Superconducting Materials Suitable for Magnets

1. Superconducting Materials Suitable for Magnets David C Larbalestier Applied Superconductivity Center Department of Materials Science and Engineering Department of Physics CERN January 14-18, 2002 Note: Slight changes have been made to the final text which will differ from the video feed. Such changes are noted by highlighted text in this fashion wherever possible.

2. HgBa2Ca3Cu4Oy Oxide, high temperature superconductors Metallic low temperature superconductors Transition Temperatures Onnes 1911

3. H-T Plane of Superconductors 40 Helium Neon Cooling liquids Nitrogen Hydrogen 30 Nb3Sn BSCCO Field (T) 20 YBCO MgB2 film 10 Nb-Ti MgB2 bulk 0 0 30 60 90 120 Temperature (K)

4. Peter Lee UW: www.asc.wisc.edu

5. Generations of Conductors Nb-Ti Nb3Sn Coated conductor. (IBAD, RABiTS or ISD) MgB2 powder inside Fe/Nb/Ni barrier inside Cu Bi-2223

6. Outline of Lectures As advertised in lecture 1 • I. Basic Superconducting Parameters, mainly Critical Current Density • II. Basic Materials Issues • III. Niobium Titanium • IV. Niobium Tin and Niobium Aluminum • V. BSCCO • VI. YBCO • VII. Magnesium Diboride • VIII. Summary Issues As actually given: I. Basic Materials suitable for magnets II. Niobium Titanium III. HTS conductors (mainly BSCCO) – key issues IV. MgB2 conductors – key issues V. Nb3Sn conductors – key issues.

7. I a. “Zero Resistivity” • Non-Superconducting Metals • r = ro + aT for T > 0 K* • r = ro Near T = 0 K *Recall that r(T) deviates from linearity near T = 0 K • Superconducting Metals • r = ro + aT for T > Tc • r = 0 for T < Tc • Superconductors are more resistive in the normal state than good conductors such as Cu

8. M H M=-H Superconductor Normal Metal I b. Perfect Diamagnetism • c m = -1 • Means: B = mo(H + M) B = mo(H + cm H) B = 0 Flux is excluded from the bulk by supercurrents flowing at the surface to a penetration depth (l) ~ 200-500 nm

9. Oxide, high temperature superconductors Metallic low temperature superconductors MgB2 I c. Tc History HgBa2Ca3Cu4Oy

10. I d. Low Temperature Superconductors Type I Bc Bc2 Type II

11. I e. Type I and Type II • Type II • Material Goes Normal Locally at Hc1, Everywhere at Hc2 • Type I • Material Goes Normal Everywhere at Hc Complete flux exclusion up to Hc1, then partial flux penetration as vortices Current can now flow in bulk, not just surface Complete flux exclusion up to Hc, then destruction of superconductivity by the field

12. I f. Vortex properties • Two characteristic lengths • coherence length x, the pairing length of the superconducting pair • penetration depth l, the length over which the screening currents for the vortex flow • Vortices have defined properties in superconductors • normal core dia, ~2x • each vortex contains a flux quantum f0 currents flow at Jd over dia of 2l • vortex separation a0 =1.08(f0/B)0.5 Hc2 =f/2px2 f0 = h/2e = 2.07 x 10-15 Wb

13. I g. Vortex Imaging by Decoration Vortex state can be imaged in several ways Magnetic decoration Small angle neutron scattering Hall probes Magneto optics Scanning probe methods First was by sputtering magnetic smoke on to a magnetized superconductor in the remanent state Lattice structure confirmed and defects in lattice seen Trauble and Essmann 1967

14. I h. Vortex Imaging by Magneto Optics Prof. Tom H. Johansen Department of Physics, University of Oslo NbSe2

15. Bean (1962) and London (1963) introduced the concept of the critical state in which the bulk currents of a type II superconductor flow either at +Jc, -Jc or zero. Critical State is a static force balance between the magnetic driving force JxB and the pinning force exerted on vortices by the microstructure FP |(Bx(xH))| = BJc(B) Solutions define the macroscopic current patterns and enable the Jc to be determined from magnetization measurements I j. Bean Model

16. After Peter Kes in Concise Encyclopedia on Magnetic and Superconducting Materials, Ed J. Evetts Pergamon 1991 I k. Macroscopic Current Flow and Flux Patterns Transport Magnetization Jc = f(H)

17. m=MV=0.5(rxj)dV where j=(1/m0)xB or m=MV=IixSi Slab geometry is very simple dB/dx = ±Jc(B) I l. Magnetization and the Bean Model Magneto optical image of current flow pattern in a BSCCO tape. The “roof” pattern defines the lines along which the current turns.

18. Defects cause variation in DG of FLL up to 107A/cm2 at >30T Vortex separation few x for b>0.5 Dense interaction of FLL with defect array unperturbed vortex array is a FLL defects perturb the FLL defects seldom form a lattice Experiment measures global summed pinning force Fp=JcxB, often >20GN/m3 Elementary interaction is fp, generally small, e.g.~ 10-14N for binding to a point defect Predictive, quantitative theory of flux pinning is mostly lacking 3 step process compute fp compute elastic/plastic interactions of defect(s) and FLL Sum interactions over all pins and vortices 2 main cases: weak pinning, statistical summation (Labusch, Larkin and Ovchinnikov) strong pinning with full summation Useful materials try to fall into the second category I m. Flux Pinning Theory

