MS-EST143_HW4_2011

MS-EST143_HW4_2011 - MS/EST 143, Problem Set #4 assigned...

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1 MS/EST 143, Problem Set #4 assigned 04/18/11 due 04/22/11 1. Construct the Brouwer diagram for a pure binary oxide M 2 O, where M is a 1+ cation, for which, at the temperature of interest, the predominant defects are Schottky vacancies. Frenkel defects are negligible. Consider three regions (reducing; neither reducing nor oxidizing; and oxidizing), show Brouwer approximation and derive how each species changes in each region. Problems 2 - 6 refer to tin oxide: SnO 2-x an oxide of the rutile structure (cubic close- packed oxygen ions with one-half of the octahedral sites occupied by Sn 4+ ), reduces readily with a decrease in oxygen partial pressure. For the purposes of this exercise, you may assume that oxygen vacancies are the primary compensating defect. The material does not tolerate any oxygen excess to speak of. E g = 4 eV, (N C N V ) 1/2 = 10 20 cm -3 , # nearest neighbor sites to which O 2- could jump is 12 and  2 ] [ O V O D D V O 2. (a) Write formally correct (i.e., physically meaningful) defect reactions and, where
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