Low Temperature Properties of Materials - USPAS

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1.2 Low Temperature Properties of Materials „

„

Materials properties affect the performance of cryogenic systems. Properties of materials vary considerably with temperature „

„ „

„

„

Thermal Properties: Heat Capacity (internal energy), Thermal Expansion Transport Properties: Thermal conductivity, Electrical conductivity Mechanical Properties: Strength, modulus or compressibility, ductility, toughness Superconductivity

Many of the materials properties have been recorded and models exist to understand and characterize their behavior „ „ „

Physical models Property data bases (Cryocomp®) NIST: www.cryogenics.nist.gov/MPropsMAY/material%20properties.htm

What are the cryogenic engineering problems that involve materials? USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

1

Cooldown of a solid component Cryogenics involves cooling things to low temperature. Therefore one needs to understand the process. „

m

Ti = 300 K

If the mass and type of the object and its material are known, then the heat content at the designated temperatures can be calculated by integrating 1st Law.

dQ = Tds = dE + pdv „

m

Tf = 80 K

Liquid nitrogen @ 77 K USPAS Cryogenics Short Course

~0

The heat removed from the component is equal to its change of internal energy,

⎛ Ti ⎞ ⎜ ΔE = m ∫ CdT ⎟ ⎜T ⎟ ⎝ f ⎠

Boston, MA 6/14 to 6/18/2010

2

Heat Capacity of Solids „

„

„

C(T)

General characteristics:

The heat capacity is defined as the change in the heat content with temperature. The heat capacity at constant volume is, ∂s ∂E C = T Cv = and at constant pressure, p ∂T ∂T v

0

T(K)

p

3rd Law: C

These two forms of the heat capacity are related through the following thermodynamic relation, 2 1 ∂v ⎞ Tvβ 2 ∂v ⎞ ∂p ⎞ ⎟⎟ κ = − C p − Cv = −T ⎟ ⎟ = v ∂p ⎠T ∂T ⎠ p ∂v ⎠T κ Note: Cp – Cv is small except for gases, where ~ R = 8.31 J/mole K.

USPAS Cryogenics Short Course

Isothermal compressibility

Boston, MA 6/14 to 6/18/2010

300

0 as T

β =−

0

1 ∂v ⎞ ⎟ v ∂T ⎠ p

Volume expansivity 3

Heat Capacity of Solids (Lattice Contribution) „

Lattice vibration (Phonon) excitations are the main contribution to the heat capacity of solids at all except the lowest temperatures.

„

Internal energy of a phonon gas is given by E ph = „

D(ω) is the density of states and depends on the choice of model

„

n(ω) is the statistical distribution function

1

n(ω ) =



e „

h ωdωD(ω )n(ω ) ∫ 2π

2πk BT

−1

h = Planck’s constant = 6.63 x 10-34 J.s kB = Boltzmann’s constant = 1.38 x 10-23 J/K

Debye Model for density of states „

Constant phonon velocity

„

Maximum frequency = ωD

„

Debye temperature: ΘD = hωD/2πkB

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

4

Debye Internal Energy & Heat Capacity In Debye model the internal energy and heat capacity have simple forms

E ph C ph „ „

⎛T ⎞ = 9 RT ⎜⎜ ⎟⎟ ⎝ θD ⎠ ⎛T ⎞ = 9 R⎜⎜ ⎟⎟ ⎝ θD ⎠

3x

3x

K-l

„

x3 ∫0 dx e x − 1 D

D

∫ dx (e 0

x 4e x x

− 1)

2

where x = hω/2πkBT and xD = ΘD/T Limits: „

„

T > ΘD, C ≈ 3R ph T << ΘD, C

ph

R = N0kB =

(Dulong-Petit value)

⎛T ⎞ ≈ 234 R⎜⎜ ⎟⎟ ⎝θD ⎠

3

8.31 J/mole K (gas constant)

USPAS Cryogenics Short Course

Example

Boston, MA 6/14 to 6/18/2010

5

Values of Debye Temperature (K) Metals1

ΘD

Non-metals & Compounds2

ΘD

Ag

225

C (graphite)

