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AKS doped tungsten wires-investigated by electrical measurements
International Journal of Refractory Metals & Hard Materials 20 (2002) 319–326 www.elsevier.com/locate/ijrmhm
AKS doped tungsten wires-investigated by electrical measurements II. Impurities in tungsten L. Uray Research Institute for Technical Physics and Materials Science of the Hungarian Academy of Sciences, Budapest, P.O. Box 49, H-1525, Hungary Received 29 April 2002; accepted 21 June 2002
Abstract The Al, K, Si doped tungsten wires contain several minor impurities (in the ppm range), which are usually measured by chemical analysis. The excess electrical resistivity measures only those impurities, which are present in solute form. However, this property enables the resistivity to follow solution–dissolution processes, and solute interactions with lattice defects. Combining the resistivity measurements e.g. by thermoelectric power, it helps separating several kinds of solute impurities from each other. Processes like segregation–desegregation (Fe, Co), oxidation–reduction (Al, Si), and the development of the stationary evaporation profile, can be studied as well. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Tungsten; Electrical resistivity; Thermoelectric power; Segregation; Oxidation
1. Introduction In the production of non-sag tungsten wires and filaments the Al, K, Si (AKS) doping has basic importance. The majority of the dopes evaporates during sintering, except the insoluble potassium, which can be partly entrapped in the bubbles. The non-sag property develops only in the wire, in connection with the development of the potassium bubble rows [1–4]. Several other impurities occur in tungsten, some of which can have specific importance. Dopes like Fe and Co are sometimes added to improve the high temperature mechanical properties [5]. Thoriated wire (0.5–3% ThO2 ) can be used for filaments subject to vibrational or impact loading, and tungsten–rhenium wire (3–5% Re) in cases where a particular combination of high strength, ductility and impact resistance is essential, and also for high temperature thermocouples [6]. The usual method for determining the dope or impurity concentration is the chemical analysis, which is quantitative and selective. Accordingly, at a first glance, the role of the resistivity measurements seems questionable. However, chemical analysis measures the total
E-mail address: [email protected] (L. Uray).
impurity content, while electrical resistivity measures only those impurities, which are present in solid solution. In this way the resistivity is not too sensitive to second phases like K or ThO2 , but it is rather sensitive (even in the ppm range) to solute impurities, like e.g. Fe, Ni, Co, Al, Si. In this way resistivity is especially applicable to follow solution–dissolution processes. In addition, by combining resistivity with other methods, like e.g. with thermoelectric power, the measurements will be suitable to separate different kinds of solutes. When tungsten rods or wires are heated at very high temperatures, the usual solute impurities are mostly volatile, compared to tungsten. According to this, the solutes evaporate from the surface layers, compensated partly by diffusion from the interior. During this process a surface condition, D grad c ¼ aðcs co Þ, exists, in which a characterizes the relative evaporation rate of solute to tungsten, cs and co are the actual and equilibrium concentrations of solute just below the surface [7]. Applying sufficiently long evaporation time, a stationary evaporation profile develops, having the form of Bessel functions, like Jo ðb1 r=r0 Þ, in which r is the local radius, r0 is the radius of the wire and b1 is the first root of the equation, bJ1 ðbÞ LJo ðbÞ ¼ 0 (at L ! 1 b1 2:405). Here L ¼ ar0 =D is a dimensionless parameter, which may be called volatility parameter, and D is the diffusion constant [7].
0263-4368/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 2 ) 0 0 0 3 2 - X
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difference of about 20 K. According to the Nordheim– Gorter rule [12], DS is connected to the excess resistivity by the following equation: DS ¼ Sx d=ð1 þ dÞ
ðwith d ¼ Dqbulk =qw ðTo ÞÞ
ð1Þ
in which Sx is the so called ‘‘characteristic thermopower’’ for the specific impurity. The differences in the Sx values for different solutes can help in distinguishing between them (like in copper or tungsten [13]). Sx is usually high for magnetic or transition metal impurities and low for common impurities or for lattice defects. Fig. 1. (a) The development of the evaporation pffiffiffiffiffiffiprofiles at L ! 1. (The profile is near to the stationary one at Dt=r0 P 0:4.) (b) The variations of the average concentration with decreasing radius, cav ðr=r0 Þ at stationary evaporation profiles with different L values. The relative radius, r=r0 , is normalized to 1 at r=r0 ¼ 1.
The evaporation profiles are illustrated in Fig. 1a and b. Starting with homogeneous solute distribution in the cross-section, Fig. 1a shows the p variations in the profile ffiffiffiffi (at L ! 1) with annealing. If Dt=r0 > 0:3, then the evaporation profile is near to the stationary one (t is the annealing time). The stationary evaporation profiles for different L values are presented in Fig. 1b. For common solutes in tungsten wires L is typically as high as 107 – 109 , but it can be much less for some refractory metal solutes.
2. Evaluation of measurements The electrical resistivity of the specimens is determined in the following way (see in more details in the part I of this paper): The so called ‘‘effective’’ resistivity, qeff , is obtained from the measured resistance, R, by using the external geometrical sizes of the specimen (length and cross-section). The ‘‘bulk’’ resistivity, qbulk , takes into account also the internal geometrical obstacles, like second phases and cracks. qbulk cannot be measured directly, it can be calculated only from the resistivity ratios, from which the geometrical factors disappear. In porous materials qeff and qbulk are much different from each other, while in thin non-sag tungsten wires they are almost the same (qeff =qbulk 1:004 is suggested from the K bubble concentrations [8]). Comparing the resistivity to that of a ‘‘pure’’ tungsten, qw , the excess electrical resistivity, Dq ¼ qbulk ðT Þ qw ðT Þ, is about proportional to the concentration of solute impurities, and it is nearly independent of temperature (due to the MatthiessenÕs rule (MR) [9]). By all means the temperature dependence of Dq is much less than that of the resistivity [10,11]. Thermoelectric power, DS, was applied as a different kind of electrical measurement, in which the specimens were compared to a pure dummy, at a temperature
3. Solute impurities in tungsten 3.1. Comparison with chemical analysis A series of measurements were made on tungsten wires containing some single solute impurities, to compare their excess resistivities (near the ambient), Dq(300 K), to their chemical concentrations. Single solutes could be obtained in the specimens e.g. in the following ways: (a) The soluble element is doped to the material in majority concentration, and at measurements correction is made for the possible other impurities. (b) The element is deposited on the wire surface (electrolytically or by evaporation in vacuum) and a part of it is diffused into the wire through grain boundaries (at 1800–2000 K). Then the solute in the wire is homogenized by annealing at high temperatures (at 2800–3000 K), and at last the homogeneity can be improved by reducing the diameter of the wire by etching. At most solutes the measured concentrations were between about 0.01 and 0.1 at.%, except Mo and Re (4 and 2 at.%). Fig. 2 shows the measured excess resistivities, Dq(300 K), against the chemical concentrations, c [14,15]. For comparison, the line for vacancies is also shown [16,17]. The slopes of the lines, Dq(300 K)/c, are listed also in Table 1. For most solutes the Dq=c values are not too far from each other (between 6 and 14 lX cm/at.%) and from that for vacancies. This means, that Dq=c is not too specific for the different kinds of solute atoms. Exceptions are some refractory metals, which are near to tungsten in the Periodic Table, like Mo and Re. Naturally, the insoluble potassium, forming the bubble rows in tungsten, cannot be included in this table. Interstitial impurities, like carbon, can be compared to the chemical concentrations only after appropriate quenching [18,19]. Beside excess resistivity measurements at the ambient, Dq(300 K), low temperature measurements, e.g. at 77 or 4.2 K, are often preferred due to the expected higher
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Fig. 2. The ambient excess resistivities, Dq300 K , against the concentrations of solutes (in at.%) in tungsten, compared to that of vacancies.
