Answer:
[tex]\mathbf{\Delta V = -0.63 \%}[/tex]
Contraction
Explanation:
From the given information;
Above 88° C
zirconium has a BCC crystal structure with a = 0.332 nm
Below this temperature
zirconium has an HCP structure with a = 0.2978 nm and c = 0.4735 nm
the volume of BCC can now be:
[tex]V_{BCC} = (a)^3[/tex]
[tex]V_{BCC} = (0.332 \ nm)^3[/tex]
[tex]V_{BCC} =0.03660 \ nm^3[/tex]
the volume of HCP can now be:
[tex]V_{HCP} = (a)^2 (c) cos \ 30^0[/tex]
[tex]V_{HCP} = (0.2978)^2 (0.4735) \ cos 30[/tex]
[tex]V_{HCP} =0.03637 \ nm^3[/tex]
Ths; the volume percent change when BCC zirconium transforms to HCP zirconium can be calculated as:
[tex]\Delta V = \dfrac{V_{HCP}-V_{BCC}}{V_{BCC}} * 100 \%[/tex]
[tex]\Delta V = \dfrac{0.03637 \ nm^3-0.03660\ nm^3}{0.03660\ nm^3}} * 100 \%[/tex]
[tex]\mathbf{\Delta V = -0.63 \%}[/tex]
Hence; it is contraction due to what the negative sign portray, The negative sign signifies that there is contraction during cooling
