Camagni , P.

Cingolani, A.

Manara, A.

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®Bm :fSi; Tf^WwmS^1 ^ î :OMMUNITY - EURATOM j ï l ■; , p*i*» ■ *"■ jt'V ■ t f · Ti vt ¿ ' ' • i l * T^Slf^T EUROPEAN ATOMIC ENERGY CÖÏ" lellisiiliS ¡ei i iÉÉl AND POLARI7ARTT T T « OF UC AT OPTICAL FREQUENCIES Materials Department Solid State Physics Service tlfrHr1'· '■»'"■> É!»JÍ!8^K»i»IÍE!Í er ice Atomic is document was prepared under the sponsorship of the Commission of the European — r x j . ic Energy Community (EURATOM). Neither the EURATOM Commission, its contractors nor any person acting on their behalf : to the accuracy, or that the use iment may not infringe privately owned rights; or WådHS$' : ^ ^ f I t ì l ¿M — Assume any naDinty wixn respeci ιυ me use υχ, or for damages resulting from any information, apparatus, method or process disclosed in this document. .. · j a t Η — to BANQUE DE LA SOCIETE GENERALE (Agence Ma Campagne) - Brussels - account No 964.558, — to BELGIAN AMERICAN BANK AND TRUST COMPANY - New York - account No 121.86, to LLOYDS BANK (Foreign) Ltd. - 10, Moorgate London E.C. 2, giving the reference : „EUR 463.e - Measurements of the conductivity and polarizability of U and UC at optical fre-i EU R 4 6 3 . e ι MEASUREMENTS OF T H E CONDUCTIVITY AND POLARIZABILITY OF U AND UC AT OPTICAL FREQUENCIES by P. CAMAGNI, A. CINGOLANI and A. MANARA. European Atomic Energy Community - EURATOM Joint Nuclear Research Center Ispra Establishment (Italy) Materials Department - Solid State Physics Service" Brussels, October 1963 - pages 18 - figures 6. The electrical conductivity and polarizability of Uranium and Uranium Cart ide have been measured a t optical frequencies, by means of a technique based on the polarization of reflected light. Dispersion curves for both para­meters have been determined in this way for the region of the spectrum going from ~ 0.35 μ to ~ 2.8 μ. The results are systematic enough to justify a certain comparison between the electronic structures of the two materials. However, the present data refer to polycrystalline specimens; they need to be implemented by further research on single crystals of UC and U, before definite conclusions can be reached. Such work is now in progress, using the same experimental methods. EUR 4 6 3 . e MEASUREMENTS OF T H E CONDUCTIVITY AND POLARIZABILITY OF U AND UC AT OPTICAL FREQUENCIES by P. CAMAGNI, A. CINGOLANI and A. MANARA. European Atomic Energy Community - EURATOM -Joint Nuclear Research Center Ispra Establishment (Italy) Materials Department - Solid State Physics Service Brussels, October 1963 - pages 18 - figures 6. The electrical conductivity and polarizability of Uranium and Uranium Carbide have been measured at optical frequencies, by means of a technique based on the polarization of reflected light. Dispersion curves for both para­meters have been determined in this way for the region of the spectrum going I from ~ 0.35 μ to ~ 2.8 μ. The results are systematic enough to justify a certain comparison between I the electronic structures of the two materials. However, the present data refer ι to polycrystalline specimens; they need to be implemented by further research on single crystals of UC and U, before definite conclusions can be reached. Such work is now in progress, using the same experimental methods. E U R 4 6 3 . e EUROPEAN ATOMIC ENERGY COMMUNITY - EURATOM MEASUREMENTS OF THE CONDUCTIVITY AND POLARIZABILITY OF U AND UC AT OPTICAL FREQUENCIES by P. CAMAGNI, A. CINGOLANI and A. MANARA 1963 Joint Nuclear Research Center Ispra Establishment - Italy Materials Department Solid State Physics Service MEASUREMENTS OF THE CONDUCTIVITY AND POLARIZABILITY OF U AND UC AT OPTICAL FREQUENCIES SUMMARY The electrical conductivity and polarizability of Uranium and Uranium Carbide have been measured at optical frequencies, by means of a technique based on the polarization of reflected light. Dispersion curves for both parameters have been determined in this way for the region of the spectrum going from''*' 0.35 H t o ~ 2.8// . The results are systematic enough to justify a certain comparison between the electronic structures of the two materials. However, the present data refer to polycrystalline specimens} they need to be implemented by further research on single crystals of UC and U, before definite conclusions can be reached. Such work is now in progress, using the same experimental methods. - 5 I N T R O D U C T I O N The optical properties of a conducting medium (metal) are expressed usually in terms of two constants! the index of refraction n « o/v (where o « velocity of light in vaouumj ν « phase velocity of a plane wave-front having constant amplitude) and the coefficient of extinction k, which is defined in termsof the amplitude attenuation of an eleotromagnetio wave when it goes through the metal· It is known from physical optics that all developments of the basic Maxwell equations for a