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7УГ/JEPOÄHLIE НАНОСТРУКТУРЫ Ä^Jß AJJÛTFPÎJATÈÂÎKJÉ ОН^РГЁОШ] È ОКШЮПШ HaiytètTyMû: аянгез, caoijcraa, ир>]Л1енен>е
CARBON J JANDSTRUCTURES FOR RENEWABLE ENERGY AND ECOLOGY j Janosysiemjs: synthesis, properties, and application
THE CARBON PHASE DIAGRAM NEAR THE SOLID-LIQUID-VAPOR TRIPLE POINT
I.I. Klimovskii, V. V. Markovets
Joint Institute for High Temperatures of Russian Academy of Sciences Izhorskaya, 13/19, Moscow, 125412, Russia Fax: (495)4832289; e-mail: [email protected]
Literature data are analyzed to infer about the influence of the heating rate of carbon on its specific heat and melting temperature. How the heating rate affects the dependence of the carbon saturated vapor pressure on temperature is examined too. It is established that at heating rates uh < 10 K/s the carbyne region on the carbon phase diagram exists in the range of temperatures approximately from 2600 to 3800 K. At rates of 10 to 107 K/s for each heating rate there is its own metastable phase diagram; in doing so the increase in the heating rate results in increasing both the graphite-carbyne phase transition temperature and the carbyne melting one. At heating rates uh > 107K/s the carbyne region is not realized and the carbon metastable phase diagram is actually that of graphite with the temperature and pressure at the solid-liquid-vapor triple point equal to Ttt = 5000 K and pTT = = 107 Pa, respectively. Thus due to the presence of the graphite-carbyne phase transition, the thermody-namic carbon properties in the vicinity of the solid-liquid-vapor triple point are determined not only by the pressure and temperature, but also by the rate of heating. The carbon phase diagram suggested in this paper combines in a consistent way the known carbon phase diagrams with the temperatures and pressures at the solid-liquid-vapor triple point being TTT = 3800 K and pTT a 105 Pa and TTT = 5000 K and pTT = 107 Pa.
1. Introduction
Current literature on the carbon phase diagram discusses two possibilities. It is now more than 25 years after the publication of the first [1,
2] by Whittaker. According to this diagram, within the temperature range of 2600 to 3800 K stable carbyne phases exist and thus, when graphite is heated to T > 2600 K, a graphite-carbyne phase transition occurs. The time for changing 80-90 % of graphite to carbyne at about 3800 K is report-<t ed in [1] to be Tc = 2-3 s. For carbyne the pressure § and temperature at the triple point (solid-liquid-vapor) are PTp = 2104Pa and TTp = 3800 K, respec-^ tively. The second phase diagram is given in [3]. '! According to this diagram, PTp = 107Pa and | TTp = 5000 K, and the existence of the carbyne | phase is called into question.
8 The last few years have seen considerable in-
3 terest in critically analyzing both the possibilities g to bridge the gap between them. Among other ™ things, this would open the door to understand-
ing all the totality of the experimental data accumulated from a unified point of view. Most of these data confirm the Whittaker's phase diagram (see, e. g. [4]). Therefore it is this diagram that we will further use, along with the others, in order to construct the carbon phase diagram near the solid-liquid-vapor triple point.
Because of a plausible graphite-carbyne phase transition (in a time of 2-3 s) and fundamental differences between the temperatures and pressures at the graphite and carbyne triple points, graphite leaves the category of the highest-temperature structural materials used, for example, in nuclear power for that of materials possessing the melting point at a level of 4000 K. Moreover, the graph-ite-carbyne phase transition can result in a noticeable change of the heat capacity and heat conductivity of a source material and, as a consequence, in deterioration, for example, of heat exchange in high-temperature constructions. In the light of the aforesaid, the problem of the graphite-carbyne phase transition ceases to be of pure scientific interest
* The data presented were reported in 2004 at the All-Russian Symposium «Modern Problems of Non-Equilibrium Thermodynamics and Complicated System Evolution» in commemoration of I. Prigozhin» (Moscow, 13—24 April) and at the Conference «Carbon: Fundamental Problems of Science, Material Authority, Thechnology» (Moscow, Moscow State Univ., 13-15 October).
Статья поступила в редакцию 18.04.2007 г. The article has entered in publishing office 18.04.2007.
and becomes one of most important material authority problems, for example, in nuclear power.
The prime objective of this work is to investigate the graphite-carbyne phase transition based on the examination of available experimental data and thereby to develop a scientific approach to analyzing the impact of this phase transition on the material authority (structural) peculiarities of graphite.
