Effect of Microwave Irradiation to Kinetics of Carbothermic Reduction of NiO

Abstract

The carbothermic reduction of NiO was carried out by microwave irradiation at 2.45 GHz under a constant rate of temperature rise. The state of reaction was analyzed by means of non-equilibrium thermodynamics. The rates of the dominant reaction was the Boudouard reaction followed by NiO + CO → Ni + CO₂, differing from that by conventional radiant heating. The uncompensated heat of reactions and the enthalpy change of reactions were almost same amount. The activation energy was 141 kJ/mol for the carbothermic reduction of NiO, 115 kJ/mol for the NiO reduction by CO gas and 166 kJ/mol for the Boudouard reaction. The former two values were smaller than conventional radiant heating.

Entropy production rate and rate of enthalpy change of the carbothermic reduction of NiO heated by multi-mode microwave at 2.45 GHz.

1. Introduction

Nagata et al.¹⁾ measured the carbothermic reduction rate of Fe₃O₄ by microwave irradiation from the composition of the product gas of CO and CO₂. The reaction rate is much faster than that by conventional radiant heating, and local heating occurs due to the absorption of microwave by the reactant particles.

The characteristics of microwave irradiation to materials are that the system is not in thermal equilibrium between the materials and microwave generator. The reason is that materials absorb microwave to generate energy with the wave length of 12 cm at 2.45 GHz and irradiate radiant heat with that of about 2 µm at 1000°C. On the other hand, the most of experiments have been studied under the assumption of thermal equilibrium using conventional heating by radiant heat and slow reaction rate.

In the present study, the kinetics of carbothermic reduction of NiO irradiated by microwave with 2.45 GHz was studied by mean of the non-equilibrium thermodynamics, and the effect of microwave to the state of reaction was investigated.

Yoshikawa et al.²⁾ performed the carbothermic reduction of NiO by microwave heating, which was a relatively simple reaction in comparison with Fe₃O₄. NiO powder generates heat in electric field but not in magnetic field, and carbon powder generates heat in both fields. It was also reported that the reaction rate by microwave irradiation was faster than that by conventional radiant heating using an electric furnace.

There are some studies on the carbothermic reduction of NiO using conventional radiant heating. Krasuk et al.³⁾ measured the reduction rate of NiO by CO gas in 1972 and stated that the diffusion of gas in the pellets determined the reaction rate. Jagtab et al.⁴⁾ in 1992 reported the catalytic effect of CaO on the frequency factor of reaction rate constant. In 1997, Sharma et al.⁵⁾ measured the partial pressures of CO and CO₂ gases between 900°C and 1000°C under drawing in vacuum. They obtained the activation energy of first-order reaction.

2. Experiments

2.1 Reaction furnace

As shown in Fig. 1, the furnace was a hexagonal cylinder closed both ends by cylindrical lids. There were two holes in the center of facing walls of the hexagonal cylinder that allowed a reaction tube to set horizontally. 8 microwave generators with variable-output of maximum 1.5 kW (UM-1500-IS-B, Micro Denshi Co., Ltd.) were installed in the cylindrical parts on both sides. The facing waveguides were 90° out of phase to prevent interference. An isolator (WR430, Mitsubishi Electric Co.) that absorbed reflected wave was installed in each waveguide. Each waveguide has a silica window for separating the generator and the furnace. A power monitor was connected to one microwave generator. A directional coupler that separates incident and reflected wave was used for the power monitor.

Fig. 1

Microwave furnace with variable-output of maximum 12 kW at 2.45 GHz.

Two stirrers were installed on cylindrical lids, and microwave was agitated in multi-mode. Regarding the distribution of microwave output in the furnace, microwave was irradiated to a heat-sensitive paper coated with graphite powder at 400 W for 1 min. The paper was discolored to irradiate uniformly in the vicinity of the center of furnace.

A temperature controller by PID (KMC1102A, Konan Electronic Co., Ltd.) was connected to the power supply of microwave generators. A radiation thermometer (FTK9-P300R-50L21, 300°C to 2000°C, effective wavelength 0.8 µm to 1.6 µm, Japansensor Co.) was used for measuring temperature. The measurement area of temperature on sample surface was 6 mm in diameter.

