4 Crystals Flashcards
what is a crystal?
solid with long range order
- infinite array atoms/molecules that extend in 3d
what are the 3 crystal forms, describe them
- polymorph: similar substance, have diff arrangements atoms and unit cell dimensions
- pseudo polymorphs: diff chemical content (solvent, host-guest atoms)
- allotropes: polymorphs with only one element
3 allotropes of P
-white (P4), molecular solid, very reactive
- red (P8)
- black, network covalent
what is a unit cell
smallest potion of structure that can be repeated by translation (along unit cell) and show full symmetry
How many crystal classes are there? name them
7
cubic (all angles/ edges same)
Tetragonal
orthorhombic
trigonal
Hexagonal
Monoclinic
Triclinic (all angles/ edges different)
How to draw 3D-2D projections?
bottom atoms 0
top =1
what is a lattice?
array equiv pt in 3D
- gives info translational sym of material
- doesn’t give info about actual atom position space
what are the 4 types of Bravais lattices
- primitive/simple (atom each corner)
- face centered (primitive and one in center of face)
- body centered (primitive and atom in middle)
-side centered (primitive and atom in middle each side)
how many possible systems are there in Bravais lattices
14
what type of lattices does cubic have
Simple
face
body
what are Millar indices?
(hkl) witch intersects unit cell at (a,b,c): (1/h, 1/k, 1/l)
if h,k, or l, =0 plane is parallel to a,b,orc
bar over indicies rep negative, move axis over
what does {100} rep
family (100), (010), (001) ect
6 total
what do these rep?
- (a,b,c)
- [abc]
- (hkl)
- {hkl}
- (a,b,c): point
- (hkl): plane
- {hkl}: family of planes
what is d-spacing
how to calculate
distance b/w parallel lattice planes
- can be used to determine lattice constant
1/d^2 = (h^2+k^2+l^2)/a^2
what are the 2 types of packing
-simple
-closed (more efficient)
types of closed pack
-hexagonal: ABA
-cubic: ABC
how to count atoms in cell
divide by fraction actually in the cell
what is the diff b/w fcc and ccp?
same but
ccp - cubic closed packed: is a packing type
fcc - face centered cubic: is a lattice type
density=?
depends on
(# atoms/cell)(mass atoms)/Volume unit cell
-unit cell dimensions (d-space), crystal structure, atomic mass
what are holes
small hole that has a diff smaller atom (usually cation)
cubic, tetrahedral, octahedral
how many holes are in fcc?
- 8 tetrahedral
- 4 octahedral
- not all has to be occupied
what is radius ratio?
used to predict type hole cation could occupy
r+/r-
most stable if large enough minimize repulsion b/w neighboring anions and small enough for enough cation/anion contact
Packing efficiency for cubic
= (# atoms/unit cell)(V atom)/ V unit cell *100
measures how tightly packed the crystal is, least empty space
-closed pack has highest
what is the V of a Sphere
4/3pir^3
