FLUX DENSITY GRADIENTS IN PLASTICALLY DEFORMED NIOBIUM SINGLE CRYSTALS

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FLUX DENSITY GRADIENTS IN PLASTICALLY

DEFORMED NIOBIUM SINGLE CRYSTALS

H. Habermeier, W. Klein, H. Kronmüller

To cite this version:

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JOURNAL DE PHYSIQUE Colloque C6, supplbment au no 8, Tome 39, aofit 1978, page C6-635

FLUX DENSITY GRADIENTS IN PLASTICALLY DEFORMED NIOBIUM SINGLE CRYSTALS

H.U. Habermeier, W. Klein and H. Kronmiiller

Institut fZir Physik am Max-Ptanck-Institut fZir MetaZZforschung, 0-7000 Stuttgart 80

Fed. Rep. Gemany

R6sumd.- En utilisant l'effet magndto-optique de Faraday, nous avons analysd la pdndtration de la phase de Shubnikov dans des monocristaux d niobium dGformds plastiquement. L'anisotropie de l'interaction entre les vortex et l'arrangement d

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s dislocations conduit 2 une pdndtration du flux fortement anisotrope. Une ddterminatian quantitative du profil de l'induction magndtique nous a permis de ddter- miner les gradients locaux de l'induction et des forces d'ancrage des vortex.

Abstract.- By means of the Faraday magneto-optical technique the penetration of the Shubnikov phase into plastically deformed niobium single crystals was analysed. The anisotropy of the interaction between the flux line lattice and the dislocation arrangements leads to an strongly anisotropic flux penetration. By a calibration of the flux density it was possible to determine the local flux density gradients and pinning forces.

EXPER-IFNTAL PROCEDURE.- Niobium single crystals orientated for single slip were deformed in tension at room temperature with a deformation velocity of H = 6 x 10-~s-l. Under these conditions mainly edge dislocations of the prim9ry glide system were produ- ced (Burgers vector

p

l

g ,

slip plane (i01)). From undeformed and plastically defromed rods (a = 0.45 ; 0.78 ; 1.08) flat discs of cylindrical shape were prepared by spark cutting with orientations parallel and perpendicular to the primary slip plane. In ok- der to obtain large Faraday a thin layer of mixed -

euroium compounds (EuS+EuF2) was evaporated on the discs as described by Kirchner/l/. The domain pat- terns were observed by a polarization microscope/2/ with high resolution starting from the Meissner sta-

Fig. 1 : Penetration of the Shubnikov phase into a undeformed niobium specimen (a=g) orientated parallel to the primary slip plane (101).

te in an increasing homogeneously magnetic field. The specimen's temperature in our experiments was 4.8 K.

EXPERIMENTAL RESULTS.- In undeformed niobium for all crystallographic orientations a nearly radialsymme- trical penetration of the Shubnikov phase is inves- tigated. With increasing applied magnetic field the flux front moves symmetrically towards the center as shown in figure I. The bright domains correspond to the Shubnikov phase whereas the Meissner phase remains dark. With increasing tensile deformation the penetration of flux becomes strongly anisotropic. For specimens orientated parallel to the slip plane (i01) the penetration of flux takes place preferen- tially along the direction of the primary edge dislocation lines as shown in figure 2. The photograph shows the nucleation of the Shubnikov phase at the

Fig. 2 : Penetration of the Shubnikov phase into a strongly deformed niobium specimen (a=0.78) orientated parallel to the primary slip plane for poHext = 60 mT.

surface as a fingerlike structure. For this geome- try the flux lines are orientated perpendicular to the dislocation lines. In niobium specimens cut per- penducular to the line direction of primary edge

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dislocations the penetration of flux occurs parallel to the (i~l)-~lide plane, i.e. parallel to wi- despread dislocation sheets. In this case the dislocation lines are aligned parallel.

FLUX DENSITY GRADIENTS AND VOLUME PINNING FORCES.- The photometric contrast of flux carrying domains decreases in radial direction starting from the specimen's edge towards the flux front. By compari- son of the measured photometric contrast with known flux densities of a homogeneously magnetized lead specimen the flux density profiles of the niobium specimens were calibrated/3/. A photometric analysis leads to nonlinear flux density profiles as shown in figure 3 for a undeformedniobiumspecimen.

Fig. 3 : Flux density gradients in undeformed niobium as measured by photometric analysis.

This result is in strong contradiction to ealier papers where linear flux density profiles are pro- posed. As a further interesting result we found that the width of the flux carrying zone respecti- vely the length of the fingers increases linearly with the applied magnetic field. The local volume pinning force can be derived from the flux gradients aB/ar using Friedel's formula/4/ :

pv = B - (aHext/a~)rev' (a~lar)

Here (aHext/aB)rev has to be derived from the re- versible magnetization curve of a pinning free niobium specimen. The determination of the local volume pinning force along the flux density profiles yields an unexpected result as shown in figure 4 :

the volume pinning force at the_specimenls edge is independent of the applied magnetic field and increases monotonous towardsthe flux front where the volume pinning force reaches its maximum value which is found to be independent of the applied field.

Fig. 4 : Volume pinning forces along the flux density profiles of the undeformed niobium specimen (dia- meter 4 mm) orientated parallel to the primary slip plane.

CONCLUSION.- The above mentioned results suggest that the pinning of flux lines in niobium at the flux front is governed by the interaction between single flux lines and extended dislocation arrangements. This suggestion is confirmed by the dependen- ce of the volume pinning force on the flux density.

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As shown in.figure 5 the volume pinning force is nearly constant for low inductiom (b<O.l)but decreases abruptly with increasing b=B/Bc2. This be- haviour is in good agreement with theoretical cal- culations of Schmucker and ~ror&ller/5/ who ex- plain the sharp decrease of the volume pinning force for b>O.l by a coherent motion of flux line bundles.

ACKNOWLEDGEMENTS.- The authors are grateful for helpful discussions with Dr. U. Essmann. The finan- cial support by the Deutsche Forschungsgemeinschaft is kingly acknowledged.

References

/I/ Kirchner,H., Phys. Stat. Sol.(a) i(1971) 631 / 2 / Habermeier,H.U. and Zaiss,R., will be published

/3/ ~ibertueier,~.~.

,

Aoki,R. and lZlein,W., submitted to Phys. Stat. Sol.

/4/ Friedel,J., De Gennes,P.G.andMatricon,H., Appl. Phys. Lett.

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