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A comparison of some thermodynamic parameters between superhard fullerite, some metals and some covalent elements
PERGAMON
Carbon 39 (2001) 905–908
A comparison of some thermodynamic parameters between superhard fullerite, some metals and some covalent elements V.D. Blank, A.A. Nuzdin, R.Kh. Bagramov*, V.M. Prokhorov Technological Institute for Superhard and Novel Carbon Materials, 142190 Troitsk, Moscow region, Russia Received 4 May 2000; accepted 28 July 2000
Abstract Specific heat and sound velocities measurements were carried out on samples of C60 fullerene treated at high (up to 13 GPa) pressure and temperature (up to 1200 K). With an increase in specific gravity from 2.35 to 3.15 g / cm 3 the specific heat decreases, but remains 7–8% higher than the specific heat of diamond. For the new materials obtained, the Debye temperature, the DC 5 Cp 2 Cv parameter, and the work of heat expansion were calculated in an ideal approach. Similar calculations were performed for graphite, diamond, silicon, germanium and some refractory metals for comparison. The results obtained made it possible to draw qualitative conclusions about the structural stability of the new materials and to trace general tendencies for different carbon substances. A C60 sample with specific gravity 3.15 g / cm 3 had a hardness comparable with the hardness of diamond. 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Fullerene; B. Heat treatment, High pressure; D. Elastic properties, Thermodynamic properties
1. Introduction A new molecular form of carbon, fullerene, is now under investigation not only for basic understanding but also for possible applications. In Ref. [1] the influence of different pressures and temperatures on fullerene C60 is reviewed. Of the variety of structures obtainable, the most interesting are probably ‘disordered’ and ‘amorphous’ ones, that exhibit record hardness and are obtained with 9.5–13 GPa pressure at temperatures of 900–20008C. These samples [1] have different densities ranging from 2.6 to 3.3 g / cm 3 . Some of them are able to scratch the hardest face of diamond [1]. In Ref. [2] the results of heat capacity measurements on samples obtained with 11–13 GPa and different temperatures are presented. The relation between the heat capacity and other properties was found. In general, the heat capacity seems to be a function of the density of the materials measured. The higher the density the lower the heat capacity. However, there are some samples that exhibit a different behavior. They have specific heat curves running across the diamond curve or even below it. This makes us suspect some weak ongoing
*Corresponding author. Fax: 17-095-330-9925. E-mail address: [email protected] (R.K. Bagramov).
processes in the samples that influence heat capacity measurements. The work presented there is an attempt to compare specific heat values measured for different forms of carbon, namely pristine C60, superhard fullerites (obtained from C60 at pressures 9.5–13 GPa and different temperatures), graphite (with 99.99% purity and with 10–100 nm grain size) and natural diamond. For all materials in question DC 5 Cp 2 Cv , the thermal expansivity and some other values were calculated within an ideal approach. Some refractory metals and covalent elements are taken into consideration also.
2. Experimental Three superhard fullerite samples were investigated. The high-pressure–high-temperature technique to treat fullerite C60 is described elsewhere [3]. The pressure–temperature parameters used and the densities obtained were the following. Sample C1 — 9.5 GPa, 7708C, 2.35 g / cm 3 . Sample C2 — 12 GPa, 10008C, 3.1 g / cm 3 . Sample C3 — 13 GPa, 12008C, 3.15 g / cm 3 . The specific gravity was measured with the ‘weighting in liquid’ method, with 3% accuracy. Heat capacity measurements were performed with a
0008-6223 / 01 / $ – see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S0008-6223( 00 )00197-4
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V.D. Blank et al. / Carbon 39 (2001) 905 – 908
differential scanning calorimeter with an accuracy about 4–5% in the temperature interval of 350–600 K, with 2 degrees / min scanning rate.
