal characteristics on opposite sides must be identical.
Crystal characteristics on opposite sides must be identical.
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Symmetry operations include both reflection and rotation.
Symmetry operations include both reflection and rotation.
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Angles located at the corners of the crystal are relevant for determining symmetry.
Angles located at the corners of the crystal are relevant for determining symmetry.
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A face or corner angle cannot be repeated more than twice during a full 360-degree rotation around the axis of symmetry.
A face or corner angle cannot be repeated more than twice during a full 360-degree rotation around the axis of symmetry.
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A crystal can have faces that are not opposite and corresponding to each other.
A crystal can have faces that are not opposite and corresponding to each other.
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The axis of symmetry is a physical line that can be seen in a crystal.
The axis of symmetry is a physical line that can be seen in a crystal.
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Every face, letter, or corner of a symmetrical object is identical when viewed from the opposite side.
Every face, letter, or corner of a symmetrical object is identical when viewed from the opposite side.
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Rotation around the axis of symmetry ensures displacement of the faces.
Rotation around the axis of symmetry ensures displacement of the faces.
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The total shape of a crystal is called Axial cross.
The total shape of a crystal is called Axial cross.
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Crystal systems with three crystal axes include the hexagonal system.
Crystal systems with three crystal axes include the hexagonal system.
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In three-axis crystal systems, axial angles are defined with the relationships α=β=γ.
In three-axis crystal systems, axial angles are defined with the relationships α=β=γ.
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The angle between the axes c and a is referred to as beta.
The angle between the axes c and a is referred to as beta.
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All crystal systems with four axes have three horizontal axes and one vertical axis.
All crystal systems with four axes have three horizontal axes and one vertical axis.
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In four-axis crystal systems, the angle between the horizontal axes a1, a2, and a3 is 120°.
In four-axis crystal systems, the angle between the horizontal axes a1, a2, and a3 is 120°.
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The axial angle gamma between the axes a and b is 90° in four-axis crystal systems.
The axial angle gamma between the axes a and b is 90° in four-axis crystal systems.
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Four-axis crystal systems have three axial angles between their three horizontal axes.
Four-axis crystal systems have three axial angles between their three horizontal axes.
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In four-axis crystal systems, there are only two horizontal axes.
In four-axis crystal systems, there are only two horizontal axes.
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The angle gamma is a crucial aspect in describing the structure of four-axis crystal systems.
The angle gamma is a crucial aspect in describing the structure of four-axis crystal systems.
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In a hexagonal system, the parameters a1, a2, and a3 are equal to each other.
In a hexagonal system, the parameters a1, a2, and a3 are equal to each other.
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All crystal structures that share the same axial system belong to different crystal systems.
All crystal structures that share the same axial system belong to different crystal systems.
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In a hexagonal system, the angle δ can be defined as 120 degrees.
In a hexagonal system, the angle δ can be defined as 120 degrees.
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The parameters α and β in a hexagonal system are equal to 90 degrees.
The parameters α and β in a hexagonal system are equal to 90 degrees.
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The axial parameters do not influence the classification of crystal systems.
The axial parameters do not influence the classification of crystal systems.
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Study Notes
Crystallography
- Crystallography is the study of crystals and crystallized materials found in nature.
- These materials can exist in single forms, or groups of forms.
- Crystallography focuses on the shape of crystals, the relationship between crystal faces, and various natural properties.
- A crystal is a part of a solid medium that has a homogeneous chemical composition.
- It's defined by flat surfaces with symmetrical relationships.
- Crystals are formed by natural forces under specific pressure and temperature conditions.
- Crystals possess a specific atomic structure.
Crystal Characteristics
- Crystal faces: These are the outer surfaces of a crystal. They shape the crystal, creating a regular geometry, a result of the crystal's internal atomic arrangement. Typically, crystal faces are flat.
- Edges: These are lines formed where crystal planes or faces meet.
- Interfacial angles: These angles are created by the convergence of two crystalline faces.
- Solid angles: These angles result from the convergence of more than two crystal faces.
Crystal Symmetry
- Crystal symmetry refers to the process that results in certain crystal facets occupying the same positions, as if by repetition.
- Symmetry operations are the repetitive operations applied to produce symmetry.
- Elements of symmetry include:
- Planes of symmetry: These planes divide the crystal into two symmetrical halves. Each face, edge, or corner on one side of the plane has a similar counterpart on the other side.
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Axes of symmetry:
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Rotation axis of symmetry: An imaginary line through the crystal center, rotating the crystal. A face, letter or corner angle is repeated upon rotation by specific incremental degrees:
- Diagonal axis: rotates 180 degrees.
- Trigonal axis: rotates 120 degrees
- Tetragonal axis rotates 90 degrees
- Hexagonal axis: rotates 60 degrees.
- Rotation-inversion axis of symmetry: Involves a rotation followed by an inversion (flipping) through a center point.
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Rotation axis of symmetry: An imaginary line through the crystal center, rotating the crystal. A face, letter or corner angle is repeated upon rotation by specific incremental degrees:
- Crystal symmetry center: An imaginary central point around which crystal faces, etc. are arranged in pairs, with similar positions on opposite sides, equidistant.
Crystal Systems
- Crystal systems are groups of crystals that share similar shapes, areas, and physical/chemical properties.
- They are categorized based on their axial systems.
- There are seven crystal systems.
- Cubic
- Tetragonal
- Orthorhombic
- Monoclinic
- Triclinic
- Trigonal (Rhombohedral)
- Hexagonal
- These systems have specific relationships between the axial lengths (a, b, c) and the angles (α, β, γ) between them.
C-Axis
- The c-axis of a crystal can indicate the crystal system:
- Hexagonal symmetry if the c-axis is hexagonal.
- Trigonal symmetry if the c-axis is trigonal.
- Quadrilateral symmetry if the c-axis is quadrilateral.
- Binary symmetry if the c-axis is binary, which indicates an orthorhombic system.
Stereographic Projection
- Stereographic projection is a method to represent three-dimensional crystal data on a two-dimensional plane (a flat surface).
- Crystals are placed at the center of a sphere, and the normals to crystal faces intersect the sphere, defining points ("poles").
- The angles between poles on the sphere correlate to angles between faces in the crystal.
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Description
This quiz explores the fundamental concepts of crystallography, including the characteristics of crystals such as faces, edges, and interfacial angles. Learn about the formation, structure, and properties of crystals in nature. Test your understanding of how crystals are defined and categorized based on their atomic arrangements.
