this is a material science related question

this is a material science related question

[50 points] The dominant defects in Nb2O5 at 1000 °C are oxygen vacancies with a double positive effective charge and Nb interstitials with a double positive effective charge. These conditions apply to all of the questions below. Assume that the materials is pure. Write an equation for the formation of doubly charged oxygen vacancies in Nb2O5. Write an equation for the formation of doubly charged Nb interstitials in Nb2O5. [please write the reaction so that a single interstitial defect is formed with a positive 2 effective charge] Is Nb2O5 n-type or p-type? Write an equilibrium constant (KV) for the reaction in i). Write an equilibrium constant (Ki) for the reaction in ii). The equilibrium constants for these reactions have been measured. They are: KV = 2.4×105 (atm1/2) ´ exp(-4.5(eV)/kT) Ki = 4.9×109 (atm5/4) ´ exp(-8.7(eV)/kT) Determine the ratio of oxygen vacancies to Nb interstitials at 10-10 atm and at 10-20 atm of O2. (T = 1000°C and k = 8.6×10-5 eV/K) Taking the formula unit to be Nb2O5-x, determine x at both of these pressures (10-10 atm and 10-20 atm). Write the electroneutrality condition for the concentrations of charged defects in Nb2O5. Write equations for the concentration of Oxygen vacancies and Nb interstitials at low partial pressure of oxygen and high partial pressure of oxygen. In the each case, assume one of the two defects is dominant to simplify the electroneutrality condition. Make a plot of log concentration v log partial pressure (in the range of 10-10 atm to 10-20 atm) of oxygen showing the concentrations of the oxygen vacancies, Nb interstitials, and electronic charge carriers. (T = 1000°C) [25 points] Crystals with the Fluorite crystal structure have a {100} slip system. How many independent combinations of planes and directions occur in the crystal structure? Please list all of the distinguishable combinations. For a Fluorite crystal loaded in pure tension along the [210] direction, which of these slip systems will be activated first? Along which directions will slip steps be observed on {111} type surfaces? A cylindrical fcc single crystal of Al is loaded in tension on a tensile testing machine. The cross sectional area of the cylinder is 1 cm2 and the [112] axis is parallel to the applied tensile load. The critical resolved shear stress of Ag is 6 x 106 dynes/cm2 . What tensile force must be applied to plastically deform this crystal by slip?

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