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Assignment 1 Sol

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  ENGR 2220 Assignment #1Structure & Properties of Materials To get part marks, show all your work  1. Determine the density of BCC iron, hich has a lattice parameter of !. $$ nm.Solution%or a BCC cell,Atoms'cell ( cma )#! 1!* .#$$(nm!. #$$( ’ Atomic mass ( ++.- g'mololume of unit cell ( cell cm xcma '1!+,. /01!*  .#$$( / ,/)# /! − = ’ A2ogadro3s num4er  N   A ( $.! * 1! /  atoms'molDensity 050 00'  ( number  savogadrocell unit of  volume ironmassof  atomiccell atomsof  number   ρ  / /  '## .- 01!! .$0+,. / 0#,-.++0   (  cm g  x =  ρ  . 6he density of thorium, hich has the CC structure and one atom per lattice point, is 11.- g'cm / . 6he atomic eight of thorium is / g'mol. Calculate a0 the lattice parameter7 and 40 the atomic radius of thorium.Solution%a0Density 050 00'  ( number  savogadrocell unit of  volume ironmassof  atomiccell atomsof  number   ρ  cm xaor cm xa  xacm g  #!/ /! //!/ 1!!#+$.+ 1!/1+ 8-.1 01!! .$0 0 / 0, '11.- −− === 40 rom the relationship 4eteen atomic radius and lattice parameter  cm xcm xr   ## 1!-8#!.1 0,01!!#+$.+0   (  −− = /. Copper has an atomic radius of !.1 - nm, an atomic eight of $/.+ g'mol and a density of .8 g'cm / . Determine hether it has a BCC or an CC crystal structure.Solution%or BCC%  /  A N anA =  ρ  1 of   ENGR 2220 Assignment #1Structure & Properties of Materials 00 /, '1!! .$0'1!1. -# g'mol0cell0$/.+atoms'unit  (  //#) mol atomscell unit cm  x  ×× ( . 1 g'cm / or CC  A N  RnA A N anA /  / 0 ==  ρ  [ ] { } 00 '1!! .$0' 1!1. -# 0 g'mol0cell0$/.+atoms'unit,  (  //#) 0  mol atomscell unit cm  ×× ( .8/ g'cm / 9hich is closest to the density pro2ided in the :uestion. 4. 9ithin a cu4ic unit cell, s;etch the folloing% Solution%a0 of   ENGR 2220 Assignment #1Structure & Properties of Materials40+. Determine the Miller indices for planes A  and B  in the figure 4elo% Plane A is a ( ) 111  plane. 6he determination of its indices is summari<ed 4elo.  xyz  =ntercepts a-bc =ntercepts in terms of   a , b , and c  1 )1  1 >eciprocals of intercepts1)11 / of   ENGR 2220 Assignment #1Structure & Properties of Materials ?nclosure  ( ) 111 Plane A is a ( ) !/!  plane. 6he determination of its indices is summari<ed 4elo.  xyz  =ntercepts@ ab/3 @ c =ntercepts in terms of   a , b , and c @1'/@>eciprocals of intercepts!/!?nclosure  ( ) !/!  of 
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