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
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
OUTLINE







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
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
INTRODUCTION
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.
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
Main principles of RRR determination
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:
 AC    i
'
''
9    sinh(2a /  )  sin(2a /  ) 3
   

4  a  cosh(2a /  )  cos(2a /  ) 2
9    sinh(2a /  )  sin(2a /  ) 9   
    
  
4  a  cosh(2a /  )  cos(2a /  ) 4  a 
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*f/ ρ
RRR 
 300 K
 4.2 K
• 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]
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
2
Single crystal samples
 Sample N1 (as delivered)
 Sample N2, BCP, 70 μm
 Sample N3, BCP, 150 μm
(011)
800°C /2h
The single crystal samples of company Heraeus have
been used. The samples were cut out using EDM method.
1.3 - 2 mm
3 - 4.5 mm
Magnetic field applied along directions of type <100>, <011>, <111>
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
Equipment
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
Measuring contour
magnetic field
sample
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
Squid response
Superconducting solenoid for DC
fields + copper coils for AC fields
pick-up coil
compensating coils
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
Sample N1 (as delivered)
magnetic field along <111>
frequency extrapolation
B=2 T
B=1.5 T
B=1 T
Linear Fit
0.03
0.010
0.008
0.02
''
''
0.006
B=5 T
B=4.5 T
B=4 T
B= 3.5 T
B= 3 T
B=2.5 T
Linear Fit
0.004
0.01
0.002
0.00
0
5
10
15
20
25
30
0.000
0
10
f, Hz
20
30
40
50
f, Hz
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).
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
5000
frequency extrapolation
0.0005
T=2K B || <111>
Linear Fit
T=300K B=0 B || <111>
Linear fit
0.0004
4000
0.0003
3000
''
1/A2, Hz
Sample N1 (as delivered)
magnetic field along <111>, <110>, [100]
0.0002
2000
0.0001
1000
0
0.0000
0
1
2
3
4
5

Magnetic field dependence of coefficient 1/A2
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;
0
100
200
300
400
500
f, Hz
Imaginary part of AC susc. versus f
RRR (4-point DC method, I || [110], as delivered) = 269
RRR (4-point DC method, I || [111], as delivered) = 280
- good correlation with current results
RRR 
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
1/ A2
1/ A2
300 K
2K
Sample N2, 70μm BCP 800°C/2h annealing,
magnetic field along [100], <011>, <111>
T=300 K B=0T B || [100]
T=300 K B=3T
Linear Fit
0.0005
frequency extrapolation
T=2 K B || [100] B=3T
Linear Fit
0.003
0.0004
0.002
''
''
0.0003
0.0002
0.001
H=0: A2= 9.38617E-7(1.02402E-9)
H = 30 kOe: A2 = 9.69203E-7(8.29842E-10)
0.0001
0.000
0.0000
0
100
200
300
400
500
600
0
2
4
6
8
f, Hz
f, Hz
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.
10 12 14 16 18 20
B=3 T; B ||
RRR
[100]
169 (207 B=0T)
<011>
198
<111>
226
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
Sample N2, 70μm BCP 800°C/2h annealing,
magnetic field along [100]
B=3T B || [100] f=33Hz
0,000160
8000
B || [100] B=3T f=33 Hz
Linear Fit
7600
1/A2, Hz
0,000152
A2, 1/Hz
temperature extrapolation
0,000144
0,000136
7200
6800
0,000128
0
2
4
6
8
10
12
14
16
6400
T, K
0
RRR=166 (B || [100]) by temperature extrapolation method
RRR=169 (B || [100]) by frequency extrapolation method
1000
2000
3
T,K
3000
3
1/A2 dependence of T3
correlation of RRR values obtained by frequency and temperature extrapolation
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
Sample N3, 150μm BCP 800°C/2h
annealing magnetic field along [100]
0
1000
Nb fine grain (1400 C annealing)
14000
12000
N3 T=2K B|| [100]
Linear Fit
1/A2, Hz
10000
U, arb.units
800
600
without BCP - No effect
0.5 m BCP - No effect
200
0
6000
2000
80 m BCP Hc=0.29 T
400
8000
4000
20 m BCP Hc=0.33 T
0,0
0,5
, T
At B≥1.5 T curve 1/A2 vs B follows
the Kapitza law: R=K*f(B)
1,5
2,0
2,5
3,0
0H, T
B || [100]: RRR (Т=2K, B=0)= 205
B || [100]: RRR (Т=2K, B=3T)= 181
0
0.0 0.4 0.8 1.2 1.6 2.0 2.4 2.8
1,0
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
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA
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.
Symposium on the Superconducting Science and Technology of Ingot Niobium
September 22-24, 2010, Thomas Jefferson National Accelerator Facility, Newport News, VA