Spectrum, Crystal

The optical spectra of crystals vary greatly in structure. They may contain narrow lines, broad bands (where the ratio of the frequency v to the speed of light c ranges from fractions of a cm^–1 to several thousands of cm^–1), and continuous spectral regions extending over tens of thousands of cm^–1.

In the infrared region of absorption spectra, bands are observed that are associated with quantum transitions between energy levels arising from vibrational motions of the particles of the crystal that are accompanied by changes in the electric dipole moment: a photon is absorbed, and a phonon, or quantum of lattice vibrations, is created. The processes involving the creation of several phonons broaden and complicate the observed spectrum. Defects are usually present in the structure of real crystals (seeDEFECTS, CRYSTAL); near these defects there can occur localized vibrations, such as the internal vibrations of an impurity molecule. In this case, additional lines appear in the spectrum. The additional lines may have satellites resulting from the coupling of the localized vibrations with the lattice vibrations. In semiconductors, some impurities form centers in which electrons move in hydrogen-like orbits. These centers give rise to absorption spectra in the infrared region consisting of a series of lines ending in a continuous absorption band, which corresponds to the ionization of the impurity. The absorption of light by conduction electrons and holes in semiconductors and metals also begins in the infrared region (seeMETAL OPTICS). Magnons, in much the same way as phonons, show up in the spectra of magnetically ordered crystals.

Figure 1. Raman spectrum of a crystal of potassium dihydro-gen phosphate (KDP) at different temperatures; the ratio of the frequency shift (v – v_o to the speed of light is plotted along the horizontal axis

The interaction of light with lattice vibrations, which are accompanied by a change in the polarizability of the crystal, produces a scattered-light spectrum that contains not only the line of the original frequency v₀ but also lines on both sides of it. The new lines are shifted from the original frequency by the frequency of the lattice vibrations (see Figure 1). This effect corresponds to the creation or absorption of phonons (seeRAMAN EFFECT). The existence of the acoustic lattice vibrations means that when light is scattered by thermal fluctuations, the central (unshifted) Rayleigh line is also accompanied on both sides by satellites (Brillouin components), which are due to scattering by propagating density fluctuations (seeSCATTERING OF LIGHT).

Most nonmetallic crystals are transparent in a certain frequency range outside the infrared region. Absorption occurs again when the energy of the photon becomes great enough to cause electronic transitions from the occupied upper valence band to the lower part of the conduction band of the crystal. The spectrum of this intense intrinsic absorption reflects the structure of the crystal’s electronic energy bands and extends further into the visible region as transitions between other energy bands become possible. The location of the intrinsic absorption edge determines

Figure 2. Long-wavelength portion of the intrinsic absorption of a KBr crystal at the temperature of liquid nitrogen. The first two intense peaks on the low-energy side correspond to excitons. The region of intrinsic absorption begins after the second peak.

the color of an ideal crystal, that is, a crystal without defects. For semiconductors, the long-wavelength limit of the intrinsic absorption region lies in the near infrared region; for ionic crystals, the long-wavelength boundary is in the near ultraviolet region. Besides direct electronic transitions, indirect transitions, in which additional phonons are created or captured, contribute

Figure 3. No-phonon line and phonon wing in the absorption spectrum of the impurity molecule N0⁻₂in Kl at the temperature of liquid helium

to the intrinsic absorption of a crystal. Electronic transitions from conduction bands to valence bands can be accompanied by recombination radiation.

Owing to electrostatic attraction, a conduction electron and a hole can form a bound state known as an exciton. Exciton spectra can vary from hydrogen-like series to broad bands. Exciton absorption lines are located at the long-wavelength boundary of a crystal’s intrinsic absorption (Figure 2). Excitons are responsible for the electronic absorption spectra of molecular crystals. Exciton luminescence also occurs.

The energies of electronic transitions between the localized levels of defect centers usually fall in the transparent region of an ideal crystal and are therefore often responsible for the crystal’s color. In alkali halide crystals, for example, the excitation of an electron localized in an anionic vacancy (an F-center) gives rise to the characteristic color of the crystal. Various impurity ions—for example, Tl in KCl—form luminescent centers in crystal phosphors. These centers give rise to electron-vibrational (vibronic) spectra. If the electron-phonon (vibronic) interaction in a defect center is weak, there appears in the spectrum an intense, narrow, no-phonon line, which is the optical analogue of a line due to the Mössbauer effect. Adjacent to the no-phonon line is what is known as a phonon wing, whose structure corresponds to the characteristics of the dynamics of a crystal with an impurity (Figure 3). As the vibronic interaction increases, the intensity of the no-phonon line decreases. A strong vibronic coupling yields wide structureless bands. Since part of the excitation energy is scattered in the rest of the crystal during vibration relaxation before emission, the maximum of the luminescence band lies on the long-wavelength side of the absorption band (Stokes’ law). Sometimes an equilibrium distribution for the vibrational sublevéis does not have time to be established before the light quantum is emitted; hot luminescence is then possible.

If the impurities contained in a crystal are atoms or ions of transition or rare-earth elements with incomplete f−or d-shells, it is then possible to observe discrete spectral lines that correspond to transitions between sublevéis resulting from the splitting of the atomic levels by the intracrystalline electric field (seeCRYSTAL FIELD and QUANTUM MECHANICAL AMPLIFIER).