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C6
Crystallography
27
Science
Undergraduate 3
05/31/2011

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Term
What are the hkl conditions for different lattice types for diffraction
Definition
P cubic- none
I - h+k+l = 2n
C - h+k = 2n
F h,k,l all odd or all even
Term
What are the characteristics (lattice parameter restrictions, angle restriction, characteristic symmetry) of the seven crystal systems?
Definition
Triclinic a1 not= a2 not= a3; alpha not= beta not= gamma; monad symmetry
monoclinic a1 not = a2 not= a3; alpha = gamma beta>= 90; 1 diad
orthorhombic a1 not= a2 not=a3; alpha= beta= gamma = 90; 3 diads
tetragonal a1 = a2 not= a3; alpha= beta= gamma = 90; 1 tetrad
trigonal a1 = a2 = a3; alpha = beta = gamma not= 90; 1 triad
hexagonal a1 = a2 not= a3; alpha = beta = 90 gamma = 120; 1 hexad
cubic a1=a2=a3; alpha= beta= gamma= 90;; 4 triads
Term
What are the 14 bravais lattices?
Definition
Triclinic P; Monoclinic P&C; Orthorhombic P,C, I&F; Tetragonal P&I, Hexagonal, Trigonal P; Cubic P,F &I
Term
What are the 14 bravais lattices?
Definition
Triclinic P; Monoclinic P&C; Orthorhombic P,C, I&F; Tetragonal P&I, Hexagonal, Trigonal P; Cubic P,F &I
Term
What is Weiss zone rule? How do you prove it?
Definition
If a direction [uvw] is contained in a plane (hkl) then the normal to the plane is perpendicular to the direction:
(ha*+kb*+lc*)(ua+vb+wc) = 0
a*a = 1, b*b = 1, c*c=1
hu + kv+ lw = 0 (weiss zone rule)
Term
Which Bravais lattices have a centre of symmetry?
Definition
all
Term
What is a point group?
Definition
the collection of symmetry operations passing through a point.
Term
What does m represent? What do bars on top of rotation axes represent? 2/m? mm2? how else can you write mm2? What does the first number represent? What's the exception to the rule stated earlier
Definition
m - mirror; bars- inversion axes; 2/m- mirror plane perpendicular to a diad axes; mm2- two mirror planes intersecting at a two-fold axis- can also be written as mm or 2m; the first number always refers to a c-axis except in the monoclinic system where the b axis is unique.
Term
In a cubic crystal/stereogram, which planes have triad symmetry? tetrad symmetry? diad symmtery?
Definition
triad- {111}
tetrad- {100}
diad- {100} and {110}
Term
What is the requirement for a crystal to be piezoelectric?
Definition
Must lack a centre of symmetry
Term
What are polar point groups?
Definition
point groups that have a unique direction which is not related by the symmetry elements to any other
Term
In the hkil notation used for hexagonal crystal systems, what is the relationship between i and h, k, and l?
Definition
i = -(h+k)
Term
What is a diagonal glide plane and what is its symbol?
Definition
the translations involve two orthogonal steps parallel to a face of the unit cell. It's symbol is n.
Term
What are the different types of glides? there symbols and characteristics?
Definition
An axial glide is parallel to one of the lattice vectors and has the symbol of the axis it's parallel to.
A diagonal glide is parallel to a face diagonal and has the symbol n.
A diamond glide (f.c.c) is parallel to the face diagonal and has the symbol d.
A diamond glide (b.c.c) is parallel to the body diagonal and has the symbol d.
Term
explain the statement k'-k = g.
Definition
This is another way of stating Bragg's law. k and k' have magnitudes of 1/lambda and g has a magnitude of 1/d.
Term
how are Intensity and structure factor related?
Definition
I is the square of F
Term
What's the Schmidt factor?
Definition
cos(theta)cos(lambda); gives the shear on a slip plane in the slip direction. Slip occurs when Schmidt factor reaches a maximum
Term
How do you tell which slip direction, you have slip along using stereographic projection? (Diehl's rule)
Definition
1) Identify the triangle containing the tensile axis
2) to find slip plane take {111} type pole and reflect across opposite side
3)to find the slip direction take the <110> type pole and reflect across the opposite side
4) this is for ccp crystals do opposite for bcc crystals; rather reflecting the <111> type pole will give you the direction etc.
5) tensile axis moves towards slip direction
6) once tensile direction reaches triangle side changes slip system
Term
pole figure
Definition
a stereogram with its axes defined relative to the external frame of reference , and with particular hkl poles from each of the crystals in the polycrystalline aggregate plotted on it.
Term
inverse pole figure
Definition
pole figure in which the sample frame is plotted relative to the crystal axes of a reference crystal.
Term
How is crystallographic texture measured?
Definition
using a variety of techniques such as X-ray diffraction, EBSD
Term
What are some disadvantages of pole figures? Give an alternative method and define it.
Definition
They do not give information about the orientation of a particular crystal relative to another, since the poles are not identified with particular crystals in the final plot. Use an orientation distribution function which plots the euler angles
Term
Why does the the interfacial energy pf a tilt boundary as a function of misorientation angle not consistently rise with increasing theta?
Definition
formation of CSLs
Term
What is the General Rotation Matrix given a vector unit vector u = [u1 u2 u3] and an angle of rotation theta?
Definition
let m = cos theta and n = sin theta
u1u1(1-m)+m u1u2(1-m)+u3n u1u3(1-m)-u2n
u1u2(1-m)-u3n u2u2(1-m)+m u2u3(1-m)+u1n
u1u3(1-m)+u2n u2u3(1-m)-u1n u3u3(1-m)+m
Term
How can you find the angle of rotation for an axis of rotation if you are given the general rotation matrix J?
Definition
J11+J22+j33 = 1+2cos(theta)
Term
What is the meaning of Epsilon in CSL notation?
Definition
1/epsilon is the number of lattice sites common to both crystals out of the numbe rof total lattice point.
Term
What is Bain strain? What are the two inconsistencies associated with Bain strain?
Definition
The strain necessary to transformf.cc austenite into b.cc martensite. you would expect the
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