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Advances in the purification of niobium by solid state gettering with titanium
ELSEVIER
Journal
Advances
of Alloys and Compounds
in the purification
232 (1996) 281-288
of niobium by solid state gettering with titanium
H. Safa, D. Moffat, B. Bonin, F. Koechlin Centre d’Etudes
Saclay, DAPNIAISEA, Received
91191 Gif sur Yvette Gdex,
France
22 May 1995
Abstract Post-purification of commercially available niobium of moderate purity can be an effective method of producing significant quantities of high purity material. A model is presented which demonstrates how heat treatments in the presence of titanium influence the residual resistivity ratio (RRR). At short heat treatment times, nitrogen, oxygen and carbon are gettered from the bulk, causing the RRR to increase significantly. At very long times, titanium contamination causes the RRR to decrease slowly. Many samples were submitted to purification heat treatments to verify this model. An unexpected discovery was the appearance
of a temperature-dependent maximum RRR, which was interpreted as a temperature-dependent impurity concentration. It was found that lower temperatures yielded higher maximum RRRs and that increased heat treatment times were necessary to reach these RRR values. Inspired by these results, a heat treatment program was conceived which produced two samples with RRR values of about 1900, an improvement of more than an order of magnitude from the initial values. Keywords:
Niobium;
Residual
resistivity
ratio;
Solid state
purification
1. Introduction
The low temperature thermal conductivity of niobium is of great interest in the field of r.f. superconductivity (the higher, the better). The thermal conductivity K of niobium is strongly dependent on the purity of the material at low temperatures. For temperatures above 0.3T,, i.e. about 3 K, it is dominated by the electron contribution and is given by [l]
(1) where L, is the Lorentz constant, p,,, is the residual resistivity (about ~4.2 K), a is constant and f is the ratio of the superconducting to normal-state thermal conductivity [2]. For T 3 T,, f - 1. The residual resistivity ratio (RRR) may be defined as
RR&k!? p4.2
(2)
K
Thus, from these two equations, one finds that K, at low temperatures, is proportional to RRR. For this reason we shall focus on the calculation and measurement of RRR for the rest of this article. 0925~8388/96/$15.00 0 19% Elsevier SSDI 0925-8388(95)01997-9
Science
S.A. All rights
reserved
One has two options for obtaining niobium of higher purity: to purchase it directly from a vendor or to post-purify sheets of moderate purity. At present, material with an RRR of about 300 costs about five times that of material with an RRR of 30. It is expected that vendors will have difficulty in supplying sufficient quantities of higher purity niobium at an affordable price. Thus post-purification may provide niobium of a purity not otherwise available or offer an alternative to the present production method. It has been shown that either yttrium or titanium can be used as a solid state getter to purify niobium [3,4]. For a variety of reasons, titanium is at present the getter of choice. We were interested in learning the extent to which the RRR of readily available niobium could be improved using the present simple technique. In addition, if purification could be performed at lower temperatures, it could have desirable consequences. 1.1. The relationship
between
RRR and impurities
The resistivity of a metal in the normal state can be written as:
P=
Pimp
+
pdisl
+
Pgb
’
Pp~honon(~)
(3)
282
H. Safa et al. I Journal of Alloys and Compounds
where the components are the contributions due to impurities, dislocations, grain boundaries and phonons respectively. Only the phonon contribution depends on temperature. A typical value measured in this study was Pphonon (T) = 6.5 x 10P14T3 LRm (T s 25 K); this is within the measurement of [5-71. In annealed niobium, the dominant term in the resistivity at 4.2 K is that due to impurities [5,6]. The Pimp term can be expressed as a sum over the different impurities:
Pimp =
Q F,( c~ z ) I
(4)
where ci is the concentration of impurity i and aplacis its resistivity coefficient. Values for apiacfor impurities in niobium are given in Table 1. Table 2 presents a typical analysis of the niobium used in this study and shows that the light elements N, 0 and C are the most significant in terms of resistivity contribution. One can affect pimp by coating a piece of niobium with titanium. Indeed, this has two effects. Because the free energy of reaction for forming titanium carbides, nitrides and oxides is favourable (proposed purification reactions are shown in Table 3), titanium will remove these light impurities from niobium, causing pimp to decrease. On the contrary, the deposited titanium will diffuse into the niobium, causing Pimp to increase. The net effect on firnp is determined by the relative diffusivities of these impurities and the
Table 1 Resistivity coefficients of several impurities Impurity
(aplac) (X10~12nmat.ppm-’
Reference
N 0 C Hf Zr Ti W Ta
5.2 4.5 4.3 1.4 1.0 0.96 0.4 0.25
PI PI PI ]91 [91 ]9,101 [ill ]121
Table 2 Impurity analysis and resistivity contributions approximately 170 Impurity
N 0 C Zr W Ta
Impurity content (atppm) Measured
Assumed
<260 <230 <300 31 30 152
55 55 55
for niobium of RRR Resistivity (XlO~‘*nm) 286 247 236 31 12 38
232 (19%)
281-288
Table 3 Free energies of reaction for possible purification processes [13] Reaction
AG” (J mole-‘)
N(Nb) + Ti = TIN” 0( Nb) + Ti = TiO C( Nb) + Ti = TiC
-160300+24.7T -12400&7.1T -174000+53.1T
’ In this reaction, nitrogen titanium to form TiN.
in solution
in niobium
reacts with
reaction rates. Titanium has no effect on the heavy impurities such as tantalum, zirconium and tungsten. 1.2. The application of titanium The easiest manner in which to coat a sample with titanium is to wrap it in titanium foil and to place everything in a vacuum furnace. During heat treatment, titanium will evaporate from the foil and coat the sample. The vapor pressure of titanium is given by
u41 PTi = 1.56 X 1Or2exp ( -5y)(Pa)
(5)
In a Boltzmann gas, pressure is the result of atoms striking a surface. If a fraction r] of the evaporated titanium atoms which strike the niobium sample remain on it, the thickness E of the titanium layer on the sample will grow at the following rate: de dt
-=
112
(m s-l)
(6)
where M = 47.9 X 10m3kg mall’, p = 4520 kg m3 and R = 8.314 J mall’ K-‘. Note that this definition of r7 combines factors such as the sticking coefficient, the geometrical relationship of the sample to the titanium foil, and re-evaporation. One would expect v to be a function of time. Initially the deposition rate should be high. As the layer grows in thickness, equilibrium between deposition and re-evaporation should be reached and 77 should go to zero. A sample was weighed before and after a 1000 min heat treatment at 1300 “C to measure the titanium deposition rate. Using this datum and Eq. (6) an average value of 77= 0.09 was calculated. Another sample yielded a similar value. The time dependence of v has not yet been determined for our particular furnace arrangement, The purification reactions shown in Table 3 imply that one titanium atom is required for each light impurity atom in the niobium sheet in order to purify it completely. (It should be noted that there are several possible purification reactions; we propose that those in Table 3 are the most plausible.) Thus the estimated minimum titanium layer thickness is
