Symposium on the Superconducting Science and Technology of Ingot Niobium September 22-24, 2010,...

Symposium on the Superconducting Science and Technology of Ingot Niobium September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA

A New Approach for RRR Determination of Niobium Single Crystal Based on AC Magnetic Susceptibility

A. Ermakov, A. V. Korolev*, W. Singer, X. Singer

presented by A. Ermakov

Deutsches Elektronen-Synchrotron, Hamburg, Germany* Institute of Metal Physics, Ekaterinburg, Russia


Introduction Main principles of RRR determination Single crystal samples Equipment RRR data obtained by AC magnetic susceptibility Comparison with RRR obtained by DC method Summary

OUTLINE


Residual resistivity ratio (RRR) value is an important characteristic of material purity. AC magnetic susceptibility of a number of single crystal niobium samples for different orientations of type <100>, <011>, <111> and treatments (BCP 70, 150 µm, annealing 800°C/2h) were measured. The RRR value was determined on base of these results using a relation between the imaginary part ’’ of AC magnetic susceptibility at low frequency f of AC magnetic field and resistivity ρ of the sample: ’’ = k*f/ρ.

INTRODUCTION


2

3

)/2cos()/2cosh(

)/2sin()/2sinh(

4

9

aa

aa

a

2

4

9

)/2cos()/2cosh(

)/2sin()/2sinh(

4

9

aaa

aa

a

The AC susceptibility caused by eddy current can be expressed for spherical sample in terms of it radius α, and the skin penetration depth δ:

δ = 1/(πμ0μσf)0.5= (ρ/(πμ0μf)0.5

μ0 = 4π×10-7 H/m; μ - the relative permeability; ρ – resistivity; f - frequency.

AC method: at low f - χ’’ can be expressed as χ’’=A1+A2*f. In homogeneous sample A1=0, A2=k*σ (k=const); σ =1/ρ ;1/A2=ρ/k; σ – electrical conductivity

K

KRRR24

300

.

Main principles of RRR determination

• Magnetic susceptibility of superconductors and other spin systems, Ed. By Robert A. Hein et. al., Plenum Press New York, 1991, page. 213 [A. F. Khoder, M. Gouach, Early theories of χ’ and χ’’ of superconductors for controversial aspects]

''' iAC

’’ = k*f/ ρ


Sample N1 (as delivered) Sample N2, BCP, 70 μm Sample N3, BCP, 150 μm

The single crystal samples of company Heraeus have been used. The samples were cut out using EDM method.

800°C /2h

(011)

Magnetic field applied along directions of type <100>, <011>, <111>

1.3 - 2 mm

3 - 4.5 mm

Single crystal samples


The Quantum Design MPMS 5XL SQUID Magnetometer uses a (SQUID) detector is extremely sensitive for all kinds of AC and DC magnetic measurements. Magnetic moments down to 10-8 emu (G*cm3) (10-11 Am2 ) can be measured. The MPMS has a temperature range between 1.9 K and 400 K, the superconducting magnet can reach magnetic fields up to 5 T. Multiple functions make possible in particular following: A supplement for measuring anisotropic effects of magnetic moments An addition for measuring electrical conductivity (magneto-resistance) and Hall constant AC susceptibility measurements which yield information about magnetization dynamics of magnetic materials

sample

Equipment

Superconducting solenoid for DC fields + copper coils for AC fields

AC-method: h = hasin(2πf), h – intensity of AC magnetic field, ha – amplitude value of h, f - frequency

ha = 0.1 – 4 Oe; f = 3 – 1000 Hz

compensating coils

pick-up coil

Squid responseMeasuring contour

magnetic field


Frequency dependencies of imaginary part of AC-susceptibility for different values of applied magnetic field. At low frequency at B < 3T observed the scattering of the points

(left figure). At B ≥ 3 T change of the curve slope (right figure).