The quartz reaction tube had the inner diameter of 45 mm, and one end of it was squeezed to weld a thin quartz tube with the inner diameter of 5 mm, as shown in Fig. 2. To reduce the volume of reaction chamber, a one-end-closed quartz tube with a slightly smaller outer diameter than the reaction tube was inserted. This made it possible to prevent gas stay and backflow.

Fig. 2

Reaction chamber of silica tube.

A sample holder of a porous refractory brick (LBK-3000, Isolite Insulating Products Co., Ltd.) was processed into concave shape with coating alumina cement, as shown in Fig. 3. The inner size of the crucible is 38 × 22 × 22 mm. The reaction tube was covered to insulate with alumina fiber board. Silica, crucible materials and alumina fiber board did not absorb microwave.

Fig. 3

Crucible, including sample.

2.2 Samples

NiO (purity 99.9 mass%, Kanto Chemical Co., Inc.) and graphite (Gr) (purity 99 mass%, particle size 37 µm, Oriental Industry Co., Ltd.) were employed. NiO was pulverized in an alumina mortar, classified into a particle size of 20 µm, and mixed with Gr. The stoichiometric composition of the carbothermic reduction of NiO is NiO:Gr = 0.861:0.139 (mass ratio), but more Gr powder was added as an exothermic material to make it 0.25:0.75.

2.3 Experimental procedure

A sample holder was filled with 10 g of sample and the surface was leveled flat. The bulk density was about 0.5 g/cm³. Holes were made in several places on the sample to reduce gas expansion and to prevent powder from scattering due to rapid heating. The sample in a crucible was dried at 120°C and then placed in the reaction tube. The reaction tube was evacuated and then cleaned with N₂ gas twice. After then, 99.9995 vol% N₂ gas was flowed with 100 ml/min, and microwave irradiation was started.

Heating was performed at a constant heating rate up to about 900°C. The rate of temperature rise is 30°C/min, 50°C/min and 100°C/min, respectively.

About 1.0 ml of gas was sampled from the sampling point using a micro syringe (Ito Micro syringe MS-GAN250, Ito-Seisakusho Co., Ltd.). It took about 30 s for gas to reach the sampling point from the sample holder at the gas flow rate of 100 ml/min, and the reaction time was corrected by the total gas volume.

The mass loss of sample was measured from that of sample holder containing sample before and after microwave irradiation.

2.4 Gas analysis

Gas was analyzed by a gas chromatograph (GC-8APT, Shimadzu Co.) using N₂ gas as carrier gas. A chromate pack (C-R8A, Shimadzu Co.) was used for data output. A stainless-steel column filled with a carbon-based absorption material (SHINCAEBON ST, Shinwa Chemical Ind. Ltd.) was used.

The temperature of column was 50°C for O₂, N₂, and CO and 180°C for CO₂. It took about 20 min to analyze gas in one syringe. The needle tip of syringe was pierced into silicone rubber to maintain airtightness and prevent air from entering. However, a few percent of O₂ gas were mixed in some samples. The concentration of N₂ gas was corrected from that of O₂ gas using the composition of air N₂:O₂ = 79.36:20.64 mol%.

3. Results

The samples were not sintered. Table 1 shows the mass loss of the samples before and after reaction. Figure 4 shows the production rates of CO and CO₂ gas calculated from their compositions with the reaction time. The production rates of CO and CO₂ gas are expressed by the following equations.   

\begin{equation} f_{\text{i}} = f_{\text{N${_{2}}$}}^{0}(\text{i}\%)/(\text{N$_{2}$}\%)\quad (\text{ml}/\text{min}) \end{equation} (1)

where $f_{\text{N}_{2}}^{0}$ is the flow rate of N₂ gas and i is CO or CO₂. At low temperature, CO₂ gas began to generate little by little. The production rates of CO₂ and CO gas increased over about 650°C and decreased after reaching at maximum. CO₂ gas decreased earlier than CO gas.

Table 1 Comparison of mass decrease with calculated mass decrease from gas composition of CO and CO₂.

Fig. 4

Production rate of CO and CO₂ gas by the carbothermic reduction of NiO ((a) for sample No. 3).