H. Safa et al.
wd .-?a 2(w + d) 6% +
aO
+
I Journal of Alloys and Compounds 232 (1996) 281-288
(7)
+>
where uN is the atomic fraction of nitrogen etc., and w and d are the width and thickness of the sample to be purified. By way of example, for a concentration of 55 at.ppm for each impurity in a niobium sheet 2 mm thick (i.e. w = m), it would take approximately 2400 min at 1200 “C to deposit sufficient titanium for complete purification (0.16 Fm), 230 min at 1300 “C. 1.3. The diffusion of impurities The impurities in the niobium must diffuse to the niobium-titanium interface in order for purification to occur. Let us consider an infinite sheet of niobium with thickness d. Let us also assume that the impurities are uniformly distributed with an initial concentration cO. The solution to the diffusion equation D c~~c/~x~= &I& is c(x, t) = 2
For titanium, one can approximate the solution to the diffusion equation in the same manner, with the exception that the concentration at the surface is unity, yielding cTi
=
-t (1
1 - exp _r~i
exp(<)
1.4. RRR calculations
Combining the equations from Sections 1.1 and 1.3 we have ~4.2k(ty T) =i=zz,7u1 ($)ici
cos( (2n :l)Tx) +
where l/r, = (2n + 1)2r2Dld2 and D = D, exp(-T,/ T) is the diffusion coefficient. The assumption that all impurities are gettered at the niobium-titanium interfaces gives the condition c(x = &d/2) = 0 at all times. Because the diffusion times r,, decrease as 1/(2n + 1)2, the largest contribution to the sum in Eq. (8) will be the IZ= 0 term. It can be shown without too much difficulty that, for a rectangular bar of dimensions w and d, the diffusion time constant (for it = 0) becomes (9) where now 3 refers to the time constant for each impurity and Di is the corresponding diffusion coefficient. It turns out that the concentration profiles are reasonably flat; so we can approximate them with the values at the center of the sample: ci = ~(0, t) = cn
Table 4 Diffusion Impurity
N 0 C Ti a Calculated
coefficients
(10)
exp f ( ,)
(11)
Diffusion coefficients in bulk niobium for the important impurities are given in Table 4. Diffusion times for these impurities in a 2 mm X 2.5 mm bar are also shown.
+ ,=~;,
= (-1)” n-,, 2n
G%
5.1 x 1om6 1.38 x IO-’ 1.0 x lomh 9.9 x lomh for a 2 mm
X
2.5 mm bar.
Reference
T,
18 13 17 43
870 410 070 750
exp(?)
(12)
where t and T refer to the heat treatment time and temperature respectively and the contributions of pgb and pdis, have been ignored. The first two terms in Eq. (12) are not affected by titanium purification. In fact, they are the minimum value of p and yield the ultimate value of RRR. Using the values in Table 2, and the equation for pphonongiven in Section 1.1, one finds that P,,,~,= 8.58 X 10-” R m and RRR,,, = 1699. Because the quantities of light impurities in moderate purity niobium are below the detection limits of the methods normally used by niobium suppliers (see Table 2) we shall assume the same initial value of c,, for these impurities. (If desired, one could resort to more elaborate and expensive analysis techniques.) Recalling the boundary condition of Eq. (8), it is implicitly assumed in Eq. (12) that there is sufficient titanium at all times and temperatures to effect the calculated degree of purification. If this assumption is not met, the purification kinetics could be affected. The individual contributions to the resistivity as a
qr a (min) 1200°C
1300 “C
1151
296 27
131 15
P31 [I61
444 3.3 x 10’
213 5 x lox
[151
+ ~phonon(4*2K)
M,,[l-e&y
and times
D, (m’ s-‘)
283
284
H. Safa et al. I Journal of Alloys
and Compounds
232 (19%)
281-288
element impurities plus phonons. At very long times, titanium diffusion results in a slowly increasing resistivity. Calculations of RRR as a function of heat treatment time and temperature for 2 mm X 2.5 mm samples are shown in Fig. 2. A value of pzg8k = 1.458 X lo-'fim [12] was used for these calculations. At any temperature, the RRR increases relatively quickly to a maximum value and then decreases slowly. For heat treatments at 1200°C and lower, the maximum in RRR is very broad and RRR,,,‘heO = RRR,,,. The maximum Niobium bar: 2 x 2.5 mm is narrower at higher temperatures, however, and Purification temperature : 1300°C RRR,,, theo is diminished. These effects are due to increased titanium contamination of the bulk. Note that the time needed to reach RRR,,,‘h’” at 1200 “C is approximately equal to the time required to deposit sufficient titanium for complete purification. Sum Thus, we would anticipate the purification kinetics at ._~~~~__~~~~.~~--_~~~_________.--------._____-~ temperatures below 1200 “C to be limited by the titanium deposition rate. At 1200 “C and higher, we would expect purification to be diffusion limited.
function of heat treatment time at 1300°C are shown in Fig. 1. The impurity calculations were for a 2 mm x 2.5 mm niobium bar. A value of c,, = 55 at.ppm was used, which yields an initial RRR of 170. One immediately notices the rapid fall in the oxygen, nitrogen and carbon contributions. These result in a rapid decrease in the total resistivity to a point limited by the heavy
1E-09
2 g
3
lE-10
i z .G? .s .Y lE-11
2. Experimental details
3
2.1. Sample preparation and heat treatment IE-12
I I 0
500
10002000
.,
, , , , 4000
I,,
,
6Mw)
I
,
8C00
,
,
10000
Heat treatment time (minutes) Fig. 1. Calculations of the impurity contributions to the 4.2 K resistivity of a niobium bar. Note the change in scale on the time axis. The phonon contribution at 4.2 K is 4.8 X lo-‘* R m.
