On the galvanomagnetic properties of -uranium at low temperaturesV. M. Kuz’menko and T. P. Chernyaeva

Citation: Low Temperature Physics 36, 180 (2010); doi: 10.1063/1.3314255 View online: http://dx.doi.org/10.1063/1.3314255 View Table of Contents: http://scitation.aip.org/content/aip/journal/ltp/36/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Imaging capability of pseudomorphic high electron mobility transistors, Al Ga N Ga N , and Si micro-Hall probesfor scanning Hall probe microscopy between 25 and 125 ° C J. Vac. Sci. Technol. B 27, 1006 (2009); 10.1116/1.3056172 Magnetic, magnetotransport, and optical properties of Al-doped Zn 0.95 Co 0.05 O thin films Appl. Phys. Lett. 90, 242508 (2007); 10.1063/1.2748343 Magnetotransport properties in near-stoichiometric hydride films of YH 2 + under weak fields J. Appl. Phys. 101, 103713 (2007); 10.1063/1.2733602 Magnetotransport properties of ferromagnetic Ga 1 x Mn x As layers on a (100) GaAs substrate J. Appl. Phys. 97, 063902 (2005); 10.1063/1.1861139 Room temperature ferromagnetic n -type semiconductor in ( In 1 x Fe x ) 2 O 3 Appl. Phys. Lett. 86, 052503 (2005); 10.1063/1.1851618

This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

89.160.155.250 On: Tue, 06 May 2014 00:46:46

LOW TEMPERATURE PHYSICS VOLUME 36, NUMBER 2 FEBRUARY 2010

This ar

ELECTRONIC PROPERTIES OF CONDUCTING SYSTEMS

On the galvanomagnetic properties of -uranium at low temperatures

V. M. Kuz’menkoa

National Science Center “Kharkov Physicotechnical Institute,” ul. Akademicheskaya 1, Kharkov 61108,Ukraine

T. P. Chernyaevaa

National Science Center “Kharkov Physicotechnical Institute” and Scientific-Technical Complex “NuclearFuel Cycle,” ul. Akademicheskaya 1, Kharkov 61108, UkraineSubmitted June 5, 2009; revised August 11, 2009Fiz. Nizk. Temp. 36, 227–233 February 2010

The magnetoresistance of and Hall effect in polycrystalline -U in the temperature interval4.2–77 K and transverse magnetic fields B to 4 T have been investigated. It is found that below43 K the Hall coefficient RH of -uranium depends on the magnetic field. The strong tempera-ture dependence of the RH below 43 K which is due to three charge-density-wave type transi-tions is confirmed. Above 43 K the Hall coefficient is weakly temperature dependent and is inde-pendent of the magnetic field. The magnetoresistance is approximately parabolic and does notexhibit any indications of saturating even in strong fields. The application of the isotropic two-band model made it possible to evaluate qualitatively the dependence of the charge carrier den-sity n and mobility on the magnetic field to 4 T and on the temperature in the interval4.2–77 K. It is shown that charge-density-wave type transitions at T43 K are accompanied bya considerable change in n and . It is found that at 4.2 K n and depend strongly on the mag-netic field from 0 to 4 T. There is no such dependence at temperatures T50 K.© 2010 American Institute of Physics. doi:10.1063/1.3314255

I. INTRODUCTION

Most investigations of the electronic properties of-uranium concern superconductivity and a phase transitionoccurring at 43 K. It is generally believed that almost allanomalies of the physical properties of -U below 43 K ex-ist because of changes in the topology of the Fermi surfaceas a result of a periodic distortion of the lattice due to theformation of a charge density wave CDW.1 The appearanceof CDW was discovered in pure -U single crystals in aninvestigation of the elastic and inelastic neutron scatttering.1

It was found that below 43 K new Bragg peaks arise fromsuperstructures, attesting to a structural phase transition withformation of a CDW. In the CDW phase the uranium atomsare displaced by 0.0006 nm from their initial positions. As aresult the lattice expands by 0.4% as compared with the-phase.

