POLARIZED LUMINESCENCE OF CUBIC CRYSTALS*)

P. P. Feofilov

Crystals were the first objects that made it possible to observe polarization in elementary acts of radiation. The history of the study of polarized luminescence begins with Grailich’s discovery of the polarized radiation of optically anisotropic crystals of platinocyanide salts, described by him almost a hundred years ago in Crystallographic-Optical Investigations1. The polarization of luminescence of isotropic media—gases and liquids—was discovered only more than half a century later (Wood—diatomic molecules, 1908; Weigert—solutions of complex molecules, 1920; Rayleigh—atoms, 1922). The relatively early discovery of polarized radiation in anisotropic crystals is connected with the fact that in this case polarization is a natural consequence of the orientation of individual radiating centers with respect to distinguished directions—the optical axes—and no special conditions need be created for its observation. On the contrary, in media with a chaotic arrangement of luminescing atoms and molecules it is necessary to create this orientation by producing anisotropic excitation and, as far as possible, by eliminating all known depolarizing factors. Nevertheless, at the present time we possess, to a considerable extent thanks to the work of S. I. Vavilov and his school, abundant experimental material and a sufficiently developed theory of the polarized luminescence of isotropic media.**) Therefore the question naturally arises whether the investigation of polarized radiation of crystals of the cubic system, which are generally considered to be media completely isotropic in the optical respect, can yield any essentially new results. It turns out that, despite the absence of dichroism and double refraction—the characteristic features of anisotropic crystals—peculiar manifestations of anisotropy may be observed in luminescing cubic crystals, associated with the specificity of the crystalline state and with the presence in crystals of definite distinguished directions—the axes of symmetry.

*) Report presented at the Fourth Conference on Luminescence (Minsk, June 1955).

**) A review of work on the polarized luminescence of molecular solutions was published in Uspekhi Fizicheskikh Nauk, vol. 36, p. 417, 1948.

P. P. FEOFILOV

§ 1. ORIENTATION OF LUMINESCENT CENTERS IN CUBIC CRYSTALS

The luminescence of cubic crystals excited by polarized light may prove to be polarized if the acts of absorption and emission of light are not separated by semiconductor processes, as often occurs in crystals, and take place in one and the same center. The very possibility of exciting polarized radiation in an optically isotropic medium is sufficiently obvious and has been well studied in numerous works on the polarization of the luminescence of solutions of complex molecules. Somewhat unexpected and surprising at first glance, however, may be the dependence, discovered by us in 1953, of the degree of polarization of the luminescence of cubic crystals on the relative position of the plane of polarization of the exciting light and the symmetry axes of the crystal\(^{2,3}\). The presence of this dependence undoubtedly shows that, despite the optical isotropy of luminescent cubic crystals, they cannot be completely likened, even with respect to their optical properties, to a chaotic aggregate of luminescent molecules, for example, to luminescent solutions.

Fig. 1. Diagram of the apparatus for observing azimuthal dependences of luminescence polarization: \(S\)—excitation source; \(F_1\), \(F_2\)—light filters; \(L\)—lens; \(P\)—polarizer; \(C\)—crystal under study; \(Pm\)—polarimeter.

An elementary consideration shows that the presence of a sharply expressed azimuthal dependence of the degree of polarization (so we shall call the dependence of the degree of polarization of the luminescence, observed according to the scheme of Fig. 1, on the angle of rotation of the plate under study \(\alpha\)) testifies to the existence of several symmetric directions along which anisotropic luminescent centers can be oriented.

The establishment of the fact of orientation of luminescence centers along the symmetry axes of cubic crystals formed the basis of the set of investigations to the survey of which the present article is devoted.

In crystals of the cubic system there are, as is known, three symmetry axes of the fourth order, four axes of the third order, and six axes of the second order (Fig. 2). Proceeding from the most general considerations, one may assert that if anisotropic luminescence centers introduced into a crystal or created in it are arranged regularly in the crystal, then the axes of the centers will be oriented along one or another of the symmetry axes of the crystal. The character and degree

orientations of the centers will be determined by the crystal-chemical structure of the system, by the nature of the centers, and by the character of their incorporation into the crystal lattice of the host substance. It is not difficult to see that, irrespective of the character of the orientation of the centers, dichroism will not arise in the medium, since, for an equiprobable distribution of the centers over the possible directions of orientation, the sums of the squares of the projections of the amplitudes of the elementary oscillators (by means of which the absorption process can be described) onto two arbitrarily chosen mutually perpendicular directions will be identical. Nevertheless, despite the apparent isotropy of the excited plates, the degree of polarization of the luminescence will, as a rule, depend strongly on the position of the exciting electric vector in the plane of the plate.

