Description
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 v
n o exp(
Q
)
RT
900 oC is 3.85·10-2 determine
. If the fraction of lattice points containing vacancies at 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)
