High temperature heat capacities and electrical conductivities of boron carbides

Journal of Nuclear North-Holland

Materials

jourual of nuclear materials

186 (1991) 7-12

High temperature heat capacities and electrical conductivities of boron carbides Tsuneo Matsui ‘, Yuji Arita ‘, Keiji Naito a and Hisashi Imai b oDepartment of Nuclear Engineering, Faculty of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-01, Japan h Department of Fuels and Materials Research, Japan Atomic Energy Research Institute, Tokai-mura, Ibaraki 319-11, Japan Received

23 May 1991; accepted

5 August

1991

The heat capacities and the electrical conductivities of B,C (x = 3, 4, 5) were measured by means of direct heating pulse calorimetry in the temperature range from 300 to 1500 K. The heat capacities of B,C increased with increasing x value. This increase in the heat capacity is probably related to the change of the lattice vibration mode originated from the reduction of the stiffness of the intericosahedral chain accompanied with a change from C-B-C to C-B-B chains. A linear relationship between the logarithm of UT (D is the electrical conductivity and T is the absolute temperature) of B,C and the reciprocal temperature was observed, indicating the presence of small polaron hopping as the predominant conduction mechanism. The electrical coductivity of B,C also increased with increasing x value (from 4 to 5) due to an increase of the polaron hopping of holes between carbon atoms at geometrically nonequivalent sites, since these nonequivalent sites of carbon atoms were considered to increase in either B,,C icosahedra or in icosahedral chains with increasing x. The electrical conductivity of B,C was higher than that of B,C, which is probably due to the precipitation of high-conducting carbon. The thermal conductivity and the thermodynamic quantities of B,C were also determined precisely from the heat capacity value

1. Introduction Boron carbide has been recognized as a promising neutron absorbing material for potential use as the control element in a nuclear reactor. Heat capacity is one of the important thermophysical properties to evaluate its thermal stability. The heat capacities of boron carbides (B,C, x = 2.56-9) above room temperature have been measured by several inverstigators [l-6]. The previous results below 900 K are shown in fig. 1 together with those of boron [7] and graphite [8]. King [l] and Sheindlin et al. [2] determined the heat capacity of B,C in the temperature ranges of 298-2743 K and 373-2574 K, respectively, indirectly from the enthalpy values obtained by the drop method. But the heat capacity values determined by Sheindlin et al. are considerably lower than those determined by King in the whole temperature range, probably due to the difference in the composition of the samples between B,C [l] and a B,C + C mixture [2]. Besides these two measurements, the heat capacity has been measured directly by differential 0022-3115/91/$03.50

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scanning calorimetry (DSC) at temperatures below 973 K [3-61. As for the heat capacity of B,C measured by DSC, the values reported by Wood et al. [3], Ihara et al. [S] and Gilchrist and Preston [6] are different from each other in the whole temperature range (from room temperature to 873 K), although the heat capacity values determined by Wood et al. using DSC [3] are close to those determined by Sheindlin et al. using the drop method below 500 K [2] and, on the other hand, the other two results [5,6] by DSC arc close to those of King, who used the drop method [l]. Therefore the precise and direct heat capacity measurements of B,C at high temperatures (especially above 600 Kl is called for. In the present study, the heat capacities and the electrical conductivities of B,C (X = 3, 4 and 5) were measured simultaneously from 300 to 1500 K by means of direct heating pulse calorimetry. The thermal conductivities of B,C were calculated from the heat capacity measured in this study using the thermal diffusivity data by Wood et al [3]. From the dependence of the thermal and the electrical conductivities of B,C on the

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T. Matsui et al. / Heat capacities und electrical conductrt~ities o/’ boron carhde\