2. The carbon specific heat dependence on the rate of heating the samples
The dependence of the carbon specific heat on the rate of carbon heating can be inferred from papers [5, 6], [7-9], and [10-12]. In papers [5, 6], the enthalpies and specific heats of different kinds of graphite with densities of p= 1.8-1.9 g/cm-3 were determined using the mixture method. In papers [7-9], the same technique was applied to measuring the enthalpies of a UPB-1T graphite (quasi-monocrystalline graphite) and of a glass carbon. The experimental values of the enthalpies of both these substances approached each other within the accuracy of measurements. In the studies [10-12] were used the samples made of 1.7-1.8 g/cm3 MPG-6 graphite and of 2.1 g/cm3 pyrographite. They were the rods of about 25 mm in length with circular (1 mm in diameter for PMG-6 graphite) or rectangular (0.5x1.5-1.0x1.5 mm2 for pyrographite) cross sections. The data on the specific heats for each kind of graphite were obtained from the so-called «slow» and «fast» experiments. In the first case, the heating rate approached 106K/s, while in the second one it was about 2107K/s. In «slow» experiments, the temperature was ~3500 K at maximum. In «fast» experiments, the temperatures as high as 4200 K were attained. As noted in [11], no dependence of the graphite specific heat on the rate of heating was observed.
At Fig. 1 are represented the data of [6], [8], and [12] on the carbon specific heat cp(T). Comparison of these data is clearly indicative of not only quantitative, but also a qualitative difference between them. In paper [11], this difference is attributed to the attenuation, not taken into account in [6, 8], of the sample radiation on its passage through a layer of a condensed vapor be-
1800 2600 3400 4200 5000
T, K
Fig. 1. Carbon specific heat: 1 — domestic graphite principally of densities p = 1.8-1.9 g/cm3 [6]; 2 - UPB-1T graphite (p = 2.26 g/cm3) and a glass carbon (p = 1.45 g/cm3) [8]; 3 — pyrographite of p « 2 g/cm3 [12]
tween the sample and the optical element of a furnace. This attenuation leads to the difficult-to-include underestimating of the brightness temperature and thus to the overestimating of the enthalpy and specific heat of graphite.
The explanation suggested in [11] seems to be insufficiently justified for a number of reasons. <t First, according to [5], the set-up was employed t in [11] for investigating the enthalpies and spe- | cific heats of graphite and carbide materials and u of some other substances over a wide range of S temperatures. Taking into account that the high-temperature unit of the set-up heater is made of ^ graphite, one could assume the existence of iden- | tical carbon vapor layers beneath each sample (ir- ^ respective of its material) at high temperatures § capable of partly absorbing the radiation. As a © result, the temperature measured is to be underestimated compared to its true value. If a systematic underestimating of the measured temperatures due to the presence of carbon vapors above the sample tested were actually observed it would be most likely to be revealed. As no influence of carbon vapors on the results of measurements was observed in [5], it is felt to be absent.
Second, assuming the difference between the results of carbon enthalpy measurements in [6] and [12] to arise from underestimating the temperatures measured in [6], one must conclude that a maximum temperature attained in [6] during measurements exceeded the upper limit of the setup working temperatures by 90-100 K.
Third, according to [13], the specific heats of
diamond cdp, graphite cg, and carbyne ccp increase
on going from diamond to carbyne (cdp < cp < ccp),
which is attributed to decreasing their atomic structure rigidities in the same order. Therefore at low rates of heating the samples investigated, an increase in their specific heats should be expected under the solid-phase graphite-carbyne transition. This is actually observed in experiments (see Fig. 1).
Thus the explanation suggested in [11] for the difference in the enthalpies and specific heats presented in papers [5, 6], [7-9], and [10-12] is unlikely to be valid. Nevertheless it is evident that, starting from the Whittaker's phase diagram, one <t cannot explain neither all the totality of the data ¡j represented at Fig. 1, nor the results of [10-12] g-on carbon enthalpy measurements, which show no abnormalities in the carbon enthalpy dependence 1 below the temperatures of about 4000 K capable | of being referred to the phase transition. |
c
3. The dependence of the carbon melting i temperature on the rate of heating the samples x
r--
o
The dependence of the carbon melting temper- ° ature on the time of heating the samples was first 0 discussed in paper [2] wherein the following explanation for this dependence was suggested. At the heating times %h noticeably exceeding the characteristic time t for the change of graphite to carbine and temperatures approaching 3800 K, graphite has time to be converted into carbyne and
it is carbyne which melts at a temperature of about 3800 K. If Th < Tc, graphite does not change to carbyne thereby the carbon melting temperature increases. However, the data presented in papers [14, 15] allow one to conclude that the carbon melting temperature depends not only on the rate of heating the samples investigated, but also on some other factors not yet revealed.
