INSC: MatProp: Graphite: Enth and Heatcap

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Enthalpy and Heat Capacity of Graphite

Russian Graphite

In the book "Nuclear Graphite," R. E. Nightingale[1] defined nuclear graphite as graphite with a density on the order of 1.7 g/cm3. In his tabulation of graphite used in nuclear reactors, Nightingale gives three graphites used in Russian reactors. These are: RPT, IR, and APS with densities of 1.8, 1.65, and 1.65 g/cm3, respectively. No thermophysical property data have been found on any of these Russian graphites. Soviet reactor graphites have been tabulated in a paper on thermal expansion of graphitic materials by Platonov et al.[2] These graphites are: GMZ, KPG, RBM-K, RBM-KP, VPG, and PGG. No enthalpy nor heat capacity data have been found on any of these graphites but data on thermal expansion, thermal conductivity, electrical resistivity, and the effects of irradiation are available on some of these graphites and on pyrolytic carbon.

Three sets of enthalpy measurements on Russian graphites and carbon have been located. None of these measurements are on the grades of graphites identified as reactor graphite. Sheindlin et al.[3] made measurements from 273 to 3650 K on Soviet brands of graphite: 204, 435, 753, N, ARV, and PROG-2400. Except for PROG-2400, these graphites are fine-grained dense graphites (densities in the range of 1.8-1.9 g/cm3) formed by repeated impregnation with pitch or by hydrostatic compaction. After impregnation and/or compaction, they were heated to 3000- 3300 K. Buchnev et al.[4] made enthalpy measurements from room temperature to 3250 K on quasi-single crystal carbon, glass (fused) carbon, and pyrolytic carbon. The densities of these samples were, respectively, 2.26, 1.45, and 2.24 g/cm3. Impurities in the samples were less than 0.01%. Lutcov et al.[5] measured enthalpies from 100 to 300 K of dense graphites (densities 1.9, 2.0, 2.1 g/cm3), baked carbon, extreme heat treated pyrolytic carbon, and natural Taigyinski graphite. Lutcov et al. used the same equation to represent the heat capacities of graphites with densities of 2 and 2.1 g/cm3. The data for Taigyinski graphite were represented by the same equations as for pyrolytic carbon. They observed that, for these low temperatures, the thermodynamic functions decreased as the crystal structure of the graphites became more perfect. At 298.15 K, their enthalpy of baked carbon was about 11% higher than that for pyrolytic graphite.

In their review of data on the specific heat of graphite, Butland and Maddison[6] refer to measurements by Kraftmakher and Shestopal[7] from 1750 to 2850 K on a pure grade of graphite with a density of 1.61 g/cm3. The samples were heated with an alternating current and temperatures measured by optical pyrometry. Butland and Maddison rejected these data in their analysis because above 900 K, the heat capacities of Kraftmakher and Shestopal[7] were consistently low compared with other data.

Early Assessments of Available Data

Figure 1

Heat capacity data obtained on a wide variety of types of graphite between 1953 and 1965 showed considerable disagreement and scatter. In Volume 5 of the handbook on thermophysical properties,[8] the Center for Information and Numerical Data Analysis and Synthesis (CINDAS) tabulated data above 298 K on the heat capacity of a number of grades of graphite from measurements made from 1953 through 19629-19 but gave no recommendation for the heat capacity of graphite. The large scatter and disagreement in the data of Rasor and McClelland,[9] Barriault et al.,[10] Lucks et al.,[12-13] Neel et al.,[14] and Fieldhouse et al. [15] are evident in Figure 1. In the book Nuclear Graphite,[1] Nightingale tabulated heat capacities for nuclear graphite from the experimental data of DeSorbo and Tyler[16] and of Rasor and McClelland.[9,17] Butland and Maddison[7] examined heat capacity data on various grades of graphite in an effort to determine the best values for nuclear graphite for the temperature range 250 to 3000 K. They rejected data of Rasor and McClelland,[9,17] Barriault et al.,[10] Fieldhouse et al.,[15] and Neel et al.,[14] because these data were far removed from the main body of data or showed a large spread indicative of large experimental errors. They rejected the Russian data of Kraftmakher and Shestopal[7] and the data of Lucks et al.[12-13] because these data consistently exhibited low specific heat above 900 K. They performed an unweighted least-squares fit to the data of DeSorbo and Tyler,[16,18-20] Magnus,[21,22] Worthing,[23] West and Ishihara,[11] and McDonald.[24] The data of West and Ishihara and that of McDonald has been included in Figure 1 as well as the more recent data of Cezairliyan and Righini.[25-26] for comparison with the rejected data.

