Lattice parameters

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A lattice parameter or a lattice constant , sometimes also called a cell parameter , is either a length specification or an angle that is required to describe a lattice , in particular the smallest unit of the lattice, the unit cell . The lattice parameter is either a side length of the unit cell or an angle between the edges of the cell. Lattice parameters are important in crystallography and optics .


The grid is generated by periodically shifting a unit cell by the same distance in a certain spatial direction (grid vector ):

  • A single grating parameter is sufficient for a one-dimensional optical grating , namely the specification of the distance between adjacent ( parallel ) grating elements.
  • In two dimensions, there are two different grid vectors and three necessary grid parameters - two lengths and the angle between the grid vectors.
The lattice constants of a three-dimensional lattice
  • A maximum of six parameters are required to describe a three-dimensional grid, three lengths and three angles. These six parameters that define the unit cell are often referred to as a , b , c and α, β, γ. Three of them, a , b and c , are the lengths of the lattice vectors that span the unit cell. The other three, α, β and γ, are the angles between these vectors, namely
    • α is the angle between  b and  c,
    • β is the angle between  a and  c,
    • γ is the angle between  a and  b .

The description of a grid by grid parameters is ambiguous, different sets of grid parameters can describe the same grid. Therefore, the conventional cell is generally used as the unit cell . With this choice of the unit cell, individual lattice parameters can already be fixed in the individual crystal systems , so that the number of independent lattice parameters is reduced. Therefore you need


The transmission electron microscope or the scanning tunneling microscope can be used to directly measure the parameters of crystalline substances . In most cases, however, the lattice parameters are determined using diffraction methods , for example with X-ray diffraction . In X-ray structure analysis , determining the lattice parameters is the first step in determining the complete crystal structure .

The cell parameters of surface structures can be determined with the help of the diffraction of slow electrons ( Low Energy Electron Diffraction , LEED).


The lattice parameter of silicon , which forms a diamond structure , was measured with very high accuracy and is 543.102 0511 (89)  pm . The exact measurement was carried out in advance of the redefinition of the kilogram and the mole .

The mass density of a crystalline substance can be determined from the lattice parameters. In the simple case of cubic lattices, the density is:


The bond length in the diamond structure is , in the face-centered cubic lattice , in the body-centric cubic lattice and in the primitive cubic lattice .

The lattice parameter of iron with a body-centric cubic lattice is 286.65 pm. For the lattice parameter of face-centered cubic structures, the examples nickel 352.4 pm, copper 361.48 pm, silver 408.53 pm, and gold 407.82 pm may be mentioned.

See also

Individual evidence

  1. CODATA Recommended Values. National Institute of Standards and Technology, accessed July 8, 2019 . Lattice parameters of silicon. The numbers in brackets denote the uncertainty in the last digits of the value; this uncertainty is given as the estimated standard deviation of the specified numerical value from the actual value.
  2. The measurement of the lattice constant was carried out with silicon with a naturally occurring isotopic composition at a temperature of 22.5 ° C in a vacuum, cf. P. 33 ( Memento of the original from October 15, 2011 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF file; 855 kB) and p. 676 (PDF file; 2.02 MB). @1@ 2Template: Webachiv / IABot /
  3. Kilograms and moles: Counting atoms Communication from the Physikalisch-Technische Bundesanstalt accessed on November 25, 2018