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AKS doped tungsten––investigated by electrical resistivity I. Manufacturing tungsten bar and wire
International Journal of Refractory Metals & Hard Materials 20 (2002) 311–318 www.elsevier.com/locate/ijrmhm
AKS doped tungsten––investigated by electrical resistivity I. Manufacturing tungsten bar and wire 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 properties of the Al, K, Si doped (AKS) tungsten bars and wires are mostly controlled or investigated by studying mechanical and/or structural properties. The aim of the present work is to show, that electrical measurements can give also useful and often very specific information about their properties. In addition, by determining both ‘‘effective’’ and ‘‘bulk’’ resistivities, one can distinguish between the porosity and the lattice defects. The investigations survey the production from the powder state, when the metallic conduction just appears, through sintering, swaging and wire drawing, to the production of thin wires or even coils. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Tungsten; Electrical resistivity; Powder metallurgy; Recrystallization; Size effect
1. Introduction Tungsten wires used for filaments in incandescent lamps, are produced from tungsten oxides with the addition of doping compounds of Al, K and Si (AKS tungsten). Then hydrogen reduction transforms it into metal powder, which (with or without washing) is pressed and then sintered. During sintering the porosity of the ingot helps in the evaporation of dopes, but after the closure of porosity, the insoluble potassium is entrapped in the bar in the form of bubbles. The non-sag (NS) property develops only in thin wires, in connection with the development of the potassium bubble rows, hindering the motion of grain boundaries [1–4]. The investigation of tungsten bars or wires is often made by studying mechanical and/or structural properties, supposing these control the most important features [5–7]. However, several other investigation methods exist, which can be more sensitive in some specific properties. At heat treatments the high temperature electrical resistivity of wires is often applied as a temperature control [8]. However, it is the excess electrical resistivity, which can measure variations in the internal properties, e.g. due to strain or impurities. The main differences between mechanical, structural and electrical
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properties are typically the followings: Mechanical and structural investigations reveal mostly local properties, while electrical measurements reveal mostly the average properties in the investigated specimens. Otherwise, each method can have some specific advantages, for which its application may be more beneficial. For metals the electrical resistivity and its temperature dependence are described in more comprehensive works, like [9,10]. The present work is limited to tungsten with some possible applications of a few electrical properties, like the ‘‘effective’’ or ‘‘bulk’’ electrical resistivity, their temperature dependence and the thermoelectric power. This paper is divided into two parts, I and II, from which part I is concerned with the manufacturing of the tungsten bar and wire, while part II considers the impurities and their interactions with the lattice defects.
2. Evaluation of measurements In a uniform wire or bar the electrical resistance, RðT Þ, and the ‘‘external’’ geometrical factor, L=Q, (L is the length and Q is the cross-section) are directly measurable and they are connected with the ‘‘effective’’ resistivity like this: RðT Þ ¼ qeff ðT ÞL=Q
0263-4368/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 2 ) 0 0 0 3 1 - 8
ð1Þ
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(the temperature dependence of the geometrical factors is neglected). The pores or cracks in the material behave also like geometrical obstacles, which in effect modify L=Q by an ‘‘internal’’ geometrical factor, Gint . Taking this into account, one can define a so-called ‘‘bulk’’ resistivity, qbulk ðT Þ, i.e. the resistivity in the microscopic volumes between the pores or cracks: qeff ðT Þ ¼ Gint qbulk ðT Þ
ð2Þ
Gint and qbulk ðT Þ can hardly be measured directly. If we measure the resistance at two temperatures, T and To , their ratio is characteristic only to the qbulk properties: r ¼ RðT Þ=RðTo Þ qbulk ðT Þ=qbulk ðTo Þ
ð3Þ
and rw qw ðT Þ=qw ðTo Þ
ð4Þ
is the same ratio for a ‘‘pure’’ (zone melted) tungsten. Supposing that the bulk excess resistivity, Dqbulk ¼ qbulk ðT Þ qw ðT Þ, is independent of temperature due to the MatthiessenÕs Rule (MR) [9,10], it can be determined from the resistivity ratios like this: Dqbulk ¼ qw ðTo Þðr rw Þ=ð1 rÞ
3. Comparison with technology 3.1. Pre-sintering and sintering Tungsten bars, being in different stages of compacting, pre-sintering or sintering, were prepared by the technology described in [1]. Their properties were investigated by determining both the ‘‘effective’’, and ‘‘bulk’’ electrical resistivities (qeff and qbulk ), compared to their densities (Fig. 2, Table 1, [13]). The resistivity versus density diagrams are rather dissimilar at the two curves. For completion, SEM pictures show the structural variations connected with sintering (Fig. 3a and b). The extremely high variations in qeff with the density (Fig. 2) can be explained by the followings: The compacted powder consists of separated grains, and after heat treatments more and more random contacts appear between them. This process can be explained by a so called ‘‘skeleton model’’ [14]. According to this, metallic conduction starts at a given average number of contacts between the single grains. At first the effective resistivity is high, but with further annealing it decreases in two parallel processes, so with the increasing of the number of contacts and also with the increasing neck diameter at the contacts.
ð5Þ
(Slight deviations from the MR often occur, and these deviations are usually more in transition metals, like tungsten [10,11].) In porous materials the internal geometrical factor, Gint , can be high, but if the pores or cracks have small volume fractions, c, (like in wires) then Gint 1 þ Kc, in which K is the shape factor of the single defects. The value K varies with the shape and direction of the second phases and/or cracks as it is illustrated in Fig. 1a and b. In case of single spherical pores K ¼ 1:5 [12], for bubble rows with varying distances between the bubbles, K is between about 1 and 1.5 (Fig. 1a). At ‘‘thin’’ longitudinal cracks K 1, while at transversal cracks, found e.g. after torsion, K 1 (Fig. 1b). Fig. 2. Variations of the ‘‘effective’’ and ‘‘bulk’’ resistivities, qeff and qbulk , with the density of the rod during compacting, pre-sintering and sintering.
