Negative Temperature Coefficient of Resistivity in Samples of Nb 3Ge

Negative temperature coeﬀicient of resistivity in samples of Nb 3Ge irradiated by electrons or heavy ions F. Rullier-Albenque, L. Zuppiroli, F. Weiss

To cite this version:

F. Rullier-Albenque, L. Zuppiroli, F. Weiss. Negative temperature coeﬀicient of resistivity in samples of Nb 3Ge irradiated by electrons or heavy ions. Journal de Physique, 1984, 45 (10), pp.1689-1698. 10.1051/jphys:0198400450100168900. jpa-00209910

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Classification Physics Abstracts 61.80F201361.80J201372.15E

Negative temperature coefficient of resistivity in samples of Nb3Ge irradiated by electrons or heavy ions

F. Rullier-Albenque, L. Zuppiroli Section d’Etude des Solides Irradiés, Centre d’Etudes Nucléaires, B.P. n° 6, 92260 Fontenay-aux-Roses, France

and F. Weiss

Laboratoire des Matériaux, ENSIEG, ER 155, B.P. 46, 38402 St Martin d’Hères, France

(Reçu le 2 décembre 1983, révisé le 4 avril 1984, accepté le 21 juin 1984)

Résumé. 2014 Des échantillons de Nb3Ge ont été irradiés à basse température (T~ 20 K) par deux projectiles aussi violemment différents que des électrons de 2,5 MeV et des ions lourds d’environ 100 MeV (fragments de fission de l’uranium). La résistivité a été mesurée en fonction de la température avant et après irradiation. Pour les deux types de particules des valeurs négatives du coefficient de résistivité avec la température d03C1/dT sont mesurées et corrélées à la résistivité résiduelle. Ces propriétés de transport anormales sont discutées et comparées aux résultats des récentes théories consacrées à ce sujet. Qualitativement, il semble clair que, s’agissant d’un système où le libre parcours des électrons est de l’ordre de la distance interatomique, le changement de signe du coefficient d03C1/dT est relié à un processus de localisation des électrons avec la participation d’interactions électron-phonon et électron-électron. En d’autres termes, l’ecart entre les valeurs expérimentales et la théorie de Boltzmann du transport dans un gaz d’électrons presque libres est dû à l’interférence entre les collisions sur les impuretés, les collisions électron-phonon et (ou) les collisions électron-électron. Alors que la théorie de Belitz et Schirmacher sur l’effet tunnel induit par les défauts dans les métaux très désordonnés semble la plus appropriée pour expliquer les résultats d’irradiation aux ions lourds, bien qu’elle n’inclue que les interactions électron-phonon, les résultats des irradiations aux électrons révèlent la nécessité d’inclure les interactions coulombiennes comme dans le modèle de Alts’huler et Aronov.

Abstract. 2014 Nb3Ge samples have been irradiated at low temperature (T ~ 20 K) by two drastically different irradiation projectiles : 2.5 MeV electrons and ~ 100 MeV heavy ions (uranium fission fragments). The resistivity has been measured versus temperature before and after these irradiations. For both projectiles negative temperature coefficients of resistivity d03C1/dT were measured and correlated with the residual resistivity p. These anomalous transport properties are discussed and compared to the results of the recent theories on the subject. It is qualitatively clear that the change of sign of the temperature coefficient of resistivity, occurring in a system where the electronic mean free path is of the order of the atomic distance, is indeed related to some localization process, helped by electron-phonon and electron-electron interactions. In other words, the deviation of the resistivity from the Boltz- mann nearly free electron behaviour is due to some interference effect between impurity scattering and electron- phonon and/or electron-electron scattering. While the theory of defect induced tunnelling in strongly disordered metals developed by Belitz and Schirmacher seems to be the most appropriate for the explanation of the heavy ion irradiation results, although it includes electron-phonon interactions only, electron irradiation results reveal the necessity of including the interplay with Coulomb interactions as in the model of Alt’shuler and Aronov.

1. Introduction. superconducting transition temperatures. Secondly, they exhibit anomalies in various normal state pro- There has been a great deal of interest in the A-15 perties. In particular, the fact that the A-15 resistivities compounds such as V3Si, Nb3Sn or Nb3Ge because do not increase linearly with temperature and struc- of their various peculiar properties. First of all, tural damage but rather tend to saturate at about they are among the compounds with the highest 120 to 160 u.cm, corresponding roughly to a mean

