Podcast
Questions and Answers
Which crystal structure has a maximum achievable Atomic Packing Factor (APF) of 0.74?
Which crystal structure has a maximum achievable Atomic Packing Factor (APF) of 0.74?
- Simple Cubic
- Face-Centered Cubic (FCC) (correct)
- Body-Centered Cubic (BCC)
- Hexagonal Close-Packed (HCP)
In a Face-Centered Cubic (FCC) crystal structure, how many atoms are located at the corners of the unit cell?
In a Face-Centered Cubic (FCC) crystal structure, how many atoms are located at the corners of the unit cell?
- 4
- 8 (correct)
- 0
- 1
How many total atoms are there in a Face-Centered Cubic (FCC) unit cell?
How many total atoms are there in a Face-Centered Cubic (FCC) unit cell?
- 1
- 8
- 4 (correct)
- 2
What is the volume of a Face-Centered Cubic (FCC) unit cell with side length 'a'?
What is the volume of a Face-Centered Cubic (FCC) unit cell with side length 'a'?
Which type of atom stacking sequence is characteristic of a Hexagonal Close-Packed (HCP) crystal structure?
Which type of atom stacking sequence is characteristic of a Hexagonal Close-Packed (HCP) crystal structure?
What type of lattice is the Hexagonal Close-Packed (HCP) lattice according to F.M. Miller Chemistry: Structure and Dynamics?
What type of lattice is the Hexagonal Close-Packed (HCP) lattice according to F.M. Miller Chemistry: Structure and Dynamics?
What are Miller Indices?
What are Miller Indices?
What does multiplying by 4 do when converting fractions to integers in crystallography?
What does multiplying by 4 do when converting fractions to integers in crystallography?
What is the process for determining Miller Indices?
What is the process for determining Miller Indices?
What are the Miller Indices for a plane with intercepts of 1, 3, and 2 along the x, y, and z axes respectively?
What are the Miller Indices for a plane with intercepts of 1, 3, and 2 along the x, y, and z axes respectively?
Which crystal system has a = b = c and α = β = γ = 90°?
Which crystal system has a = b = c and α = β = γ = 90°?
What is the common feature of all parallel planes based on Miller Indices?
What is the common feature of all parallel planes based on Miller Indices?
Which crystal system has α = β = 90° and γ = 120°?
Which crystal system has α = β = 90° and γ = 120°?
Based on crystallographic principles, what do the Miller Indices (100) represent?
Based on crystallographic principles, what do the Miller Indices (100) represent?
Which lattice type has a lattice point at the center of the cube in addition to vertices?
Which lattice type has a lattice point at the center of the cube in addition to vertices?
Which lattice type has a lattice point at the center of each face of the cube in addition to vertices?
Which lattice type has a lattice point at the center of each face of the cube in addition to vertices?
Which type of crystal system has α = γ = 90° and β ≠90°?
Which type of crystal system has α = γ = 90° and β ≠90°?
Which crystal system has all lattice constants unequal (a ≠b ≠c) and all angles between axes acute (α ≠β ≠γ ≠90°)?
Which crystal system has all lattice constants unequal (a ≠b ≠c) and all angles between axes acute (α ≠β ≠γ ≠90°)?
What is the coordination number in the given crystal structure?
What is the coordination number in the given crystal structure?
What is the ideal ratio of c/a in the given crystal structure?
What is the ideal ratio of c/a in the given crystal structure?
In a cubic unit cell, which axis is directed to the right?
In a cubic unit cell, which axis is directed to the right?
What is the purpose of direction indices in cubic crystals?
What is the purpose of direction indices in cubic crystals?
How are the direction indices (1, 1/2, 0) converted to integers?
How are the direction indices (1, 1/2, 0) converted to integers?
What are the emergence coordinates of the vector in the example?
What are the emergence coordinates of the vector in the example?
What are the Miller indices of the crystallographic direction in Fig. 3.24(a)?
What are the Miller indices of the crystallographic direction in Fig. 3.24(a)?
