Superconducting magnets for High Energy Physics, Fusion, Magnetic Resonance Imaging (NMR) and Nuclear Magnetic Resonance, benefit from the extremely high current densities that can be achieved in superconductors compared to normal conducting materials. These magnets are usually constructed starting with a composite wire of typically 1 mm in diameter, in which the superconducting material is embedded in a copper matrix in the form of micrometer scale filaments. The present superconducting workhorse is Niobium-Titanium

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Godeke, Arno

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Lawrence Berkeley National LaboratoryLawrence Berkeley National LaboratoryTitlePerformance Boundaries in Nb3Sn SuperconductorsPermalinkhttps://escholarship.org/uc/item/6sv7x08fAuthorGodeke, ArnoPublication Date2006-05-01eScholarship.org Powered by the California Digital LibraryUniversity of CaliforniaPerformance Boundaries in Nb3Sn SuperconductorsArno GodekeBerkeley, CAMay 1, 2006A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  AcknowledgmentsBennie ten HakenHerman ten KateSasha Golubov…David LarbalestierPeter LeeAlex GurevichMatt JewellChad Fischer…University of TwenteA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependence (time allowing)Present status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Wire Jc progress versus timeParrell, ACE 2004A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Pinning capacityAverage grain sizeJc → Ic ?What determines Jc?Effective H – T phase boundaryCompositionStrain state+                                  = Jcat.% Sn and εA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What determines Ic?Powder-in-tube wire (SMI) 50% Non – Cu fractionOnly 20% of the wire carries Jc40% 25%10%25%JcA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition: Nb3Sn → Nb1 – β SnβBinary phase diagram → 18 to 25 at.% Sn → ‘A15’Charlesworth, JMS 1970, Flükiger, ACE 1982A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Nb3Sn diffusion reaction in wiresReaction at 675°C vs time in Powder-in-Tube wire (SMI)NbSn2, Cu, SnNb(Ta)6Sn5Nb(Ta)3SnNb(Ta)A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition variation in wiresComposition analysis on SMI Powder-in-Tube wire0.3 at.% Sn/μmJc(12T,4.2) =2250 A/mm2A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition variation in wiresBronze process wireUniv. of Geneva4 at.% Sn/μmJc(12T,4.2) =720 A/mm2Abächerli,TAS 2005A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition variation in wiresOST Internal-Tin wireFlat Sn content at 24 at.%Jc(12T,4.2) = 3000 A/mm2Uglietti, MT19 2005A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Increasing Jc with increasing SnJc(12T,4.2) =3000 A/mm224 at.% Snno gradientOSTInternal Tin Jc(12T,4.2) =2250 A/mm225 at.% Sn @ source0.3 at.% Sn/µm gradientSMIPowder-In-TubeJc(12T,4.2) =720 A/mm225 at.% Sn @ source4 at.% Sn/µm gradientGenevaBronze ProcessSn richerHigher JcWhy?A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What happens with changing Sn content?Pure Nbbcc Nb spacing 0.286 nmTc = 9.2 KNb3Sn → A15 unit cellbcc Sn, orthogonal Nb chainsNb spacing 0.265 nmHigh peaks in d-band DOSIncreased Tc = 18 KOff-stoichiometrySn vacancies unstableExcess Nb on Sn sitesAdditional d-bandLess electrons for chainsRounded off DOS peaksReduced TcA15 lattice and DOSDew-Hughes, Cryogenics 1975Sn NbA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Nb chain continuity, N(EF), λep, Tc, Hc2In generalSn deficiencyTetragonal distortion24.5 – 25 at.