Material Science Chapter 3
Crystallographic Planes
1. Read off intercepts of plane with axes in terms of a, b, c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no commas i.e., (hkl)
Three factors that effect which interstitial sites will cations occupy in Ceramic structures?
1. Size of sites, does the cation fit in the site? 2. Stoichiometry, if all of one type of site is full, the remainder have to go into other types of sites. 3. Bond Hybridization, if % ionic character is low, covalent bonding dominate, lead to directional bonding.
HCP Crystallographic Directions
1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a1, a2, or c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas [u' v′ wʹ ]
lattice
A three- dimensional array of points coinciding with atom positions or sphere centers.
Families of directions
All directions that have the same linear density, example <100> family: [001] [010] [100]
Families of planes:
All planes that have the same planar density. e.g.(100), (001), (010) → {100} family
Tetrahedral site
An interstitial position that has a coordination number of 4. An atom or ion in the cubic sites touches 4 other atoms or ions.
Cubic site
An interstitial position that has a coordination number of 8. An atom or ion in the cubic sites touches 8 other atoms or ions.
AX-Type Crystal Structures
Ceramic materials in which there are equal numbers of cations and anions
crystal system
Divide crystal structures into groups according to unit cell configurations and/or atomic arrangements. The seven are cubic, tetragonal, hexagonal, orthorhombic, rhombohedral (also called trigonal),
allotropy
Elemental solids that have more than one crystal structure.
tetrahedral position
Four atoms, three in one plane and a single one in the adjacent plane surround one type that are in Ceramics.
AmXp-Type Crystal Structures
If the charges on the cations and anions are not the same, a compound can exist with the chemical formula AmXp, where m and/or p can not equal 1.
The largest interstitial sites for FCC are the octahedral sites.
In FCC Positions: in the unit cell with coordinates (1/2,1/2,1/2) and equivalent positions, i.e. (0,1/2,0), (0,0,1/2) and (1/2,0,0). Only 4 sites per unit cell due to Stoichiometry and the balancing of atoms. Interstitial radius: 0.414R
unit cell
Is the basic structural unit or building block of the crystal structure. Defines the crystal structure by virtue of its geometry and the atom positions within.
Carbon type Fullerenes
It exists in discrete molecu- lar form and consists of a hollow spherical cluster of 60 carbon atoms
AmBnXp-Type Crystal Structures :Perovskite crystal structure
It is also possible for ceramic compounds to have more than one type of cation; for two types of cations (represented by A and B), their chemical formula may be designated as AmBnXp.
Carbon type Diamond
Its crystal structure is a variant of the zinc blende structure in which carbon atoms occupy all positions
Interstitial sites
Locations between the "normal" atoms or ions in a crystal into which another usually different atom or ion is placed.
polymorphism
Materials that have more than one crystal structure.
amorphous
Materials that lack a systematic and regular arrangement of atoms over relatively large atomic distances.
Linear Density
Number of atoms /Unit length of direction vector
In BCC, the smaller interstitial sites are at "O" octahedral sites
Positions in the unit cell with coordinates (1/2,1/2, 0) and equivalent positions. 6 nearest neighbors, irregular octahedral. 6 sites per unit cell Interstitial radius = 0.15R
The largest interstitial sites for BCC are at "X" tetrahedral sites.
Positions: in the unit cell with coordinates (1/2,1/4,0) and equivalent positions and have 12 sites per unit cell. Interstitial radius = 0.288R
The next largest interstitial sites for FCC are the tetrahedral sites
Positions: in the unit cell with coordinates (1/4,1/4,1/4) and equivalent positions and have 8 per unit cell. Interstitial radius: 0.225R
anisotropy in Polycrystals
Properties vary with direction and increases with decreasing structural symmetry.
Layered silicates
SiO₄ tetrahedra connected together to form 2-D plane A net negative charge is associated with each (Si₂O₅)²⁻ unit, which is balanced by adjacent plane rich in positively charged cations
SILICATE CERAMICS
Silicates are materials composed primarily of silicon and oxygen. Each atom of silicon is bonded to four oxygen atoms, 4 which are situated at the corners of the tetrahedron. Silicates are not considered to be ionic because there is a significant covalent character.
isotropic
Substances in which measured properties are independent of the direction of measurement and have randomly oriented grains.
Simple Silicates
The Si₂O⁶₇ ion is formed when two tetrahedra share a common oxygen atom. 1. maintain charge neutrality 2. ionically bond SiO₄⁴⁻ to one another
Cesium Chloride Structure
The anions are located at each of the corners of a cube, whereas the cube center is a single cation. The coordination number is 8.