accuracy. The temperature dependence of the excess resistivities, DqðT Þ, usually called deviations from the MR, were determined for different solutes of tungsten between T 2 and 300 K, and Fig. 3 presents the normalized ratios, DqðT Þ=Dqð300 KÞ [11]. The data were measured on homogenized wires to avoid effects of inhomogeneous distribution of solutes. The DqðT Þ= Dqð300 KÞ ratios were found similar for the solute impurities Fe, Ni, Pt, Al and also for Co (except the minimum in WCo at T 10 K, due to Kondo effect [20]). The slopes of the curves become small between T 200 and 300 K. However, these functions are markedly different for Mo and Re solutes, surely due to the fact, that direct scattering of electrons on these atoms is relatively small, while their effect on the phonon spectrum is more emphasized due to the mass or charge differences [11]. 3.2. Evaporation profiles in tungsten wire In tungsten rods the sintering usually results in evaporation profiles of the solutes, like in cases of solute Al [21] or Fe (part I, Fig. 4). These profiles can survive
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Fig. 3. The temperature dependence of the excess resistivities, DqðT Þ, due to different solute impurities in tungsten (normalized to 1 at T ¼ 300 K).
Fig. 4. The measured solute distributions in the cross-section of tungsten wires (diam. 0.17 mm), compared to the theoretical integral distributions (from Fig. 1b), (a) after annealing at 2800 K for 15 min., and (b) after annealing at 3000 K for 3 h.
swaging and drawing, and are expected to be visible also in wires. To see this, a series of measurements were made on different wires (with diameter 0.17 mm), having some surplus Fe, Co or Al þ Si solutes (0.02–0.03 at.%), or some excess Mo or Re (1–0.5 at.%). They were recrystallized at 2800 K for 15 min or annealed at 3000 K for
Table 1 The excess resistivity for unit concentration (Dqbulk =c) and the characteristic thermoelectric power (Sx ¼ ½1 þ d =d) for different solutes in tungsten Element
Dqbulk (300 K)/c (lX cm/at.%)
Dqbulk (300 K)/c (lX cm/wt.%)
Sx (lV/K)
Fe Co Ni Pt Al Mo Re Nb Ta Si Vacancies Grain boundaries
8 14 6 10 9 0.25–0.3 1.3 0.5 1–0.3 – 6–7 –
19 30 13 9 64 0.5–0.6 1.2 1 1–0.3 –
24 17 13 6 )1.3 16 15
)2.5 þ6 0( 1)
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3 h, then their diameters were decreased in several steps by electropolishing to about 50% or 60%, measuring the resistivities in each step. The measured relative excess resistivities, DqðrÞ=Dqðr0 Þ, are presented in Fig. 4a and b. The measurements were made at temperatures near the ambient (between T 200 and 300 K) to avoid effects of inhomogeneous distribution on Dq. The measured data are compared to the curves for stationary evaporation profiles with different L ‘‘volatility’’ parameters. Annealing the wires at 2800 K for 15 min they recrystallized, while only a small fraction of the solute evaporated, not altering much the inherited profile (see Fig. 1a). The profiles for wires with excess Fe or Co lay near to stationary evaporation profiles with high volatility parameters (L ! 1), while those with excess Al þ Si differ from that markedly (Fig. 4a). The different behavior might be due to the fact, that this sort of wire was taken from different source, made probably with different sintering technology. Annealing the wires at 3000 K for 3 h the solute concentration decreased near to its half, and this effective evaporation helped the development of a nearly stationary evaporation profile (Fig. 4b). In this case the data lay on curves with large L values even at wires with excess Al þ Si. For refractory metal solutes, like Mo or Re, the volatility parameters, L, are expected to be much less. This is especially true in case of solute Re, at which L 1 (see Fig. 4b).
Fig. 5. Norton–Gorter diagrams (DSð1 þ dÞ against d), measured on different tungsten wires, doped by diffusion from the surface; (a) with Ni, or (b) with Al.
3.3. Distinguishing between solutes The excess electrical resistivity, Dq, is not too specific to the different solutes (Fig. 2). This can be improved by measuring also another, more specific parameter, like the thermoelectric power, DS. Measuring both Dq and DS, the DSð1 þ dÞ versus d ð¼ Dq=qw Þ lines are expected to be linear for the single solutes, with slopes, Sx , which are called characteristic thermopowers for the ‘‘x’’ solute (Eq. (1)). Fig. 5 presents an example, when different concentrations of Ni or Al were diffused into some tungsten wires from their surfaces. The effects of Ni in the different wires are parallel lines with high slopes, Sx 13, while the effects of Al are also parallel lines, but with negative slopes, Sx 1:5. The diagram demonstrates a vectorial addition rule for solutes. (It is worth mentioning here, that at further increase of the Ni content the wire became brittle, suggesting varied structure due to the so called ‘‘diffusion induced grain boundary motion’’ (DIGM) [22].) DS and Dq were measured on tungsten wires with several different solute impurities, and the measured DSð1 þ dÞ versus d ð¼ Dq=qw Þ lines are presented in Fig. 6 [13,23,24]. In addition, an annealing diagram is also shown, showing the effects of different types of lattice
Fig. 6. DSð1 þ dÞ against d ð¼ Dq=qw Þ diagrams for tungsten with different solute impurities and with lattice defects (marked by the stage numbers, III, IV, V, VI.).
defects (marked by the annealing stages, III, IV, V) [13,24]. The characteristic thermopowers, Sx are enlisted also in Table 1. Sx is high for magnetic impurities, like Fe, Co or Ni, but also high for transition metal impurities, like Mo and Re, which have otherwise only small effects on the resistivity (Fig. 2). Sx is not only small, but even negative for common solutes Al and Si. For grain boundaries or dislocations Sx 0 (stages IV and V), while for point defects (stage III) Sx 4–6.
