1. University of Wisconsin-Madison Applied Superconductivity Center 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. University of Wisconsin-Madison Applied Superconductivity Center HgBa 2 Ca 3 Cu 4 O y Metallic low temperature superconductors Oxide, high temperature superconductors Transition Temperatures Onnes 1911

3. University of Wisconsin-Madison Applied Superconductivity Center 0 10 20 30 40 0306090120 Temperature (K) Field (T) Helium Nb- Ti Nb 3 Sn MgB 2 film MgB 2 bulk Hydrogen Neon Nitrogen BSCCO YBCO Cooling liquids H-T Plane of Superconductors

4. University of Wisconsin-Madison Applied Superconductivity Center Peter Lee UW: www.asc.wisc.edu

5. University of Wisconsin-Madison Applied Superconductivity Center Nb-TiNb 3 Sn Coated conductor. (IBAD, RABiTS or ISD) MgB 2 powder inside Fe/Nb/Ni barrier inside Cu Bi-2223 Generations of Conductors

6. University of Wisconsin-Madison Applied Superconductivity Center 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. MgB 2 conductors – key issues V. Nb 3 Sn conductors – key issues.

7. University of Wisconsin-Madison Applied Superconductivity Center I a. “Zero Resistivity” Non-Superconducting Metals –  =  o + aT for T > 0 K* –  =  o Near T = 0 K *Recall that  (T) deviates from linearity near T = 0 K Superconducting Metals –  =  o + aT for T > T c –  =  for T < T c Superconductors are more resistive in the normal state than good conductors such as Cu

8. University of Wisconsin-Madison Applied Superconductivity Center I b. Perfect Diamagnetism  m = -1 Means: B =  o (H + M) B =  o (H +  m H) B = 0 Normal MetalSuperconductor Flux is excluded from the bulk by supercurrents flowing at the surface to a penetration depth ( ) ~ 200-500 nm H M M=-H

9. University of Wisconsin-Madison Applied Superconductivity Center I c. T c History HgBa 2 Ca 3 Cu 4 O y Metallic low temperature superconductors Oxide, high temperature superconductors MgB 2

10. University of Wisconsin-Madison Applied Superconductivity Center I d. Low Temperature Superconductors Type I Type II BcBc B c2

11. University of Wisconsin-Madison Applied Superconductivity Center I e. Type I and Type II Type I –Material Goes Normal Everywhere at H c Type II –Material Goes Normal Locally at H c1, Everywhere at H c2 Complete flux exclusion up to H c, then destruction of superconductivity by the field Complete flux exclusion up to H c1, then partial flux penetration as vortices Current can now flow in bulk, not just surface

12. University of Wisconsin-Madison Applied Superconductivity Center I f. Vortex properties Two characteristic lengths –coherence length , the pairing length of the superconducting pair –penetration depth, the length over which the screening currents for the vortex flow Vortices have defined properties in superconductors –normal core dia, ~2  –each vortex contains a flux quantum  0 currents flow at J d over dia of 2 –vortex separation a 0 =1.08(  0 /B) 0.5 H c2 =  2  2    h/2e = 2.07 x 10 -15 Wb

13. University of Wisconsin-Madison Applied Superconductivity Center 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. University of Wisconsin-Madison Applied Superconductivity Center I h. Vortex Imaging by Magneto Optics Prof. Tom H. Johansen Department of Physics, University of Oslo NbSe 2

15. University of Wisconsin-Madison Applied Superconductivity Center I j. Bean Model 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 +J c, -J c 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 F P |(Bx(  xH))| = BJ c (B) –Solutions define the macroscopic current patterns and enable the J c to be determined from magnetization measurements

16. University of Wisconsin-Madison Applied Superconductivity Center I k. Macroscopic Current Flow and Flux Patterns After Peter Kes in Concise Encyclopedia on Magnetic and Superconducting Materials, Ed J. Evetts Pergamon 1991 Magnetization Transport J c = f(H)

17. University of Wisconsin-Madison Applied Superconductivity Center I l. Magnetization and the Bean Model m=MV=0.5  (rxj)dV –where j=(1/m 0 )  xB or m=MV=  I i xS i Slab geometry is very simple –dB/dx = ±J c (B) Magneto optical image of current flow pattern in a BSCCO tape. The “roof” pattern defines the lines along which the current turns.