Table 1 The measured densities, qeff and qbulk data on NS tungsten bars after compacting, pre-sintering and sintering (see Fig. 2)
Fig. 1. The illustration of the shape factors K: (a) for single bubbles and bubble rows and (b) for axial and transversal cracks.
Specimens in Fig. 2
Density (g/cm3 )
qeff (lX cm)
qbulk (lX cm)
1. 2. 3. 4. 5. 6.
9.0 9.8 11.6 11.8 16.2 19.3
4050 880 110 17.6 7.0 5.4
9.71 8.39 6.88 5.84 5.51 5.4
Compacted + + Pre-sintered Sintered Zone melted
L. Uray / International Journal of Refractory Metals & Hard Materials 20 (2002) 311–318
Fig. 3. SEM pictures on (a) pre-sintered (No. 4.) and on (b) sintered (No. 5.) tungsten bars.
Since the internal geometrical factor, Gint ¼ qeff =qbulk (Eq. (2)), is a function of the number and size of contacts between the grains, this explains the dissimilarity of the qeff and qbulk curves. (One must mention here yet, that the resistivity versus density function is not unambiguous, since e.g. in case of the so called ‘‘washed’’ powders [1] the grain surfaces are cleaner, which results in better contacts and less resistivity.) At compacting or pre-sintering (no. 1–4), the material consists of single grains, and only the number and size of contacts varies. This involves variations mostly in the effective resistivity but not in the density (Fig. 2). However, at sintering (between no. 4–5) the density of the bar increases effectively, while qeff varies less. These variations are connected with the large structural changes seen in Fig. 3a and b, in which Ôthe skeleton of grainsÕ changes into a Ôsolid material with independent poresÕ. Let us suppose, that in the sintered bar (no. 5.) Gint is an effect of pores (1.27, Table 1.). With the Gint 1 þ Kc approximation the deficit in density, c 0:16, suggests K 1:7, somewhat more than expected for spherical bubbles (Fig. 3a). While in the whole process qeff varies several magnitudes, qbulk varies less than two times. qbulk is possibly not too high even in earlier stages of compacting, but––in the absence of contacts––it cannot be measured by the present DC method. Since qbulk is the average resistivity in the inside of the single grains, it is an effect of scattering of electrons on some defects in the grains. These defects may be e.g. (solute) impurities, dislocations (causing internal stresses) or even surfaces of the neck. All these effects can be reduced by further annealing. Electron scattering on the neck walls could be estimated from WexlerÕs model [15], by approximating the small neck between two grains as a conducting circular orifice in an insulating plane diaphragm, dividing an infinite conductor into two parts. If we identify this re-
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Fig. 4. The ‘‘bulk’’ and ‘‘effective’’ resistivities (qbulk and qeff ), measured along a sintered tungsten bar (with sizes: 7 7 380 mm3 ). The markers on the bar, m1 (up) and m2 mark the ends of the usable part. The inlet at the middle shows the distribution of solutes in the crosssection, measured on axial sticks cut from the bar.
sistivity with the measured differences in the bulk resistivities between bars no. 4 and 5 (Table 1), i.e. with Dqbulk ¼ 0:33 lX cm, it suggests neck diameters of 1.5 lm [13], in rough agreement with Fig. 3a. A possible application of resistivity measurements on sintered tungsten bars is presented in Fig. 4. The investigations represent non-destructive testing by measuring both effective and bulk resistivities along a sintered tungsten bar (like no. 5. in Fig. 2). Since qbulk decreases slightly towards the ends of the bar, this suggests somewhat more effective evaporation of solute at the ends. On the contrary, qeff increases towards the ends, indicating more residual porosity there. Since the evaporation of solutes is connected mostly with the closure of porosity, this kind of investigation can help tracing the sintering process. At the central part of the bar the internal distribution of solutes in the cross-section was also investigated by measuring Dqbulk on specimens cut axially from an axial section of the bar (see the inset of Fig. 4) The data reveal nearly parabolic solute impurity profile, in which the impurity content decreases near to zero at the surface. 3.2. Swaging and drawing Fig. 5 present effective resistivities, qeff , on swaged bars and wires against the nominal deformation, e 2 logðd=d0 Þ, while their diameters, d, are shown on the upper scale (d0 7 mm is the initial diameter) (from [16,17]). The data are shown both on ‘‘as drawn’’ wires and on wires annealed at 2700 °C for 2 min. With increasing deformation the resistivity is expected to increase due to the more and more created lattice defects. However, the porosity, and with it also the internal geometrical factor, qeff =qbulk , decreases during swaging. As a result, between e ¼ 0 and e 2 the effective
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splits turn cross-wise, for which K 1 (Fig. 1b). According to this the internal geometrical factor increases to Gint 1:2–1:4 [19]. 3.3. Recovery and recrystallization
Fig. 5. The ‘‘effective’’ resistivity, qeff , against the nominal swaging or drawing strain, e 2 logðd=do Þ, (after [16] or [17]). The diameters of the bars or wires are shown on the upper scale.