4. Interaction between solutes and lattice defects 4.1. Segregation and evaporation of solutes Interactions between solutes and lattice defects are not easily investigated by electrical resistivity due to the large background effects of dislocations or grain boundaries (part I, Fig. 6). The application of thermo-
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electric power seems preferable, since for dislocations and grain boundaries Sx 0 (Table 1.) so their effects are negligible. Therefore, a non-sag tungsten wire with excess cobalt dope [5] was investigated. The specimens were annealed at different temperatures between T ¼ 1000 and 3000 K for 15 min and thermoelectric powers, DS, were measured on them (d 1, Eq. (1)). Fig. 7 present DS against T on two non-sag tungsten wires, with or without excess Co dope, (marked by ‘‘W þ Co’’ or ‘‘W’’, respectively). The ‘‘WCo’’ diagram reveals two minima, one at T 1500 K, and the other at T 2400 K, while no similar effects can be seen on the ‘‘W’’ diagram. The first minimum was identified on the fracture surfaces by AES with the segregation of Co to the grain boundaries (5 at.%, [25]). (Similar segregation was found in iron doped W [26].) Segregation is expected to occur at temperatures, at which the solute atoms can diffuse to the grain boundaries. According to the diffusion data for WFep[27] ffiffiffiffi and WCo [28], the estimated diffusion lengths, Dt 0:07–0:3 nm, are too small compared to the grain size (400 nm [29]), so diffusion to grain boundaries ought to be negligible. However, segregation could occur by another effect, namely that grain growth occurs, when the moving grain boundaries collect the solute atoms from the bulk, like in [30]. Annealing above 1500 K, the segregation diminishes, partly due to the re-solution of the segregated atoms, and partly due to the decreasing grain boundary area. The nature of the second minimum in Fig. 7 is further investigated in Fig. 8. Here annealing was made at different temperatures between T 1700 and 2800 K, and the annealing time was increased successively from (1, 5 min) 15 to 90 min, and finally the specimens were recrystallized (dotted line) at 2800 K for 15 min. Between T ¼ 1700 and 2000 K a part of the solute segregated to the grain boundaries, but this segregation disappeared after recrystallization. However, between about 2200
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Fig. 8. The thermoelectric powers, DS, against the annealing temperature, T (K), on tungsten wire with excess Co dope. The annealing time is increased from (1, 5 min) 15 to 90 min successively, and then recrystallized at 2800 K for 15 min.
and 2600 K the minimum deepened with increasing annealing time, and the recrystallization did not change DS any more. Accordingly, an annealing at 2400 K for 90 min made a permanent decrease in DS, to about its 20%, which means that the total Co concentration decreased to a very low value. Since in this process the axial grain size was only about 1 lm, this suggests an effective outdiffusion of Co through the grain boundaries to the surface [31–33] from where it could evaporate. This outdiffusion of Co from the wires was controlled also by chemical analyses, presented in Table 2 [34]. Recrystallization increased the grain size to about the wire size (170 lm) so after it only the bulk diffusion was effective [28], which was much slower. Since the recrystallization was full after an annealing at 2800 K for 15 min, a further increase of the annealing time to 90 min varied DS only little, so bulk diffusion resulted only in the evaporation of a small fraction of the Co content. 4.2. Oxidation–reduction of Al and Si
Fig. 7. The thermoelectric power, DS, measured on wires with or without excess Co dope (‘‘W þ Co’’ and ‘‘W’’ respectively), after annealing at different temperatures between 1000 and 3000 K. The two minima are marked by 1 and 2.
An AKS (non-sag) tungsten wire was investigated, which was first recrystallized at 2700 K for 15 min. Then the wire was annealed at 2200 K for longer time, while the measured excess resistivity, Dq, continuously decreased (Fig. 9). The rate of decreasing depended also on the vacuum (105 or 106 mbar O2 ). Annealing the wire again at 2700 K, Dq increased to its initial value within 5–10 min (Fig. 9). The whole cycle could be repeated several times [35]. The decrease of Dq at 2200 K was explained by the internal oxidation of Al and Si, and similarly its increase at 2700 K was due to their reduction. The oxidation at 2200 K was confirmed also by its vacuum dependence. The process of oxidation–reduction was investigated also by measuring both excess resistivity and
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Table 2 The analytical Co concentration and thermoelectric power on samples annealed at the indicated temperatures for 90 min and measured after a final anneal at 2800 K for 15 min Annealing
1700 K, 90 min þ recryst:
2000 K, 90 min þ recryst:
2200 K, 90 min þ recryst:
2400 K, 90 min þ recryst:
2600 K, 90 min þ recryst:
2800 K, 15 min
DS (lV/K) Co (at.ppm) Co (wt.ppm)
1.274 255 82
1.105 215 69
0.769 162 52
0.283 50 16
0.750 137 44
1.239 283 91
The data of the last column were obtained on samples on which only the final anneal was carried out (see also Fig. 8).
Fig. 9. An AKS doped tungsten wire was first recrystallized at 2700 K for 5 min. Then at annealing at 2200 K for long time, the excess resistivity, Dq, was found to decrease (its rate depends on the vacuum). Annealing the wire again at 2700 K, Dq was found to increase (oxidation–reduction process).
thermoelectric power, to be able to distinguish between different solutes. Therefore measurements were made on a wire with some excess dopes (35 wt ppm K, 62 wt ppm Al, 27 wt ppm Si and 14 wt ppm Fe). The measured data are presented on a DSð1 þ dÞ versus d ð¼ Dq=qw ; 1Þ diagram in Fig. 10. The wire was first recrystallized at 2800 K for 15 min. Then it was annealed at 2200 K for 1 and 5 h, successively, while the data points were found to move along a straight line with slope: Sx 1:5 lV/ K. Annealing it again at 2800 K for 15 min, the data points returned to the initial point along the same line. The negative Sx slope corresponds to Al or Si (Fig. 6), suggesting their internal oxidation and reduction. Annealing a specimen from the same wire at 2900 K for 5 and for 14 h, and another one at 3000 K for 1 and for 3 h, the data points moved along straight lines but with slopes Sx þ 4 lV/K. This characteristic thermopower corresponds to about the weighted average for those of Al, Si and Fe (Table 1). Annealing at very high temperatures (2900, 3000 K) results in an evaporation of solute impurities from the wire. The straight line for the evaporation suggests about similar diffusion constants for the enlisted solutes, and the calculated diffusion constants are near to that for WFe [27].
