Tungsten
`Properties, Chemistry, Technology of the
`Element, Alloys, and Chemical Compounds
`
`Erik Lassner and
`Wolf-Dieter Schubert
`
`Vienna University of Technology
`Vienna, Austria
`
`Kluwer Academic / Plenum Publishers
`New York, Boston, Dordrecht, London, Moscow
`
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`Library of Congress C a t a l o g i n g - i n - P u b l i c a t i on Data
`
`Lassner, Erik.
`Tungsten
`.- properties, chemistry, technology of the element,
`a l l o y s, and c h e m i c al compounds / Erik Lassner and Wolf-Dieter
`Schubert.
`cm.
`p.
`Includes b i b l i o g r a p h i c al references and index.
`ISBN 0-306-15Q53-4
`1. Tungsten.
`I. Schubert, Wolf-Dieter. II. Title.
`QD181.W1L37 1998
`620 . 1 ' 8934—dc21
`
`98-45787
`CIP
`
`ISBN 0-306-45053-4
`
`© 1999 Kluwer Academic / Plenum Publishers, New York
`233 Spring Street, New York, N.Y. 10013
`
`1 0 9 8 7 6 5 4 3 21
`
`A C.I.P. record for this book is available from the Library of Congress.
`All rights reserved
`
`No part of this book may be reproduced, stored in a retrieval system, or transmitted in any form or by any
`means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written
`permission from the Publisher
`
`Printed in the United States of America
`
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`affect the recrystallization grain morphology and the retained dislocation substructure. In
`particular, non-sag tungsten is significantly more creep-resistant than pure tungsten,
`mainly as a result of the interlocking grain structure, which forms on recrystallization
`and which prevents both grain boundary sliding and difrusional creep. In addition, the fine
`dispersion of potassium bubbles contributes to the outstanding creep resistance through
`pinning of dislocations [1.62,1.66].
`Non-sag tungsten wires are the most creep-resistant wires, with the exception of
`monocrystalline tungsten. They are therefore used for sag-free lamp filaments at service
`temperatures of up to 300O0C (0.88 rm), and shear stresses in the range of 0.5 to 10 MPa
`[1.66].
`
`1.2.4. Thermal Properties
`
`Melting point: 3422 ± 15 0C (3695 K) [1.67],
`3390 ±40 0C (3663 K) [1.68],
`3423 ±30 0C (3696) [1.69].
`
`The high melting point (highest of all metals) is the most prominent and important
`property in regard to all applications as refractory metal. It is a consequence of the electron
`density of states. Small amounts of impurities, such as carbon, lower the melting point.
`The molar volume increases by 8% on melting. This is the largest expansion
`observed for bcc metals [1.7O].
`The melting curve of W has been determined to 5GPa [1.71].
`Enthalpy of fusion: 46±4kJ-mol"1 [1.68].
`Entropy of fusion: 14 J - mol"! - K~ ! [1.7O].
`Enthalpy of sublimination: 858.9±4.6U-HiOl"1 [1.35].
`Vapor Pressure. Tungsten has the lowest vapor pressure of all metals. Within the
`temperature range from 2600 to 3100 K, it obeys the following equation [1.76]:
`
`log /?[Pa] = -453957"1 + 12.8767
`
`At 200O0C, the vapor pressure is 8.15 x 10"8Pa; at 300O0C it is 10" * Pa. Experimental
`data for p over liquid W are not available.
`The rate of evaporation in vacuum is about 6.2 x 10" ug - c m "2^ s "1 at 200O0C,
`about7xlO"8g.cm"2-s"1 at 250O0C, and about 2.5 x 10""5S-Cm"2^"1 at 30000C
`[1.72]. It is markedly reduced by an inert gas atmosphere (Ar, Kr). Therefore, modern
`incandescent lamps contain inert gas fillings to avoid enhanced wall-blackening (the rate of
`evaporation in vacuum is about 500 times larger as compared to an Ar atmosphere of 1.2
`bar) [1.73].
`
`Boiling Point: calculated from rates of evaporation of solid tungsten,
`
`5663 0C (5936 K) [1.74],
`5700 ±200 0C [1.64].
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`Critical temperature: 13400 ± 140OK [1.75].
`Critical pressure: (3.37 ±0.85) x 1O8Pa [1.75].
`Critical density: 4.31 g • cm~3 [1.35].
