Mathematically, the electric field gradient (EFG) is the hessian matrix (the matrix of the second derivatives) of the electrical potential V: In mathematics, the Hessian matrix is the square matrix of second partial derivatives of a scalar-valued function. ... Electrical potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential or the electric potential, typically measured in volts. ...

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 V_ij form a symmetrical and traceless tensor. The principal tensor components are usually denoted V_zz, V_yy and V_xx in order of decreasing modulus. Given the tensor's traceless character, Crystal (disambiguation) Insulin crystals A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions. ... In jewelry, a solid gold piece is the alternative to gold-filled or gold-plated jewelry. ... A stylized representation of a lithium atom. ... In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i. ... In mathematics, a tensor is a certain kind of geometrical entity, or alternatively generalized quantity. The tensor concept includes the ideas of scalars, vectors, and linear operators. ... In advanced theoretical physics, a modulus is a scalar field with no potential energy. ...

V_zz + V_yy + V_xx = 0

holds, which allows for a description of the EFG using only two parameters, V_zz and the asymmetry η or perturbed angular correlation (PAC), provided the nucleus in question has a quadrupolar moment. PAC or Pac may refer to several articles: Pan Africanist Congress, a political party in South Africa. ...