Experimental Studies of Thermophysical Properties for Refractory Carbides and Carbon at High Temperatures in the Interests of Rocket and Space Technologies

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Дата публикации:
16 декабря 2021, 19:07
Секция 11. Наукоемкие технологии в ракетно-космической технике
The results of experimental studies of the physical properties of metal-based carbides (zirconium, hafnium, tantalum), as well as the properties of carbon at high temperatures are presented. It is shown that the pulsed current heating technique has significant advantages in comparison with other research methods (stationary or pulsed with laser heating). The input energy (enthalpy), specific heat, heat of fusion, electrical resistance were measured. The temperature was measured with a high-speed brightness pyrometer calibrated against a temperature lamp. In this case, either the literature data on the emissivity of a flat surface were used, or measurements were performed on a wedge-shaped model of a black body made from the samples themselves. The results obtained can be used in the development of thermal protection for aircraft and missiles.
Ключевые слова:
refractory carbides, carbon, solid and liquid state, temperature measurement, pulse heating, specific heat, enthalpy, electrical resistance
Основной текст труда


It is known that the properties of refractory carbides allow us to consider them as promising materials for the development of high-temperature devices, including rocket engines, hypersonic aircraft, thermal protection elements, high-temperature nuclear reactors. However, stationary studies are limited to temperatures of the order of 3000...3500 K. The properties of the liquid phase of refractory carbides have remained unexplored until recently. Rapid current heating allows significantly increase the temperature of the study and obtain reliable physical properties at temperatures of 5000 K and above. This made it possible to study the solid phase, melting, as well as the liquid phase of carbides in a single act of rapid heating.

The results of an experimental study of physical properties are considered: input energy (enthalpy), specific heat, heat of melting, electrical resistance, — depending on the measured temperature for carbides ZrC +C [1], ZrC [2], TaC+HFC [3], HfC [4] and carbon [5–7] at temperatures of 2000-7000 K.

Experimental methodology

The research method is presented in [1–7]. Heating by an electric current pulse with duration of 5-10 microseconds corresponds to a heating rate of ~ 109 K/s. These heating rates look exotically large. However, it is known that the electron-ion relaxation time in a solid is several picoseconds (10–12 s). Thus, during microseconds (5×10–6 s) heating, the electron and ion subsystems are in equilibrium with each other, which gives grounds for applying the concept of local thermodynamic equilibrium to the description of the state of the specimens (thin plates The input energy (enthalpy) was calculated from the current through the sample and the voltage across the sample, measured using digital oscillography.

The short duration of the heating process makes it possible to preserve the stoichiometry of the carbide composition during heating and neglect the interaction of the specimen with the environment.

At the same time, rapid current heating has a peculiarity — for all the substances studied, there is a sharp increase in the specific heat of the solid phase just before the moment of melting. The same effect was observed earlier in the study of the properties of metals and graphite under rapid current heating, i. e. this effect has a common nature with rapid heating of substances. It is assumed that this effect may be associated with the formation of paired Frenkel defects (interstitial atom plus vacancy) under conditions of short heating time. Upon rapid heating, the loss of long-range order and melting occur as a result of the formation of Frenkel defects.

Carbide samples were thin plates (100...200 µm) cut from sintered blocks, or thin layers (1...10 µm) deposited on glass substrates. In the first case, a carbide plate was placed between two glass plates. In the second, the deposited layer was covered from above with a second glass plate.

Method of measuring temperature and thermal properties

The temperature was measured by optical method using a high-speed pyrometer based on PDA-10A photodetectors (Thorlabs). Reference temperatures of Tsolidus and Tliquidus for carbides were recorded. The literature data on the normal spectral emissivities of the studied substances were used. Calibration of temperature measurements was carried out using a temperature lamp at T ~2500 K. Next, the temperature was calculated using the Planck formula, taking into account the emissivity en, of a flat surface, at a wavelength 856 nm.

In its absence, a wedge-shaped blackbody model (BBM) was created, consisting of two glass plates covered with a thin layer of the studied carbide [1]. These plates were folded at a certain angle, forming an wedge-shaped model of a blackbody. Such a model withstands rapid heating and continues to exist, without changing its shape in the liquid phase, for a time (several microseconds) sufficient to measure temperature. The effective emissivity of such a model with a mirror reflection of its walls equals 0,95...0,99. A wedge-shaped blackbody model was used with a success for measuring a true temperature under the experimental investigations for metals Zr, Hf and carbon.

Under measuring the specimens temperature covered with glass, the absorption of the upper cover glass was taken into account. The absorption of the protective glass located in front of the pyrometer lens was taken into account for the all specimens (including the blackbody model). The method of measuring the specific heat (taking into account temperature measurements) during pulsed current heating is described in detail in [1–7].

The enthalpies of the beginning and the end of melting were obtained for all the carbides studied, their difference gives the heat of the phase transition during melting. Solidus and liquidus temperatures were measured. Comparison with the calculated phase diagrams is carried out. The agreement is quite acceptable, however, it has been noticed that the maximum temperatures of the phase diagrams are sometimes slightly lower than those measured (for example, zirconium carbide by 150 K, which is confirmed not only by us, but also by the experiment with laser pulse heating).