The microwave output began to vibrate violently from around 650°C when the reaction proceeded actively, as shown in Fig. 5. Temperature also oscillated.

Fig. 5

Temperature and microwave power at (a) 30°C/min, (b) 50°C/min and (c) 100°C/min.

4. Discussions

4.1 Accuracy of gas analysis

The mass of carbon and oxygen contained in CO and CO₂ gas in total produced gas was compared with the mass loss of sample, Δm.   

\begin{equation} \Delta m = (P_{\text{T}}/6\times 10^{7}RT_{r}) \int_{0}^{t_{f}}\{M_{\text{CO}}f_{\text{CO}} + M_{\text{CO${_{2}}$}}f_{\text{CO${_{2}}$}}\}dt\ \ (\text{g}) \end{equation} (2)

where T_r is room temperature (280 K), P_T is the atmospheric pressure, M_i is the molecular weight of i gas, R is the gas constant, t is reaction time (s), and t_f is total reaction time. The integration was performed by trapezoid approximation on Fig. 4. Table 1 shows the mass loss of samples and Δm which agree within the range of 86.7% to 103.5%.

4.2 Vibration of microwave output

As shown in Fig. 5, the microwave output vibrated violently with increasing the rate of temperature rise, and the vibration width increased from around 700°C at which the reaction started to proceed. This vibration is caused by the interference between incident and reflected waves from sample. As electromagnetic field tends to concentrate on the protrusions of particles and the electromagnetic properties changed locally in short time, the phase of reflected wave changes from that of incident wave. Therefore, the microwave output seemed to fluctuate.

By producing Ni, CO and CO₂ gas, the electromagnetic properties of sample changed. Furthermore, and electron in reactants was excited by microwave. Then, the vibration of microwave output became intenser with higher power of microwave.

4.3 Temperature

It was difficult to measure temperature in the local sites of sample, and the average temperature of sample surface was measured. As the reaction rate was determined from the average composition of CO and CO₂ in gas, the average temperature was available for the analysis of reaction.

Microwave is attenuated from the sample surface toward the inside. The penetration depth, δ, at which the microwave intensity becomes 1/e is expressed by the following equation under the assumption of σ²/ω²ε′² ≪ 1.   

\begin{equation} \delta \cong [\mu'/(2\varepsilon')]^{-1/2}\sigma^{-1} \end{equation} (3)

where ω is the angular velocity of microwave, ε′ the real part of permittivity, μ′ the real part of magnetic permeability, and σ the electrical conductivity.

For Gr powder with a relative bulk density of 0.4, ε′ = 20ε⁰ and μ′ = μ⁰ at room temperature.⁶⁾ ε⁰ and μ⁰ are the permittivity and the magnetic permeability in vacuum, respectively. Though the electrical conductivity of Gr crystals with the density of 2.3 g/cm³ is about 1 × 10⁴ Ω⁻¹m⁻¹ at room temperature, and 40 mass% of Gr powder dispersed in high-density polyethylene (HDPE) has the electrical conductivity of about 10⁻¹ Ω⁻¹m⁻¹.⁷⁾ In this case, δ = 17 cm calculated from eq. (3). In the present study, as the depth to the center of sample was 2 cm, the average temperature was uniform throughout sample.

4.4 Dominant elementary reactions

The carbothermic reduction of NiO is expressed by the following equations.   

\begin{equation} \text{NiO} + \text{CO}\to \text{Ni} + \text{CO$_{2}$} \end{equation} (4)

  

\begin{equation} \text{C} + \text{CO$_{2}$}\to \text{2CO} \end{equation} (5)

Equation (5) is the Boudouard reaction. Also, in the direct reaction with carbon   

\begin{equation} \text{NiO} + \text{C}\to \text{Ni} + \text{CO} \end{equation} (6)

  

\begin{equation} \text{NiO} + \text{(1/2) C}\to \text{Ni} + \text{(1/2) CO$_{2}$} \end{equation} (7)

There are 2 independent reactions determined by the phase rule.