dielectric still hold formally for a conductor) provided use be made of a complex refraction index N m n - ik. It is then possible to derive a double relationship between the above said quantities n and k and the electric constants of the metal (eleotrioal conductivity Ö' » dielectric constant 6 )? one finds easily the well known equations* ' 2 v2 c n - k - c nk CO r 2π<5" The macroscopic constants are dependent on the angular frequenoy CO of the incident radiation. Their "spectral" behaviour (dispersion) reflects their relationship to the electronic structure, f 2 1) and has been treated by several authors on the basis of classicalv ' ' ( 1 4.) as well as quantum-mechanical theories^ ' '· Drude treated the frequency dependence of <5" and S t supposing that the conducting medium contains free electrons, subjected to "visoous" damping and aoted only by the eleotrio field of the incident wave. His results are in agreement with later quantum developments, and give the following relations» r- V2 t (1) - 6 -CX ν! w m* (co+y2) where: 'V* - damping constant (reciprocal of relaxation time or collision time) € - 1 Oi « ._ = polarizability 47C n m number of free electrons/unit volume o ' m' - mass of the electron: in the quantum mechanical case it represents the effeotive mass. In addition to the effect of conduction electrons, there are usually contributions coming from the electronic transitions between normally occupied levels and empty levels of the solid. Thus for instance additional absorption takes place at certain characteristic frequencies and modifies the (5*(^ϋ) or 0( ( **0 curves which are predicted on the basis of free-electron theories. These problems can be dealt with quantum-mechanically^ , least in principle, and formal connections can be established between the energy bands of a solid and the spectral dispersion of the optical or electric constants. The detailed theoryj however, cannot be pushed very far but for the simpler metals(alkali metals). In the specific case of Uranium Carbide, a study of the optical constants was felt to be of considerable interest for the following reasons: up to date, no direct informations on the electronic structure of this material are available; on the other hand, the complexity of the isolated U atom leads one to doubt that the problem of U-C bonding in the solid compound will ever be treated fully by - 7 -theoretical means. Some knowledge, however, might be gained by linking (5) together the few data ooming from X-ray structural studiesw/ with (6 7) those on the d.c. electrical conductivity^ ' '· The study of the optioal properties is apt to provide such linkj in this respect, our research may well fit with other trends of activity of the Solid State Physics at Ispra, concerning Uranium Carbide (measurements of conductivity and thermoelectric power)· The present report accounts on a series of preliminary measurements on the optioal properties of UC in the visible and near-infrared region of the spectrum· The research outlined here pointed particularly to investigate the 6* ( λ ) and o( ( λ ) spectra^ with the help of a reflection technique which is briefly described below. For obvious reasons, similar measurements were also performed on Uranium, in the hope to explore the correlations between the compound and the pure element· The data refer in both cases to polycrystalline materials. A detailed account of the experimental methods, together with a fuller discussion of the results, will be given in a future report, when the work on single-crystal materials will be completed· PRINCIPLE OF MEASUREMENTS In the present work we were interested primarily to have direot measurements of €T and Ot · Many techniques, based on the reflection of light, are now available for the determination of these quantities (see for instance refs· 8, 9» 10)· We have adopted a method whioh is based on the analysis of polarized light, after reflection from the material to be studied· A reflection technique is a necessary choice, since UC is known to be highly oonduotive, and transmission measurements would hardly be possible. ­ 8 ­The principle of measurement is known. It Was already seen that a conducting material is characterized by a complex index of refraction N » n — ik. By analogy with the formal treatment of non­conducting media, one may derive the refraction law senV, » NsenU" : υ. i (11) r however, if N is complex, it follows that \? is also complex* · Let us suppose that a linearly polarized electromagnetic wave inpinges on the conductor; the azimuth of polarization be given Ax by tang W . ­ —r—, where A« and A, are the amplitude components of the incident light which are parallel or perpendicular to the incidence plane. Formally, there is a well known link between these components and the corresponding components R« and R¿ of the reflected light J this is provided by Fresnel's relations: sen (θ- -$) tí . m Ρβ· Χ Γ , Sen *fri + Jfr L The