3. Results and discussion The results of our heat capacity measurements are presented in Fig. 1. Curve 1 corresponds to C60 as received with specific gravity 1.6860.05 g / cm 3 , curve 2 corresponds to graphite with specific gravity 1.8060.06 g / cm 3 , curve 3 to natural diamond with specific gravity 3.5160.14 g / cm 3 , curves C1, C2 and C3 to superhard fullerites described above. For comparison, in Fig. 1 we have also plotted the data (triangles) taken from Ref. [4] for C60 as received. Our measurements for C60 as received coincide within 2–3% accuracy with the data presented in Ref. [4]. Our measurements for natural diamond coincide within 2% accuracy of reference data [5], so it is within the accuracy of measurements. The positions of the heat capacity curves seem to be a smooth function of the specific gravity. The higher the specific gravity the higher the specific heat of the materials measured. The similarity of Cp for C60 as received and graphite is mentioned elsewhere [6], but the difference between different types of graphite should be kept in mind. Curve 3 for superhard fullerite runs 7–8% (absolute values) above curve 4 for natural diamond. From experimental low temperature heat capacity data
Fig. 1. Temperature dependence of Cp for some carbon materials: (1) fullerite C60 as received; (2) graphite (3–5 mm average grain size); (3) superhard fullerite; (4) natural diamond. Superhard fullerites (dashed lines). C1, 11 GPa, 7708C, 2.35 g / cm 3 . C2, 12 GPa, 10008C, 3.1 g / cm 3 . C3, 13 GPa, 12008C, 3.15 g / cm 3 . D, heat capacity values for C60 as received, from Ref. [4].
[4,7] the Debye temperature for pristine C60 could be estimated. It is about 58 K. This Debye temperature could also be estimated from elastic constants and / or from sound velocities. We have performed this estimation to compare it with the value obtained from thermodynamic data. We used the following equation [8]:
u 5 (h /k)(3Nr / 4p M)1 / 3Vm
(1)
where h is Planck’s constant, k is Boltzmann’s constant, N is Avogadro’s constant, M is molecular mass, r is specific gravity, Vm is a specially averaged speed of sound. Vm could be calculated from the longitudinal Vl and shear Vt sound velocities for isotropic (homogeneous) samples with the formula Vm 5 [1 / 3(1 /V 3l 1 2 /V 3t )] 21 / 3
(2)
or (for cubic crystals) from the elastic constants Vm 5 [(C11 1 2C44 ) / 3r ]
1/2
.
(3)
As we did not have a proper compact C60 pristine sample, we used sound velocity data from Ref. [9], Vl 5 2.49 3 10 3 m / s and Vt 51.2310 3 m / s. This estimate, based on the homogeneous elastic continuum approach, gives a value u ¯45 K for pristine C60 with r 51.62 g / cm 3 . If the porosity of the sample is taken into account and the elastic constants are taken from Ref. [9], the value u ¯56 K could be obtained. In Ref. [10], measured elastic constants are presented and a u value of 66 K for C60 monocrystal is calculated. This value is valid for the FCC phase of pristine C60. From our comparison of the u value calculated with the ‘sound waves’ approach, with the thermodynamic approach and with the value taken from Ref. [10], we can conclude that the ‘sound waves’ approach for calculating u seems to be working reasonably well. To estimate u for the superhard fullerite sample C3 we have measured the longitudinal Vl and shear Vt sound velocities. Vl 5(1760.3)310 3 m / s and Vt 5(9.460.3)3 10 3 m / s. (For comparison, diamond monocrystal [11] have the values Vl 5 18.3 3 10 3 m / s and Vt 511.6310 3 m / s.) Afterwards we calculated Vm with Eq. (2), and then calculated u with Eq. (1). For superhard fullerite C3 Vm 510.3310 3 m / s and u ¯1650 K. (For comparison, for diamond u 51800–2000 K.) So for superhard fullerite and diamond, the higher the Cp value the lower the u value. This seems to be a general tendency for different forms of carbon. As is well known, the difference between Cp (constant pressure specific heat) and Cv (constant volume specific heat) is quite small and grows in accordance with the classic thermodynamic law if the temperature increases, Cp 2 Cv 5 DC 5 a 2 BT,
(4)
where a is the thermal expansivity coefficient, B is the bulk modulus and T is temperature.
