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Vol. 8. Issue 4.
Pages 3635-3643 (July - August 2019)
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Vol. 8. Issue 4.
Pages 3635-3643 (July - August 2019)
Original Article
DOI: 10.1016/j.jmrt.2019.06.001
Open Access
Possibilities of complex experimental study of thermophysical and thermodynamic properties of selected steels
Lenka Řeháčkováa,
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Corresponding author.
, Vlastimil Nováka, Bedřich Smetanaa, Dalibor Matýsekb, Petra Váňováa, Ľubomíra Drozdováa, Jana Dobrovskáa
a Faculty of Materials Science and Technology, VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic
b Faculty of Mining and Geology, VŠB-Technical University of Ostrava, 17. listopadu 15, 708 33 Ostrava-Poruba, Czech Republic
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Tables (3)
Table 1. Chemical composition of the steels (wt.%).
Table 2. Phase transition temperatures and heats of fusion of selected steels (wt.%).
Table 3. Linear dependencies of surface tension on temperature.
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In this paper, selected key thermophysical and thermodynamical properties of steels (three alloys based on Fe–C–Cr) such as solidus (TS) and liquidus (TL) temperatures, peritectic transformation temperatures (TP), heats of fusion (ΔHF), specific heat capacities(cP), surface tension (σ), and wettability expressed by the wetting angle (θ) of liquid steel on alumina substrate were experimentally determined in a high-temperature area up to the temperature of 1600°C. The effect of the temperature and the chemical composition of steel on these properties was investigated using 3D heat flux DSC (Differential Scanning Calorimetry) and a sessile drop method. The interaction of the steel samples with the alumina substrate was studied by SEM, EDX and XRD methods. To assess the influence of the major elements (carbon and chromium), the steels with different carbon and chromium content, which varied in the range of 0.077–0.381wt.% and 0.049–4.990wt.%, were chosen. It was shown that increasing carbon and chromium content led to a decrease in phase transformation temperatures and thermal capacities, as well as an increase in the heat of fusion, surface tension, and wetting angle. Furthermore, the rising temperature increases the thermal capacities and wetting angles. Whereas the surface tension followed the opposite trend.

Fe–C–Cr alloys
Surface properties
Phase transition temperatures
Heat of fusion
Heat capacity
Interface (liquid metal/solid ceramic phase)
Full Text

Iron-based alloys are of great practical importance, but due to their variability, there is not enough experimental thermophysical and thermodynamical data for particular metal systems [1]. Proper experimental data regarding solidus and liquidus temperatures, peritectic transformation temperatures, heats of fusion, specific heat capacities, surface tension, and wetting angle is needed for many real technological processes [2], e.g., steel refining, steel casting, solidification of steels, welding, etc. They play a crucial role in the whole steel process production in a liquid and semisolid phase, and also help to solve problems more accurately through simulation. Continuous improvement and optimization of the production processes are necessary for every steel production company to ensure competitiveness on the global market. The better control of the entire steel production cycle, from a selection of quality raw materials, through proper control of primary and secondary metallurgy processes to the optimum setting of casting and solidification conditions is necessary for a modern competitive steel making company. The knowledge of the process alone [2], and of the material under production [3], is a way of optimizing production processes.

Although the temperatures of the solidus, liquidus and other phase transitions were studied for many years, several gaps in the knowledge still exist concerning mainly the solidus temperatures [4]. These temperatures are usually determined by TA (Direct Thermal Analysis), DTA (Differential Thermal Analysis), and DSC (Differential Scanning Calorimetry). Besides the experimental approach, there are also different applications frequently involved (e.g., Thermo-Calc, DICTRA, FactSage, and JMatPro) to acquire phase transition temperatures. Despite this fact, it is not easy to find or calculate these data regarding Fe–C–Cr steels of a particular composition. Nevertheless, the phase transition temperatures were investigated in Refs. [5,6].

