Chapter 3 Flashcards
What are two types of packing?
- Non dense, random packing
- Dense, ordered packing
Why are ordered structures more stable?
They tend to be nearer to the minimum bonding energy
What are the two types of materials/arrangements?
- Crystalline
- Noncrystalline/amorphous
What are some characteristics of crystalline materials?
They have atoms arranged in periodic, 3D arrays, and are typical of metals, many ceramics, and some polymers
What are some characteristics of noncrystalline/amorphous materials?
They have no periodic arrangement, are found in complex structures, and are often caused by rapid cooling
What are the characteristics of metallic crystal structures?
- Dense atom packing
- Simpler structures compared to ceramics and polymers
Why do metallic crystal structures have dense packing?
- Bonds between atoms are nondirectional
- Nearest neighbor distances are small which lowers bond energy
- High degree of shielding of ion cores due to the free electron cloud
- Typically only one element is present so all atomic radii are the same
What is a unit cell?
The smallest repetitive volume that contains the complete lattice pattern of a crystal
What are the unit cell geometries for the seven crystal systems?
- Cubic
- Hexagonal
- Tetragonal
- Rhombohedral (Trigonal)
- Orthorhombic
- Monoclinic
- Triclinic
Sides/angles of cubic unit cells
All sides equal, all angles equal 90
Sides/angles of hexagonal unit cells
Two sides equal with 90 deg angles, other has 120
Sides/angles of tetragonal unit cells
Two sides equal, all angles equal 90
Sides/angles of rhombohedral unit cells
All sides equal, all angles do not equal 90
Sides/angles of orthorhombic unit cells
No sides equal, all angles equal 90
Sides/angles of monoclinic unit cells
No sides equal, two angles equal 90
Sides/angles of triclinic unit cells
No sides equal, all angles do not equal 90
What are simple cubic (sc) crystal structures?
Cubic, with the centers of atoms located at each of the eight corners. They are rare because they have low packing density (only Po has it). Closed-packed directions are cube edges, the coordination number is 6, have 1 atom/unit cell, and the APF = 0.52.
What is a coordination number?
The number of nearest-neighbor/touching atoms
What is the atomic packing factor?
The volume of atoms in a unit cell divided by the volume of the cell
What are body-centered cubic (bcc) structures?
Cubic, centers of atoms at each corner and a single atom in the center. They have 2 atoms/unit cell, have a coordination number of 8, and an APF of 0.68. Often in metals that have covalent bonding. Ex: Cr, W, Fe, Ta, Mo
What are face-centered cubic (fcc) structures?
Cubic, centers of atoms at each corner and six atoms at the center of each face. They have 4 atoms/unit cell, a coordination number of 12, an APF of 0.74 (which is the maximum possible APF), and an ABC stacking sequence. Ex: Al, Cu, Au, Pb, Ni, Pt, Ag
What are hexagonal close-packed (hcp) structures?
Hexagonal, centers of atoms on each corner and center for A sites, and 3 atoms for B sites. They have 6 atoms/unit cell, a coordination number of 12, an APF of 0.74, ABA stacking sequence, and an ideal height/side length ratio of 1.633. Ex: Cd, Mg, Ti, Zn
What is the theoretical density of metals?
Mass of atoms in the unit cell/total volume of the unit cell
What is the order of densities for materials?
Metals > ceramics > polymers
Metals are close-packing and have large atomic masses
Ceramics often have lighter elements
Polymers have low packing density and lighter elements
Composites have moderate to low densities
What are single crystals?
When the periodic arrangement of atoms (crystal structure) extends without interruption throughout the entire specimen (atoms are all aligned in one direction).
What do the properties of crystalline materials depend on?
Crystal structure
What are polycrystalline materials?
Materials composed of many small single crystals (grains)
What is anisotropy?
Exhibiting different values of a property in different crystallographic directions, observed in single crystals. When grains of a polycrystal are textured, properties are anisotropic.
What is isotropy?
Having identical values of a property in all directions, is observed in polycrystals when grains are randomly oriented
What is polymorphism?
The ability of a solid material to exist in more than one form or crystal structure.
What is allotropy?
The possibility of the existence of two or more different crystal structures for a substance (generally an elemental solid).
What are point coordinates and how are they calculated?
A point coordinate is a lattice position in a unit cell determined as fractional multiples of a, b, and c unit cell edge lengths.
What is a family of directions?
All directions that are crystallographically equivalent (have the same atomic spacing) – indicated by indices in angle brackets (< >).
What is the linear density (ld) of atoms?
The number of atoms centered on a direction vector/length of the direction vector.
What are Miller Indices?
A set of three integers (four for hexagonal) that designate crystallographic planes, as determined from reciprocals of fractional axial intercepts.
What is a grain boundary?
The interface separating two adjoining grains having different crystallographic orientations.
What are the steps to finding the Miller Indices of a plane?
1.If plane passes through selected origin, establish a new origin in another unit cell
2. Read off values of intercepts of plane (designated A, B, C) with x, y, and z axes in terms of a, b, c
3. Take reciprocals of intercepts
4. Normalize reciprocals of intercepts by multiplying by lattice parameters a, b, and c
5.Reduce to smallest integer values
6.Enclose resulting Miller Indices in parentheses, no
commas i.e., (hkl)
What are the steps to finding the Miller Indices of a plane in a hexagonal unit cell?
- Relocate origin
- Intercepts
- Reciprocals
- Normalize
- Reduce
- Determine index: i = -(h + k)
- MBI (hkil)
What is planar density?
The number of atoms centered on a plane/area of the plane
What is interplanar spacing?
The distance between parallel planes of atoms
How is light diffracted?
The diffraction grating spacing must be comparable to the light wavelength