Fig. 2 illustrates the dependence of the carbon melting temperature Tm on the heating rate u^ Since many data represented in Fig. 2 are obtained assuming the carbon radiant emittance g = 1, the data of papers [26, 31, 36] and [37, 38] (points 12, 20, 23, and 24, respectively) obtained beyond this assumption were recalculated per g = 1. How the results of [25] (point 10) were corrected is described in the next section of our paper. In paper [24] (point 9), temperature T = 3740 K is taken to be identical to the graphite sublimation temperature. However, this temperature, as the relevant analysis shows, is actually the melting temperature.
5500
5000
4500
4000
3500
3000
10 23 20 12 ♦ /19 2^ 21
27 \ у. н
N V 15 * 25
16 2 4 8< . б ♦ , /l3 19 v / \ 11
/ 18 /
<•4 1 3 "22 9+< V7
<> s 7
10"1
10'
10;'
10° , K/s
10'
10s
Fig. 2. The dependence of the carbon melting temperature on the rate of carbon heating: 1 —[16]; 2— [17]; 3— [18]; 4 — [19]; 5 — [20]; 6 — [21]; 7 — [22]; 8 — [23]; 9 —[24]; 10 —[25]; 11 —[12]; 12 — [26]; 13 — [27]; 14 — [28]; 15 — [29]; 16, 17, 18 — [14]; 19 — [30], 20 — [31], 21 — [32-34]; 22 — [35]; 23 — [36]; 24 — [37, 38]; 25 — [39, 40]; 27 — [41]
It can be inferred from Fig. 2 that all the results of measurements, including those corrected, are laid in the vicinity of curve 27. According to the above-mentioned phase diagrams of papers [1, 2] and [3], the temperature Tm shows a weak dependence on pressure up to the pressures of several hundred bars. Therefore the curve 27 in Fig. 2 can be thought of as the dependence of temperature TTP on the rate Uh. According to this dependence, at Uh <10 K/s the temperature TTP = 3800 K and is thus equal to the carbyne triple point temperature. On rising Uh approximately from 10 to 107 K, the magnitude of TTP increases approximately from 3800 to 4800 K. At uh >107K/s temperature TTP = 4800 K and approaches the value 5000 K, which is ordinarily taken as the graphite triple point (see, e. g. [3]).
By this means the dependence of the carbon melting temperature (the triple point temperature) is in qualitative agreement with the idea that at low heating rates Uh < 10 K/s the change of graphite
to carbyne and melting of carbyne at a temperature of about 3800 K do occur. At higher heating rates Uh > 107K/s, this change does not take place and it is just graphite that melts at a temperature of about 4800 K. However the question of which modification (form) of graphite melts at intermediate heating rates ranging from 10 to 107K/s remains to be yet clarified.
The crossed sign corresponds to the results of measurements admitted by their authors as being incorrect. The arrows connecting rhombic and rectangular signs show the measurement results correction made in the present work.
4. The influence of the heating rate on the temperature dependence of a carbon saturated vapor pressure
Fig. 3 shows the temperature dependence of the carbon saturated pressure ps on ps - 1/T coordinates. The 1'1''-dependence is constructed by averaging the data of paper [20] representing the results of the steady state measurements carried out in 13 different works. The 2'2''-dependence shows the results of calculation for graphite [42]. It should be noted here that the results of calculation [42] are in good agreement with the experimental results of [43, 44]. The straight line 3'' represents the results of measurements [25].
It is evident that in the context of the present analysis the 1'1''-dependence, generalizing the results of the steady state measurements, corresponds to slow carbon heating and may be referred to the Whittaker's phase diagram. Since the 2'2''-dependence is calculated for graphite, it should correlate with the phase diagram suggested in [3]. The 3''-dependence corresponds to the case of the intermediate heating rates and it does correlate with none of these phase diagrams. It should be noted that the corrected data of [25] (point 10 in Fig. 2) correspond to the cross-point of curves 3'' and 2'.
Taking into account the fact that the difference between the straight lines 1' and 2' arises from experimental and calculation errors, the straight line 1' and a segment of the straight line 2' are to coincide with each other. Therefore, for the sake of definiteness, we will further use the 2'-dependence [42] as the temperature dependence of the carbon saturated vapor pressure on the solid carbon temperature. Hence for each heating rate there should be its own dependence of a carbon saturated vapor pressure on temperature.
According to the shapes of the curves given in Fig. 3, the carbon sublimation heat is AHsUbl = = 720 kJ/mole and does not depend on the heating rate. For liquid carbon, formed from carbyne at low heating rates and from graphite at high temperatures, the vaporization heat remains also constant and equals AHvap = 360 kJ/mole. As a result, the melting heat AHm remains constant too and does not depend on the rate of carbon heating
AHm = AHSUbl - AHvap = 360 kJ/mole.