resistivity, qeff , was found to decrease (from q1 6:1–5:4 lX cm). In this period the porosity decreased due to the thermomechanical treatment. Since the specified annealing at 2700 °C had no further influence on the porosity, qeff decreased similarly on the annealed wires too. During this process the density of the swaged bar or wire was found to increase from 17 to 18.22 g/cm3 [16]. With further deformation (from e 2–11) the diameter of the wire decreased to d 30 lm, while the measured resistivity increased continuously up to q ¼ 7:1 lX cm (Fig. 5). Since in these thin wires the porosity did not change any further [16], this resistivity increase was due only to the creation of lattice defects. During this process the drawing temperature decreased step by step, so the slope of the resistivity versus e line is expected to increase. After annealing at 2700 °C the created lattice defects annihilated, which resulted in about constant resistivity (q 5:4 lX cm). In the wire-drawing process the tensile strength of the wire continuously increases [6], due to which splitting becomes easier in the thin wires. The danger for splitting becomes high in very thin wires, where the high concentration of the created lattice defects is connected with low drawing or coiling temperatures, at which the tungsten is more brittle. Therefore, in the usual drawing process stress–relieve annealing must be inserted at some intermediate diameters (e.g. at d 200 lm) to avoid splitting. That gives a serrated like curve instead of the ‘‘as drawn’’ curve in Fig. 5. In thin wires the volume fraction of second phases is as low as 0.2–0.3% [18], which correspond to internal geometrical factors: Gint ¼ qeff =qbulk 1:003–4 (with K 1:5, Fig. 1a). The occasionally occurring axial splits have low volume fractions, and for them K 1 (Fig. 1b). The splits remain axial also after coiling. However, in experiments with torsional deformation the axial
In heavily drawn tungsten wires isochron annealing decreases the excess electrical resistivity in several welldefined stages [20,21]. Fig. 6 presents this on two wires, having diameters of 0.12 and 0.173 mm. The first stage above the ambient is called stage III, which is terminated below T 750 K. This stage is identified with the movement of vacancies and/or interstitials, and is often investigated after irradiation or quenching [22,23]. Stage III is usually less after wire drawing, due to the high drawing temperature, but larger if the deformation is made at the ambient, like after coiling [24] or after torsion [25]. In stages IV and V continuous fibre- or grain-growth can be observed [26]. Stage IV is connected partly to the annihilation of extrinsic grain boundary dislocations and partly to subboundary movement, during which the fibresize increases [21]. In the vicinity of 1500 K the fibres transform into axially elongated grains, having large-angle boundaries. Further annealing results in continuous grain growth [26], called stage V (in some papers stages IV and V are not separated [20,24]). After an annealing at 1800 K for 15 min the axial grain structure is presented on SEM picture in Fig. 7. A NS tungsten wire (with diameter 0.17 mm) was investigated by annealing specimens at different temperatures and times. The bulk excess resistivities due to grain boundaries, Dqgb , were determined on them (Eq. (5)). Similarly, the volume densities, S=V , of grain surfaces (S is the grain surface, V is the volume) were calculated from the TEM data [27]. The Dqgb versus S=V line was presented in Fig. 8, revealing straight line for the annealed specimens no. 2–6. The ‘‘as drawn’’ wire
Fig. 6. The excess resistivities, Dqbulk , measured on wires with diameters 173 and 120 lm, after annealing them at different temperatures between 300 and 2800 K.
L. Uray / International Journal of Refractory Metals & Hard Materials 20 (2002) 311–318
Fig. 7. SEM picture taken on a NS tungsten wire (diameter 173 lm) after annealing at 1800 K for 15 min., showing axial grain boundary system.
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pending much on the applied strain, i.e. on the wire diameter. As the wire is drawn from 4.5 to 0.5 mm, Trecr remains in the vicinity of 2000 K, but with further reduction in diameter to d 0:15 mm it rises sharply to 2500 K [7]. This effect is attributed to the increasingly effective inhibition of recrystallization by the potassiumstabilized bubble dispersion [29]. At even less diameters Trecr may decrease again, but a detailed investigation e.g. of the bubble dispersion would help to clarify the present state of knowledge [30]. If the wire drawing is continued by another type of deformation, the temperature of recrystallization usually decreases. Accordingly, in a wire (with diameter of 0.063 mm), coiling decreased Trecr with about 200–300 K [24]. Similarly, on a wire with diameter 0.39 mm, torsional strains of c 0:34–1.76, decreased Trecr with about 260–450 K [31]. 3.4. Comparison of resistivity and flow stress
Fig. 8. The excess resistivities due to grain boundaries, Dqgb , measured on specimens of a NS tungsten wire (diameter 173 lm) with different annealing, against the density of grain boundaries, S=V , calculated from TEM data [27]. The numbers refer to: (1) ‘‘as drawn’’ wire, (2) wire annealed at 1200 K for 6 h, (3) at 1600 K, 30 s, (4) at 1600 K, 3 min, (5) at 2000 K, 30 s and (6) ‘‘recrystallized’’ at 2800 K for 15 min.
(no. 1.) did not fit to the line, since it contained point defects too. The straight line corresponds to specific grain boundary resistivity of: Dqgb =ðS=V Þ 4 106 lX cm2 . The resistivity of a single grain boundary can also be determined by applying superconducting quantum interference device (SQUID) [28]. With that, single boundaries in a bi-crystal can be studied, and by varying their direction or structure, the angular dependence of the resistivity could also be studied. The process of grain growth is terminated by an exaggerated grain growth, called stage VI (Fig. 6), at which the grain size increases to about the wire size [26]. At the end of stage VI the residual excess resistivity was about Dq 0:1 lX cm (Fig. 6), which was due to the residual solute impurity content. The start of stage VI is called the temperature for recrystallization, Trecr , de-
Since in the general practice the mechanical investigations are more common, it seems worthwhile to compare the annealing effects measured by electrical and mechanical properties. So Fig. 9 present the excess resistivities, Dqbulk , against the flow stress, r0:2 , (belonging to 0.2% strain), measured on several specimens (0.17 mm diameter) after different annealing [32]. The regions of the diagram are separated according to the different stages (like in Fig. 6). The diagram suggests, that point defects (stage III) affect only the excess resistivity, while the recrystallization (stage VI) has more effect on the flow stress. In the ranges of fibre––or grain growth (stages IV and V) Fig. 8 suggests roughly linear connection between them. Usually for grains with random sizes and orientations the flow stress, r, is expected to follow a Hall–Petch type relation [33,34]:
Fig. 9. qbulk against the flow stress, r0:2 , (for 0.2% strain), measured on several specimens, annealed at different temperatures. The annealing stages, III–VI are marked on the diagram [32].
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L. Uray / International Journal of Refractory Metals & Hard Materials 20 (2002) 311–318
r ¼ r0 þ kd 1=2
ð6Þ
in which r0 is a friction stress, k is constant and d is the average grain size. In Fig. 9 the scattering of data is too high to be able to determine the exact connection between resistivity and flow stress. Otherwise, Eq. (6) was established mostly for grains with random extensions, while now the grains are axially elongated (Fig. 7). Since this paper is only resistivity oriented, a deeper comparison of Figs. 8 and 9 will not be forced now.
