Lecture 3 and 4 Flashcards
Density is linked to
atomic weight - but is not always the case
As increase temperature density does what and why
the density decreases as atoms;
amplitude of vibration increases
atoms gets further apart as it would require more energy to stay at the same distance and vibrate with greater amplitude see lennord jones
same mass for larger volume therefore lower density
thermal expansion
At certain temperature some materials undergo
a phase change ie FCC to BCC different structure
what can happen in a phase change
change in density
magnetic properties alter
a lot of mechanical properties
at certain temperature property you are relying on may disappear due to phase change
BCC
body centered cubic atoms touch across internal diagonal not a close packed system atoms all corners one in the middle not a stable structure
FCC
face centered cubic close packed structure based on layers of atoms, atoms touch across diagonal of face packing sequence ACB ACB ACB
Most materials are
crystalline structure (not are but focus on crystalline atm)
crystalline structures can be descirbed as
regular array of atoms can be described as unit cells which is a basic building block to make the whole structure
lattice spacing
a - length width and depth of unit cell (volume of unit cell = a^3)
sharing of atoms between unit cells meaning
if you had a unit cell of simple cubic structure at each corner was an atom then each atom would be shared with 8 other unit cells therefore an eighth of that atom would be inside the unit cell
total atoms in unit cell = 1/8 * 8 = 1
What can we tell from unit cell of an atom
everything dont care about the number of unit cells as it just makes the crystal larger repeat of the same unit cell can characterize the crystal by characterizing the unit cell
atomic packing fraction
number of particles x volume of particle (4/3pi r^3) / volume of unit cell
method for finding APF
find lattice structure in terms of radius of atoms (see what plane atoms touching on)
find volume of unit cell in terms of radius of atom
find number of atoms in unit cell (remember some shared)
insert into APF equation, radius cancels giving %
simple cubic structure
one atom at each corner of cube
What does the APF tell you
% of unit cell filled with atomic volume
HCP
hexagonal close packed close packed structure based on layers of atoms packing structure AB AB AB
number of atoms in FCC unit cell
1/2 * 6 + 1/8 * 8 = 4
types of materials FCC
aluminium copper
FCC close packed plane
(1 1 1)
FCC a in terms of r equation
a^2 + a^2 = (4R)^2
a^2 = 8R^2
a= 2root2 * R
perfect dislocation is where
atom crystal moved but maintained the structure of the crystal - hoped from one to the other
HCP materials
cobalt alpha titanium
HCP structure unit cell
hexagonal prism each face is a place A and A with the B layer in the middle unit cell is a third of this structure
HCP unit cell
2 atoms per unit cell V = (root3 * a^2 *c)/2
where c is the distance between two layers of the same structure ie A and A
BCC
not a close packed system atoms all corners one in the middle not a stable structure
BCC materials
alpha iron
Some materials will have different properties in
different directions - easy to split in one direction hard in another direction
miller indices are
a way of describing a crystals orientation
miller indices used to describe
planes
brackets for planes groups of planes
directions and groups of directions
(planes) {collection of planes} [directions]
goes x y z
what is a plance
a surface of a cube, due to symmetry will be the same as another surface this is how we group together (1 0 0) same as (0 1 0) (0 0 1) therefore group {1 0 0} or {0 1 0}
where it cuts the axis that we put the point same crystal structure no difference in information from plane mechanically respond the same
diagram if (1 1 1) plane and (2 1 0)
see powerpoint
miller indices equation
lattice constant (a) / distance at which it cuts as fraction of a ie a/a = 1 a/infinity = 0 ie parallel to this axis a/ 0.5 a = 2
how to do negative in miller indices
put bar over top of number
miller indices directions vs planes
the plane and direction with same miller indices will perpendicular to each other take start point of direction as origin and indices with respect to that
direction in miller indices is
how far it travels in a certain direction
(1 1 1) plane for FCC
is close packed plane as its plane in which atoms are in contact with each other slip plane
orientation of stresses defined in
similar way to miller indicies x axis is 1 y axis is 2 z axis is 3
normal stress
acting out of surface
shear stress
acting parallel to surface
stress notation
sigma ij where i is the plane and j is the direction the force acts
how many components of stress on a cube
9 but gets cut down to 6 unique ones as you cannot generate stress on one surface of cube without having equal and opposite on other side
each surface has what kind of stresses on it
2 shear and one normal (first number will all be the same if on the same plane, the normal the number will be the same, the shear stresses will be the other two directions)
1 0 0 plane also known as
x plane or yz plane
how are shear stresses written
with a tau instead of a sigma
what the three normal stresses and 3 shearing stresses
sigma 11 sigma 22 sigma 33
tau 12 tau 13 and tau 23 these cover all forces due to equal and opposite reactions
show that there are only 3 unique shear stresses and state why
see powerpoint due to equal and opposite and static equilibrium - material will push back in opposite direction therefore tau 13 = tau 31
tau 23 = tau 32
tau 12 = tau 21
why can we cancel the z stresses
as we often work in 2 dimensions as forces in third are negligible (walls and thin plates) interested in stresses in surface not thickness
shear is rotating clockwise this is
positive if anticlockwise motion it is negative
normal is tension this is
positive if compression it is negative
in static equilibrium stresses are balanced shear stresses are
complimentary (see powerpoint)
