Strain effect on the critical temperatures of superconducting Nb3Ge tapes

CqYJ~rnk~ 0 Printed

36 ( 1996) 579-%X

1996 Elsevier

in Great Britain.

SOOll-2275(96)00029-X

All

Science

Limited

rights

reserved

Ml I I -227Y9bl$

I S.00

ELSEVIER

Strain effect on the critical temperatures of superconducting Nb,Ge tapes Y. Nakagawa

and M. Umeda

Electrotechnical Laboratory, lbaraki 305, Japan

Frontier Technology

Division,

l-l-4

Umezono,

Tsukuba,

Received 29 August 1995; revised 17 December 1995 The resistively measured critical temperature, T,, was found to increase by 0.4-0.6 K due to an applied strain of about 0.5% for chemical-vapour-deposited Nb,Ge tapes that had different Nb,Ge layer thicknesses and different Nb/Ge composition ratios. The TCshave also been measured using a magnetization method for these tapes and the Nb,Ge films made by removing the O.l-mm thick Hastelloy substrates from the Nb,Ge tapes. The triaxial strain analysis that includes measurements of lattice spacing showed that both the hydrostatic and the non-hydrostatic strain components may considerably contribute to the T, strain effect in the present Nb,Ge tapes. 0 1996 Elsevier

Science

Limited

Keywords: Nb,Ge tape; bending strain effect; critical temperature

Nomenclature

a,

Lattice spacing

Thickness of Hastelloy substrate Thickness of Nb,Ge layer Elastic modulus at 4.2 K E Elastic modulus at 293 K E, Volume strain component, E,+E,+E~ Length of a separated Nb,Ge film and a ;, substrate tape at the deposition temperature 1x2h Length of a separated substrate tape at measurement temperature 1X2” Length of a separated Nb,Ge film at measurement temperature Final length of a Nb,Ge film and its 1x3 substrate tape r Bending radius Superconducting critical temperature TC T T, at a strain-free state T, at applied strain E T:‘(E) Tc (E,, ) T, at applied strain E, T Magnetically measured T, TI,” Resistively measured T, T, (on) Onset T, T, (mid) Midpoint T, T, (end) Fully superconducting T, Volume fraction V

D d

Greek letters a

Mean thermal expansion coefficient for temperature region between deposition

temperature (1107 K) and measurement temperature (4.2 K) Mean thermal expansion coefficient between room temperature (293 K) and measurement temperature (4.2 K) Mean thermal expansion coefficient between deposition temperature ( 1107 K) and room temperature (293 K) Coefficient of volume strain term, e, in Equation ( 10) Difference between deposition temperature ( 1107 K) and measurement temperature (4.2 K) Difference between deposition temperature ( 1107 K) and room temperature (297K) Coefficient of non-hydrostatic strain term in Equation (10) Coefficient of ( 1/2)e2 in Equation ( 10) Applied strain Applied strain in longitudinal direction Applied virtual strain at maximum T, in TC-~ curve, if no cracks are formed in the Nb3Ge layer. For specimen A, we regarded the value of E’, as that of E,. For specimens B and C, the applied strain at the strain components ratio E_JE,= 1.7, which is valid for specimen A Applied strain corresponding to observed maximum T, in T,-•E curve Applied strain at zero intrinsic strain calculated assuming a uniaxial strain Applied strain at zero intrinsic strain in

Cryogenics

1996 Volume

36, Number

8

579

Strain effect on T, of Nb,Ge

tape: Y. Nakagawa

longitudinal direction calculated assuming triaxial strain Intrinsic strain expressed as E-E,,, EO Residual strain calculated assuming a EP uniaxial strain Internal strain components l&& E,,E~,,,E~” Residual strain components in Nb,Ge E..ZB1 Eya,Eza Additive strain components when E, is applied

and M. Umeda a

Among conventional low-critical-temperature (T,) superconductors, the A-15 structure Nb3Ge compound has the highest T,, 22 K’, and a high upper critical field Hc2, 34 T’. Recently, low-T, Nb,Sn cryocooler-cooled superconducting magnets with high-T, oxide superconductor current leads have been developed3. Furthermore, Nb,Sn fibre-reinforced superconductors have been investigated for use in Tokamak fusion reactors4. For such purposes, Nb3Ge superconductors having high T, and Hcz values may possibly be used instead of Nb3Sn superconductors. In practical superconducting tapes and wires, the dependence of applied strain, E, on the relationship between critical current density, J,, and magnetic field, H, namely, J, (H, E), is important when superconducting coils are designed. This dependence has already been studied for a series of A-15 structure superconductors, such as Nb,Sn, Nb,Al, Nb,Ge and V3Ga5. Ekin proposed that J, (H,E) is scaled by the strain-dependent upper critical field, Hc2 (E)~. The Hc2 is closely related to T,. Whereas there are many reports on the strain effect on J, for A-15 structure superconductors, there are few reports on the strain effect on T, for superconductors other than Nb,Sn. In this study, we measured the bending strain effect on T, for Nb3Ge tapes that have different Nb,Ge layer thicknesses and different Nb/Ge composition ratios. In an attempt to explain the experimental results, we performed uniaxial and triaxial strain analyses. Finally, we compared the strain effect on T, for Nb,Ge tapes with that for bronzeprocessed Nb$n wires reported by Luhman et aL7 and by Kuroda and Wada6.

Materials

and methods

A chemical-vapour-deposition method was used to deposit the Nb,Ge compound on both sides of Hastelloy B tape substrates that were 2.5 mm wide and 0.1 mm thickg. Hastelloy B (MO: 28%, Fe: 5%, Ni: 67%) was supplied by Mitsubishi Materials Co. We used three Nb,Ge tapes (labelled A, B and C) of different Nb,Ge layer thicknesses and Nb/Ge composition ratios. The layer thickness was controlled by the moving speed of the substrate tape during deposition, and the composition ratio by the delivered chloride gas ratio (Nb/Ge). The characteristics of the tapes are shown in Table I. The ratio of Nb/Ge for specimen A was slightly less than those for specimens B and C, and the layer thickness of specimen C was significantly less than those of specimens A and B. The dependence of T, on bending strain, E, was measured using a four-probe resistance method. To avoid any effect of the edge of the Nb,Ge tapes on the T, change during bending, both edges of each tape were removed, thus reducing the width of each tape from the original 2.5 mm to 2.1 mm. The sample tapes were 15-30 mm long and the distance between a pair of voltage leads was about 6 mm.