4. Discussion The specific grain boundary resistivity is usually measured on equiaxial grains, while in the NS tungsten wire an axially elongated grain boundary system develops (Fig. 7). In the two cases the measured specific resistivities are not necessarily the same. In deposited metal layers the specific grain boundary resistivity is usually determined by the Mayadas–Shatzkes M–S model [36], in which the grain boundaries are represented by parallel lines, perpendicular to the direction of the electric field, E, with an average separation, d. At the same time the effect of boundaries, parallel to E, are neglected. In this model the ratio of bulk and measured resistivities are: qbulk =qmeas ¼ 3½1=3 1=2a þ a2 a3 lnð1 þ 1=aÞ
ð7Þ
in which a ¼ lo =dR=ð1 RÞ, lo is the electronic mean free path and R is the ‘‘reflection coefficient’’ of electrons at the grain boundaries. In case of deposited tungsten layers R 0:5 was found if the grain-size was estimated from X-ray, or R 0:65 if the grain-size was measured directly from TEM. These R values correspond to specific grain boundary resistivities, Dqgb 10 or 20 106 lX cm2 respectively [37]. At the same time the specific grain boundary resistivity for axially elongated grains was found only Dqgb 4 106 lX cm2 (Fig. 8). The large discrepancy between these data needs some comment. Although the M–S model neglects grain boundaries parallel to E, these boundaries can have rough, dislocational substructure, scattering the electrons [38]. Otherwise, in case of tungsten the electronic scattering is relatively high due to its relatively complicated Fermi surface [39]. Electrical conduction in wires with axially elongated grains (Fig. 7) suggests some similarity to the Fuchs–Dingle ‘‘size-effect’’ model in thin films and wires [40,41] naturally, only similarity but not equivalency. In the high temperature limit the ‘‘size effect’’, gives a linear connection between the excess resistivity, Dq, and the reciprocal diameter, 1=d: Dq ¼ 3=4ðqw kw Þ=dð1 pÞ
ð8Þ
in which qw is the resistivity, kw is the electronic mean free path in pure tungsten (qw kw 2:2 1011 lX cm2 [39]), and p is the reflectivity of electrons at the surface. In Fig. 9 S=V was calculated from the average diameter, d 0 , of the axial grains, measured by TEM (by S=V ¼ ðp=2Þ1=d 0 [35]), giving also linear dependence from 1=d 0 . Fitting the result to Eq. (8), p 0:6 is obtained. To go further in this comparison, the excess resistivity for grain boundary resistivity, Dqgb ðT Þ, was measured on a NS tungsten wire (0.3 mm diameter) between temperatures T ¼ 4 and 200 K, and presented in Fig. 10. The two specimens were annealed at 1500 or at 1700 K. The average diameters of the axial grains were d ¼ 0:6 or 0.5 lm respectively (measured on SEM pictures [42]). The Dqgb ðT Þ versus T curves (solid lines) reveal maxims at T 60 K, corresponding to electronic mean free paths: kw 0:5 lm. The Fuchs–Dingle size effect model with fitting parameters: d ¼ 0:55 lm and p ¼ 0:6 gives a similar curve between them with similar maximum. The proximity of kw to the grain or wire size, d, verifies also the size-effect like behavior. From these data the specific grain boundary resistivity was: Dqgb 3 106 lX cm2 [42]. The excess resistivities were measured on the wires not only axially, Dq* , but also transversally, Dq? . For this purpose, tiny little discs were cut transversally from the wire (diameter ¼ 0:3 mm, height 0:2 mm), as illustrated in Fig. 11, on which the resistivity was measured with the help of microscopic spark-welded contacts. Measuring on several disks, the transversal grain boundary resistivity was found: Dq? 9 106 lX cm2 . These results reveal high anisotropy of the electron scattering between transversal and axial mea-
Fig. 10. The excess resistivities, qbulk ðT Þ, measured on NS tungsten wires (diameter 0.3 mm) at temperature between 4–200 K. The specimens were annealed at 1500 or 1700 K. The curves are compared to the Fuchs–Dingle size-effect model (F–D) (dotted line), having parameters: diameter: 0.55 lm and p ¼ 0:6. Maximums occur at about 60 K, at which the electronic mean free path in tungsten is kw 0:7 lm.
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References
Fig. 11. Illustration of cutting a little transversal specimen from the NS tungsten wire (diameter 0.3 mm) with welded contacts, for the investigation of the anisotropy of grain boundary resistivity.
surements: Dq? =Dq* 2:8ð0:5Þ [42]. Anisotropy could be measured also on a ‘‘split-free’’ wire by applying high torsional strain (c 1:5). Applying stress–relieve annealing before and after torsion, increased by about 2.3 times [43]. The high anisotropy can explain the large grain boundary resistivity in deposited layer, since it may correspond to about Dq? ., i.e. to the cross-sectional excess resistivity in the wire.
5. Conclusions Direct current electrical measurements can be applied to follow several specific properties of NS tungsten from compacted powder to thin wires or coils: 1. In pre-sintered tungsten bars the ‘‘giant’’ effective resistivity describes a skeleton structure of grains, with increasing number and size of contacts between the grains. During sintering this structure transforms into a compact material with closed porosity. 2. At swaging the effective resistivity at the ambient decreases due to the diminishing porosity, but at further drawing it increases again. 3. Annealing the wire at different temperatures, the excess resistivity decreases in stages (III–VI). 4. The specific grain boundary resistivity is high in the deposited tungsten layers: Dqgb 10–20 106 lX cm2 , and small in the axially elongated grain boundary system: Dqgb 3–4 106 lX cm2 . This must be due to the high anisotropy of resistivity on the grain boundaries: Dq? =Dq * 3. 5. Excess resistivity can measure also the recrystallization temperature, which depends much on the drawing strain and also on further strain (e.g. with coiling or twisting).