A simple calculation makes it possible to obtain theoretically the azimuthal dependences for various cases of the orientation of centers inside a crystal2. As a model of the center one may take the classical oscillator model, which fully justified itself in the study of the polarization of the luminescence of isotropic solutions of complex molecules. This model is a combination of linear oscillators coinciding in direction and describing long-wavelength absorption and emission, and of a circular oscillator responsible for absorption in the second band and situated in a plane perpendicular to the linear oscillators. The introduction of a circular oscillator or (which, from the point of view of interpreting the experimental results, is the same thing) of several linear oscillators symmetrically arranged in a plane perpendicular to the direction of the emitting oscillator is necessary for explaining the polarization spectrum of luminescence, i.e., the dependence of the degree of polarization on the wavelength of the exciting light*).

Fig. 2. Axes of symmetry of crystals of the cubic system.

The direction of the emitting oscillator is the axis of symmetry of the center and, consequently, the direction determining its orientation.

Proceeding from this model, we carried out, for three possible cases of the orientation of centers—along symmetry axes of the fourth, third, and second orders—a calculation of the azimuthal dependences of the polarization of the luminescence of plates cut from the crystal parallel to the planes of the cube (100), the rhombic dodecahedron (110), and the octahedron (111). The calculation was performed both for “long-wavelength” excitation (the absorbing and emitting oscillators are parallel) and for “short-wavelength” excitation (the absorbing circular oscillator is perpendicular to the emitting one). The results of the calculation are shown graphically in Figs. 3–5. As can be seen from comparison of the azimuthal curves obtained for the various cases, their study makes it possible to establish quite unambiguously the character of the orientation of centers in the crystal lattice.

Fig. 3. Azimuthal dependences of luminescence polarization for orientation of the oscillators along fourth-order axes.

At first glance it is surprising that there is an azimuthal dependence of the intensity of the luminescence of plates cut from the crystal parallel to the plane (110) and not possessing, as we have seen, absorption dichroism. It is not difficult, however,

make sure that this result, predicted by calculation and observed experimentally, has a simple explanation. Although the probability of absorption of light polarized in two arbitrary, mutually perpendicular directions in the plane of the plate is the same, the relative intensity of the light emitted in the direction of observation by oscillators having different orientations is different; this determines both the azimuthal dependence of the luminescence intensity and another phenomenon, likewise unexpected for optically isotropic media—“spontaneous” polarization, i.e., polarization of the luminescence excited in plates cut parallel to the plane (110) by natural light.

Fig. 4. Azimuthal dependences of luminescence polarization for oscillator orientations along third-order axes.

The method of studying the azimuthal dependences of luminescence polarization was used by us to establish the character of the orientation of luminescent color centers in ionic crystals and of europium ions introduced into the fluorite crystal lattice*).

*) All single crystals investigated in this work were grown and placed at our disposal by I. V. Stepanov. I take this opportunity to express my sincere gratitude to I. V. Stepanov, thanks to whose work on artificial single crystals it proved possible to carry out the investigations described here.

a) Orientation of luminescing color centers in fluorite crystals$^2$. The azimuthal dependences of the degree of polarization of the luminescence of the color centers found by us in fluorite crystals are expressed extremely sharply (Fig. 6).

Comparison of the dependences found experimentally with the calculated ones (Figs. 3–5) leaves no doubt that in this

Fig. 5. Azimuthal dependences of luminescence polarization for the orientation of oscillators along axes of the second order.

case the anisotropic luminescing color centers are oriented along axes of symmetry of the fourth order. For the purpose of a comprehensive verification of the calculated dependences, the investigation was carried out with plates cut parallel to the planes of the cube, rhombic dodecahedron, and octahedron, and excited both in the long-wavelength absorption band and in the band following it ($\lambda_{\text{exc}} = 365\,m\mu$), upon excitation in which the degree of polarization changes sign. The character of all the dependences proved in detail to correspond to the calculation. In complete agreement with the calculated data, in plates cut parallel to the face of the rhombic dodecahedron (110), an azimuthal dependence of the luminescence intensity and a “spontaneous” polarization of the emitted light were observed.

b) Orientation of luminescent color centers in crystals of alkali-metal fluorides. A completely analogous investigation was carried out with crystals of lithium fluoride and sodium fluoride colored by X-ray irradiation. In these cases, however, the character of the azimuthal dependences proved to be entirely different from that in the case of fluorite (Fig. 7).

Fig. 6. Azimuthal dependences of the polarization of luminescence of color centers in fluorite crystals.

