Unit Cell Volume of Cadmium (HCP)

[ming2194]

Homework Statement

Q 2.

(a) For the HCP crystal structure, show that the ideal c/a ratio is 1.633. (10%)

(b) Hence, calculate the unit cell volume of cadmium with a HCP structure and atomic radius of
0.1490 nm. Assume that the lattice period is equal to two times of the atomic radius. (5%)

Homework Equations

The Attempt at a Solution

(a) part is okay.
For (b) part, may i use the equation Vc=6(R^2)C(3^1/2) without proving?
or are there any other methods to find Vc by using the data c/a=1.633? (i know the equation p=nA/(Vc)(Na) but seems not related to a=2R/1.6333)

 

[KataKoniK]

it is important to always provide a thorough explanation and justification for any equations or methods used in solving a problem. In this case, you can use the equation Vc=6(R^2)C(3^1/2) to calculate the unit cell volume of cadmium with a HCP structure, as long as you provide a clear explanation for why this equation is valid and how it relates to the given data of c/a=1.633. You can also consider using other methods, such as calculating the volume of the hexagonal prism formed by the unit cell or using the lattice parameter a=2R/1.6333 to determine the volume. Whichever method you choose, it is important to clearly explain your reasoning and show your calculations.

 

[Mene]

Yes, you can use the equation Vc=6(R^2)C(3^1/2) without proving as long as you clearly state your assumptions and show your calculations. Another method to find Vc using the given data would be to use the formula Vc=4R(1+cosθ), where θ is the angle between the c-axis and the a-axis. However, this method may require more complex calculations.