Midterm 2 - Crystalline Solids

phase diagram

a map of the state or phase of a substance

* region between lines - specific state is stable
* any line - an equilibrium of two states is stable
* includes triple point and critical point

triple point

all 3 states are in equilibrium

critical point

above this, a super critical fluid is present (neither liquid nor gas)

3 types of crystalline solids

1. molecular
2. ionic
3. atomic

crystalline solids - molecular

composite units are molecules

* low melting points
* ex - ice, butter, dry ice (CO2)

crystalline solids - ionic

composite units are ions

* high melting points
* ex - table salt, epsom salts

crystalline solids - atomic

composite units are atoms

* non-bonding
* metallic
* network covalent

non-bonding

low melting points, dispersion forces

* ex - noble gases

metallic

variable melting points, metallic bonding

* ex - gold, iron, copper

network covalent

high melting points, network covalent bonds

* ex - quartz (SiO2), diamond

unit cell

the minimum unit needed to repeat the pattern

* aggregates in a manner to minimize

crystal lattices

repeating regular arrangement of attoms (pattern)

simple cubic unit cell

a cube with an atom at each corner (atoms per cell)

* 1/8 per cell (8 atoms) = 1 atom/cell

coordination number

number of atoms with each atom is in direct contact

simple cubic unit cell - coordination number

6 atoms = 4 corners in plane, 1 on top, 1 on bottom

(when you put multiple unit cells together)

simple cubic - geometry

edge length (l) = 2r

body centered cubic unit cell

a cube with an atom at each corner and an atom in the center

* 2 atoms per unit cell = (1/8 x 8 corner) + 1 center

body cubic unit cell - coordination number

8 atoms = 4 corners on top + 4 corners on top

* focus on the center atom in the figure

body centered cybic - geometry

l = 4r/√3

c = 4r

b^2 = 2l^2

face centered cubic unit cell

a cube with an atom at each corner and an atom on each face

* 4 atoms/cell = (1/8 x 8 atoms per corner ) + (1/2 x 6 atoms per face)

face centered cubic unit cell - coordination number

12 = 4 corners, 4 faces on one side, 4 faces on other side

face centered cubic - geometry

1 = 2 r√2

b = 4r

b^2 = 2l^2

find the edge length of the unit cell

1. use the molar mass to find mass per cell (g/cell) using avogadro’s number
2. use g/cell and convert to volume using density (cm^3/cell)
3. plug into the volume equation and find l

find the atomic mass

1. find mol/cell
2. find volume
3. cancel out values for g/mol

calculate the density

goal - find M/V (g/ml or g/cm^3)


1. find M = molar mass to find g/cell
2. find V = plug in values into volume equation

two closest-packed structures

hexagonal closest packed and cubic closest packed (same as fcc)

hexagonal closest packed

layered ABA (every other layer aligns to form hexagonal shape)

* 1 unit cell = 1/3 of full hcp

cubic closest packed

layered ABCAC (forms a fcc unit cell but on diagonal)

ionic solids - 1:1 ratio

1 cation = 1 anion

similar sized: body centered cubic

medium difference in size

very differently sized radii (“zinc blende”)

* ionic radii are least different

differentiating zinc blends

r(cation) - r(anion)

* larger number is more likely to crystallize in the zinc blend

ionic solids - 1:2 ratio

fluorite (1 cation = 2 anion)

* based on the subscript of the element

ionic solids - 2:1 ration

antifluorite (2 cation: 1 anion)

allotrope

a physical form that something that can exist in

* ex - graphite, diamond

carbon buckminsterfullerene

type of allotrope where clusters stick together with dispersion forced in soccer ball shape

* C60 is generally soft
* can be other sizes

carbon nanotubes

lightweight and strong allotropes

* used for electronic devices, x-rays, biosensors, and small chipset

silicates

silicon and oxygen

* silicon bonds to 4 oxygen in tetrahedral shape
* if quartz heated and cools quickly, before it can crystallize, it becomes amorphous glass