Acknowledgements The author wishes to thank Dr. I. Ga al for helpful discussions. This work was supported by the National Research Fund (OTKA), contract no. T.32730.
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AKS doped tungsten––investigated by electrical resistivity I. Manufacturing tungsten bar and wire 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 properties of the Al, K, Si doped (AKS) tungsten bars and wires are mostly controlled or investigated by studying mechanical and/or structural properties. The aim of the present work is to show, that electrical measurements can give also useful and often very specific information about their properties. In addition, by determining both ‘‘effective’’ and ‘‘bulk’’ resistivities, one can distinguish between the porosity and the lattice defects. The investigations survey the production from the powder state, when the metallic conduction just appears, through sintering, swaging and wire drawing, to the production of thin wires or even coils. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Tungsten; Electrical resistivity; Powder metallurgy; Recrystallization; Size effect
1. Introduction Tungsten wires used for filaments in incandescent lamps, are produced from tungsten oxides with the addition of doping compounds of Al, K and Si (AKS tungsten). Then hydrogen reduction transforms it into metal powder, which (with or without washing) is pressed and then sintered. During sintering the porosity of the ingot helps in the evaporation of dopes, but after the closure of porosity, the insoluble potassium is entrapped in the bar in the form of bubbles. The non-sag (NS) property develops only in thin wires, in connection with the development of the potassium bubble rows, hindering the motion of grain boundaries [1–4]. The investigation of tungsten bars or wires is often made by studying mechanical and/or structural properties, supposing these control the most important features [5–7]. However, several other investigation methods exist, which can be more sensitive in some specific properties. At heat treatments the high temperature electrical resistivity of wires is often applied as a temperature control [8]. However, it is the excess electrical resistivity, which can measure variations in the internal properties, e.g. due to strain or impurities. The main differences between mechanical, structural and electrical
E-mail address: [email protected] (L. Uray).
properties are typically the followings: Mechanical and structural investigations reveal mostly local properties, while electrical measurements reveal mostly the average properties in the investigated specimens. Otherwise, each method can have some specific advantages, for which its application may be more beneficial. For metals the electrical resistivity and its temperature dependence are described in more comprehensive works, like [9,10]. The present work is limited to tungsten with some possible applications of a few electrical properties, like the ‘‘effective’’ or ‘‘bulk’’ electrical resistivity, their temperature dependence and the thermoelectric power. This paper is divided into two parts, I and II, from which part I is concerned with the manufacturing of the tungsten bar and wire, while part II considers the impurities and their interactions with the lattice defects.
2. Evaluation of measurements In a uniform wire or bar the electrical resistance, RðT Þ, and the ‘‘external’’ geometrical factor, L=Q, (L is the length and Q is the cross-section) are directly measurable and they are connected with the ‘‘effective’’ resistivity like this: RðT Þ ¼ qeff ðT ÞL=Q
0263-4368/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 2 ) 0 0 0 3 1 - 8
ð1Þ
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(the temperature dependence of the geometrical factors is neglected). The pores or cracks in the material behave also like geometrical obstacles, which in effect modify L=Q by an ‘‘internal’’ geometrical factor, Gint . Taking this into account, one can define a so-called ‘‘bulk’’ resistivity, qbulk ðT Þ, i.e. the resistivity in the microscopic volumes between the pores or cracks: qeff ðT Þ ¼ Gint qbulk ðT Þ
ð2Þ
Gint and qbulk ðT Þ can hardly be measured directly. If we measure the resistance at two temperatures, T and To , their ratio is characteristic only to the qbulk properties: r ¼ RðT Þ=RðTo Þ qbulk ðT Þ=qbulk ðTo Þ
ð3Þ
and rw qw ðT Þ=qw ðTo Þ
ð4Þ
is the same ratio for a ‘‘pure’’ (zone melted) tungsten. Supposing that the bulk excess resistivity, Dqbulk ¼ qbulk ðT Þ qw ðT Þ, is independent of temperature due to the MatthiessenÕs Rule (MR) [9,10], it can be determined from the resistivity ratios like this: Dqbulk ¼ qw ðTo Þðr rw Þ=ð1 rÞ
3. Comparison with technology 3.1. Pre-sintering and sintering Tungsten bars, being in different stages of compacting, pre-sintering or sintering, were prepared by the technology described in [1]. Their properties were investigated by determining both the ‘‘effective’’, and ‘‘bulk’’ electrical resistivities (qeff and qbulk ), compared to their densities (Fig. 2, Table 1, [13]). The resistivity versus density diagrams are rather dissimilar at the two curves. For completion, SEM pictures show the structural variations connected with sintering (Fig. 3a and b). The extremely high variations in qeff with the density (Fig. 2) can be explained by the followings: The compacted powder consists of separated grains, and after heat treatments more and more random contacts appear between them. This process can be explained by a so called ‘‘skeleton model’’ [14]. According to this, metallic conduction starts at a given average number of contacts between the single grains. At first the effective resistivity is high, but with further annealing it decreases in two parallel processes, so with the increasing of the number of contacts and also with the increasing neck diameter at the contacts.
ð5Þ
(Slight deviations from the MR often occur, and these deviations are usually more in transition metals, like tungsten [10,11].) In porous materials the internal geometrical factor, Gint , can be high, but if the pores or cracks have small volume fractions, c, (like in wires) then Gint 1 þ Kc, in which K is the shape factor of the single defects. The value K varies with the shape and direction of the second phases and/or cracks as it is illustrated in Fig. 1a and b. In case of single spherical pores K ¼ 1:5 [12], for bubble rows with varying distances between the bubbles, K is between about 1 and 1.5 (Fig. 1a). At ‘‘thin’’ longitudinal cracks K 1, while at transversal cracks, found e.g. after torsion, K 1 (Fig. 1b). Fig. 2. Variations of the ‘‘effective’’ and ‘‘bulk’’ resistivities, qeff and qbulk , with the density of the rod during compacting, pre-sintering and sintering.
Table 1 The measured densities, qeff and qbulk data on NS tungsten bars after compacting, pre-sintering and sintering (see Fig. 2)
Fig. 1. The illustration of the shape factors K: (a) for single bubbles and bubble rows and (b) for axial and transversal cracks.
