Question

Which of the following relations are correct for the cubic crystal:
A. a = b \( \neq \) c
B. a = b = c
C. \( \alpha = \beta = \gamma = 90^\circ \)
D. \( \alpha \neq \beta = \gamma = 90^\circ \)
Choose the correct answer from the options given below:

• A. A and B only
• B. B and C only
• C. B and D only
• D. A and D only

Hint:

Memorize the lattice parameters for the 7 crystal systems. The cubic system is the most symmetric and easiest to remember: all sides are equal, and all angles are 90 degrees.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The question asks for the defining characteristics of a cubic crystal system in terms of its lattice parameters. The lattice parameters consist of the lengths of the unit cell edges (a, b, c) and the angles between them (\(\alpha, \beta, \gamma\)).
Step 2: Detailed Explanation:
By definition, a cubic crystal system is characterized by:
1. Three equal lattice constants, meaning the lengths of the unit cell edges are identical.
\[ a = b = c \]
Therefore, statement B is correct and statement A is incorrect.
2. Three interfacial angles that are all right angles (90 degrees).
\[ \alpha = \beta = \gamma = 90^\circ \]
Therefore, statement C is correct and statement D is incorrect.
Step 3: Final Answer:
The correct relations for a cubic crystal are \(a = b = c\) and \( \alpha = \beta = \gamma = 90^\circ \). Thus, statements B and C are correct.