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The electrical resistance of boron and of tungsten borides in boron filaments
137
Journal of the Less-Common Metals, 67 (1979) 137 - 141 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
THE ELECTRICAL RESISTANCE OF BORON BORIDES IN BORON FILAMENTS*
AND OF TUNGSTEN
A. M. TSIRLIN, G. Ya. KHODOV, A. F. ZHIGACH, R. A. RABINOVICH and V. P. GUZHOV Institute of Chemistry, (U&S. R.)
Ministry of Chemical Industry,
Kirov Str. 20, 101851
Moscow
Summary The electrical resistance of boron filaments prepared by chemical vapour deposition of boron on a heated tungsten substrate was measured. The measurements were carried out by a compensation method on direct heating with a continuous current. The electrical resistances of filaments with diameters of 30 - 165 pm at room temperature and in the temperature range 1173 - 1473 K were investigated. The electrical resistivity of the core (tungsten borides) of the boron filament and the electrical resistivity of the boron deposit on the boron filament were calculated approximately at various temperatures from empirical equations, which can also be used in practical calculations.
The boron filaments we used have a three-ply structure consisting of tungsten, tungsten borides and boron. The value of the electrical resistance determines the heat evolution and the temperature distribution during the process of filament formation, when its composition, structure and diameter change continually lengthwise. The data in the literature on the resistance of boron itself [l - 61 vary over a wide range because of the differences in specimen purity and in the method of preparation. There are not many data given [ 1 - 71 for tungsten borides WB4 and WzBs and it is difficult to apply these data to the complex mixture of borides which occur in the boron filament core [8]. In this paper the direct measurement of the electrical resistance of boron filaments with diameters in the range 30 - 165 pm and at temperatures of 1173 - 1473 K is reported. The data we obtained were used to determine the electrical resistances of the boron deposit and of the core and to construct a mathematical model of electrical resistance which takes into account the three-ply structure of the boron filament. *Paper presented at the 6th International Symposium on Boron and Borides, Varna, Bulgaria; October 9 - 12, 1978.
138
The measurements were carried out by a compensation method in which the voltage drop across the measured part of the filament is balanced by the voltage from the external supply source of current. Thus the compensating circuit was free of current and the effect of contact resistance was eliminated. The measurement unit was composed of a hermetic glass cylindrical chamber with current contacts (30 mm in length) and potential mercury contacts (1.5 mm in length), and this enabled us to measure the electrical resistances of specimens with lengths up to 120 mm. The specimen was heated by an accumulator or by a stabilized power source, and the compensating voltage was supplied from anode batteries. The total error in the electrical resistance measurement was +2%. The boron filament temperature was measured with an optical micropyrometer with an accuracy of + 10 “C. The specimen diameter was determined by using a microscope with a measuring head (of accuracy kO.25 pm); the average value of 20 measurements along the specimen length at regular intervals was taken. The electrical resistance was measured at room temperature with a current of 7 mA (this gave a minimum electrical resistance within the range of current changes from 2 to 16 mA). The experimental data averaged over many measurements for boron filaments with various diameters at various temperatures indicated that the electrical resistivity uersus temperature curves pass through a maximum at 1013 - 1073 K regardless of the size of the diameter. The boron filament conductivity appears to be determined by the boride core conductivity for temperatures up to 1000 K; however, at temperatures above 1100 K the sharply increasing conductivity of the boron sheath begins to exert an effect (Fig. 1). At room temperature the resistance of unit axial length of boron filament (Fig. 2) initially increases as the diameter increases up to 65 70 pm and then remains constant at 33 f 1.5 a cm-‘. We concluded that the constant value of the electrical resistance of the filament was connected with the termination of the transition from the tungsten core to borides. The filaments of diameter greater than 70 pm, in which the core is fully boronized, consist of two layers, a core and a boron sheath. They are connected in parallel in the electrical circuit; at high temperatures their electrical resistances are comparable in value, but at room temperature the boron electrical resistance exceeds the core electrical resistance by several orders of magnitude. The experimental data enabled us to obtain the following electrical resistivity uersus temperature relationship for these layers: PwB = 60.0 +.37.9 X 10-3T~s2
cm
pB = 49.02 exp where T is the temperature (K) and pB and p WB of boron and of tungsten borides respectively.
are
the electrical
resistivities
139 7ooo p,406 ncm 1 I I
I
I
I
6000
Fig. 1. A plot of the electrical resistivity against the diameter for boron filaments at various temperatures: curve 1, 1173 K; curve 2, 1273 K; curve 3, 1373 K, curve 4, 1473 K.