The Gibbs energy change of each reaction, ΔG, is obtained from the partial pressure of CO and CO₂ gas and the standard Gibbs energy change of reaction.⁸⁾

Figure 6 shows ΔG from eq. (4) to eq. (7) with respect to reaction time. As ΔG < 0, any reaction proceeds to the right. The absolute value |ΔG| of eq. (5) is the smallest except for the initial stage of reaction. This indicates that the Boudouard reaction under microwave irradiation dominates the state of system, though the reduction of eq. (4) dominates under conventional radial heating.⁵⁾ In the initial stage of the reaction at low temperature, more CO₂ gas is generated than CO gas, and eq. (4) dominates the state.

Fig. 6

ΔG of elemental reactions in the carbothermic reduction of NiO.

4.5 Rate of enthalpy change of reaction

When the reactions of eq. (4) and eq. (5) are coupled at a ratio of 1:b in molar ratio, the overall reaction is expressed by the following equation.   

\begin{equation} \text{NiO} + \text{$b$C} \to \text{Ni} + \text{($2b-1$) CO} + \text{($1-b$) CO$_{2}$} \end{equation} (8)

b is given by the law of mass action and eq. (1).   

\begin{equation} b = (f_{\text{CO}} + f_{\text{CO${_{2}}$}})/(f_{\text{CO}} + 2f_{\text{CO${_{2}}$}}) \end{equation} (9)

The rate of enthalpy change of reaction for eq. (8) is obtained as   

\begin{equation} (d\Delta H/dt)_{t} = \Delta H^{0}(T)(\text{dn}_{\text{Ni}}/\text{d}t)_{t}\quad (\text{W}) \end{equation} (10)

The enthalpy change of reaction at temperature, T, is calculated from the standard enthalpy change and the heat capacity change of reactions of eq. (4) and eq. (5).   

\begin{align} (\text{d}n_{\text{Ni}}/dt)_{t} &= (\text{d}n_{\text{O}}/dt)_{t} \\ &= (P_{\text{T}}/6\times 10^{7}RT_{r})(f_{\text{CO}} + 2f_{\text{CO${_{2}}$}})\ \ (\text{mol/s}) \end{align} (11)

As shown in Fig. 7, the rate of enthalpy change of reaction has maximum of about 20 W near the maximum reaction rate.

Fig. 7

Rates of entropy production and enthalpy change of the carbothermic reduction of NiO.

4.6 Entropy production by chemical reactions

The entropy production⁹⁾ is caused from chemical reaction, diffusion, heat flow and momentum flow. The value of ΔG of the Boudouard reaction is close to zero, indicating that the partial pressure difference of CO and CO₂ gas between reaction surface and gas phase is small. The viscosity coefficient of gas is small. The average temperature in sample is nearly to uniform. Therefore, the entropy production dominates by chemical reaction.

Equation (4) is the reaction of oxygen removal from NiO, and eq. (5) is the reaction of carbon oxidation. The entropy production rate by the reactions is expressed by   

\begin{equation} T(\Delta_{i}S/dt)_{t} = \text{A}_{\text{O}}(\text{d}n_{\text{O}}/dt)_{\text{t}} + \text{A}_{\text{C}}(\text{d}n_{\text{C}}/dt)_{\text{t}} \end{equation} (12)

where (dn_O/dt)_t is expressed by eq. (11), and (dn_C/dt)_t is expressed by   

\begin{equation} (\text{d}n_{\text{C}}/dt)_{\text{t}} = (P_{\text{T}}/6\times 10^{7}RT_{r})(f_{\text{CO}} + f_{\text{CO${_{2}}$}})\quad (\text{mol/s}) \end{equation} (13)

A_O and A_C are the affinities of eq. (4) and eq. (5), respectively, and are expressed by Ao = −ΔG₄ and A_C = −ΔG₅. ΔG₄ and ΔG₅ are the Gibbs energy change of reactions of eq. (4) and eq. (5), respectively.

Figure 7 shows the uncompensated heat rate, T(Δ_iS/dt)_t. This value is positive, and the reactions of eq. (4) and eq. (5) are coupled. The value is almost same as the rate of enthalpy change of reaction. The energy generated by microwave absorption is consumed for the uncompensated heat and the enthalpy change of reaction.