V.D. Blank et al. / Carbon 39 (2001) 905 – 908
As our samples were not sufficiently big (¯1.5 mm), we could not measure a directly, but instead estimated a as follows. DC could be expressed as DC 5 Kt aT
(5)
¨ where Kt 5 aB 5 (g Cv ) /V and g is the Gruneisen constant. We can then estimate a. From thermodynamic equations Kt could be expressed as Kt 5 (≠p / ≠T )V , so it characterizes the pressure (or stress) changes during heating at constant volume. (Please note that this approximation is very ‘ideal’, meaning it assumes ideal, isotropic solid.) We assumed the bulk modulus B for C60 as received to be about 0.140310 11 Pa [10], and for our super hard sample we assume B5(5.460.6)310 11 Pa (obtained from ultrasonic measurements). After calculations we got for C60 as received a¯25310 26 K 21 , and for superhard fullerite a¯6310 26 K 21 , assuming g 51.8. In Fig. 2 we present the dependence of DC on temperature, for the hard phases of C60, graphite and diamond. For comparison the same dependencies are also presented for some covalent elements. Input data for the calculations were taken from Ref. [12]. The DC curve for as-received C60 runs below the curve for graphite. DC for the superhard fullerite C3 is quite close to that for diamond, which corresponds to lower values of Kt . The correlation between structural stability and Kt for crystal structures was reviewed for elements of the periodic table and for some metal-like compounds in Ref. [13]. Low DC values are typical for the diamond-like structures of germanium and silicon up to |0.5T melt (the
Fig. 2. Temperature dependence of DC 5 Cp 2 Cv . (1) Diamond, (2) boron, (3) graphite, (4) germanium, (5) silicon, (6) fullerite C60 as received. Superhard fullerites (dashed lines). C1, 11 GPa, 7708C, 2.35 g / cm 3 . C2, 12 GPa, 10008C, 3.1 g / cm 3 . C3, 13 GPa, 12008C, 3.15 g / cm 3 .
907
curves are also presented in Fig. 2). For comparison, at 298 K, 0.5T melt and T melt , W, Pt and Zr metals have the following DC (310 3 J / m 3 K) values: 16, 97 and 324; 44, 128, and 450; 7, 37 and 110. The not very high value for DC for Zr is probably due to its partly covalent crystal bonds. We would like to note that covalent solids have lower DC than metals. To estimate the properties in question in carbon crystal structures it is worth comparing A /H, where A 5 Kt aT 2
(6)
is the work of heat expansion and H the enthalpy at a certain temperature. All the other values are defined above. As can be seen from the data shown in Fig. 3, asreceived C60 has the lowest A /H value, which qualitatively indicates that part of the heat energy is absorbed intramolecularly during heating. This absorption increases as temperature rises and at 1100 K it causes destruction of the molecules. A little bit higher values of A /H for graphite could be explained by the partly metallic character of its bonds that leads to special electrical conductivity behavior, for example. High-pressure–high-temperature treatment creates new structural states of superhard fullerite C60. A /H becomes closer to that of diamond (see curves C1, C2, C3). Formally, the quite similar values of the bulk modulus and the thermal expansivity coefficients of superhard fullerite C3 and diamond could explain why A /H values are also close. To make comparisons with W, Pt, and Zr we made the same A /H calculations for them.
Fig. 3. Temperature dependence of A /H. (1) Diamond, (2) boron, (3) graphite, (4) germanium, (5) silicon, (6) fullerite C60 as received. Superhard fullerites (dashed lines). C1, 11 GPa, 7708C, 2.35 g / cm 3 . C2, 12 GPa, 10008C, 3.1 g / cm 3 . C3, 13 GPa, 12008C, 3.15 g / cm 3 .
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V.D. Blank et al. / Carbon 39 (2001) 905 – 908
The following values were obtained. At the temperatures 298 K, 0.5T melt and T melt , A /H (310 2 ) for W, Pt, Zr equals 0.9, 2.8 and ¯11.0; 1.6, 4.5 and ¯15.0; 0.55, 2.3 and ¯5.0, respectively. Bulk W samples do not show any transition while being treated with pressure and temperature (though small particles do). There are theoretical works demonstrating that a BCC–HCP transition is possible for W at 100 GPa. Zirconium is known to have several transitions at 55 GPa and different temperatures. It is ‘structurally unstable’, a fact that is in accordance with the low value of A /H. So, the correlation between the structural stability and the A /H value shown is not only valid for carbon structures, but could be applied for other elements and materials.
4. Conclusions In the temperature interval investigated, general relations were found between the specific heat, specific gravity and Debye temperature for different carbon materials (superhard and as received fullerenes C60, graphite and diamond) was traced. The higher the specific gravity the lower the specific heat and the higher the Debye temperature. The specific heat of the hardest C60 sample (C3) was about 7–8% higher than that of diamond monocrystal. The Debye temperature calculated for the C3 sample equals u ¯1650 K. (For comparison, for diamond u 51800–2000 K.) The calculations and comparison made for the A /H value (where A is the work of heat expansion and H the enthalpy at a certain temperature) for different carbon materials, some covalent elements and metals, showed that the A /H value could be used to estimate the materials temperature stability. An A /H value comparison made for different C60 materials shows that a greater part of the
heat is absorbed ‘intramolecularly’ in comparison to ‘monoatomic’ carbon materials.