Recent Assessments and Recommendations

Figure 2

Figure 3

The most recent assessments of JANAF,[27] CODATA,[28] and the Scientific Group Thermodata Europe (SGTE)29 are in excellent agreement. The thermodynamic functions tabulated in the 1986 edition of JANAF are from a 1978 assessment and are identical with the CODATA values. The SGTE equations for the thermodynamic properties of graphite are based on the 1986 assessment of Gustafson.[33] Enthalpy increments and heat capacities in the JANAF and CODATA tables agree with values from the SGTE equations within 0.5% below 500 K and 0.1% from 500 through 3800 K. No comments regarding the Gustafson assessment are given here because the journal Carbon, in which it was published, is not available at ANL after the 1976 edition. Figure 2 and Figure 3, respectively, compare the SGTE values for graphite enthalpy and heat capacity with the most reliable experimental data and the Russian data. Because the JANAF and SGTE values for enthalpy and heat capacity are identical within the resolution of the graphs, only the SGTE equation is designated in the figures.

Below 298.15 K, the JANAF values are based on the data of DeSorbo and Tyler[14-17] Above 298.15 K, enthalpy increments and heat capacities are based on the enthalpy data of McDonald[24] and of West and Ishihara[9] and the heat capacity data of Cezairliyan and Righini.[25-26] These measurements are in fairly good agreement in regions of overlap (as shown in Figure 3) even though they utilized different grades of graphite. New laser flash[30] and differential scanning calorimetry[31] measurements tend to confirm the JANAF heat capacities (and therefore the SGTE heat capacities) between 350 and 950 K where the largest deviations (~3%) are on the order of experimental error. Chase et al. comment that discrepancies in the heat capacity data of different grades of graphite are of concern because the heat capacity has not been measured on a single grade of graphite for the entire temperature range of interest. Lutcov et al.[5] reported differences in the low temperature (below 300 K) heat capacities of two graphites and pyrolytic carbon. The heat capacities of Lutcov et al. at 298.15 K and 300 K for graphites with densities of 1.9 and 2 g/cm3 (shown in Figure 3) are in reasonable agreement with the JANAF and SGTE values. The heat capacity data of Rasor and McClelland[18] and the enthalpy data of Sheindlin et al.[3] (Figure 2) gave heat capacities that rise rapidly near 3500 K, as shown in Figure 3. However, the pulse-heating data of Cezairliyan and Righini[25-26] gave slowly rising heat capacities that are linear up to 3800 K. The rapid rise in the enthalpies and heat capacities of some grades of graphites above 3000 K may arise from degradation of the sample with vaporization of impurities. Rasor and McClelland[9] comment that when the sample of type 7087 graphite was heated, an odorous vapor was released that created a lacy white deposit. Smaller amounts of vaporization were observed for graphite types GBH and GBE and none for type 3474D. However, the heat capacity data of Rasor and McClelland from all four samples were consistent with a rise in the heat capacity above 3300 K that was numerically represented by inclusion of an exponential term with an activation energy that is approximately the heat of vaporization of atomic carbon. Whittaker has proposed[32] that graphite is metastable in this high-temperature region and slowly transforms to carbynes. If this is the case, then the very rapid measurements of Cezairliyan and Righini[25-26] should give heat capacity values which are the most appropriate for graphite.

The SGTE equations for the enthalpy increments and heat capacities of graphite are recommended because (1) equations are preferred to tabulated values and (2) values calculated with these equations are in excellent agreement with the tabulated values of JANAF and CODATA. The SGTE equation for the graphite enthalpy increment relative to the enthalpy in the standard state at 298.15 K is:


H(T)-H(298.15) = - 17368.441 + 24.3 T + 4.723 10^-4 T^2
                 + 5.1252 10^6 T^-1 - 7.929 10^8 T^-2   (1)
                 + 4.8 10^10 T^-3

where enthalpy is in J/mol and temperature is in K. The SGTE equation for the heat capacity of graphite in J/(mol-K) is :


Cp = 24.3 + 9.446 10^-4 T - 5.1252 10^6 T^-2 +          (2)
     1.5858 10^9 T^-3 - 1.44 10^11 T^-4

where temperature is in K. Values calculated with Eqs.(1-2) are given in Table 1.