580

Cryogenics

1996 Volume

36, Number

8

Poisson’s ratio Stress Additive stress

V

u o,

Subscripts additive Hastelloy Nb,Ge

: n

Table 1 Chemical vapour deposition (CVD) process conditions and Nb,Ge layer thickness of superconducting Nb,Ge tapes

Specimen

A

Deposition temperature (“C)

Ratio of chloride gases introduced in CVD apparatus (Nb/Ge)

Moving speed of Nb,Ge substrate layer tape thickness (cm min-r) (pm)

834 834 834

3.5 3.6 3.6

4 4 32

11.7x2 10.6 x 2 1.3x2

For the measurements of the dependence of T, on E, we used a copper block of various curvatures, which allowed us to choose the bending radius, r, from infinity (i.e. a flat plane) to 3.6 mm. We fixed the tape using a copper wire 0.5 mm in diameter. We visually confirmed (using a telescope) that the tape was in close contact with the copper block in liquid NZ. For T, measurements, the temperature difference due to the sample position on the copper block was within 0.1 K, and the accuracy of the T, measurements was within 0.2 K. For each Nb3Ge tape, two samples were measured, with opposite sides bent towards each other. For all three tapes, there was no significant difference in the dependence of T, on E between these pairs of samples, confirming that the Nb,Ge compound was homogeneously deposited on both sides of the tape. To make Nb,Ge samples that were strain free in all three dimensions, we fabricated Nb,Ge films (about 2.5 mm x 3 mm in size) by first grinding off one side of the Nb,Ge layer in each of the Nb3Ge tapes, and then etching out the O.l-mm thick Hastelloy substrate. The lattice spacing for both tapes and films was measured using an X-ray diffractometer with Ni-filtered Cuk, radiation. We determined the value of the lattice spacing by extrapolating to 180” the 20 values computed from several diffraction peaks, namely, from (400) to (610), to an accuracy within 0.002 A. T, was also measured magnetically using a SQUID magnetometer.

Experimental

results

Figure I shows the temperature dependence of resistivity at various r values for specimen A as an example. We started the measurements at r = infinity, and decreased it to r = 4.6 mm for this specimen. Figures 2-4 show T, as a function of both r and E for specimens A, B and C, respectively. The range of E values created in the outer Nb,Ge layer is calculated using the formula

Strain effect on T, of Nb,Ge

tape: Y. Nakagawa

and M. Umeda

-.--.._

L

t

20

Tc (on)

P

-619

i

l-

-. Specimen0 (lo.6 km)

18 16

17

18

20

21

t

22

Tlg(K)

I

Figure 1 Normalized resistivity at various bending radii as a function of temperature for Nb,Ge tape of specimen A with Nb,Ge layer thickness of 11.7 pm per side

Bending radius 25.015,,12.1,0,t 7.6 6 .pm)

.-.w..

.---_rre--.

.A-

.

-

--r

.-.\

A

I

I

f..-

b Tc(end) I 1 I I

I

I70

‘.

.A

..-.

__ I

1

I

I

0.5

1.5

Applied Strain E :%I Figure 3 T, as a function of applied strain, E, or bending radius, r, for Nb,Ge tape of specimen 6. Parameter E, is the applied virtual strain at the maximum T, in the T,-•E curve, if no cracks are formed in the Nb,Ge layer, corresponding to the applied strain at a strain component ratio of E$E~= 1.7, which is valid for specimen A

4.6

t \

A

.

4’. ‘a E,, Gil ‘,. ‘\. \

Tc(on)

Tc (mid)

t #I,. Em-_.

0 &lied

Strain E 1%)

1.5

Figure 2 T, as a function of applied strain, E, or bending radius, r, for Nb,Ge tape of specimen A. Parameter d,,, is the applied strain at which T, peaked in the T,-•E curve. Parameter E,, is the applied strain at zero intrinsic strain calculated assuming a uniaxial strain and E,,, is the applied virtual strain at the maximum T, in the T,-•E curve, if no cracks are formed in the Nb,Ge layer. For specimen A, we regarded the value of d, as that of E,

Dl( 2r+2d+D)

5~5

(2d+D)l(

2r+2d+D)

(1)

where d and D are the thicknesses of the Nb@e layer and the Hastelloy substrate in the Nb,Ge tapes, respectively (see Figure 7). The horizontal bars in Figures 2-4 show the calculated strain range. As T, at the outer surface is highest in the outer Nb3Ge layer when T, increases with E, we took the highest value in each strain range as a true E value, considering the tendency of the T, (mid)+ curve. To determine if there was any irreversible effect of E, we measured T, at r = 03 again after the measurements at r =15.1 mm (open circles). The difference between this vaule and that measured at a virgin state (solid circle at r = “) was within the experimental error, confirming that the T, change was reversible up to the r = 15.1 mm point. The parameter E’, in Figures 2-4 is the strain at which T, peaked in the T,-•E curves. Tables 2 and 3 show the values of Elm, T, (E = E’,) and T, (E = 0) for all specimens. We found that the difference between T, (mid) at E = E’, and

17

0

’

’

’

’

’ ’ ’ ’ ’ I ’ 0.5 Applied Strain & (k-1

I

I

I 1.5

Figure 4 T, as a function of applied strain, f, or bending radius, r, for Nb,Ge tape of specimen C. Parameter E, is the applied virtual strain at the maximum T, in the Tc-c curve, if no cracks are formed in the Nb,Ge layer, corresponding to the applied strain at a strain component ratio of &= 1.7, which is valid for specimen A

that at E = 0 was 0.60 K for specimen A, 0.63 K for specimen B, and 0.38 K for specimen C. Figure 5 shows the temperature dependence of magnetization for the Nb3Ge tape and the Nb,Ge film of specimen B as an example. After a sample was zero-field cooled, its temperature was raised at intervals of 0.5 K under a magnetic field of 10 Oe applied normal to the plane of the tape or the film. For all specimens (A, B and C) the tape contained two ‘undamaged’ Nb,Ge layers, whereas the film contained many cracks that were produced when the substrate Hastelloy was removed from the tape during the fabrication of the film. Accordingly, there were differences between the demagnetization factors for the tapes and the films. Therefore, the difference between the magnetically measured T, for the tapes and films was not necessarily accurate, except near T, (on). The accuracy of the determi-

