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Consider a two-dimensional square lattice with a lattice constant a. What is the reciprocal lattice vector corresponding to the (1,1) direction in the direct lattice?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Consider a two-dimensional square lattice with a lattice constant a. W...
The reciprocal lattice is a lattice of points in momentum space that is dual to the direct lattice of points in real space.
It is defined as the set of all vectors G that satisfy the equation.
G⋅R=2πn,
where, R is any vector in the direct lattice,
and n is an integer.
In two dimensions, the reciprocal lattice is also a two-dimensional lattice.
For a square lattice with lattice constant a, the direct lattice is defined by the vectors.

The reciprocal lattice vectors are given by;

To find the reciprocal lattice vector corresponding to the (1,1) direction in the direct lattice,
we take a linear combination of the reciprocal lattice vectors.
Thus, the reciprocal lattice vector corresponding to the (1,1) direction in the direct lattice is.
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Consider a two-dimensional square lattice with a lattice constant a. What is the reciprocal lattice vector corresponding to the (1,1) direction in the direct lattice?a)b)c)d)Correct answer is option 'D'. Can you explain this answer?
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