% SnStrainAlloying (Ti, Ta, …)DislocationsAnti-site disorderAll affect Nb chain integrity (‘Long Range Order’)And thus N(EF) and λepAnd thus Tc and Hc2A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Tc and Hc2 versus Sn contentSingle crystal, bulk and thin film samples( )c12.3 18.30.221 exp0.009T ββ−= +−⎛ ⎞+ ⎜ ⎟⎝ ⎠( ) 300 c2 10 exp 577 1070.00348H βμ β β− ⎛ ⎞= − + −⎜ ⎟⎝ ⎠A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Hc2(T ) versus Sn contentJewell, ACE 2004, bulk samplesSn richer A15 has higher Hc2(T ) (until ~ 24.5 at.% Sn)Less SnA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Hc2(T ) in wiresHc2(T ) from small current, resistive transitions1% normal stateA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Normalized Hc2(T ) all available resultsShape Hc2(T ) independent ofCompositionMorphologyStrain stateApplied critical state criterion( )( )( )( ) ( )0 c2c 0 B1.52c2c2 c1 1ln0 2 2 2Approximation:1 ,0 0D H TTT k TH t Tt tH Tμψ ψφ⎛ ⎞ ⎛ ⎞⎛ ⎞= − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠≅ − =A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Highest Hc2(T ) in wiresµ0Hc2(0) = 30 T, Tc(0) = 18 K is upper limitA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Pinning: Why does Nb3Sn need it?Nb3Sn slab in Hc1 < H < Hc2Field quanta φ0 = h / 2e (flux-lines) penetrate slabTransport current (∇×B = μ0J) causes gradient BxFlux-lines repel → move (∇×E = – dB/dt) → Ey → LossNeed to be ‘pinned’ at ‘pinning centers’ by ‘pinning force’ FPOptimal pinning at 1 pinning center / flux-linezyxHJvA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What determines pinning capacity?Pinning centersPositions with minima in SC wave functionNormal regionsGrain boundariesLattice imperfections…Nb3SnGrain boundaries→ Main pinning centersGrain size determines FPmaxA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What determines grain size?Presence of grain nucleation pointsReaction time and temperatureA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What is an optimal grain size?Ideal: One pinning center per flux-line → aΔ ≈ davFlux-line spacing → field dependentE.g. at 12 T aΔ = (4/3)¼(φ0/μ0H)½ = 14 nmGrain size in Nb3Sn wires → 100 – 200 nmOrder of magnitude from optimalFor any practical field aΔ << davCollective pinning (‘shearing’ of FLL) aΔ→ dav only for μ0H << 1 TNbTi in contrastNano-scale distribution of α-Ti precipitatesaΔ ≈ α-Ti distribution for application fieldsNbTi is fully optimizedA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What does aΔ << dav mean in practice?De-pinning → Synchronous shearing of FLLFPmax at H/Hc2 = 0.2About 6 T for Nb3SnFar below application fieldsGrain refinement / APCFPmax to higher fieldFPmax → H/Hc2 > 0.4 shown by Cooley, ACE 2002Higher fields accessible with Nb3SnMuch room for improvement!Example: Bronze processed ITER wire (Furukawa)BetterA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Alternative presentation aΔ << davFlux shear modelKramer JAP 1973aΔ << dav: Kramer plotLinear in H( ) ( ) ( )( )( )( ) ( )( )( )2.5 20.530 c2P 221 c2av50.250.5 0 c2c 01 av112.8 , GN/m11.1 101H h h HF H hHa H dH HJ Ha H dμκμμκ−⎡ ⎤= = ⎣ ⎦−−×∴ =−( ) ( ) ( ) ( )50.250.5K c 0 0 c2 K11.1 10       f H J H H H f H Hμ μκ×≡ ≅ − ∴ ∝A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  ‘Kramer’ plotPlot of fK(H ) at various temperaturesA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Are Kramer plots linear?Linearity from h ≅ 0.03 to 0.8Confirmed by measurementsaΔ ≅ dav only below h ≅ 0.03Different pinning mechanism?only below h ≅ 0.03Non-linearity below h ≅ 0.03Different pinning mechanismNon-linearity above h ≅ 0.8Inhomogeneity artifactsAveraging over Hc2 distribution( ) ( ) ( )( ) ( )2.520.50 