Cryogenics

1996 Volume

36, Number

8

581

Strain effect on T, of Nb,Ge

tape: Y. Nakagawa

T, at applied strain E = 0, E = E’, and E = E,, magnetically

Table 2 Resistively measured tapes and Nb,Ge films

T, (mid) (resistive)

Specimen A

Tape Film” Tape Film Tape Film

6 C

and M. Umeda

(K)

T, (end) (resistive)

measured

T, and lattice spacing for Nb,Ge

T, (on) (magnetic) (K)

(K)

Lattice spacing (A)

E=O

E = El,*

E=E,b

E=O

E=e’,

t=E,

l=O

E=O

E= E,

19.93

20.53

20.53

19.70

20.37

20.37

20.26

20.43d

19.45

20.04

20.23d

18.25

18.63

18.82d

18.00

18.43

18.62d

5.162 5.150 5.165 5.150 5.175 5.160

5.155”

19.63

19.5 21.0 19.5 20.5 18.0 19.5

5.157” 5.167”

BE’, is the applied strain at which T, peaked in the T,--E curve b E, is the applied virtual strain at the maximum T, in the T,--E curve, if no cracks are formed in the Nb,Ge layer. For specimen we regarded the value of E’, as that of E,. For specimens 6 and C, we took the applied strain at a strain components ratio E&= 1.7, which is valid for specimen A “Film was made by removing the Hastelloy substrate from the tape dObtained by a linear extrapolation e Calculated using Equations (7) and (9) Table 3 Poisson’s ratio calculated for Nb,Ge specimens, E, and calculation parameters Mean thermal expansion coefficient Tape component

Occupied layer thickness (pm)

1107-u4.2 K 1107-?93 (-1O-6 K-‘)

11.7x2 10.6 x 2 1.3x2

Nb,Ge A B C Hastelloy

6.81 ‘%14

B 100

11.39’6,”

applied strain at maximum

T,, E’,, calculated applied strains, E,,, dm3, and

Elastic modulus E 4.2 K

K

7.21’3.‘4

1 2.8816

E‘ 293 K (GPa)

Poisson’s ratio v

Applied strain at maximum T,.

,

Calculated

220’5

0.23 0.27 0.24

225”

211

0.3120

0.61 0.50 0.51

applied strain

b

&la

2,

21315

A,

%

;k 0.41 0.42 0.49

0.42 0.42 0.49

0.61 0.65 0.73

a &n? is the applied strain at zero intrinsic strain calculated assuming uniaxial strain b~‘,Q is the applied strain at zero intrinsic strain in the longidudinal direction calculated assuming triaxial strain “For E,, (elastic modulus at 4.2 K for Hastelloy), we used a value of 1.07 times E,,, (=211 GPa) where 1.07 is the ratio of E,, to E,,, given by Schwartz and KnightI

. *

0.2

. I .

. . u.

. . I. . . ’ I . ’ .. I

’ . .

onset SpecimenB (10.6 pm)

0.0 -

sQ) -0.2

-

2 g -0.4 c g-0.6

-

-0.8 -1 .o 0

.&

5

10

20

25

I 30

Figure 5 Temperature dependence of magnetization for Nb,Ge tape and Nb,Ge film of specimen B. The film was made by removing the O.l-mm thick Hastelloy substrate from the Nb,Ge tape nation of T, (on) is estimated to be about 0.25 K. As shown in the enlarged plots in Figure 5, magnetically measured T, (on) for the film was 1 .O K higher than that for the tape of specimen B. The difference between the T, (on) for the film and the tape was 1.5 K for specimens A and C (plots not shown). These results are presented in Table 2.

582

Cryogenics

1996 Volume

36, Number

8

Figure 6 shows the X-ray diffraction patterns of the (200), (210), (211) and (400) lines for the tape and the film of specimen A and for the tape of specimen B. The patterns show the single phase of the A-15 structure with a strongly textured (200) line. By comparing the X-ray pattern of the (400) line for the tape with that for the film of specimen A, we see that the lattice spacing for the tape was larger than that for the film (Figure 6a2 and b2). Specimens B and C showed a similar tendency. For all films, the lattice spacing measured at the substrate side was similar to that at the outer side. The results for the lattice spacing are shown in Table 2. The lattice spacing for specimen C was higher than that for specimens A and B, whose values of T, were higher than for specimen C.

Discussion Because the thermal expansion coefficient of the substrate Hastelloy is larger than that of the Nb,Ge compound, the Nb,Ge compound is subjected to a compressive strain when the temperature is lowered from the deposition temperature to the measurement temperature. It is well known that in bronze-processed Nb,Sn mono-filament superconductors that have A-15 structure, the T, in the T,--E chracteristics usually increases as tensile strain l increases7.8. After peak-

Strain effect on T, of Nb,Ge (al )

Specimen A

g

Tape

r

s

i=

5.

buL. W

g

s Et ,

5.

1

, a. Specimen A Film (7

Side)

tape: Y. Nakagawa

and M. Umeda

a thicker one. The effects of composition and layer thickness on E’, are similar to those seen in tensile strain studies of J,--E characteristics for similar specimens”‘. In that case, the values of E’, were 0.44%, 0.43% and 0.46% for specimens A, B and C (with a 25-km copper layer on both sides), respectively.

