Question

Which of the following statement(s) is/are correct regarding 2-D crystal lattice?

• A. For square unit cell, $a=b;\gamma ={90}^o$
• B. For parallelogram, $a=b;\gamma \ne {120}^o$
• C. 2 parameters are required to define the lattice
• D. For hexagonal unit cell, $a=b;\gamma ={120}^o$

Answer 1

Answer: (A), (D)

For hexagonal unit cell, $a=b;\gamma ={120}^o$

In 2-D crystal lattice, there will be regular arrangement of lattice points in a plane.
Three parameters are required to define the 2-D lattice.
They are, two edge lengths 'a' and 'b' and angle between the edges, γ.
Thus, statement (c) is wrong.
There are 5 crystal systems for 2-D crystall lattice.

Crystal system	Edge lengths	Angles
Square unit cell	$a=b$	$\gamma ={90}^o$
Rectangular unit cell	$a\ne b$	$\gamma ={90}^o$
Hexagonal unit cell	$a=b$	$\gamma ={120}^o$
Rhombic unit cell	$a=b$	$\gamma \ne {120}^o,{60}^o,{90}^o$
Parallelogram	$a\ne b$	$\gamma ={120}^o$

Thus, statement (a) and (d) are correct.