R
zii
G 30
20
40
0
m
Fig. 2. The electrical resistance of 1 cm of a boron filament plotted against diameter at room temperature.
The electrical resistivity of the total boron filament can be calculated from a three-ply model using eqns. (1) and (2) and an approximate expression for the tungsten data [9] in the range 773 - 1573 K PW = -5.19
+ 0.03T~a
cm
The relationship between the radii of the layers was determined approximately by measuring the radii in a boron filament cross section with a microscope.
(3)
(4) rwB
=
r&B + (rkB
-r&B)[l
-exp{-_(R
-r%B)@(R))l
(5)
where f(R) = 2(2rw’ - R2/3)3/2, @(R) = 0.07155 - 5.12 X lo-* (R - r&) + 1.2 x lo-*(R -r&~)~, r$B and rka are the initial and final radii of the core as boronized and rw, rwB and R are the present radii of the tungsten layer, of its borides and of the filament respectively. The selection of coefficients and correlation functions f(R) and G(R) was made using the principle of minimum divergence for experimental data. The divergence of calculated and experimental data did not exceed +5%. The value of the electrical resistivity of boron calculated from the empirical eqn. (2) (Fig. 3) agrees well with the data [6] for zone-melted boron and it lies below the data [2 - 51 for more porous sintered material.
Fig. 3. A plot of the electrical resistivity against the temperature for boron: curve 1, ref. 5; curve 2, ref. 2; curve 3, ref. 10; curve 4, ref. 4; curve 5, ref. 3; curve 6, ref. 6; 0, our data.
At working temperatures the electrical resistance of the filament core (Fig. 4) is significantly below the value for tungsten boride W2B5 [l],it is close to the value obtained for the same boride by Kolomoets et al. [ 71 and it is very close to one of the other metal borides in its temperature coefficient of resistance. The experimental data we obtained may be applied to the practical calculation of electric circuits using boron filaments and these results are also of interest for the evaluation of the electrical resistivity values of boron and of tungsten borides in connection with the vapour phase deposition of boron.
141
Fig. 4. A plot of the electrical resistivity against the temperature for various borides: curve 1, W& [l] ; curve 2, WzB5 [7] ; curve 3, our data; curve 4, TaB2; curve 5, NbB2 curve 6, TiB, ; curve 7, VB2 ; curve 8, ZrBz [ 11.
References G. V. Samosnov, L. Ya. Markovski, A. F. Zhigach and M. G. Valjashko, Bor, ego Soedinenija i Splaui, Akademii Nauk Ukrainskoi SSR, Kiev, 1960, pp. 52 - 54. 2 F. Weintraub, Ind. Eng. Chem., 5 (1913) 106. 3 E. S. Greiner and I. A. Gutowski, J. Appl. Phys., 28 (1957) 1364. 4 I. R. King, F. E. Wawner, S. R. Tailor and C. P. Talley, in 0. K. Gaule (ed.), Boron: Preparation, Properties and Applications, Vol. 2, Plenum Press, New York, 1965, pp. 45 - 62. 5 F. S. Maron and M. S. Germaidze, Izu. Akad. Nauk SSSR, Neorg. Mater., 3 (1967) 2144. 6 R. M. Babaev, M. N. Iglitsin and G. E. Chuprikov, Izu. Akad. Nauk SSSR, Neorg. Mater., 3 (1967) 1963. 7 N. V. Kolomoets, V. S. Neshpor, G. V. Samsonov and S. A. Semenkovich, Zh. Tekh. Fiz., 28 (1958) 2382. 8 A. F. Zhigach, A. M. Tsirlin et al., in Bot. Polutchenie, Struktura i Svoistva, Nauka, Moscow, 1974, pp. 147 - 153. 9 B. P. Nikolski, 0. N. Grigorov, M. E. Posin et af. (eds.), Spra~ochnik Kkimika, Vol. 1, Goschimizdat, Moscow, 2nd edn., 1962, pp. 764,765. 10 T. S. Moss, Photoconductivity in the Elements, Academic Press, New York, 1952, p. 78.