c2P av21P Pmax12.8 1    1 0.5, 2qpHF h h h a dF h F h h p qμκ= −= − = =A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Effective Hc2(T )* for JcJc scales with ‘some’ average Hc2(T )*Jc gain if all A15 is stoichiometric?Jc(12T,4.2K)From 2250 A/mm2 to 2900 A/mm2A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity of Hc2(T )Longitudinal strain effects on effective Hc2(T )*Strain and composition have similar effectsNeed for a separation of parametersStrainA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity of Jc(H,T )Jc(10 T, T, εaxial) Jc(H, 8 K, εaxial)Why is strain sensitivity increased at higher H and T ?Higher T Higher HA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity versus compositionAt higher H and TLow Sn A15 sections “die out”Benefit PIT and IT vs Bronze:Larger volume fraction high SnHigh Sn sections determineSC propertiesIncreased strain sensitivityIs Sn rich A15 more strainsensitive than Sn poor A15 ?Does wire optimization through Sn enrichment cause higher strain sensitivity?Less SnA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity versus LROS → Bragg-Williams order parameterHigher LRO ( more Sn) → larger strain sensitivityFlükiger, ACE 1984A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain in ternary and binary wiresAlloyed → more disorder → reduced strain sensitivity?A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Prospects for critical current densityPinning?SMI-PIT grains ~ 140 nmOST-IT grains ~ 170 nm12 T → aΔ = 14 nmLarge gains possible25%40%10%25%Non-Cu: Ternary 64h/675°CC.M. FischerMS thesisUW-MadisonPIT measured: ~140nm, 40% A15 in non-CuOI-ST: ~170nm, ~60% A15 (?), 24%SnPIT, all           = best bit, ~140nm, 40% A15PIT,          +            =           65% A15, ~140nm, ~24%SnPIT,           +           =           65% A15, ~140nm, all best bitA15 QUALREAL ESTATE AND A15 QUALITYREAL ESTATE  Simulations on SMI-PIT Nb(Ta)3Snassuming all have same pinning5000 A/mm2 (+65%) physical limit with present wire designs?Unless pinning is improved4000 A/mm2 realistic optimization goal?A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  SummaryWire optimizations past decadeSn enrichmentA15 fraction in non-Cu optimizationPhysical limit 5 kA/mm2, realistic limit 4 kA/mm2Grain refinement / APCThe next big step?Grain size one order above optimalGrain 10 – 20 nm desired → nano technologyStrainStrain and composition parameter separation neededSn enrichment = more strain sensitivity?Much work to be done (3D, theory, bulk, film,…)A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  More informationAvailable on request → agodeke@lbl.govA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Optional theory sectionA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  N(EF) and λep → Tc and Hc2Weak coupling (BCS based)Interaction strength independent (Eliashberg based)( ) ( )Ec c c DB 0 F ep2 1 10 exp 0 1.134 exp( )eT Tk V N Eγωπ λ⎡ ⎤⎡ ⎤≅ − ∴ ≅ Θ −⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦( ) ( ) ( ) ( )0 c2 B F n c n c2B30 0 0eH k eN E T Tkμ ρ γρπ≅ =( ) ( )2ep 2Fdα ω ωλ ωω= ∫( )( )ep*epeff 0.28* *ep1 2 1.5 eλλ μλμ λ μ −−=+ +( )eff12 2c 12 20.25e 1Tλω=−0 c2Hμ =…A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Is Nb3Sn weak or strong coupling?Moore, PRB 1979, thin film samplesWeak coupling below 23 – 24 at.% SnStrong coupling approaching stoichiometryA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Applicable theoryN(EF) and λep → Tc and Hc2Wires → 18 – 25 at.% Sn, polycrystallineInteraction strength independent theoryNot done for entire composition rangeN(EF) and λep → Tc and Hc2 remains empiricalPromising recent workEliashberg-based description of Tc(ε ) and Hc2(ε )Markiewicz, Cryogenics 2004Oh, JAP 2006