To determine heats of fusion, DSC and/or calorimeters equipped with precise 3D DSC sensors are commonly used [6]. Experimental data or systematic works are challenging to find. The scientific papers regarding this topic deal mainly with systems of a specific composition. For carbon steels, heats of fusion can be found in articles [1,7–9] where their values varied between 180 and 285Jg−1. Furthermore, in the paper [7] the values were of 160–200Jg−1 for Cr–Ni, super austenitic steels and duplex steels. The heat of fusion depends on chemical composition, as mentioned in papers [7–9]. On the basis of the findings, the carbon increases its values contrary to chromium, but further research needs to be performed in this regard.

Specific heat capacities (cP) and their dependence on temperature are applied when designing the processes where heat is released/absorbed, and heating/cooling plays a key role. This quantity is very often used as input data for the simulation of these processes. Information about experimental values of specific heat capacities can be found very seldom, principally, in the high-temperature region. There exist several experimental methods for cP determination, e.g., DSC [6], drop calorimetry [10], pulse heating [11] and laser flash techniques [12]. Experimental determination of heat capacities concerns, particularly solid phase and rarely liquid phase (melt). More frequently, this quantity can be obtained by theoretical calculations using appropriate applications like Thermo-Calc [13].

Another fundamental thermodynamic property of liquid metals and their alloys is surface tension, a quantity which is related to the fact that surface particles are mutually less firmly bound than the ones in bulk. This quantity becomes significant when the liquid steel is in contact with a solid phase during refining, welding and casting processes [14]. Its value determines the physical behavior of the melt on the one hand, and indicates the adsorption of surface-active agents (whose presence can significantly affect the processes at the phase interface) on the other. The sessile drop method is one of the most commonly used techniques for assessing the surface tension. As other contacting methods, it is affected by trace amounts of impurities presented on the ceramic plate, physical characteristics of the substrate surface, partial pressure of surface-active elements, interaction with a substrate, and by other effects [15]. Nevertheless, even though measurement difficulties are not rare, measured data are often more valid than those calculated by prediction models since they better characterize the processes occurring on the phase interface.

The surface tension decreases with the temperature for most of the pure metals [16]. In contrast, multicomponent alloys and steels possess different behavior at high temperatures. In such cases, during heating, the surface-active elements are desorbed from a surface monolayer into the bulk of a liquid metal causing a slight increase of surface tension. This phenomenon was described by McNallan for Fe–Cr–Ni steel with sulfur content [17]. As outlined, experiments concerning multicomponent systems at high temperatures have practical relevance. Among the elements which are mainly of interest are oxygen, carbon and chromium.

Oxygen is a strong surface-active element which decreases the values of surface tension. Controlling its activity is a crucial issue during experiments. Oxygen partial pressure should be treated under 10−10Pa [18]. Many authors have described the carbon effect on surface tension in Fe–C melts, but with a lack of consensus [19]. Chromium, as well as other elements in its group, also exhibits surface activity. Tret’yakova et al. investigated the dependence of surface tension on chromium content (up to 1wt.% Cr) in Fe–Cr–O systems. According to their study, the surface tension was closely related to the structure. The minimal surface tension was reached when the melt was most microheterogeneous [20]. The fact that chromium has a strong affinity to oxygen and facilitates its adsorption should be considered when assessing chromium effects [21]. Mukai summarized different scientific works concerning multicomponent systems and found notable inconsistencies between them caused by the presence of surface-active impurities, especially, oxygen in Fe alloys, and inaccurate experimental techniques [22].

2Experimental2.1Sample characterization

Three steel grades, i.e., alloys based on Fe–C–Cr (samples 1–3), were used for experimental measurements of phase transition temperatures, heats of fusion, specific heat capacity and surface properties. The chemical composition is shown in Table 1. It was determined using a glow discharge optical emission spectrometer GDA 750 (Spectruma Analytik GMBH), as well as the combustion analyzers ELTRA CS – 2000 and ELTRA ONH – 2000. The latter two served for determination of carbon, sulfur, oxygen and nitrogen. Cylindrical samples (diameter 5mm×height 8mm, weight 1.2g) were used for DSC measurements. As for the measurement of surface properties, samples were: diameter 5mm×height 5mm, and weight 0.7g. Before the experiments, samples were brushed, polished (to remove any surface oxides and metallic burrs), and then cleaned in acetone and subjected to the ultrasound.

Table 1.