The atomic weight for carbon given by the SGTE (12.011 g/mol) has been used to convert from moles to kilograms of graphite. The SGTE equations for graphite enthalpy increments and heat capacities in kJ/kg and kJ/(kg-K) are:


H(T) - H(298.15) = - 1446.04454 + 2.023145 T +
               3.9322 10^-5 T^2 + 4.26709 10^5 T^-1     (3)
             - 6.60145 10^7 T^-2 + 3.9963 10^9 T^-3

and


Cp = 2.023145 + 7.8645 10^-5 T - 4.26709 10^5 T^-2 +    (4)
     1.3203 10^8 T^-3 - 1.199 10^10 T^-4

where temperature is in K. Table 2 gives graphite enthalpy increments and heat capacities in kJ/kg and kJ/(kg-K).

Comparison of Recommendations with Russian Data

Figure 4

Figure 2 shows that the enthalpy data of Buchnev et al. are in good agreement with the SGTE recommendations and the data of McDonald. Although the data of Buchnev et al. above 3000 K, lie above the SGTE curve, the equation recommended by Buchnev et al. is within 0.5% of the SGTE values above 3000 K. However, the data of Sheindlin et al. rise much faster above 3000 K than the recommended values. Figure 4 shows the deviations, expressed as a percent, of these enthalpy increments relative to the recommended SGTE values. These percent deviations are defined by:


            [Del H (other) - Del H (recommended)] 100%
Deviation = ------------------------------------------  (5)
                     Del H (recommended)

where


Del H = H(T) - H(298.15)                                (6)

Figure 5

Deviations of enthalpy increments calculated with the equation of Buchnev et al. are greatest at low temperatures and are less than 3%. Deviations of values calculated with the equation of Shendlin et al. are high at both low and high temperatures. Deviations of the JANAF values have been included in Figure 4.

The rapid increase in the enthalpy increments of Sheindlin et al. above 3000 K, leads to the large deviation observed for the heat capacities (Figure 3). Heat capacity deviations defined as in Eq.(5) with heat capacity replacing the enthalpy increment are shown in Figure 5. Heat capacities given by the equations of Sheindlin et al. deviate by as much as 10% at low temperatures, decrease to around 1% from 1000 through 2400 K, and increase sharply above 2500 K. At 3000 K, deviations are 11%. At 3600 K, deviations are 56%. The heat capacities given by Buchnev et al. have negative deviations above 2600 K, ie. at high temperatures, the heat capacities of Buchnev et al. are lower than the recommended values. Deviations of the heat capacities of Butland and Maddison and of JANAF have been included in Figure 5 for comparison. Deviations of the heat capacities of Butland and Maddison are within 1% except at low temperatures. JANAF values are within 0.5%.

Uncertainties

Figure 6

Figure 7

The good agreement of the measurements of McDonald,[24] Cezairliyan and Righini,[25-26] West and Ishihara,[11] and Buchnev et al.[4] and the recent recommendations of CODATA, JANAF, and the SGTE would indicate low uncertainties (within 5%) for the recommended enthalpies and heat capacities of graphite. Unfortunately, the lack of data on the grades of graphite used in Russian reactors and the significant differences at high temperatures between values obtained with the equations of Sheindlin et al[3]. and those of Buchnev et al.[4] make it difficult to determine whether the recommended equations for high-purity graphite are suitable for Russian reactor graphites. The graphites used in experiments by Buchnev et al. were of high purity with high densities except for the fused carbon sample. The purities of the graphites used in the experiments of Sheindlin et al. are unknown but the densities of these graphites are consistent with nuclear graphites. If impuriities are present in the nuclear graphites, then these impurities may vaporize at high temperature giving heat capacities similar to those of Sheindlin et al. or those of Rasor and McClelland. If graphite is metastable at high temperatures as proposed by Whittaker,[32] then the heat capacities at high temperature may vary depending on grade of graphite and how rapidly the graphite is transformed to carbynes. Thus, large uncertainties are estimated for the heat capacity at high temperatures to include these effects.

The recommended values for the enthalpy and heat capacity of graphite are shown in Figure 5 and Figure 6 with estimated uncertainties designated by dotted lines. Uncertainties in the enthalpy increments are: 8% below 500 K, 3% from 800 to 2500 K, and 10% above 3000 K. Between 500 and 800 K, enthalpy increment uncertainties decrease linearly from 8% to 3%. Between, 2500 and 3000 K, uncertainties increase linearly from 3% to 10%. Uncertainties in the graphite heat capacities are: 10% below 500 K; 5% from 800 through 2500 K. Between 500 and 800 K, the heat capacity uncertainties decrease linearly from 10% to 5%.. Above 2500 K, uncertainties increase linearly from 5% at 2500 K to 11% at 3000 K. Above 3000 K, the negative uncertainty remains at -11% but the positive uncertainty increases linearly to +50% at 3600 K. So at 3600 K, the uncertainties in the heat capacity values are: +50%, -11%.

Assessed 6/95
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