Performance Boundaries in Nb3Sn Superconductors

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Performance boundaries in Nb<sub>3</sub>Sn superconductors

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Performance boundaries in Nb3Sn superconductors

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Performance Boundaries in Nb3Sn SuperconductorsArno GodekeBerkeley, CAMay 1, 2006A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  AcknowledgmentsBennie ten HakenHerman ten KateSasha Golubov…David LarbalestierPeter LeeAlex GurevichMatt JewellChad Fischer…University of TwenteA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependence (time allowing)Present status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Wire Jc progress versus timeParrell, ACE 2004A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Pinning capacityAverage grain sizeJc→ Ic ?What determines Jc?Effective H – T phase boundaryCompositionStrain state+                                  = Jcat.% Sn and εA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What determines Ic?Powder-in-tube wire (SMI) 50% Non – Cu fractionOnly 20% of the wire carries Jc40% 25%10%25%JcA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition: Nb3Sn → Nb1 – β SnβBinary phase diagram → 18 to 25 at.% Sn → ‘A15’Charlesworth, JMS 1970, Flükiger, ACE 1982A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Nb3Sn diffusion reaction in wiresReaction at 675°C vs time in Powder-in-Tube wire (SMI)NbSn2, Cu, SnNb(Ta)6Sn5Nb(Ta)3SnNb(Ta)A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition variation in wiresComposition analysis on SMI Powder-in-Tube wire0.3 at.% Sn/μmJc(12T,4.2) =2250 A/mm2A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition variation in wiresBronze process wireUniv. of Geneva4 at.% Sn/μmJc(12T,4.2) =720 A/mm2Abächerli,TAS 2005A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Composition variation in wiresOST Internal-Tin wireFlat Sn content at 24 at.%Jc(12T,4.2) = 3000 A/mm2Uglietti, MT19 2005A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Increasing Jc with increasing SnJc(12T,4.2) =3000 A/mm224 at.% Snno gradientOSTInternal Tin Jc(12T,4.2) =2250 A/mm225 at.% Sn @ source0.3 at.% Sn/µm gradientSMIPowder-In-TubeJc(12T,4.2) =720 A/mm225 at.% Sn @ source4 at.% Sn/µm gradientGenevaBronze ProcessSn richerHigher JcWhy?A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What happens with changing Sn content?Pure Nbbcc Nb spacing 0.286 nmTc = 9.2 KNb3Sn → A15 unit cellbcc Sn, orthogonal Nb chainsNb spacing 0.265 nmHigh peaks in d-band DOSIncreased Tc = 18 KOff-stoichiometrySn vacancies unstableExcess Nb on Sn sitesAdditional d-bandLess electrons for chainsRounded off DOS peaksReduced TcA15 lattice and DOSDew-Hughes, Cryogenics 1975Sn NbA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Nb chain continuity, N(EF), λep, Tc, Hc2In generalSn deficiencyTetragonal distortion24.5 – 25 at.% SnStrainAlloying (Ti, Ta, …)DislocationsAnti-site disorderAll affect Nb chain integrity (‘Long Range Order’)And thus N(EF) and λepAnd thus Tc and Hc2A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Tc and Hc2 versus Sn contentSingle crystal, bulk and thin film samples( )c 12.3 18.30.221 exp0.009T β β−= +−⎛ ⎞+ ⎜ ⎟⎝ ⎠( ) 300 c2 10 exp 577 1070.00348Hβμ β β− ⎛ ⎞= − + −⎜ ⎟⎝ ⎠A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Hc2(T ) versus Sn contentJewell, ACE 2004, bulk samplesSn richer A15 has higher Hc2(T ) (until ~ 24.5 at.