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Total Categories: 6
The hexagonal crystal family comprises two Bravais lattices: the hexagonal and the rhombohedral lattices.
Answer: True
The hexagonal crystal family is constituted by the hexagonal lattice system and the rhombohedral lattice system, each containing a single Bravais lattice.
The hexagonal crystal family is associated with a total of 52 space groups.
Answer: True
The hexagonal crystal family encompasses precisely 52 space groups, corresponding to those assigned to either the hexagonal or rhombohedral lattice systems.
Which two crystal systems are included within the hexagonal crystal family?
Answer: The hexagonal and trigonal crystal systems
The hexagonal crystal family is defined as the union of the hexagonal crystal system and the trigonal crystal system.
The hexagonal crystal family is composed of which two lattice systems?
Answer: Hexagonal and rhombohedral lattice systems
The hexagonal crystal family is constituted by the hexagonal lattice system and the rhombohedral lattice system.
What is the total number of space groups associated with the hexagonal crystal family?
Answer: 52
The hexagonal crystal family is associated with a total of 52 space groups, which are precisely those assigned to either the hexagonal or rhombohedral lattice systems.
What is the distinction between a crystal family and a crystal system?
Answer: A system groups point groups, a family groups crystal systems
A crystal system classifies based on point group symmetry and lattice assignment, while a crystal family groups crystal systems that share common lattice types and symmetry characteristics.
The hexagonal crystal family includes both the hexagonal and rhombohedral lattice systems.
Answer: True
The hexagonal crystal family is defined by its inclusion of both the hexagonal lattice system and the rhombohedral lattice system.
The hexagonal crystal family encompasses crystal systems defined by specific rotational symmetry axes. Which statement accurately reflects this relationship?
Answer: The hexagonal crystal family contains systems characterized by both three-fold and six-fold axes of rotation.
The hexagonal crystal family is defined as the union of the trigonal crystal system (characterized by a three-fold axis of rotation) and the hexagonal crystal system (characterized by a six-fold axis of rotation).
What symmetry element characterizes the hexagonal crystal system?
Answer: A six-fold axis of rotation
The defining characteristic of the hexagonal crystal system is the presence of at least one six-fold axis of rotation.
How many space groups are associated with the hexagonal crystal system, and where are they assigned?
Answer: 27 space groups, assigned exclusively to the hexagonal lattice
The hexagonal crystal system is associated with 27 space groups, all of which are assigned exclusively to the hexagonal lattice system.
The hexagonal crystal system is characterized by point groups with at least one six-fold axis of rotation.
Answer: True
The defining characteristic of the hexagonal crystal system is the presence of at least one six-fold axis of rotation.
The hexagonal crystal system is associated with 27 space groups, all assigned to the hexagonal lattice system.
Answer: True
The hexagonal crystal system is associated with 27 space groups, and all of these are exclusively assigned to the hexagonal lattice system.
The trigonal crystal system is unique in that its space groups are assigned to more than one lattice system.
Answer: True
The trigonal crystal system is unique because its space groups are assigned to both the rhombohedral and the hexagonal lattice systems, unlike most other crystal systems which are tied to a single lattice system.
Alpha-quartz exhibits trigonal symmetry and is classified under the hexagonal lattice system.
Answer: True
Alpha-quartz is a mineral that demonstrates trigonal symmetry but is classified within the broader hexagonal lattice system, illustrating the relationship between symmetry and lattice classification.
What is the defining symmetry requirement for the trigonal crystal system?
Answer: Presence of at least one three-fold axis of rotation
The trigonal crystal system is defined by point groups that possess at least one three-fold axis of rotation.
How many space groups are associated with the trigonal crystal system, and how are they distributed between lattice systems?
Answer: 25 space groups, with 7 assigned to the rhombohedral and 18 to the hexagonal lattice
The trigonal crystal system is associated with a total of 25 space groups; 7 are assigned to the rhombohedral lattice system, and 18 are assigned to the hexagonal lattice system.
What is unique about the trigonal crystal system concerning its associated lattice systems?
Answer: Its space groups are assigned to both the rhombohedral and hexagonal lattice systems
The trigonal crystal system is unique because its space groups are assigned to both the rhombohedral and the hexagonal lattice systems, unlike most other crystal systems which are tied to a single lattice system.
The trigonal crystal system is defined by point groups possessing at least one six-fold axis of rotation.
Answer: False
The trigonal crystal system is defined by point groups possessing at least one three-fold axis of rotation, not a six-fold axis.
