Question

Fig. Q4 shows a hexagonal close packed structure (hcp). (a) Show that for an ideal hcp, $\frac{c}{a} = 2\sqrt{\frac{2}{3}} = 1.633$. (8 marks) (b) Show that the packing ratio (or packing efficiency) of hcp is the same as that of fcc structure, that is 0.74. (10 marks) (c) $\alpha$-Co has an hcp structure with lattice spacing $a = 2.51$ Å and $c = 4.07$ Å, whereas $\beta$-Co is fcc. What is the difference in density (in %) between the two forms? (Hint: $\alpha$-Co obviously does not have ideal hcp structure. Refer your answer in (b) to see how c/a related to density) (6 marks) (d) Sodium transform from bcc to hcp at about $T = 23K$. Assuming that the density remain fixed and the c/a ratio is ideal, calculate the hcp lattice spacing a given that the cubic lattice spacing a'=4.23 Å in the bcc phase. (8 marks)

          Fig. Q4 shows a hexagonal close packed structure (hcp).
(a) Show that for an ideal hcp, $\frac{c}{a} = 2\sqrt{\frac{2}{3}} = 1.633$.
(8 marks)
(b) Show that the packing ratio (or packing
efficiency) of hcp is the same as that of fcc
structure, that is 0.74.
(10 marks)
(c) $\alpha$-Co has an hcp structure with lattice spacing
$a = 2.51$ Å and $c = 4.07$ Å, whereas $\beta$-Co is
fcc. What is the difference in density (in %)
between the two forms? (Hint: $\alpha$-Co obviously
does not have ideal hcp structure. Refer your
answer in (b) to see how c/a related to density)
(6 marks)
(d) Sodium transform from bcc to hcp at about $T = 23K$. Assuming that the
density remain fixed and the c/a ratio is ideal, calculate the hcp lattice spacing
a given that the cubic lattice spacing a'=4.23 Å in the bcc phase. (8 marks)

Fig. Q4 shows a hexagonal close packed structure (hcp).
(a) Show that for an ideal hcp, (c)/(a) = 2√((2)/(3)) = 1.633.
(8 marks)
(b) Show that the packing ratio (or packing
efficiency) of hcp is the same as that of fcc
structure, that is 0.74.
(10 marks)
(c) α-Co has an hcp structure with lattice spacing
a = 2.51 Å and c = 4.07 Å, whereas β-Co is
fcc. What is the difference in density (in %)
between the two forms? (Hint: α-Co obviously
does not have ideal hcp structure. Refer your
answer in (b) to see how c/a related to density)
(6 marks)
(d) Sodium transform from bcc to hcp at about T = 23K. Assuming that the
density remain fixed and the c/a ratio is ideal, calculate the hcp lattice spacing
a given that the cubic lattice spacing a'=4.23 Å in the bcc phase. (8 marks)

Added by Lawrence P.

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