Uniaxial strain analysis The prestrain, lp, produced in the Nb,Ge layer when the temperature of the Nb,Ge tape was changed from the deposition temperature to the measurement temperature can be calculated in the framework of the uniaxial strain by assuming that the composite materials of the Nb,Ge tape remain elastic. The resulting equation” is

lP = - AT ( a”---(Y,,)EhV,,/(E,Vn+EhV,,)

Figure6 X-ray diffraction patterns of the (200), (210). (211) and (400) lines for Nb,Ge tape and Nb,Ge film of specimen A and for Nb,Ge tape of specimen B

ing, T, gradually decreases as E continues to increase. In our case, T, (end) for specimens A, B and C, and T, (mid) for specimens A and B, decreased abruptly as E exceeded the E’, at which T, peaked in the T,-•E curve. This abrupt decrease is almost certainly caused by the occurrence of cracks in the outer Nb,Ge layer. The inner Nb,Ge layer is subjected to a compressive strain by bending. Consequently, the Tcs of the inner Nb,Ge layer may be lower than that at E = 0 in the T,--•E curves in Figures 2-4. The inner-side compressed NbJGe layer may be more resistant to cracks than the outer layer. Therefore, the T,s at E above l‘,, whose values are lower than that at E = 0, may mostly be those of the inner-side compressed Nb,Ge layer. T, (on) at E > E’,,, seems to indicate the T, (on) of the outer-side Nb,Ge layer, which has many cracks but a T, as high as that at E = E’,,, because of relief of stress by the cracks. When E exceeded i,,, we temporarily took the midpoint of each strain range as the true E value, as shown in Figures 2-4. It is probable that the value of E’, is smaller than the virtual strain value E, corresponding to the maximum T, if no cracks are formed in the Nb,Ge layer, as was previously reported for the J,-•E characteristics of similar samples’“. As mentioned above, we found that the Nb,Ge films were usually cracked due to their removal process from the Hastelloy substrate. We confirmed by optical microscopy that the film of specimen B contained significantly more cracks than that of specimen A, which suggests that the Nb,Ge layer of specimen B is more easily cracked than that of specimen A. This explains why the E’, for specimen B (0.50%) was lower than that for specimen A (0.61%). This difference in cracking may be due to a slight difference in the crystal texture between the two specimens that arose from the slight difference in their composition. When compared with the Nb,Ge tape of specimen A, the X-ray pattern of the (400) line for the Nb,Ge tape of specimen B had a broad line-width and no sign of a split between the k,, and k,? lines, as shown in Figures 6~2 and c2. This is due to nucleation of the Nb,Ge, particles which were ascertained from SEM micrographs for the Nb,Ge tape of specimen B”. The reason why the E’,, for specimen B (0.50%) was lower than that for specimen C (0.51%) is that a thinner Nb,Ge layer is more resistant to cracks than

(2)

where LYis the mean thermal expansion coefficient in the temperature region between the deposition temperature ( 1107 K) and the measurement temperature (4.2 K), E is the elastic modulus at 4.2 K, V is the volume fraction, AT is the temperature difference and subscripts n and h indicate Nb,Ge and Hastelloy B components, respectively. In the calculation of lP in Equation (2), the accuracy of each parameter is important. Here we obtain LY,from a,, (the thermal expansion coefficient in the temperature range of 1107 K to 293 K) and a,, (that in the temperature range of 293 K to 4.2 K). For (Y,, of the Nb,Ge studied here that had a lattice constant of 5.150 A, we take the average of two referenced values for Nb,Ge compounds that had different lattice constants, though we cannot tell whether cr, depends directly on the lattice constant of the sample or not. The first referenced value was for a temperature range of 1107 K to 293 K for samples that had a lattice constant of 5.159 A’3, and the other was for a range of 675 K to 293 K for a lattice constant of 5.144 A’“. For (Y,,, we took this latter referenced value. For the elastic constant of Nb,Ge, we approximate a value from Bussiere et ~1.“. For the thermal expansion coefficient of Hastelloy B, ahr (from 1 107 K to 293 K), we used the value given in the manufacturer’s specification sheetsih, which is a value similar to that given by Touloukian et al.“. For (Y,,,(from 293 K to 4.2 K), we used the value given by Touloukian ef al.“. We determined the elastic constant of Hastelloy B at 293 K, E,,, by measuring the stress-strain characteristics of Hastelloy tape similar to that used as the substrate. We found that this measured value was similar to that listed in the specification sheets” and that given by Schwartz and Knight’*. For E,, (at 4.2 K), we used a value of 1.07 times E,,,, in which 1.07 is the ratio of Eh to Ehr given by Schwartz and Knight”. We estimated that the error in d in Equation ( 1) is within lo%, that for D is 2% and that for r is 0.2 mm. Thus, the error for the applied strain calculated using Equation ( 1) is within about 0.03%. Using the values of the parameters shown in Table 3”-“, we calculated ep for specimens A, B and C as -0.41%, -0.42% and -0.49% (in this case a compressive strain). Accordingly, assuming uniaxial strain, the estimated applied bending strains, the E,,s, at which the intrinsic strain in the longitudinal direction may become zero, are 0.4 l%, 0.42% and 0.49% for these specimens, respectively. Table 3 and Figures 2-4 (arrows) show the values of E,,, for specimens A, B and C. Although for both specimens B

Cryogenics

1996 Volume

36, Number

8

583

Strain effect on T, of Nb,Ge

tape: Y. Nakagawa

and M. Umeda

and C, E,, is near the strain at the maximum T,, d,, for specimen A, E,,,, (= 0.41%) is significantly lower than E’, (= 0.61%). The term that most affects Equation (2) is (Y.-C+ If E,, is equal to i, (= 0.61%) for specimen A, the value of (Y,--LY,,should be 6.75 x 10e6, instead of the 4.58 x 10m6 obtained from the referenced values of (Y,= -6.81 x 10v6 and (Y,,= -11.39 x lOA, as in Table 3. Triaxial strain analysis By assuming the triaxial strain, Welch” showed that the residual strains in the plane of the Nb3Ge layer, E,, E,,,, and that perpendicular to it, lZn, are expressed, under the condition that the thickness of the tape is very small compared to the length and breadth, as E, = EY”= -AT ( (Y,--(Y,,)E,,V,, (l-v,)/{E,V,, + &V,(l-r+l)l

(l-v,)

(3)

EZ”= _-2lJ”,E,/( l-u,)

(4)

where u is Poisson’s ratio (see Figure 7 and Appendix). When v, is equal to v,,, Equation (3) reduces to Equation (2). To obtain the values of E,, lyn and E,, for our specimens, we used the following method. Because the change in the elastic constants between 297 K and 4.2 K is small for the Nb,Ge and Hastelloy, eZn is expressed as