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198400450100168900 1690

free path I of the order of the interatomic distance a, 2. Experiments. has attracted considerable attention [1, 2]. The disordered character of these alloys is also reflected 2.1 SAMPLES. - All the Nb3Ge samples used in this in the breakdown of Matthiessen’s rule, the tempe- work have been prepared by chemical vapour deposition. The elaboration techniques are described in rature coefficient of dp resistivity (TCR) dT becoming detail elsewhere [8, 9]. Except for one (Nb3Ge-9) the films thickness from 1.5 to 4.5 even negative at low temperatures for sufficiently Nb3Ge (of J.1m) are on 300 thick substrate. disordered samples [3, 4]. This last point appears to deposited J.1m sapphire be quite universal as emphasized by Mooij who The resistivities of these samples were measured by a standard four points method. The estimated error found such correlations between and the resisti- dlnpdT in the absolute values of resistivity is about 20 % due to an of the vity p for a large class of materials [5]. The critical primarily imprecise knowledge value of resistivity beyond which the TCR becomes sample thickness. For the last sample (Nb3Ge-9) are made on both sides of a steel foil negative at room temperature was found by Mooij depositions [9]. In this the is about 20 to be approximatively 150 uQ . cm. It is striking to case, sample tim thick. This small thickness is for electron notice that this value is precisely the one we have relatively very helpful mentioned for the A-15 saturation resistivity. irradiation because high electron beam current can then be used without producing important heating Presently the A-15 superconductor with the highest of the sample. On the other hand the resistivity transition temperature, Nb3Ge, is prepared by sputter- determination is more difficult. At each measurement ing, coevaporation or chemical vapour deposition. point, we have to measure both the resistance of the These elaboration methods allow the A-15 Nb3Ge Nb3Ge-9 sample (Nb3Ge on steel) and the resis- metastable phase to be stabilized and provides films tance of a steel sample of the same nature. In this way with transition temperatures which can reach 23 K. we were able to obtain the absolute Nb3Ge resistivity The transition temperatures, Tc, residual resistivities with an estimated error of 40 %. and temperature coefficients have been shown to be The initial sample specifications are given in table I. strongly correlated to each other and to all depend The different critical temperature Tc and resistivity p on the global degree of disorder of the material [3, 4, 6]. (25 K) values are the results of different growth condi- But the precise nature of this disorder is not at present tions. clear. One may wonder if the disorder is concentrated mainly at the atomic scale such as disorder in amor- 2. 2 IRRADIATIONS. phous alloys (metallic glasses) or if it is related to an 2. 2 .1 Electrons. - The electron irradiation has been inhomogeneity of any kind which could depend on carried out in the Vinkac low the « metallurgical )) qualities of the films. In the temperature facility. This described elsewhere consists of a present paper we try to discuss this problem in device, [10], liquid to a Van der Graaff connection with a set of new radiation damage hydrogen cryogenerator coupled irradiation between 18 and 25 K. experiments in Nb3Ge films. We have tried to change accelerator, allowing the level and the spatial distribution of damage by In addition, it is possible to isolate the irradiation from the and to warm the using two kinds of very different irradiation projec- cryostat cryogenerator up tiles : 2.5 MeV fast electrons which produce mainly sample by a linear increase of the temperature between isolated point defects and ~ 100 MeV heavy ions 20 to 300 K with heating rates from 0.1 to 10 Kelvin minute. The and a steel sam- (uranium fission fragments) which deposit high energy per sample Nb3Ge-9 densities in the form of electronic excitation and ple were irradiated together with 2.5 MeV electrons atomic collisions. Studies of the effects of electron, up to a dose of 4 x 102° e/CM2 corresponding to an electron flux of about 5 x 1014 The irradia- neutron, a-particle and heavy-ion irradiation on the e/cm2/s. electrical resistivity have been reported by other tion temperature never increased above 22 K. The investigators [3, 4, 6, 7]. One of the originalities of sample resistivity was measured continuously during irradiation. After irradiation the irradia- the present work lies in irradiating the same material given times, tions were and the versus tem- by projectiles which are expected to produce very interrupted resistivity different damage distributions. perature curves p(T) were determined between 18 and 60 K after annealings at 300 or 60 K. The outline of this paper is as follows. In section 2 Electron irradiations are known to produce isolat- we describe the experimental techniques and present ed point defects. In a diatomic compound such as our results. In section 3 the different models which Nb3Ge it is possible to determine their number by have been proposed to explain the anomalous beha- using a calculation due to Lesueur [12]. Knowing viour of resistivity are reviewed and experimental the two respective displacement threshold energies results are discussed in connection with the theoretical [14] this calculation gives the fraction of atoms displac- predictions and the defect structure in irradiated ed (displacements per atom (dpa)) for each atomic Nb3Ge samples is analysed. Section 4 contains our species. The outline of this calculation and its appli- conclusion. cation to Nb3Ge are indicated in the appendix. It is 1691

Table I. - Sample specifications.

shown that an electron flux of 5 x 1014 e/cm2 . s the damage production rate is found to be of the corresponds to a damage production rate of about order of 7 x 10-6 dpa/s. 5 x 10- 8 dpa/s. 2. 3 EXPERIMENTAL RESULTS.