The trigonal crystal system has 25 associated space groups, all assigned to the hexagonal lattice system.
Answer: False
While the trigonal crystal system has 25 associated space groups, only 18 are assigned to the hexagonal lattice system; the remaining 7 are assigned to the rhombohedral lattice system.
The hexagonal description of the rhombohedral lattice is generally preferred for calculations because its coordinate system includes two 90-degree angles, simplifying mathematical operations.
Answer: True
While the rhombohedral axes description better illustrates the inherent 3m symmetry, the hexagonal description is preferred for calculations due to its simpler coordinate system with two right angles.
The Pearson symbol for the rhombohedral Bravais lattice is not 'hP'.
Answer: True
The Pearson symbol for the rhombohedral Bravais lattice is 'hR', whereas 'hP' denotes the hexagonal Bravais lattice.
The formula V = a²c * sin(60°) is used to calculate the unit cell volume within the hexagonal crystal family.
Answer: True
This formula correctly accounts for the geometry of the hexagonal prism unit cell, where 'a' represents the lengths of the base axes and 'c' is the height.
What is the conventional description of a unit cell within the hexagonal crystal family?
Answer: A right rhombic prism
Conventionally, a unit cell in the hexagonal crystal family is described as a right rhombic prism, characterized by two equal axes at 120 degrees and a perpendicular third axis.
In the hexagonal unit cell description, what is the angle between the two equal 'a' axes?
Answer: 120 degrees
The hexagonal unit cell is defined by two equal axes ('a') that are separated by an angle of 120 degrees.
When the rhombohedral lattice system is represented using a hexagonal unit cell, what type of centering is used?
Answer: R-centered
When the rhombohedral lattice system is described using a hexagonal unit cell, it is represented by an R-centered cell.
Why is the hexagonal description of the rhombohedral lattice often preferred over the rhombohedral axes description?
Answer: Its coordinate system includes two 90-degree angles, simplifying math
The hexagonal description is generally preferred for practical calculations because its coordinate system includes two 90-degree angles, simplifying mathematical operations.
What is the formula for calculating the unit cell volume in the hexagonal crystal family?
Answer: V = a²c * sin(60°)
The volume of a unit cell in the hexagonal crystal family is calculated using the formula V = a²c * sin(60°), accounting for the geometry of the hexagonal prism.
What is the Pearson symbol for the rhombohedral Bravais lattice?
Answer: hR
The Pearson symbol for the rhombohedral Bravais lattice is 'hR'.
A unit cell in the hexagonal crystal family is conventionally described as a cube.
Answer: False
A unit cell in the hexagonal crystal family is conventionally described as a right rhombic prism, not a cube.
The hexagonal close-packed (hcp) structure is classified as a Bravais lattice.
Answer: False
The source states that hcp is not classified as a Bravais lattice because it contains two distinct sets of lattice points.
Lonsdaleite possesses identical atomic positions to the hexagonal close-packed (hcp) structure.
Answer: True
The source material indicates that the atomic positions within the hexagonal close-packed (hcp) structure are identical to those found in lonsdaleite.
The Wurtzite crystal structure is designated by the Hermann-Mauguin symbol P6_3mc.
Answer: True
The Wurtzite crystal structure is associated with space group No. 186 in the International Union of Crystallography classification, denoted as P6_3mc.
Wurtzite crystals are non-centrosymmetric.
Answer: True
The source material classifies Wurtzite crystals as non-centrosymmetric, meaning they lack inversion symmetry.
In the Wurtzite structure, each atom is tetrahedrally coordinated.
Answer: True
The Wurtzite structure is characterized by tetrahedral coordination, where each atom is surrounded by four nearest neighbors arranged in a tetrahedral geometry.
The Nickel Arsenide structure can be conceptualized as comprising two interpenetrating sublattices: a primitive hexagonal nickel sublattice and a hexagonal close-packed arsenic sublattice.
Answer: True
This structure is understood as a primitive hexagonal nickel sublattice and a hexagonal close-packed arsenic sublattice.
In the Nickel Arsenide structure, nickel atoms are octahedrally coordinated by arsenic atoms.
Answer: True
Within the Nickel Arsenide structure, nickel atoms exhibit octahedral coordination, being surrounded by six arsenic atoms.
The Wurtzite structure is designated B4 in the Strukturbericht system.
Answer: True
The Wurtzite structure is indeed classified as B4 within the Strukturbericht system, indicating its specific crystallographic notation.
The Nickel Arsenide structure is not understood as a face-centered cubic arrangement of arsenic atoms with nickel atoms in the interstitial sites.
