Transport properties of virconium hydrides

Journal of the Less-Common

TRANSPORT

183

Metals, 118 (1986) 183 - 190

PROPERTIES OF ZIRCONIUM

Institute of Experimental Physics, Slovak Academy 04154 Kogice (C~echoslouakia)

HYDRIDES

of Sciences,

ndm. Febr. vit’azstva 9,

A. FEHER and P. PETROVIC! Department of Experimental Physics, P. J. gafririk University, ntim. Febr. vit’azstva 9, 04154 KoHice (Czechoslovakia) Z. MALEK Research Institute of Electrical Engineering,

25097 Praha-B~chouice (Czechoslovakia)

(Received March 15.1985)

Summary

The electrical and thermal condu~ti~ty of ZrN1_66 and ZrH,_s, was measured at low temperatures. It has been shown that there are phase transitions in the ZrH, system at temperatures between 160 and 170 K. The temperature of the phase transition decreases with increasing hydrogen concentration. The extrapolated residual resistivity p. for both hydrides is 3.9 X lo-’ S2 m, Lorenz numbers are Lo(ZrH,_sO) = 2.83 X lop8 W 52 K-’ and ~o(ZrH~.~~) = 3.37 X 10m8W St K-l. Both electrons and phonons ~on~ibute to the thermal conductivity. Magnons have not been proved to contribute experimentally.

1. Introduction

Hydrides of zirconium have an outstanding position among the hydrides of metals, mainly thanks to their technological applications. ZrH, is well known for its use as a moderator, and also as a shield material in nuclear reactors [ 11. Compounds of zirconium mainly with nickel, titanium, manganese, seem to be perspective materials for hydrogen storage. Comparatively low price, simple activation of hydrogen, great storage capacity and relatively good stability make them very attractive in this field. Nevertheless only information on zirconium hydrides is found in literature. Heat capacity, magnetic susceptibility and thermal electromotive force were studied by Ducastelle et aE. [2], measu~ment of electrical resistivity was reported in refs. 3 and 4 and thermal properties were reported in refs. 5 and 6. Electrical properties and electron-phonon interaction in zirconium hydrides were reported in ref. 7. Neutron spectra can be found in refs. 8 and 9 and X-ray structural analysis in ref. 10. 0022-5038/86/$3.50

0 Elsevier Se~uoia~~~~nted in The Netheriands

This work presents the results of measurements of electrical and thermal conductivity on polycrystalline samples of zirconium hydrides ZrH, for x = 1.66 and x = 1.80. Thermal conductivity was measured in the range 1.5 - 10 K and the electrical conductivity of ZrH,_,, determined in the range 42 - 10 K. Electrical conductivity of both samples was measured from liquid nitrogen ~mperature up to room temperature with special attention paid to the 160 - 170 K range where the existence of phase transitions was expected.

2. Sample parameters The samples were compact cylinders with a diameter of 5 mm and a length of 42 mm, having metallic lustre, but also microscopic cracks resulting probably from hydrogen diffusion into the zirconium. Preparation of the samples was described in ref. 11. The hydrogen content was determined by a pycnometric method and using a Balzers Exhalograph with an accuracy better than 1%. The ZrH,.,6 sample with 62.4 at.% H lies on the boundary between the 6 and e phase. The 6 phase is f.c.c. with hydrogen occupying some tetrahedral positions f 11. The oxygen and nitrogen content in this sample was very small (of the order of 10 ppm). Other elements were not determined. The ZrH1.sO sample contains 64.29 at.% H corresponding to a pure e phase. This phase has a tetragonal face-centred lattice with zirconium atoms at the corners. The impurity content of both samples was identical Because of the character of the phase diagram it is not possible to predict unambiguously the phase composition of samples at the lowest temperatures. More detailed study of this problem is being carried out.

3. Electrical resistivity The electrical resistivity was measured using a standard four point d.c. compen~tion method in a cryostat as described in ref. 12. ~ech~i~~ point contacts were reliable during the whole experiment and introduced no additional noise. The sample temperature was measured using a platinum thermometer (Rosemount type 102 D) with an accuracy of better than kO.2 K. In the temperature range of 77 - 300 K the stability was better than kO.1 K. The electrical resistivity of a ZrH,.,, sample was also measured in the 4.2 - 10 K range. The temperature was measured using a germanium thermometer (Lake Shore type CR-200A-1000) with an accuracy of 0.2%, while the temperature stability during me~urement was better than +O.Ol K. The temperature dependence of the electrical resistivity for ZrHi.sa is shown in Fig. 1, and in Fig. 2 the corresponding data for ZrH1.66are shown.

185

42

80

+.

140

200

\

T b+-

300

Fig. 1. Temperature dependence of the electrical resistivity for an&naly appearing at 161.8 f 0.2 K (inset).

, 4280 I

4

L

140

details of the

200

TlKl-

300

Fig. 2. Temperature dependence of the electrical resistivity for ZrH1.g; hysteresis in the range 165 - 170 K (inset): 0, heating; +, cooling,

the thermal

4, Thermal conductivity For measurement of the thermal conductivity we used a modified steady-state potentiometric method with axial heat ffow in the sample [ 133.

