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MSE405-505 2013C Problem Set 2

# MSE405-505 2013C Problem Set 2 - MSE/MEAM 405/505 FALL 2013...

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MSE/MEAM 405/505 F ALL 2013 M ECHANICAL B EHAVIOR OF M ACRO /N ANOSCALE M ATERIALS U NIVERSITY OF P ENNSYLVANIA P ROBLEM S ET #3 - DUE WEDNESDAY, SEPTEMBER 25 HAND IN AT BEGINNING OF CLASS NOTES:’Please’write’clearly,’show’all’of’your’steps,’and’comment’with’text’to ’ demonstrate’your’ approach.’Also,’remember’that’we’encourage’forming’groups’to’discuss’the’course’concepts’and’ general’problem -solving’strategy,’but’your’final’solution’must’show’your’individual’work. 1. Sn’is’tetragonal’with’a’=’5.82’A’and’c’=’3.17’A.’Electrical’conductivity’ σ ij ’ is’a’2 nd ’ rank’tensor’ that’relates’the’current’density’ J ’ to’the’electric’field’ E ’ according’to: ’ J i = ij E j ’ The’electrical’conductivity’is ij = 10 0 0 0 10 0 0 0 7 # \$ % % % & ' ( ( ( × 10 6 ( Ω⋅ m ) 1 .’ An’electric’field’of’0.1’V/m’is’applied’parallel’to’the’[011]’direction’of’a’single’crystal’of’Sn. (a)’What’are’the’components’of’the ’ electric’field’along’the’three’unit’cell’axes?

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MSE405-505 2013C Problem Set 2 - MSE/MEAM 405/505 FALL 2013...

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