2. Experimental

A mixture of B203, C and Mg powder in an appropriate ratio was heated, in order to obtain B,C (.u = 3. 4, 5) sample powders, at 1173 K for 2h and then at 1873 K for 2 h in Ar gas atmosphere. The sample powders thus obtained were shaped into a cylindrical rod of about 10 mm in diameter and 100 mm in length by hot pressing with a graphite cell at about 30 MPa and 2273 K for 40 min in air. From these the cylindrical rods of B,C of about 7 mm in diameter and 75 mm in length were prepared for the measurements. The B/C atomic ratio and the main impurities are shown in table 1 together with the results of X-ray diffraction. For the B,C sample X-ray diffraction analysis showed the presence of C in addition to B,C (see table 1). which is consistent with the phase diagram [lo]. In this paper the samples with compositions of B,,,,C, B, ,,jC and B s,lt,C are called B,C, B,C and B,C, respectively. The heat capacity and the electrical conductivity were measured simultaneously by a direct heating pulse calorimeter, of which details have been given elscwhere [ 111. In this calorimeter, the temperature of the sample rod was varied from room temperature to 1500 K by an external heater, and a current pulse was supplied to both sample rod and the double cylindrical thermal shields of molybdenum simultaneously so as to obtain the same small temperature rise. The imprecision of the heat capacity in this study was + 1.5% up to 1500 K, which was estimated from both the repro ducibility of the heat capacity values of boron carbides in this study and the comparison of the heat capacity of UO, measured by a direct heating pulse calorimeter used in this study with that reported previously by other methods [12,13]. The electric potential drop, the current and the temperature rise of the sample rod were measured to determine the heat capacity and the electrical conductivity.

7-/K Fig. 1. Previous results of the heat capacity of boron carbides (B,C, x = 2.54-9) up to about 900 K [l-6]. (1) B,C [l], (2) B,C [21, (3) B,C: 0 [31, (4) B,,C: A [3],(5) B,,,C: . [31, (6) B,C: A ]31, (7) B,,,,C: 0 [51, (8) B,,,C: W [51, (9) Bs,&: <> [51,(10) B,,,,C: l [5], (11) B,C: v [6], (12) B [7], (13) graphite @I.

boron content X, the transport mechanism was considered. The thermodynamic quantities of B,C such as entropy, enthalpy and the free energy function, were also calculated from the heat capacity value obtained in this study using the value of S&s,,, from the JANAF tables [9].

Table 1 Composition, density, impurity and phase of samples Sample

B,C B,C B,C

B/C atomic ratio

Density (g/cm”)

3.03 3.94 5.16

2.05 2.06 2.29

Phase by X-ray

Impurity (in ppm)

0.21 0.08 0.30

400 20 500

<2 <2 <4

< 25 < 25 < 25

Ti

CU

10 < 10 20

<4 <4 4

B,C+C B,C B,C (+ trace B)

9

T. Matsui et al. / Heat capacities and electrical conductivities of boron carbides

mined by Wood et al. [3] in the temperature range (300 4 T/K 5 900), although a very weak temperature dependence of the heat capacity reported by Wood et al. above 600 K seems to be inconsistent with the high Debye temperature of B,C 1470 K [14]. As is also seen in the figure, the heat capacity of B,C increases with increasing x value. This tendency of increase in heat capacity with x value is in good accord with the previous results of B,C (4 $X 5 9) [3] and B,C (2.56 s x 5 3.97) [5], except for the heat capacities of B,,,C and B,C determined by Wood et al. [3] above 700 K, where the heat capacity of B,,,C is smaller than that of B,C. The smaller heat capacity of B,C (compared to the heat capacity of B,C) observed in this study is probably due to the precipitation of C with smaller heat capacity (see fig. 1) in B,C. In the figure the heat capacity of B,C calculated from the heat capacity of B,C obtained in this study and C from the JANAF table using the additivity law (Neuman-Kopp’s law) is also shown for comparison. The heat capacity of B,C obtained experimentally in this study is in fairly good agreement with the calculated value below about 700 K but it is higher than the calculated value above about 700 K (the difference is less than 2% above 700 K). The reason for this small difference is not clear at the moment but is thought to be originating from the inaccuracy of the heat capacity value of B,C and/or B,C. The increase in the heat capacity of B,C with x value (X 2 4) is