It has been established that on cooling an -U samplepasses through a series of three charge density waves: 1 atT43 K, 2 at T37 K, and 3 at T22 K. Measurementsof the thermal expansion of -U samples on heating in therange 4.2–60 K 2have shown that a first-order phase transi-tion in which the relative volume change is V /V=−1.7·10−4 occurs at 22 K, a first-order phase transitionwith V /V=−1.5·10−4 occurs at 37 K, and a second-orderphase transition occurs at 43 K. Calculations have shownthat in the 1 phase gaps open at the Fermi level. Theseregions on the Fermi surface attest to the presence of a strongcontribution which is actually due to narrow f bands.3

1063-777X/2010/362/6/$32.00 180ticle is copyrighted as indicated in the article. Reuse of AIP content is subje

89.160.155.250 On: Tue, 0

In 1994 Lander et al. published a good review of thesuperconductivity and phase transitions in -U.4 To our sur-prise there are only a few known works where the low-temperature galvanomagnetic properties of -U have beenstudied and the magnetoresistance and Hall effect in one andthe same samples have been studied in only isolated cases.We shall briefly dwell on the most informative of theseworks. In Ref. 5 Berlincourt found for two polycrystalsRRR=6.5,121 that the Hall coefficient RH is independentof the strength of the magnetic field to 3 T in the tempera-ture range 1–300 K. It was found that RH is sensitive toimpurities and is strongly temperature dependent in the range20–50 K. The magnetoresistance of the sample with RRR=12 was measured in a transverse magnetic field at 4.2 K. Itwas approximately parabolic in weak fields and approacheda linear dependence on the magnetic induction B in strongfields.

In Ref. 6 Cornelius and Smith found that the Hall coef-ficient for an -U polycrystal with average grain size0.1 mm RRR=9 is positive, reaches its maximum valueat T30 K, does not pass through zero to 4.2 K, and incontrast to Ref. 5 increases with the field. For a single crystalwith substantial substructure small-angle grain boundariesRRR=11 RH is negative in the interval 4.2–17 K and de-creases in absolute magnitude with increasing transversemagnetic field. In the interval 19–40 K RH is positive andincreases with the field. The Hall coefficient is independentof B only for T40 K.

The resistivity, magnetoresistance, and Hall effect wererecently measure in four -U single crystals RRR

© 2010 American Institute of Physicsct to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

6 May 2014 00:46:46

Low Temp. Phys. 36 2, February 2010 V. M. Kuz’menko and T. P. Chernyaeva 181

This ar

=66–315 and one polycrystal RRR=13, obtained by elec-trofusion of similar crystals.7 Features were observed in Tat all three CDW transitions; these features were especiallydistinct in the single crystal with RRR=315 and indistinct orabsent completely for the polycrystal. For single crystalsthese features in the curves T were more strongly mani-fested with the transverse magnetic field increasing from0 to 18 T. The magnetoresistance / for single crystals isanisotropic and reaches 10 for the best single crystal at T=2 K and B=18 T. For the polycrystalline sample at T=3 K and B=15 T / reaches 0.4. For T40 K the mag-netoresistance of the single crystals varies approximatelyquadratically as a function of the field, and it manifests nega-tive curvature near CDW transitions. At T2 K the ratio / becomes an approximately quadratic function of B.The negative curvature of the magnetoresistance of singlecrystals at intermediate temperatures is absent in the poly-crystal. Especially important for subsequent analysis is that-U samples do not show any indications of / tending tosaturation as a function of B to 18 T at all temperatures infields.

In Ref. 7 the Hall coefficient at T40 K is positive,does not depend on the magnetic field, and depends onlyslightly on temperature. As temperature decreases to ap-proximately 35 K the value of RH drops off precipitously andbecomes negative and much greater in absolute magnitudethan proved previously in Refs. 5 and 6. In addition, RH

acquires a dependence on the field. At 5 K the absolute valueof RH at first increases with B, reaches its maximum value atB=6.4 T, and then starts to decrease.

It is obvious from what has been said above that the signof the Hall coefficient at T4.2 K correlates with the valuesof RRR: the greater RRR, the greater the negative value of RH

is in absolute magnitude. If the single crystals are good, thevalue of RH at the lowest temperatures reaches approxi-mately −9·10−10 m3 /C at B=9 T.7 For polycrystals with 6RRR9 RH is positive and 4.2 K and ranges from+0.15·10−10 m3 /C to zero, respectively.