Niobium bar: 2 x 2.5 mm
2ooo,““,““,“.‘,““,‘.‘.,....,....,....,
Ol....‘....‘....‘...,‘,,“‘,,,,‘,,,,”,.,J 0
lOOil
2000
3000
4000
5000
6000
7000
The samples used in the present study were cut from niobium sheets 2mm thick purchased from Heraeus. The nominal RRR of this sheet was about 170. The samples varied in width from 2 to 3 mm and were about 100 mm long. The starting grain size was about 50 pm. The samples were etched before the first heat treatment only, in the standard mixture of HF, HNO, and H,PO, used for superconducting cavities, 1: 1: 2 by volume. The vacuum furnace used for the heat treatments is about 300 mm in diameter and about 600 mm tall. The maximum temperature of this furnace is 1300 “C. At this temperature, the typical operating pressure is about 4 X low5 Pa (about 4 X lo-'mbar). Several samples, surrounded by a cylinder of titanium, were placed in the center of the furnace for each heat treatment cycle. The titanium cylinder is 40 mm in diameter. A plot of the temperature and pressure in the furnace during a heat treatment is shown in Fig. 3. Each sample was used for multiple heat treatments. To illustrate this, the RRR of a sample heat treated for 1OOOmin was measured; this sample was then heat treated for another 2000min to yield a sample with a total heat treatment time of 3OOOmin. The samples were not etched between heat treatments.
8000
Heat treatment time (minutes) Fig. 2. Calculations of RRR as a function of heat treatment temperature. The calculations are based on Eq. (12). RRR,,, is 1699 for this material.
2.2. RRR measurements There are at least two methods of measuring the normal-state residual resistivity of a superconducting
H. Safa et al. I Journal of Alloys and Compounds
232 (1996) 281-288
28.5
I320
6E-4
I080
1.5E-4
360
4E-5 720
l .SE-5
4.5E-6 360
I .5E-6
8E-7
4E-7
5E-8
3
6
9
12
15
21
18
24
27
Time (hours) Fig. 3. The pressure
and temperature
of the furnace
sample below its transition temperature. One can measure the resistance of a sample at 4.2 K as a function of magnetic field above Hc3 and extrapolate to zero field. Alternatively, one can measure the resistance in zero field as a function of temperature above T, and extrapolate to 4.2 K. A typical temperature extrapolation is shown in Fig. 4. Several samples were measured using both techniques. The results for purified low initial RRR samples are shown in Fig. 5. The values obtained by both methods were in quite good agreement. Because of its relative ease, the temperature extrapolation method was used throughout this study. The definition of RRR given in Eq. (2) was used in this study. Absolute resistivities at room temperature and 4.2 K were not calculated as we were interested only in the ratio of resistivities. It was, however, necessary to correct the “room-temperature” value of the sample resistance for temperature deviations from 295 K. This was done assuming that [7,17,18]
during
a purification
treatment.
Sample purified
loo0 minutes
25
~““‘“““‘““.‘,“~1
20
0.006
0
2500
5m
Temperature3
j$=4.7X10-10QmoC-1 A quick measurement this value.
@ 1250°C
7500
loom
12503
(K3)
(13) of
dp/dT
was in agreement with
Fig. 4. Extrapolation of sample resistance as a function value of the resistance at 4.2 K (T3 = 74 K3) is needed determine RRR. This sample had an RRR of 410.
of T3. The in order to
H. Safa et al. I Journal of Alloys and Compounds
286
232 (19%)
281-288
Purification temperature: 1300°C
Purification temperature: 1300°C
‘mm 5wm
P P 0 O”..“.“...“,“.““.,‘.““”
0
1000
3ooo
zoo0
4coO
5Om
6cm
7000
8000
Heat treatment time (minutes)
3. Results aud discussion The data for samples whose initial RRR was about 170 are shown in Figs. 6 and 7. (Fig. 5 showed the results of purification heat treatments on samples whose initial RRR was about 34.) An initial increase in RRR was observed followed by a saturation in RRR. A slight decrease in RRR from RRR,,,‘“P was observed for samples heat treated at 1300 “C for long Purification temperature: 1200°C
.II,...,,.*,.,,,,,,,,,,,,,,
a 0
800 -
0 0
0
??
600 -
0
3 “I’. 2000
.
2’ .‘S 4OOa
0
“““I 6cfJ.l
8000
3 ’ ” 1mOO
3 ‘3 ” 12cm 14000
Heat treatment time (minutes) Fig. 6. RRR data for samples with c, = 6.5 atppm.
purified
at 1200 “C: -,
2000
4000
6000
8CGU
1OOOo 12000
14000
Heat treatment time (minutes)
Fig. 5. RRR data for low initial RRR samples purified at 1300°C: H, RRR values determined by temperature extrapolation; 0, measurements made with a magnetic field. The dimensions of these samples were 3 mm X 3 mm.
loo0
0
calculations
Fig. 7. RRR data for samples with c, = 13 at.ppm.
purified
at 1300 “C: -,
calculations
times. The value of RRR,,,““P was higher at 1200 “C, while the time required to reach RRR,,,““P was less at 1300°C. The increase in RRR with heat treatment time was not as fast as expected. There are several possible explanations for this: (i) it may simply be due to the uncertainty in the diffusion coefficients (the literature values vary by a factor of 2-10 [15]); (ii) the deposition rate of titanium may affect the purification kinetics; (iii) the kinetics of the reactions at the niobiumtitanium interface may be the limiting process. The experimentally observed purification rate does not appear to be strongly temperature dependent, whereas the titanium deposition rate is expected to vary by an order of magnitude between 1200 and 1300°C. One would also expect the reaction kinetics to be temperature dependent. Further investigation is required in order to determine the rate-limiting step. The data indicate a temperature-dependent RRR,,,““P which is less than RRR,,,‘h”“. This is particularly apparent for the samples heat treated at 1300 “C. This result cannot be explained by enhanced titanium diffusion alone. To confirm this, three 1 mm X 2 mm samples were heated treated at 1300 “C. The results are shown in Fig. 8. The decrease in RRR with increasing heat treatment time is in accord with that expected by titanium contamination. The observed behavior of RRR,,,““P may be interpreted as indicating a temperature-dependent equilibrium condition in the purification process (neglecting for the moment the increasing titanium contamination). This can be incorporated in the model presented above by replacing Eq. (10) with
H. Safa et al. I Journal of Alloys and Compounds
232 (1996) 281-288
1 x 2 mm samplespurified at 1300°C
281
Cooled slowly from 1300°C
10”m
.I’:/
2 lz 1 b lx
0.005 0.004 0.003 0.002 0.001
0
Fig. 8. RRR data showing the influence of titanium diffusion. Small samples (1 mm X 2 mm) were used to decrease the time needed to
observe the effect.