3. Results and discussion 3.1. Heat capacity The heat capacities (C,) of B,C (x = 3,4 and 5) per gram measured in this study are shown in fig. 2 in comparison with those of B3,i4C [S], B,C [1,3] and B,,,C [3] reported previously. The equations for the heat capacity (C,) of B,C (x = 3, 4 and 5) are determined in the temperature range from 300 to 1500 K by the least-squares method to be eqs. (11, (2) and (3), respectively: C,/J

g-’ K-* = 1.6251 +4.8621x

10-4(T/K)

- 7.3780 x 104(T/K)-‘, C,/J

- 8.4527 x 104(T/K)-*, C,/J

(1)

g-’ K-’ = 1.6859 + 4.7893 x lo-“(T/K) (2)

g-l KP1 = 1.8515 + 4.3526 x 10-4(T/K) - 9.6448 x 104( T/K) -‘.

(3) It is seen in the figure that the heat capacity of B,C obtained in this study is smaller below about 900 K and, on the contrary, larger above about 900 K compared with that determined by King [l]. The difference is about 4% at 1500 K. The heat capacity of B,C in this study is also seen to be larger than that of B,C deter-

2.5

2.0

T/K

0

Fig. 2. Heat capacity of boron carbides per gram: -V- B,C, -0B,C and -A - B,C in this study, ---B,C calculated from the heat capacities of B,C and C by the additivity law, . B,C by King [ll, - - -B3,,4C by Ihara et al. [5], -, -B,C and -. -B,,,C by Wood et al. [3].

T. Matsui et ul. / Heat capaches und electrical conductrtvtie.~ ?f‘horon carhdr.~

IO

Table 2 Thermodynamic quantities of B,C T

C’P

(K)

(Jmol

298.15 300 400 SO0 600 700 x00 900 IO00 1 100 I200 1300 1400 1500 1600 1700

49.82 50.30 72.52 86% 96.20 102.74 107.73 Ill.82 I IS.38 118.62 121.68 124.6 1 127.47 130.20 133.09 135.88

s”

‘K

‘)

(Jmol .‘K

I{” ~. f{” LOX ‘) ~___. 0

-(G’:-H;48)/T

‘)

(Jmol

27.18 27.49 45.20 63.05 79.77 95.11 109.17 122.10 134.07 145.22 155.68 165.53 174.87 183.76 I92.2h 200.4 I

thought to be related to the change of the lattice vibration mode produced by the reduction of the stiffness of the intericosahedral chain accompanied with a change from C-B-C to C-B-B chain, as will also be discussed in relation to the variation of the electrical conductivity and the thermal conductivity of B,C with x value. The thermodynamic quantities such as entropy, free energy function, and enthalpy change of B,C have been calculated and summarized in the JANAF tables [9] based on the low temperature (54-298 K) heat capacities by Kelley [15] and the high temperature (29% 1726 K) heat capacities by King [ 11, using S”(B,C, 298.15 K) = 27.18 J mol-’ Km ‘, In this study the thcrmodynamic quantities of B,C were recalculated from the heat capacity values obtained in this study using the same value of S”(298.15 K) as in the JANAF tables. They are summarized in table 2.

’ Km-‘)

iJ;,ol

27. I8 27.1x 29.35 31.3’) 40.58 47.29 54. Ih hl .oo 67.72 74.76 XO.hl X6.77 Y2.73 YH.5I 104. IO lOY.S3

Wood and Emin [16]. This nonequivalence arises from two sources [3]. First, carbon atoms can be distributed among nonequivalent sites within B, ,C icosahedra. Second, only a fraction of the available positions of intericosahedral chain is generally filled by C-B-C chains. Ideally, at the high-carbon end of the singlephase region B,C, each intericosahedral chain positions is filled by a C-B-C chain, and each icosahedron contains a single carbon atom as B, ,C. Thus apart from the nonequivalence of the carbon locations within icosahedra, B,C resembles an ideal crystals and, therefore, is considered to have the lowest electrical conduc-