19. Magnetic interactions on ~l Perturbations tocurrents by interfaces and surfaces no normal component of J Strong in low-k materials Vortex core interactions on ~x Possibility for point defects, precipitates, dislocations to pin Perturb local ||2 through Ddensity, Delasticity or Delectron-phonon Can also perturb electron mean free path and hence x I n. Defect-Fluxline Interactions F= d3r(A|D|2 +(B/2)|D|4 + C|D|2 + (h2/2m0) , A=N(0)(1-t), B= 0.1N(0)/(kBTc)2, C=0.55x2N(0)(a) Core interactions dominate in useful materials

20. Strong pinning materials (Nb-Ti wires, irradiated HTS) often exhibit full summation Fp=ndefectsfpdefect Weak pinning requires statistical summation as already noted many adjustable, often non-verifiable parameters I o. Summation and Scaling Scaling of the global pinning force with H, T can often be seen: Fp(B,T) = bp(1-b)q Nb-Ti often b(1-b), Nb3Sn b0.5(1-b)2, b=B/Bc2 HTS scaling functions complicated by thermal activation effects

21. Simple H-T diagram for LTS: Suenaga, Ghosh, Xu, Welch PRL 66, 1777 (1991) Complex H-T diagram for HTS Nishizaki and Kabayashi SuST 13, 1 (2000) I p. The Irreversibility Field

22. I q. Summary of Current Density Issues • Enormous Jc can be obtained in some systems • ~10% of depairing current density (~Hc/l) in Nb-Ti and for many HTS at low temperatures • HTS suffer from thermal activation and lack of knowledge about what are the pins • Practical materials want full summation to get maximum Jc • To compute Fpa prioriin arbitrary limit is so far beyond us • Useful materials tend to be made first and optimized slowly as control of nanostructure at scale of 0.5-2 nm is not trivial

23. II. Basic Materials Issues • Crystal Structures • Nb-Ti: body centered cubic simple, ductile • Nb3Sn: cubic A15 Crystal structure with range of off-stoichiometric compositions • Nb3Al is always off stoichiometry • BSCCO: complex layered phase(s) not found at fixed stoichiometry of nominal phase • YBCO: layered phase of fixed cation stoichiometry but variable O content • MgB2: Mg cages B • Only Nb-Ti is ductile! • Essential Phase Diagram Information • well known for LTS, poorly known for HTS

24. II a. Nb-Ti Phase Diagram • Key features: • Very high melting points • Large separation liquidus and solidus leads to segregation on cooling • Nb is bcc at all T, while Ti is bcc at high T and hcp at low T • Nb-Ti alloys want to become 2 phase hcp and bcc at low T but cannot transform by diffusion • The lattice acquires a soft phonon that has very important consequences: • E declines on cooling • p increases on cooling • The martensitic phase transformation is only incipient for Nb47wt.%Ti but the resistivity is greatly increased and Hc2 increased too

25. C T C C T C: Cubic A15, higher Hc2 phase, T: Tetragonal A15 phase II b. Nb-Sn Phase Relations Broad composition range 18-25at.%Sn, LT shear transformation to a small tetragonality, lowering Tc and Hc2

26. II c. Nb3Sn Structure Cubic structure with 3 orthogonal chains in which the Nb atoms are more closely spaced than in pure Nb: high N(0). Departures from stoichiometry must be accommodated by vacancies or anti-site disorder

27. Bi-O double layer Sr CuO2 Ca CuO2 Ca CuO2 Sr Bi-O double layer CuO2 II d. The BSCCO Family Tc ~30K ~70-95K ~105-110K g ~ 200-300 g may be ~ 50

28. CuO2 layer Y CuO2 layer Ba Cu-O chain layer Ba CuO2 layer Y CuO2 layer II e. YBCO • YBCO (YBa2Cu3O7-x) possesses the first crystal structure with Tc > 77K • It has defined cation stoichiometry 1:2:3, but O content is variable from 6-7 • Tc > 90K demands x<0.05 • YBCO is often thought of as being archetypal but in fact the Cu-O chain layers are very unusual • Make charge reservoir layer metallic • Most HTS are 2D, but YBCO is anisotropic 3D with electron mass anisotropy g= (mc/ma)0.5 of ~7

29. II f. MgB2 Smaller B, larger Mg atoms

30. CuO2 layer Y Bi-O double layer CuO2 layer Sr Ba CuO2 Ca Cu-O chain layer CuO2 Ca Ba CuO2 CuO2 layer Sr Bi-O double layer Y CuO2 CuO2 layer Mg B II g. Higher Tc – greater complexity 9 K a. 18-23 K b 39 K c 92-95 K 110 K d e

31. II h. Summary Materials Issues • Higher Tc means greater crystal complexity • body centered cubic Nb-Ti with random site occupation, ductile • phonon anomalies • Nb3Sn ordered A15 phase, brittle • other intermetallics often distort phase field • YBCO is anisotropic 3D, low carrier density, cation stoichiometric, brittle • metallic charge reservoir layer • BSCCO has 3 layered phases none of which exist at cation stoichiometry, micaceous with self-aligning tendencies • strongly anisotropic, 2D (but depends on doping state) • poorly understood phase relations • Materials quality at scale of x is always an issue!

32. Global UW References • L. D. Cooley, P. J. Lee, and D. C. Larbalestier, "Conductor Processing of Low-Tc Materials: The Alloy Nb-Ti," to appear as Chapter 3.3 of “The Handbook on Superconducting Materials," Edited by David Cardwell and David Ginley, Institute of Physics UK to appear March 2002. • L. D. Cooley, C. B. Eom, E. E. Hellstrom, and D. C. Larbalestier, “Potential application of magnesium diboride for accelerator magnet applications”, Proceedings of the 2001 Particle Accelerator Conference to appear. • David Larbalestier, Alex Gurevich, Matthew Feldmann and Anatoly Polyanskii, “High Transition Temperature Superconducting Materials For Electric Power Applications”, Nature 414, 368-377, (2001).