In Refs. 6, 8, and 9 individual features distinguish thefield dependence of the Hall coefficient at T4.2 K for dif-ferent metals, and it is difficult to find a general dependence.This situation was first observed in investigations of the low-temperature galvanomagnetic properties of beryllium andaluminum in strong fields. The author of Refs. 8 and 9 useda two-band model for analysis. It was found that, specifically,beryllium is a compensated metal, its conduction electrondensity ne is equal to the hole density nh, which is in agree-ment with the even valence of beryllium. Aluminum is anuncompensated metal, nenh for it, and correspondingly thevalence is odd. A strong dependence of RH on B is seen inboth metals but is completely different.8

Hall-effect measurements clearly demonstrate the exis-tence of at least two Brillouin zones near the Fermi surfaceof -U. Although the possibility of using a two-band modelto estimate the parameters characterizing the transport prop-erties of -U was proposed a long time ago,5 this has still notbeen done. The use of the two-band model to describe thesuperconductivity of -U is an exception.7

The objective of the present work is to use the two-bandmodel in an attempt to give a qualitative description of the

ticle is copyrighted as indicated in the article. Reuse of AIP content is subje

89.160.155.250 On: Tue, 0

electronic system of -U before and after a CDW transition.Since the two-band model has been constructed for an iso-tropic substance, an -U polycrystal is a more suitable objectfor investigation than a single crystal of this metal, whichexhibits stronger anisotropy.

II. SAMPLES AND MEASUREMENT PROCEDURE

Electrolytically pure, natural uranium was used to pre-pare the samples. Two -U samples with almost identicaldimensions were cut out of a 0.1 mm thick rolled sheet. Thesamples were 16 mm long; one sample was 0.4 mm and theother 0.45 mm wide. The shape of the samples is shownschematically in Fig. 1. Platinum wire contacts are secured atthe points 1, 2, and 3 by point welding; measuring wireswere soldered to the platinum wires: 1—current,2—voltage—for measuring the resistivity and magnetoresis-tance, 3—for Hall voltage measurements. The main impuri-ties in the samples were in at.%: C—4·10−2, Mo—10−2,Fe—2.3·10−3, Al—2·10−3, and Si—1.1·10−3, giving samplepurity 99.94 at.% RRR=10.05. The measurements wereperformed on one sample while the other served for controlchecks for individual results. The difference in the resultsalways fell within the limits of accuracy of the measure-ments. The resistivity, magnetoresistance, and Hall voltagemeasurements were performed with dc current using a six-probe arrangement see Fig. 1 and a R363-3 potentiometer.A superconducting solenoid was used to produce magneticfield with induction to 4 T. A platinum resistance thermom-eter was used to measure the temperature. The relation 1below was used to calculate the Hall constant RH in the SIsystem:

RH =UHd

IB, 1

where UH is the Hall voltage, I is the measuring currentflowing perpendicular to the direction of the field, B is themagnetic induction, and d is the sample thickness.

III. EXPERIMENTAL RESULTS

The temperature dependence of the resistivity for the-U sample is displayed in Fig. 2. In the temperature interval40–293 K is a strictly linear function of T0.7. From15 K to 4.2 K is a linear function of T3. These results arein good agreement with Ref. 7. The analysis performed inRef. 7 points to difficulties associated with the interpretationof these results. The observed decrease of the slope of the

11

22

33

11

22

33

FIG. 1. Schematic diagram of the -U samples: 1, 2, 3—current, voltage,and Hall contacts, respectively,

ct to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

6 May 2014 00:46:46

182 Low Temp. Phys. 36 2, February 2010 V. M. Kuz’menko and T. P. Chernyaeva

This ar

temperature dependence of the resistance above 40 K pre-supposes a decrease of the electron-phonon scattering prob-ability and or an increase in the number of chargecarriers.10 When temperature is lowered below 4.2 K the de-crease of is steeper, probably because of the existence ofsuperconducting fluctuations. A section of the function Tnear CDW phase transitions is shown on an enlarged scale inthe inset in Fig. 2. Just as for the high-quality polycrystalwith RRR=13,7 here, in contrast to T for single crystals,no sharp features appear at the temperatures 43, 37, and22 K.

The magnetoresistance as a function of the squared mag-netic induction for an -U polycrystal is shown in Fig. 3curve 1. Although this dependence is quadratic in the entireinterval of fields, a steeper section is observed in weakerfields B=0–1.6 T and a less steep section is observed inthe range 1.7–4 T. The curve 2 was constructed in conform-ance to Ref. 5 for a polycrystal with RRR=12. Although thenumber of points here is too small, a kink is present in thequadratic dependence in weak fields also. Apparently, thisbehavior of the magnetoresistance does not completely agreewith the two-band model for compensated metals, and we

00 5050 100100 150150 200200 250250 300300

55

1010

1515

2020

2525

3030

3535

00 2020 4040 6060

44

66

88

,1

0,1

0–

8Ω·m

,1

0,1

0–

8Ω·m

T, K

T, K

FIG. 2. Temperature dependence of the resistivity of an -U polycrystal.