For samples of a cyiindrkal shape we may express the thermal conductivity Kas .

186

where C$is the heat flow in the sample, 1 is the distance between the thermometers, S is the sample cross-sectional area, AT = T2 - T1 is the temperature difference between the measured points, T, is the mean sample temperature, and Ti is the temperature measured by thermometer ABI. Description of the method and of the experimental arrangement can be found in ref. 12. We used calibrated Allen Bradley carbon resistors as thermometers ABi. Using the thermal conductivity Etalon SRM 735 for calibration of our method, we found that the relative accuracy of our thermal conductivity data in the temperature range investigated is better than 5%. The results of thermal conductivity measurements of ZrH1.s, and ZrHIeb6are given in Fig. 3 and Fig. 4 respectively. Thermal conductivity was measured also in a magnetic field up to 3 T. We found that the effect of a magnetic field on thermal conductivity at 4.2 K was less than l%, which is within the limit of our experimental error.

Fig. 3. Thermal conductivity

0

2

4

6

Fig. 4. Thermal conductivity

of ZrHl.s,-, as a function of temperature.

a

IO

T[KJ

of ZrH1.66 as a function of temperature.

5, Results and discussion After ~~n~e~ and Jena il.41 the ~o~~buti~~ of ~~drug~~ ta the efectricat resistivity of metals inereaes with increasing temperature. However, Westlake and Miller [15] have shown that in hydrides of Nb-V and Nb-Ti the opposite behaviour can be found. Savin et al. [4] report that with increasing hydrogen content in zimonium the electrical resistivity decreases, indicating an increase in the number of free electrons, The main effect of hydrogen cm the electrical resistivity is believed to be due to the scattering of electrons by defects in the hydrogen sublattice. None of these theories can be fully supported by our measurements, Anomalies have been found on the electrical resistivity curves in the temperature range from 160 to 170 K. For the ZrHIs,, sample this anomaly appears at 161.8 i: 0.2 K (Fig. I, inset) and coincides with the phase lotions as found from heat capacity rne~u~rne~~ f 163. The temperature dependence of the electric resistivity for the ZrM,,G, sample does not show any equally well developed anomaly but there is a thermal hysteresis in the 165 - 170 K range (Fig. 2, inset). Its magnitude depends on the heating or cooling rate. In the range 160 - 170 K the p(T) dependences of the two hydrides studied cross each other. For ZI%I~.~~and temperatures below 160 K the experimentat values of p(T) can be expressed with the correlation coefficient r = 0.999 as p(T) = (3.9248 + 0.07792’) X lo-’

s1 m

(2)

The electric re~stivity of the ZrH,.se sample can be expressed in the range SO - I.60 K as p(T) = 13.3832 + 0.1107T)‘X 10e7 s2 m

(3)

with r = 0.990. For temperat~es between 4.2 - 10 K the best fit is obtained using the formuh p(T) = (3.9548 t ~,01~34~~ X lO+ 52 m

(41

where the correlation factor r = 0.999. A relatively small value of the residual resistivity ratio for this sample (RRR = 1.676) indicates the presence of defects in the crystal structure. From the experimental data we can eonelude that the slupe dp{dT is very smdt. Residual resist&&y of b&h samples is p. = 3.9 X 16’f2

m

(51

The temperature dependence of the thermal conductivity for each hydride was studied between 1.5 and 1Q K. In this temperature region three m~h~isms of heat transfer may be ~rnpo~~t: electron, phonon and rn~u~ mechanisms, The heat tamtier by rn~o~s has not been found experimentally. Thus it is possible to express the thermal conductivity as

188

where K, is the electron contribution and Kb the phonon contribution. The scattering mechanisms for both contributions influence the thermal resistivity of a given heat conductor additively in the first approx~ation: 1 w, = - = Wed+ w,*-t Web+ w,e K, and 1

Wp= - =W/+ w~*~w~b~ w*e

(71

(8)

KP

where the symbols have there usual meaning. For the electron contribution the dominant mechanism are scattering by impurities and by phonons with the corresponding temperature dependences Wed+

T-'

We*- TZ

(91

For the thermal conductivity of the hydrides the phonon contribution plays a role even at the lowest temperatures. Its temperature dependence is mainly caused by phonon-electron and phonon-grain boundary scattering. As we have mentioned in Section 2, our samples had microcracks, especially the ZrII,~,, sample. The above-mentioned mechanisms result in the following dependences W,b -

T-3

W;

-

T-2

(10)

Conduction electrons in metals transport both electrical charge and heat. The ratio between the thermal and electrical resistivity for a given metal can be found using the Wiedemann-Franz law w d = e

9

T-1

(11)

where p. is the residual resistance and Lo = 2.445 X 10e8 W a K-’ is the Lorenz number for the case of pure metals, Calculation of Wep,based on the solution of the Boltzman transport equation, using a variation method [ 171, leads to the following dependence