According to the data of [43], the difference between the enthalpies of graphite and carbyne is
u
h
AfH0 = -37.03 kJ/mole. One can therefore assume that the melting heats of carbyne (curve 1'1'' in Fig. 3) and of graphite (curve 2'2'' in Fig. 3) should be most likely to differ by a quantity of kJ/mole. However this difference is actually about 10 % of the melting heat and, apparently, it is for this reason that the difference above-mentioned is difficult to be derived from the dependences presented in Fig. 3.
10'°
10B
10B
Л
104
102
10
3 " 2"
1"
V2'
ч 1'
1
1,5
3,5
10a
10'
10=
10'
101
10"1
10"J
10"
I I / ' А —3
CO- 1 ш — \ 1 2 ''
TP, \ TP; \ ТРз
РТ,
К
\ РТ,
2000 2500 3000 3500
4000
T, K
4500 5000 5500 6000
2 2,5 3
104/T, K-1
Fig. 3. The temperature dependence of the carbon saturated vapor pressure
5. The carbon phase diagram taken into account the carbon rate heating
The construction of the carbon phase diagram is based on the following statements stemming from the above consideration.
1. At low heating rates uh < 10 K/s, the Whit-taker's phase diagram is valid.
2. For each heating rate there exists its own set of carbon states, which are consecutively passed during heating. It is formally possible to describe this set of states using a diagram similar to that at equilibrium and being further referred to as a metastable diagram. In other words, near the solid-liquid-vapor triple point the carbon phase diagram is a combination of equilibrium and metast-able phase diagrams.
3. On increasing uh, the boundaries (curves) of the solid-phase graphite-carbyne transition and of the melting shift into the range of higher temperatures. At Uh > 107K/s the change of graphite to carbyne does not occur and the melting temperature is T = 4800 K.
m
In Fig. 4 are represented schematically three carbon phase diagrams. Those are the Whittak-er's diagram, the diagrams corresponding to Uh = 0K/s and Uh >107K/s, and that at intermediate values of Uh. The boundary curve for the graphite-carbyne phase transition and the melting curve are schematically drawn with reference to the phase diagrams of [1, 2] and [3]. The pressure at the carbyne triple point is set to equal 105 Pa and the graphite melting temperature is take as being 4800 K.
It is obvious that only the Whittaker's phase diagram is in agreement with the present day understanding of the term «phase diagram». The carbon lifetime on the metastable phase diagram
ized at non-zero values of u,
i. e. using the three-
and dT/dt.
Fig. 4. Schematic representation of the carbon phase diagram near the solid-liquid-vapor triple point at different heating rates. PTP is the graphite-carbyne phase transition point, TP, the triple point. Figs. 1, 2, and 3 are referred to the curves and points of the phase diagram at heating rates uh1 < 10 K/s, at intermediate rates uh2 from 10 K/s to 10' K/s, and at uh3>10'K/s, respectively. The hatched areas correspond to the carbyne domains
should appear to coincide, by an order of quantity, with the characteristic time for changing graphite to carbyne. Hence the carbon phase diagram at the solid-liquid-vapor triple point must be constructed allowing for the metastable carbon states real-
dimensional coordinate system: T, p 6. Conclusion
In the present paper, the analysis of different experimental studies of carbon is given and the carbon phase diagram near the solid-liquid-vapor triple point is suggested. At the heating rates Uh <10 K/s, the carbon thermodynamic states are described by the Whittaker's diagram [1, 2]. In the range of the heating rates from 10 K/s to 107 K/s, to each heating rate corresponds its own metastable (quasi-stationary) phase diagram. At rates Uh >107K/s a metastable (quasi-stationary) phase diagram is realized, which is close at the triple point (solid-liquid-vapor) to that suggested in paper [5]. Hence the carbon phase diagram near the solid-liquid-vapor triple point must be constructed in the three-dimensional coordinate system: T, p, and dT/dt. It is however possible that a necessity for additionally including parameter dp/dt will be revealed on a more sophisticated treatment of experimental data.
The phase diagram suggested removes the conflict between those proposed in papers [1, 2] and [3]. Besides, it allows understanding a number of experimental data, which are not explained by neither the Whittaker's phase diagram [1, 2], nor that suggested in paper [3].
It should be noted that in recent work [46], using the method suggested in papers [47, 48], for the first time in the real time regime was observed melting of graphite heated by radiation of a neodymium YAG-laser (1.06 mm) in air at atmospheric pressure.
This work was partially supported by the Russian Foundation for Basic Research (Grant No. 05-08-33410).
International Scientific Journal for Alternative Energy and Ecology ISJAEE № 5(49) (2007) Международный научный журнал «Альтернативная энергетика и экология» АЭЭ № 5(49) (2007)
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