References [1] Blank VD, Buga SG, Dubitsky GA, Serebryanaya NR, Popov MYu, Sundqvist B. High pressure polymerized phases of C60. Carbon 1998;36(4):319–43. [2] Blank VD, Buga SG, Serebryanaya NR, Dubitsky GA, Bagramov RH, Popov MYu et al. Appl Phys A 1997;64:247–50. [3] Blank VD, Buga SG, Serebryanaya NR, Denisov VN, Dubitsky GA, Ivlev AN et al. Phys Lett 1995;A205:208–16. [4] Jin J, Cheng J, Varma-Nair M, Liang G, Fu Y, Wunderlich B et al. J Phys Chem 1992;96:5151–6. [5] Hultgren R, Decai RD, Hawkins DT, Gleiser M, Kelley KK, Wagman DD. Selected values of the thermodynamic properties of the elements, Metals Park, OH: American Society for Metals, 1973. [6] Dresselhaus MS, Dresselhaus G, Eklund PC. Science of fullerenes and carbon nanotubes, San Diego: Academic Press, 1996. [7] Korobov MV, Sidorov LN. Thermodynamic properties of fullerenes. J Chem Thermodynam 1994;26:61–73. [8] Mason P, editor, Physical acoustics, vol. 3, New York: Academic Press, 1965, part B. [9] Kobelev NP, Soifer YM, Bashkin IO, Gyruv AF, Moravskii AP, Ryabchenko OG. Phys Stat Sol (b) 1995;190:157–62. [10] Kobelev NP, Nikolaev RK, Soifer YaM, Khasanov SS. Chem Phys Lett 1997;276:263–5. [11] Berman R, editor, Physical properties of diamond, Oxford: Clarendon Press, 1965. [12] Grigorieva IS, Mejlihova EZ. Physics values, Moscow: Energoatomizdat, 1991. [13] Nuzdin AA. Izvetiya Akad Nauk (Neorganicheskie Materiali) 1988;24(10):1639–44.
Carbon 39 (2001) 905–908
A comparison of some thermodynamic parameters between superhard fullerite, some metals and some covalent elements V.D. Blank, A.A. Nuzdin, R.Kh. Bagramov*, V.M. Prokhorov Technological Institute for Superhard and Novel Carbon Materials, 142190 Troitsk, Moscow region, Russia Received 4 May 2000; accepted 28 July 2000
Abstract Specific heat and sound velocities measurements were carried out on samples of C60 fullerene treated at high (up to 13 GPa) pressure and temperature (up to 1200 K). With an increase in specific gravity from 2.35 to 3.15 g / cm 3 the specific heat decreases, but remains 7–8% higher than the specific heat of diamond. For the new materials obtained, the Debye temperature, the DC 5 Cp 2 Cv parameter, and the work of heat expansion were calculated in an ideal approach. Similar calculations were performed for graphite, diamond, silicon, germanium and some refractory metals for comparison. The results obtained made it possible to draw qualitative conclusions about the structural stability of the new materials and to trace general tendencies for different carbon substances. A C60 sample with specific gravity 3.15 g / cm 3 had a hardness comparable with the hardness of diamond. 2001 Elsevier Science Ltd. All rights reserved. Keywords: A. Fullerene; B. Heat treatment, High pressure; D. Elastic properties, Thermodynamic properties
1. Introduction A new molecular form of carbon, fullerene, is now under investigation not only for basic understanding but also for possible applications. In Ref. [1] the influence of different pressures and temperatures on fullerene C60 is reviewed. Of the variety of structures obtainable, the most interesting are probably ‘disordered’ and ‘amorphous’ ones, that exhibit record hardness and are obtained with 9.5–13 GPa pressure at temperatures of 900–20008C. These samples [1] have different densities ranging from 2.6 to 3.3 g / cm 3 . Some of them are able to scratch the hardest face of diamond [1]. In Ref. [2] the results of heat capacity measurements on samples obtained with 11–13 GPa and different temperatures are presented. The relation between the heat capacity and other properties was found. In general, the heat capacity seems to be a function of the density of the materials measured. The higher the density the lower the heat capacity. However, there are some samples that exhibit a different behavior. They have specific heat curves running across the diamond curve or even below it. This makes us suspect some weak ongoing
*Corresponding author. Fax: 17-095-330-9925. E-mail address: [email protected] (R.K. Bagramov).