= 4

%r%d%nr = %“r%l~Gl, T ( an-w,)/{AT, ( G--LY,,, )>

(5)

where eznr is the residual strain at 297 K and AT, is the difference between the deposition temperature ( 1107 K) and room temperature (293 K). In this equation, E,,, is expressed as EZ”r= {a,( tape) -a,( film)}/u,( film),

(6)

where a, is a lattice spacing, which is usually measured in the direction normal to a film or tape plane. From Equations

Figure7 Three-dimensional strain state for specimen A. ‘0’ denotes the strain-free state in all three dimensions, corresponding to the Nb,Ge film, ‘A” denotes the residual strain state calculated assuming a uniaxial strain, ‘A’ denotes the residual strain state calculated assuming a triaxial strain, ‘6’ denotes the strain state at zero intrinsic strain in the longitudinal direction assuming a triaxial strain and ‘C’ denotes the strain state where T, was a maximum at the applied bending strain E= E’m = 0.61%

584

l, = E, + E, = E,, + (2d+D)l( 2r+2d+D)

Cryogenics

1996 Volume

36, Number

8

(7)

EY= Em + Eyan= Em -v, E, -E,,D* (v,,--v,)/{(2r+2d+D) (E,,D+4E,d) - D( v,E,,D+4v,E,d)}

(8)

and ez = EZ”+ Ezan= E,” - V”E,

and

%” =

(3)-(6) and the parameters presented in Table 3’3-‘8,20, we obtained values of E,,, eyn, lZn and u, for specimens A, B and C. The residual strain state for specimen A, for example, is described by ‘A’ in Figure 7. The values of v, for specimens A, B and C thus calculated are presented in Table 3. When a bending strain, E,,, is applied in the longitudinal direction of the Nb3Ge tape, the strain components in the Nb,Ge, E,, lY and lz are expressed as (see Figure 7 and Appendix)

(9)

where cyan and E,,, are additive strain components. Using Equation (7), we calculated the applied strain e’m3, at which the x component of the strain, E,, is zero, and found that im3 is at most 0.01% higher than E,, for all specimens (Table 3). The strain state at E’,,,~for specimen A is indicated by ‘B’ in Figure 7. The strain components for specimen A, at an applied strain E =E’,,, = 0.61%, where T, is a maximum, were calculated to be e,=O.19%, eY=-0.59% and E,= O.ll%, respectively. The strain state is indicated by ‘C’ in Figure 7. As specimen A is most resistant to cracks and in fact the value of E’, was the largest in the present specimens, we regarded the value of i, as the virtual strain value E,,, corresponding to the maximum T,, if no cracks are formed in the Nb,Ge layer, for specimen A. Furthermore, assuming that T, becomes a maximum at a strain component ratio of eJez = 0.19/0.11 = 1.7 in the triaxial strain state, as for specimen A, we calculated the values of E, for specimens B and C as 0.65% and 0.73%, respectively. As mentioned above, when 6.75 x low6 is used for CY,- CY,,instead of 4.58 x 10m6 in the case of the uniaxial strain analysis, the value of E,, is equal to that of E’,, i.e. 0.61%, for specimen A. Using the same value for cr, - a,,, the values of E,, for specimens B and C become 0.62% and 0.73%, respectively, which are similar to the expected values of E,, 0.65% and 0.73%, calculated using the triaxial strain analysis. Figures 2-4 (arrows) show the values for E, for specimens A, B and C. For specimen C, the value of E, is plausible because it is located near the strain corresponding to the virtual strain at the maximum T,, considering the tendency of the T, (mid)+ curve. Tables 2 and 3 show the values of Q and T, (E = E,) for all specimens (for specimens B and C, the T, (E = E,)S were obtained by linear extrapolation). The strain dependence of T, for a random distribution of grains of cubic symmetry is introduced as follows by Welch19: T, = T,, + r,e + (1/2)Aue* + (e,-e/3)* + ( l z-e/3)*}

+ (2/5) A,{(e,-e/3)*

where T,, is the transition temperature at a strain-free the volume strain component, e, is given by

(10)

state,

(11)

Strain effect on T, of Nb,Ge and l ,-e/3, e,-e/3, and l ,-e/3 are the non-hydrostatic strain components, respectively. The sizes of I’, and A, show the relative efficacy of the hydrostatic component of strain in altering T,, respectively, and the size of A, shows that of the nonhydrostatic component of strain. We have found that a chemical-vapour-deposited Nb,Ge film similar to the present specimens remains cubic at 10 K”, which is different from the cases where the structure of Nb$n and V,Si transforms from the cubic A-15 to the tetragonal low-temperature phase at 43 K and 21 K, respectively 22-24 . The Nb,Ge compounds in the present specimens are polycrystals with columnar grains that grew perpendicular to the tape surface”. We discuss the relationship between T, and the strain components of the specimens using Equation (lo), although the grains of the specimens are not randomly distributed. Solid lines in Figure 8 show the applied bending strain dependence of the hydrostatic strain terms, e and ( 1/2)e2, and that of the non-hydrostatic strain term, (2/5) {(e, - e/3)* + (e,-e/3)2 + (e,-e/3)*}, for specimen A, that are multiplicands of I,, A,, and AI in Equation (lo), respectively. In Figure 8, the applied strain at the minimum of the non-hydrostatic strain term, E = 0.26%, is lower than that at the maximum T,, E = l‘m = 0.61%, while the hydrostatic strain term, ( 1/2)e2, decreases with E until it becomes zero at E = 1.19% and le 1changes linearly with E. Therefore, the applied strain at the maximum T, in the T,-•E characteristics for specimen A may be interpreted by taking the effects of both the non-hydrostatic strain component and the hydrostatic strain components on T, into consideration. For specimens B and C, the applied strains at the minimum of the non-hydrostatic term are calculated to be 0.28% and 0.30%, which are lower than the strains at the maximum T,‘s, i.e. 0.50% and OSl%, respectively. The results of the strain calculation differ from those described above if parameters are used other than those presented in Table 3. When 6.75 x 10m6 is used instead of 4.58 x 10m6for (Y,- (Y,,in the strain calculation for specimen A, as in the previous example, the minimum values of the non-hydrostatic term are in the range 0.33-0.36%, which are lower than the applied strain at the maximum T,, E= d m = 0.61%. In that case, the values of the Poisson’s ratio of the Nb,Ge layer, vn, are calculated to be in the range 0.17-0.21 instead of 0.23 in the case of 4.58 x lO-‘j for a,--(~~. We examined the values of F,, A, and At in Equation (10) from the T, (mid)+ characteristics for specimen A in

z

’