The melting point of a mixed carbide based on tantalum and hafnium (4300 K) is slightly higher than for hafnium carbide (4200 K). Attention is drawn to the high enthalpy of the liquid phase of zirconium carbide with the addition of carbon  –5.55 kJ/g at a liquidus temperature of 3640 K, as well as the high melting heat (3.2 kJ/g). In the references to [1] it is noted that the presence of free carbon in this system improves the heat resistance and increases the erosion resistance of zirconium carbide when it is used in the nozzles of solid-fuel rockets.

Carbon research

The relative expansion of graphite with an initial density of 2.1...2.2 g/cm3 (heated by a current in a glass capillary during a few microseconds) was measured by us for the first time [7]. The moment of filling the capillary with carbon was recorded by a clear measurement of electrical resistance against the input of energy (the steep dependence changed dramatically to a smoother one). These results relate to low external pressures (about 200 bar).

The change in the volume of graphite during melting was calculated in 2003 [7], on the basis of experimental data and the Clapeyron-Clausius equation. The ratio of volumes of liquid and solid phases Vliq / Vsol ≫ 1.7 was obtained. As it turned out, graphite expands significantly; the expansion is ~ 70 %, during melting only (at low pressures 200...500 bar).

A significant expansion of graphite at low external pressures was also confirmed under laser heating conditions (see the description and references in [7, Fig.10, a].

The electrical resistance of HAPG graphite (Highly annealing pyrolytic graphite) with a density of 2.26 g/cm3, related to the initial dimensions, changes from 450 to 630 µΩ·cm during melting (T = 4900 K). The temperature was recorded from a clean graphite surface, through a layer of  silica glass. Note that in the case of melting of a thin layer of the plate, the optical transmission of silica glass does not change (this is positive difference to sapphire Al2O3). Attention should be paid to the clear fixation of the end of graphite melting when recording electrical resistance, even clearer than under recording with an optical pyrometer. With a further increase in temperature, the electrical resistance increases slightly, reaching 900 µΩ×cm at 8000 K. Since up to 8000 K, there are no any features on the electrical resistance curve, — it can be assumed that the boiling point of liquid carbon is above 8000 K. Another possibility to explain the absence of boiling marks is the increased pressure in the cell that occurs at the late stages of pulsed heating (pressure was not measured in these experiments). But it was not as high as during pulsed heating in the  thick-walled sapphire capillaries (measurement of CV for liquid carbon).

Thus, when graphite is melted by current, a slight change in electrical resistance is observed. In any case, liquid carbon is a fairly well-conducting material. Therefore, the statement given in some works that a metal-nonmetal transition occurs during the melting of graphite is insufficiently substantiated. Measurement methods for pulsed current heating, especially with short pulse durations of the order of fractions of microseconds, require careful justification. Otherwise, erroneous results may be obtained, an example of one of which is considered in [7].

For liquid carbon at temperatures of 5000...7000 K, we additionally measured the specific heat CV (~2 J/gК), which turned out to be half as low as Cp (~ 4 J/gК), measured earlier. Measurements of CV [7] were carried out with rapid heating of an anisotropic graphite plate sandwiched between two thick-walled plates of TF-5 glass (heavy flint). The experimental result obtained is useful for thermal calculations under high pressure conditions.

We can note that the use of graphite layers is effective, since having a high sublimation energy (≫ 60 kJ/mol), the carbon removed at low external pressures contributes to the cooling of the surface.


It is established that the specific heat of carbides in the solid state (in a wide temperature range) may be slightly higher than the data obtained in stationary experiments. Under rapid heating, the initial lattice defects and impurities remain in the un-annealed specimen until the liquid state is reached. This leads to a slightly higher specific heat of the solid specimen far from the melting point. The additional energy associated with an increase in the specific heat immediately before melting (due to the appearance of Frenkel defects) is within the error of the enthalpy measurements: from 5 to 7 %.

It should be noted that rapid current heating of quasi-crystalline anisotropic graphite with a purity of 99.99 (i. e. with a small amount of impurities and defects) gives a specific heat of the solid phase, which coincides with the specific heat during stationary heating [7], except for the region of steep Cp growth just before melting. It can be expected that preliminary annealing of carbide specimens before experiments with rapid heating will lead to a decrease in the difference in the values of the specific heat of the solid phase obtained by rapid and stationary heating methods. Despite this remark, the specific heat of liquid metals, carbides and carbon in the range of 4000...8000 K can be investigated only with the use of rapid heating by an electric current pulse.

The conclusions are made that the results of the studied carbides and graphite at temperatures of 2000...8000 K can be used in the reasonable manufacture of thermal protection.

In 2021, we started (in cooperation with MISIS) research on the physical properties of high-entropy mixed carbides and mixed alloys at high temperatures. Such alloys (for example) contain a significant number of elements (up to 5 or more), as a rule, in equal parts and are —  a new class of promising materials for creating thermal protection. As noted in the publications high-entropy alloys have:

  • high thermodynamic stability of the existence of a solid solution;
  • high strength, heat resistance and corrosion resistance.
Russian Scientific Fund (RSF) grant No. 19-79-30086
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