Fig. 10. On recrystallized (at 2800 K for 15 min) AKS tungsten wire oxidation occurs at 2200 K (for 1 and 5 h) and reduction at 2800 K for 15 min, resulting in a straight line with slope: Sx 1:5 lV/K. Annealing the wire at 2900 K (for 5–14 h) or at 3000 K (for 1–3 h), the slope of variations is: Sx þ4 lV/K.
5. Discussion 5.1. Deviations from the MR at evaporation profiles If the concentration of solute has cylindrical symmetry in the wire (with radius r0 ), the local excess resistivity (at radius r) is Dqðr=r0 Þ, so the resistivity is qw ðT Þ þ Dqðr=r0 Þ, supposing the MR is locally true [9]. Since in parallel conductors the measured resistivity is obtained from the average conductivity, rav , instead of the average resistivity, qav , so qmeas ðT Þ 1=rav ðT Þ Z s0 1 1 ðqw ðT Þ þ Dqðr=r0 ÞÞ 2rpdr ¼
ð2Þ
0
At the given small concentrations of solutes at the ambient qw ðT Þ ðr=r0 Þ, so in this case 1=rav qav . However, at very low temperatures, i.e. at T ! 0 K, qw ðT Þ ! 0 too, so in Eq. (2). it is only ðDqðr=r0 ÞÞ1 , which is averaged over the cross-section. If tungsten wires contain only the common volatile solutes, the estimated volatility parameters are as high as L ¼ 107 –109 , hardly distinguished from the L ! 1 case. In this case at T ¼ 0 K a surface layer has near zero resistivity,
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which short-circuits the whole measured resistivity. According to this, the measured resistivity ought to be near to zero, in contrast to the relative values 0.5–0.7, measured on homogenized solutes (Fig. 3). Although the concentration of solutes goes near to zero in the depleted zone at the surface, this is not really true for the local resistivity at the surface. The reason for this is, that especially in thin wires, the electronic mean free path, k, can be much larger than the size of this depleted zone. This case can be calculated from the Boltzmann equation, in which a new characteristic parameter, r0 =khom , appears. Here khom would be the electronic mean free path at T ! 0 K, supposing the same solute was homogeneously distributed in the cross-section [20]. According to this parameter, the measured DqðT Þ depends much on the diameter of the wire and on the average concentration of the solute. So in rods with high solute concentrations at T ! 0 K, Dq=Dqhom ! 0, but at very thin wires with some ppm concentrations of solutes Dq=Dqhom 1. These considerations call the attention, that the low temperature DqðT Þ values in Fig. 3 can be measured only after careful homogenization. 5.2. Evaporation by diffusion If we have homogeneous solute distribution in the cross-section of the wire, then an annealing at very high temperatures for long time results in a stationary evaporation profile (see Fig. 1a). Its shape does not vary with further annealing, but the total concentration decreases exponentially, like this [7]: c=co ¼ expðb21 Dt=r02 Þ
ð3Þ
where D is the diffusion constant at the given temperature, t is the diffusion time and r0 is the radius of the wire. In some cases the solute profile was found near to the stationary one already after recrystallization (e.g. at Fe or Co solutes, like in Fig. 4a). In these cases Eq. (3) is formally valid even after annealing at shorter times. Very long annealing times can be attained by heating coils or coiled coils in ready made lamps. So in different types of lamps the total outdiffusion could be followed within temperatures 2480–3000 K [36]. However, in these measurements the errors were relatively large, mostly due to the weldings and the uncertain contacts with the consoles. Together with this, the determination of the diffusion constant may be connected with several problems, some of which are enlisted here: • The presence of the stationary evaporation profile must be verified. • The validity of the MR, in DqðT Þ can be doubtful, especially when measuring at 4 or 77 K. • The different solutes must be separated from each other.
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• Tungsten itself evaporates during annealing, so at current heating the annealing temperature needs special control.
6. Conclusions In contrast to the chemical analysis, direct currrent electrical measurements are sensitive only to the impurities, present in solute form. However, electrical measurements are sensitive to very small concentrations, and as non-destructive test, applicable to follow small variations occurring in different processes. Some applications described in this paper are enlisted here: 1. The specific resistivities for common solutes are between about Dqð300 KÞ ¼ 6 and 14 lX cm=at:%, but much less for some transition metal impurities, like Mo, Re. Their temperature dependencies are also similar (between 2 and 300 K), but different for Mo, Re. 2. The internal distribution of volatile solutes in tungsten wires varies with annealing temperature and time, and finally a stationary evaporation profile develops in the wires. Its shape is different for some transition metal solutes (like Mo and especially Re). 3. Measuring also thermoelectric power, several solutes can be distinguished from each other. Magnetic or transition metal solutes (Fe, Co, Ni and even Mo and Re!) have large effect on the thermoelectric power, but the effect of some common solutes (Al, Si) are even negative. 4. Fe and Co segregates to the grain boundaries at about 1500 K. The majority of solutes (Co) can evaporate from the wire by grain boundary diffusion at 2400 K for 90 min (with 1 lm grain size), while bulk diffusion makes this possible only at about 3000 K for 3–14 h. 5. In case of Al and Si solutes internal oxidation appears at about 2200 K, the oxidation rate is depending on the oxygen pressure.
Acknowledgements The author wishes to thank Dr. I. Gaal for helpful discussions. This work was supported by the National Research Fund (OTKA), contract no. T.32730.