Chemical composition of the steels (wt.%).

Sample  Cr  Mn  Si  Cu  Ni  Mo  Al 
0.077  0.049  0.635  0.201  0.021  0.008  0.064  0.027  0.003  0.026  0.004  0.002 
0.318  1.539  0.460  0.270  0.008  0.001  0.100  0.887  0.194  0.820  0.002  0.001 
0.381  4.990  0.380  0.940  0.008  0.001  0.090  0.264  1.160  0.025  0.0068  0.001 

Contents of other elements were as follows: <0.003 Ti, <0.003 Nb, <0.0005 B, the rest is iron.

For measurement of the surface properties, the high purity alumina plate (99.8wt.% Al2O3, <0.1wt.% CaO and <0.1wt.% SiO2) was used as a non-wettable substrate. Each Al2O3 plate was annealed at the temperature of 1150°C for 6h. Their surface was then cleaned by acetone immediately before the experiment. Consequently, the steel sample was set on the upper surface of the Al2O3 substrate.

2.2DSC measurements

DSC measurements were performed for obtaining temperatures of solidus (TS), peritectic transformation (TP) and liquidus (TL). The same experiments were used to determine heats of fusion (ΔHF) and specific heat capacities (cP). A Multi High Temperature Calorimeter (MHTC) equipped with a special 3D heat flux DSC sensor (B – type thermocouples) was used for experimental measurements. Temperature calibration was performed using standard high purity metals: Pd (5N) and Ni (5N). Palladium and nickel were analyzed by a heating rate of 5°Cmin−1. Furthermore, a correction of phase transition temperatures to the heating rate and sample mass was performed [23].

In total, three cycles of heating and cooling were realized. Samples were inserted into the alumina crucibles and covered with alumina lids. Then, they were put in the platinum crucibles and again closed by platinum lids before placing them on the 3D DSC sensor. The inner space of the furnace (space around sample) was flushed with He (6N), evacuated, and then filled with He. This procedure was realized 3 times. After the last evacuating and filling, the samples were heated up to 1300°C by 30°Cmin−1. Consequently, samples underwent three cycles. Each cycle consisted of 2h isothermal dwell at 1300°C, heating up to 1580°C by 5°Cmin−1 followed by 2h isothermal dwell and cooling down to 1300°C by 5°Cmin−1. The last cycle was capped by cooling to the room temperature at the rate of 30°Cmin−1. The same procedure as for the samples was applied to blank and standard (Pt 3N5). Measurements were performed by a continuous method in a dynamic atmosphere of He during the heating step within the temperature interval of 1300–1580°C. Each of the aforementioned quantities was evaluated from three experiments. Specific heat capacities of alloys were calculated according to the general methodology [24], and heats of fusion were evaluated as a difference of enthalpies (at the temperature of solidus and temperature of liquidus) obtained by recalculating the cP to enthalpy.

2.3Measurement of surface properties

Experimental measurement of surface properties (wetting angles, surface tension) was performed in a CLASIC resistance observation furnace [25] in the temperature interval from liquidus temperature of given steel sample, up to the temperature of 1600°C by a sessile drop method. This method is based on automatic recognition of the geometric shape of a drop, which is sessile on a non-wettable plate. Recognition of the drop shape is divided into two steps. Firstly, the approximate height of the drop is estimated. And secondly, the contour segments of the drop are found. The Laplace–Young equation is used for the evaluation of the image.

A prepared sample (steel/Al2O3 substrate) was settled at the center of the furnace near the thermocouple. The reaction chamber was sealed, evacuated (<8×10−3mbar) and then purified with argon gas (>99.9999%). After that, the system was heated to the temperature of 1600°C at the heating rate of 5°Cmin−1. The temperature was measured by the thermocouple Pt–13%Rh/Pt. The shape of the sessile drop was monitored by a CANON EOS 550D camera when the sample was melted. The images of the drop were recorded only during the heating. Also, the experiment was performed under an inert atmosphere of argon to avoid oxidation of the sample.