azimuth [O of polarization for the reflected light will be given by H, cos (C7 + ft) and will be complex (in general), being \f a complex quantity. In other words, there simply is no linear polarization after reflection: a characteristic phase change /\ takes place between the two components (formerly in phase with each other) ­ and consequently the reflected light is elliptically polarized. The relationship 2) can be written also in the form ­ 9 *L ^ ­ f e " 1 tg φ . where ^ J ­ γ tg φ . It can be seen clearly that by making two independent measurements i) on the absolute ratio of the reflected components R A R« , and ii) on the orientation of the major axis of the ellipse, we determine the two elements O and Za ; these in turn are connected to XT t therefore to η ­ ik (see 11)): thus the real part η and the imaginary part k of the complex index may be evaluated. Actually the equations giving n and k in terms of the experimental quantities are often complicated, depending on the method at hand ' . EXPERIMENTAL METHOD In order to analyze the state of polarized light after reflection from a specular surface of UC, we have set upYtechnique (12) which is based on the method of Beattie · The experimental apparatus is described schematically in figure 1). A beam of monocromatic light goes through a first polarizing nicol, whose azimuth of vibration is 7Γ/4 with respect to the plane of incidence (plane of the figure). After reflection from the sample, the radiation passes through a second nicol, which is used as the analyzer; finally the light goes to a detector. The analyzing nicol is rotated on succession into four distinct vibrational azimuths, giving rise to four different levels in the intensity of the transmitted light: I. (analyzer «J. to the plane of incidence) Ig (analyzer // to the plane of incidence) I., (analyzer at TT/á to the plane of incidence) I. (analyzer at —* TT/4 to the plane of incidence). -ΙΟ-The above defined intensities are measured by an infrared-sensitive cell or by a phototube according to the region of the spectrum to be explored. The signals are fed into a frequency-analysing voltmeter; this is tunable at the frequency of modulation of the light, which is intercepted at a rate of *J 240 oyoles/sec· by a rotating sector set in front of the primary source· Signal modulation is adopted, as usual, in order to minimize problems of drift and dark-current} typical of d.c. detection. In the method of Beattie the parameters O and Δ are connected to the above said intensities by the following relationships: o - ^yi , cos à- hf* f-^^ h + h fr. These quantities, together with the measured angle of incidence 2 2 allow us to evaluate direotly nk and η - k (i.e. conductivity and polarizability), when use is made of the known equations given in the theories of physioaljoptics* ' · In particular, working at a special angle of inoidenoe \j , which is called the prinoipal angle,and is characteristic of the material, one has / \ m 7T/2 and formulae reduoe tot The accuracy in the determination of the optical constants is essentially conditioned by the measure of 0 , i.e. of the ratio I2/*«· This is especially true, when one operates in such conditions that I, «. χ. « 0 (in this oase ¿\ is equal to ΤΓ/2, and the angle \J is, as we said, fcke - 1 1 -principal angle of incidence: it could be seen, following Beattie, that these conditions correspond to minimizing the systematic errors connected with angular measurements). The light source was a standard tungsten-filament lamp for spectrofotometric work in the visible and near-infrared region· The monochromator was a Hilger & ¥atts, with interchangeable prisms; it was used with a quartz or a glass prism for the range 0.35 M. 2.8 U Ö U . The samples of U and UC were in the form of polycristalline discs. The reflecting face was polished down to optical planarity with the use of emery papers and diamond paste; the surface was then cleaned of all dirt or oxidized layers by means of a rinse in a suitable ultra-(°) sonic bath ' · The samples were mounted onto a goniometer, especially designed and equipped for measuring.incidence and reflection angles. The niools were in Calcite, with a polarization efficiency well over 99$î they are sufficiently transparent up to about 2.9 U, « The infrared detector was a PbS photoconductive cell of Eastman Kodak, Type Ektron N-2· The photomultiplier was the E.M.I. type 6255 for visible and u.v. The tunable voltmeter is a Bruel & Kjaër type 2105 (45 Hz to 12.000 Hz). (°) We acknowledge gratefully the assistance received from the Section of Metallography (Metallurgy, C.C.R.) in the preparation of our samples. - 12 -R E S U L T S Systematic calibrations have been performed in the first place, by measuring the G> ( Λ ) characteristics of monocrystalline Cu· It can be seen in fig· 2) that our values of GT are in consistent agreement with those reported in the literature: account must he