-t ( ,I +c, 7
5OOa
7500
1OOCG
12500
Temperature3 (K3)
Heat treatment time (minutes)
c,=(co-czc)exp
2500
(14)
where c, is the light element impurity concentration for an infinitely long heat treatment. The data imply dependent and, from the that c, is temperature thermodynamics presented in Table 3, one would expect c, to vary as exp(-constant/ T). Preliminary results also indicate that c, may depend on the furnace pressure. The physical origin of c, and the variables which affect it are presently under investigation. (For the calculations shown in Figs. 6 and 7 the same value of c, was used for nitrogen, carbon and oxygen.) The data from Figs. 6 and 7 allowed us to estimate the coefficients of c, as a function of temperature and to correct the earlier calculations of RRR,,,‘h”“. To validate this improved model, samples were subjected to a specially designed heat treatment program. Two samples, 1 mm x 2 mm with an initial RRR of about 155, were heated to 1300 “C and held there for 2 h. This should have provided a thick titanium layer and also been sufficiently long to establish equilibrium impurity concentrations. The temperature was then decreased in 50 “C steps, always allowing sufficient time for equilibrium to be reached at each step. (The stepwise decrease in temperature was made necessary by the furnace programming.) The final holding temperature was 1000 “C. The total heat treatment time was 2640 min (44 h). After this treatment, one sample had an RRR of 1880, and the other an RRR of 1940. A resistance vs. temperature curve for the sample with
Fig. 9. Extrapolation of sample resistance as a function of T’ for a well-purified sample. This sample had an initial RRR of 155; after purification the RRR was 1940.
RRR = 1940 is shown in Fig. 9. Note that these RRR values are greater than the value calculated earlier for RRR,,,. These results indicate that the heavy element contribution to pm,, was overestimated and that it is at least 20% less than expected.
4. Summary A model to predict the RRR of a niobium sample submitted to a purification heat treatment has been presented. The purification variables explicitly included in this model were sample dimensions, heat treatment time and temperature, and initial impurity concentrations. Several samples were purified to corroborate this model. It was found that the kinetics of purification were slower than expected and a temperature-dependent value of RRR,,,‘“P was also observed. For fixed-temperature heat treatments, RRR,,,‘“P was lower than the expected RRRmaXtheO. This limitation on RRR could be understood in terms of a temperature-dependent impurity concentration c,. The origin of c, is unknown. Other purification variables which may influence it are titanium layer thickness and vacuum pressure, neither of which were explicitly included in the present model. A better understanding of the thermodynamics of the purification reactions may yield a theoretical basis for c,. The data indicated that higher values of RRR could be achieved by heat treating at lower temperatures. Using the improved purification model incorporating c,, a heat treatment program was devised in which the
288
H. Safa et al. I Journal of Alloys and Compounds
furnace temperature was slowly lowered from 1300 to 1000 “C. Two samples, whose initial RRRs were about 155, were purified to yield RRRs of about 1900, exceeding our predicted value of RRR,,,. The values of RRR produced in this study are a significant advance over past results using the solid state getter technique. The procedure used is simple and does not required an expensive upgrade of furnace capability. It can also be used with niobium of lower initial purity, although the final RRR values may not be as high as those achieved with better feedstock. The procedure herein described does, however, require a longer heat treatment time. Perhaps the cost and performance benefits derived from the higher RRR values can offset this inconvenience.
Acknowledgements
The authors wish to thank M. BolorC, E. Jacques and Y. Boudigou for their assistance in making measurements. Helpful discussions with C. Antoine were also appreciated.
[l] E.A. Lynton, Superconductivity, 101.
[2] J. Bardeen, G. Rickayzen and L. Tewordt, Whys. Ref., 113(4) (1959) 982. [3] H. Padamsee, IEEE Trans. Magn., Z(2) (1985) 1007. [4] P. Kneisel, J. Less-Common Met., 139 (1988) 179. [5] G.W. Webb, Whys. Rev., 181(3) (1969) 1127. [6] R.W. Meyerhoff, J. Elecfrochem. Sot., 118(6) (1971) 997. [7] G.K. White and S.B. Woods, Can. J. Phys., 35 (1957) 892. [8] K. Schulze, J. Fuf3, H. Schultz and S. Hofmann, 2. Metallkol, 67(11) (1976) 737. [9] T.G. Berlincourt and R.R. Hake, Whys. Rev., 131( 1) (1963) 140. [lo] D.L. Moffat, Ph.D. Thesis, University of Wisconsin-Madison,
1985. [ll] J. Barthel, K.-H. Berthel, K. Fischer, R. Gebel, G. Giintzler, M. Jurisch, W. Neumann, J. Kunze, P. Miill, H. Oppermann, R. Petri, G. Sobe, G. Weise and W. Wisner, Fit. Met Metalloved., 35(5) (1973) 921; Phys. Met. Metallogr., 35(5) (1973) 23. [12] K.K. Schulze, J. Met., 33 (1981) 33. [13] E. Fromm and E. Gebhardt, Case und Kohlenstoff in Metallen,
Springer, Berlin, 1976. [14] R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.G. Wagman, Selected Values of the Thermodynamic Properties of the Elements, American Society for Metals, Metals Park, OH, 1973. [15] G. HGrz, H. Speck, E. Fromm and H. Jehn, Physik Daten: Gases and Carbon in Metals, Part VIII, Fach-informationszentrum, Energie Physik Mathematik GmbH, Karlsruhe, 1981. [16] J. Pelleg, Philos. Mag., 21 (1970) 735. [17] E. Gebhardt, W. Diirrschnabel and G. Hlirz, J. Nucl. Mater., 28 (1966) 119. [18] R.A. Pasternack and B. Evans, Trans. Metall. Sot. AIME, 233(6)
References Methuen,
London,
1969, p.