2.4SEM–EDX and XRD methods

The semiquantitative X-ray microanalysis of microstructural particles was carried out by a JEOL 6490LV scanning electron microscope (SEM) equipped with an INCA EDX analyser in the mode of backscattered electrons (BSE). The local chemical composition was determined by detecting the characteristic X-rays generated at the point of impact of the primary electron beam on the sample. The experiments were performed using these settings: thermo-emission cathode LaB6, voltage 20kV, resolution of 3.0nm, vacuum 2.5×10−6Pa for metal, and 25Pa (low vacuum) for ceramics samples.

A Quanta-650 FEG auto-emission electron microscope (Thermo Fisher Scientific/FEI) was used for the acquisition of high-resolution images. The measurement parameters were as follows: voltage 20kV, current 8–10nA, beam diameter 6μm and reduced vacuum with pressure in chamber 50Pa. The samples were measured without metal coverage.

The X-ray powder diffraction (XRD) measurements were conducted by a Bruker-AXS D8 Advance equipped with a silicon strip LynxEye position-sensitive detector under the following conditions: radiation CuKα/Ni filter, voltage 40kV, current 40mA, and a step by step mode of 0.014° 2Θ. Total time on the step was 25s, and angular extent was 5–80° 2Θ. The data were processed by the Bruker AXS Diffrac, Bruker EVA, and Bruker Topas software. The PDF-2 database (International Center for Diffraction Data) was used for phase identification, which was carried out by the diffraction pattern modeling using the Rietveld method. The samples were measured on untreated surfaces through their central parts.

3Results and discussion3.1Phase transition temperatures, heats of fusion and specific heat capacities

Phase transition temperatures were obtained from temperature dependencies of specific heat capacities (Fig. 1). Numerical integration of this dependence according to Kirchhoff's equation gives enthalpy as a function of temperature from which heats of fusions were evaluated. Corrected phase transition temperatures are listed in Table 2: TS (solidus temperature), TP (temperature of peritectic transformation), TL (liquidus temperature); DSC means obtained by DSC measurements, and DTA means obtained by DTA measurements [6]; ΔHF is enthalpy change during fusion.

Fig. 1.

DSC curves of analyzed samples (cP=f(T)) with marked uncorrected phase transition temperatures (Tγ-δ,S start of gamma to delta transformation, Tγ-δ,E end of gamma to delta transformation, TS, TP, TL).

Table 2.

Phase transition temperatures and heats of fusion of selected steels (wt.%).

Sample  TS,DSC (°C)  TS,DTA (°C)  TP,DSC (°C)  TP,DTA (°C)  TL,DSC (°C)  TL,DTA (°C)  ΔHF (J/g) 
1492±1492±–  –  1526±1523±277±

The solidus temperatures were taken by two methods, DSC and DTA. These temperatures decreased, with rising content of carbon and chromium. Their values are presented in Table 2. The differences between the results determined by the given methods were not significant for samples 1 and 2. The higher differences were observed for sample 3. However, it is not an exception at these measurements [5,26].

The temperatures of peritectic transformation were also obtained by DSC and DTA method [4,6]. In the first case, they were of 1473°C and 1441°C for sample 2 and 3, respectively. In the second case, they were slightly lower, at 1471°C and 1438°C. Concerning sample 1, a peritectic transformation was not observed and, therefore, the corresponding temperature was not evaluated (Fig. 1). In the case of experimentally determined temperatures, the temperatures of peritectic transformation followed the declining trend with rising content of carbon and chromium.

The liquidus temperatures, measured by the DSC/DTA method (Table 2), were in relatively good agreement with a data published formerly [5]. The temperatures were influenced by carbon and chromium in terms of their lowering [27]. The comparison of data regarding the DSC and DTA methods clearly shows that temperatures were close to each other.

Values of heats of fusion are presented in Table 2. These values are close to the upper interval limit mentioned in Ref. [9]. For low carbon steel (sample 1), the obtained value was 277Jg−1. This value is about 8 or 9Jg−1 lower than those obtained for sample 2 and 3. Therefore, it seems that the heat of fusion depends on carbon (carbon generally has the highest influence on properties of Fe based alloys [27], mainly on a shift of phase transition temperatures) and chromium content. Other elements, such as silicon and molybdenum, can also play an important role. According to Ref. [4], carbon increases the heat of fusion, and chromium has the opposite effect. Therefore, a more significant shift was observed between sample 1 and 2 where the difference of carbon content was higher and chromium content was lower, contrary to these differences between samples 2 and 3. It can be concluded that chromium does not have such a significant impact on the heat of fusion, like carbon. Taking into account that the samples also contain other elements, mainly Si and Mo, whose influence is not apparent, further systematic research should be performed to approve the assumptions mentioned above.