- 2. 2. 2 Ions. In order to irradiate the films with 2. 3.1 Electrons. - Figure 1 shows the evolution of heavy ions we have used sources of fission fragments containing 90 % of 2 3 5 uJ. The samples together with uranium or uranium dioxyde sources were irradiated with thermal neutrons producing the fission of 2 3 5 U nuclei. The neutron irradiations of these « sandwiches)) were performed in the Vinka low temperature facility of the Triton reactor of Fontenay-aux-Roses. This device allows neutron irradiation at liquid hydrogen temperature [11]. The thermal neutron flux was about 7 x 1011 n/cm2/s corresponding to a fission fragment flux of order of 4 x 1010 FF/CM2/S for a bulk uranium source. During irradiation the temperature always remained below 35 K. Uranium fission fragments are expected to deposit high densities of energy both in electronic excitation

and atomic collisions. One can calculate the latter - Fig. 1. Evolution of resistivity versus temperature curves contribution and evaluate the number of atomic dis- of the Nb3Ge-9 sample under electron irradiation. See placements (see appendix). For the thermal neutron table I for the sample description. The arrows indicate the flux used in our experiment (7 x 1011 th.n./cm2 . s) resistivity minima. 1692 the resistivity versus temperature curves p(T) for lar to those reported after a-particle [3] or heavy-ion [4] different electron doses. Although it is not very visible irradiations. The most damaged samples exhibit a in this figure, a resistivity minimum is observed after negative TCR in the whole temperature range investi- a dose of 2.3 x 102° e/cm2 (corresponding to gated (20-300 K). In these cases the p(T) curves are ~ 0.02 dpa). It appears at about 40 K and is weakly very similar to that observed for amorphous shifted towards higher temperature with irradiation. Nb3Ge [14]. On figure 2 the negative TCR is shown with a more 2. 3 . 3 Comparison between electron and fission frag- appropriate scale; this curve obtained particular - ment irradiations. The most striking resdlt of the at the end of irradiation after annealing at 300 K is present study is the appearance of a negative TCR reproduced together with the curve before irradiation. after both electron and fission fragment irradiations. But whereas the negative TCR is extending up to room temperature after fission fragment irradiation, it appears only at low temperatures (T 50 K) after electron irradiation. Figure 4, where the temperature coefficient of resistivity values are plotted versus the resistivity values at room temperature for all the samples, shows clearly that there is a strong correlation between these two quantities : the larger the resistivity p, the lower the coefficient dp which temperature dT becomes negative at a resistivity of the order of 150 uQ2. cm. In order to compare irradiation effects at low Fig. 2. - Comparison between the shapes of p(T) curves temperature we have represented the same plot at and for the irradiated before after irradiation Nb3Ge sample 25 K on figure 5. It can been seen on this figure that with 2.5 MeV electrons.

During this electron irradiation the critical tem-

a rate perature c has decreased at AP is the Tc ApAp (Ap corresponding resistivity increase) equal to - 0.1 K/pf2. cm, which is the value that we have already reported for previous electron and neutron irradiation [13].

2.3.2 Fission fragments. - Eight different Nb3Ge samples ( 1 to 8) were irradiated with fission fragments. Figure 3 shows some typical p(T) curves obtained before and after irradiation. These curves are simi-

Fig. 4. - Correlation between temperature coefficient of resistivity (TCR) and resistivity values at 280 K for all Fig. 3. - Some of typical p(T) curves for as-grown and the samples (as-grown, electron or fission fragment irra- fission fragment irradiated Nb3Ge samples. See table I diated). * and o symbols refer respectively to electron- for the sample descriptions. and fission fragment-irradiated samples. 1693

