diffusion of muons in v, nb and ta

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Hyperfine Interactions 4 (1978) 824-827 North-Holland Publishing Company DIFFUSION OF MUONS IN V, Nb AND Ta O. HARTMANN, E. KARLSSON, L.-O. NORLIN AND K. PERNESTAL University of Uppsala, Uppsala, Sweden M. BORGHINI AND T. NIINIKOSKI, CERN, Geneva E. WALKER, University of Geneva, Geneva The diffusion of positive muons in metals can be studied by measure- ments of the p+SR line-width as function of temperature. If the muons freeze in at certain interstitial positions in the lattice at low temperatures it should be possible to conclude from the static dipolar width which position in the lattice that is the most stable. Since a positive muon can in this context be looked upon as a light isotope of hydrogen (m~/m m ~ 1/9) these results have also a bearing on the problem of hydrogen~impurities in metals. This point is espe- cially interesting in the case of b.c.c, metals, where the stable sites of dilute hydrogen-like impurities are not well known, while at the same time it is known that these metals can disolve large amounts of hydrogen. Most of our muon experiments were done on polycrystalline samples of high purity. Theywere performed in the temperature range 10-300 K (which means that the superconducting phases were avoided). The static dipolar line-width AB o in the b.c.c, metals depends on whether the muons occupy octahedral or tetrahedral interstices (see Fig. i) in the lattice. For polycrystalline material the static Fig. I. Interstitial sites of diffe- rents symmetries in a b.c.c. crystal: octrahedral tetrahedral A triangular widths AB o expected for the two types of sites can be calculated from the magnitude and position of the neighbouring nuclear dipoles by averaging the expression AB 2 -~ h2I(I+l) Z (1-3 c~ 2 r 824

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Hyperfine Interactions 4 (1978) 824-827 North-Holland Publishing Company

DIFFUSION OF MUONS IN V, Nb AND Ta

O. HARTMANN, E. KARLSSON, L.-O. NORLIN AND K. PERNESTAL University of Uppsala, Uppsala, Sweden

M. BORGHINI AND T. NIINIKOSKI, CERN, Geneva

E. WALKER, University of Geneva, Geneva

The diffusion of positive muons in metals can be studied by measure- ments of the p+SR line-width as function of temperature. If the muons freeze in at certain interstitial positions in the lattice at low temperatures it should be possible to conclude from the static dipolar width which position in the lattice that is the most stable. Since a positive muon can in this context be looked upon as a light isotope of hydrogen (m~/m m ~ 1/9) these results have also a bearing on the problem of hydrogen~impurities in metals. This point is espe- cially interesting in the case of b.c.c, metals, where the stable sites of dilute hydrogen-like impurities are not well known, while at the same time it is known that these metals can disolve large amounts of hydrogen.

Most of our muon experiments were done on polycrystalline samples of high purity. Theywere performed in the temperature range 10-300 K (which means that the superconducting phases were avoided).

The static dipolar line-width AB o in the b.c.c, metals depends on whether the muons occupy octahedral or tetrahedral interstices (see Fig. i) in the lattice. For polycrystalline material the static

Fig. I. Interstitial sites of diffe- rents symmetries in a b.c.c. crystal:

�9 octrahedral

�9 tetrahedral

A triangular

widths AB o expected for the two types of sites can be calculated from the magnitude and position of the neighbouring nuclear dipoles by averaging the expression

AB 2 -~ h2I(I+l) Z (1-3 c~ 2

r

824

O.Hartmann et al./Diffusion of Muons in V,Nb, and Ta 825

over all directions of the crystallites with respect to the applied field, under the condition that the dipoles precess only in the applied magnetic field. However, as shown by Hartmann [i] and Camani et al. [2] for the case of Cu it is necessary to apply strong magnetic fields to most samples in order to overcome the effect of field gradients caused by the muons themselves on the precession of the nuclear dipoles.

The polycrystal results were obtained with applied fields of the order of 400 G, which is lower than the fields needed for a de- coupling of the electric interaction. Final conclusions about the sites of the muons at low temperatures must therefore await further experiments at higher field strengths and, preferably, on single crystals. Such experiments are in progress and the present data for the static widths should be taken mainly as indications that the muons are not diffusing (at least not in a classical sense) at low temperatures in these metals.

Fig. 2 shows results for muons in Nb [3] and Ta. The static line- width observed in Nb below 60 K is 0.285(15) Ds -I, which should be compared with computed values for fixed interstitial positions of (0.34-0.37 depending on site. The static width for Ta is, although of low accuracy, in agreement with those theoretically calculated.

030

' ~ 0.20"

b

0.10

0

,u+SR LINE W~D~'HS IN bcc.

