ME $207$ MATERIALS SCIENCE

HOMEWORK $1$

Draw the direction vectors in the cubic unit cells for the following directions.

a$)\frac{1}{b}ar(3)3$

b$)121$

c$)103$

Draw the crystal planes in the cubic unit cells for the following Miller indices.

b$)(\frac{0}{b}ar(1)2)$

c$)(1$vec$(3)1)$

a$)$ Determine the indices for the direction in the cubic unit cell shown in the figure.

b$)$ Determine the indices for the plane in the cubic unit cell shown in the figure.

a$)$ Calculate the planar atomic density in atoms per square millimeter for the $(111)$ plane in BCC chromium, which has a lattice constant of $0,28846nm.$

b$)$ Calculate the linear atomic density in atoms per milimeter for the $[111]$ direction in FCC iridium, which has a lattice constant of $0,38289nm.$

Below are listed the atomic weight, density and lattice parameter for two hypothetical alloys. For ach determine whether its crystal structure is FCC$,$ BCC$,$ SC $($Simple Cubic$)$ and then justify your determination.

$\backslash$table$[[$Alloy$,$Atomic mass $($g$/$mol$),$Density $($g$/$cm ${?}^3),$Atomic Radius $($nm$)],[$A$,77,4,10,69,0,125],[$B$,107,6,9,49,0,133],[$C$,127,3,13,06,0,142]]$