`Thermal expansion. At room
`temperature, values between 4.32 and 4.68
`x 10"6K"1 were obtained for the linear coefficient of expansion ex, depending on the
`material (P/M sheet, arc-cast sheet, etc.) and the type of measurement. Values for low and
`high temperatures are listed in Table 1.12. The linear coefficient of expansion can also be
`calculated according to the following equations [1.76]:
`
`temperature range: 293-1395 K
`
`a = 4.266 x 10~6(7 - 293) + 8.479 x 10-10(r - 293)2 - 1.974 x 10~13(r - 293)3
`
`temperature range 1395-2495 K
`
`oc = 0.00548 + 5.416 x 10~6(r - 1395) H-1.952
`x 10~10(r - 1395)2 + 4.422 x 10~13(r - 1395)3
`
`temperature range 2495-3600 K
`
`a = 0.01226 + 7.451 x 10~6(7 - 2495) + 1.654 x 10~9(r - 2495)2 + 7.568
`x 10~14(r-2495)3
`
`The very low thermal expansion of tungsten makes it compatible with glass and
`ceramics in high temperature applications.
`
`Thermodynamic functions [1.35]. Thermodynamic functions for solid tungsten are
`listed in Table 1.13. For more details and data for liquid tungsten, see elsewhere [1.1O].
`
`TABLE 1.12. Thermal Expansion Coefficient for
`Low and High Temperatures [1.35]
`
`T(K)
`
`106-Qt(K-1)
`
`T(K)
`
`106-Ot(K-1)
`
`10
`15
`20
`25
`30
`40
`50
`60
`70
`80
`100
`130
`
`0.006
`0.019
`0.048
`0.102
`0.20
`0.53
`0.90
`1.43
`1.88
`2.30
`2.82
`3.42
`
`160
`190
`220
`260
`300
`600
`1000
`1400
`1800
`2200
`2600
`3000
`3400
`
`3.82
`4.06
`4.20
`4.32
`4.49
`4.75
`5.02
`5.46
`6.11
`6.89
`7.76
`9.05
`11.60
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`TABLE 1.13. Thermodynamic Functions [1.35]
`
`T
`(K)
`
`HT — //298 5
`(kJ . mor1)
`
`Hj — HQ
`
`S
`
`Cv
`(kJ • mor1) (kJ • mol'1 • K"1) (kJ - mor1 • K'1) (kJ - mor1 • K'1) (kJ • mor1 • K"1)
`
`S~SQ
`
`Cp
`
`298.15 O
`500
`5.022-5.024
`1000
`18.23-18.25
`1500
`32.33-32.62
`2000
`47.59-48.11
`2500
`64.52-64.78
`3000
`83.10-83.88
`3500
`105.19
`3600
`110.5-111.8
`
`4.970
`10.007
`23.142
`37.249
`52.599
`69.476
`88.310
`109.845
`114.574
`
`32.640
`45.516
`63.658
`75.068
`83.881
`91.399
`98.254
`104.880
`106.212
`
`32.618
`45.457
`63.686
`75.099
`83.585
`91.397
`98.442
`—
`106.89
`
`24.10-24.42
`24.33-25.44
`27.19-27.60
`29.23-29.86
`31.37-32.13
`34.67-36.00
`39.25-41.80
`46.49-50.85
`48.11-54.68
`
`23.96
`25.16
`26.70
`28.12
`29.80
`—
`35.91
`—
`—
`
`Analyses of thermodynamic properties of tungsten at high temperatures are available
`[1.77,1.78].
`The heat capacity at low temperatures is*
`
`80
`70
`60
`50
`40
`35
`30
`25
`Tin K
`100
`Cp (J-mor1-K-1) 0.73
`10.74 12.81 16.04
`8.39
`5.82
`3.30
`1.35 2.22
`T in K
`260
`300
`220
`200
`180
`140
`160
`120
`Cp (J-mor1-K-1) 18.28 19.87 21.01 21.86 22.54 23.04 23.81 24.35
`
`The heat capacity of liquid tungsten is 35.564JmOl"1 -K"1 [1.10]
`
`[1.35]. At a certain temperature, the diffusion process is characterized
`Self-diffusion
`by the diffusion coefficient D. Its temperature dependency is given by the Arrhenius
`equation D = DQQxp(-Q/R-T) with D0 a constant in crn^g"1, T the absolute
`temperature, R the molar gas constant in J - K"1 • mol"1, and Q the activation enthalpy
`in kJ-mol"1.
`Activation enthalpies for the lattice (volume) diffusion were derived between 586 and
`628 kJ « mol"1 for single crystals and between 502 and 586 kJ - mol"1 for polycrystalline
`tungsten. Accordingly, the following equations were set up [1.79]:
`
`Self-diffusion in tungsten single crystals: D = 42.8 exp(- 64Q/RT).