4.7 Activation energy of reaction rate constant

4.7.1 Carbothermic reduction of NiO

Since the amount of carbon is larger than NiO, the reaction rate of the carbothermic reduction of NiO is expressed as   

\begin{equation} dn_{\text{Ni}}/dt = kn_{\text{NiO}}^{m} = S_{\text{NiO}}k(n_{\textit{Ni}}^{0} - n_{\textit{Ni}})^{\text{m}} \end{equation} (14)

where the reverse reaction is ignored. m is the reaction order (m ≥ 1). $n_{\text{Ni}}^{0}$ is the number of moles of Ni in NiO before reaction, and n_Ni is that of produced Ni. k is the reaction rate constant.   

\begin{equation} k = k^{0}\exp (-E/RT) \end{equation} (15)

E is the activation energy of reaction, and k⁰ is the frequency factor. Using the mole fraction of Ni, $x = n_{Ni}/n_{Ni}^{0}$ (0 ≤ x ≤ 1), and assuming that the reaction surface area of NiO is equal to the surface area of unreacted material, $S_{\text{NiO}} = S_{\text{NiO}}^{0}(1 - x)^{2/3}$ where $S_{\text{NiO}}^{0}$ is the surface area before reaction, eq. (14) can be represented as   

\begin{equation} dx/dt = {n_{\text{Ni}}^{0}}^{(\text{m} - 1)}(1 - x)^{\text{m} + 2/3}S_{\text{NiO}}^{0}k^{0}\exp(-E/RT) \end{equation} (16)

When the reaction proceeds under the constant temperature rise, the reaction rate reaches a maximum and then decays. Following the derivation of equation by Murray et al.,¹⁰⁾ the next equation is obtained under the assumption of 1 > 2RT_m/E   

\begin{equation} \frac{E\varphi}{RT_{m}{}^{2}} = \left(m + \frac{2}{3}\right){\text{n}_{\text{Ni}}^{0}}^{(m - 1)}\text{S}_{\text{NiO}}^{0}k^{0}e^{-\frac{E}{RT_{m}}} \end{equation} (17)

  

\begin{equation} d\ln (\varphi/T_{m}{}^{2})/dT_{m}{}^{-1} = -E/R \end{equation} (18)

T_m is the temperature at the maximum reaction rate. This equation holds regardless of reaction order and reaction surface area. Using eq. (18), the activation energy E is obtained. Table 2 shows T_m for each rate of temperature rise. Figure 8 plots the relationship of eq. (18). The activation energy of the reaction obtained from this slope is 141 kJ/mol. As RT_m is about 9 kJ/mol, 1 > 2RT_m/E is established.

Table 2 Temperature of T_m at the maximum reduction rate of the carbothermic reduction of NiO under a constant rate of temperature rise.

Fig. 8

Relation of ln(ϕ/T_m²) to 1/T_m for the reaction of NiO + bC → Ni + (2b − 1)CO + (1 − b)CO₂.

Using $\text{n}_{\textit{Ni}}^{0} = 0.0335$ mol and $S_{\text{NiO}}^{0} = 0.108$ m², k⁰ is 16.0 s⁻¹m⁻² for the first-order reaction and 299 s⁻¹mol⁻¹m⁻² for the second-order reaction.

4.7.2 Reduction reaction of NiO by CO gas and Boudouard reaction

Ignoring the reverse reactions of the reduction reaction of NiO according to eq. (4) and the Boudouard reaction according to eq. (5), and assuming that the reaction surface area is equal to the surface area of the unreacted product, the following rate equations are obtained respectively.   

\begin{equation} dn_{\text{O}}/dt = {n_{\text{O}}^{0}}^{-2/3}S_{\text{NiO}}^{0}p_{\text{CO}}(n_{\text{O}}^{0} - n_{\text{O}})^{\text{m} + 2/3}k_{4}^{0}\exp(-E_{\text{O}}/RT) \end{equation} (19)

  

\begin{equation} dn_{\text{C}}/dt = {n_{\text{C}}^{0}}^{-2/3}S_{\text{C}}^{0}p_{\text{CO${_{2}}$}}(n_{\text{C}}^{0} - n_{\text{C}})^{\text{m} + 2/3}k_{5}^{0}\exp(-E_{\text{C}}/RT) \end{equation} (20)