CERAMIC CRYSTAL STRUCTURES
The atomic bonding in these materials ranges from purely ionic to totally covalent and are composed of at least two elements. Having cations and anions in one structure. The coordination numbers depend on the Radius of Cation / Radius of Anion. The most common coordination numbers for ceramic materials are 4, 6, and 8.
METALLIC CRYSTAL STRUCTURES
The atomic bonding in this group of materials is metallic and thus nondirectional in nature. The crystal structures for most of the common metals are face-centered cubic, body-centered cubic, and hexagonal close-packed.
Rock Salt Structure
The coordination number for both cations and anions is 6 and the cation-anion radius ratio is between approximately 0.414 and 0.732. The rock salt crystal structure may be thought of as two interpenetrating FCC lattices—one composed of the cations, the other of anions.
Zinc Blende Structure
The coordination number is 4, all ions are tetrahedrally coordinated, all corner and face positions of the cubic cell are occupied by S atoms, whereas the Zn atoms fill interior tetrahedral positions.
Linear Density and Planar Density
The highest linear density directions are found in the highest density planes.
crystal structure
The manner in which atoms, ions, or molecules are spatially arranged.
coordination number
The number of nearest-neighbor or touching atoms.
POINT COORDINATES
The position of any point located within a unit cell may be specified in terms of its coordinates as fractional multiples of the unit cell edge lengths. Example 1/2 1/2 1/2 and 1 1 1 Note: no commas.
hexagonal close-packed (HCP)
The top and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the center. Another plane that provides three additional atoms to the unit cell is situated between the top and bottom planes. There are 6 atoms in this unit cell and the coordination number is 12. Edge length: a =
lattice parameters
The unit cell geometry is completely defined in terms of six parameters: the three edge lengths a, b, and c and the three interaxial angles alpha, beta , and lamda.
single crystal
a crystalline solid whose periodic and repeated arrangement of atoms is perfect, or extend throughout the entire specimen without interruption.
Miller indices
a four-axis system.The three a1, a2, and a3 axes are all contained within a single plane called the basal plane and are at 120 angles to one another. The z axis is perpendicular to this basal plane. Indices [uvtw] are calculated from (u'v'w')
crystalline
atoms are situated in a repeating or periodic array over large atomic distances. The atoms position themselves in a repetitive three-dimensional pattern in which each atom is bonded to its nearest-neighbor atoms.
body-centered cubic (BCC)
atoms located at all eight corners and a single atom at the cube center. There are 2 atoms in this unit cell and the coordination number is 8. Unit cell edge length : a = 4R/3¹/²
face-centered cubic (FCC)
atoms located at each of the corners and the centers of all the cube faces. There are 4 atoms in this unit cell and the coordination number is 12. Unit cell edge length : a=2R2¹/²
grain
crystalline solids that are composed of a collection of many small crystals.
CRYSTALLOGRAPHIC DIRECTIONS
direction is defined as a line directed between two points, or a vector. 1. Vector repositioned (if necessary) to pass through origin. 2. Read off projections in terms of unit cell dimensions a, b, and c 3. Adjust to smallest integer values 4. Enclose in square brackets, no commas [uvw].
Carbon type Graphite
has a crystal structure distinctly different from that of diamond and is also more stable than diamond at ambient temperature and pressure.
Octahedral site
in interstitial position that has a coordination number of 6. An atom or ion in the cubic sites touches 6 other atoms or ions.
CARBON
is an element that exists in various polymorphic forms, as well as in the amorphous state.
octahedral position
is produced by joining these six sphere centers in ceramic.
atomic packing factor (APF)
is the sum of the sphere volumes of all atoms within a unit cell divided by the unit cell volume.
noncrystalline
lack a systematic and regular arrangement of atoms over relatively large atomic distances.
polycrystalline
materials are composed of single crystal "grains" that are randomly oriented.
DENSITY COMPUTATIONS—METALS
n = number of atoms associated with each unit cell A = atomic weight VC = volume of the unit cell NA = Avogadro's number (6.022 1023 atoms/mol)
DENSITY COMPUTATIONS-CERAMICS
n = the number of formula units within the unit cell2 AC = the sum of the atomic weights of all cations in the formula unit AA = the sum of the atomic weights of all anions in the formula unit VC = the unit cell volume NA = Avogadro's number, 6.022 1023 formula units/mol
Bragg's law
relationship among x-ray wavelength, interatomic spacing, and angle of diffraction for constructive interference.
What are the two characteristics of the component ions in crystalline ceramic materials?
the magnitude of the electrical charge on each of the component ions, and the relative sizes of the cations and anions.
grain boundary
there exists some atomic mismatch within the region where two grains meet.
Stable ceramic crystal structures form
when those anions surrounding a cation are all in contact with that cation