X2. Electrical conductirity The electrical conductivities (a) of B,C (x = 3, 4 and 5) simultaneously measured with the heat capacities in this study are shown as a function of temperature (T) in fig. 3 together with those of B,C (x = 4, 4.68 and 6.69) reported by Wood and Emin [16]. The nearly linear relationship between log UT and l/T indicates that the predominant conduction mechanism is small polaron hopping between carbon atoms at geometrically nonequivalent sites, as was proposed by

5 5

10

dK/

T

15

Fig. 3. Variation of the electrical conductivity of boron cxbides with temperature: -vB,C, -‘1:- B,C and -AB,C B,C, - .- B,,xC and - .- B, h,,C by Wood in this study. and Emin [16].

11

T. Matsui et al. / Heat capacities and electrical conductiuities of boron carbides

tivity in a single-phase region. The higher electrical conductivity of B,C compared to B,C is thought to be due to the precipitation of high-conducting carbon. These dependences of the electrical conductivity upon the B/C atomic ratio in both a single-phase region (B/C 2 4) and a two-phase region (B/C = 3) found in this study at high temperature have been similarly observed for B,C (X = 2.40-6.30) in the low temperature region from 100 to 400 K by Werheit et al. [17]. 3.3. Thermal

conducticity

The thermal conductivities (A) of B,C (X = 4, 6.5, 7.5 and 9) have been determined by Wood et al. ]3] from the thermal diffusivities C(Y), using the relation A = Cpap, using heat capacities CC,) and the sample densrtres (p) which were also obtained by themselves. However, as was discussed in section 3.1, the heat capacities obtained by Wood et al. seem to be too small especially at high temperatures (above 600 K). Moreover, they assumed that the heat capacities of all B,C samples were constant above 900 K for the calculation of thermal conductivities. Therefore the thermal conductivities of B,C with x = 4, 6.5, 7.5 and 9 were recalculated by the present authors from the thermal diffusivities and the sample densities reported by Wood et al. [3] and from the heat capacities of B,C experimentally obtained in this study and of B,C with x = 6.5, 7.5 and 9 calculated from the present experimental values of B,C and B [7] using an additivity law (Kopp’s law), since the experimental value of B,C was found to be close to the value calculated from B,C and B by the additivity law in this study. The thermal conductivities of B,C with x = 4, 6.5, 7.5 and 9 thus calculated are shown in fig. 4 in comparison with those of Wood et al. [3]. It is seen in the figure that both the magnitude and the temperature dependence of the thermal conductivity of B,C are significantly different from those of B,C with x = 6.5, 7.5 and 9: The thermal conductivity of B,C, with the highest carbon concentration, is not only largest but also decreases with increasing temperature, which is characteristic of a non-metallic crystal. On the contrary, the thermal conductivities of B,C with lower carbon concentrations are much smaller, with much weaker temperature dependences, which are similar to those of glasses (or disordered crystals). These results can be interpreted by the difference in the crystal structure of B,C similarly to the case of the electrical conductivity discussed in the previous section. In B,C all the intericosahedral bonds are filled with stiffly bonded C-B-C chains which results in crystal-like behavior [3,18]. Lower carbon concentrations result in

503

15CU T/K

Fig. 4. Variation of the thermal conductivity of boron carbides with temperature: - this study, - - Wood et al. [3].

these C-B-C chains being randomly replaced by CB-B configurations which are less stiffly bonded [3,18]. Thus, with increasing x, B,C samples become more disordered (= glass-like) where thermal conductivities become lower and have much weaker temperature dependences.

Acknowledgement The authors wish to express their gratitude to Denki Kagaku Kogyo KK for providing them with the samples used in this study.

References

[II

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T. Matsui et al. / Heat capacities and electricul conductil~ities of boron carbides

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