Journal of the Less-Common Metals, 67 (1979) 137 - 141 0 Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
THE ELECTRICAL RESISTANCE OF BORON BORIDES IN BORON FILAMENTS*
AND OF TUNGSTEN
A. M. TSIRLIN, G. Ya. KHODOV, A. F. ZHIGACH, R. A. RABINOVICH and V. P. GUZHOV Institute of Chemistry, (U&S. R.)
Ministry of Chemical Industry,
Kirov Str. 20, 101851
Moscow
Summary The electrical resistance of boron filaments prepared by chemical vapour deposition of boron on a heated tungsten substrate was measured. The measurements were carried out by a compensation method on direct heating with a continuous current. The electrical resistances of filaments with diameters of 30 - 165 pm at room temperature and in the temperature range 1173 - 1473 K were investigated. The electrical resistivity of the core (tungsten borides) of the boron filament and the electrical resistivity of the boron deposit on the boron filament were calculated approximately at various temperatures from empirical equations, which can also be used in practical calculations.
The boron filaments we used have a three-ply structure consisting of tungsten, tungsten borides and boron. The value of the electrical resistance determines the heat evolution and the temperature distribution during the process of filament formation, when its composition, structure and diameter change continually lengthwise. The data in the literature on the resistance of boron itself [l - 61 vary over a wide range because of the differences in specimen purity and in the method of preparation. There are not many data given [ 1 - 71 for tungsten borides WB4 and WzBs and it is difficult to apply these data to the complex mixture of borides which occur in the boron filament core [8]. In this paper the direct measurement of the electrical resistance of boron filaments with diameters in the range 30 - 165 pm and at temperatures of 1173 - 1473 K is reported. The data we obtained were used to determine the electrical resistances of the boron deposit and of the core and to construct a mathematical model of electrical resistance which takes into account the three-ply structure of the boron filament. *Paper presented at the 6th International Symposium on Boron and Borides, Varna, Bulgaria; October 9 - 12, 1978.
138
The measurements were carried out by a compensation method in which the voltage drop across the measured part of the filament is balanced by the voltage from the external supply source of current. Thus the compensating circuit was free of current and the effect of contact resistance was eliminated. The measurement unit was composed of a hermetic glass cylindrical chamber with current contacts (30 mm in length) and potential mercury contacts (1.5 mm in length), and this enabled us to measure the electrical resistances of specimens with lengths up to 120 mm. The specimen was heated by an accumulator or by a stabilized power source, and the compensating voltage was supplied from anode batteries. The total error in the electrical resistance measurement was +2%. The boron filament temperature was measured with an optical micropyrometer with an accuracy of + 10 “C. The specimen diameter was determined by using a microscope with a measuring head (of accuracy kO.25 pm); the average value of 20 measurements along the specimen length at regular intervals was taken. The electrical resistance was measured at room temperature with a current of 7 mA (this gave a minimum electrical resistance within the range of current changes from 2 to 16 mA). The experimental data averaged over many measurements for boron filaments with various diameters at various temperatures indicated that the electrical resistivity uersus temperature curves pass through a maximum at 1013 - 1073 K regardless of the size of the diameter. The boron filament conductivity appears to be determined by the boride core conductivity for temperatures up to 1000 K; however, at temperatures above 1100 K the sharply increasing conductivity of the boron sheath begins to exert an effect (Fig. 1). At room temperature the resistance of unit axial length of boron filament (Fig. 2) initially increases as the diameter increases up to 65 70 pm and then remains constant at 33 f 1.5 a cm-‘. We concluded that the constant value of the electrical resistance of the filament was connected with the termination of the transition from the tungsten core to borides. The filaments of diameter greater than 70 pm, in which the core is fully boronized, consist of two layers, a core and a boron sheath. They are connected in parallel in the electrical circuit; at high temperatures their electrical resistances are comparable in value, but at room temperature the boron electrical resistance exceeds the core electrical resistance by several orders of magnitude. The experimental data enabled us to obtain the following electrical resistivity uersus temperature relationship for these layers: PwB = 60.0 +.37.9 X 10-3T~s2
cm
pB = 49.02 exp where T is the temperature (K) and pB and p WB of boron and of tungsten borides respectively.
are
the electrical
resistivities
139 7ooo p,406 ncm 1 I I
I
I
I
6000
Fig. 1. A plot of the electrical resistivity against the diameter for boron filaments at various temperatures: curve 1, 1173 K; curve 2, 1273 K; curve 3, 1373 K, curve 4, 1473 K.