55 1010 1515

00

00

11

22

33

44

55

B, T2 22 2

T = 4.2 K

11

22

FIG. 3. Magnetoresistance of -U versus the squared magnetic induction:data of the present work 1 and from Ref. 5 2.

ticle is copyrighted as indicated in the article. Reuse of AIP content is subje

89.160.155.250 On: Tue, 0

shall discuss it below. For T50 K / versus B is ap-proximately quadratic for B in the interval 0–4 T.

The quite steep temperature dependence of the Hall co-efficient near CDW transitions is confirmed by the authors ofRefs. 5–7. For our sample the Hall coefficient in the tem-perature range 17–50 K increases from 0.1·10−10 m3 /C B=0.5 T to 0.35·10−10 m3 /C. In contrast to Ref. 5, where theHall coefficient is field independent at 4.2 K, we observed analmost linear decrease of RH with B increasing from0.4 to 3.5 T see Fig. 4. For T50 K the Hall coefficient isindependent of B.

IV. DISCUSSION

We shall briefly dwell on the final results of the two-band model. It is known that the radius of curvature of anelectron trajectory in a field B Larmor radius is

rL =mvF

eB, 2

where m is the electron mass, e is the electron charge, and vF

is the electron velocity on the Fermi surface.For weak magnetic fields rL l, where l is the electron

mean-free path length. In strong magnetic fields we haverL l. The estimated values of l and vF presented belowshow that for our sample l114 nm, and the Larmor radii inthe fields 1, 2, 3, and 4 T are approximately 130, 65, 43, and33 nm, respectively. Thus the kink in the function / ver-sus B2 Fig. 3 at B1.6 T could be due to a transition fromweak to strong magnetic fields. According to theory theweak-field behavior of metals with nenh does not differmuch from the case ne=nh. In both cases the Hall field Ey

should increase linearly and resistivity quadratically with in-creasing magnetic field.

In strong fields the behavior of metals with ne=nh andnenh is different. If ne=nh, then the ratio Ey /Ex of the Hallfield to the electric field in the direction of the current passesthrough a maximum as the magnetic field increases and instrong fields it decreases with increasing field: Ey /Ex1 /B.Here one also observes an unbounded increase, quadratic inthe field, of the magnetoresistance with increasing field: /B2. If n n , then in strong magnetic fields the ratio

00 11 22 33 44

0.37

R,10

/ CHH

–1

0–

10m33

Â, Ò

T = 4.2 K

T = 77 K0.360.35

0.10

0.09

0.08

FIG. 4. Hall coefficient versus the magnetic induction for an -U polycrys-tal at different temperatures.

e hct to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

6 May 2014 00:46:46

Low Temp. Phys. 36 2, February 2010 V. M. Kuz’menko and T. P. Chernyaeva 183

This ar

Ey /ExB increases without bound with increasing fieldwhile the magnetoresistance goes to saturation.

It appears that -U, which in most cases manifests evenvalence, is a compensated metal containing equal numbers ofelectrons and holes. The main proof is the quadratic increaseof magnetoresistance as a function of B in strong fields Fig.3 without even the smallest indication of going to saturationto B=18 T.7 The latter is also valid for a polycrystal RRR=13 and for a good single crystal RRR=315.7 As concernsthe second indication of the equality ne=nh, specifically, thepresence of the dependence Ey /ExB in strong fields, forour sample such a dependence occurs only for B4 T Fig.5. Dependences of Ey /Ex on B similar to Fig. 5 have beenobserved before for the compensated metals Zn, Be, andZr.9,5 Dependences demonstrating Hall voltage decreasingwith increasing B for strong fields have also been observed attemperatures 20 K in -U single crystals.6,7

We shall now estimate the density and mobility of thecharge carriers in an -U polycrystal, using the two-bandmodel relations for the case ne=nh=n. For this the followingsystem of equations in the SI system is solved:8,9

= −1 = ene + h , 3

RH =1

en

h − e

h + e, 4

B2 = eh, 5

where e and h are the electron and hole mobility, respec-tively.

Figure 6 displays the computational results for the mag-netic field dependences of the electron density and mobilityat 4.2 K. The hole mobility is not shown; it is 0.5–0.6%higher than the electron mobility.