2700

Al

428

C (diamond)

2028

Au

165

H2 (solid)

105-115

Cd

209

He (solid)

30

Cr

630

N2 (solid)

70

Cu

343

O2 (solid)

90

Fe

470

Si

630

Ga

320

SiO2 (quartz)

255

Hf

252

TiO2

450

Hg

71.9

In

108

Nb

275

Ni

450

Pb

105

Sn

200

Ti

420

V

380

Zn

327

Zr USPAS Cryogenics Short Course

291

The Debye temperature is normally determined by measurements of the specific heat at low temperature. For T << ΘD,

C ph

⎛T ⎞ ≈ 234 R⎜⎜ ⎟⎟ ⎝ θD ⎠

3

Kittel, Introduction to Solid State Physics Timmerhaus and Flynn, Cryogenic Process Engineering

1 2

Boston, MA 6/14 to 6/18/2010

6

Electronic Heat Capacity (Metals) T=0 „

„

f(ε)

The free electron model treats electrons as a gas of particles obeying Fermi-Dirac statistics

T>0

Ee = ∫ εdεD(ε ) f (ε )

Where

1

f (ε ) =

ε −ε f

e

k BT

+1

2

N⎞ ⎛ ε f ≡ 2 ⎜ 3π 2 ⎟ V⎠ 8π m ⎝ h

ε

εφ 2

3

3

V ⎛ 8π m ⎞ 2 12 ⎜ 2 ⎟⎟ ε D(ε ) = 2 ⎜ 2π ⎝ h ⎠ 2

„

and

„

At low temperatures, T << εf/kB ~ 104 K

1 2 Ce ≈ π D (ε f )k B2T = γT 3 The electronic and phonon contributions to the heat capacity of copper are approximately equal at 4 K

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

7

Summary: Specific Heat of Materials General characteristics: „

„

„

Specific heat decreases by ~ 10x between 300 K and LN2 temperature (77 K) Decreases by factor of ~ 1000x between RT and 4 K Temperature dependence „ „ „

C ~ constant near RT C ~ Tn, n ~ 3 for T < 100 K C ~ T for metals at T < 1 K

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

8

Thermal Contraction „

All materials change dimension with temperature. The expansion coefficient is a measure of this effect. For most materials, the expansion coefficient > 0 D D-ΔD

T1 T~2 < 300 T1K

Linear expansion coefficient

α=

1 ∂L ⎞ 1 β = ⎟ L ∂T ⎠ p 3

ΔL

For isotropic materials

Bulk expansivity (volume change):

1 ∂v ⎞ 1 ∂ρ ⎞ ⎟⎟ β= ⎟ =− ρ ∂T ⎠ p v ∂T ⎠ p Expansivity caused by anharmonic terms in the lattice potential USPAS Cryogenics Short Course

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9

Temperature dependence to α and β „

Most materials contract when cooled „

„

„

The magnitude of the effect depends on materials Plastics > metals > glasses

Coefficient (α) decreases with temperature „

Thermodynamics:

C p − Cv =

Tvβ 2

From Ekin (2006)

→0

κ ∂s ⎞ ∂v ⎞ ⎟⎟ → 0 = − ⎟ ∂p ⎠T T →0 ∂T ⎠ p

(Third law: s

T →0

0)

USPAS Cryogenics Short Course

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10

Expansion coefficient for materials

USPAS Cryogenics Short Course

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11

Thermal contraction of supports „

TH L

A

„

ΔL (greatly exaggerated)

m m T TLL

„

L Actual T(x)

x

The change in length of a support is determined by the temperature distribution along the support Tabulated ΔL/L values are for uniform temperature of support For non-uniform temperature L

TH

0

T (x)