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[18] Krautz E, Kuhlmann HH, Schultz H. Z Metallkde 1958;49:399– 403. [19] Kuhlmann HH. In: Technisch Wissenschaftliche Abhandlungen der Osram-Gesellschaft, II. Berlin: Springer; 1973. p. 328–32. [20] Uray L, Vicsek T. Philos Mag B 1978;37:341–52. [21] Krautz E, Schultz H. In: Technisch-wissenschaftliche Abhandlungen der Osram-Gesellschaft, Band 7. Berlin: Springer Verlag; 1958. p. 259–68. [22] Cahn JW, Pan JD, Balluffi RW. Scripta Met 1979;13:499–502. [23] Greig D. In: Blatt FJ, Schroeder PA, editors. Thermoelectricity in metallic conductors. NY: Plenum Press; 1978. p. 91–106. [24] Uray L. Phys Stat Sol (a) 1985;91:729–35. [25] Sulyok A, private communication. [26] Uray L, Menyhard M. Phys Stat Sol (a) 1984;84:65–72. [27] van Liempt IAM. Rac Trav Chim Phys-Bas 1945;64:239. [28] Klotsman SM, Osetrov SV, Timofeev AN. Phys Rev B Condens Matter 1992;46:2831–7. [29] Snow DB. Met Trans A 1976;7A:783–94. [30] Kasen MB. Acta Metall 1983;31:489–97. [31] Tyshkevich VM. Metallofiz 1971;37:58. [32] Lee JS, Vieregge K, Herzig C. Scripta Met 1988;22:1639–43. [33] Arkhipova NK, Kaygorodov VN, Klotsman SM, Kozhevina EV. J Appl Phys 1992;72:454–60. [34] Tekula-Buxbaum P, private communication. [35] Gaal I, Harmat P, Kele A, Liptak L, Major J, Uray L. The rate of oxygen uptake and release in tungsten. In: Ortner HM, editor. Proceedings of the 10th International Plansee Seminar, RM31, vol. 1. AG.Reutte: Plansee; 1981. p. 207–9. [36] Uray L, Neugebauer JM, Gaal I. Acta Tech Acad Sci Hung 1974;78:393–404.
AKS doped tungsten wires-investigated by electrical measurements II. Impurities in tungsten L. Uray Research Institute for Technical Physics and Materials Science of the Hungarian Academy of Sciences, Budapest, P.O. Box 49, H-1525, Hungary Received 29 April 2002; accepted 21 June 2002
Abstract The Al, K, Si doped tungsten wires contain several minor impurities (in the ppm range), which are usually measured by chemical analysis. The excess electrical resistivity measures only those impurities, which are present in solute form. However, this property enables the resistivity to follow solution–dissolution processes, and solute interactions with lattice defects. Combining the resistivity measurements e.g. by thermoelectric power, it helps separating several kinds of solute impurities from each other. Processes like segregation–desegregation (Fe, Co), oxidation–reduction (Al, Si), and the development of the stationary evaporation profile, can be studied as well. 2002 Elsevier Science Ltd. All rights reserved. Keywords: Tungsten; Electrical resistivity; Thermoelectric power; Segregation; Oxidation
1. Introduction In the production of non-sag tungsten wires and filaments the Al, K, Si (AKS) doping has basic importance. The majority of the dopes evaporates during sintering, except the insoluble potassium, which can be partly entrapped in the bubbles. The non-sag property develops only in the wire, in connection with the development of the potassium bubble rows [1–4]. Several other impurities occur in tungsten, some of which can have specific importance. Dopes like Fe and Co are sometimes added to improve the high temperature mechanical properties [5]. Thoriated wire (0.5–3% ThO2 ) can be used for filaments subject to vibrational or impact loading, and tungsten–rhenium wire (3–5% Re) in cases where a particular combination of high strength, ductility and impact resistance is essential, and also for high temperature thermocouples [6]. The usual method for determining the dope or impurity concentration is the chemical analysis, which is quantitative and selective. Accordingly, at a first glance, the role of the resistivity measurements seems questionable. However, chemical analysis measures the total
E-mail address: [email protected] (L. Uray).
impurity content, while electrical resistivity measures only those impurities, which are present in solid solution. In this way the resistivity is not too sensitive to second phases like K or ThO2 , but it is rather sensitive (even in the ppm range) to solute impurities, like e.g. Fe, Ni, Co, Al, Si. In this way resistivity is especially applicable to follow solution–dissolution processes. In addition, by combining resistivity with other methods, like e.g. with thermoelectric power, the measurements will be suitable to separate different kinds of solutes. When tungsten rods or wires are heated at very high temperatures, the usual solute impurities are mostly volatile, compared to tungsten. According to this, the solutes evaporate from the surface layers, compensated partly by diffusion from the interior. During this process a surface condition, D grad c ¼ aðcs co Þ, exists, in which a characterizes the relative evaporation rate of solute to tungsten, cs and co are the actual and equilibrium concentrations of solute just below the surface [7]. Applying sufficiently long evaporation time, a stationary evaporation profile develops, having the form of Bessel functions, like Jo ðb1 r=r0 Þ, in which r is the local radius, r0 is the radius of the wire and b1 is the first root of the equation, bJ1 ðbÞ LJo ðbÞ ¼ 0 (at L ! 1 b1 2:405). Here L ¼ ar0 =D is a dimensionless parameter, which may be called volatility parameter, and D is the diffusion constant [7].
0263-4368/02/$ - see front matter 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 2 ) 0 0 0 3 2 - X
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difference of about 20 K. According to the Nordheim– Gorter rule [12], DS is connected to the excess resistivity by the following equation: DS ¼ Sx d=ð1 þ dÞ
ðwith d ¼ Dqbulk =qw ðTo ÞÞ
ð1Þ
in which Sx is the so called ‘‘characteristic thermopower’’ for the specific impurity. The differences in the Sx values for different solutes can help in distinguishing between them (like in copper or tungsten [13]). Sx is usually high for magnetic or transition metal impurities and low for common impurities or for lattice defects. Fig. 1. (a) The development of the evaporation pffiffiffiffiffiffiprofiles at L ! 1. (The profile is near to the stationary one at Dt=r0 P 0:4.) (b) The variations of the average concentration with decreasing radius, cav ðr=r0 Þ at stationary evaporation profiles with different L values. The relative radius, r=r0 , is normalized to 1 at r=r0 ¼ 1.
The evaporation profiles are illustrated in Fig. 1a and b. Starting with homogeneous solute distribution in the cross-section, Fig. 1a shows the p variations in the profile ffiffiffiffi (at L ! 1) with annealing. If Dt=r0 > 0:3, then the evaporation profile is near to the stationary one (t is the annealing time). The stationary evaporation profiles for different L values are presented in Fig. 1b. For common solutes in tungsten wires L is typically as high as 107 – 109 , but it can be much less for some refractory metal solutes.