Specimens in Fig. 2
Density (g/cm3 )
qeff (lX cm)
qbulk (lX cm)
1. 2. 3. 4. 5. 6.
9.0 9.8 11.6 11.8 16.2 19.3
4050 880 110 17.6 7.0 5.4
9.71 8.39 6.88 5.84 5.51 5.4
Compacted + + Pre-sintered Sintered Zone melted
L. Uray / International Journal of Refractory Metals & Hard Materials 20 (2002) 311–318
Fig. 3. SEM pictures on (a) pre-sintered (No. 4.) and on (b) sintered (No. 5.) tungsten bars.
Since the internal geometrical factor, Gint ¼ qeff =qbulk (Eq. (2)), is a function of the number and size of contacts between the grains, this explains the dissimilarity of the qeff and qbulk curves. (One must mention here yet, that the resistivity versus density function is not unambiguous, since e.g. in case of the so called ‘‘washed’’ powders [1] the grain surfaces are cleaner, which results in better contacts and less resistivity.) At compacting or pre-sintering (no. 1–4), the material consists of single grains, and only the number and size of contacts varies. This involves variations mostly in the effective resistivity but not in the density (Fig. 2). However, at sintering (between no. 4–5) the density of the bar increases effectively, while qeff varies less. These variations are connected with the large structural changes seen in Fig. 3a and b, in which Ôthe skeleton of grainsÕ changes into a Ôsolid material with independent poresÕ. Let us suppose, that in the sintered bar (no. 5.) Gint is an effect of pores (1.27, Table 1.). With the Gint 1 þ Kc approximation the deficit in density, c 0:16, suggests K 1:7, somewhat more than expected for spherical bubbles (Fig. 3a). While in the whole process qeff varies several magnitudes, qbulk varies less than two times. qbulk is possibly not too high even in earlier stages of compacting, but––in the absence of contacts––it cannot be measured by the present DC method. Since qbulk is the average resistivity in the inside of the single grains, it is an effect of scattering of electrons on some defects in the grains. These defects may be e.g. (solute) impurities, dislocations (causing internal stresses) or even surfaces of the neck. All these effects can be reduced by further annealing. Electron scattering on the neck walls could be estimated from WexlerÕs model [15], by approximating the small neck between two grains as a conducting circular orifice in an insulating plane diaphragm, dividing an infinite conductor into two parts. If we identify this re-
313
Fig. 4. The ‘‘bulk’’ and ‘‘effective’’ resistivities (qbulk and qeff ), measured along a sintered tungsten bar (with sizes: 7 7 380 mm3 ). The markers on the bar, m1 (up) and m2 mark the ends of the usable part. The inlet at the middle shows the distribution of solutes in the crosssection, measured on axial sticks cut from the bar.
sistivity with the measured differences in the bulk resistivities between bars no. 4 and 5 (Table 1), i.e. with Dqbulk ¼ 0:33 lX cm, it suggests neck diameters of 1.5 lm [13], in rough agreement with Fig. 3a. A possible application of resistivity measurements on sintered tungsten bars is presented in Fig. 4. The investigations represent non-destructive testing by measuring both effective and bulk resistivities along a sintered tungsten bar (like no. 5. in Fig. 2). Since qbulk decreases slightly towards the ends of the bar, this suggests somewhat more effective evaporation of solute at the ends. On the contrary, qeff increases towards the ends, indicating more residual porosity there. Since the evaporation of solutes is connected mostly with the closure of porosity, this kind of investigation can help tracing the sintering process. At the central part of the bar the internal distribution of solutes in the cross-section was also investigated by measuring Dqbulk on specimens cut axially from an axial section of the bar (see the inset of Fig. 4) The data reveal nearly parabolic solute impurity profile, in which the impurity content decreases near to zero at the surface. 3.2. Swaging and drawing Fig. 5 present effective resistivities, qeff , on swaged bars and wires against the nominal deformation, e 2 logðd=d0 Þ, while their diameters, d, are shown on the upper scale (d0 7 mm is the initial diameter) (from [16,17]). The data are shown both on ‘‘as drawn’’ wires and on wires annealed at 2700 °C for 2 min. With increasing deformation the resistivity is expected to increase due to the more and more created lattice defects. However, the porosity, and with it also the internal geometrical factor, qeff =qbulk , decreases during swaging. As a result, between e ¼ 0 and e 2 the effective
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splits turn cross-wise, for which K 1 (Fig. 1b). According to this the internal geometrical factor increases to Gint 1:2–1:4 [19]. 3.3. Recovery and recrystallization
Fig. 5. The ‘‘effective’’ resistivity, qeff , against the nominal swaging or drawing strain, e 2 logðd=do Þ, (after [16] or [17]). The diameters of the bars or wires are shown on the upper scale.