peak position of the X-ray interference function deter- mines the sign of the temperature coefficient. The main success of this model was to explain the change in the temperature coefficient of resistivity when the Fermi wave vector is shifted by changing the compo- sition of glassy metallic alloys [19, 20]. This diffraction model was used by Bieger et al. [22] to explain the shape of the resistivity curves of some A-15 compounds. In our case, it is worth mentioning that the p(T) curves for the most heavily irradiated Nb3Ge samples (Fig. 3) are very similar to those of many other metallic glasses [14, 19-21]. There are two serious criticisms, in principle, concerning the application of the extended Ziman theories to transition metal glassy alloys and to A-15 compounds. First these models are all based on a nearly free electron approach. One may wonder if they can properly describe electronic systems for which a tight binding approach should be much more appropriate. Secondly, most of the Ziman extended theories assume weak coherent scattering of electrons despite the fact that the mean free paths are of the order of one atomic distance and that the resistivities are approaching the « maximum metallic resistivity », which indicates that these alloys are not far from the regime of localization. These remarks have inspired Fig. 5. - Correlation between temperature coefficient of some of the following alternative models. resistivity (TCR) and resistivity values at 25 K for all the samples (as-grown, electron or fission fragment irradiated). 2) Imry evoked the possible role of incipient * and . symbols refer respectively to electron- and fission Anderson localization in describing the resistivities fragment-irradiated samples. of highly damaged A-15 alloys and more generally in explaining the universality of the Mooij correlation in highly disordered metals [24]. His interesting specu- lations are based on the recent ideas of Thouless a correlation between (25 K) and p (25 K) is [25] dp and the scaling theory of localization of Abrahams again visible but the values for ion and electron et al. [26] which predict that the zero temperature irradiations are not situated on the same correlation resistance of a disordered electronic system depends curves. At 25 K the change from a positive to a nega- on its length scale in a universal manner. Extensions tive TCR occurs for 60 p 80 uQ. cm for elec- of these theories to higher temperatures are somewhat tron irradiation and for 120 p 160 uQ. cm for controversial [27, 50]. They are based on the compari- ion irradiation. son of the different lengths characteristic of the electron propagation (critical localization length ç, elastic 3. Discussion. mean free path le, size of the sample L, inelastic mean free path li the temperature dependence of which plays 3.1 THE DIFFERENT MODELS EXPLAINING NEGATIVE the main role in the resistivity variation). Moreover, TEMPERATURE COEFFICIENTS OF RESISTIVITY. - The localization theories are, basically, independent elec- observation of a negative coefficient of resistivity tron theories and they cannot be applied crudely and its correlation with the resistivity has.stimulated to a system in which a particularly strong electron- a lot of theoretical work. The numerous theories can phonon interaction and a substantial electron-elec- be classified in the five following categories. tron interaction are expected to occur. 1) The extended Ziman theories [15-18] have been It is worth mentioning here that localization toge- remarkably successful to explain the resistivity versus ther with Coulomb interactions have been envisaged temperature curve of metal glasses [19-21]. Like in the by Anderson et al. [31] to be responsible for the « uni- theory of the resistivity of liquid metals [15], the con- versal » degradation of the transition temperature ducting electrons are considered to be quasi-free T, in high-T, superconductors like A-15 compounds. and weakly scattered due to the random position of They argue that the anomalous behaviour of the atoms (pseudopotentials). The resistivity can be electron diffusion constant associated with localiza- related to the pair distribution function (or, in the tion leads to an increase of the repulsive interaction k-space, to the X-ray interference function). The posi- between Cooper pair electrons, which results in a tion of the Fermi wave vector kF with respect to the decrease of Tc. Once the resistivity exceeds some 1694 critical value p,, Tc is found to decrease as a universal 3.2 CORRELATIONS BETWEEN THE TEMPERATURE COEF- function of p/pc. FICIENT OF RESISTIVITY dpld T AND THE RESISTIVITY. - Figures 4 and 5 clearly show that there is a strong corre- 3) The electron-phonon interaction is the main lation between the temperature coefficient of resis- concern of Girvin and Jonson [23] and Belitz and tivity and the resistivity p, not only at room tem- Schirmacher [49] in their study of the resistivity of -72013 disordered metals. In normal metals the additional perature (Mooij plot) but also at low temperatures. disorder associated with phonons causes the mobility This correlation is better in the former case than in the to decrease with temperature. The new feature which latter where two different curves can be distinguished appears in the high resistivity regime is the fact that depending on the irradiation type. Thus the kind the phonons can increase rather than decrease the of defects created does influence the behaviour of the electron mobility. A new contribution called defect resistivity. It is remarkable anyway that the change induced tunnelling appears in the conductivity when of sign of the TCR occurs around 100 u. cm for both the Boltzmann hypothesis of independent scattering cases, that this value is close to the saturation value events fails. Jonson and Girvin developed a theory of the resistivity at high temperature and is not so far in the case where the usual adiabatic approximation from values obtained at the same temperature in breaks down. Although their numerical calculations other systems with quite different electronic proper- give a qualitative agreement with the Mooij correla- ties [48]. tion, they do not give the correct numbers : this theory The systems of interest are dirty metals with mean would be more appropriate for the description of free paths of the order of one atomic distance. This metals with resistivities of the order of 1 000 pQ . cm indicates that they are not far from the regime of loca- than for metals with resistivities of the order of lization. A priori, the models of category 2 in sec- 100 gfl . cm. Belitz and Schirmacher have developed tion 3.1 are the most attractive for explaining the very similar ideas with a different formalism. We properties of interest but we have already mentioned will show that their results can account rather accu- that they are not able to account for the shapes of rately for the heavy ion irradiation results shown in the p(T) curves that have been observed in heavily the present paper. irradiated samples (Fig. 3). The theories able to explain the strong deviation from the Boltzmann 4) Whereas the theories of the previous category behaviour leading to a negative TCR up to room concentrate on the electron-phonon interaction, Alt’- temperature are the models of categories 1, 3 and 4 shuler and Aronov [32, 33] proposed a description of in section 3.1. All of them explain the negative TCR disordered materials which deals with interacting by some interference effect between two scattering electrons in the presence of weak impurity scattering. events. In three dimensional systems, the interaction model In the Ziman extended model, the origin of the predicts that 1 /p varies as 1/ T at low temperatures [32]. negative TCR has to be found in the interference bet- Such a dependence has been observed, for the low ween waves diffracted by two adjacent centres of the temperature electrical resistivity of semi-metallic bis- amorphous material. But because A-15 alloys are muth in form of evaporated films and even of polyme- narrow d-band metals with bandwidths of approxi- ric sulfur nitride (SN)x [34]. matively 0.3 eV it is reasonable to exclude the extended Ziman theories to explain the temperature variations 5) Several other theories have been proposed to of the resistivity. explain the anomalous transport properties of disorder- In the Alt’shuler and Aronov interaction model ed metals. In the two level tunnelling model [28, 29, the interference between impurity scattering and 51], the negative TCR arises from a Kondo type Coulomb scattering is responsible for the anomalous exchange between the conduction electrons and two behaviour of the resistivity : the electron impurity equivalent atomic positions separated by a low energy scattering process is influenced by the presence of the barrier. This model has been applied to amorphous surrounding interacting electrons and in turn Cou- Nb3Ge by Tsuei [14]. lomb interactions between electrons are enhanced In a general way, a negative TCR can be observed when these particules are substantially slowed down each time the electrons have to cross a distribution of by frequent collisions with impurities. We have tried barriers even if the distances between these barriers to fit the low temperature parts of the 1 curves to the are larger than atomic distances and are more related p to the macroscopic granularity of the samples. This T1/2 law of the interaction model. In the case of the introduces a new class of models which, to our know- electron irradiation (curves similar to this of Fig. 2) ledge, have not yet been applied to Nb3Ge. Let us the signal to noise ratio is approximately 5. Thus point out that a theory of disordered materials gene- numerous temperature increasing functions can be rally characterized by large conducting regions sepa- fitted to 1/p including a T 1/2 variation. In the case of rated by small insulating barriers has been proposed ion irradiations the parts of the curves with negative recently by Sheng [30]. TCR are far more extended but the fit is less good 1695 below 40 K. It is better above 60 K in a region where it has less sense. Finally, the interference between impurity and phonon scattering is also very important for under- standing the deviations from the Boltzmann theory as mentioned by Girvin and Jonson who have emphasized that in the dirty limit the electrons are diffusing so slowly that they are sensitive to the time dependence of the phonon amplitudes. Unfortuna- tely, their numerical calculations imply that when the TCR changes sign, the resistivity is by one order of magnitude larger than the experimental value. A theory of phonon controlled conductivity in the high resistivity metals has been developed more 6. - of two curves measured after recently by Belitz and Schirmacher [49] on the basis Fig. Comparison p(T ) ion irradiations with the model of Belitz and Schir- of similar concepts. They obtained for the temperature heavy macher [49]. Dots are experimental data presented on dependent conductivity figure 3 (see table I for sample description). Symbols (*) are the fits using curves P of the figure I (a) PM = f 0T in reference [49]. Here, pm is the value of Mott’s « maximal resistivity » pm = 3 n’hle’kf and 0 is the Debye tempe- - Mo and Lo are static contributions due to rature equal to 302 K for N b3Ge [52]. Best fits for p(T) disorder. curves 6 and 9 are obtained using respectively the fourth -- MT is the generalized phonon scattering rate and fifth (from bottom) 1!.... curves of Belitz et al. with a which reduces to the nearly free electron expression PM when the mean free path is large compared to the value of pM of the order of 700 gf2. cm. Fermi wavelength ÀF. - LT is the new term due to the interference pro- The following section is an attempt to determine cess that they call phonon controlled tunnelling rate. in a more microscopic way which are the defects increases with The random tunnelling process responsible of these macroscopic effects on the resis- temperature as does the scattering rate but the former tivity and to compare electron and fission fragment is proportional to the conductivity thus allowing for irradiation. negative TCR. When the time scale for the electronic motion is much smaller than that of the phonons 3.3 DEFECT STRUCTURE IN IRRADIATED Nb3Ge SAM-