232 (1996) 281-288
(1965) 1194.
Journal
Advances
of Alloys and Compounds
in the purification
232 (1996) 281-288
of niobium by solid state gettering with titanium
H. Safa, D. Moffat, B. Bonin, F. Koechlin Centre d’Etudes
Saclay, DAPNIAISEA, Received
91191 Gif sur Yvette Gdex,
France
22 May 1995
Abstract Post-purification of commercially available niobium of moderate purity can be an effective method of producing significant quantities of high purity material. A model is presented which demonstrates how heat treatments in the presence of titanium influence the residual resistivity ratio (RRR). At short heat treatment times, nitrogen, oxygen and carbon are gettered from the bulk, causing the RRR to increase significantly. At very long times, titanium contamination causes the RRR to decrease slowly. Many samples were submitted to purification heat treatments to verify this model. An unexpected discovery was the appearance
of a temperature-dependent maximum RRR, which was interpreted as a temperature-dependent impurity concentration. It was found that lower temperatures yielded higher maximum RRRs and that increased heat treatment times were necessary to reach these RRR values. Inspired by these results, a heat treatment program was conceived which produced two samples with RRR values of about 1900, an improvement of more than an order of magnitude from the initial values. Keywords:
Niobium;
Residual
resistivity
ratio;
Solid state
purification
1. Introduction
The low temperature thermal conductivity of niobium is of great interest in the field of r.f. superconductivity (the higher, the better). The thermal conductivity K of niobium is strongly dependent on the purity of the material at low temperatures. For temperatures above 0.3T,, i.e. about 3 K, it is dominated by the electron contribution and is given by [l]
(1) where L, is the Lorentz constant, p,,, is the residual resistivity (about ~4.2 K), a is constant and f is the ratio of the superconducting to normal-state thermal conductivity [2]. For T 3 T,, f - 1. The residual resistivity ratio (RRR) may be defined as
RR&k!? p4.2
(2)
K
Thus, from these two equations, one finds that K, at low temperatures, is proportional to RRR. For this reason we shall focus on the calculation and measurement of RRR for the rest of this article. 0925~8388/96/$15.00 0 19% Elsevier SSDI 0925-8388(95)01997-9
Science
S.A. All rights
reserved
One has two options for obtaining niobium of higher purity: to purchase it directly from a vendor or to post-purify sheets of moderate purity. At present, material with an RRR of about 300 costs about five times that of material with an RRR of 30. It is expected that vendors will have difficulty in supplying sufficient quantities of higher purity niobium at an affordable price. Thus post-purification may provide niobium of a purity not otherwise available or offer an alternative to the present production method. It has been shown that either yttrium or titanium can be used as a solid state getter to purify niobium [3,4]. For a variety of reasons, titanium is at present the getter of choice. We were interested in learning the extent to which the RRR of readily available niobium could be improved using the present simple technique. In addition, if purification could be performed at lower temperatures, it could have desirable consequences. 1.1. The relationship
between
RRR and impurities
The resistivity of a metal in the normal state can be written as:
P=
Pimp
+
pdisl
+
Pgb
’
Pp~honon(~)
(3)
282
H. Safa et al. I Journal of Alloys and Compounds
where the components are the contributions due to impurities, dislocations, grain boundaries and phonons respectively. Only the phonon contribution depends on temperature. A typical value measured in this study was Pphonon (T) = 6.5 x 10P14T3 LRm (T s 25 K); this is within the measurement of [5-71. In annealed niobium, the dominant term in the resistivity at 4.2 K is that due to impurities [5,6]. The Pimp term can be expressed as a sum over the different impurities:
Pimp =
Q F,( c~ z ) I
(4)
where ci is the concentration of impurity i and aplacis its resistivity coefficient. Values for apiacfor impurities in niobium are given in Table 1. Table 2 presents a typical analysis of the niobium used in this study and shows that the light elements N, 0 and C are the most significant in terms of resistivity contribution. One can affect pimp by coating a piece of niobium with titanium. Indeed, this has two effects. Because the free energy of reaction for forming titanium carbides, nitrides and oxides is favourable (proposed purification reactions are shown in Table 3), titanium will remove these light impurities from niobium, causing pimp to decrease. On the contrary, the deposited titanium will diffuse into the niobium, causing Pimp to increase. The net effect on firnp is determined by the relative diffusivities of these impurities and the
Table 1 Resistivity coefficients of several impurities Impurity
(aplac) (X10~12nmat.ppm-’
Reference
N 0 C Hf Zr Ti W Ta
5.2 4.5 4.3 1.4 1.0 0.96 0.4 0.25
PI PI PI ]91 [91 ]9,101 [ill ]121
Table 2 Impurity analysis and resistivity contributions approximately 170 Impurity
N 0 C Zr W Ta
Impurity content (atppm) Measured
Assumed
<260 <230 <300 31 30 152
55 55 55
for niobium of RRR Resistivity (XlO~‘*nm) 286 247 236 31 12 38
232 (19%)
281-288
Table 3 Free energies of reaction for possible purification processes [13] Reaction
AG” (J mole-‘)
N(Nb) + Ti = TIN” 0( Nb) + Ti = TiO C( Nb) + Ti = TiC
-160300+24.7T -12400&7.1T -174000+53.1T
’ In this reaction, nitrogen titanium to form TiN.
in solution
in niobium
reacts with
reaction rates. Titanium has no effect on the heavy impurities such as tantalum, zirconium and tungsten. 1.2. The application of titanium The easiest manner in which to coat a sample with titanium is to wrap it in titanium foil and to place everything in a vacuum furnace. During heat treatment, titanium will evaporate from the foil and coat the sample. The vapor pressure of titanium is given by
u41 PTi = 1.56 X 1Or2exp ( -5y)(Pa)
(5)
In a Boltzmann gas, pressure is the result of atoms striking a surface. If a fraction r] of the evaporated titanium atoms which strike the niobium sample remain on it, the thickness E of the titanium layer on the sample will grow at the following rate: de dt
-=
112
(m s-l)
(6)
where M = 47.9 X 10m3kg mall’, p = 4520 kg m3 and R = 8.314 J mall’ K-‘. Note that this definition of r7 combines factors such as the sticking coefficient, the geometrical relationship of the sample to the titanium foil, and re-evaporation. One would expect v to be a function of time. Initially the deposition rate should be high. As the layer grows in thickness, equilibrium between deposition and re-evaporation should be reached and 77 should go to zero. A sample was weighed before and after a 1000 min heat treatment at 1300 “C to measure the titanium deposition rate. Using this datum and Eq. (6) an average value of 77= 0.09 was calculated. Another sample yielded a similar value. The time dependence of v has not yet been determined for our particular furnace arrangement, The purification reactions shown in Table 3 imply that one titanium atom is required for each light impurity atom in the niobium sheet in order to purify it completely. (It should be noted that there are several possible purification reactions; we propose that those in Table 3 are the most plausible.) Thus the estimated minimum titanium layer thickness is