Temperature dependencies of specific heat capacities are presented in Fig. 1. The slope of heat capacity temperature dependence for sample 1 is steeper compared to samples 2 and 3, whose course is almost constant. From Fig. 1, it is also apparent that the largest values are reached for sample 1, and lowest for sample 2. Therefore, specific heat capacities were affected by chemical composition. It can be concluded that with increasing element content, the experimental values were decreasing. Since the multicomponent system was analyzed, it is difficult to assess which element had the largest effect. It is very likely that the most substantial influence on a shift of obtained experimental values comes from carbon and chromium. Nevertheless, other elements such as silicon, nickel, molybdenum and aluminum, whose content differed in investigated samples, could also play an important role. Fig. 2 illustrates the temperature dependencies of heat capacities in the melt. Measured data were extrapolated from liquidus temperature up to 1600°C.

Fig. 2.

Linear approximation of temperature dependencies of heat capacities.

3.2Surface properties

Fig. 3 shows the surface tension data of analyzed steel samples as a function of temperature. These data were acquired in the temperature interval from liquidus temperature up to the temperature of 1600°C. As can be seen in the figure, the temperature coefficient of the surface tension is negative, thus the surface tension decreases with increasing temperature. The linear relations listed in Table 3 were adjusted to the data according to Eq. (1):

where σref is the surface tension at reference temperature Tref and /dT is the temperature coefficient of the surface tension.

Fig. 3.

Temperature dependencies of the surface tension of investigated steels.

Table 3.

Linear dependencies of surface tension on temperature.

Sample  Tref (°C)  σref (mNm−1/dT (mNm−1°C−1ΔT (°C) 
1536  1417  2.62×10−1  1536–1600 
1500  1665  1.66×10−1  1500–1600 
1478  1738  3.66×10−1  1478–1600 

Furthermore, this figure shows that increasing content of carbon and chromium acted positively on the steel surface tension, as reported by Lee and Morita [28]. The surface tension of investigated steel samples can be affected by the presence of surface-active elements, such as oxygen and sulfur, which were present in the steels before the experiment. According to Divakar et al. [29], carbon itself does not influence the surface tension, but reduces oxygen activity in the melt which causes an increase in the surface tension. Chromium has a similar effect to carbon. It lowers the oxygen activity and consequently increases the surface tension. Besides, in a multicomponent alloy, alloying elements that affect surface tension are segregated to the surface. Chromium belongs among elements which tend to segregate onto an alloy surface. Nonetheless, since the magnitudes of energy changes, accompanied by the segregation, are relatively smaller than in the case of strongly surface-active elements (like sulfur and oxygen), its effect is lesser [30].

Fig. 4 shows wetting angles dependence on temperature in the same temperature interval as mentioned above.

Fig. 4.

Temperature dependencies of wetting angles of investigated steels on the alumina substrate.


From Fig. 4 it is apparent that higher chromium content increases the wetting angles, unlike sample 2 with a higher amount of aluminum (0.820wt.%). SEM analysis indicated that Al2O3 was locally formed on the sphere surface at the contact with the alumina substrate (Figs. 6c and 7). It probably influenced the value of wetting angles. Fig. 5 compares the measured contact angles with values reported by different investigators. The angles were slightly higher than that for liquid iron in contact with alumina [31,32], and lower than that published by Mukai et al. [22] for Fe–16mass%Cr–O.

Fig. 5.

Variation of the contact angle with oxygen activity at 1550°C.

Adapted from [22].

