Crystal Field

the electric field that exists in crystals (less frequently, the term is used to describe a magnetic field that develops in some crystals). For short (on the order of inter-atomic) distances the positive and negative charges within a crystal do not compensate one another, thereby generating electric fields. The electric field intensity in a crystal can reach values of ∼ 108 volts per cm and more.

The concept of the crystal field is used in computing the energy spectrum of paramagnetic ions in ionic crystals and complex compounds (in this case the crystal field is called the ligand field). A crystal field is classified as weak, medium, or strong, according to whether the energy of interaction of the electrons of a paramagnetic ion is less than, comparable to, or greater than the energy of the spin-orbital interaction or of the electrostatic interaction of the electrons. An approximation frequently used in crystal-field calculations is that of point charges, where the real dimensions of the ions, atoms, or groups of ions or atoms are not taken into account but treated as point charges or electric dipoles located at the nodes of the crystal lattice. The potential of the crystal field exhibits symmetry, which is determined by the symmetry of the crystals. The magnitude and symmetry of the crystal electric field at any point of the crystal depend on the symmetry in the neighborhood of the point and on deformations in the sample (arising, for example, from external influences or from the presence of impurities, defects, or electric polarization in the crystal). Within narrow limits, the crystal field varies continuously around its mean value, in correspondence with vibrations of the crystal lattice.

Crystal electric fields are being investigated by optical and radiospectroscopic methods (electron paramagnetic resonance, nuclear magnetic resonance, and nuclear quadrupole resonance). To evaluate the magnitude of a crystal field and to determine its local symmetry (by optical methods or by electron paramagnetic resonance), small numbers of paramagnetic ions are frequently introduced as “atomic probes” into a diamagnetic crystal (matrix). Studies of the magnitude and symmetry of crystal fields make it possible to investigate the structure of solid bodies and the energy of interaction of ions with their crystalline surroundings. Such diamagnetic matrices with an admixture of paramagnetic ions are the basis for the solid-state laser and the ultrahigh-frequency quantum amplifier.

Crystal magnetic fields of significant magnitude arise in crystals containing paramagnetic ions and atoms. A distinction is made between ultrathin and dipole crystal magnetic fields. Ultrathin fields (10⁵ to 10⁶ oersteds) result from the ultrathin interaction of the magnetic moments of the nuclei and their electronic surroundings and are observed primarily in the nuclei of magnetic ions. Dipole magnetic fields are generated in the surrounding space by paramagnetic ions, just as they are by conventional magnetic dipoles. The maximum values of dipole fields range from 10³ to 10⁴ oersteds for distances from the magnetic ion of ∼10⁻⁸ cm. These values are typical also for magnetically ordered crystals. In other cases the magnetic field fluctuates rapidly under the influence of thermal vibrations, and its mean value approaches zero. Crystal magnetic fields are being investigated by the method of nuclear magnetic resonance and with the aid of the Mossbauer effect.