processes in the samples that influence heat capacity measurements. The work presented there is an attempt to compare specific heat values measured for different forms of carbon, namely pristine C60, superhard fullerites (obtained from C60 at pressures 9.5–13 GPa and different temperatures), graphite (with 99.99% purity and with 10–100 nm grain size) and natural diamond. For all materials in question DC 5 Cp 2 Cv , the thermal expansivity and some other values were calculated within an ideal approach. Some refractory metals and covalent elements are taken into consideration also.
2. Experimental Three superhard fullerite samples were investigated. The high-pressure–high-temperature technique to treat fullerite C60 is described elsewhere [3]. The pressure–temperature parameters used and the densities obtained were the following. Sample C1 — 9.5 GPa, 7708C, 2.35 g / cm 3 . Sample C2 — 12 GPa, 10008C, 3.1 g / cm 3 . Sample C3 — 13 GPa, 12008C, 3.15 g / cm 3 . The specific gravity was measured with the ‘weighting in liquid’ method, with 3% accuracy. Heat capacity measurements were performed with a
0008-6223 / 01 / $ – see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S0008-6223( 00 )00197-4
906
V.D. Blank et al. / Carbon 39 (2001) 905 – 908
differential scanning calorimeter with an accuracy about 4–5% in the temperature interval of 350–600 K, with 2 degrees / min scanning rate.
3. Results and discussion The results of our heat capacity measurements are presented in Fig. 1. Curve 1 corresponds to C60 as received with specific gravity 1.6860.05 g / cm 3 , curve 2 corresponds to graphite with specific gravity 1.8060.06 g / cm 3 , curve 3 to natural diamond with specific gravity 3.5160.14 g / cm 3 , curves C1, C2 and C3 to superhard fullerites described above. For comparison, in Fig. 1 we have also plotted the data (triangles) taken from Ref. [4] for C60 as received. Our measurements for C60 as received coincide within 2–3% accuracy with the data presented in Ref. [4]. Our measurements for natural diamond coincide within 2% accuracy of reference data [5], so it is within the accuracy of measurements. The positions of the heat capacity curves seem to be a smooth function of the specific gravity. The higher the specific gravity the higher the specific heat of the materials measured. The similarity of Cp for C60 as received and graphite is mentioned elsewhere [6], but the difference between different types of graphite should be kept in mind. Curve 3 for superhard fullerite runs 7–8% (absolute values) above curve 4 for natural diamond. From experimental low temperature heat capacity data
Fig. 1. Temperature dependence of Cp for some carbon materials: (1) fullerite C60 as received; (2) graphite (3–5 mm average grain size); (3) superhard fullerite; (4) natural diamond. Superhard fullerites (dashed lines). C1, 11 GPa, 7708C, 2.35 g / cm 3 . C2, 12 GPa, 10008C, 3.1 g / cm 3 . C3, 13 GPa, 12008C, 3.15 g / cm 3 . D, heat capacity values for C60 as received, from Ref. [4].
[4,7] the Debye temperature for pristine C60 could be estimated. It is about 58 K. This Debye temperature could also be estimated from elastic constants and / or from sound velocities. We have performed this estimation to compare it with the value obtained from thermodynamic data. We used the following equation [8]:
u 5 (h /k)(3Nr / 4p M)1 / 3Vm
(1)
where h is Planck’s constant, k is Boltzmann’s constant, N is Avogadro’s constant, M is molecular mass, r is specific gravity, Vm is a specially averaged speed of sound. Vm could be calculated from the longitudinal Vl and shear Vt sound velocities for isotropic (homogeneous) samples with the formula Vm 5 [1 / 3(1 /V 3l 1 2 /V 3t )] 21 / 3
(2)
or (for cubic crystals) from the elastic constants Vm 5 [(C11 1 2C44 ) / 3r ]
1/2
.
