MATSE 201: Exam 1 Review

How to solve?

A substance is 20 wt% Sn and 80 wt% Au.
What are the atomic percentages of each?

-recall that atomic % = (atoms of X)/(total # atoms)
-assume basis of 100 g
-convert grams to moles to # atoms for each
-add to get total # atoms
-calculate atomic %
Aufbau Principle of electron configuration
2s 2p
3s 3p 3d
4s 4p 4d 4f
Hund’s Rules of electron configuration
1. Electron pairs with opposing spins are low energy
2. Electrons orbiting in the same direction are low energy
3. Make half-filled subshells when applicable
E = h?
c = ??
Most pure elements exist as ___
atoms with same number of protons but different numbers of neutrons
quantum number 1
called: principle quantum number
symbol: n
defines: shell
related to: energy level; distance from nucleus
ex: 1, 2, 3
quantum number 2
called: angular momentum number
symbol: l
defines: subshell
related to: orbital shapes
ex: 0, 1, 2, 3 (s, p, d, f)
quantum number 3

called: magnetic number

symbol: ml

defines: orbitals for e pairs within subshells

ex: 0, +1, -1, +2, -2

quantum number 4
called: spin number
symbol: ms
defines: spin
ex: + or –
In transition metal ions, the relative energy levels of subshells can shift such that electrons from the ___ subshell are usually given up first.
describe bond types


strong covalent within a sheet
weak secondary bonds between sheets
describe bond types

Al + Si + Mg alloy

it’s a metal alloy, so the bonding is metallic
describe bond types


it’s a hydrocarbon polymer, so it has strong covelent bonding
describe bond types

ice (frozen water)

covalent intra-atomic bonds
secondary (hydrogen) inter-atomic bonds
Covalent bonds are highly ___ and are characterized by sharing of electrons and relatively ___ coordination numbers.
crystal system
describes shape of unit cell
can completely fill space with translational symmetry
there are 7 (cubic, tetragonal, hexagonal, etc.)
lattice parameters
(aka lattice constants)
lengths of sides a, b, c of a unit cell for a crystal system
lattice points
arrangement of atoms in 3D
points in space that are equivalent thru translational symmetry
each may consist of more than one atom (the basis)
Primitive cell vs.
non-primitive cell
primitive cell has only one lattice point per unit cell
Bravais Lattices
possible arrangements of lattice points in the 7 crystal systems
there are 14 (simple cubic, fcc, bcc, etc.)
crystal structure
Bravais lattice + basis
(unit cell) (atom complex)
ex, simple cubic + atom pair = crystal structure
lattice position
just a location in the unit cell
lattice direction
[ ]
[(a displacement) (b disp.) (c disp.)]
use lowest whole numbers
family of lattice directions
(aka general direction)
< >
set of directions that are equivalent through symmetry
lattice planes

( )

((a intercept)-1 (b intcpt.)-1 (c intcpt.)-1)


note: of the plane inter cepts the origin,

translate it before you give the indeces

family of lattice planes
{ }
linear/planar density
number of atoms per unit length/area
in a given crystal direction/plane
a vs. r
sc: a = 2r
fcc: a = 4r/rt(2)
bcc: a = 4r/rt(3)
hcp: a = 2r
calculate density
from unit cell
density = [(# atoms)/(volume)]*[(atomic wt)/(NA)]
atomic packing factor

APF = (V of atoms in cell)/(V of cell)


APF = [(# atoms/cell)(4?r3/3)]/(a2)


diffraction rules

simple cubic

any h k l
diffraction rules


h k l all odd or all even
Bragg’s Law
? = 2dhklsin?
lattice plane distance
dhkl= a/rt(h2+k2+l2)
applications of
X-ray diffraction
1. determination of crystal structure (computer-aided)
ex, DNA structure
2. determination of glassy-to-crystalline phase transitions in glassy materials
ex, take XRD at different temperatures and compare them
3. determination of crystal quality
ex, impurities make for wider peaks; the skinnier the peaks, the higher the crystal quality
4. amounts and phases present in multiphase systems
coordination number
number of immediate neighbors surrounding an atom
Pauli exclusion principle
no two electrons in an atom can have the same four quantum numbers
Bohr model of atom
1. e move about nucleus in defined orbits
2. each e has quantized energy
3. transition form one state to another requires a quantized amount of energy to be absorbed or released

1. works correctly only for hydrogen

bond energy vs. distance
ionic bond properties
bond strength?
directional bonds?
relatively high bond energy
(high melting points, high stiffness, low thermal expansion)
low electrical conductivity
hard + brittle
high CNs
covalent bond properties
bond strength?
directional bonds?
high directionality
relatively strong bonds (but less than ionic)
tend to be brittle
electric insulating or semi-conducting
low CNs
metallic bond properties
bond strength?
directional bonds?
can be weak or strong bonds
non-directional bonds
delocalized electrons
good conductors
high CNs
ductile at room temp
opaque and shiny
amorphous or glassy
no long-range order
no periodic packing–non-dense, random packing
long-range order
dense, ordered packing
periodic, 3D arrays
lower energy than amorphous
Zachariasen Rules

glass formers

1. each O should be linked to no more than 2 cations
2. CN of oxygen about each cation must be small (4 or less)
3. oxygen polyhedra share corners (not edges nor faces)
4. at least 3 corners of polyhedra should be shared

cation-O bond are strong
usually cation is relatively electronegative -> less ionic character

some typical glass formers
diffraction rules


h+k+l = even
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