`Self diffusion in polycrystalline tungsten: D — 54 exp(— 504/RT).
`Over the range of 1900 to 280O0C, a linear relationship between log D and 1/7 was
`obtained for polycrystalline tungsten.
`The self-diffusion parameters D0 and Q are influenced by the impurity content of the
`diffusion zone. Higher values for both were obtained for impure tungsten. This effect is
`more pronounced at low temperatures and vanishes above 2043 K. (It is assumed that
`impurities attract vacancies and the higher vacancy concentration disturbs the diffusion
`process).
`The fact that lower Q values were obtained for polycrystalline tungsten than for single
`crystals, especially for T < 0.7rm, is due to a more or less significant contribution of grain
`boundary diffusion to the total bulk diffusion. Observed rates of volume diffusion,
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`obtained on polycrystalline tungsten, will therefore always depend on the microstructure of
`the material under investigation.
`Grain boundary diffusion
`is the dominant mechanism in polycrystalline tungsten
`below 210O0C. For grain boundary diffusion, activation enthalpies between 377 and
`46OkJ- mol"1 were measured.
`
`[1.35,1.80,1.81]. At room temperature, the
`Thermal conductivity and diffusivity:
`thermal conductivity coefficient X is about 1.75 W • cm"1 • K"1. Its temperature depen-
`dence is shown in Fig. 1.19. Some typical data are given in Table 1.14. In the low-
`temperature range, it is strongly dependent on the RRR (residual resistivity ratio PO/PT)>
`which is also an indication of the purity. Table 1.15 shows the differences between samples
`of varying purity.
`Between 1200 and 280OK, A, obeys the following equation [1.8O]:
`
`2^4 199
`X(W - cm'1 - K-1) = 1.0834 - 1.052 x 10'4F + —-—
`
`At the melting point, A, drops from 0.895 (solid) to 0.705 (liquid) [1.35].
`Sintered and arc-cast tungsten specimens differ in A, values at elevated temperatures.
`The thermal conductivity of single crystals and polycrystalline tungsten, both having the
`same degree of purity, coincide at high temperature.
`There exist certified NBS standards of arc-cast as well as sintered tungsten as
`reference material for the temperature range of 4 to 300OK [1.83].
`The high thermal conductivity of tungsten (very suitable for use as heat sinks) in
`combination with the low specific heat results in high cooling rates during hot-working of
`the metal, which makes the handling during working more difficult.
`The thermal diffusivity of tungsten at 30OK is 0.662 cm2 • s"1, and decreases to
`0.246 cm2 -s"1 at the melting point. At low temperatures (<200 K) the values are strongly
`
`FIGURE 1.19. Temperature dependence of the thermal conductivity A, of well-annealed high-purity tungsten
`[1.35]; source [1.81].
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`TABLE 1.14. Thermal Conductivity
`Coefficient at Different Temperatures
`[1.35,1.81]
`
`Temperature
`(K)
`
`A,
`(W-cm-1-K-1)
`
`O
`10
`50
`100
`300
`500
`1000
`2000
`3400
`
`O
`97.1
`4.28
`2.08
`1.74
`1.46
`1.18
`1.00
`0.90
`
`dependent on the impurity level and the density of lattice defects. For more information see
`elsewhere [1.82].
`
`TABLE 1.15. Thermal Conductivity Coefficient in the
`Low-Temperature Range and Dependence on the
`Residual Resistivity Ratio [1.35,1.80]
`
`X(W-Cm-1 -K-1)
`
`Temperature (K)
`
`RRR 100
`
`RRR 300
`
`1
`5
`10
`20
`50
`100
`150
`200
`300
`
`0.50
`2.49
`4.88
`7.99
`3.57
`2.17
`1.97
`1.89
`1.74
`
`1.51
`7.49
`14.04
`17.34
`3.98
`2.24
`2.01
`1.91
`1.76
`
`7.2.5. Electromagnetic Properties [1.35]
`
`Electrical Resistivity (|ifi • cm). In the low-temperature range <0.07 K the electrical
`resistivity p0 is independent of the temperature and will be only determined by the
`impurity level.