Comparison of the experimental curves with the calculated ones shows that, in the alkali-halide crystals investigated, the luminescent color centers are oriented along axes of symmetry of the second order.

The character of the orientation of luminescent color centers in ionic crystals, established in these experiments, in combination with the data on the absolute values of the degree of polarization, made it possible to suggest that the color centers in the ionic crystals studied are the so-called \(F_2\)-centers, i.e.

Fig. 7. Azimuthal dependences of the polarization of luminescence of color centers in sodium fluoride crystals.

pairs of electrons localized at neighboring vacant anion sites \(^{4}\). Indeed, consideration of the crystal-chemical structure of the crystals studied (Fig. 8) shows that \(F_2\)-centers formed in the fluorite crystal lattice are oriented along the fourth-order symmetry axes, whereas analogous centers in alkali-halide salt crystals must be oriented-

POLARIZED LUMINESCENCE OF CUBIC CRYSTALS

be oriented along axes of the second order. As we have seen, precisely such is the character of the orientation of the centers, established on the basis of polarization measurements.

Fig. 8. Structure of crystal lattices: a) fluorite; b) fluorides of alkali metals.
●—M; ○—F; ○—○—$F_2$ center

c) Orientation of Eu+++ ions in fluorite crystals[^6]. As is known, the fluorides of yttrium and of rare-earth metals (TR) form mixed crystals with CaF$_2$ (for example, the natural minerals yttrofluorite, yttrocerite, etc.), preserving the cubic fluorite lattice with somewhat altered parameters. The formation of mixed crystals is favored by the closeness of the ionic radii of Ca++ and TR+++, which are in one isomorphous heterovalent series.

The rare-earth ions introduced into fluorite crystals luminesce brightly, exhibiting a characteristic line emission spectrum. The presence of polarization of the luminescence of europium ions introduced into fluorite crystals made it possible to apply the luminescence-polarization method to the study of the character of their orientation. The degree of polarization of the luminescence proved to be different for different lines in the Eu+++ emission spectrum and revealed a sharply expressed azimuthal dependence (Fig. 9), comparison of which with the calculated dependences makes it possible to conclude unambiguously that in this case the luminescent centers—Eu+++ ions—are oriented along the four axes of the third order.

If one assumes, in accordance with the generally accepted point of view, that the rare-earth ions enter the crystal lattice of fluorite by isomorphously replacing Ca++ ions, then it is not difficult to see that in the first coordination sphere surrounding each TR+++ ion there will be 8 F− ions, situated along the axes of third-order symmetry. In an ideal crystal all these four directions of possible orientation are completely equivalent and at the same time

azimuthal dependences of the polarization of luminescence indicate the stability of the orientation of europium ions along one of these directions. This can readily be explained by means of the principle of local charge compensation, often invoked in considering the detailed structure of luminescent centers. Indeed, upon isomorphic replacement of a Ca++ ion by an Eu+++ ion, it is necessary to compensate the excess positive charge. This compensation may be accomplished in various ways; however, in all cases it will be accompanied by the introduction of asymmetry into the nearest surroundings of the TR+++ ion. One of the possible paths

Fig. 9. Azimuthal dependence of the degree of polarization of individual lines in the luminescence spectrum of CaF₂:Eu: a—5735 Å; b—6165 Å; c—6309 Å. Dashed lines—theoretical curves.

of this compensation, apparently realized in the case under consideration, is the isomorphic replacement of one of the F⁻ ions in the coordination sphere surrounding the Eu+++ ion by an O-- ion. The possibility of isomorphic replacement of F⁻ by O-- is ensured by the closeness of their ionic radii (1.33 and 1.36 Å). The resulting asymmetry of the coordination sphere determines the stability of the orientation of the given europium ion along one of the four possible directions. On the average, of course, the ions are oriented with equal probability along all four directions. Thus, the results obtained in studying the character of the orientation of Eu+++ ions also fully agree with crystallochemical conceptions of the structure of mixed crystals CaF₂—TRF₃.

The examples considered show, one may suppose, that the study of the azimuthal dependences of the polarization of luminescence in cubic crystals makes it possible, on the one hand, to shed light on the nature of luminescent centers and, on the other hand, to express certain considerations concerning the character of the arrangement of foreign atoms and ions in a given crystal lattice.

§ 2. ANISOTROPIC PHOTOCHEMICAL PROCESSES IN CUBIC CRYSTALS

If polarized light capable of producing photochemical transformations of particles falls on an isotropic ensemble of anisotropic particles, then their distribution becomes anisotropic, since those particles that have a quite definite orientation relative to the acting vector of the light wave will predominantly absorb the light and, consequently, undergo photochemical changes.