the formula is - (adiabatic approximation) previous PLES. In an ordered diatomic compound AB, a generalisation of the Ziman theory for amorphous irradiation produces point defects either isolated that such a formalism metals. Thus it is not surprising (electrons) or in cascades (neutron or heavy ions) can account for the conductivity of the heavy-ion and antisite defects, i.e. A atoms occupying B sites 3 coefficients irradiated samples of figure (negative and vice versa. This atomic interchange results in a 6 shows that this model from 20 to 300 K). Figure decrease of the long range order parameter S. The can indeed account for the resistivity curves obtained existence of antisite defects has been demonstrated after heavy ion irradiation with Mott’s maximum in neutron irradiated A-15 compounds using neutron metallic resistivity value of the order of 700 gf2.cm. and X-ray diffraction techniques [35, 36]. Due to the Even if the initial concept of maximum metallic structural instability of high-T, A-15 alloys, the the resistivity is in contradiction with scaling theory presence of defects can result in local atomic rearran- [26] in which the conductivity vanishes continuously, gements. Testardi et al. [37, 38] have suggested that this it has been shown [49], and experimental study the major effect of point or antisite defects is to is relevant scale also confirms, that pm the resistivity generate microscopic strains occurring over dimen- near the Anderson transition. It is worth mentioning sions of the order of some unit cells. to the that this theory is also able explain resistivity In the case of fission fragment irradiation, the large at a value of about saturation at high temperature energy deposited by electronic excitation can be 150 gfl. cm. thought to strongly influence the damage production. Moreover, the observation that p(T) curves for sam- However the small negative dp parts of the curves dT ples irradiated at the highest doses are very similar for the electron irradiated samples can probably not to that for amorphous Nb3Ge could be interpreted be explained in the same way and some Coulomb in terms of local amorphization. Let us point out that interactions halve probably to be included as men- a mechanism by thermal spikes has been proposed tioned in the semi-quantitative analysis of Kaveh by Lesueur [39] to explain the Pd80S’20 amorphiza- and Mott [50]. tion under fission fragment irradiation. In this assump- 1696 tion, fission fragment irradiated Nb3Ge samples are considered as binary mixtures composed of small amorphous regions in an undamaged matrix, and electrical resistivity can be expressed within the framework of the effective medium theory [40]. Attempts to fit experimental resistivity production curves with this interpretation have been unsuccess- ful showing that a’ more homogeneous model is required to explain these resistivity results. It is possible to relate the long range order parameter S to the resistivity by using the relationship of Muto [47] Fig. 7. - Schematic sketch illustrating in the A-15 structure the 102 > directions along which replacement collisions can produce disorder. where PD and po are the electrical resistivities for the disordered and the ordered states, respectively. More- over, a functional dependence of S with irradiation Thus the main difference between fission fragment- based on probability arguments has been derived by and electron-irradiated Nb3Ge samples at a given Aronin as number of dpa appears to be a much larger concen- tration of antisite defects in the former (1 ) than in the latter. One can see here the indication that the effect where A is the replacement effectiveness per atomic of antisite defects is mainly to affect the electron- displacement c (dpa). phonon interaction while point defects tend to inter- In the case of fission fragment irradiated Nb3Ge fere with the electron-electron interactions. samples, a linear dependence between S (deduced from resistivity measurements) and the number of atomic 4. Conclusion. displacements, is observed once the dose exceeds about 0.04 value of A is found to dpa. Experimental We have studied the influence of two very different be N 6. The same value of A has been reported by types of irradiation (electrons and fission fragments) Brown et al. of [42] upon measuring the r sistivity on the transport properties of Nb3Ge samples. In a Nb3Ge sample irradiated by fission dP Then we reach the conclusion both cases a change of sign of TCR was observed thf t gment.amorphous dT behaviour observed in the most radiation-damaged is not due to a local induced and a correlation between dp and the residual resis- samples amorphization dT by irradiation but results from a very large accumula- tivity was established either at high or at low tempera- tion of antisite defects. This interpretation is consis- tures. The problem is to decide if these correlations tent with the experimental X-ray results of Cox are universal in the sense of Mooij. In the detail of the et al. [36] in neutron irradiated Nb3Ge samples; values, they are not universal and the type of disorder they found a relation between the transition tem- has some influence ; but in all cases the sign of the perature and the long-range order parameter up to TCR changes at values of the order of 100 uQ. cm a dose of - 0.1 and observed a loss of dpa crystalli- which is a fraction of about 0.15 of the maximum nity after a dose of N 0.2 dpa. metallic resistivity pm initially suggested by Mott In the case of electron irradiation, antisite defects (in three dimensions Pm ~ hale 2 = 600 u cm when probably play also a role in the damage mechanisms, a = 3 A). The scaling theories [26] have shown that but it is not possible to determine their contribution there is no maximum metallic resistivity in 3 D. from resistivity measurements. It seems clear anyway that pm is the relevant resis- Antisite defects can be created during electron tivity scale near the Anderson transition [49] though irradiation by replacement collision sequences. In the conductivity vanishes continuously. In the same A-15 compounds production of large amounts of way the Mooij criterium give the correct numbers for antisite defects in such sequences is anyhow unlikely most of the changes of sign of the TCR, even if there because the 102 > atomic rows which along repla- is no real reason for this correlation to be valid in cements produce disorder, are « broken » between detail, at any temperature. the ABA sequences (see Fig. 7), whereas the very Among all the models proposed to explain the probable collision sequences along 100 ) do not anomalous transport properties, the most appro- produce antisites. A detailed study of electron irra- priate seem to us those which are related to some inter- diation effects in V3Si samples [41] suggested that antisite defects are produced at about the same con- centration levels as are point defects in electron (1 ) In this case disordering by thermal spikes is probably irradiated A-15 compounds. the most efficient mechanism. 1697 ference effects between impurity scattering and elec- Emb (resp. Eme ) represents the maximal energy tron-phonon or electron-electron scattering. In order transferred to a Nb (resp. Ge) primary atom and to distinguish between these two models, further d 6 (resp.(-rp) ) the differential cross section experimental work is needed. In particular magne- dE IVb p V/Ge/ toresistance measurements should be very helpful. for collisions between electrons and Nb (resp. Ge) atoms. Acknowledgments. In a previous experiment we have determined the respective threshold energies in Nb3Ge. By using It is a pleasure to thank Dr. Y. Quere for many valua- numerical results tabulated by Oen [45] it is straight- ble and comments. We wish to suggestions also thank forward to calculate these integrals for 2.5 MeV elec- S. Paidassi who some provided samples used trons. The results are : and J. Dural and R. Blot for their technical assis-hire tance during the neutron and electron irradiations. Several useful comments from the referees are grate- resulting in a total dpa production rate of 5 x 10-8 fully acknowledged. dpa/s for an electron flux of 5 x 1014 e/cm2/s.