2. Evaluation of measurements The electrical resistivity of the specimens is determined in the following way (see in more details in the part I of this paper): The so called ‘‘effective’’ resistivity, qeff , is obtained from the measured resistance, R, by using the external geometrical sizes of the specimen (length and cross-section). The ‘‘bulk’’ resistivity, qbulk , takes into account also the internal geometrical obstacles, like second phases and cracks. qbulk cannot be measured directly, it can be calculated only from the resistivity ratios, from which the geometrical factors disappear. In porous materials qeff and qbulk are much different from each other, while in thin non-sag tungsten wires they are almost the same (qeff =qbulk 1:004 is suggested from the K bubble concentrations [8]). Comparing the resistivity to that of a ‘‘pure’’ tungsten, qw , the excess electrical resistivity, Dq ¼ qbulk ðT Þ qw ðT Þ, is about proportional to the concentration of solute impurities, and it is nearly independent of temperature (due to the MatthiessenÕs rule (MR) [9]). By all means the temperature dependence of Dq is much less than that of the resistivity [10,11]. Thermoelectric power, DS, was applied as a different kind of electrical measurement, in which the specimens were compared to a pure dummy, at a temperature
3. Solute impurities in tungsten 3.1. Comparison with chemical analysis A series of measurements were made on tungsten wires containing some single solute impurities, to compare their excess resistivities (near the ambient), Dq(300 K), to their chemical concentrations. Single solutes could be obtained in the specimens e.g. in the following ways: (a) The soluble element is doped to the material in majority concentration, and at measurements correction is made for the possible other impurities. (b) The element is deposited on the wire surface (electrolytically or by evaporation in vacuum) and a part of it is diffused into the wire through grain boundaries (at 1800–2000 K). Then the solute in the wire is homogenized by annealing at high temperatures (at 2800–3000 K), and at last the homogeneity can be improved by reducing the diameter of the wire by etching. At most solutes the measured concentrations were between about 0.01 and 0.1 at.%, except Mo and Re (4 and 2 at.%). Fig. 2 shows the measured excess resistivities, Dq(300 K), against the chemical concentrations, c [14,15]. For comparison, the line for vacancies is also shown [16,17]. The slopes of the lines, Dq(300 K)/c, are listed also in Table 1. For most solutes the Dq=c values are not too far from each other (between 6 and 14 lX cm/at.%) and from that for vacancies. This means, that Dq=c is not too specific for the different kinds of solute atoms. Exceptions are some refractory metals, which are near to tungsten in the Periodic Table, like Mo and Re. Naturally, the insoluble potassium, forming the bubble rows in tungsten, cannot be included in this table. Interstitial impurities, like carbon, can be compared to the chemical concentrations only after appropriate quenching [18,19]. Beside excess resistivity measurements at the ambient, Dq(300 K), low temperature measurements, e.g. at 77 or 4.2 K, are often preferred due to the expected higher
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Fig. 2. The ambient excess resistivities, Dq300 K , against the concentrations of solutes (in at.%) in tungsten, compared to that of vacancies.
accuracy. The temperature dependence of the excess resistivities, DqðT Þ, usually called deviations from the MR, were determined for different solutes of tungsten between T 2 and 300 K, and Fig. 3 presents the normalized ratios, DqðT Þ=Dqð300 KÞ [11]. The data were measured on homogenized wires to avoid effects of inhomogeneous distribution of solutes. The DqðT Þ= Dqð300 KÞ ratios were found similar for the solute impurities Fe, Ni, Pt, Al and also for Co (except the minimum in WCo at T 10 K, due to Kondo effect [20]). The slopes of the curves become small between T 200 and 300 K. However, these functions are markedly different for Mo and Re solutes, surely due to the fact, that direct scattering of electrons on these atoms is relatively small, while their effect on the phonon spectrum is more emphasized due to the mass or charge differences [11]. 3.2. Evaporation profiles in tungsten wire In tungsten rods the sintering usually results in evaporation profiles of the solutes, like in cases of solute Al [21] or Fe (part I, Fig. 4). These profiles can survive
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Fig. 3. The temperature dependence of the excess resistivities, DqðT Þ, due to different solute impurities in tungsten (normalized to 1 at T ¼ 300 K).
Fig. 4. The measured solute distributions in the cross-section of tungsten wires (diam. 0.17 mm), compared to the theoretical integral distributions (from Fig. 1b), (a) after annealing at 2800 K for 15 min., and (b) after annealing at 3000 K for 3 h.
swaging and drawing, and are expected to be visible also in wires. To see this, a series of measurements were made on different wires (with diameter 0.17 mm), having some surplus Fe, Co or Al þ Si solutes (0.02–0.03 at.%), or some excess Mo or Re (1–0.5 at.%). They were recrystallized at 2800 K for 15 min or annealed at 3000 K for
Table 1 The excess resistivity for unit concentration (Dqbulk =c) and the characteristic thermoelectric power (Sx ¼ ½1 þ d =d) for different solutes in tungsten Element
Dqbulk (300 K)/c (lX cm/at.%)
Dqbulk (300 K)/c (lX cm/wt.%)
Sx (lV/K)
Fe Co Ni Pt Al Mo Re Nb Ta Si Vacancies Grain boundaries
8 14 6 10 9 0.25–0.3 1.3 0.5 1–0.3 – 6–7 –
19 30 13 9 64 0.5–0.6 1.2 1 1–0.3 –
24 17 13 6 )1.3 16 15
)2.5 þ6 0( 1)
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3 h, then their diameters were decreased in several steps by electropolishing to about 50% or 60%, measuring the resistivities in each step. The measured relative excess resistivities, DqðrÞ=Dqðr0 Þ, are presented in Fig. 4a and b. The measurements were made at temperatures near the ambient (between T 200 and 300 K) to avoid effects of inhomogeneous distribution on Dq. The measured data are compared to the curves for stationary evaporation profiles with different L ‘‘volatility’’ parameters. Annealing the wires at 2800 K for 15 min they recrystallized, while only a small fraction of the solute evaporated, not altering much the inherited profile (see Fig. 1a). The profiles for wires with excess Fe or Co lay near to stationary evaporation profiles with high volatility parameters (L ! 1), while those with excess Al þ Si differ from that markedly (Fig. 4a). The different behavior might be due to the fact, that this sort of wire was taken from different source, made probably with different sintering technology. Annealing the wires at 3000 K for 3 h the solute concentration decreased near to its half, and this effective evaporation helped the development of a nearly stationary evaporation profile (Fig. 4b). In this case the data lay on curves with large L values even at wires with excess Al þ Si. For refractory metal solutes, like Mo or Re, the volatility parameters, L, are expected to be much less. This is especially true in case of solute Re, at which L 1 (see Fig. 4b).
Fig. 5. Norton–Gorter diagrams (DSð1 þ dÞ against d), measured on different tungsten wires, doped by diffusion from the surface; (a) with Ni, or (b) with Al.