resistivity, qeff , was found to decrease (from q1 6:1–5:4 lX cm). In this period the porosity decreased due to the thermomechanical treatment. Since the specified annealing at 2700 °C had no further influence on the porosity, qeff decreased similarly on the annealed wires too. During this process the density of the swaged bar or wire was found to increase from 17 to 18.22 g/cm3 [16]. With further deformation (from e 2–11) the diameter of the wire decreased to d 30 lm, while the measured resistivity increased continuously up to q ¼ 7:1 lX cm (Fig. 5). Since in these thin wires the porosity did not change any further [16], this resistivity increase was due only to the creation of lattice defects. During this process the drawing temperature decreased step by step, so the slope of the resistivity versus e line is expected to increase. After annealing at 2700 °C the created lattice defects annihilated, which resulted in about constant resistivity (q 5:4 lX cm). In the wire-drawing process the tensile strength of the wire continuously increases [6], due to which splitting becomes easier in the thin wires. The danger for splitting becomes high in very thin wires, where the high concentration of the created lattice defects is connected with low drawing or coiling temperatures, at which the tungsten is more brittle. Therefore, in the usual drawing process stress–relieve annealing must be inserted at some intermediate diameters (e.g. at d 200 lm) to avoid splitting. That gives a serrated like curve instead of the ‘‘as drawn’’ curve in Fig. 5. In thin wires the volume fraction of second phases is as low as 0.2–0.3% [18], which correspond to internal geometrical factors: Gint ¼ qeff =qbulk 1:003–4 (with K 1:5, Fig. 1a). The occasionally occurring axial splits have low volume fractions, and for them K 1 (Fig. 1b). The splits remain axial also after coiling. However, in experiments with torsional deformation the axial
In heavily drawn tungsten wires isochron annealing decreases the excess electrical resistivity in several welldefined stages [20,21]. Fig. 6 presents this on two wires, having diameters of 0.12 and 0.173 mm. The first stage above the ambient is called stage III, which is terminated below T 750 K. This stage is identified with the movement of vacancies and/or interstitials, and is often investigated after irradiation or quenching [22,23]. Stage III is usually less after wire drawing, due to the high drawing temperature, but larger if the deformation is made at the ambient, like after coiling [24] or after torsion [25]. In stages IV and V continuous fibre- or grain-growth can be observed [26]. Stage IV is connected partly to the annihilation of extrinsic grain boundary dislocations and partly to subboundary movement, during which the fibresize increases [21]. In the vicinity of 1500 K the fibres transform into axially elongated grains, having large-angle boundaries. Further annealing results in continuous grain growth [26], called stage V (in some papers stages IV and V are not separated [20,24]). After an annealing at 1800 K for 15 min the axial grain structure is presented on SEM picture in Fig. 7. A NS tungsten wire (with diameter 0.17 mm) was investigated by annealing specimens at different temperatures and times. The bulk excess resistivities due to grain boundaries, Dqgb , were determined on them (Eq. (5)). Similarly, the volume densities, S=V , of grain surfaces (S is the grain surface, V is the volume) were calculated from the TEM data [27]. The Dqgb versus S=V line was presented in Fig. 8, revealing straight line for the annealed specimens no. 2–6. The ‘‘as drawn’’ wire
Fig. 6. The excess resistivities, Dqbulk , measured on wires with diameters 173 and 120 lm, after annealing them at different temperatures between 300 and 2800 K.
L. Uray / International Journal of Refractory Metals & Hard Materials 20 (2002) 311–318
Fig. 7. SEM picture taken on a NS tungsten wire (diameter 173 lm) after annealing at 1800 K for 15 min., showing axial grain boundary system.
315
pending much on the applied strain, i.e. on the wire diameter. As the wire is drawn from 4.5 to 0.5 mm, Trecr remains in the vicinity of 2000 K, but with further reduction in diameter to d 0:15 mm it rises sharply to 2500 K [7]. This effect is attributed to the increasingly effective inhibition of recrystallization by the potassiumstabilized bubble dispersion [29]. At even less diameters Trecr may decrease again, but a detailed investigation e.g. of the bubble dispersion would help to clarify the present state of knowledge [30]. If the wire drawing is continued by another type of deformation, the temperature of recrystallization usually decreases. Accordingly, in a wire (with diameter of 0.063 mm), coiling decreased Trecr with about 200–300 K [24]. Similarly, on a wire with diameter 0.39 mm, torsional strains of c 0:34–1.76, decreased Trecr with about 260–450 K [31]. 3.4. Comparison of resistivity and flow stress
Fig. 8. The excess resistivities due to grain boundaries, Dqgb , measured on specimens of a NS tungsten wire (diameter 173 lm) with different annealing, against the density of grain boundaries, S=V , calculated from TEM data [27]. The numbers refer to: (1) ‘‘as drawn’’ wire, (2) wire annealed at 1200 K for 6 h, (3) at 1600 K, 30 s, (4) at 1600 K, 3 min, (5) at 2000 K, 30 s and (6) ‘‘recrystallized’’ at 2800 K for 15 min.
(no. 1.) did not fit to the line, since it contained point defects too. The straight line corresponds to specific grain boundary resistivity of: Dqgb =ðS=V Þ 4 106 lX cm2 . The resistivity of a single grain boundary can also be determined by applying superconducting quantum interference device (SQUID) [28]. With that, single boundaries in a bi-crystal can be studied, and by varying their direction or structure, the angular dependence of the resistivity could also be studied. The process of grain growth is terminated by an exaggerated grain growth, called stage VI (Fig. 6), at which the grain size increases to about the wire size [26]. At the end of stage VI the residual excess resistivity was about Dq 0:1 lX cm (Fig. 6), which was due to the residual solute impurity content. The start of stage VI is called the temperature for recrystallization, Trecr , de-
Since in the general practice the mechanical investigations are more common, it seems worthwhile to compare the annealing effects measured by electrical and mechanical properties. So Fig. 9 present the excess resistivities, Dqbulk , against the flow stress, r0:2 , (belonging to 0.2% strain), measured on several specimens (0.17 mm diameter) after different annealing [32]. The regions of the diagram are separated according to the different stages (like in Fig. 6). The diagram suggests, that point defects (stage III) affect only the excess resistivity, while the recrystallization (stage VI) has more effect on the flow stress. In the ranges of fibre––or grain growth (stages IV and V) Fig. 8 suggests roughly linear connection between them. Usually for grains with random sizes and orientations the flow stress, r, is expected to follow a Hall–Petch type relation [33,34]:
Fig. 9. qbulk against the flow stress, r0:2 , (for 0.2% strain), measured on several specimens, annealed at different temperatures. The annealing stages, III–VI are marked on the diagram [32].
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L. Uray / International Journal of Refractory Metals & Hard Materials 20 (2002) 311–318
r ¼ r0 þ kd 1=2
ð6Þ
in which r0 is a friction stress, k is constant and d is the average grain size. In Fig. 9 the scattering of data is too high to be able to determine the exact connection between resistivity and flow stress. Otherwise, Eq. (6) was established mostly for grains with random extensions, while now the grains are axially elongated (Fig. 7). Since this paper is only resistivity oriented, a deeper comparison of Figs. 8 and 9 will not be forced now.
