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.