Quiz 2 Flashcards
How are Crystal directions defined?
Directions in a crystal is defined as a multiple of the coordinate axes. Start with a unit cell, (a,b,c) (1,1,1). The directions are marked [u v w]
How to convert abc into uvw
u = n(x2- x1)/a
v = n(y2-y1)/b
w = n(z2-z1)/c
How do you mark a negative number in material science?
You put a bar above the negative number, no negative signs
The procedure for identifying crystal planes:
1) pick axes and origin
2) determine coordinates of the intercept’s of the plane with the unit cube. (Parallel =infinity)
3) Take inverse of intercepts (1/a, 1/b, 1/c)
4) multiply to get integers
5) Write in the form ( h k l) index of plane. Watch negative notation
How many axis in a HCP crystal
HCP crystals use 4 axis systems. [u v t w]
How to convert between a 3 axis cubic system and a 4 axis system.
u = 1/3(2U -V)
v = 1/3(2V -U)
t = -(U+V)
w= W
How to distinguish between 3 axis and 4 axis systems
Three axis is capitalized (UVW) and doesn’t have t
Four axis is lowercase (uvtw)
Linear density formula
of atoms / length of distance
Planar density formula
of atoms on a plane /area of plane
How does density impact crystal structure?
It effects the planes stacking sequence
HCP stacking sequence
ABABAB
FCC stacking sequence
ABC ABC ABC
X Ray Diffraction
Similar to skipping a rock over water. With materials we can use the crystal planes in a material to bounce back x-rays. This can identify a material
What information do you meed when using x ray diffraction to identify a material
You need to know the wavelength (lambda) of the x rays
What is Braggs law and what do the variables stand for
n(lambda) = 2d sin (theta)
n = order of diffraction
lambda= wavelength
Theta = angle of diffraction
d = distance between 2 planes
What must be true about the timing of two waves for x ray diffraction to work?
The waves enter the material at the same time and must emerge in phase. The only way the waves are in phase is if the extra distance of the 2nd wave is a multiple of the wavelength.
Extra distance = 2 dsin(theta)
Are d spacings the same in a crystal structure
No the s spacing changes between plane orientations. D(111) is not = d(100)
For FCC and BCC what is the formula for d spacing.
d(hkl) = a/sqrt(h^2 + k^2 + l^2)
What is the formula for HCP d spacing
1/d^2 = 4/3 * (h^2+hk+k^2)/a^2 + l^2/c^2
Angstrom (A) to meters
1A = 10^(-10)m
For a BCC crystal when can a peak be visible during X ray diffraction?
A peak is only visible if h+k+l is an even number
For a FCC crystal when can a peak be visible during X-ray diffraction
A peak is only visible is h k and l are all odd or all even
Crystalline definition
A material where the atoms are situated in a repeating of periodic array over large atomic distances.
Crystal structure
The manner in which atoms, ions or molecules are spatially arranged.
Atomic hard sphere model
Spheres represent nearest neighbor atoms touch one another
Lattice
A three dimensional array of points coinciding with atom positions or sphere centers
Unit cells
Parallelepipeds or prisms having three sets of parallel faces. One is drawn within the aggregate of spheres which in this case happens to be a cube
Face centered cubic FCC
The crystal structure found for many metals has a unit cell of cubic geometry, with atoms, located at each of the corners and the center of all the cubic faces.
Common metals with FCC crystals
Copper, aluminum, silver, and gold.
Unit cell length for face centered cubic crystals
a = 2Rsqrt(2)
Number of atoms in FCC crystal structures
4
Coordination number
For metals, each atom has the same number of nearest neighbor or touching atoms, which is called the coordination number for face centered cubics the coordination numbers 12
Atomic packing factor APF
The APF is the sum of the sphere volumes of all atoms within a unit cell assuming that atomic cards sphere model divided by the unit cell volume. APF = Volume of atoms/total unit cell volume
FCC atomic packing factor
0.74
Body centered cubic BCC
Another common metallic crystal structure also has a cubic unit cell with atoms located at all eight corners and a single atom in the center of the cube
Unit cell length for BCC crystals
a = 4R/sqrt(3)
Common metals with BCC crystal structures
Chromium, iron, tungsten
Number of atoms per BCC unit cell
2
Coordination number of BCC crystals
8
Atomic packing factor for BCC
0.68
Hexagonal close packed HCP
Not all metals have unit cells with Q ex symmetry for the final common metallic crystal structure to be discussed has a unit cell that is hexagonal.