% Sn)Less SnA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Hc2(T ) in wiresHc2(T ) from small current, resistive transitions1% normal stateA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Normalized Hc2(T ) all available resultsShape Hc2(T ) independent ofCompositionMorphologyStrain stateApplied critical state criterion( )( )( )( ) ( )0 c2c 0 B1.52c2c2 c1 1ln0 2 2 2Approximation:1 ,0 0D H TTT k TH t Tt tH Tμψ ψ φ⎛ ⎞ ⎛ ⎞⎛ ⎞= − +⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠≅ − ==A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Highest Hc2(T ) in wiresµ0Hc2(0) = 30 T, Tc(0) = 18 K is upper limitA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Pinning: Why does Nb3Sn need it?Nb3Sn slab in Hc1 < H < Hc2Field quanta φ0 = h / 2e (flux-lines) penetrate slabTransport current (∇×B = μ0J) causes gradient BxFlux-lines repel → move (∇×E = – dB/dt) → Ey→ LossNeed to be ‘pinned’ at ‘pinning centers’ by ‘pinning force’ FPOptimal pinning at 1 pinning center / flux-linezyxHJvA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What determines pinning capacity?Pinning centersPositions with minima in SC wave functionNormal regionsGrain boundariesLattice imperfections…Nb3SnGrain boundaries→ Main pinning centersGrain size determines FPmaxA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What determines grain size?Presence of grain nucleation pointsReaction time and temperatureA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What is an optimal grain size?Ideal: One pinning center per flux-line → aΔ ≈ davFlux-line spacing → field dependentE.g. at 12 T aΔ = (4/3)¼(φ0/μ0H)½ = 14 nmGrain size in Nb3Sn wires → 100 – 200 nmOrder of magnitude from optimalFor any practical field aΔ << davCollective pinning (‘shearing’ of FLL) aΔ→ dav only for μ0H << 1 TNbTi in contrastNano-scale distribution of α-Ti precipitatesaΔ ≈ α-Ti distribution for application fieldsNbTi is fully optimizedA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  What does aΔ << dav mean in practice?De-pinning → Synchronous shearing of FLLFPmax at H/Hc2 = 0.2About 6 T for Nb3SnFar below application fieldsGrain refinement / APCFPmax to higher fieldFPmax→ H/Hc2 > 0.4 shown by Cooley, ACE 2002Higher fields accessible with Nb3SnMuch room for improvement!Example: Bronze processed ITER wire (Furukawa)BetterA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Alternative presentation aΔ << davFlux shear modelKramer JAP 1973aΔ << dav: Kramer plotLinear in H( ) ( ) ( )( )( )( ) ( )( )( )2.5 20.530 c2P 221 c2av50.250.5 0 c2c 01 av112.8 , GN/m11.1 101H h h HF H hHa H dH HJ Ha H dμκμμ κ− ⎡ ⎤= = ⎣ ⎦−−×∴ = −++( ) ( ) ( ) ( )50.250.5K c 0 0 c2 K11.1 10       f H J H H H f H Hμ μκ×≡ ≅ − ∴ ∝A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  ‘Kramer’ plotPlot of fK(H ) at various temperaturesA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Are Kramer plots linear?Linearity from h ≅ 0.03 to 0.8Confirmed by measurementsaΔ ≅ dav only below h ≅ 0.03Different pinning mechanism?only below h ≅ 0.03Non-linearity below h ≅ 0.03Different pinning mechanismNon-linearity above h ≅ 0.8Inhomogeneity artifactsAveraging over Hc2 distribution( ) ( ) ( )( ) ( )2.520.50 c2P av21P Pmax12.8 1    1 0.5, 2qpHF h h h a dF h F h h p qμκ= −= − = =+ A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Effective Hc2(T )* for JcJc scales with ‘some’ average Hc2(T )*Jc gain if all A15 is stoichiometric?Jc(12T,4.2K)From 2250 A/mm2 to 2900 A/mm2A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity of Hc2(T )Longitudinal strain effects on effective Hc2(T )*Strain and composition have similar effectsNeed for a separation of parametersStrainA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity of Jc(H,T )Jc(10 T, T, εaxial) Jc(H, 8 K, εaxial)Why is strain sensitivity increased at higher H and T ?Higher T Higher HA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity versus compositionAt higher H and TLow Sn A15 sections “die out”Benefit PIT and IT vs Bronze:Larger volume fraction high SnHigh Sn sections determineSC propertiesIncreased strain sensitivityIs Sn rich A15 more strainsensitive than Sn poor A15 ?Does wire optimization through Sn enrichment cause higher strain sensitivity?Less SnA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain sensitivity versus LROS→ Bragg-Williams order parameterHigher LRO (? more Sn) → larger strain sensitivityFlükiger, ACE 1984A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Strain in ternary and binary wiresAlloyed → more disorder → reduced strain sensitivity?A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  OutlineCritical current density and critical currentComposition variation in Nb3Sn wiresComposition and Hc2(T )Pinning capacity, grain boundary pinning, grain sizeComposition and JcStrain dependencePresent status and future prospectsA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Prospects for critical current densityPinning?SMI-PIT grains ~ 140 nmOST-IT grains ~ 170 nm12 T → aΔ = 14 nmLarge gains possible25%40%10%25%Non-Cu: Ternary 64h/675°CC.M. FischerMS thesisUW-MadisonPIT measured: ~140nm, 40% A15 in non-CuOI-ST: ~170nm, ~60% A15 (?), 24%SnPIT, all           = best bit, ~140nm, 40% A15PIT,          +            =           65% A15, ~140nm, ~24%SnPIT,           +           =           65% A15, ~140nm, all best bitA15 QUALREAL ESTATE AND A15 QUALITYREAL ESTATE  Simulations on SMI-PIT Nb(Ta)3Snassuming all have same pinning5000 A/mm2 (+65%) physical limit with present wire designs?Unless pinning is improved4000 A/mm2 realistic optimization goal?A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  SummaryWire optimizations past decadeSn enrichmentA15 fraction in non-Cu optimizationPhysical limit 5 kA/mm2, realistic limit 4 kA/mm2Grain refinement / APCThe next big step?Grain size one order above optimalGrain 10 – 20 nm desired → nano technologyStrainStrain and composition parameter separation neededSn enrichment = more strain sensitivity?Much work to be done (3D, theory, bulk, film,…)A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  More informationAvailable on request → agodeke@lbl.govA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Optional theory sectionA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  N(EF) and λep→ Tc and Hc2Weak coupling (BCS based)Interaction strength independent (Eliashberg based)( ) ( )Ec c c DB 0 F ep2 1 10 exp 0 1.134 exp( )eT Tk V N Eγωπ λ⎡ ⎤⎡ ⎤≅ − ∴ ≅ Θ −⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦=( ) ( ) ( ) ( )0 c2 B F n c n c2B30 0 0eH k eN E T Tkμ ρ γρπ≅ =( ) ( )2ep 2Fdα ω ωλ ωω= ∫( )( )ep*epeff 0.28* *ep1 2 1.5 eλλ μλ μ λ μ −−= + +( )eff12 2c 12 20.25e 1Tλω=− 0 c2Hμ =…A. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Is Nb3Sn weak or strong coupling?Moore, PRB 1979, thin film samplesWeak coupling below 23 – 24 at.% SnStrong coupling approaching stoichiometryA. Godeke – May 1, 2006 Performance Boundaries in Nb3Sn Superconductors – Berkeley, CA  Applicable theoryN(EF) and λep→ Tc and Hc2Wires → 18 – 25 at.% Sn, polycrystallineInteraction strength independent theoryNot done for entire composition rangeN(EF) and λep→ Tc and Hc2 remains empiricalPromising recent workEliashberg-based description of Tc(ε ) and Hc2(ε )Markiewicz, Cryogenics 2004Oh, JAP 2006

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