ΔL = ∫ dx ∫ α (T )dT Where T(x) is defined according to, TH

TL

TH

USPAS Cryogenics Short Course

TH

⎛ x⎞ ( ) = k T dT ⎜ ⎟ ∫ k (T )dT ∫T ⎝ L ⎠ TL x

Boston, MA 6/14 to 6/18/2010

12

Thermal stress in a composite A2 A1 L „

Assumptions: „

Composite is stress free at T0

„

Materials remain elastic: σ

„

No slippage at boundary

„

Ends are free

= E yε

Force balance

F1 = σ 1 A1 = F2 = σ 2 A2 ε1 =

ΔL ΔL − L 1 L composite

ε2 =

ΔL ΔL − L composite L 2

⎡ ⎤ ⎢ ΔL − ΔL ⎥ L L 1 2 ⎥ σ 1 = E y1ε1 = E y1 ⎢ ⎞⎥ ⎢ ⎛1 + E y1 A1 ⎜ ⎢⎣ ⎝ E y 2 A2 ⎟⎠ ⎥⎦ USPAS Cryogenics Short Course

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13

Electrical conductivity of materials „

The electrical conductivity or resistivity of a material is defined in terms of Ohm’s Law: V = IR V

L I

R = dV/dI

A

V

I „

„

Heat generation by electrical conduction Q = I2R Conductivity (σ) or resistivity (ρ) are material properties that depend on extrinsic variables: T, p, B (magnetic field)

R=

ρL A

=

USPAS Cryogenics Short Course

L σA

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14

Instrumentation leads „

TH

An instrumentation lead usually carries current between room temperature and low temperature „

L

A

m TL Instrumentation lead

„ „

„

Leads are an important component and should be carefully designed „

„

USPAS Cryogenics Short Course

Material selection (pure metals vs. alloys) Lead length determined by application Optimizing the design

Often one of the main heat loads to the system Poor design can also affect one’s ability to make a measurement.

Boston, MA 6/14 to 6/18/2010

15

Cryogenic temperature sensors „

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„

A temperature sensor is a device that has a measurable property that is sensitive to temperature. Measurement and control of temperature is an important component of cryogenic systems. Resistive sensors are frequently used for cryogenic temperature measurement R(T ) =

V I

T

„

Knowing what temperature is being measured is often a challenge in cryogenics (more later)

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

16

Electrical Conductivity in Metals „

Resistivity in metals develops from two electron scattering mechanisms (Matthiessen’s rule) „

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„

„

Electron-phonon scattering, T > ΘD Scattering probability ~ mean square displacement due to thermal motion of the lattice: ~ kBT and ρ ~ T Electron-defect scattering (temperature independent), T << ΘD Scattering depends on concentration of defects ρ ~ ρ0 ~ constant; Residual Resistivity Ratio (RRR = ρ(273 K)/ρ0) indication of the purity of a metal Intermediate region, T ~ ΘD/3 ρ ~ (phonon density) x (scattering probability) ~ T5 Scattering process:

l

USPAS Cryogenics Short Course

“l “ is the mean free path τ is the mean scattering time = l/vf Boston, MA 6/14 to 6/18/2010

17

Resistivity of Pure Metals (e.g. Copper)

dR/dT ~ constant Residual Resistivity

R ~ constant

USPAS Cryogenics Short Course

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18

Kohler plot for Magneto-resistance The resistance of pure metals increases in a magnetic field due to more complex electron path and scattering (Why?) How to use a Kohler plot?

Copper

1. 2. 3. 4.

Determine RRR of metal Compute product: RRR X B Use graph to estimate incremental increase in R (or ρ). Add to base value

Example: RRR = 100 B = 10 T

( ) = 1000

ΔR/R = 3 R(10 T)/R(0 T) = 4 RRR (equival.) = 25 USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

19

Electrical conductivity of alloys Electrical resistivity of various alloys (x 10-9 Ω-m) (from Cryocomp) Alloy

10 K

20 K

50 K

100 K

200 K

300 K

RRR

AL 5083

30.3

30.3

31.3

35.5

47.9

59.2

1.95

AL 6061-T6

13.8

13.9

14.8

18.8

30.9

41.9

3

304 SUS

495

494

500

533

638

723

1.46

BeCu

56.2

57

58.9

63

72

83

1.48

Manganin

419

425

437

451

469

476

1.13

Constantan

461

461

461

467

480

491

1.07

Ti-6%Al4%V

1470

1470

1480

1520

1620

1690

1.15

4.0

5.2

16.8

43.1

95.5

148

37

PbSn (56-44)

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

20

Electrical conductivity of semiconductors „ „ „ „ „

Carrier concentration Energy gap Impurity concentration ρ ~ 10-4 to 107 Ω−m Basis for low temperature thermometry Log R

Conductivity depends on the number of carriers in the conduction band.

