X-ray diffraction (XRD)
spacing between planes
• Measurement of critical angle, c , allows computation of planar
spacing, d.
X-ray intensity (from detector)
θ θ c
d = n λ
2 sin θ c
X-Ray Diffraction Pattern
Adapted from Fig. 3.22, Callister 8e.
(110)
(200)
(211)
z
x
a b y
c
Diffraction angle 2θ
Diffraction pattern for polycrystalline α-iron (BCC)
Intensity (relative)
z
x
a b y
c z
x
a b y
c
2
Example
A diffraction analysis experiment is performed on a sample of BCC crystal structure on the plane (110). It is required to calculate the atom radius and the density of the sample.
Given that the wavelength of the first order X-ray, equals 1.54 Å, the incidence angle of the X-ray =19.3
oand the atomic weight of the sample 92.9 g/mol.
4
MATERIAL SCIENCE
Chapter 4:
Imperfections in Solids
Point Defects
•
A vacancy is produced when an atom or an ion is missing from its nor- mal site in the crystal structure as in Figure 4-1(a).
•
An interstitial defect is formed when an extra atom or ion is inserted into the crystal structure at a normally unoccupied position, as in Figure 4-1(b).
•
A substitutional defect is introduced when one atom or ion is replaced by a different type of atom or ion as in Figure 4-1(c) and (d) .
6
Linear Defects (Dislocations)
•
Dislocations are line imperfections in an otherwise perfect crystal. They typically are
introduced into a crystal during solidification of the material or when the material is
deformed permanently. Although dislocations are present in all materials, including
ceramics and polymers, they are particularly useful in explaining deformation and
strengthening in metallic materials. We can identify three types of dislocations: the
screw dislocation, the edge dislocation, and the mixed dislocation.
Home work
1.
Rhodium has an atomic radius of 0.1345 nm and a density of 12.41 g/cm
3. Determine whether it has an FCC or BCC crystal structure.
1.
The metal rubidium has a BCC crystal structure. If the angle of diffraction for the (321) set of planes occurs at 27.00
o(first-order re- flection) when monochromatic x-radiation having a wavelength of 0.0711 nm is used, compute (a) the interplanar spacing for this set of planes and (b) the atomic radius for the rubidium atom.
2.
The metal iridium has an FCC crystal struc- ture. If the angle of diffraction for the (220) set of planes occurs at 69.22
o(first-order re- flection) when monochromatic x-radiation having a wavelength of 0.1542 nm is used, compute (a) the interplanar spacing for this set of planes and (b) the atomic radius for an iridium atom.
3.
Draw the different types of point defects?
4.
Draw the different types of linear defects (dislocations)?
8
MATERIAL SCIENCE
Chapter 5:
Diffusion
Diffusion Phenomena
•
Examples of diffusion:
•
You can smell perfume because it diffuses into the air and makes its way into your nose.
•
A teabag placed in a cup of hot water will diffuse into the water.
•
Cigarette smoke diffuses into the air.
•
Diffusion is the process of mass transport by atomic motion.
•
In its simplest form, it occurs by random atomic jumps from one position to another and takes place in gaseous, liquid and solid states for all classes of materials.
•
Diffusion is most rapid in gaseous state and least rapid in the solid state.
•
Types of diffusion: Interdiffusion (impurity diffusion) and self diffusion.
•
Interdiffusion is the diffusion of atoms from one metal to another metal.
•
Self diffusion is the atomic migration in pure metal.
•
Factors that effect Diffusion in solids:
•
Temperature
•
Time
•
Type of diffusion
•
Type of crystal structure and bonding
•
Concentrations of diffusing species.
10
• Interdiffusion: In an alloy, atoms tend to migrate
from regions of high concentration to regions of low concentration.
Initially
Figs. 5.1 & 5.2, Callister &
Rethwisch 9e.
Diffusion
After some time
12
• Self-diffusion: In an elemental solid, atoms also migrate.
Label some atoms
Diffusion
A
B C D
After some time
A
B C
D
Diffusion Mechanisms
Vacancy Diffusion:
• atoms exchange with vacancies
• applies to substitutional impurities atoms
• rate depends on:
-- number of vacancies
-- activation energy to exchange.
increasing elapsed time
14
Diffusion Mechanisms
• Interstitial diffusion – smaller atoms can diffuse between atoms.
More rapid than vacancy diffusion
Fig. 5.3 (b), Callister & Rethwisch 9e.
Steady-State Diffusion
Fick ’ s first law of diffusion
C
1C
2x C
1C
2x
1x
2D diffusion coefficient
(Rate of diffusion independent of time)
Flux proportional to concentration gradient =
The rate at which atoms, ions, particles or other species diffuse in a material can
be measured by the flux J. Here we are mainly concerned with diffusion of ions
or atoms. The flux J is defined as the number of atoms passing through a plane
of unit area per unit time. Fick’s first law explains the net flux of atoms:
16
Diffusion rate - Fick’s first law
A plate of iron is exposed to a carburizing (carbon-rich) atmosphere on
one side and a decarburizing (carbon-deficient) atmosphere on the other
side at 700C (1300F). If a condition of steady state is achieved, calculate
the diffusion flux of carbon through the plate if the concentrations of
carbon at positions of 5 and 10 mm (5 x 10
-3and 10
-2m) beneath the
carburizing surface are 1.2 and 0.8 kg/m
3, respectively. Assume a
diffusion coefficient of 3 x 10
-11m
2/s at this temperature.
• 5.1 Briefly explain the difference between self- diffusion and interdiffusion.
• 5.2 Compare interstitial and vacancy atomic mechanisms for diffusion.
• 5.3 Cite two reasons why interstitial diffusion is normally more rapid than vacancy diffusion.
• 5.4 A sheet of steel 1.5 mm thick has nitrogen atmospheres on both sides at 1200C and is permitted to achieve a steady-state diffusion condition. The diffusion coefficient for nitrogen in steel at this temperature is 6 x 10-11 m2/s, and the diffusion flux is found to be 1.2 x 10-7 kg/m2 s. Also, it is known that the concentration of nitrogen in the steel at the high- pressure surface is 4 kg/m3. How far into the sheet from this high-pressure side will the concentration be 2.0 kg/m3? Assume a linear concentration profile.
5.5 Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn.
If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove?
Data:
diffusion coefficient in butyl rubber:
D = 110 x10-8 cm2/s surface concentrations:
C2 = 0.02 g/cm3 C1 = 0.44 g/cm3