Where E_O and E_C are the activation energies of the reactions, $k_{5}^{0}$ and $k_{6}^{0}$ are the frequency factors of the reaction rate constants for eq. (4) and eq. (5), respectively. $S_{\text{NiO}}^{0}$ and $S_{\text{C}}^{0}$ are the initial surface areas of NiO and Gr, respectively. Taking the logarithm of both sides, the activation energies of E_O and E_C are obtained, respectively. $n_{\text{O}}^{0}$ and $n_{\text{C }}^{0}$ are the initial number of moles of NiO and Gr and are 0.0335 mol and 0.625 mol, respectively. n_O and n_C can be obtained from the integral with respect to time in Fig. 4 using the equation of state for ideal gas. Figure 9 shows the relationship for the first-order reaction, using the data between 680°C and 780°C at 30°C/min and 50°C/min.

Fig. 9

Relations of $\ln [(dn_{\text{i}}/dt)p_{\text{j}}^{ - 1}(n_{\text{i}}^{0} - n_{\text{i}})^{ - 5/3}n_{\text{i}}^{0}{}^{2/3}]$ to 1/T for the reactions of NiO + CO → Ni + CO₂ (i = O, j = CO) and C + CO₂ → 2CO (i = C, j = CO₂), respectively.

The activation energy is 115 kJ/mol for NiO reduction reaction by eq. (4) and 166 kJ/mol for the Boudouard reaction of eq. (5).

4.7.3 Effect of microwave irradiation to the activation energy of reaction

Jagtap et al.⁴⁾ measured the carbothermic reduction rate of NiO by mass change between 760°C and 900°C using conventional radiant heating in N₂ gas and obtained the activation energy of reaction of 207 kJ/mol. Sharma et al.⁵⁾ obtained the activation energy of reaction of 314 kJ/mol from the partial pressures of CO gas and CO₂ gas generated in the carbothermic reduction of NiO while drawing in vacuum between 900°C and 1000°C. Krasuk et al.³⁾ reduced NiO with CO gas and measured the mass change and obtained 194 kJ/mol as the activation energy of reaction between 566°C and 682°C.

The activation energy of the carbothermic reduction of NiO obtained in this study is 141 kJ/mol, 115 kJ/mol for the NiO reduction reaction by CO gas, and 166 kJ/mol for the Boudouard reaction. Obviously, the activation energy of reaction by microwave irradiation is smaller than conventional radiant heating.

The Gibbs energy change of reaction from the reactant to the activated one, ΔG^#, is equal to the activation energy, E. The reaction rate is proportional to the probability of creating an activated state, expressed as exp(ΔS^#/R). Assuming that the reactant and the activated one are in equilibrium, −TΔS^# = ΔG^# − X_m. Therefore, the following equation is obtained.   

\begin{equation} k = k^{0}\exp\{-(E - X_{\text{m}})/RT\} \end{equation} (21)

The generated energy, X_m, by absorbing microwave is accumulated in the reaction system. X_m becomes about 60 kJ/mol at the maximum reaction rate.

5. Conclusions

The carbothermic reduction of NiO was performed under a constant rate of temperature rise by microwave irradiation at 2.45 GHz. The reaction rate was obtained from CO and CO₂ partial pressure. The effect of microwave irradiation to the reaction is following,

1. (1)    The dominant reaction was the Boudouard reaction followed by NiO + CO → Ni + CO₂, differing from conventional radial heating.
2. (2)    The energy generated by microwave absorption was consumed by the uncompensated heat due to entropy production and the enthalpy change of reaction in the almost same amounts.
3. (3)    The activation energy of the carbothermic reduction of NiO was 141 kJ/mol, that of the NiO reduction by CO gas was 115 kJ/mol and that of the Boudouard reaction was 166 kJ/mol. The former two values were about 60 kJ/mol smaller than those by conventional radiant heating.

Acknowledgements

This work was supported by the Ritsumeikan Global Innovation Research Organization (R-GIRO), Ritsumeikan University and partly supported by JSPS KAKENHI (Grant Number 22K18431).

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