SpecimenA

tape: Y. Nakagawa

and M. Umeda

Figure 2. By the least-squares method, we made an approximated T, (mid)+ curve for specimen A, assuming no cracks are formed in the Nb3Ge layer, from six T, (mid) points which consisted of five data points at E = O-0.61% and one assumed point of T, (mid, E = 1.19%) = 20 K, in which 1.19% is the strain corresponding to the zero hydrostatic strain components shown in Figure 8; and the value of T, (mid, E = 1.19%) is obtained when T, (mid) at E above E’, changes symmetrically with respect to l = E’,,,= 0.61% in the T, (mid)+ characteristics with E below E’,. We assumed the value of T,, in Equation (10) for specimen A as

T,o= Tcm,~lm (on> + {Tcr.tape (mid, E = 0.61%)-Tcr,,,, (end, E= 0.61%)) = 21.16 K

(12)

where T,, and T,, express the magnetically measured T, and the resistively measured T,, respectively (see Table 2 and Figure 9). By fitting Equation (10) with 21.16 K for T,, to the approximated curve, we obtained the values of I,, A, and A, as -82 K, -2.7 x lo4 K and -2.6 x lo4 K, respectively. When we took as the assumed points in above calculation T, (mid, E = 1.19%) = 20.53 K (= T, (E = E’,)) and T, (mid, E = 1.19%) = 18.2 K, which is the data point, although the Nb,Ge layer was most probably cracked, the values of A,, were found to be comparable to those of At, as in the above case. The value of A,/A, is very sensitive to the value of T,, - T, (E = i,) in this calculation. As the value of T,, - T, (E = E’,) increases, AJAh, rapidly decreases. When 2 1.5 K was used for T,, instead of 21.16 K (in this case, 20.53 K for T, (E = E’,) was not changed) in the above case, for example, we obtained the values of I,, A,, and A, as 200 K, -1.7 x lo3 K and -3.3 x 10“ K, respectively. The value of AJA, changes from 1.1 to 0.05 due to a change of only 0.34 K in T,,. The size of At (about -3 x 10”) obtained in this example, is smaller than the value -8 x 10m4 reported for composite Nb,Ge tapes”. In studies of the effects of hydrostatic pressure, uniaxial pressure and uniaxial tensile strain on the T, of Nb,Sn compounds and composite wires 8.25-28,the sizes of A” are calculated to be about one order smaller than those of A18.19. When a tensile strain, E,, is applied in the longitudinal direction of the Nb,Ge tape, the strain components in the Nb,Ge, e,, lY and eZ are expressed as (see Appendix)

Y-

~

bendingstrain tensilestrain

_._ Figure8 Applied strain dependence of hydrostatic strain terms, e and (l/Z)e2, and that of non-hydrostatic strain term, (2/5) {(eX-e/3)* + (e,e/3)z + (cz-e/3)2}, for specimen A, which are multiplicands of r,, A, and At in Equation (lo), respectively

5.17

5.15

Applied Strain E (%)

Lattice S$ng

5.18

a0 (I)

Figure 9 Resistively measured, fully superconducting T,, T,, (end) and magnetically measured onset 7,. Tcm (on), as a function of lattice spacing for Nb,Ge tapes and Nb,Ge films of specimens A, 6 and C

Cryogenics

1996 Volume

36, Number

8

585

Strain effect on T, of Nb,Ge

tape: Y. Nakagawa

and M. Umeda (13)

EhVhl(

vh(EhVh+E”Vn)

(14)

11

and

(15)

where E,,, and ezan are additive strain components. The values of the strain components at the applied tensile strains are similar to those at the applied bending strains. The differences are within 0.02% for applied strains below 1%. For example, the strain components for specimen A, at an applied strain E = i, = 0.61%, where T, is a maximum, are lY= -0.60% and ez = 0.12%, instead of E,=-0.59% and l z=O.ll% in the case of the bending strain, respectively. In the dashed lines in Figure 8, the applied tensile strain dependencies of the hydrostatic and non-hydrostatic strain terms are shown, which are similar to their applied bending strain dependencies. The applied tensile strain at the minimum of the non-hydrostatic term is 0.24%. In previous” measurements of the tensile strain dependence of J, for a sample similar to specimen A (with a 25pm copper layer on both sides) the applied tensile strain at the maximum J,, E’,, was 0.44% (which corresponds to 0.42% if the sample has no copper layer). From this result, with Hc2 expressed as a linear function of 7’c29.30, the applied tensile strain at the maximum T, in the T, versus tensile strain characteristics for specimen A, E’,, if measured, may be above 0.42%, which is above the applied strain at the minimum of the non-hydrostatic term, 0.24%. Therefore, for an applied tensile strain, the hydrostatic strain components may noticeably affect T, for the present specimens, too. Figure 9 shows a plot of TcT and T,, as a function of lattice spacing (data shown in Table 2). The T,, shows the highest T, path in the sample, whereas the Tcm shows average sample properties. In general, T,, (end) is equal to Tcm (on). Figure 9 shows that for all tapes studied here, the T,, (end)s are nearly equal to the T,, (on)s. The values of the lattice spacing at E = E, were calculated for specimens A, B and C using Equations (7) and (9) with the parameters cy, (from 1107 K to 293 K) and ,!Z,(at 293 K) presented in Table 3. Figure 9 shows that the T,,, (on)s for the films are 0.3-0.9 K higher than the T,, (end)s at E = E, obtained by extrapolation for the tapes. This is because the Nb,Ge films are strain free in all three dimensions (the strain state corresponds to ‘0’ in Figure 7), whereas, for the tapes, strain is only partially relieved (shown as ‘C’ in the same figure). For all the tapes and films, T, tends to increase with decreasing lattice spacing. It is well known that, as the lattice spacing in A- 15 structure superconductors decreases, T, increases. This is true not only for Nb,Ge compounds with various values of the lattice spacing”, but also for A15 structure superconductors with various values of lattice spacing, such as Nb,Ge, Nb,Ga, Nb3Al and Nb3Sn32-36. In the case of Nb3Ge compounds, T, may decrease due to disorder”, which results in an increase in lattice spacing. In A-15 structure superconductors, the origin of T,, including the relationship between T, and lattice spacing, is not sufficiently explained by McMillan-type theory38. The T, for specimen C, which had an Nb,Ge layer thick-

