Lecture 8 Flashcards
What is a crystal?
a solid composed of atoms that are arranged in a periodic pattern
What kind of symmetry do crystalline solids have?
translational symmetry (are composed of a regular array of atoms)
Do amorphous solids have symmetry? What do we consider them?
they don’t. we consider them frozen liquids.
What is the crystal structure formed from?
crystal structure = lattice + basis
What is a lattice?
a lattice is an infinite and regular array of points (atoms) in which the environment of each point is identical
What kind of symmetry do lattice points have?
translational symmetry, so every point in the lattice can be generated by the addition of two lattice vectors, a and b
What is a unit cell?
The minimum repeating unit that can fill all the space
The smallest repetitive volume which can be translated in three dimensions
- parallelepiped
- six parameters needed to describe the unit cell dimensions and angles
What are the six lattice constants or lattice parameters?
Length: |a|, |b|, |c|
* Angles between axes: alpha beta gamma
What are the lattice constants for cubic?
What are the lattice constants for tetragonal?
What are the seven crystal systems?
- cubic
- tetragonal
- orthorhombic
- rhombohedral
- hexagonal
- monoclinic
- triclinic
What are the lattice constants for orthorhombic?
What are the lattice constants for rhombohedral (trigonal)?
all sides the same and all angles the same but not 90
What are the lattice constants for hexagonal?
two sides the same, two angles are 90
one angle is 120
What are the lattice constants for monoclinic?
no sides are the same ,
two angles are 90
What are the lattice constants for triclinic?
no sides the same
no angles are 90
What are orthogonal systems? What are the three different types?
systems where alpha = beta = gamma = 90
*so all edges are perpendicular
simple cubic, simple tetragonal, simple orthorhombic (all same l, 2 same l, 3 dif)
What are the lattice vectors to describe the unit cell dimensions for orthogonal systems?
SC - all the same
S tetragonal - one dif.
S orthorhombic - all dif.
How do you calculate a crystallographic direction vector?
- subtract head - tail coordinates
- normalize
- reduce to the smallest integer value
How do you denote a family of directions?
< >
what is a family of directions?
the distance between atoms along the directions are the same
ex: [100],[010],[001],[-100],[0-10],[00-1]
in the <100> family
How is a crystallographic plane represented?
{ }
How do you denote a family of lattice planes?
( )
How do you calculate miller indicies?
- find the intersects with the xyz system
- calculate the reciprocals
- common factor
- enclose in ( )
What are the common miller indicies for crystallographic planes?
What would be the plane of this?
if you can’t seem to figure out how to do miller indices, think about what?
remember it’s a family
translate it to the right or left one then identify it in the “family” – it’s still the miller indicie
How do you draw a plane given the indicies?
take inverse of indicies
find intercepts
What do the planes of the {100} family look like?
What does the interplanar spacing look like with orthorhombic crystals (ones w all dif side lengths)?
What are the different formulas for the interplanar spacing in orthorhombic, tetragonal, and cubic?
it’s always h2 k2 l2
correlate to dif side lengths– ortho (all dif), (tetragaonal a=b, so no b and group), cubic all same
What formulas do you use to calculate interplanar distance?
interplanar spacing formulas– “d” spacing
What do low hkl indicies mean?
larger d-spacing
What is the pm to A conversion
100 pm = 1A
in what system is [hlk] perpendicular to (hlk)
a cubic system
What are the 3 bravis lattices in cubic systems?
simple cubc
BCC
FCC
what are the 2 bravis lattices in tetragonal systems?
simple tetragonal
body-centered tetragonal
what are the 4 bravis lattices in the orthorhombic system?
simple orthorhombic
body-centered orthorhombic
bass-centered orthorhombic
face-centered orthorhombic
what bravis lattice is the trigonal system? what’s something to remember?
it can have either hexagonal or rhombohedral lattice
what bravis lattice is in the hexagonal system?
what two bravis lattices are in the monoclinic system?
simple monoclinic
bass-centered monoclinic
is [hlk] generally perpendicular to (hlk)?
no, unless for cubic systems
What are the two choices of hexagonal unit cells?
- primitive hexagonal unit cell ex: (110), (100), (010)
- hexagonal (four index) ex: (1100) (1010) (0110)
What are Weber symbols/zone axis symbols?
<UVTW>
4 base vectors in 3D space
</UVTW>
what are the formulas to remember for Weber symbols?
- go through the patterns in your mind
What are the end points of a hexagonal crystal lattice?
- think about the patterns
- top right start with neg
- right diag starts with 2, middle has middle 2, left has end 2
- they’re all the opposite signs of the other side
How do you identify a crystallographic plane in a hexagonal crystal?
using miller-bravais indicies: h k i l
i = -(h+k)
**others are the same that you would think
What’s another way to write miller-bravais indicie (always about planes) h k i l
h k . l
How do you go about finding the miller-bravais indicies for a hexagonal crystal?
- find where it intersects with a/x b/y/ and z
- put that into () remember the negs
- change to hkil by i = -(h+k)