Number of atoms per HCP crystal structure
6
HCP coordination number
12
HCP atomic packing factor
0.74
HCP metal examples
Cadmium, magnesium, titanium, and zinc
Theoretical density for metals
p = nA/(Vc Na)
n - number of atoms associated with each unit cell
A- atomic weight
Vc -volume of the unit cell
Na- avocados number 6.022×10 ^23 Atoms/mol.
Theoretical density for metals
p = nA/(Vc Na)
n - number of atoms associated with each unit cell
A- atomic weight
Vc -volume of the unit cell
Na- avocados number 6.022×10 ^23 Atoms/mol.
Polymorphism
Some metals as well as nonmetals may have more than one crystal structure of phenomenon known as polymorphism
Polymorphism
Some metals as well as nonmetals may have more than one crystal structure of phenomenon known as polymorphism
Alotropy
When polymorphism is found in elemental solids
How to define a unit cell
A unit cell is fully defined by six parameters. The three edges a, B, C and the three internal angles, alpha, beta gamma. These are called lattice parameters
Crystal system
The seven different possible combinations of a, B, and C and alpha, beta, and gamma, which represents distinct crystal systems
What are the crystal systems?
There are seven crystal systems. Cubic, tetragonal, hexagonal, orthodontic, rhombohedral, monoclinic, and triclinic.
Miller indices
In all, but the hexagonal crystal system, crystal graphic planes are specified by three Miller indices each, K, L any two planes, parallel to each other are equivalent and have identical indices the procedure to determine the HK and L in the numbers is as follows.
One if the plane passes through the origin, another parallel plane must be constructed within the unit cell by an appropriate translation or a new origin must be established at the corner of another unit unit cell.
Two the crystal graphic plane, either intersects or parallels each of the three axis coordinates for the intersections of the crystal graphic planes with each of these axis is determined their considered a, b, c respect to x, y, z
Three the reciprocals of these numbers are taken the planes that are parallel of an axis are considered to have infinite intercepts, and therefore a zero index
Reciprocals of the intercepts are normalized by their lattice parameters
If necessary, these three numbers are changed to the set of small integers by multiplication or division by common factor
Six finally, the integer indices, not separated by commas are enclosed within parentheses .
Miller Bravis system for hexagonal crystals
This convention leads to four index HKIL. I =-(h+k). Otherwise the indexing systems are identical.
Linear density
LD = number of atoms centered on direction vector / length of direction vector
Planar density
PD= number of atoms centered on a plane/area of plane
Diffraction
A distracted beam is one composed of a large number of scattered waves that mutually reinforced one another
A crystalline defect
Refers to a lot of irregularity, having one or more of its dimensions on the order of an atomic diameter
Vacancy
The simplest type of point defect is a vacancy or vacant lattice site one normally occupied, but from which an atom is missing. All crystalline solids contain vacancies and in fact it’s not possible to create session material that is free of these.
Equilibrium number of vacancies
Nv = N exp(-Q/kT)
N= number of atomic sites
Q the energy required for the formation of vacancy
T the absolute temperature in kelvins
k the Boltzman constant which is 1.3×10 to the -23 J per Atom times Kelvin
Self interstitial
A self interstitial is an atom from the crystal that is crowded into an interstitial site. A small void space that under ordinary circumstances is not occupied. Metals a self interstitial introduces relatively large distortion in the surrounding lattice because the atom is substantially larger than the interstitial position in which it is situated consequently, the formation of the defect is not highly probable, and it exists in very small concentrations that are significantly lower than For vacancies.
Alloy
Most familiar metals are not highly pure, rather their allies in which impurity atoms have been added, intentionally to impart specific characteristics on the material. Ordinarily alloying is used in metals to improve mechanical strength and corrosion resistance for example sterling silver is 93% silver and 7% copper.
Solid solution
The addition of impurity atoms to a metal result in the formation of a solid solution and or a new second phase. Depending on the kind of impurity their concentrations and the temperature of the alloy
Solute solvent
Solvent is the element or compound that is present in greatest amount or on occasion solvent atoms are called host atoms. Salute is used to denote an element or compound present in a minor concentration.
