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Reciprocal Lattice

Dr. Saloni Sharma

PG Department of Physics

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Reciprocal Lattice

  • Reciprocal lattice is an important concept to which helps in study of crystal lattice and their diffraction properties.

  • It was introduced by P.P. Ewald in 1921 and later developed by Von Laue.

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Reciprocal Lattice

  • The nature of Laue diffraction pattern obtained is governed by the periodicity of the crystal structure and the positions of diffraction spots obtained depend upon the properties of direct lattice

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  • Miller indices represent a family of parallel planes. Each set of planes can be represented by a normal drawn to these planes from a fixed point so that the length of the normal is proportional to the reciprocal of the interplanar spacing.

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Reciprocal Lattice

  • Thus, we may draw a reciprocal lattice applying certain rules.

  • A lattice point in the reciprocal lattice may be used to represent a reflecting plane of the crystal assigning it same indices as that of the reflecting plane in the direct lattice

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Rules to obtain reciprocal lattice from direct lattice

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Reciprocal lattice from direct lattice

  • The array of points in space obtained according to the above rules represents a lattice called the reciprocal lattice.
  • The formation of two dimensional reciprocal lattice for a monoclinic lattice is explained further.

Monoclinic Lattice

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Reciprocal lattice from direct lattice

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Reciprocal lattice from direct lattice

 

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Reciprocal lattice from direct lattice

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Reciprocal Lattice Vector

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Properties of the Reciprocal Lattice

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K-Space

  • According to the concept of reciprocal lattice, a reciprocal lattice is a set of points which are used to describe the planes of a crystal system.
  • In case of a perfect crystal, this set of points extend to infinity in three dimensions and we get an infinite arrangement of points in space such that the distance between the points in a particular direction is inversely proportional to the distance between the (hkl) planes perpendicular to that direction in the direct lattice.
  • This arrangement of points is called the reciprocal lattice and the space obtained from these points is called reciprocal space.

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Reciprocal Lattice to a Simple Cubic Lattice

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Reciprocal Lattice to FCC Lattice

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Reciprocal Lattice to BCC Lattice

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THANKS