The two-band model relation for the Hall coefficient 4does not reflect the experimental fact that the Hall constant

00 11 22 33 44 55 66

0.1

0.2

0.3

0.4

0.5

0.6

0.7E

/E/Ey

x

Â, ÒÂ, Ò

FIG. 5. Ratio of the Hall field to the longitudinal electric field versus themagnetic induction at T=4.2 K.

ticle is copyrighted as indicated in the article. Reuse of AIP content is subje

89.160.155.250 On: Tue, 0

depends on the field strength: the magnetic induction B doesnot appear explicitly in this relation. As follows from Fig. 6,this contradiction could be due to the existence of a depen-dence of the mobile-carrier density on the field.

Figure 7 displays the computational results obtainedwith Eqs. 3–5 for the temperature dependences of theelectron hole density and mobility near CDW phase transi-tions. The hole mobility, not shown in Fig. 7, with tempera-ture decreasing from 50 K to 4.2 K is 7–0.7% higher, re-spectively, than the electron mobility. The dependence nTin Fig. 7 can be made to conform qualitatively to theGardener-Smith version.11 According to this version, -Upossesses a virtual bound state, originating from 5f-typewave functions. Below 43 K the virtual bound state is par-tially occupied as a result of a transition of electrons fromtheh 5f36d17s2 conduction band. Above 43 K the virtualbound state is vacant.

According to the two-band model the electron mean-freepath length can be estimated using the relation9 in the SIsystem

l = 3.23 · 10−34n1/3e + h2e

. 6

We obtain for our sample l=114.4 nm at T=4.2 K and l=27.7 nm at 50 K.

00 11 22 33 443.5

4.00

4.5

2.1

2.2

2.3

2.4

2.5

nn

Â, Ò

åå

å,

10

,10

–2

2–2

2

n,10m

27

27

–3

–3

m/V·s

FIG. 6. Variation of the conduction electron density and mobility as a func-tion of the transverse magnetic field induction for an -U polycrystal at T=4.2 K.

00 1010 2020 3030 4040 5050 6060 7070 8080

22

44

66

00

22

44

66

nn

T, K

åå

å,

10

,1

0–

22

–2

2

27

27

–3

–3

m/V·s

n,10m

FIG. 7. Temperature dependences of the electron density and mobility for an-U polycrystal at B=2 T.

ct to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

6 May 2014 00:46:46

184 Low Temp. Phys. 36 2, February 2010 V. M. Kuz’menko and T. P. Chernyaeva

This ar

We shall now estimate some parameters characterizingthe transport properties of electrons in -U. There are manyworks see Ref. 12 devoted to the experimental determina-tion of the electronic specific heat of -U single crystals.The results range from 7.23·102 to 8.6·102 J /m3·K2. If theaverage value =7.92·102 J /m3·K2 is taken and the densityof states for two directions of the spin is expressed as

NEF =3

2kB2 , 7

where kB is Boltzmann’s constant, then we obtain for -UNEF=1.27·1048 J−1 ·m−3. Using Einstein’s relation for theconductivity

=1

=

1

3e2NEFvFl , 8

the electron velocity at the Fermi surface can be estimated asvF=0.25·105 m /s.

We made similar estimates for n, e, h, l, and vF fromthe measurements of , /, and RH in Ref. 7 and 5. Wedenote them as U-II and U-III, respectively, and comparewith our results U-I in Table I. Even though in the case of theU-II sample we took the values of / and RH for muchstronger fields than in our experiments B=9–15 T and nodependence of RH on B was observed for U-III, the valuesfound for n, e, h, l, and vF are close for all three samples.

This gives hope that the two-band model, though itshould be applied to metals with great care, still gives thesimplest qualitative physical explanation of the observed gal-vanomagnetic properties of -U. In examining the propertiesof the isotropic two-band model no assumptions are madeabout the specific forms and positions of the surfaces of en-ergy divergence or about the form of the Fermi surface. Itcan be assumed that the information obtained about the car-rier mobilities and densities from the general relations of theisotropic model to a certain extent do reflect the average realproperties of the electrons in metal irrespective of the defi-ciencies of the band model.

V. CONCLUSIONS

We shall now formulate the results obtained in thepresent work for -U polycrystals.

1. The Hall coefficient at 4.2 K decreases approximately lin-early as the transverse magnetic field increases from0 to 4 T.