H. Safa et al.
wd .-?a 2(w + d) 6% +
aO
+
I Journal of Alloys and Compounds 232 (1996) 281-288
(7)
+>
where uN is the atomic fraction of nitrogen etc., and w and d are the width and thickness of the sample to be purified. By way of example, for a concentration of 55 at.ppm for each impurity in a niobium sheet 2 mm thick (i.e. w = m), it would take approximately 2400 min at 1200 “C to deposit sufficient titanium for complete purification (0.16 Fm), 230 min at 1300 “C. 1.3. The diffusion of impurities The impurities in the niobium must diffuse to the niobium-titanium interface in order for purification to occur. Let us consider an infinite sheet of niobium with thickness d. Let us also assume that the impurities are uniformly distributed with an initial concentration cO. The solution to the diffusion equation D c~~c/~x~= &I& is c(x, t) = 2
For titanium, one can approximate the solution to the diffusion equation in the same manner, with the exception that the concentration at the surface is unity, yielding cTi
=
-t (1
1 - exp _r~i
exp(<)
1.4. RRR calculations
Combining the equations from Sections 1.1 and 1.3 we have ~4.2k(ty T) =i=zz,7u1 ($)ici
cos( (2n :l)Tx) +
where l/r, = (2n + 1)2r2Dld2 and D = D, exp(-T,/ T) is the diffusion coefficient. The assumption that all impurities are gettered at the niobium-titanium interfaces gives the condition c(x = &d/2) = 0 at all times. Because the diffusion times r,, decrease as 1/(2n + 1)2, the largest contribution to the sum in Eq. (8) will be the IZ= 0 term. It can be shown without too much difficulty that, for a rectangular bar of dimensions w and d, the diffusion time constant (for it = 0) becomes (9) where now 3 refers to the time constant for each impurity and Di is the corresponding diffusion coefficient. It turns out that the concentration profiles are reasonably flat; so we can approximate them with the values at the center of the sample: ci = ~(0, t) = cn
Table 4 Diffusion Impurity
N 0 C Ti a Calculated
coefficients
(10)
exp f ( ,)
(11)
Diffusion coefficients in bulk niobium for the important impurities are given in Table 4. Diffusion times for these impurities in a 2 mm X 2.5 mm bar are also shown.
+ ,=~;,
= (-1)” n-,, 2n
G%
5.1 x 1om6 1.38 x IO-’ 1.0 x lomh 9.9 x lomh for a 2 mm
X
2.5 mm bar.
Reference
T,
18 13 17 43
870 410 070 750
exp(?)
(12)
where t and T refer to the heat treatment time and temperature respectively and the contributions of pgb and pdis, have been ignored. The first two terms in Eq. (12) are not affected by titanium purification. In fact, they are the minimum value of p and yield the ultimate value of RRR. Using the values in Table 2, and the equation for pphonongiven in Section 1.1, one finds that P,,,~,= 8.58 X 10-” R m and RRR,,, = 1699. Because the quantities of light impurities in moderate purity niobium are below the detection limits of the methods normally used by niobium suppliers (see Table 2) we shall assume the same initial value of c,, for these impurities. (If desired, one could resort to more elaborate and expensive analysis techniques.) Recalling the boundary condition of Eq. (8), it is implicitly assumed in Eq. (12) that there is sufficient titanium at all times and temperatures to effect the calculated degree of purification. If this assumption is not met, the purification kinetics could be affected. The individual contributions to the resistivity as a
qr a (min) 1200°C
1300 “C
1151
296 27
131 15
P31 [I61
444 3.3 x 10’
213 5 x lox
[151
+ ~phonon(4*2K)
M,,[l-e&y
and times
D, (m’ s-‘)
283
284
H. Safa et al. I Journal of Alloys
and Compounds
232 (19%)
281-288
element impurities plus phonons. At very long times, titanium diffusion results in a slowly increasing resistivity. Calculations of RRR as a function of heat treatment time and temperature for 2 mm X 2.5 mm samples are shown in Fig. 2. A value of pzg8k = 1.458 X lo-'fim [12] was used for these calculations. At any temperature, the RRR increases relatively quickly to a maximum value and then decreases slowly. For heat treatments at 1200°C and lower, the maximum in RRR is very broad and RRR,,,‘heO = RRR,,,. The maximum Niobium bar: 2 x 2.5 mm is narrower at higher temperatures, however, and Purification temperature : 1300°C RRR,,, theo is diminished. These effects are due to increased titanium contamination of the bulk. Note that the time needed to reach RRR,,,‘h’” at 1200 “C is approximately equal to the time required to deposit sufficient titanium for complete purification. Sum Thus, we would anticipate the purification kinetics at ._~~~~__~~~~.~~--_~~~_________.--------._____-~ temperatures below 1200 “C to be limited by the titanium deposition rate. At 1200 “C and higher, we would expect purification to be diffusion limited.
function of heat treatment time at 1300°C are shown in Fig. 1. The impurity calculations were for a 2 mm x 2.5 mm niobium bar. A value of c,, = 55 at.ppm was used, which yields an initial RRR of 170. One immediately notices the rapid fall in the oxygen, nitrogen and carbon contributions. These result in a rapid decrease in the total resistivity to a point limited by the heavy
1E-09
2 g
3
lE-10
i z .G? .s .Y lE-11
2. Experimental details
3
2.1. Sample preparation and heat treatment IE-12
I I 0
500
10002000
.,
, , , , 4000
I,,
,
6Mw)
I
,
8C00
,
,
10000
Heat treatment time (minutes) Fig. 1. Calculations of the impurity contributions to the 4.2 K resistivity of a niobium bar. Note the change in scale on the time axis. The phonon contribution at 4.2 K is 4.8 X lo-‘* R m.