METALS ~;~oNL~,C R~S TA L

+ + }} *+ ~ , / I i I , , i . . . . i , i , _ i

IO 20 50 100 200 T [K]

Fig. 2. Temperature dependence of line-widths in Nb and Ta

030

~ 0.20 b

0.10

I , , I,,,,; , I

'II0 20 50 100 200 0 i

T-K

Fig. 3. Temperature dependence of line-widths in V

Fig. 3 shows results for muons in V. The irregular behaviour of the temperature dependence around 60 K has been checked by repeated mea- surements.

The jump times T were calculated from the Kubo-Tomita formula [4] C

for different temperatures in the diffusion region and the activation energies for muons were then derived and compared with data for hyd- rogen. This comparison is shown in Table 2.

Table i. Theoretical line-widths in the high-field limit for poly-crystals (in Ds'i) ....

V (octa) V (tetra) Nb (octa) Nb (tetra) Ta (octa)

0. 430 0 �9 400 O. 367 0. 341 0. 128

Ta (tetra)

0.119

826 O.Hartmann et al./Diffusion of Muons in V,Nb, and Ta

Table 2

Metal Impurity Low-T Activ. <c(S) at T(K) Comments o(Ds-I) energy

(meV)

V ~ 0.208 5(4) 8x10 -7 150 Activ.energy

H 43 2x10 -12 150 from all points 40-200 K

-6 Nb ~ 0.285 26(5) 2x10 120

H 68 I0 -I0 120

Ta D 0.ii --- 7x10 -7 60

H 140 --

The jump times T are 4 orders of magnitude longer for muons than for protons in th~ same material. This large difference lies in the pre-exponential factor in diffusion equation and is as yet unexplain- ed. Fig. 4 is an Arrhenius plot of the high temperature data.

Iogl'r c) JUMP TIMES FOR HYDROGEN ISOTOPES

-IO H

-9! dD

-7

5

5

& 1000 ~ F 500 300

T b

Fig. 4. Arrhenius plots for muons in Cu and Nb compared to corresponding data from diffusion of H and D in the same metals and in Pd (taken from ref. 5).

The activation energy for muons in Nb is smaller, but of the same order of magnitude as for hydrogen. The figure for muons in V should be taken as preliminary, considering the anomalous temperature depen- dence which has not yet been well explained. A suggestion for the dip in the o(T) curve for vanadium is that when going up in tempera- ture above 40 K the muons start diffusing normally, but at 70 K they diffuse far enough to be trapped by vacancies which they can leave only at much higher temperatures. This explanation rests on the assumption that the vacancy concentration is relatively high in our vanadium sample.

The low-temperature line-widths for the poly-crystalline vanadium presented in Fig. 3. are based on a single-frequency analysis. The line-shapes are, however, of such a nature that they can be equally

O.Hartmann et al./Diffusion of Muons in V,Nb, and Ta 827

well be fitted with the assumption that 70% of the muons have o = 0.155 ~s -I and 30% have o = 0.40 ~s -I. A freezing in at two inequivalent sites or the occupation of two different levels within the same site cannot, therefore, be excluded.

A few experiments have also been performed on single crystals, but are presently only in a preliminary stage. Our results should be compared to the theory of Hartmann [i] for combined electric and magnetic fields acting on the neighbouring nuclear dipoles. There is, at the highest field, a clear orientation dependence, but we have not been able to go to high enough applied fields to decouple the electric interaction. With a field of 5-10 kG it should be possible to reach complete decoupling and conclude whether the widths correspond to one or the other of the possible interstitial sites. A third possibility for the ground state of interstitial par- ticles has also been suggested by Birnbaum and Flynn [6]: a tunneling state involving the four tetrahedral and the 4 tri- angular sites in the cube faces of Fig. IF Similar experiments are also in progress with vanadium, where decoupling should be reached earlier.

REFERENCES

i. O. Hartmann, CERN report April 1977 (submitted to Phys. Rev. Letters)

2. M. Camani, F.N. Gygax, W. Ruegg, A. Schenck and H. Schilling, submitted to Phys. Rev. Letters.

3. O. Hartmann, E. Karlsson, K. Pernest[l, M. Borghini and T. Niinikoski, Physics Letters 61 A (1977) 141

4. R. Kubo and K. Tomita, J. Phys. Soc. Japan 9 (1954) 888

5. J. V61kl and G. Alefeld in Diffusion in Solids (eds. A.S. Nowick and J.J. Burton) Acad. Press, London 1975

6. H.K. Birnbaum and C.P. Flynn, Phys. Rev. Letters 37 (1976) 25.

b~-']

0.30

N b SINGLE CRYSTAL

0.20

~ [loo]

Fig. 5. Variation of the DSR line-width with applied field B for muons in a Nb single crystal. The Field was applied along the [I00] and [IIi] directions.

*Recent information on hydrogen (2nd Int. Congress on Hydrogen in metals, Paris 6-10 June, 1977) suggests still another possi- bility: the muons may be bound to N, O or C impurities, which would affect the line-widths and reduce T c drastically.

Editor's Note: See discussion after succeeding paper.