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Questions and Answers
What is the effective number of atoms per hexagonal unit cell in HCP structure?
What is the effective number of atoms per hexagonal unit cell in HCP structure?
- 6 atoms (correct)
- 8 atoms
- 2 atoms
- 4 atoms
How much does each corner atom contribute to the total number of atoms in a unit cell?
How much does each corner atom contribute to the total number of atoms in a unit cell?
- 1/4 atom
- 1/6 atom (correct)
- 1/3 atom
- 1/2 atom
What formula represents the Atomic Packing Factor (APF)?
What formula represents the Atomic Packing Factor (APF)?
- APF = (N * Volume of atoms) / Volume of unit cell (correct)
- APF = Volume of unit cell / (N * Volume of atoms)
- APF = (Volume of unit cell) / N
- APF = N / Volume of atom
Which atoms contribute to the effective number of atoms in HCP structure?
Which atoms contribute to the effective number of atoms in HCP structure?
What is the APF in HCP structure indicative of?
What is the APF in HCP structure indicative of?
What is the contribution of each face centered atom in HCP structure per unit cell?
What is the contribution of each face centered atom in HCP structure per unit cell?
Which of the following metals crystallizes in HCP structure?
Which of the following metals crystallizes in HCP structure?
What value must be used as 'N' in the APF formula for HCP?
What value must be used as 'N' in the APF formula for HCP?
What is a group of equivalent directions in crystallography called?
What is a group of equivalent directions in crystallography called?
How are families of directions indicated in crystallography?
How are families of directions indicated in crystallography?
What is the first step in determining the indices for a crystallographic plane?
What is the first step in determining the indices for a crystallographic plane?
What indicates a negative direction in the Miller indices notation?
What indicates a negative direction in the Miller indices notation?
If a plane is parallel to an axis, what is its intercept considered?
If a plane is parallel to an axis, what is its intercept considered?
Which of the following is true regarding crystallographic planes?
Which of the following is true regarding crystallographic planes?
What is step 3 in the process of finding Miller indices?
What is step 3 in the process of finding Miller indices?
What must be done to the intercepts before enclosing them in parentheses?
What must be done to the intercepts before enclosing them in parentheses?
What is the first step in defining any direction of a vector?
What is the first step in defining any direction of a vector?
How are the projections of a vector on the X, Y, and Z axes determined?
How are the projections of a vector on the X, Y, and Z axes determined?
What is the final outcome after computing the Miller indices from a vector's projections?
What is the final outcome after computing the Miller indices from a vector's projections?
In the Miller indexing system, how is a negative direction represented?
In the Miller indexing system, how is a negative direction represented?
When finding the Miller indices, what transformation is applied to ensure the values are whole numbers?
When finding the Miller indices, what transformation is applied to ensure the values are whole numbers?
What are the intercepts for the given vector when $a = b = c$?
What are the intercepts for the given vector when $a = b = c$?
What represents a 'step' moved parallel to an axis when pinning down a vector in 3D space?
What represents a 'step' moved parallel to an axis when pinning down a vector in 3D space?
How are the directional indices represented according to the conventions used in the Miller system?
How are the directional indices represented according to the conventions used in the Miller system?
What are the Miller indices for a plane that is perpendicular to the Z axis?
What are the Miller indices for a plane that is perpendicular to the Z axis?
Which of the following is true about point imperfections in crystals?
Which of the following is true about point imperfections in crystals?
Which type of crystal defect is defined as a three-dimensional imperfection?
Which type of crystal defect is defined as a three-dimensional imperfection?
What impact can Schottky and Frankel point defects have on metals?
What impact can Schottky and Frankel point defects have on metals?
What is a characteristic of an ideal crystal?
What is a characteristic of an ideal crystal?
How can crystal defects be reduced?
How can crystal defects be reduced?
Which type of imperfection in a crystal lattice is classified as a one-dimensional defect?
Which type of imperfection in a crystal lattice is classified as a one-dimensional defect?
What causes point defects to form during the crystal lattice formation?
What causes point defects to form during the crystal lattice formation?
Which crystal system has the property that all axial lengths are unequal and all interaxial angles are also unequal?