3.3. Distinguishing between solutes The excess electrical resistivity, Dq, is not too specific to the different solutes (Fig. 2). This can be improved by measuring also another, more specific parameter, like the thermoelectric power, DS. Measuring both Dq and DS, the DSð1 þ dÞ versus d ð¼ Dq=qw Þ lines are expected to be linear for the single solutes, with slopes, Sx , which are called characteristic thermopowers for the ‘‘x’’ solute (Eq. (1)). Fig. 5 presents an example, when different concentrations of Ni or Al were diffused into some tungsten wires from their surfaces. The effects of Ni in the different wires are parallel lines with high slopes, Sx 13, while the effects of Al are also parallel lines, but with negative slopes, Sx 1:5. The diagram demonstrates a vectorial addition rule for solutes. (It is worth mentioning here, that at further increase of the Ni content the wire became brittle, suggesting varied structure due to the so called ‘‘diffusion induced grain boundary motion’’ (DIGM) [22].) DS and Dq were measured on tungsten wires with several different solute impurities, and the measured DSð1 þ dÞ versus d ð¼ Dq=qw Þ lines are presented in Fig. 6 [13,23,24]. In addition, an annealing diagram is also shown, showing the effects of different types of lattice
Fig. 6. DSð1 þ dÞ against d ð¼ Dq=qw Þ diagrams for tungsten with different solute impurities and with lattice defects (marked by the stage numbers, III, IV, V, VI.).
defects (marked by the annealing stages, III, IV, V) [13,24]. The characteristic thermopowers, Sx are enlisted also in Table 1. Sx is high for magnetic impurities, like Fe, Co or Ni, but also high for transition metal impurities, like Mo and Re, which have otherwise only small effects on the resistivity (Fig. 2). Sx is not only small, but even negative for common solutes Al and Si. For grain boundaries or dislocations Sx 0 (stages IV and V), while for point defects (stage III) Sx 4–6.
4. Interaction between solutes and lattice defects 4.1. Segregation and evaporation of solutes Interactions between solutes and lattice defects are not easily investigated by electrical resistivity due to the large background effects of dislocations or grain boundaries (part I, Fig. 6). The application of thermo-
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electric power seems preferable, since for dislocations and grain boundaries Sx 0 (Table 1.) so their effects are negligible. Therefore, a non-sag tungsten wire with excess cobalt dope [5] was investigated. The specimens were annealed at different temperatures between T ¼ 1000 and 3000 K for 15 min and thermoelectric powers, DS, were measured on them (d 1, Eq. (1)). Fig. 7 present DS against T on two non-sag tungsten wires, with or without excess Co dope, (marked by ‘‘W þ Co’’ or ‘‘W’’, respectively). The ‘‘WCo’’ diagram reveals two minima, one at T 1500 K, and the other at T 2400 K, while no similar effects can be seen on the ‘‘W’’ diagram. The first minimum was identified on the fracture surfaces by AES with the segregation of Co to the grain boundaries (5 at.%, [25]). (Similar segregation was found in iron doped W [26].) Segregation is expected to occur at temperatures, at which the solute atoms can diffuse to the grain boundaries. According to the diffusion data for WFep[27] ffiffiffiffi and WCo [28], the estimated diffusion lengths, Dt 0:07–0:3 nm, are too small compared to the grain size (400 nm [29]), so diffusion to grain boundaries ought to be negligible. However, segregation could occur by another effect, namely that grain growth occurs, when the moving grain boundaries collect the solute atoms from the bulk, like in [30]. Annealing above 1500 K, the segregation diminishes, partly due to the re-solution of the segregated atoms, and partly due to the decreasing grain boundary area. The nature of the second minimum in Fig. 7 is further investigated in Fig. 8. Here annealing was made at different temperatures between T 1700 and 2800 K, and the annealing time was increased successively from (1, 5 min) 15 to 90 min, and finally the specimens were recrystallized (dotted line) at 2800 K for 15 min. Between T ¼ 1700 and 2000 K a part of the solute segregated to the grain boundaries, but this segregation disappeared after recrystallization. However, between about 2200
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Fig. 8. The thermoelectric powers, DS, against the annealing temperature, T (K), on tungsten wire with excess Co dope. The annealing time is increased from (1, 5 min) 15 to 90 min successively, and then recrystallized at 2800 K for 15 min.
and 2600 K the minimum deepened with increasing annealing time, and the recrystallization did not change DS any more. Accordingly, an annealing at 2400 K for 90 min made a permanent decrease in DS, to about its 20%, which means that the total Co concentration decreased to a very low value. Since in this process the axial grain size was only about 1 lm, this suggests an effective outdiffusion of Co through the grain boundaries to the surface [31–33] from where it could evaporate. This outdiffusion of Co from the wires was controlled also by chemical analyses, presented in Table 2 [34]. Recrystallization increased the grain size to about the wire size (170 lm) so after it only the bulk diffusion was effective [28], which was much slower. Since the recrystallization was full after an annealing at 2800 K for 15 min, a further increase of the annealing time to 90 min varied DS only little, so bulk diffusion resulted only in the evaporation of a small fraction of the Co content. 4.2. Oxidation–reduction of Al and Si
Fig. 7. The thermoelectric power, DS, measured on wires with or without excess Co dope (‘‘W þ Co’’ and ‘‘W’’ respectively), after annealing at different temperatures between 1000 and 3000 K. The two minima are marked by 1 and 2.
An AKS (non-sag) tungsten wire was investigated, which was first recrystallized at 2700 K for 15 min. Then the wire was annealed at 2200 K for longer time, while the measured excess resistivity, Dq, continuously decreased (Fig. 9). The rate of decreasing depended also on the vacuum (105 or 106 mbar O2 ). Annealing the wire again at 2700 K, Dq increased to its initial value within 5–10 min (Fig. 9). The whole cycle could be repeated several times [35]. The decrease of Dq at 2200 K was explained by the internal oxidation of Al and Si, and similarly its increase at 2700 K was due to their reduction. The oxidation at 2200 K was confirmed also by its vacuum dependence. The process of oxidation–reduction was investigated also by measuring both excess resistivity and
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Table 2 The analytical Co concentration and thermoelectric power on samples annealed at the indicated temperatures for 90 min and measured after a final anneal at 2800 K for 15 min Annealing
1700 K, 90 min þ recryst:
2000 K, 90 min þ recryst:
2200 K, 90 min þ recryst:
2400 K, 90 min þ recryst:
2600 K, 90 min þ recryst:
2800 K, 15 min
DS (lV/K) Co (at.ppm) Co (wt.ppm)
1.274 255 82
1.105 215 69
0.769 162 52
0.283 50 16
0.750 137 44
1.239 283 91
The data of the last column were obtained on samples on which only the final anneal was carried out (see also Fig. 8).
