Al:Texture(Chapter 2) 7.5 points a)Define the concept of the crystallographic texture.Please describe shortly how textures can be measured?(2.5 points) b) Please sketch the {200)pole figure of a cube,which has been clockwise rotated by 45 around the transverse direction (TD).Please determine the Miller indices and the rotation matrix of this orientation.(5 points) w s 1 A2:Crystal Defects (Chapter 3) 10 points a)Name the most important types of crystal defects.From a physical metallurgy point of view,each of these defects has some profound influence on certain specific processes happening in metals.Name these processes.(3 points) b) During the formation of n vacancies in a crystal the Gibbs free energy changes according to AG=nH-T(nS,+S). n=number of vacancies H=vacancy formation enthalpy St=vibration entropy per vacancy Sa=configuration entropy The variety of arrangements of n vacancies on N different lattice sites can be N! expressed as @ Derive by application of Stirling's formula (N-n)!n! In(x!)=x.Inx-x an expression for the atomic equilibrium concentration of vacancies ca.(7 points) Estimate the formation enthalpy of a vacancy in tungsten.The equilibrium concentration of vacancies at the melting point (3410C)is given as 10,the vibration entropy can be assumed as 2-k.Express the result with the dimension of eV. (1.5 points)A1: Texture (Chapter 2) 7.5 points a) Define the concept of the crystallographic texture. Please describe shortly how textures can be measured? (2.5 points) b) Please sketch the {200} pole figure of a cube, which has been clockwise rotated by 45° around the transverse direction (TD). Please determine the Miller indices and the rotation matrix            w s l v r k u q h g of this orientation. (5 points) A2: Crystal Defects (Chapter 3) 10 points a) Name the most important types of crystal defects. From a physical metallurgy point of view, each of these defects has some profound influence on certain specific processes happening in metals. Name these processes. (3 points) b) During the formation of n vacancies in a crystal the Gibbs free energy changes according to   L L    G nH T nS S B k  . n = number of vacancies L HB = vacancy formation enthalpy L S = vibration entropy per vacancy Sk = configuration entropy The variety of arrangements of n vacancies on N different lattice sites can be expressed as   ! ! ! N N N nn    . Derive by application of Stirling’s formula ( ln ! ln   x   x xx ) an expression for the atomic equilibrium concentration of vacancies a L c . (7 points) c) Estimate the formation enthalpy of a vacancy in tungsten. The equilibrium concentration of vacancies at the melting point (3410°C) is given as 10–4, the vibration entropy can be assumed as 2·k. Express the result with the dimension of eV. (1.5 points)