Question 1: Calculate the expected number of vacancies that will exist in a cubi

Question

Question 1: Calculate the expected number of vacancies that will exist in a cubic inch of Aluminum at room temperature (25°C), provided that the activation energy for vacancy formation in Aluminum is equal to 0.75 eV/atom.

Question 2: At what temperature will Aluminum have a) 1017 vacancies per cubic centimeter, b) 1020 vacancies per cubic centimeter, and c) 0 vacancies per cubic centimeter.

Question 3: Draw a) a Frenkel Defect for an AX-type rock salt ceramic crystal and b) a Schottky Defect for an AX-type cesium chloride ceramic crystal.

Explanation / Answer

1) no. of vacancies = N*exp(-Q/kT)

N = avogadro no.*density/molar mass

density of aluminium = 43 g/inch^3

N = 6.022*10^23*43/26.98

Nv= N*exp[-0.75/{8.62*10^-5*(25+273)}] = 2*10^11 per cubic inch

2) Now data is in cubic centimeter, so density in cubic cm = 2.62 g/cm^3

N = 6.022*10^23*2.62/26.98 = 5.84*10^22

a) 1017 = N*exp[-0.75/{8.62*10^-5*T}]

T= 191.23 K

b) 1020 = N*exp[-0.75/{8.62*10^-5*T}]

T = 191.25 K

c) 0 = N*exp[-0.75/{8.62*10^-5*T}]

That is possible only at absolute zero temp...i,e., T=0K

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