R
zii
G 30
20
40
0
m
Fig. 2. The electrical resistance of 1 cm of a boron filament plotted against diameter at room temperature.
The electrical resistivity of the total boron filament can be calculated from a three-ply model using eqns. (1) and (2) and an approximate expression for the tungsten data [9] in the range 773 - 1573 K PW = -5.19
+ 0.03T~a
cm
The relationship between the radii of the layers was determined approximately by measuring the radii in a boron filament cross section with a microscope.
(3)
(4) rwB
=
r&B + (rkB
-r&B)[l
-exp{-_(R
-r%B)@(R))l
(5)
where f(R) = 2(2rw’ - R2/3)3/2, @(R) = 0.07155 - 5.12 X lo-* (R - r&) + 1.2 x lo-*(R -r&~)~, r$B and rka are the initial and final radii of the core as boronized and rw, rwB and R are the present radii of the tungsten layer, of its borides and of the filament respectively. The selection of coefficients and correlation functions f(R) and G(R) was made using the principle of minimum divergence for experimental data. The divergence of calculated and experimental data did not exceed +5%. The value of the electrical resistivity of boron calculated from the empirical eqn. (2) (Fig. 3) agrees well with the data [6] for zone-melted boron and it lies below the data [2 - 51 for more porous sintered material.
Fig. 3. A plot of the electrical resistivity against the temperature for boron: curve 1, ref. 5; curve 2, ref. 2; curve 3, ref. 10; curve 4, ref. 4; curve 5, ref. 3; curve 6, ref. 6; 0, our data.
At working temperatures the electrical resistance of the filament core (Fig. 4) is significantly below the value for tungsten boride W2B5 [l],it is close to the value obtained for the same boride by Kolomoets et al. [ 71 and it is very close to one of the other metal borides in its temperature coefficient of resistance. The experimental data we obtained may be applied to the practical calculation of electric circuits using boron filaments and these results are also of interest for the evaluation of the electrical resistivity values of boron and of tungsten borides in connection with the vapour phase deposition of boron.
141
Fig. 4. A plot of the electrical resistivity against the temperature for various borides: curve 1, W& [l] ; curve 2, WzB5 [7] ; curve 3, our data; curve 4, TaB2; curve 5, NbB2 curve 6, TiB, ; curve 7, VB2 ; curve 8, ZrBz [ 11.
References G. V. Samosnov, L. Ya. Markovski, A. F. Zhigach and M. G. Valjashko, Bor, ego Soedinenija i Splaui, Akademii Nauk Ukrainskoi SSR, Kiev, 1960, pp. 52 - 54. 2 F. Weintraub, Ind. Eng. Chem., 5 (1913) 106. 3 E. S. Greiner and I. A. Gutowski, J. Appl. Phys., 28 (1957) 1364. 4 I. R. King, F. E. Wawner, S. R. Tailor and C. P. Talley, in 0. K. Gaule (ed.), Boron: Preparation, Properties and Applications, Vol. 2, Plenum Press, New York, 1965, pp. 45 - 62. 5 F. S. Maron and M. S. Germaidze, Izu. Akad. Nauk SSSR, Neorg. Mater., 3 (1967) 2144. 6 R. M. Babaev, M. N. Iglitsin and G. E. Chuprikov, Izu. Akad. Nauk SSSR, Neorg. Mater., 3 (1967) 1963. 7 N. V. Kolomoets, V. S. Neshpor, G. V. Samsonov and S. A. Semenkovich, Zh. Tekh. Fiz., 28 (1958) 2382. 8 A. F. Zhigach, A. M. Tsirlin et al., in Bot. Polutchenie, Struktura i Svoistva, Nauka, Moscow, 1974, pp. 147 - 153. 9 B. P. Nikolski, 0. N. Grigorov, M. E. Posin et af. (eds.), Spra~ochnik Kkimika, Vol. 1, Goschimizdat, Moscow, 2nd edn., 1962, pp. 764,765. 10 T. S. Moss, Photoconductivity in the Elements, Academic Press, New York, 1952, p. 78.