What is the intercept of the basal plane on the a3 axis in the hexagonal unit cell?
What is the intercept of the basal plane on the a3 axis in the hexagonal unit cell?
In the hexagonal close-packed (HCP) crystal structure, what is the relationship between the 'a' and 'b' voids?
In the hexagonal close-packed (HCP) crystal structure, what is the relationship between the 'a' and 'b' voids?
What is the difference between the HCP and FCC crystal structures?
What is the difference between the HCP and FCC crystal structures?
What are the Miller-Bravais indices of the plane ABCD?
What are the Miller-Bravais indices of the plane ABCD?
What is the direction of the dashed red lines in Fig. 3.24(a)?
What is the direction of the dashed red lines in Fig. 3.24(a)?
Study Notes
Face-Centered Cubic (FCC) Structure
- All atoms are identical in an FCC structure.
- The coordination number for FCC is 12, and there are 4 atoms per unit cell.
- The atomic packing factor (APF) for an FCC structure is 0.74, which is the maximum achievable APF.
- The close-packed directions in an FCC structure have a length of 4R, where R is the atomic radius.
Hexagonal Close-Packed (HCP) Crystal Structure
- The HCP lattice is not a Bravais lattice because not all lattice points have the same environment.
- The HCP structure has an ABAB... stacking sequence.
- The 3D projection of the HCP structure can be represented as a 2D projection with a, c, and A, B, and C sites.
Miller Indices
- Miller indices are reciprocals of the axial intercepts for a plane, cleared of fractions and common multiples.
- The algorithm to calculate Miller indices involves:
- Reading off intercepts of the plane with axes in terms of a, b, and c.
- Taking reciprocals of the intercepts.
- Reducing to smallest integer values.
- Enclosing in parentheses, with no commas.
- Examples of Miller indices include (100), (110), (111), (634), and (1011).
Crystal Systems and Bravais Lattice
- There are 7 crystal systems, which are necessary to create all point lattices.
- The 7 crystal systems are:
- Cubic
- Tetragonal
- Orthorhombic
- Rhombohedral
- Hexagonal
- Monoclinic
- Triclinic
- According to Bravais, there are 14 standard unit cells that can describe all possible lattice networks.
- The 14 unit cells include:
- Simple Cubic (SC)
- Body-Centered Cubic (BCC)
- Face-Centered Cubic (FCC)
- Simple Tetragonal
- Body-Centered Tetragonal
- Simple Orthorhombic
- Body-Centered Orthorhombic
- Face-Centered Orthorhombic
- Base-Centered Orthorhombic
- Simple Rhombohedral
- Simple Hexagonal
- Simple Monoclinic
- Base-Centered Monoclinic
- Simple Triclinic
Directions in Cubic Unit Cells
- Direction indices are position coordinates of the unit cell where the direction vector emerges from the cell surface, converted to integers.
- In cubic crystals, direction indices are vector components of directions resolved along each axis, reduced to the smallest integers.
- Examples of direction indices include (1,0,0) and (1,1/2,0).
HCP Crystallographic Directions
- The direction indices for HCP crystal structures can be calculated using the same method as for cubic crystals.
- Examples of HCP direction indices include [1120].
Crystallographic Planes (HCP)
- The Miller-Bravais indices for HCP crystal structures can be calculated using the same method as for cubic crystals.
- Examples of HCP Miller-Bravais indices include (1011).
Structural Difference between HCP and FCC
- The main difference between HCP and FCC structures is the arrangement of atoms in the crystal lattice.
- In HCP, the third layer of atoms is placed in the 'b' voids of the previous layer, resulting in a different stacking sequence compared to FCC.
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Description
Test your knowledge on crystal systems and Bravais lattice in this quiz. Learn about the 7 different crystal systems: cubic, tetragonal, orthorhombic, rhombohedral, hexagonal, monoclinic, and triclinic. Explore the 14 unit cells according to Bravais to understand lattice networks.