T(K) USPAS Cryogenics Short Course

Nc ≈ e Boston, MA 6/14 to 6/18/2010



Eg k BT

21

Steady heat leak of a support „

TH

The cross section and length of the support is determined by the requirements of the application „ „

L

A

m TL

„

Gravitational loading, vibration, etc. Strength of material used for support

Heat leak is determined by the temperature dependent thermal conductivity of the material, k(T) and physical dimensions (A, L) TH

⎛ A⎞ Q = ⎜ ⎟ ∫ k (T )dT ⎝ L ⎠ TL

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

22

Thermal Conductivity of Materials „

The thermal conductivity is defined in terms of the relationship between the temperature gradient and heat flux (Fourier’s Law):

dT Q& = −k (T )A dx

A

Note that in general k(T) and may vary significantly over the temperature range of interest „

dT/dx x

Two contributions to the thermal conductivity „ „

„

T

Electronic contribution dominates in pure metals Lattice (Phonon) contribution mostly in insulating materials

Kinetic theory

1 k = ρCvl 3

ρC = volumetric heat capacity v = characteristic velocity l = mean free path

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

23

Electronic Thermal Conductivity „

Free electron model:

k=

π 2 nk B2Tτ 3me

Recall: τ is scattering time = l/v

~ constant at high temperature ~ T at low temperature „

Weidemann-Franz law (for free electron model) k

σ „

= f (T ) =

π 2 k B2 3e 2

T ≡ L0T

L0 = Lorentz number = 2.443 x 10-8 WΩ/K2

Note that no real material obeys the W-F law, although it is a good approximation at low T and near and above RT.

USPAS Cryogenics Short Course

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24

Thermal Conductivity of Pure Metals

Copper

k~T k ~ constant

USPAS Cryogenics Short Course

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25

Lorentz Number for Pure Metals

USPAS Cryogenics Short Course

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26

Thermal Conductivity (continued) „

„

„

„

„

Thermal conduction by lattice vibrations (phonons) is a significant contributor to overall heat conduction particularly in non-metals and alloys. Metals (Alloys): ktotal = kelectrons + kphonons (Typ. 1 to 3 orders less than that of pure metals) Insulating crystals only have lattice contribution, which can be large for single crystals (e.g. Al2O3, Sapphire) Insulating polymers have very low thermal conductivity (Nylon, Teflon, Mylar, Kapton) Insulating composites have complex behavior depending on components

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

27

Examples „

Low temp. range, k ~ Tn with 1 < n < 3 Pure metals and crystalline insulators Alloys

Non-crystalline Non-metallics

USPAS Cryogenics Short Course

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28

Thermal Conductivity Integrals T2

k (T1 , T2 ) = ∫ k (T )dT

, [W/m]

T1

To use the graph

k (T1 , T2 ) = k (0, T2 ) − k (0, T1 ) Heat conduction along a rod A T2

T1 L

Q = k (T1 , T2 )

Many materials can be approximated by k ~ Tn

A L

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

29

Contact Resistance (conductance) „

„

Joints or contacts can lead to considerable resistance in a thermal (electrical) circuit. Contact resistance can vary considerably depending on a number of factors „ „

Bulk material properties (insulators, metals) Surface condition (pressure, bonding agents)

Q

Q Heat transfer coefficient

Q = hcAΔT

ΔTc

ideal USPAS Cryogenics Short Course

real Boston, MA 6/14 to 6/18/2010

30

Thermal contact conductance (conductive) Contact point between two materials can produce significant thermal resistance