2) uraniumUranium fission fragments. 2013- Energetic heavy Appendix 2)ions like uranium fission fragments lose most of their energy in the form of electronic excitation. In CALCULATION OF THE NUMBER OF ATOMIC DISPLACE- this case an analytic determination of the energy MENTS. transferred to lattice, and then of the number of

1) Electrons. - Lesueur has recently proposed atomic displacements, is not possible. In a mono- an analytic calculation of the number of atomic atomic compound, one can calculate the damage displacements in polyatomic compounds [12]. The created by fission fragment sources [44] but such a principal limitation of his calculation is that the calculation is much more complicated for diatomic electronic stopping is neglected but, concerning elec- compound. On the other hand a diatomic compound tron irradiation, this approximation is quite valid. like Nb3Ge can be shown to be assimilated with a Different assumptions of this calculation (see Ref. monoatomic compound for calculations of energy [12]) result in very simple expressions; the number of losses. In this way it is possible to determine the j atoms displaced by a primary of type k moving with energy transferred to lattice by a fission fragment an energy Ek can be expressed at low energy in the source. A typical «damage profile » in Nb3Ge is form shown in figure 8. Knowing the total energy trans-

where Ckj is a constant only depending on the k - j collision and Ej is the threshold energy to displace a j atom. Let us notice here that a j atom can displace another j atom provided that its energy is at least equal to 2 Ed ; but, to displace a k-atom, its energy 4 Mk Mj has to be at least to - where = equal to - E§ Åkj£kj 2 . Ajk (Mk 4MkM. + J Mj)2 . In the case of Nb3Ge one finds

Fig. 8. - Damage profile per average fission fragment in a Nb3Ge target for a thick uranium source.

ferred to it is possible to The total cross-sections to displace Nb atoms can dEn be then written with respect to atomic concentrations estimate thelattice number E Eof = atomic displacements by as :

Ed represents here the average threshold displacement energy that we have determined from the atomic percentage of Nb and Ge and found to be equal to 30 eV. With a thermal neutron flux of 7 x 1011 n/cm2/s, one finds a damage production rate of about 7 x and a similar expression for dd e. 10-6 dpa/s for a thick uranium source. 1698