(3)
As we did not have a proper compact C60 pristine sample, we used sound velocity data from Ref. [9], Vl 5 2.49 3 10 3 m / s and Vt 51.2310 3 m / s. This estimate, based on the homogeneous elastic continuum approach, gives a value u ¯45 K for pristine C60 with r 51.62 g / cm 3 . If the porosity of the sample is taken into account and the elastic constants are taken from Ref. [9], the value u ¯56 K could be obtained. In Ref. [10], measured elastic constants are presented and a u value of 66 K for C60 monocrystal is calculated. This value is valid for the FCC phase of pristine C60. From our comparison of the u value calculated with the ‘sound waves’ approach, with the thermodynamic approach and with the value taken from Ref. [10], we can conclude that the ‘sound waves’ approach for calculating u seems to be working reasonably well. To estimate u for the superhard fullerite sample C3 we have measured the longitudinal Vl and shear Vt sound velocities. Vl 5(1760.3)310 3 m / s and Vt 5(9.460.3)3 10 3 m / s. (For comparison, diamond monocrystal [11] have the values Vl 5 18.3 3 10 3 m / s and Vt 511.6310 3 m / s.) Afterwards we calculated Vm with Eq. (2), and then calculated u with Eq. (1). For superhard fullerite C3 Vm 510.3310 3 m / s and u ¯1650 K. (For comparison, for diamond u 51800–2000 K.) So for superhard fullerite and diamond, the higher the Cp value the lower the u value. This seems to be a general tendency for different forms of carbon. As is well known, the difference between Cp (constant pressure specific heat) and Cv (constant volume specific heat) is quite small and grows in accordance with the classic thermodynamic law if the temperature increases, Cp 2 Cv 5 DC 5 a 2 BT,
(4)
where a is the thermal expansivity coefficient, B is the bulk modulus and T is temperature.
V.D. Blank et al. / Carbon 39 (2001) 905 – 908
As our samples were not sufficiently big (¯1.5 mm), we could not measure a directly, but instead estimated a as follows. DC could be expressed as DC 5 Kt aT
(5)
¨ where Kt 5 aB 5 (g Cv ) /V and g is the Gruneisen constant. We can then estimate a. From thermodynamic equations Kt could be expressed as Kt 5 (≠p / ≠T )V , so it characterizes the pressure (or stress) changes during heating at constant volume. (Please note that this approximation is very ‘ideal’, meaning it assumes ideal, isotropic solid.) We assumed the bulk modulus B for C60 as received to be about 0.140310 11 Pa [10], and for our super hard sample we assume B5(5.460.6)310 11 Pa (obtained from ultrasonic measurements). After calculations we got for C60 as received a¯25310 26 K 21 , and for superhard fullerite a¯6310 26 K 21 , assuming g 51.8. In Fig. 2 we present the dependence of DC on temperature, for the hard phases of C60, graphite and diamond. For comparison the same dependencies are also presented for some covalent elements. Input data for the calculations were taken from Ref. [12]. The DC curve for as-received C60 runs below the curve for graphite. DC for the superhard fullerite C3 is quite close to that for diamond, which corresponds to lower values of Kt . The correlation between structural stability and Kt for crystal structures was reviewed for elements of the periodic table and for some metal-like compounds in Ref. [13]. Low DC values are typical for the diamond-like structures of germanium and silicon up to |0.5T melt (the
Fig. 2. Temperature dependence of DC 5 Cp 2 Cv . (1) Diamond, (2) boron, (3) graphite, (4) germanium, (5) silicon, (6) fullerite C60 as received. Superhard fullerites (dashed lines). C1, 11 GPa, 7708C, 2.35 g / cm 3 . C2, 12 GPa, 10008C, 3.1 g / cm 3 . C3, 13 GPa, 12008C, 3.15 g / cm 3 .
907
curves are also presented in Fig. 2). For comparison, at 298 K, 0.5T melt and T melt , W, Pt and Zr metals have the following DC (310 3 J / m 3 K) values: 16, 97 and 324; 44, 128, and 450; 7, 37 and 110. The not very high value for DC for Zr is probably due to its partly covalent crystal bonds. We would like to note that covalent solids have lower DC than metals. To estimate the properties in question in carbon crystal structures it is worth comparing A /H, where A 5 Kt aT 2
(6)
is the work of heat expansion and H the enthalpy at a certain temperature. All the other values are defined above. As can be seen from the data shown in Fig. 3, asreceived C60 has the lowest A /H value, which qualitatively indicates that part of the heat energy is absorbed intramolecularly during heating. This absorption increases as temperature rises and at 1100 K it causes destruction of the molecules. A little bit higher values of A /H for graphite could be explained by the partly metallic character of its bonds that leads to special electrical conductivity behavior, for example. High-pressure–high-temperature treatment creates new structural states of superhard fullerite C60. A /H becomes closer to that of diamond (see curves C1, C2, C3). Formally, the quite similar values of the bulk modulus and the thermal expansivity coefficients of superhard fullerite C3 and diamond could explain why A /H values are also close. To make comparisons with W, Pt, and Zr we made the same A /H calculations for them.
