MAT E 201
Materials Science I
Assignment No.4 (14 marks)
1. Number of vacancies in BCC chromium at room temperature (25 oC) is 4.78·107
vac./cm3
. a) Calculate the energy required to produce a mol of vacancies. b) At what
temperature in oC the fraction of lattice points occupied by vacancies is 10-3
, if the
energy required to create vacancies in chromium is 85 kJ/mol? (3 marks)
2. HCP titanium has the lattice parameters ao = 2.9503 Å and co = 4.6831 Å. If the density
of a sample of titanium is 4.502 g/cm3
, calculate a) the fraction of the lattice points that
contains vacancies and b) the total number of vacancies in a cubic centimetre. (3
marks)
3. At 575 oC atoms are found to move from one lattice position to another at the rate of
8·108
jumps/s. If the activation energy for the movement is 300 kJ/mol, calculate the
temperature in oC at which the jump rate is 9·1013 jumps/s. (2 marks)
4. A change of number of vacancies in a material is related to temperature by an Arrhenius
equation (
n n exp( ) v o
RT
Q
. If the fraction of lattice points containing vacancies at
900 oC is 3.85·10-2
determine the activation energy Q. (3 marks)
5. A 0.5 mm thick wafer of silicon is treated so that uniform concentration gradient of
arsenic (-0.0175 at.% As/cm) is produced. If the bottom surface contains 1 As atom
per 107 Si atoms determine the number of As atoms per 107 Si atoms on the top surface
of the wafer. The lattice parameter for Si is 5. 407 Ǻ. Calculate the concentration
gradient in As [atoms/cm3
cm]. (3 marks)