Answer: True
The Nickel Arsenide structure is conceptualized as a hexagonal close-packed arrangement of arsenic atoms, with nickel atoms occupying the octahedral voids, not an FCC arrangement.
The Wurtzite structure exhibits piezoelectricity, contrary to the assertion that it lacks it due to centrosymmetry.
Answer: True
The Wurtzite structure is non-centrosymmetric, which is the prerequisite for exhibiting piezoelectricity and pyroelectricity.
Is the hexagonal close-packed (hcp) structure classified as a Bravais lattice?
Answer: No, because it contains two distinct sets of lattice points
The hexagonal close-packed (hcp) structure is not classified as a Bravais lattice because it comprises two distinct sets of lattice points, rather than the single set required for a Bravais lattice.
What is the specific space group notation for the Wurtzite crystal structure?
Answer: P6_3mc
The Wurtzite crystal structure is associated with space group No. 186, which is designated as P6_3mc in the Hermann-Mauguin notation.
Which physical properties can Wurtzite crystals exhibit due to their non-centrosymmetric nature?
Answer: Piezoelectricity and pyroelectricity
Wurtzite crystals, being non-centrosymmetric, possess the capability to exhibit piezoelectricity and pyroelectricity.
How are atoms coordinated in the Wurtzite structure?
Answer: Tetrahedrally
In the Wurtzite structure, each atom is tetrahedrally coordinated, meaning it is surrounded by four nearest neighbors arranged in a tetrahedral geometry.
In the Nickel Arsenide structure, how are the nickel atoms coordinated?
Answer: Octahedrally
In the Nickel Arsenide structure, nickel atoms are octahedrally coordinated by six arsenic atoms.
In the Nickel Arsenide structure, how are the arsenic atoms coordinated?
Answer: Trigonal prismatically
In the Nickel Arsenide structure, arsenic atoms are coordinated trigonal prismatically by six nickel atoms.
The Nickel Arsenide structure can be conceptualized as a hexagonal close-packed arrangement of which element, with the other element occupying specific voids?
Answer: Arsenic atoms packed, Nickel in octahedral voids
The Nickel Arsenide structure is understood as a hexagonal close-packed arrangement of arsenic atoms, with nickel atoms occupying the octahedral voids within this packing.
Compounds that commonly adopt the Nickel Arsenide structure are typically formed between which classes of elements?
Answer: Transition metals and chalcogens, arsenic, antimony, or bismuth
The Nickel Arsenide structure is characteristic of compounds formed between transition metals and elements such as chalcogens, arsenic, antimony, and bismuth.
How are multi-element structures, such as binary compounds, often conceptualized within the hexagonal crystal family?
Answer: As multiple interpenetrating sublattices
Multi-element structures within the hexagonal crystal family are frequently conceptualized as multiple interpenetrating sublattices.
What does the Hermann-Mauguin symbol P6_3mc for the Wurtzite structure signify?
Answer: A primitive lattice, a six-fold screw axis, and mirror/glide planes
The symbol P6_3mc indicates a primitive lattice ('P'), a six-fold screw rotation axis along the c-axis ('6_3'), and mirror/glide planes ('.m.' and '..c').
Minerals such as dolomite and calcite do not belong to the hexagonal crystal system.
Answer: True
The source lists calcite as an example of the trigonal crystal system, not the hexagonal crystal system.
Minerals such as nepheline and beryl are examples of the hexagonal crystal system.
Answer: True
The source material explicitly lists nepheline and beryl as minerals belonging to the hexagonal crystal system.
Gallium Nitride (GaN) is a notable example of a compound that crystallizes in the Wurtzite structure.
Answer: True
Gallium Nitride (GaN) is frequently cited as a semiconductor compound that adopts the Wurtzite crystal structure.
Which of the following minerals is cited as an example of the trigonal crystal system?
Answer: Calcite
Calcite is explicitly listed as an example of a mineral belonging to the trigonal crystal system.
Which of the following minerals is cited as an example of the hexagonal crystal system?
Answer: Apatite
Apatite is listed as a mineral that exhibits the symmetries of the hexagonal crystal system.
Which of the following is a common example of a compound crystallizing in the Wurtzite structure?
Answer: Gallium Nitride (GaN)
Gallium Nitride (GaN) is frequently cited as a semiconductor compound that adopts the Wurtzite crystal structure.
Which mineral is listed as an example of the hexagonal crystal system?
Answer: Beryl
Beryl is explicitly listed as a mineral belonging to the hexagonal crystal system.