MAE 3324 Ch3 Flashcards
Define “crystalline material.”
A crystalline material is one in which the atoms are situated in a repeating or periodic array over large atomic distances.
Define “amorphous” with respect to materials.
Amorphous materials do not crystalize and have no long-range atomic order.
Describe the atomic hard-sphere model.
Atoms are considered solid spheres having well-defined diameters. The spheres are used to show the structure of atoms in a unit cell and how the atoms touch their nearest neighbors.
Define “Lattice.”
A three-dimensional array of points coinciding with atom positions.
T or F
Corners or unit cells usually coincide with the centers of hard-sphere atoms.
True
Name some common metals that have a face-centered cubic (FCC) unit cell.
Copper
Aluminum
Silver
Gold
For FCC, how many face atoms are there?
Nf = 6
For FCC, how many corner atoms are there?
Nc = 8
For FCC, how many interior atoms?
Ni =0
How many total atoms in an FCC unit cell?
Four
Define “Coordination number.”
The number of nearest neighbor touching atoms.
What is the coordination number for FCC?
12
Define atomic packing factor?
The sum of the sphere volumes of all atoms within a unit cell divided by the unit cell volume.
APF = (volume of atoms in the cell)/(total unit cell volume)
T or F
Metals typically have relatively large atomic packing factors to maximize the shielding provided by the free electron cloud.
True
Describe the body centered cubic BCC structure.
Atoms are located at all eight corners and a single atom at the center of the cube.
Give some examples of elements having BCC structures.
Chromium, iron, & tungsten.
How many corner atoms in BCC?
Nc = 8
How many center atoms in BCC?
Ni = 1
How many face atoms in BCC?
Nf = 0
What is the total number of atoms in a BCC unit cell?
N = 2.
What is the coordination number for the BCC crystal structure?
8
What is the atomic packing factor for FCC?
0.74
What is the atomic packing factor for BCC?
0.68
Describe the Hexagonal Close Packed HCC structure.
The tops and bottom faces of the unit cell consist of six atoms that form regular hexagons and surround a single atom in the center. Another horizontally orientated plane of three atoms is directly in the middle of the top and bottom planes.
How many corner atoms in HCP?
Nc = 12
How many face atoms for HCP?
Nf = 2
How many interior atoms for HCP?
Ni = 3
How many total atoms for HCP?
6
What is the coordination number for HCP?
12
What is the atomic packing factor for HCP
0.74
T or F
The atomic packing factor and coordination number for HCP are the same as FCC?
True
Define “Polymorphism” with respect to materials.
When a material contains more than one crystal structure.
What is “allotropy?”
When a material is polymorphic and also an elemental solid.
T or F
In an allotropic solid, the prevailing crystal structure depends on both the temperature and the external pressure?
True
Give examples of polymorphism in solids.
Carbon is one example. Graphite is the stable polymorph at ambient conditions, whereas diamond is formed at extremely high pressure.
Also, pure iron has a BCC crystal structure at room temperature which changes to FCC iron at 1674 degrees F.
T or F
Most often, a polymorphic transformation is NOT accompanied by a modification of the density or other physical properties of a material.
False
Reference: 3.6, pg 57 and 58
How many distinct crystal systems are there?
Seven
Describe the process by which the seven crystal systems are defined using the geometry of the structure.
The shape of the unit cell parallelepiped is taken without regard to the atomic position in the cell. Within this framework, an XYZ coordinate system is established with its origin at one of the unit cell corners and each of the x,y, and z axes coincides with one of the three parallelepiped edges.
What are the six lattice parameters of a crystal structure?
Edge Lengths: a, b, and c
Internal Angles: Alpha, Beta, and Gamma
Extra Notes: On this basis, seven different structures can be made.
What are the seven crystal systems?
- Cubic
- Tetragonal
- Hexagonal
- Orthorhombic
- Rhombohedral
- Monoclinic
“Cats Take Hares Over Round Mice.”
What crystal system do FCC and BCC structures belong to?
Cubic
What crystal system does HCC belong to?
Hexagonal
List the XYZ lattice position coordinates with their respective unit multiples.
Px = qa Py = rb Pz = sc
“Quails rarely sing.”
What is a crystallographic direction analogous to?
A vector
Describe how a crystallographic direction is defined.
- Establish an xyz coordinate system and find vectors in each of the coordinate directions.
- Normalize the vectors by dividing by the lattice parameters (a for x, b for y, etc), then reduce to integer values if necessary.
- The following three values [uvw] are enclosed in brackets with no commas. Bars are placed over a negative direction.
What coordinate system is used when the crystallographic structure is hexagonal?
Miller-Bravais
Describe the Miller-Bravais coordinate system.