Which crystal system has the property that all axial lengths are unequal and all interaxial angles are also unequal?
What is the total effective number of atoms per unit cell in a body-centered cubic (BCC) structure?
What is the total effective number of atoms per unit cell in a body-centered cubic (BCC) structure?
In which crystal structure do the atoms located at the corners of the cubic cell touch the face-centered atoms?
In which crystal structure do the atoms located at the corners of the cubic cell touch the face-centered atoms?
Which of the following statements is true regarding the interaxial angles of the orthorhombic crystal system?
Which of the following statements is true regarding the interaxial angles of the orthorhombic crystal system?
Which of the following metals crystallizes in a body-centered cubic (BCC) structure?
Which of the following metals crystallizes in a body-centered cubic (BCC) structure?
Which crystal system is also known as Cubic Close Packed (CCP)?
Which crystal system is also known as Cubic Close Packed (CCP)?
How many corner atoms contribute to the effective atom count in a body-centered cubic unit cell?
How many corner atoms contribute to the effective atom count in a body-centered cubic unit cell?
Which of the following characterizes the tetragonal crystal system?
Which of the following characterizes the tetragonal crystal system?
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Study Notes
Triclinic Crystal System and Summary of Crystal Systems
- Triclinic crystals have variable axial lengths where a≠b≠c and all interaxial angles (α, β, γ) are unequal and ≠90°.
- The seven crystal systems include:
- Cubic: a = b = c; α = β = γ = 90°
- Tetragonal: a = b ≠c; α = β = γ = 90°
- Hexagonal: a = b ≠c; α = β = 90°, γ = 120°
- Orthorhombic: a ≠b ≠c; α = β = γ = 90°
- Rhombohedral: a = b = c; α = β = γ ≠90°
- Monoclinic: a ≠b ≠c; α = β = 90°, γ ≠90°
- Triclinic: a ≠b ≠c; α ≠β ≠γ ≠90°
Body Centered Cubic Structure (BCC)
- Atoms located at eight corners of the cubic cell and one at the geometric center.
- Total atoms per BCC unit cell is 9 (8 corner + 1 center).
- Corner atoms contribute 1/8 each, and the center atom contributes 1, leading to:
- Effective number of atoms in BCC = 2 (1 from corners + 1 from center).
- Metals such as Chromium, α-Fe, δ-Fe, Molybdenum, and Lithium exhibit BCC structure.
Face Centered Cubic Structure (FCC)
- Atoms are situated at the eight corners and six face centers of the cubic cell.
- No atoms in the body center unlike BCC.
- Effective number of atoms in FCC is calculated as:
- 12 corner atoms contributing 1/6 each + 2 face-centered atoms contributing 1/2 each + 3 internal atoms = 6 total.
- Metals such as Magnesium, Zinc, and Graphite crystallize in the FCC structure.
Atomic Packing Factor (APF)
- Indicates the volume percentage occupied by atoms in a unit cell.
- Formula for APF: ( APF = \dfrac{N \times V_{atom}}{V_{cell}} \times 100 )
- Where N = effective number of atoms, ( V_{atom} ) = volume of a spherical atom, and ( V_{cell} ) = volume of the unit cell.
Miller Indices
- Used to denote crystallographic directions and planes.
- Directions expressed as [uvw]; negative directions indicated with bars over integers.
- Families of equivalent directions shown in angular brackets.
- Indices derived from steps to intersections on axes:
- For a direction: determine intercepts, take reciprocals, convert to whole numbers.
- For a plane: determine intersections, take reciprocals, convert to whole numbers.
Crystal Imperfections
- Ideal crystals have perfect atomic arrangements; real crystals have imperfections due to finite size and surface boundaries.
- Types of crystal defects:
- Point Imperfections: Atoms missing or extra (e.g., Schottky and Frankel defects affecting properties like conductivity).
- Line or Linear Imperfections: Affecting rows of atoms.
- Surface or Plane Imperfections: Seen on boundaries.
- Volume Imperfections: Affect entire volumes of the crystal.
- Formation causes include irradiation, plastic deformation, quenching, and increased temperature leading to distortions in crystal lattice.
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