This phenomenon—the emergence of anisotropy as a result of the action of photochemically active polarized light on an isotropic medium—is known as the Weigert effect.

An analogous phenomenon was discovered by us in studying the luminescence of color centers in ionic crystals*). In this case, however, the phenomenon can be expressed much more sharply than in the case of a chaotic ensemble of centers, since, with the regular orientation of centers which, as we have seen, takes place in crystals, it is possible to choose such a direction of the acting vector of the photochemically active light that only centers having a quite definite orientation will absorb the light and undergo changes. Thus, if from a fluorite crystal, in which the color centers are oriented along fourth-order axes, one cuts a plate parallel to the cube plane \((100)\) and directs the electric vector of the photochemically active light \((\lambda = 365 \text{ m}\mu,\) the experiment is conducted at the temperature of liquid air) along one of the fourth-order axes lying in the plane of the plate, then of the two groups of centers located in this plane only one will absorb the light and, consequently, be destroyed. As a result, after a sufficiently prolonged action of the active light, all centers will prove to be oriented in one direction. Then, by measuring, for example, the spectral course of the dichroism of the plate, one can determine the orientation of the oscillators describing the absorption of light of different wavelengths relative to the axes of the center.

Such an investigation, carried out by us for color centers in crystals of fluorite and sodium fluoride, made it possible to make an unambiguous choice between two variants of the oscillator model, which with equal success describe the azimuthal dependences and polarization spectra of luminescence of color centers.

Polarization spectra give a picture of the relative arrangement of absorbing and emitting oscillators upon excitation of luminescence by light of different wavelengths and do not, in general,

*) Somewhat earlier, Ueta\(^{8}\) observed the appearance of dichroism in KCl crystals irradiated with photochemically active polarized light in the region of the absorption bands of \(M\)-centers.

speaking, to judge which of the oscillators changes its direction when the wavelength of the exciting light is changed. A study of the spectral course of the dichroism or of the “spontaneous” polarization of the luminescence of dichroic plates makes it possible to give an unambiguous answer to this question. If the dichroism does not depend on the wavelength in the absorption spectrum, then, evidently, the change in polarization should be associated with a change in the orientation of the emitting oscillator in passing from one absorption band to another. Conversely, if the dichroism, determined by the orientation of the absorbing oscillators, changes with wavelength, while the “spontaneous” polarization of the luminescence does not depend on the wavelength of the exciting light, the polarization spectrum should be interpreted by means of a model that describes the luminescing center as a combination of an emitting oscillator, unchanged in direction, and several absorbing oscillators having different orientations. The investigations we have carried out showed that the spectral course of the dichroism qualitatively coincides with the course of the polarization spectrum, while the “spontaneous” polarization does not depend on the wavelength of the exciting light, i.e. the second model proves to be correct, successfully explaining, as is known, the polarization spectra of luminescence of complex organic molecules discovered by S. I. Vavilov.

§ 3. POLARIZATION OF LUMINESCENCE OF CUBIC CRYSTALS AND THE NATURE OF ELEMENTARY OSCILLATORS

The orientation of individual luminescing centers along one or another symmetry axis of cubic crystals introduces a certain specificity into the method of polarization diagrams, developed by S. I. Vavilov9 for establishing the nature (multipolarity) of the elementary oscillators by means of which the process of luminescence can be described. The method of polarization diagrams is based on the difference in the spatial distribution of the radiation of different multipoles: electric and magnetic dipoles, quadrupoles, etc., and consists in studying the degree of polarization of luminescence while varying the angles between the direction of observation and the exciting electric vector. When extending the method of polarization diagrams to the case of cubic crystals, it is necessary to keep in mind that the characteristic form of the polarization diagrams in this case depends strongly on the conditions of observation, namely, on the orientation of the symmetry axes of the crystal relative to the directions of excitation and observation. To obtain the most characteristic dependences, observation should be carried out according to the scheme of Fig. 10, exciting the luminescence of the crystal under study through the face of the cube (100) with linearly polarized light. The plane through which the observation is made should suitably be oriented parallel

face of the cube, if the oscillators of the luminescent centers are arranged along axes of the fourth order (for example, in the case of color centers in CaF\(_2\)), and parallel to the face of the rhombododecahedron (011), if the oscillators are oriented along axes of the third or second order (europium ions in CaF\(_2\) or color centers in crystals of alkali-halide salts). By changing the angle \(\eta\), which determines the direction of the exciting electric vector in the plane perpendicular to the direction of excitation, and by studying the intensity and polarization of the luminescence, one can obtain diagrams that make it possible (in most cases unambiguously) to establish the nature (multipolarity) of both the absorbing and the emitting systems of the luminescent center.

