Functional Materials Past Paper PDF 2024

SCIENCE PASSION TECHNOLOGY Functional Materials – PHT.708UF Masters Program Technical Physics Functional Materials I – MAS.220UF Masters Pro...

SCIENCE PASSION TECHNOLOGY Functional Materials – PHT.708UF Masters Program Technical Physics Functional Materials I – MAS.220UF Masters Program Advanced Materials Science Masters Program Environmental System Sciences/Climate and Environmental Monitoring Dr. Stefan Topolovec Institute of Materials Physics 14.10.2024 1.2.2 Point defects in ceramics 1.2.2 Point defects in ceramics ▪ In ionic compounds point defects carry effective electric charge Properties of electroceramics are significantly determined by point defect ▪ Inherent lattice defects: Interstitials, vacancies ▪ Since global charge neutrality has to be maintained single inherent lattice defects can not occur in undoped ceramics ▪ They appear as ▪ Schottky pair: Pair of anion and cation vacancies ▪ Frenkel pair: Pair of vacancy and self interstitial atom No charge neutrality Functional Materials - Institute of Materials Physics 32 14.10.2024 1.2.2 Point defects in ceramics 1.2.2 Point defects in ceramics ▪ In ionic compounds point defects carry effective electric charge Properties of electroceramics are significantly determined by point defect ▪ Inherent lattice defects: Interstitials, vacancies ▪ Since global charge neutrality has to be maintained single inherent lattice defects can not occur in undoped ceramics. ▪ They appear as ▪ Schottky pair: Pair of anion and cation vacancies ▪ Frenkel pair: Pair of vacancy and self interstitial atom ▪ Inherent lattice defects can be introduced by doping (see below) or by irradiation with high energy particles ▪ Inherent lattice defects are present in the crystal even in the thermodynamic equilibrium Functional Materials - Institute of Materials Physics 33 14.10.2024 1.2.2 Point defects in ceramics Calculation of the thermodynamic equilibrium concentration CV of lattice vacancies ▪ CV is determined by the minimum of the free enthalpy ▪ Since the introduction of vacancies leads to disorder ( → entropy S increases) the formation of vacancies is favored with increasing T ▪ Change in free enthalpy due to the formation of n vacancies Enthalpy of vacancy Entropy of vacancy Configurational formation formation (evoked by change entropy of lattice vibrations around the vacancy) Functional Materials - Institute of Materials Physics 34 14.10.2024 1.2.2 Point defects in ceramics ▪ Change in free enthalpy due to the formation of n vacancies ▪ Configurational entropy: determined by the number of different ways in which one can distribute n vacancies on N’ lattice sites (N’ = N + n with the number of atoms N) ≈ ln 1 = 0 For 𝐶𝑉 ≪ 1: Formally identical to the entropy of mixing – mixing of vacancies with lattice atoms ▪ For Cv1eV) Functional Materials - Institute of Materials Physics 54 14.10.2024