M

llic a t e

y Dr

co

ds n o b

ts c a nt

l) (A

h~T

Example: USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

31

Bo nd ed

Contact conductance (Insulating)

y Dr

co

ts c a nt

h ~ T3

USPAS Cryogenics Short Course

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32

Mechanical Properties F

Definitions Stress:

dx

A

x

USPAS Cryogenics Short Course

σ=

F [N] A

dx Strain: x σ FA Modulus: E y = = ε dx x

; σu & σ y

ε=

Boston, MA 6/14 to 6/18/2010

[Pa]

33

Ey and σy at Low Temperatures

USPAS Cryogenics Short Course

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34

σy and Elongation at Low Temp

USPAS Cryogenics Short Course

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35

Figure of Merit (FOM) for structural support materials „

„

„

Simple structural supports in cryogenic systems should be designed to minimize conductive heat leak, Q. Note that Q = -kAΔT/L and A = F/σ, force/allowable stress in the material. Thus, for a constant load, the best material for supports has a minimum value of k/σ. Material

k/ σ (4 K), W/Pa*m*K k/σ (80 K) W/Pa*m*K k/ σ (300 K) W/Pa*m*K

304 ss

0.042

1.8

3.7

6061 T6 AL

2.8

36

57

G-10

0.008

0.057

0.19

brass

1.3

21

46

345

566

523

copper Note all values x 10^-8

TH L

A

m TL

Note that for a simple structural support, the cross sectional area is determined by the room temperature properties. USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

36

Superconducting Materials „

„ „

„

„

„

„

Superconductors are special materials that have (near) zero electrical resistance at low temperature Main application for superconductors is magnet technology LTS (low temperature superconductors) are used in most magnets and consist of niobium alloys (NbTi & Nb3Sn) coprocessed with copper or copper alloys HTS are ceramics and have seen some use in magnet systems. Main materials are BSCCO and YBCO Both LTS and HTS are fabricated with normal metal (copper or silver) to provide strength and electrical protection Additional normal materials (copper stabilizer or structural support) to optimize conductor for final application. Other applications (Electronics, sensors)

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

37

Superconducting vs. Resistive Materials „

Resistive Material „ „ „ „

„

V = IR; P = I2R Copper and copper alloys Aluminum and Al alloys Stainless steel

V

I

Superconducting Materials „ „ „

V = 0 below Ic V ~ In above Ic Transport properties depend on „ „ „ „

Temperature Magnetic field Metallurgical processes Strain in conductor

USPAS Cryogenics Short Course

Rm

V Ic

(I/Ic)n n ≈ 10-40

I

Boston, MA 6/14 to 6/18/2010

38

Elemental superconductors „

~ 1/3 elements are Type I superconductors „

„

Not suitable for high field, current applications

Tc (transition from superconductor to normal state) „ „

„

Critical Temperature and Critical Field of Type I Superconductors

7.2 K for Pb 1.2 K for Al

μ0Hc (critical field) „ „

80 mT for Pb 10 mT for Al

USPAS Cryogenics Short Course

Material

TC (K)

µ0H0 (mT)

Aluminum

1.2

9.9

Cadmium

0.52

3.0

Gallium

1.1

5.1

Indium

3.4

27.6

Iridium

0.11

1.6

Lead

7.2

80.3

Mercury α

4.2

41.3

Mercury β

4.0

34.0

Osmium

0.7

6.3

Rhenium

1.7

20.1

Rhodium

0.0003

4.9

Ruthenium

0.5

6.6

Tantalum

4.5

83.0

Thalium

2.4

17.1

Thorium

1.4

16.2

Tin

3.7

30.6

Tungsten

0.016

0.12

Zinc

0.9

5.3

Zirconium

0.8

4.7

Boston, MA 6/14 to 6/18/2010

39

Practical LTS Superconductors “Critical Surface”:

• Jc is defined by flux pinning • Hc2 determined by alloy composition (e/a, crystal structure) • Tc by alloy composition

USPAS Cryogenics Short Course

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40

Processing NbTi into Wire Form: • Billet diameter ≈ 10” • Extrusion ratio ≈ (20)2 • Draw ratio ≈ (15)2 Final diameter ≈ 1 mm • Heat Treatment @ 375 C anneal copper create grain structure • Final product (1 mm wire) Cu:SC ratio (1:1-4:1) Ic ≈ 500 A @ 5 T • Final processing: Cabling, insulation, etc.