0 5 10 15 20 25 300.00

0.01

0.02

0.03 B=2 T B=1.5 T B=1 T Linear Fit

''

f, Hz0 10 20 30 40 50

0.000

0.002

0.004

0.006

0.008

0.010

B=5 T B=4.5 T B=4 T B= 3.5 T B= 3 T B=2.5 T Linear Fit

''f, Hz

Sample N1 (as delivered) magnetic field along <111> frequency extrapolation


At B 3 T – Kapitza linear law - R=K*f(B) (normal conducting state): 1/A2 [RRR] (T=2K, B=0) = 3532, at Т = 300 К: RRR(T=300K, B=0) = 1095290

<111> B=0 RRR = 310;<110> B = 3 T: RRR = 270; B = 0 RRR 280 – 300; [100] B = 3 T: RRR = 260; B = 0 RRR 280 – 300;

Magnetic field dependence of coefficient 1/A2

RRR (4-point DC method, I || [110], as delivered) = 269RRR (4-point DC method, I || [111], as delivered) = 280- good correlation with current results

Imaginary part of AC susc. versus f

K

K

AA

RRR2

300

2/12/1

Sample N1 (as delivered) magnetic field along <111>, <110>, [100]

0 100 200 300 400 500

0.0000

0.0001

0.0002

0.0003

0.0004

0.0005 T=300K B=0 B || <111> Linear fit

''

f, Hz0 1 2 3 4 50

1000

2000

3000

4000

5000T=2K B || <111>

Linear Fit

1/A

2, H

z

frequency extrapolation


0 100 200 300 400 500 6000.0000

0.0001

0.0002

0.0003

0.0004

0.0005 T=300 K B=0T B || [100] T=300 K B=3T Linear Fit

''

f, Hz

H=0: A2= 9.38617E-7(1.02402E-9)H = 30 kOe: A2 = 9.69203E-7(8.29842E-10)

Frequency dependencies of imaginary part of susceptibility at B=0; 3T (T=2K; 300K). Angle

between the curves at B=0; 3T (T=300K) shows the small magnetoresistivity.

Sample N2, 70μm BCP 800°C/2h annealing, magnetic field along [100], <011>, <111> frequency extrapolation

B=3 T; B || RRR

[100] 169 (207 B=0T)

<011> 198

<111> 226

0 2 4 6 8 10 12 14 16 18 200.000

0.001

0.002

0.003 T=2 K B || [100] B=3T Linear Fit

''

f, Hz


1/A2 dependence of T3

0 2 4 6 8 10 12 14 16

0,000128

0,000136

0,000144

0,000152

0,000160

A2,

1/H

z

T, K

B=3T B || [100] f=33Hz

RRR=166 (B || [100]) by temperature extrapolation method RRR=169 (B || [100]) by frequency extrapolation method

0 1000 2000 3000

6400

6800

7200

7600

8000 B || [100] B=3T f=33 Hz Linear Fit

1/A

2, H

z

T3, K3

correlation of RRR values obtained by frequency and temperature extrapolation

Sample N2, 70μm BCP 800°C/2h annealing, magnetic field along [100]

temperature extrapolation


At B≥1.5 T curve 1/A2 vs B follows the Kapitza law: R=K*f(B)

B || [100]: RRR (Т=2K, B=0)= 205B || [100]: RRR (Т=2K, B=3T)= 181

Sample N3, 150μm BCP 800°C/2h annealing magnetic field along [100]

Similar bend at definite magnetic fields was observed on DC magnetic resistance.

This bend is probably caused by transition from SC to normal conducting state of niobium

0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.80

2000

4000

6000

8000

10000

12000

14000 N3 T=2K B|| [100] Linear Fit

1/A

2, H

z

, T

0,0 0,5 1,0 1,5 2,0 2,5 3,0

0

200

400

600

800

1000

20 m BCP Hc=0.33 T

80 m BCP Hc=0.29 T

U, arb

.units

0H, T

Nb fine grain (14000C annealing)

without BCP - No effect 0.5 m BCP - No effect


Summary

One more approach for determination the RRR values by means of AC-susceptibility examined RRR values for main crystallographic orientations of Nb single crystals are obtained Good correlation with results for RRR obtained by 4 point DC method The magnetic field dependence of value R follows to the Kapitza law R=K f(B) The advantage of this method is possibility to measure simultaneously the different magnetic and transport properties such as a very small values of resistivity. Determination of resistivity can be done by taking into account the size and the shape of the sample.

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Symposium on the Superconducting Science and Technology of Ingot Niobium September 22-24, 2010,...

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