We*=aT2

(12)

where

and n, is the number of free electrons corresponding to one atom, TD is the Debye temperature, and W,m isthe limiting value of the thermal resistivity for high temperatures. An important relation between We*and WDehas been derived in ref. 17,

4 We*

(14)

189

Using these expressions we can obtain a simple equation for n,: n, =

v

3.7 W,” i

Ii2 T

1

(15)

T,

The experimental results obtained were analysed using the theoretical models quoted above. By computer fitting the data, using the least-square method, we obtained the coefficients of the terms in various powers of T. Results for the ZrHt.sOsample were best fitted by an expression K = 7.454 X 10w2T + 5.449 X 10e3T2 W m-i K-’

(16)

with the correlation coefficient r = 0.986, i.e. aI the experimental points correspond to relation (16) at the probability level 1.4% (see Fig. 5). 038

’

-

20

.

40

’

60

1

80

’

.

,

lfx3TZtK21 OE-

< 016-

TtKl

Fig. 5. The dependence of the thermal conductivity-temperature ratio (i.e. K/T) on the temperature: 0, experimental results for ZrH 1.66 and analysis according to eqn. (19); *, experimental results for ZrHl.so and analysis according to eqn, (16).

Using expressions (11) and (5) we obtain for the Lorenz number Lo = 2.94 X lo-* W St K-‘. For temperatures T > T, the limiting value of the thermal resistivity of the ZrH,.,, is w,- = 8.5 X 1O-2 W-” m K

(17)

and using expressions (15), (16) and (17), we get 89.3 (18) Tn As a first approximation we can use the value TD = 250 K for pure zirconium [18], in spite of the fact that the real Debye temperature for zirconium hydride is lower [7 1. From eqn. (18) we get n, = 0.357. This value being approx~ately ten times greater than that for pure zirconium. (In ref. 18 McDonald et aE.report n,(Zr) = 0.03.) The increase in the number of free electrons per atom in hydrides is in agreement with the conclusion of Savin etal. [4].

n,=

190

The experimental temperature dependence of thermal conductivity is different from expression (17) which is valid for ZrH,.,,. corresponding expression for ZrH 1.66 is

for The

K = (8.47 X lO%!

(19)

Zrb.66

+ 4.79 X 10w4T3) W m-lK_’

with the correlation factor r = 0.992. This shows that the electrons are predominantly scattered at impurities, while phonons are scattered at grain boundaries (Fig. 5). The value of the Lorenz number

L, = 3.37 X lo-’ W St K-’ is within reasonable

limits for the given materials.

Acknowledgments We are grateful to Mr. A. S. TopEan from the Institute of Physics in Tbilisi, U.S.S.R., for supplying the samples and Mr. S. JBnoS from the Institute of Experimental Physics in,KoSice, C.S.S.R., for useful discussions.

References 1 E. L. Muetherties, Symp. on the Properties and Application of Metal Hydrides, Toba, Japan (1982). 2 F. Ducastelle, R. Candron and P. Costa, J. Phys. (Paris), 31 (1970) 57. 3 W. Bickel and T. G. Berlincurt, Phys. Rev. B, 2 (1970) 4807. 4 V. I. Savin, R. A. Andrievskij, E. B. Bojko and R. A. Ljutikov, Fyz. Met. Metalloved., 24 (4) (1967) 636. 5 H. E. Flotow and D. W. Osborne, J. Chem. Phys., 34 (1961) 1418. 6 W. J. Tomasch, Phys. Rev., 123 (1961) 510. 7 M. Gupta, Phys. Rev. B, 25 (2) (1982) 1027. 8 L. W. Wittemore, Symp. on Inelastic Scattering of Neutrons in Solids and Liquids, Vienna, Austria, Vol. 2, 1965, p. 305. 9 S. S. Pan, W. E. Moore and M. L. Yater, Trans. Am. Nucl. Sot., 9 (1966) 465. 10 B. W. Veal, D. J. Lam and D. G. Westlake, Phys. Reu. B, 19 (1979) 2856. 11 M. M. Antonova and P. A. Morozova, Preparatiunaja chimia gidridou, Kiev, 1976. 12 A. Feher and S. JanoX, Cas. Fiz., Cesk., A, 30 (1) (1980) 37. 13 Z. Malek, A. Ryska and S. MolokaE, Proc. 4th Conf. Czech. Phys., Liberec 1975, Academia, Prague, 1976, p. 203. 14 M. Manninen and P. Jena, Bull. Am. Phys. Sot., 24 (1979) 463. 15 D. G. Westlake and J. F. Miller, J. Phys. F, 10 (1980) 859. 16 L. J. TopEan, I. A. NaksidaHvili, R. A. Andrievskij and V. I. Savin, Fiz. Tuerd. Tela, 15 (7) (1973) 2195. 17 P. G. KIemens, Handb. Phy.. I4 (1956) 198. 18 D. K. C. McDonald, G. K. White and S. B. G. Woods, Proc. R. Sot. London, Ser. A, 235 (1956) 358.