USPAS Cryogenics Short Course

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41

NbTi/Cu Wire: „

„ „

„

„

Final wire is a composite of copper and ≈ 1000 NbTi filaments. Filament diameter is ≈ 10 μm. Good metallurgical properties allow the wire to be processed to optimum properties, insulated and then wound into coil. Fine filaments are required for stability of the SC strand and to reduce AC loss Copper “stabilizer” provides alternate current path if superconductor becomes “normal”

USPAS Cryogenics Short Course

Copper

Boston, MA 6/14 to 6/18/2010

NbTi

42

Nb3Sn/Cu wire Nb3Sn „

„

„

„

„

Sn core Diffusion barrier Copper

Nb3Sn is a metallurgical compound produced by solid state reaction at ≈ 700 C for 100 hours Grown from pure Nb + Sn or from Nb + bronze (15% Sn in copper) Diffusion barrier (Ta) prevents Sn from mixing with Cu stabilizer Final wire (after reaction) is brittle In coil applications, Nb3Sn conductor is often wound first then reacted. This requires a high temperature insulation system

USPAS Cryogenics Short Course

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43

Comparison of Jc between Nb3Sn & NbTi Jc = Ic/Asc; Asc may include material that is not superconducting, but not low resistivity

USPAS Cryogenics Short Course

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44

Oxide superconductors (BSCCO & YBCO) „

„

„ „

„

Ag/BSCCO PIT available from industry but is difficult to process & handle (high cost) poor mechanical properties, anisotropic superconducting properties Requires “wind and react” approach Useful for T > 4 K operation at low to moderate field Useful for T ≈ 4 K at high fields (B > 20 T)

Ag

BSCCO

Conductor cross section: ~ 4 mm x 0.5 mm

USPAS Cryogenics Short Course

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45

Examples of High Temperature Superconductors (HTS) (B)

Bi2Sr2Ca1Cu2Ox/AgMg tape

Cross-section, 5 by 0.2 mm

Bi2Sr2Ca1Cu2Ox/AgMg round wire

(D) Cross-sections are roughly to scale

Bi2Sr2Ca2Cu3Ox/Ag

(A) ( C)

(F)

~0.5 mm

BSCCO: Structure of ceramic filaments in silver-alloy Can be partially or fully substituted with Rare Earth metals: Y,Gd, Sm, Eu, Dy, Nd

Y1B2C3Ox: “Coated Conductor” USPAS Cryogenics Short Course

< 0.1 mm

20μm Cu

2 μm Ag 1 μm HTS ~ 30 nm LMO ~ 30 nm Homo-epi MgO ~ 10 nm IBAD MgO

50μm Hastelloy substrate 20μm Cu

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46

Jc of High Temperature Superconductors 4.2 K

10000

YBCO B⊥ Tape Plane YBCO B|| Tape Plane Nb-Ti

Complied from ASC'02 and ICMC'03 papers (J. Parrell OIOI-ST)

JE (A/mm²)

1000

427 filament strand with Ag alloy outer sheath tested at NHMFL

2212

YBCO Insert Tape (B|| Tape Plane)

100 MgB2

Minimum practical Je

SuperPower tape used in record breaking NHMFL insert coil 2007

RRP Nb3Sn

10

Maximal JE for entire LHC Nb­Ti strand production (–) CERNT. Boutboul '07, and (- -) <5 T data from Boutboul et al. MT-19, IEEETASC’06)

18+1 MgB2/Nb/Cu/Monel Courtesy M. Tomsic, Tomsic, 2007

0

5

10

YBCO Insert Tape (B⊥ Tape Plane) MgB2 19Fil 24% Fill (HyperTech)