18. University of Wisconsin-Madison Applied Superconductivity Center I m. Flux Pinning Theory Defects cause variation in  G of FLL –up to 10 7 A/cm 2 at >30T Vortex separation few  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 F p =J c xB, often >20GN/m 3 Elementary interaction is f p, generally small, e.g.~ 10 -14 N for binding to a point defect Predictive, quantitative theory of flux pinning is mostly lacking 3 step process –compute f p –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

19. University of Wisconsin-Madison Applied Superconductivity Center I n. Defect-Fluxline Interactions Magnetic interactions on ~ Perturbations to  currents by interfaces and surfaces –no normal component of J Strong in low  materials Vortex core interactions on ~  Possibility for point defects, precipitates, dislocations to pin Perturb local |  | 2 through  density,  elasticity or  electron- phonon Can also perturb electron mean free path and hence  F=  d 3 r(A|  | 2 +(B/2)|  | 4 + C|  | 2 + (h 2 /2  0 ), A=N(0)(1-t), B= 0.1N(0)/(k B T c ) 2, C=0.55  2 N(0)  (  ) Core interactions dominate in useful materials

20. University of Wisconsin-Madison Applied Superconductivity Center I o. Summation and Scaling Strong pinning materials (Nb-Ti wires, irradiated HTS) often exhibit full summation –F p =n defects f pdefect Weak pinning requires statistical summation as already noted –many adjustable, often non-verifiable parameters Scaling of the global pinning force with H, T can often be seen: F p (B,T) = b p (1-b) q Nb-Ti often b(1-b), Nb 3 Sn b 0.5 (1-b) 2, b=B/B c2 HTS scaling functions complicated by thermal activation effects

21. University of Wisconsin-Madison Applied Superconductivity Center I p. The Irreversibility Field Suenaga, Ghosh, Xu, Welch PRL 66, 1777 (1991) 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)

22. University of Wisconsin-Madison Applied Superconductivity Center I q. Summary of Current Density Issues Enormous J c can be obtained in some systems –~10% of depairing current density (~H c / ) 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 J c To compute F p a priori in 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. University of Wisconsin-Madison Applied Superconductivity Center II. Basic Materials Issues Crystal Structures –Nb-Ti: body centered cubic simple, ductile –Nb 3 Sn: cubic A15 Crystal structure with range of off-stoichiometric compositions –Nb 3 Al 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 –MgB 2 : Mg cages B Only Nb-Ti is ductile! Essential Phase Diagram Information –well known for LTS, poorly known for HTS

24. University of Wisconsin-Madison Applied Superconductivity Center 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 H c2 increased too II a. Nb-Ti Phase Diagram

25. University of Wisconsin-Madison Applied Superconductivity Center II b. Nb-Sn Phase Relations T C C C: Cubic A15, higher H c2 phase, T: Tetragonal A15 phase TC Broad composition range 18-25at.%Sn, LT shear transformation to a small tetragonality, lowering T c and H c2

26. University of Wisconsin-Madison Applied Superconductivity Center II c. Nb 3 Sn 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. University of Wisconsin-Madison Applied Superconductivity Center II d. The BSCCO Family Tc ~30K ~70-95K ~105-110K CuO 2 Ca Bi-O double layer Sr  ~ 200-300  may be ~ 50

28. University of Wisconsin-Madison Applied Superconductivity Center II e. YBCO YBCO (YBa 2 Cu 3 O 7-x ) possesses the first crystal structure with T c > 77K It has defined cation stoichiometry 1:2:3, but O content is variable from 6-7 –T c > 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  = (m c /m a ) 0.5 of ~7 Cu-O chain layer CuO 2 layer Y Y Ba

29. University of Wisconsin-Madison Applied Superconductivity Center II f. MgB 2 Smaller B, larger Mg atoms

30. University of Wisconsin-Madison Applied Superconductivity Center Mg B CuO 2 Ca Bi-O double layer Sr Cu-O chain layer CuO 2 layer Y Y Ba a. b c d e II g. Higher Tc – greater complexity 9 K 18-23 K 39 K 92-95 K110 K

31. University of Wisconsin-Madison Applied Superconductivity Center II h. Summary Materials Issues Higher T c means greater crystal complexity –body centered cubic Nb-Ti with random site occupation, ductile phonon anomalies –Nb 3 Sn 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  is always an issue!

32. University of Wisconsin-Madison Applied Superconductivity Center 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).