586

Cryogenics

1996 Volume

36, Number

8

ness of 1.3 pm, was 1.0-1.5 K lower than those for specimens A and B, which had layer thicknesses of 11.7 pm and 10.6 pm, respectively. This was true for both tapes at the applied strain E, and films. This fact shows that the lower T, for specimen C was not due to the higher compressive strain in the thinner Nb,Ge layer. As seen from the X-ray patterns in Figure 6b1, traces of unknown phases, which Braginski et al. identified for Ni,Nb or NiNb”‘, were observed in the substrate side of the Nb,Ge film. These phases may have appeared due to oxidation or alloying of Nb,Ge with the substrate. We consider this oxidation or alloying to be the main cause for the increase in the lattice spacing, and consequently for the lower T, for specimen C. Gavaler et ~1.~’ showed in a study of sputtered Nb,Ge films on sapphire0 substrates that when an Nb,Ge layer is thinner than 1000 A, it ha,s a high oxygen content and has a lattice spacing of 5.25 A, and when the thickness is increased above this level, the oxygen content decreases and the lattice spacing decreases to 5.14 A, which in turn increases the T,. Our results are similar to this. Figure 10 shows the normalized critical temperature, T, ( E)IT, (E,), as a function of intrinsic strain lo, where lo = E--E,, for all specimens. In this figure, we used T, (mid) for T,. For comparison, we also plotted similar characteristics for bronze-processed Nb,Sn mono-filament wires from the tensile strain studies conducted by Luhman et al.‘, who measured the inductive T, (80% change point), and by Kuroda and Wada’, who measured the resistive T, (mid). The instrinsic strain sensitivity of T, (E)I~‘~ (E,,) for the Nb,Ge tapes may be similar to that for the Nb,Sn wires, as a whole.

Summary Using a resistance method, we measured the dependence of critical temperature, T,, on bending strain, E, for chemicalvapour-deposited Nb3Ge tapes. A Nb,Ge compound was deposited on both sides of a 0.1 -mm thick Hastelloy substrate. T, increased by 0.4-0.6 K due to an applied strain of about 0.5% for three Nb3Ge tapes that had different Nb,Ge layer thicknesses and different Nb/Ge composition ratios. We fabricated Nb,Ge films by removing the Hastelloy substrates from the Nb,Ge tapes, and found that the magnetically measured onset Tc’s for the films are 1.O- 1.5 K higher than those for the tapes. 1-

I

,

0.96 .

‘0 0

^E w 0.96 7-Y t 5” 0.94 - , I-I’

_. -d l

/’

/-

/’

/

/.

.X66 .

.i .--. A

3

’ d .

0.92 -

0.9 -0.6

/’

..Od .’ .’ ,v’

.

I -0.6

0 I -0.4

A B c Nb$n (Luhman et al!) Nb3Sn (Kuroda et alg) I -0.2 0

Intrinsic Strain & (=E- E,)

(“X2)

Figure 10 Normalized critical temperature, T, (c)/T, (E,,,), as a function of intrinsic strain, E,,= E- E,, for specimens A, B and C

Strain effect on T, of Nb,Ge Triaxial strain analysis was conducted using measurements of lattice spacing for the tapes and films. It was shown that both the hydrostatic and non-hydrostatic strain components have a noticeable effect on T, for the present Nb,Ge tapes. The dependencies of the normalized T,, T, (E)IT, (E,), on intrinsic strain, 4, = E--E,, for the Nb7Ge tapes were found to be similar to those reported previously for bronzeprocessed Nb,Sn wires.

34 35

and M. Umeda

Willens, R.H., Geballe, T.H., Gossard, A.C., Maita, J.P., Menth, A., Hull, G.W. Jr, and Soden, R.R. Solid St Commun ( 1969) 7 837 Matthias, B.T., Geballe, T.H., Geller, S. and Corenzwit, E. Phy,\ Rev(1954)95

36 37

tape: Y. Nakagawa

1435

Vieland, LJ. J Phys Chem SoIidi ( 1972) 33 58 I Soukoulis, C.M. and Papaconstantopoulos, D.A. Phys Rev

( 1982)

B26 3673

38

Klein, B.M., Boyer, L.L. and Papaconstantopoulos,

D.A. Phys Rev

Lett ( 1979) 42 530

39

Braginski,

AI., Daniel, M.R., Roland, G.W. and Woollam, J.A. ( 1978) MAG-14 608 Gavaler, J.R., Ashkin, M., Braginski, A.I. and Santhanam, A.T. J Physique ( 1978) 39 C6-400 IEEE

40

Truns Magn

Acknowledgements The authors thank S. ment throughout this ation to H. Yamasaki for his help in using

Kosaka for his interest and encouragestudy. They also express their apprecifor a critical reading and to H. Obara the SQUID magnetometer.

References I

2 3

Testardi, L.R., Meek, R.L., Poate, J.M., Royer, W.A., Storm, A.R. and Wemick, J.H. Phys Rev B (1975) 11 4304 Suzuki, M.A., Anayama, T., Watanabe, K., Toyota, N., Kido, G. and Nakagawa, Y. Jpn J Appl Phys ( 1985) 24 L767 Watanabe, K., Awaji, S., Fukase, T., Yamada, Y., Sakuraba, J., Hata, F., Cbong, C.K., Hasebe, T. and Ishihara, M. Cryogenics ( 1994) 34 639

4 5 6 7

Arai, K., Tateishi, H., Umeda, M., Agatsuma, K. and Takizawa, S. IEEE Trans Magn ( 1994) 30 2164 Ekin, J.W. Adv Cryog Eng ( 1984) 30 823 Ekin, J.W. Cryogenics (1980) M 61 I Luhman, T., Suenaga, M. and Klamut, CJ. Adv Cryog Eng (1978)

Appendix: Triaxial strain calculation composite tape

for the

The residual strain, the internal strain at an applied bending strain and that at an applied tensile strain are calculated for the Nb,Ge layer deposited on both sides of a Hastelloy substrate tape. Figure 7 shows a schematic of the internal strain for the Nb,Ge tape. Generally, the internal strain components E,, E? and E, are expressed as e, = {a,+

(q”+C)}IE

(Al)

l.”= {cr+

(q,+a,)}/E

(A2)

ET= (r&-u (a,+a_,)}/E

(A3)

where (T is stress and v is Poisson’s

ratio.