taken of the large dispersion of the few existing data, admittedly due to the difficulty of preparation of suitable optical surfaoee· For U and UC, reflection measurements were performed in the range 3000 1 to 28,000 Â: the data for <0 ( Λ ) are reported in fig· 3) for Uranium and in fig· 4) for UC. The data for the polarizability are reported in Table I, limited to the range between 1.3 JU. and 2.9 LA. In both curves of 6" ( Λ ) the extreme branch towards the larger wavelengths appears to be due to free-electrons; this could be cheoked by us on the "basis of the expectation from Drude*s theory. As a matter of fact, if eqs· 1) are valid, it follows that φ must be a linear function of Of , precisely <5* ■ foi, at all wavelengths· The diagrams of Q' vs. (l-£) in figs· 5) and 6) show that this indeed is the case for U (above 1.3k) and for UC (above 2 u ) . The slope of the straight lines gives obviously the value ofTA-pc (damping constant, reciprocal of the relaxation time): one finds from the present data that ifø - 5·3χ1014 and y ^ - I8x1014. Thus the relaxation time appears to be sensibly smaller in the compound, as one might reasonably expect· At smaller wavelengths (below 1«3u and 2u, respectively for U and UC) the curves of §* ( ) \ ) show a series of structures: these are probably due to electronic transitions between normally occupied levels and empty levels characteristic of the band scheme of the two materials· One may observe that there is a significant correspondence between the two structures: more precisely, the peaks of UC resemble those of Uranium, with a general shift towards smaller energies· - 13 -Such similarity in the optioal behaviour might suggest that the electronic levels in UC are not drastically altered with respect to Uranium: thus the effect of U-C bonding would be merely to alter the electronic density so as to bring the highest occupied levels nearer to empty levels of the next band· However, the significance of these remarks must be limited for the time being, owing te the faot that the present data are preliminary, obtained as they are from polycrystalline speoimens. (For instance, the data for (1- £ ) were less clear than those for conductivity in the region where structures appear)· Heterogeneities connected with the microcrystalline structure of the U and UC available to us might have affected our measurements, especially those of the dielectric constant« Work has already begun on single-crystal UC, and will be extended as soon as possible to single crystal Uranium· In connection with this more critical research, the apparatus is also being improved in. order to take our measurements further out in the infrared region, and thus explore more systematically the range where free-electron contribution predominates· - 14 -TABLE Measured v a l u e s of |1 - £ ) , i . e . 4 TTOf ν Λ(microns) 1.3 ΐ·4 1.5 1.6 1.7 1.8 1 · 9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 υ 5.4 6.6 8 .1 9.2 13.6 14.5 17.6 18.9 21.2 24.6 29.4 30.0 31.6 33.4 34.6 UC 2·6 2.4 2 .0 3 .1 3.8 5.0 6.3 7.4 10.0 11.0 12.5 13.0 15.0 17.0 19.0 - 15 -R E F E R E N C E S 1) - See for instance F. SEITZ: "The Modern Theory of Solids" -Chapt. XVII. 2) - P. DRUDE: Ann. Physik _14, 677 and 936 (I904). 3) - 0. ZENER: Nature 132, 968 (1933). 4) - See for instance N.F. MOTT and H. JONES: "The Theory of Metals and Alloys" - Chapt. 5) - R.E. RUNDLE: Acta Crystall. ±, I80 (1948). R.E. RUNDLE: Acta Crystall.,12, 159 (1959). 6) - Battelle Mem. Inst. Repts., BMI-I524. 7) - CA. SMITH, F. ROUGH: Nucl. Science and Eng. 6_, 391 (1959). 8) - M. PARKER-GIVENS: Solid State Physics, vol. VI, 313 (1958). 9) - F. ABELES: J. Op. Soo. Am. 47, 473 (1957). 10) - J. GEISSE, M. QUEYREL: CR. Acad. Soiences 247» 1330 (1958). 11) - See for instance M. BORN, E. WOLF: " Principles of Optics" Pergaraon Press, 1959 - Chapt. XIII. 12) - J.R. BEATTIE and G.K.T. CONN: Phil. Mag. 46, 222 (1955). s Mf Λ/ é * S . Source M f _ Light mechanical modulator M _ Monochromator Ρ _ Polarizer V» _ Specimen A _ Analyzer D _ Detector A f _ Frequencies analyzer ¡TKT \C If Λ* C^V Experimental ' Apparatus D • Af Fig. 1 Block diagram of experimental apparatus 10" υ & (Π s> ae c IS M 10 f ID 10" H 1 I I I-+ Beattie and Conn α FORSTERLING and FREEDERIKSE ο M. BOR- HOBSON c MINOR • PRESENT WORK I I I I I ' 0.1 λ (r ) 10 Fig. 2 Dispersion of conductivity^ 6 vs. \ , in monocrystalline Cu u Ml s> C 10 λ ( / t ) Fig. 3 Dispersion of conductivity, δ vs. \ , in polycrystalline Uranium λ (/*) Fig. 4 Dispersion of conductivity, 6 vs. Χ , in polycrystalline Uranium Carbide Fig. 5 Plot of conductivity δ versus polarizability ( l -£ ) for U_. ι - ε Fig. 6 Plot of conductivity δ versus polarizability ( l - £ ) for UC. #i ^ MiiaiiiiiRiyiwiiaiiii Kftofl l'ilici sfj^iij^fiSifSflflieK.M 

MEASUREMENTS OF THE CONDUCTIVITY AND POLARIZABILITY OF U AND UC AT OPTICAL FREQUENCIES. EUR 463.e

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