Niobium bar: 2 x 2.5 mm
2ooo,““,““,“.‘,““,‘.‘.,....,....,....,
Ol....‘....‘....‘...,‘,,“‘,,,,‘,,,,”,.,J 0
lOOil
2000
3000
4000
5000
6000
7000
The samples used in the present study were cut from niobium sheets 2mm thick purchased from Heraeus. The nominal RRR of this sheet was about 170. The samples varied in width from 2 to 3 mm and were about 100 mm long. The starting grain size was about 50 pm. The samples were etched before the first heat treatment only, in the standard mixture of HF, HNO, and H,PO, used for superconducting cavities, 1: 1: 2 by volume. The vacuum furnace used for the heat treatments is about 300 mm in diameter and about 600 mm tall. The maximum temperature of this furnace is 1300 “C. At this temperature, the typical operating pressure is about 4 X low5 Pa (about 4 X lo-'mbar). Several samples, surrounded by a cylinder of titanium, were placed in the center of the furnace for each heat treatment cycle. The titanium cylinder is 40 mm in diameter. A plot of the temperature and pressure in the furnace during a heat treatment is shown in Fig. 3. Each sample was used for multiple heat treatments. To illustrate this, the RRR of a sample heat treated for 1OOOmin was measured; this sample was then heat treated for another 2000min to yield a sample with a total heat treatment time of 3OOOmin. The samples were not etched between heat treatments.
8000
Heat treatment time (minutes) Fig. 2. Calculations of RRR as a function of heat treatment temperature. The calculations are based on Eq. (12). RRR,,, is 1699 for this material.
2.2. RRR measurements There are at least two methods of measuring the normal-state residual resistivity of a superconducting
H. Safa et al. I Journal of Alloys and Compounds
232 (1996) 281-288
28.5
I320
6E-4
I080
1.5E-4
360
4E-5 720
l .SE-5
4.5E-6 360
I .5E-6
8E-7
4E-7
5E-8
3
6
9
12
15
21
18
24
27
Time (hours) Fig. 3. The pressure
and temperature
of the furnace
sample below its transition temperature. One can measure the resistance of a sample at 4.2 K as a function of magnetic field above Hc3 and extrapolate to zero field. Alternatively, one can measure the resistance in zero field as a function of temperature above T, and extrapolate to 4.2 K. A typical temperature extrapolation is shown in Fig. 4. Several samples were measured using both techniques. The results for purified low initial RRR samples are shown in Fig. 5. The values obtained by both methods were in quite good agreement. Because of its relative ease, the temperature extrapolation method was used throughout this study. The definition of RRR given in Eq. (2) was used in this study. Absolute resistivities at room temperature and 4.2 K were not calculated as we were interested only in the ratio of resistivities. It was, however, necessary to correct the “room-temperature” value of the sample resistance for temperature deviations from 295 K. This was done assuming that [7,17,18]
during
a purification
treatment.
Sample purified
loo0 minutes
25
~““‘“““‘““.‘,“~1
20
0.006
0
2500
5m
Temperature3
j$=4.7X10-10QmoC-1 A quick measurement this value.
@ 1250°C
7500
loom
12503
(K3)
(13) of
dp/dT
was in agreement with
Fig. 4. Extrapolation of sample resistance as a function value of the resistance at 4.2 K (T3 = 74 K3) is needed determine RRR. This sample had an RRR of 410.
of T3. The in order to
H. Safa et al. I Journal of Alloys and Compounds
286
232 (19%)
281-288
Purification temperature: 1300°C
Purification temperature: 1300°C
‘mm 5wm
P P 0 O”..“.“...“,“.““.,‘.““”
0
1000
3ooo
zoo0
4coO
5Om
6cm
7000
8000
Heat treatment time (minutes)
3. Results aud discussion The data for samples whose initial RRR was about 170 are shown in Figs. 6 and 7. (Fig. 5 showed the results of purification heat treatments on samples whose initial RRR was about 34.) An initial increase in RRR was observed followed by a saturation in RRR. A slight decrease in RRR from RRR,,,‘“P was observed for samples heat treated at 1300 “C for long Purification temperature: 1200°C
.II,...,,.*,.,,,,,,,,,,,,,,
a 0
800 -
0 0
0
??
600 -
0
3 “I’. 2000
.
2’ .‘S 4OOa
0
“““I 6cfJ.l
8000
3 ’ ” 1mOO
3 ‘3 ” 12cm 14000
Heat treatment time (minutes) Fig. 6. RRR data for samples with c, = 6.5 atppm.
purified
at 1200 “C: -,
2000
4000
6000
8CGU
1OOOo 12000
14000
Heat treatment time (minutes)
Fig. 5. RRR data for low initial RRR samples purified at 1300°C: H, RRR values determined by temperature extrapolation; 0, measurements made with a magnetic field. The dimensions of these samples were 3 mm X 3 mm.
loo0
0
calculations
Fig. 7. RRR data for samples with c, = 13 at.ppm.
purified
at 1300 “C: -,
calculations
times. The value of RRR,,,““P was higher at 1200 “C, while the time required to reach RRR,,,““P was less at 1300°C. The increase in RRR with heat treatment time was not as fast as expected. There are several possible explanations for this: (i) it may simply be due to the uncertainty in the diffusion coefficients (the literature values vary by a factor of 2-10 [15]); (ii) the deposition rate of titanium may affect the purification kinetics; (iii) the kinetics of the reactions at the niobiumtitanium interface may be the limiting process. The experimentally observed purification rate does not appear to be strongly temperature dependent, whereas the titanium deposition rate is expected to vary by an order of magnitude between 1200 and 1300°C. One would also expect the reaction kinetics to be temperature dependent. Further investigation is required in order to determine the rate-limiting step. The data indicate a temperature-dependent RRR,,,““P which is less than RRR,,,‘h”“. This is particularly apparent for the samples heat treated at 1300 “C. This result cannot be explained by enhanced titanium diffusion alone. To confirm this, three 1 mm X 2 mm samples were heated treated at 1300 “C. The results are shown in Fig. 8. The decrease in RRR with increasing heat treatment time is in accord with that expected by titanium contamination. The observed behavior of RRR,,,““P may be interpreted as indicating a temperature-dependent equilibrium condition in the purification process (neglecting for the moment the increasing titanium contamination). This can be incorporated in the model presented above by replacing Eq. (10) with
H. Safa et al. I Journal of Alloys and Compounds
232 (1996) 281-288
1 x 2 mm samplespurified at 1300°C
281
Cooled slowly from 1300°C
10”m
.I’:/
2 lz 1 b lx
0.005 0.004 0.003 0.002 0.001
0
Fig. 8. RRR data showing the influence of titanium diffusion. Small samples (1 mm X 2 mm) were used to decrease the time needed to
observe the effect.
