Instructions: Answer the following questions on a separate piece of paper. Be sure that your name

and date are on the first page. Upload your work as a PDF to Moodle for credit. All work must be

done individually.

At $1800K,$ the surface energy of alumina $(A{l}_2{O}_3)$ is $8\mathrm{.}5{10}^{-5}\frac{J}{c}{m}^2.$ The surface energy

for liquid nickel against its own vapor at $1800K$ is $1\mathrm{.}7{10}^{-4}\frac{J}{c}{m}^2.$ At the same

temperature, the interfacial energy between liquid nickel and alumina is $1\mathrm{.}8{10}^{-4}\frac{J}{c}{m}^2.$

From these data, calculate the contact angle of a droplet of liquid nickel on an alumina

plate at $1800K.$

A small droplet of molten silver is cooled until it solidifies via a homogeneous nucleation$-$

and$-$growth process. Calculate the amount of undercooling required to initiate the onset of

solidification $($i$.$e$.$ the temperature at which at least one viable homogeneous nuclei forms

in the volume of the droplet$).$ Given: Droplet volume $(V_{\text{d}\text{r}\text{o}\text{p}})=0\mathrm{.}10c{m}^3,T_m=962C,$

${}_{SL}=1\mathrm{.}3{10}^{-5}\frac{J}{c}{m}^2,{}_{Ag}=9\mathrm{.}3\frac{g}{c}{m}^3,M_{Ag}=107\mathrm{.}9\frac{g}{m}ol,$ and $H_{\text{s}\text{o}\text{l}\text{i}\text{d}\text{i}\text{f}\text{i}\text{c}\text{a}\text{t}\text{i}\text{o}\text{n}}=-11\mathrm{.}3$

$k\frac{J}{m}ol.$