The corresponding calculations were carried out by us for all three possible cases of center orientation (along axes of the fourth, third, and second order) and for all possible combinations of absorbing and emitting dipole oscillators. In doing so, electric and magnetic linear (\(\pi_e\) and \(\pi_m\)) and circular (\(\sigma_e\) and \(\sigma_m\)) oscillators were considered.

The calculation in all cases was carried out according to a general scheme: first of all the relative probabilities \(A_i(\eta)\) of excitation of absorbing oscillators having a definite orientation \(i\) were computed as functions of the angle \(\eta\); then the intensities \((I_i)\) and polarizations \((P_i)\) of the luminescence of the corresponding emitters in the direction of observation were determined, after which, according to the formulas

Fig. 10. Scheme of observation of polarization diagrams of luminescence in cubic crystals for center orientation along axes: a) of the fourth order, b) of the third order, c) of the second order.

\[ I(\eta)=\sum_i A_i(\eta) I_i \]

and

\[ P(\eta)=\frac{\sum_i P_i A_i(\eta) I_i}{\sum_i A_i(\eta) I_i} \]

computed the required dependences of the intensity and polarization on the angle of rotation of the exciting electric vector.

As an example, Fig. 11 presents the results of the calculation for the case of orientation of the oscillators along the symmetry axes of the fourth

Fig. 11. Polarization diagrams of dipole emitters oriented along fourth-order symmetry axes.

order.—Examination of these diagrams shows that the joint investigation of the dependences \(I(\eta)\) and \(P(\eta)\) makes it possible, in most cases unambiguously, to decide the question of the nature of the elementary oscillators. To distinguish the individual cases that give identical diagrams \((\pi_e \leftrightarrow \sigma_e;\ \pi_m \leftrightarrow \sigma_m;\ \pi_e \to \sigma_m\ \text{and}\ \sigma_e \to \pi_m;\ \pi_m \to \sigma_e\)

and \(\sigma_m \to \pi_e\)), it is necessary to use additional data or considerations. In some cases, as we have seen, the results of studying the anisotropic photochemical transformation of luminescence centers may serve as such an additional criterion.

The method developed was applied by us to the investigation of the nature of elementary emitters of color centers in fluorite crystals and of europium ions introduced into the crystal lattice of \(\mathrm{CaF_2}\).^5 In the first case it was possible to establish the electric-dipole character of the luminescence, in complete agreement with data on the lifetime of the excited state and on the oscillator strengths of the color centers. The data obtained in studying the nature of the elementary emitters of \(\mathrm{Eu}^{+++}\) ions proved to be considerably more interesting.

In this case the luminescence centers are oriented along the axes of symmetry of the third order, and the observation of polarization diagrams and intensity diagrams was carried out according to the scheme of Fig. 10, б. The results of determining the nature of the elementary emitters corresponding to individual lines in the luminescence spectrum of \(\mathrm{CaF_2}:\mathrm{Eu}\) are given in the following table:

As can be seen from this table, in the luminescence spectrum of \(\mathrm{CaF_2}:\mathrm{Eu}\) there are lines corresponding to all four possible types of elementary dipole emitters: \(\pi_e\), \(\sigma_e\), \(\pi_m\), and \(\sigma_m\). The last type of emitters—magnetic circular emitters—apparently had not been observed previously.

The examples considered in the present review show that, by studying the polarized radiation of crystals of the cubic system, whose main distinguishing features are determined by the orientation of the luminescent centers along the symmetry axes of the crystals, we obtain new possibilities both for elucidating the nature and details of the structure of elementary luminescence centers and for solving questions connected with the crystal chemistry of mixed crystals.

References Cited

1. J. Grailich, Krystallographisch-optische Untersuchungen. Wien, 1858.
2. P. P. Feofilov, DAN SSSR 92, 545 (1953).
3. P. P. Feofilov, DAN SSSR 92, 743 (1953).
4. P. P. Feofilov, ZhETF 26, 609 (1954).
5. P. P. Feofilov, DAN SSSR 99, 975 (1954).
6. P. P. Feofilov, DAN SSSR 99, 731 (1954).
7. P. P. Feofilov, DAN SSSR 98, 949 (1954).
8. M. Ueta, J. Phys. Soc. Japan 7, 107 (1952).
9. S. I. Vavilov, ZhETF 10, 1363 (1940).

1. Grailich’s Crystallographic-Optical Investigations. ↩

2. The azimuthal dependences and polarization spectra can be interpreted just as successfully by means of another oscillator model, in which a quadratic function is assigned to the linear and circular oscillators; however, as can be shown (see § 2), the model adopted here is adequate. ↩