There are three axes (a1, a2, and a3) which are all contained within a single plane called the basal plane and are at 120-degree angles to another. The z-axis is perpendicular to the basal plane.
In all but the hexagonal crystal system, crystallographic planes are specified by…?
Three miller indices (hkl)
T or F
If two crystallographic planes are parallel they will have the same miller indices?
True
T or F
A family of planes contains all planes that are crystallographically equivalent.
True
T or F
A family of planes is designated by indices enclosed in vector brackets such as <100>.
False
Families are enclosed in curly brackets such as {100}.
Define Linear Density.
The number of atoms centered on the direction vector divided by the length of the direction vector.
What are the units of linear density?
reciprocal length (e.g. 1 / length)
Define Planar Density
The number of atoms centered on a plane divided by the area of the plane.
What are the units for planar density?
Reciprocal Area
e.g. (1 / area)
What conditions must be present for a single crystal designation?
For a crystalline solid, the periodic and repeated arrangements of the atoms must be perfect and must extend throughout the entirety of the specimen without interruption.
Define polycrystalline.
When a crystalline solid is composed of a collection of many small crystals or gains.
In a polycrystalline solid, when you have two different crystal types that do not intercede and form a boundary, this is referred to as?
A grain boundary.
Define anisotropy.
A substance whose properties such as modulus of elasticity or electrical conductivity, vary in different directions.
What primary physical characteristics give rise to anisotropic materials?
The variance of atomic or ionic spacing within a specified crystallographic direction.
Define isotopic.
The measured properties of the material are independent of the direction.
T or F
The degree of anisotropy decreases with decreasing structural symmetry?
False
Anisotropy increases as the structural symmetry degrades.
T or F
Triclinic structures normally are highly anisotropic?
True
When does a material have what is considered a “texture?”
When the grains in polycrystalline materials have a preferential crystallographic orientation.
Define “diffraction” and the properties necessary for it to occur.
Diffraction occurs when a wave encounters a series of regularly spaced obstacles that;
- Are capable of scattering the wave.
- Have spacing that is comparable in magnitude to the wavelength.
What is a diffracted beam?
A wave that is composed of a large number of scattered waves that mutually reinforce one another.
What is x-ray diffractometry?
A process used for crystal structure and interplanting spacing determinations.
What are non-crystalline solids?
Materials that lack a systematic and regular arrangement of atoms over large atomic distances.
T or F
Amorphous is the same thing as Non-crystalline.
True
T or F
Dense, ordered packing structures tend to have lower energies with respect to the radial distance between atoms?
True
Extra Notes: Needs reference
T or F
Non-dense, random packing structures tend to have higher energies with respect to the radial distance between atoms?
True
Extra Notes: Needs reference.
T or F
Quenching often results in amorphous (non-crystalline) materials?
True
What are the five unique lattice structures?
- Oblique (monoclinic)
- Rectangular (orthorhombic)
- Centered Rectangular
- Hexagonal
- Square (tetragonal)
“Obese Reptiles Careened Horizontally Screaming”
What are the number of Bravais lattices in 3D?
14
What are the four lattice centerings?
- Primitive (P): Unit cells contain only a single lattice point.
- Internal (I): The Unit cell contains an atom in the body center.
- Face (F): contains atoms in all the faces of the planes composing the cell.
- Centered (C): The unit cell contains atoms centered on the sides of the unit cell.
“Pompous Idiots Followed Carefully.”
T or F
The simple cubic is common due to it’s low packing density.
False.
Simple cubic structures are very rare due to the low packing structure they possess.
T or F
Metallic crystal structures tend to densely pack.
True
What are some reasons for dense packing in metallic crystal structures?
- Typically only one element is present so all atomic radii are the same.
- Metalic bonding is non-directional.
- Nearest neighbor distances tend to be small in order to lower bond energy.
- Electron cloud shields cores from each other.
T or F
Organic crystal structures tend to densely pack?
False
Organic structures tend to loosely pack.
Give some reasons why organic structures tend to loosely pack?
- Typically more than one element is present so atomic radii is a variable parameter.
- Covalent bonding is directional.
- Nearest neighbor distances tend to be larger than in metals.
- Electron cloud overlap.
T or F
In single vs. polycrystals;
In single crystals, properties may vary with direction (anisotropic).
True
T or F
In single vs. polycrystals;
Polycrystal properties are always anisotropic.
False, properties of polycrystals may vary depending on the grain orientation. If the grains are randomly orientated the material is isotropic. If the grains are textured, the material is anisotropic.
T or F
Most engineering materials are polycrystals.
True
Give some examples of engineering systems that might require a single crystal material.
Diamond drill bits
Turbine blades
T or F
Two or more distinct crystal structures for the same material (allotopy) is commonly referred to as polymorphism.
True