Fig. 9. An AKS doped tungsten wire was first recrystallized at 2700 K for 5 min. Then at annealing at 2200 K for long time, the excess resistivity, Dq, was found to decrease (its rate depends on the vacuum). Annealing the wire again at 2700 K, Dq was found to increase (oxidation–reduction process).
thermoelectric power, to be able to distinguish between different solutes. Therefore measurements were made on a wire with some excess dopes (35 wt ppm K, 62 wt ppm Al, 27 wt ppm Si and 14 wt ppm Fe). The measured data are presented on a DSð1 þ dÞ versus d ð¼ Dq=qw ; 1Þ diagram in Fig. 10. The wire was first recrystallized at 2800 K for 15 min. Then it was annealed at 2200 K for 1 and 5 h, successively, while the data points were found to move along a straight line with slope: Sx 1:5 lV/ K. Annealing it again at 2800 K for 15 min, the data points returned to the initial point along the same line. The negative Sx slope corresponds to Al or Si (Fig. 6), suggesting their internal oxidation and reduction. Annealing a specimen from the same wire at 2900 K for 5 and for 14 h, and another one at 3000 K for 1 and for 3 h, the data points moved along straight lines but with slopes Sx þ 4 lV/K. This characteristic thermopower corresponds to about the weighted average for those of Al, Si and Fe (Table 1). Annealing at very high temperatures (2900, 3000 K) results in an evaporation of solute impurities from the wire. The straight line for the evaporation suggests about similar diffusion constants for the enlisted solutes, and the calculated diffusion constants are near to that for WFe [27].
Fig. 10. On recrystallized (at 2800 K for 15 min) AKS tungsten wire oxidation occurs at 2200 K (for 1 and 5 h) and reduction at 2800 K for 15 min, resulting in a straight line with slope: Sx 1:5 lV/K. Annealing the wire at 2900 K (for 5–14 h) or at 3000 K (for 1–3 h), the slope of variations is: Sx þ4 lV/K.
5. Discussion 5.1. Deviations from the MR at evaporation profiles If the concentration of solute has cylindrical symmetry in the wire (with radius r0 ), the local excess resistivity (at radius r) is Dqðr=r0 Þ, so the resistivity is qw ðT Þ þ Dqðr=r0 Þ, supposing the MR is locally true [9]. Since in parallel conductors the measured resistivity is obtained from the average conductivity, rav , instead of the average resistivity, qav , so qmeas ðT Þ 1=rav ðT Þ Z s0 1 1 ðqw ðT Þ þ Dqðr=r0 ÞÞ 2rpdr ¼
ð2Þ
0
At the given small concentrations of solutes at the ambient qw ðT Þ ðr=r0 Þ, so in this case 1=rav qav . However, at very low temperatures, i.e. at T ! 0 K, qw ðT Þ ! 0 too, so in Eq. (2). it is only ðDqðr=r0 ÞÞ1 , which is averaged over the cross-section. If tungsten wires contain only the common volatile solutes, the estimated volatility parameters are as high as L ¼ 107 –109 , hardly distinguished from the L ! 1 case. In this case at T ¼ 0 K a surface layer has near zero resistivity,
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which short-circuits the whole measured resistivity. According to this, the measured resistivity ought to be near to zero, in contrast to the relative values 0.5–0.7, measured on homogenized solutes (Fig. 3). Although the concentration of solutes goes near to zero in the depleted zone at the surface, this is not really true for the local resistivity at the surface. The reason for this is, that especially in thin wires, the electronic mean free path, k, can be much larger than the size of this depleted zone. This case can be calculated from the Boltzmann equation, in which a new characteristic parameter, r0 =khom , appears. Here khom would be the electronic mean free path at T ! 0 K, supposing the same solute was homogeneously distributed in the cross-section [20]. According to this parameter, the measured DqðT Þ depends much on the diameter of the wire and on the average concentration of the solute. So in rods with high solute concentrations at T ! 0 K, Dq=Dqhom ! 0, but at very thin wires with some ppm concentrations of solutes Dq=Dqhom 1. These considerations call the attention, that the low temperature DqðT Þ values in Fig. 3 can be measured only after careful homogenization. 5.2. Evaporation by diffusion If we have homogeneous solute distribution in the cross-section of the wire, then an annealing at very high temperatures for long time results in a stationary evaporation profile (see Fig. 1a). Its shape does not vary with further annealing, but the total concentration decreases exponentially, like this [7]: c=co ¼ expðb21 Dt=r02 Þ
ð3Þ
where D is the diffusion constant at the given temperature, t is the diffusion time and r0 is the radius of the wire. In some cases the solute profile was found near to the stationary one already after recrystallization (e.g. at Fe or Co solutes, like in Fig. 4a). In these cases Eq. (3) is formally valid even after annealing at shorter times. Very long annealing times can be attained by heating coils or coiled coils in ready made lamps. So in different types of lamps the total outdiffusion could be followed within temperatures 2480–3000 K [36]. However, in these measurements the errors were relatively large, mostly due to the weldings and the uncertain contacts with the consoles. Together with this, the determination of the diffusion constant may be connected with several problems, some of which are enlisted here: • The presence of the stationary evaporation profile must be verified. • The validity of the MR, in DqðT Þ can be doubtful, especially when measuring at 4 or 77 K. • The different solutes must be separated from each other.
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• Tungsten itself evaporates during annealing, so at current heating the annealing temperature needs special control.
6. Conclusions In contrast to the chemical analysis, direct currrent electrical measurements are sensitive only to the impurities, present in solute form. However, electrical measurements are sensitive to very small concentrations, and as non-destructive test, applicable to follow small variations occurring in different processes. Some applications described in this paper are enlisted here: 1. The specific resistivities for common solutes are between about Dqð300 KÞ ¼ 6 and 14 lX cm=at:%, but much less for some transition metal impurities, like Mo, Re. Their temperature dependencies are also similar (between 2 and 300 K), but different for Mo, Re. 2. The internal distribution of volatile solutes in tungsten wires varies with annealing temperature and time, and finally a stationary evaporation profile develops in the wires. Its shape is different for some transition metal solutes (like Mo and especially Re). 3. Measuring also thermoelectric power, several solutes can be distinguished from each other. Magnetic or transition metal solutes (Fe, Co, Ni and even Mo and Re!) have large effect on the thermoelectric power, but the effect of some common solutes (Al, Si) are even negative. 4. Fe and Co segregates to the grain boundaries at about 1500 K. The majority of solutes (Co) can evaporate from the wire by grain boundary diffusion at 2400 K for 90 min (with 1 lm grain size), while bulk diffusion makes this possible only at about 3000 K for 3–14 h. 5. In case of Al and Si solutes internal oxidation appears at about 2200 K, the oxidation rate is depending on the oxygen pressure.
Acknowledgements The author wishes to thank Dr. I. Gaal for helpful discussions. This work was supported by the National Research Fund (OTKA), contract no. T.32730.
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