Bronze Nb3Sn

2212 OI-ST 28% Ceramic Filaments NbTi LHC Production 38%SC (4.2 K)

4543 filament High Sn BronzeBronze-16wt.%Sn16wt.%Sn0.3wt%Ti (Miyazaki(MiyazakiMT18MT18-IEEE’ IEEE’04)

15

20

Nb3Sn RRP Internal Sn (OI-ST) Nb3Sn High Sn Bronze Cu:Non-Cu 0.3

25

30

35

40

45

Applied Field (T) Engineering critical current density in HTS and LTS conductors. Image courtesy of Peter Lee, USPAS Cryogenics Short Course Boston, MA 6/14 to 6/18/2010 http://magnet.fsu.edu/~lee/plot/plot.htm (October 2008)

47

Stress effects in SC? I V

ε > 0; ε = 0

V

I

F „

In NbTi, the stress effects are largely reversible up to ≈ 2% until filament breakage

Ey (NbTi) ≈ 82 GPa σU (ε= 2%) ≈ 2200 MPa Ey (NbTi) ≈ 82 GPa σU (ε= 2%) ≈ 130 MPa Composite is average between Copper and NbTi

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

48

Stress Effects in Nb3Sn • For Nb3Sn, Ic can increase • with strain- reversible effect • Ic increase depends on ratio • Nb3Sn to Bronze (Cu) • Bronze content in 1-4 is • greater than in 5-7 • irreversible degradation • > 0.5% past peak

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

49

Precompression of Nb3Sn Bronze Nb3Sn „

„

Composite of bronze and Nb3Sn is processed at high temperature ≈ 700 C (1000 K) then cooled to near 0 K for operation Integrated thermal contraction: ∆L/L (1000 K to 0 K) ≈ 0.8% for Nb3Sn & 1.8% for Br

σ Nb Sn 3

⎛ ΔL ΔL ⎞ ⎛ E Nb3 Sn EBr ⎞ ⎟⎜ =⎜ − ⎟ ABr L L EA + EA ⎝ Nb3 Sn Br ⎠ ⎝ Br ⎠ Nb 3Sn ≈ 1%

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

50

HTS 3-Ply Conductor, Tension RT and 77 K 0.2

Strain (%)

0.4

0.6

Normalized Ic [-]

1.2 1 0.8

Irreversible strain limit

0.6 0.4

Normalized Ic @ RT

0.2

Normalized Ic @ 77 K

0 0.0

60.0

120.0

180.0

240.0

300.0

360.0

Stress [MPa]

Critical stresses/strains ~ 200 MPa/0.4% (RT), 300 MPa/0.6% (77 K) USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

51

Superconducting Materials Summary „

„

„

„

NbTi/Cu conductor technology is well developed, with good mechanical and electromagnetic properties up to moderate magnetic fields ≈ 12 T Nb3Sn/Cu conductor is also readily available although is less reliable, costs more and is more challenging to incorporate in magnets. Significant strain degradation. BSCCO (2212 & 2223)/Ag and YBCO are the most advanced HTS conductors and are available in long lengths. Strain degradation is an issue. Other superconductors have been and are being applied in special cases, but reliable conductor technology is not available.

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

52

Low Temperature Materials- Summary „

„

Selection of proper material is important to proper design of cryogenic systems Extensive data base of materials properties „

„ „

„

New materials are being developed and introduced into cryogenic systems „ „

„

CryocompTM (thermal and transport properties) – available for download from Blackboard NIST documentation Others??

Composites (Zylon, etc.) Alloys

Other issues „ „

Contact resistance Mechanical properties of bonds, welds, etc..

USPAS Cryogenics Short Course

Boston, MA 6/14 to 6/18/2010

Knowledge base is incomplete

53

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Low Temperature Properties of Materials - USPAS

1.2 Low Temperature Properties of Materials „ „ Materials properties affect the performance of cryogenic systems. Properties of materials vary consi...

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