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For a cubic crystal structure which one of the following relations indicating the cell characteristics is correct?
A
$a \neq b \neq c$ and $\alpha = \beta = \gamma = 90^\circ$
B
$a = b = c$ and $\alpha \neq \beta \neq \gamma = 90^\circ$
C
$a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$
D
$a \neq b \neq c$ and $\alpha \neq \beta$ and $\gamma \neq 90^\circ$
Detailed Solution
A unit cell is described by three edge lengths $a$, $b$, $c$ and three angles $\alpha$, $\beta$, $\gamma$ between the edges.
For a cubic crystal all three edges are equal and all three angles are right angles:
$a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$
$a \neq b \neq c$ with all angles $90^\circ$ describes the orthorhombic system.
$a \neq b \neq c$ with all angles unequal and different from $90^\circ$ describes the triclinic system.
So the correct relation for a cubic crystal is $a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$.
For a cubic crystal all three edges are equal and all three angles are right angles:
$a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$
$a \neq b \neq c$ with all angles $90^\circ$ describes the orthorhombic system.
$a \neq b \neq c$ with all angles unequal and different from $90^\circ$ describes the triclinic system.
So the correct relation for a cubic crystal is $a = b = c$ and $\alpha = \beta = \gamma = 90^\circ$.