-t ( ,I +c, 7
5OOa
7500
1OOCG
12500
Temperature3 (K3)
Heat treatment time (minutes)
c,=(co-czc)exp
2500
(14)
where c, is the light element impurity concentration for an infinitely long heat treatment. The data imply dependent and, from the that c, is temperature thermodynamics presented in Table 3, one would expect c, to vary as exp(-constant/ T). Preliminary results also indicate that c, may depend on the furnace pressure. The physical origin of c, and the variables which affect it are presently under investigation. (For the calculations shown in Figs. 6 and 7 the same value of c, was used for nitrogen, carbon and oxygen.) The data from Figs. 6 and 7 allowed us to estimate the coefficients of c, as a function of temperature and to correct the earlier calculations of RRR,,,‘h”“. To validate this improved model, samples were subjected to a specially designed heat treatment program. Two samples, 1 mm x 2 mm with an initial RRR of about 155, were heated to 1300 “C and held there for 2 h. This should have provided a thick titanium layer and also been sufficiently long to establish equilibrium impurity concentrations. The temperature was then decreased in 50 “C steps, always allowing sufficient time for equilibrium to be reached at each step. (The stepwise decrease in temperature was made necessary by the furnace programming.) The final holding temperature was 1000 “C. The total heat treatment time was 2640 min (44 h). After this treatment, one sample had an RRR of 1880, and the other an RRR of 1940. A resistance vs. temperature curve for the sample with
Fig. 9. Extrapolation of sample resistance as a function of T’ for a well-purified sample. This sample had an initial RRR of 155; after purification the RRR was 1940.
RRR = 1940 is shown in Fig. 9. Note that these RRR values are greater than the value calculated earlier for RRR,,,. These results indicate that the heavy element contribution to pm,, was overestimated and that it is at least 20% less than expected.
4. Summary A model to predict the RRR of a niobium sample submitted to a purification heat treatment has been presented. The purification variables explicitly included in this model were sample dimensions, heat treatment time and temperature, and initial impurity concentrations. Several samples were purified to corroborate this model. It was found that the kinetics of purification were slower than expected and a temperature-dependent value of RRR,,,‘“P was also observed. For fixed-temperature heat treatments, RRR,,,‘“P was lower than the expected RRRmaXtheO. This limitation on RRR could be understood in terms of a temperature-dependent impurity concentration c,. The origin of c, is unknown. Other purification variables which may influence it are titanium layer thickness and vacuum pressure, neither of which were explicitly included in the present model. A better understanding of the thermodynamics of the purification reactions may yield a theoretical basis for c,. The data indicated that higher values of RRR could be achieved by heat treating at lower temperatures. Using the improved purification model incorporating c,, a heat treatment program was devised in which the
288
H. Safa et al. I Journal of Alloys and Compounds
furnace temperature was slowly lowered from 1300 to 1000 “C. Two samples, whose initial RRRs were about 155, were purified to yield RRRs of about 1900, exceeding our predicted value of RRR,,,. The values of RRR produced in this study are a significant advance over past results using the solid state getter technique. The procedure used is simple and does not required an expensive upgrade of furnace capability. It can also be used with niobium of lower initial purity, although the final RRR values may not be as high as those achieved with better feedstock. The procedure herein described does, however, require a longer heat treatment time. Perhaps the cost and performance benefits derived from the higher RRR values can offset this inconvenience.
Acknowledgements
The authors wish to thank M. BolorC, E. Jacques and Y. Boudigou for their assistance in making measurements. Helpful discussions with C. Antoine were also appreciated.
[l] E.A. Lynton, Superconductivity, 101.
[2] J. Bardeen, G. Rickayzen and L. Tewordt, Whys. Ref., 113(4) (1959) 982. [3] H. Padamsee, IEEE Trans. Magn., Z(2) (1985) 1007. [4] P. Kneisel, J. Less-Common Met., 139 (1988) 179. [5] G.W. Webb, Whys. Rev., 181(3) (1969) 1127. [6] R.W. Meyerhoff, J. Elecfrochem. Sot., 118(6) (1971) 997. [7] G.K. White and S.B. Woods, Can. J. Phys., 35 (1957) 892. [8] K. Schulze, J. Fuf3, H. Schultz and S. Hofmann, 2. Metallkol, 67(11) (1976) 737. [9] T.G. Berlincourt and R.R. Hake, Whys. Rev., 131( 1) (1963) 140. [lo] D.L. Moffat, Ph.D. Thesis, University of Wisconsin-Madison,
1985. [ll] J. Barthel, K.-H. Berthel, K. Fischer, R. Gebel, G. Giintzler, M. Jurisch, W. Neumann, J. Kunze, P. Miill, H. Oppermann, R. Petri, G. Sobe, G. Weise and W. Wisner, Fit. Met Metalloved., 35(5) (1973) 921; Phys. Met. Metallogr., 35(5) (1973) 23. [12] K.K. Schulze, J. Met., 33 (1981) 33. [13] E. Fromm and E. Gebhardt, Case und Kohlenstoff in Metallen,
Springer, Berlin, 1976. [14] R. Hultgren, P.D. Desai, D.T. Hawkins, M. Gleiser, K.K. Kelley and D.G. Wagman, Selected Values of the Thermodynamic Properties of the Elements, American Society for Metals, Metals Park, OH, 1973. [15] G. HGrz, H. Speck, E. Fromm and H. Jehn, Physik Daten: Gases and Carbon in Metals, Part VIII, Fach-informationszentrum, Energie Physik Mathematik GmbH, Karlsruhe, 1981. [16] J. Pelleg, Philos. Mag., 21 (1970) 735. [17] E. Gebhardt, W. Diirrschnabel and G. Hlirz, J. Nucl. Mater., 28 (1966) 119. [18] R.A. Pasternack and B. Evans, Trans. Metall. Sot. AIME, 233(6)
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