4. Discussion The specific grain boundary resistivity is usually measured on equiaxial grains, while in the NS tungsten wire an axially elongated grain boundary system develops (Fig. 7). In the two cases the measured specific resistivities are not necessarily the same. In deposited metal layers the specific grain boundary resistivity is usually determined by the Mayadas–Shatzkes M–S model [36], in which the grain boundaries are represented by parallel lines, perpendicular to the direction of the electric field, E, with an average separation, d. At the same time the effect of boundaries, parallel to E, are neglected. In this model the ratio of bulk and measured resistivities are: qbulk =qmeas ¼ 3½1=3 1=2a þ a2 a3 lnð1 þ 1=aÞ
ð7Þ
in which a ¼ lo =dR=ð1 RÞ, lo is the electronic mean free path and R is the ‘‘reflection coefficient’’ of electrons at the grain boundaries. In case of deposited tungsten layers R 0:5 was found if the grain-size was estimated from X-ray, or R 0:65 if the grain-size was measured directly from TEM. These R values correspond to specific grain boundary resistivities, Dqgb 10 or 20 106 lX cm2 respectively [37]. At the same time the specific grain boundary resistivity for axially elongated grains was found only Dqgb 4 106 lX cm2 (Fig. 8). The large discrepancy between these data needs some comment. Although the M–S model neglects grain boundaries parallel to E, these boundaries can have rough, dislocational substructure, scattering the electrons [38]. Otherwise, in case of tungsten the electronic scattering is relatively high due to its relatively complicated Fermi surface [39]. Electrical conduction in wires with axially elongated grains (Fig. 7) suggests some similarity to the Fuchs–Dingle ‘‘size-effect’’ model in thin films and wires [40,41] naturally, only similarity but not equivalency. In the high temperature limit the ‘‘size effect’’, gives a linear connection between the excess resistivity, Dq, and the reciprocal diameter, 1=d: Dq ¼ 3=4ðqw kw Þ=dð1 pÞ
ð8Þ
in which qw is the resistivity, kw is the electronic mean free path in pure tungsten (qw kw 2:2 1011 lX cm2 [39]), and p is the reflectivity of electrons at the surface. In Fig. 9 S=V was calculated from the average diameter, d 0 , of the axial grains, measured by TEM (by S=V ¼ ðp=2Þ1=d 0 [35]), giving also linear dependence from 1=d 0 . Fitting the result to Eq. (8), p 0:6 is obtained. To go further in this comparison, the excess resistivity for grain boundary resistivity, Dqgb ðT Þ, was measured on a NS tungsten wire (0.3 mm diameter) between temperatures T ¼ 4 and 200 K, and presented in Fig. 10. The two specimens were annealed at 1500 or at 1700 K. The average diameters of the axial grains were d ¼ 0:6 or 0.5 lm respectively (measured on SEM pictures [42]). The Dqgb ðT Þ versus T curves (solid lines) reveal maxims at T 60 K, corresponding to electronic mean free paths: kw 0:5 lm. The Fuchs–Dingle size effect model with fitting parameters: d ¼ 0:55 lm and p ¼ 0:6 gives a similar curve between them with similar maximum. The proximity of kw to the grain or wire size, d, verifies also the size-effect like behavior. From these data the specific grain boundary resistivity was: Dqgb 3 106 lX cm2 [42]. The excess resistivities were measured on the wires not only axially, Dq* , but also transversally, Dq? . For this purpose, tiny little discs were cut transversally from the wire (diameter ¼ 0:3 mm, height 0:2 mm), as illustrated in Fig. 11, on which the resistivity was measured with the help of microscopic spark-welded contacts. Measuring on several disks, the transversal grain boundary resistivity was found: Dq? 9 106 lX cm2 . These results reveal high anisotropy of the electron scattering between transversal and axial mea-
Fig. 10. The excess resistivities, qbulk ðT Þ, measured on NS tungsten wires (diameter 0.3 mm) at temperature between 4–200 K. The specimens were annealed at 1500 or 1700 K. The curves are compared to the Fuchs–Dingle size-effect model (F–D) (dotted line), having parameters: diameter: 0.55 lm and p ¼ 0:6. Maximums occur at about 60 K, at which the electronic mean free path in tungsten is kw 0:7 lm.
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References
Fig. 11. Illustration of cutting a little transversal specimen from the NS tungsten wire (diameter 0.3 mm) with welded contacts, for the investigation of the anisotropy of grain boundary resistivity.
surements: Dq? =Dq* 2:8ð0:5Þ [42]. Anisotropy could be measured also on a ‘‘split-free’’ wire by applying high torsional strain (c 1:5). Applying stress–relieve annealing before and after torsion, increased by about 2.3 times [43]. The high anisotropy can explain the large grain boundary resistivity in deposited layer, since it may correspond to about Dq? ., i.e. to the cross-sectional excess resistivity in the wire.
5. Conclusions Direct current electrical measurements can be applied to follow several specific properties of NS tungsten from compacted powder to thin wires or coils: 1. In pre-sintered tungsten bars the ‘‘giant’’ effective resistivity describes a skeleton structure of grains, with increasing number and size of contacts between the grains. During sintering this structure transforms into a compact material with closed porosity. 2. At swaging the effective resistivity at the ambient decreases due to the diminishing porosity, but at further drawing it increases again. 3. Annealing the wire at different temperatures, the excess resistivity decreases in stages (III–VI). 4. The specific grain boundary resistivity is high in the deposited tungsten layers: Dqgb 10–20 106 lX cm2 , and small in the axially elongated grain boundary system: Dqgb 3–4 106 lX cm2 . This must be due to the high anisotropy of resistivity on the grain boundaries: Dq? =Dq * 3. 5. Excess resistivity can measure also the recrystallization temperature, which depends much on the drawing strain and also on further strain (e.g. with coiling or twisting).
Acknowledgements The author wishes to thank Dr. I. Ga al for helpful discussions. This work was supported by the National Research Fund (OTKA), contract no. T.32730.
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