References

[1] FISK, Z., WEBB, G. W., Phys. Rev. Lett. 36 (1976) 1084. [31] ANDERSON, P. W. MUTTALIB, K. A., RAMAKRISHNAN, [2] GURVITCH, M., Phys. Rev. B 24 (1981) 7404. T. V., Phys. Rev. B 28 (1983) 117. [3] TESTARDI, L. R., POATE, J. M., LEVINSTEIN, M. J., [32] ALT’SHULER, B. L., ARONOV, A. G., Zh. Eksp. Teor. Fiz Phys. Rev. B 15 (1977) 2570. 77 (1979) 2028 (Sov. JETP 50 (1979) 968). [4] MÜLLER, P., ISCHENKO, G., ADRIAN. H.. BIEGER, J., [33] ALT’SHULER, B. L., KHMEL’NITSKII, D., LARKIN, A. I., LEHMANN, L., HAASE, E. L., Superconductivity in d LEE, P. A., Phys. Rev. B 22 (1980) 5142. and f-band metals, D. H. Douglass, ed. (Plenum, [34] BRIMLOW, G. M., PRIESTLEY, M. G., Solid State Com- NY) 1980, p. 369. mun. 45 (1983) 1063. [5] MooIJ, J. H., Phys. Status Solidi (a) 17 (1973) 128. [35] SWEEDLER, A. R., COX, D. E., MOEHLECKE, S., J. Nucl. [6] GURVITCH, M., GHOSH, A. K., LUTZ, H., STRONGIN, M., Mat. 72 (1978) 50. Phys. Rev. B 22 (1980) 128. [36] COX, D. E., SWEEDLER, A. R., MOEHLECKE, S., NEW- [7] CATON, R., VISVANATHAN, R., Phys. Rev. B 25 (1982) KIRK, L. R., VALENCIA, F. A., Superconductivity 179. in d and f-band-metals, D. H. Douglas, ed. (Plenum, [8] PAÏDASSI, S., Thesis-Grenoble (1979). NY) 1980, p. 335. [9] WEISS, F., Thesis-Grenoble (1983). [37] POATE, J. M., TESTARDI, L. R., STORM, A. R., AUGUSTY- [10] DURAL, J., Rapport CEA-R 5091 (1980). NIAK, W. M., Phys. Rev. Lett. 35 (1975) 1290. [11] CONTE, R. R., Adv. Cryogen. Eng. 12 (1967) 673. [38] DYNES, R. C., POATE, J. M., TESTARDI, L. R., STORM, [12] LESUEUR, D., Philos. Mag. A 44 (1981) 905. A. R., HAMMOND, R. H., IEEE Trans. Mag. [13] RULLIER, F., QUERE, Y. and PAÏDASSI, S., J. Physique 41 Mag. 13 (1977) 640. (1980) 515. [39] LESUEUR, D., Rapport CEA-R 4502 (1973). GELY, M. H., RULLIER-ALBENQUE, F., QUERE, Y., [40] LANDAUER, R., J. Appl. Phys. 23 (1952) 779. DUNLOP, A., J. Nucl. Mat. 103 (1982) 745. [41] RULLIER-ALBENQUE, F., Thesis, to be published (1984). [14] TSUEI, C. C. Solid State Commun. 27 (1978) 691. [42] BROWN, B. S., BIRTCHER, R. C., KAMPWIRTH, R. T., [15] ZIMAN, J. M., Philos. Mag. 6 (1961) 1013. BLEWITT, T. H., J. Nucl. Mat. 72 (1978) 76. [16] EVANS, R., GREENWOOD, D. A. and LLOYD, P., Phys. [43] MÜLLER, P., WALLNER, G., WECK, W., RULLIER- Lett. 35A (1977) 57. ALBENQUE, F., J. Nucl. Mat. 108-109 (1982) 585. [17] NAGEL, S. R. and TANC, J., Phys. Rev. Lett. 35 (1975) [44] RULLIER-ALBENQUE, F., QUERE, Y., Phys. Lett. 81A 380. (1981) 232. The threshold energy values are erro- [18] COTE, P. J. and MEISEL, L. V., Phys. Rev. Lett. 39 (1977) neous in this paper. The exact values are 102. ENbd = 33.7 eV and EGed = 22.4 eV. [19] SINHA, A. K., Phys. Rev. B 1 (1970) 4541. [45] OEN, O. S., Report ORNL-4897 (1973). [20] BOUCHER, B., J. Non Cryst. Solids 7 (1972) 277. [46] LETEUTRE, J., POUCHOU, J. L., SOULLARD, J., ZUPPIROLI, [21] COTE, P. J., Solid State Commun. 18 (1976) 1311. L., J. Nucl. Mat. 54 (1974) 254. [22] BIEGER, J., ADRIAN, H., MÜLLER, P., SAEMANN- [47] MUTO, R., Inst. Phys. Chem. Res. Sci. Tokyo 20 (1936) ISCHENKO, G., and HAASE, E. L., Solid State 99. Commun. 36 (1980) 979. [48] ZUPPIROLI, L., BANDHYOPADHYAY, A., BOUFFARD, S. [23] GIRVIN, S. M., JONSON, M., Phys. Rev. B22 (1980) 3583. and BERNARD, C., Open questions in the field of [24] IMRY, Y., Phys. Rev. Lett. 44 (1980) 469. localization in low dimensional conductors, to be [25] THOULESS, J., Phys. Rev. Lett. 39 (1977) 1167. published in 1984. [26] ANDERSON, P. W., ABRAHAMS, E. and RAMAKRISHNAN, [49] BELITZ, D. and SCHIRMACHER, W., J. Phys. C. : Solid T. V., Phys. Rev. Lett. 43 (1979) 718. State Phys. 16 (1983) 913. [27] GIORDANO, N., Phys. Rev. B 22 (1980) 5635. [50] KAVEH, M. and MOTT, N. F., J. Phys. C. : Solid State [28] COCHRANE, R. W., HARRIS, R. H., STRÖM-OHLSON, Phys. 15 (1982) L-707. J. O. and ZUCKERMANN, M. J., Phys. Rev. Lett. 35 [51] IGASAKI, Y. and MITSUHASHI, H., J. Appl. Phys. 54 (1975) 676. (1983) 836. [29] ANDERSON, P. W., HALPERIN, B. I. and VARMA, C. M., [52] STEWART, G. R., NEWKIRK, L. R. and VALENCIA, F. A., Philos. Mag. 25 (1971) 1. Solid State Commun. 26 (1978) 417. [30] SHENG, P., Phys. Rev. B 21 (1980) 2180.