TABLE I. Estimated values of some electronic param

Parameters

U-I

T=4.2 KB=2 T T=50 K

RRR 10.05 —e, 10−2 m2 /V·s 4.29 0.77h, 10−2 m2 /V·s 4.32 0.82

n, 1027 m−3 2.25 5.24l, nm 1.14 28

vF, 105 m /s 0.25 —

ticle is copyrighted as indicated in the article. Reuse of AIP content is subje

89.160.155.250 On: Tue, 0

2. For T50 K RH does not depend on B.3. At T=4.2 K / is a quadratic function of B in the

range 0–1.6 T and remains quadratic but in the range1.6–4 T the coefficient of the quadratic term is smaller.

4. For T50 K / is an approximately quadratic func-tion of B in the range 0–4 T.

5. The two-band model can be used for a qualitative descrip-tion of the galvanomagnetic properties of polycrystalline-U.

6. The values of n, e, and h estimated on the basis of thismodel for our -U sample are in good agreement with thevalues that can be estimated from the results obtained inother works Table I.

7. As follows from Table I and Fig. 7, the electron holedensity in -uranium decreases as temperature decreasesfrom 50 to 4.2 K. This is due to a CDW transition.

8. The mobile-electron density at 4.2 K increases and themobility decreases with increasing magnetic field Fig.6.

9. Although the numerical results contained in Figs. 6 and 7and Table I should not be taken as quantitatively precisebecause of the inadequacies of the two-band model, thedirections in which the results vary in the temperaturerange of the CDW phase transitions and as a function ofthe field are probably correct, and they can be used fordeveloping theoretical models.

aEmail: mlazareva@kipt.kharkov.ua1RRR residual resistivity ratio293 K /4.2 K is the ratio of the resistivi-

ties at 293 K and 4.2 K.

1H. G. Smith, N. Wakabayashi, W. P. Grummett, R. M. Nicklow, G. H.Lander, and E. S. Fisher, Phys. Rev. Lett. 44, 1612 1980.

2M. O. Steinitz, C. E. Burleson, and J. A. Markus, J. Appl. Phys. 41, 50571970.

3L. Fast, O. Eriksson, B. Johansson, J. M. Wills, G. Straub, H. Roeder, andL. Nordstrom, Phys. Rev. Lett. 81, 2978 1998.

4G. H. Lander, E. S. Fisher, and S. D. Bader, Adv. Phys. 43, 1 1994.5T. G. Berlincourt, Phys. Rev. 114, 969 1959.6C. A. Cornelius and T. F. Smith, J. Low Temp. Phys. 40, 391 1980.7G. M. Schmiedeshoff, D. Dulguerova, J. Quan, S. Teuton, C. H. Mielke,A. D. Christianson, A. H. Lacerda, E. Palm, S. T. Hannahs, T. Murphy, B.C. Gay, C. C. McPheeters, D. J. Thoma, W. L. Hults, J. C. Cooley, A. M.Kelly, R. J. Hanrahan, and J. L. Smith, Philos. Mag. 84, 2001 2004.

8E. S. Borovik, Zh. Eksp. Teor. Fiz. 23, 83–91 1952.9E. S. Borovik, Zh. Eksp. Teor. Fiz. 27, 355 1954.

s of an -U polycrystal in the two-band model.

U-II U-III

T=3–5 KB=9 T T=50 K T=4.2 K

13 — 127.29 0.817 7.0764.06 0.942 7.0632.09 5.25 1.811.46 30.8 173.70.24 — 0.21

eter

ct to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

6 May 2014 00:46:46

Low Temp. Phys. 36 2, February 2010 V. M. Kuz’menko and T. P. Chernyaeva 185

This ar

10G. T. Meaden and N. H. Jze, Cryogenics 8, 396 1968.11W. E. Gardner and T. F. Smith, Phys. Rev. 154, 309 1967.12J. C. Lashley, B. E. Lang, J. Boerio-Goates, B. F. Woodfield, G. M.

Schmiedeshoff, E. C. Gay, C. C. McPheeters, D. J. Thoma, W. L. Hults,

ticle is copyrighted as indicated in the article. Reuse of AIP content is subje

89.160.155.250 On: Tue, 0

J. C. Cooley, R. J. Hanrahan, Jr., and J. L. Smith, Phys. Rev. B 63, 2245102001.

Translated by M. E. Alferieff

ct to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP:

6 May 2014 00:46:46