24 325

8 9 10 I1

Kuroda, T. Nakagawa, 27 558 Nakagawa, Nakagawa,

and Wada, H. Cryog Eng ( 1993) 28 274 (in Japanese) Y., Umeda, M. and Kimura, Y. Cryogenics (1987)

Residual strain calculation

Y. and Umeda, M. J Appl Phys (1994) 75 2131 Y., Umeda, M. and Kimura, Y. Adv Cryog Eng ( 1988)

For our composite, (A3) reduce to

34 477

12 13

14 I5

Easton, D.S., Kroeger, D.M., Speckling, W. and Koch, CC. J Appl Phys ( 1980) 51 2748 Braginski, AI., Mauser, S.F., Roland, G.W., Burghardt, R.R., Daniel, M.R. and Janocko, M.A. An Improved Superconductor for Transmission Line Application. Phase I Westinghouse Electric Corp., U.S. ERDA, E (I i-1)-2522 (1975) 55 Hull, G.W. and Newkirk, L.R. J Low Temp Phys ( 1977) 29 297 Bussiere, J.F., LeHuy, H. and Faucher, B. Adv Cryog Eng ( 1984) 30 859

16 17

18 19 20 21 22 23 24 25 26 21 28 29 30 31 32

Specification Touloukian,

sheets by Mitsubishi Materials Co, Tokyo (in Japanese) Y.S., Kirby, R.K., Tayer, R.E. and Desai, P.D. Thermophysical Properties of Matter, Vol 12. Thermal Expansion of Metallic Elements and Alloys IFI Plenum, New York-Washington ( 1975) I246 Schwartz, F.R. and Knight, M. Cryogenic Materials Data Hand Book 2 Air Force Materials Laboratory ( 1970) 208 Welch, D.O. Adv Cryog Eng (1980) i6 48 Mitsubishi Materials Co., Tokyo. Personal communication (I 995) Nakagawa, Y. (unpublished) _ Mailfert, R. and Batterman, B.W. Phys Lett ( 1967) 24A 315 Batterman, B.W. and Barrett, C.S. Phys Rev (1965) 145 296 Labbe, J. Phys Rev ( 1967) 158 647 McEvoy, J.P. Superconductivity (Ed F. Chilton) North-Holland, Amsterdam ( I97 1) 540 Smith, T.F. J Low Temp Phys (1972) 6 17 I Neubauer, H. Z Phys ( 1969) 226 211 Chu, C.W. and Vieland, L. J Low Temp Phys (1974) 17 25 Hake, R.R. Phys Rev (1967) 158 356 Orlando, T.P., McNiff, EJ. Jr, Foner, S. and Beasley, M.R. Phys Rev ( 1979) B19 4545 Newkirk, L.R., Valencia, F.A., Giorgi, A.L., Szklarz, E.G. et al. IEEE Trans Magn ( 1975) MAG-11 221 Webb, G.W., Wieland, LJ., Miller, R.E. and Wicklund, A. Solid St Commun.

33

( 1971) 9 1769

Wood, E.A., Compton, V.B., Matthias, Acta Cyst (1958) 11 604

B.T. and Corenzwit,

E.

a, = 0, cr, = cry, and Equations

(Al )-

l, = Er = a, (I-v)/E

(A4)

and E_= -2vwJE

(As)

We assume that a separated Nb3Ge film and a substrate tape of length l,, at the deposition temperature have lengths temperature, respectof L, and L, at the measurement ively. We then obtain for l,,, and lIxh, 1x2”= lx, (l+dT)

(Ah)

lo

(A7)

= lx, ( l+a,AT)

where subscripts n and h denote Nb,Ge and substrate, respectively. We assume that both the length of the Nb,Ge film, lxzn, and that of the substrate tape, lx2,,. become lx3 in a Nb,Ge tape. Thus, using Equation (A4), we obtain 1xzn -1,s = -&I, L -L,,

= l&,,

= -c,J,,,

(A8)

( l-v,)&

(A9)

= M~zI, ( ~-r&5,

(AlO)

6” V” = -%ViI

where E, and E,,, are the residual strains. Equations (3) and (4) in the main text are derived from Equations (A4)(AlO).

Cryogenics

1996 Volume

36, Number

8

587

Strain effect on T, of Nb,Ge

tape: Y. Nakagawa

and M. Umeda

Internal strain at an applied bending strain

Internal strain at an applied tensile strain

Here we calculate the third term in Equation (8). We consider that the outer Nb,Ge layer and the Hastelloy substrate with the inner Nb,Ge layer are independently bent. The strains in the width direction (y direction) in the Nb,Ge layer, E,, and that in the Hastelloy tape, E,,, are related by the following two equations when the width of the Nb,Ge layer is equal to that of the Hastelloy substrate on the boundary between them: (l-v,D/(2r+2d+D))

(l+e,)

= (l-v,D/(2r+2d+D))

(l+$J (All)

When a tensile strain, E,, is applied in the longitudinal direction of the Nb,Ge tape, the additive strain components, Exan, cyan and lzan are derived as shown in Equations (13)(15) in the main text, using the following equations, where a, is the additive stress:

E xan =

‘&ah =

Eyan =

Eyah

(A13)

cu

(A14)

and

EYan= (%n-r~~&%

= ( o,,,-M,e,,JE,

(A15)

E,,E, d+E,e,Dl4

Eyah

=

(46)

=0

(A12)

From Equations (A 11) and (A 12), E, equal to the third term in Equation (8), is given.

588

Cryogenics

1996 Volume

36, Number

8

-

(ffyyah-

E 72” =

km-%

u,,,v,

=

Vh%h)lEh

-ayahvh

(~.,+~ya,)b%

( uyyah-VhEh&h)lEh =

-%

(~xz,,+~y,,YEn

(A17) (‘418)