Substitutional and interstitial
Impurity point defects are found in solid solutions of which there are two types of substitutional and interstitial for the substitutional type salute, or impurity atoms, replace or substitute for host. Adams several features of the salute and solvent Adams determine the degree to wish the former dissolves in the latter, these are expressed as four Hume Rothary rules:
1) atomic size factor must be within 15%
2) crystal structure must be the same
3) electronegativity factor the more electropositive one element and the more electron negative the other the greater the likelihood they will form an inter metallic compound and instead of a substitutional solution
4) valances metals have more tendency to dissolve other metals of higher valance than to dissolve one with lower valance
Edge dislocation
A linear defect that centers on the line that is defined along the edge of the extra half plain of atoms
Dislocation line
Which, for the edge dislocation is perpendicular to the plane of the page some localized loud distortion the atoms above the dislocation line are squeeze together, and those below are pulled apart
Screw dislocation
Thought of as being formed by sheer stress that is applied to produce the distortion where the upper region of the crystal is shifted one atomic distance to the right relative to the bottom portion, also linear along the dislocation line
Mixed dislocations
Most dislocations in materials are probably neither pure edge nor pure screw but exhibit components of both
Burgers vector
For an edge, they are perpendicular. whereas screws, they are parallel. They are neither perpendicular nor parallel for mixed dislocation, metallic materials. The burgers vector is a dislocation point in a close packed crystal graphic direction and it’s magnitude is equal to the interatomic spacing.
Micro structure
Include things such as grain size and shape and other micro structural characteristics
Microscopy
Investigations of micro, structural features of all materials some of these techniques employ photographic equipment and conjunction with microscopes
Grain size
Is often determined when the properties of polycrystalline and single phase materials are under consideration. In this regard, it is important to realize that for each material, the constituent grains have a variety of shapes and distribution of sizes. Green size may be specified in terms of average or mean, green diameter, and a number of techniques have been developed to measure this perimeter.
Diffusion
The phenomenon of material transport by atomic motion
Interdiffusion or impurity diffusion
The process by which atoms of one metal diffuse into another
Self diffusion
Decision also occurs in pure metals, but all atoms exchanging positions are of the same type
Vacancy diffusion
The interchange of an atom from a normal normal, let us position to an adjacent vacant, lattice, site or vacancy
Interstitial diffusion
Adams are small enough to fit into the interstitial position host or substitutional impurity Adams rarely form interstitial do not normally diffuse via this mechanism
Diffusion flux
How fast diffusion occurs
J = M/At
A- area across which diffusion is occurring
T- time elapsed
Number of atoms, M
Diffusion coefficient
D
Steady state diffusion
The diffusion process eventually reach a state to where in the diffusion flux does not change with time that is the mass of diffusing species entering the plate on the high pressure side at equal to the mass from the low pressure surface that there is no accumulation of diffusing species in the plate
Factors that influence diffusion
Temperature time
Point defect types
Vacancy atoms
Interstitial atoms
Substitutional atoms
Line defects
Dislocations
Area defects
Grain boundaries
Equilibrium
Nv/N = exp (-Qv/kT)
Nv= number of defects
N = number of potential defect sites
Qv = activation energy
k= Boltzmann constant (1.38 x 10^-23 J/ atom-K)
Alloy types
Substitutional or Interstitial(hides in-between bigger atoms)
Rules for solid solution
1) atomic size must be +-15%
2) Crystal structure should be same
2) electronagativity: stronger e- are better for mixing.
4)Valences: higher valences dissolve faster
Dislocation
Edge dislocation or screw dislocation: fracture in lattice bonds, the fractures move in the material
Grain size area method
n = 2^(G-1)
n = number of grains/in^2 at 100x magnification
G= ASTM grain size number
How to compute magnification from a scale bar.
One. Measure the length of the scale bar in millimeters using a ruler. Two. Convert the length into microns i.e. multiply the value and step one by 1000 because there are 1000 µm in a millimeter. Three. Magnification M is equal to the measure to scale length converted into microns divided by the number appearing by the scale bar in microns.
Mean intercept length
l = Lt/PM
l - mean intercept length
Ly- total length of all the lines
P- total number of intersections
M- magnification