`In order to calculate p within different temperature ranges, equations have been set
`
`up:
`
`up to 4OK
`
`p = 1.5 x 1(T5 + 7 x 10'7T2 + 5.2 x 1(T10T15
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`40-90 K
`
`p = 0.14407 - 1.16651 x 10~2r + 2.41437 x 10~4r2 - 3.66335 x 10'9T4
`
`90-750 K
`
`p = 1.06871+2.06884 x 10~2T + 1.27971 x 10~6r2 + 8.53101 x 10"9J3
`-5.14195 x 10'12T4
`
`300-1240K
`
`p = 4.33471 x 10~1272+ 2.19691 x HT8T7-1.64011 x 10~6
`
`1240-2570K
`
`p = 4.06012 x 10~12r2 +4.67093 x 10~8r - 1.94101 x 10~5
`
`Moreover, the resistivity is influenced by all kinds of lattice defects (vacancies,
`dislocations, grain boundaries, etc.) and impurities.
`Some selected values near and above room temperature are listed in Table 1.16. The
`resistivity of liquid tungsten close to the melting point and at 500OK was given as
`131 |iQ • cm and 160 JiQ • cm, respectively [1.84].
`The resistivity of thin films depends on microstructure, impurity content, and surface
`roughness. These properties are the consequence of deposition conditions, substrate
`temperature, and annealing. Therefore, a wide scatter of values was observed, for example,
`between 6 and 20 JiQ • cm at 3OK [1.35]. Under certain deposition conditions, metastable
`/J-W forms, which has a significantly higher bulk resistivity (approximately 10 times that
`of the thermodynamically stable a-W phase).
`
`Superconductivity [1.35]. Tungsten is a Type I superconductor with a transition
`temperature of 0.0154 ±0.0005 K. The critical magnetic field strength HC(T -» O) is
`1.15 ±0.03 Oe. (91.5A-Hi"1). Impurities only show a minor influence on the transition
`
`TABLE 1.16. Electrical Resistivity of Tungsten at
`Near-Room and at Elevated Temperature [1.35]
`
`T(K)
`
`p(nQ-cm)
`
`T(K)
`
`p(^iO • cm)
`
`273
`293
`298
`300
`
`4.82
`5.28
`5.40
`5.54
`
`400
`500
`600
`800
`1000
`1200
`1400
`
`8.05
`10.70
`13.35
`18.85
`24.75
`30.90
`37.20
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`temperature:
`
`RRR 57000
`RRR 7500
`
`0.0160 K
`0.0154 K
`
`In thin films, due to structural influences or the presence of P- or y-tungsten, much
`higher critical temperatures (up to 6 K) were found.
`
`Thermoelectric effects. A temperature gradient generates in tungsten a small poten-
`tial difference (the Thomson effect). This difference, called the thermoelectric power
`S (uV/K), drops with increasing temperature. Its temperature dependence is tabulated in
`Table 1.17.
`Thermocouples. For temperature measurements up to 230O0C, thermocouples
`consisting of tungsten and tungsten-rhenium alloys are employed widely. The most
`common combinations are W versus W26Re, W5Re versus W26Re, and W3Re versus
`W25Re. Electromotive forces built up by each combination for different temperatures are
`shown in Table 1.18.
`W-Re thermocouples can only be used in neutral or reducing atmospheres. Other
`combinations, such as W/Pt, W/Ta, or W/Mo, have gained no commercial importance.
`
`[1.35]. The Hall coefficient
`Magnetoelectric effects
`between 10 and 12 x 10~n m3 • A"1 - s"1.
`The Magnetic susceptibility is given either as Xmoi (10~6 cm3 -mol"1) or as %g
`(10~6 cm3 • g"1). It increases with temperature. Values for different temperatures are given
`in Table 1.19.
`
`at room temperature varies
`
`1.2.6. Optical Properties
`
`The optical properties of tungsten have been studied in more detail than those of any
`other metal or material, because tungsten is not only used as an incandescent lamp
`filament, but also as a comparison temperature standard in specially constructed strip
`lamps.
`
`TABLE 1.17. Temperature Dependence of
`Thermoelectric Power of Tungsten [1.35]
`
`T
`(K)
`
`10
`20
`50
`80
`100
`150
`200
`250
`273
`300
`
`S
`(JiV-K)
`
`+0.05
`-0.28
`-2.78
`-3.70
`-4.04
`-2.45
`- 1.41
`-0.10
`+ 0.56
`+ 1.44
`
`TS
`(K)
`
`400
`600
`800
`1000
`1200
`1400
`1500
`1600
`1800
`
`(JiV-K)
`
`4.62
`10.75
`15.51
`18.46
`20.06
`20.63
`20.70
`20.61
`19.15
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