Fig. 3. Temperature dependence of A /H. (1) Diamond, (2) boron, (3) graphite, (4) germanium, (5) silicon, (6) fullerite C60 as received. Superhard fullerites (dashed lines). C1, 11 GPa, 7708C, 2.35 g / cm 3 . C2, 12 GPa, 10008C, 3.1 g / cm 3 . C3, 13 GPa, 12008C, 3.15 g / cm 3 .
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V.D. Blank et al. / Carbon 39 (2001) 905 – 908
The following values were obtained. At the temperatures 298 K, 0.5T melt and T melt , A /H (310 2 ) for W, Pt, Zr equals 0.9, 2.8 and ¯11.0; 1.6, 4.5 and ¯15.0; 0.55, 2.3 and ¯5.0, respectively. Bulk W samples do not show any transition while being treated with pressure and temperature (though small particles do). There are theoretical works demonstrating that a BCC–HCP transition is possible for W at 100 GPa. Zirconium is known to have several transitions at 55 GPa and different temperatures. It is ‘structurally unstable’, a fact that is in accordance with the low value of A /H. So, the correlation between the structural stability and the A /H value shown is not only valid for carbon structures, but could be applied for other elements and materials.
4. Conclusions In the temperature interval investigated, general relations were found between the specific heat, specific gravity and Debye temperature for different carbon materials (superhard and as received fullerenes C60, graphite and diamond) was traced. The higher the specific gravity the lower the specific heat and the higher the Debye temperature. The specific heat of the hardest C60 sample (C3) was about 7–8% higher than that of diamond monocrystal. The Debye temperature calculated for the C3 sample equals u ¯1650 K. (For comparison, for diamond u 51800–2000 K.) The calculations and comparison made for the A /H value (where A is the work of heat expansion and H the enthalpy at a certain temperature) for different carbon materials, some covalent elements and metals, showed that the A /H value could be used to estimate the materials temperature stability. An A /H value comparison made for different C60 materials shows that a greater part of the
heat is absorbed ‘intramolecularly’ in comparison to ‘monoatomic’ carbon materials.
References [1] Blank VD, Buga SG, Dubitsky GA, Serebryanaya NR, Popov MYu, Sundqvist B. High pressure polymerized phases of C60. Carbon 1998;36(4):319–43. [2] Blank VD, Buga SG, Serebryanaya NR, Dubitsky GA, Bagramov RH, Popov MYu et al. Appl Phys A 1997;64:247–50. [3] Blank VD, Buga SG, Serebryanaya NR, Denisov VN, Dubitsky GA, Ivlev AN et al. Phys Lett 1995;A205:208–16. [4] Jin J, Cheng J, Varma-Nair M, Liang G, Fu Y, Wunderlich B et al. J Phys Chem 1992;96:5151–6. [5] Hultgren R, Decai RD, Hawkins DT, Gleiser M, Kelley KK, Wagman DD. Selected values of the thermodynamic properties of the elements, Metals Park, OH: American Society for Metals, 1973. [6] Dresselhaus MS, Dresselhaus G, Eklund PC. Science of fullerenes and carbon nanotubes, San Diego: Academic Press, 1996. [7] Korobov MV, Sidorov LN. Thermodynamic properties of fullerenes. J Chem Thermodynam 1994;26:61–73. [8] Mason P, editor, Physical acoustics, vol. 3, New York: Academic Press, 1965, part B. [9] Kobelev NP, Soifer YM, Bashkin IO, Gyruv AF, Moravskii AP, Ryabchenko OG. Phys Stat Sol (b) 1995;190:157–62. [10] Kobelev NP, Nikolaev RK, Soifer YaM, Khasanov SS. Chem Phys Lett 1997;276:263–5. [11] Berman R, editor, Physical properties of diamond, Oxford: Clarendon Press, 1965. [12] Grigorieva IS, Mejlihova EZ. Physics values, Moscow: Energoatomizdat, 1991. [13] Nuzdin AA. Izvetiya Akad Nauk (Neorganicheskie Materiali) 1988;24(10):1639–44.