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What is the vacancy concentration of Fe at 850 °C and 1250 °C given the density...

What is the vacancy concentration of Fe at 850 °C and 1250 °C given the density (7.65g/cm3 ), and activation of energy for vacancy formation (1.08eV/atom).

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Answer #1

Determination of the number of vacancies per cubic meter in iron at 850°C (1123 K) and 1250 °C (1523 K ) requires the utilization of following equation:

Nv = N * exp(-Qv/KT) = NA * ρfe / Afe *exp(-Qv/KT)

Nv = number of vacancies per cubic meter

NA = Avogadro's number = 6.022 * 1023 atoms/mol

ρfe = Density of iron = 7.65g/cm3

Afe = Atomic mass of iron = 55.85g/mol

Qv = activation of energy for vacancy formation (1.08eV/atom)

K = Boltzmann constant = 8.62 *10-5 ev/atom.K

At temperature 850°C (1123 K)

Nv = NA * ρfe / Afe *exp(-Qv/KT)

Nv = 6.022 * 1023 atoms/mol *( 7.65g/cm3/55.85g/mol) * exp(-1.08eV/atom/( 8.62 *10-5 ev/atom.K * 1123 K)

Nv = 1.18 *1018 cm-3 or 1.18 *1024 m-3

At temperature 1250°C (1523 K)

Nv = NA * ρfe / Afe *exp(-Qv/KT)

Nv = 6.022 * 1023 atoms/mol *( 7.65g/cm3/55.85g/mol) * exp(-1.08eV/atom/( 8.62 *10-5 ev/atom.K * 1523 K)

Nv = 2.20 *1015 cm-3 or 1.18 *1021 m-3

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