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Electric Field Gradient




the Electrical Potential V:
:
V_{ij} = rac{\partial^2 V}{\partial x_i \partial x_j}

It is an important structural property of a Crystalline Solid , where it is defined at the location of a Nucleus . The EFG is non-zero only if the charges surrounding the nucleus violate Cubic Symmetry and therefore generate an inhomogeneous Electric Field at the position of the nucleus. The individual components Vij form a symmetrical and Traceless Tensor . The principal tensor components are usually denoted Vzz, Vyy and Vxx in order of decreasing Modulus . Given the tensor's traceless character,

:
V_{zz} + V_{yy} + V_{xx} = 0


holds, which allows for a description of the EFG using only two parameters, Vzz and the ''asymmetry'' η

:
\eta = rac{V_{xx} - V_{yy}}{V_{zz}}


Any Quadrupolar Moment of the nucleus interacts with the inhomogeneous
field surrounding it, thus the electric field gradient can be
measured using several Spectroscopic methods, such as
Nuclear Magnetic Resonance ( NMR ), Nuclear Quadrupole Resonance ( NQR ), Moessbauer or Perturbed Angular Correlation (PAC), provided the nucleus in
question has a Quadrupolar Moment .