The interaction of steel samples with the alumina substrate was investigated using SEM, EDX and XRD analysis. A SEM image of a metal droplet (sample 2) after the experiment can be seen in Fig. 6 where individual analyzed areas are marked. Fig. 7 shows a detailed view of the contact between the metal droplet and the alumina substrate. EDX observation was carried out to clarify the surface distribution of selected elements. Based on EDX analysis, it can be stated that the oxidation layer covered none of the metal droplet samples and the dissolution of the aluminum in the melt did not occur. There was a slight decline of chromium content for all samples, which is most notable at sample 3 (up to approximately 1wt.%). All samples showed a moderate increase in silicon content.

Fig. 6.

SEM image of the metal droplet (sample 2), a–c analyzed regions.

Fig. 7.

Enlarged detail of Fig. 6c representing contact between droplet and alumina substrate.


Fig. 8A–I displays SEM images of the alumina substrate after the experiment. Analyzed surface areas and the points of the individual analyses are shown in Fig. 8A, D and G. The surface under the liquid metal droplet is in Fig. 8B, E, H, and the area around it in Fig. 8C, F and I. EDX analysis for sample 1 confirmed enrichment by iron (approximately 0.5wt.%) in the area under the metal droplet and its immediate vicinity (Fig. 8B and C). In the area under the melt, an increased amount of calcium, approximately around 3wt.%, was detected for sample 1. X-ray diffraction (Fig. 9) confirmed the occurrence of high-temperature mineral hibonite (theoretically CaAl12O19) in the surface layer under the droplet (Fig. 8B). The amount of calcium was also increased in samples 2 and 3 (Fig. 8E and H) in the same area (sample 2 (up to 5wt.%), sample 3 (up to 8wt.%)). In the case of two last-mentioned samples, chromium was found in the surface layer close to the droplet, probably in trivalent Cr(III) form. It is to be assumed that aluminum can be substituted for the chromium in corundum due to the similar atomic radius and is present there as chromium oxide. Furthermore, the Cr(III) ion possesses two strong adsorption bands in the visible part of the spectrum which explains the red color [33].

Fig. 8.

SEM images of the alumina substrate after the experiment for sample 1 (A–C), sample 2 (D–F) and sample 3 (G–I). SEM image of the alumina substrate after the experiment at low magnification (40×), the area under droplet, and the area in its vicinity are in the row from left to right.

Fig. 9.

XRD pattern of alumina substrate surface containing hibonite on corundum matrix (H, hibonite and C, corundum).


The results obtained by the experimental research can be summarized as follows:

  • The original experimental values of phase transition temperatures for steels of a particular composition were obtained by 3D DSC analysis, and were then compared with data presented earlier (obtained by DTA analysis) achieving proper compliance. The most significant difference was observed for solidus temperature. Phase transition temperatures had a declining trend depending on the rising content of alloying elements. The most substantial impact, in this regard, can be attributed to the carbon and chromium.

  • Values of heats of fusion depended on a change in steel chemical composition, whereas a stronger effect on the increasing tendency of these values has carbon rather than chromium.

  • Specific heat capacity values are also dependent on the change in the chemical composition. Nevertheless, a clear statement cannot be taken for examined samples, and further experiments have to be conducted to confirm the assumption that specific heat capacity decreases with rising carbon and chromium content. Furthermore, they increased with temperature very slightly. In the case of sample 2 and 3, they were almost constant in the investigated temperature interval.

  • The surface tension increased with increasing content of carbon and chromium for all investigated steels. The positive effect of carbon and chromium on the surface tension was probably influenced by the presence of surface-active elements – oxygen and sulfur. Carbon and chromium decreased oxygen activity and consequently increased surface tension. The surface tension decreased with rising temperature.

  • The contact angle of liquid steel samples with alumina substrate increased with increasing chromium and carbon content. The wetting angle decreased markedly with the increasing content of sulfur. The wettability of alumina by investigated steels increased slightly with increasing temperature.

  • The interaction of the melt with the alumina substrate was affirmed from the results of SEM, EDX, and X-ray diffraction analysis. Nevertheless, there was no formation of an oxidation layer on the surface of the metal droplet and aluminum dissolution in the melt during experiments. The hibonite was formed in the alumina substrate at the point under the metal droplet. Furthermore, it can be assumed that isomorphic substitution of Cr(III) for Al(III) occurred in the corundum surface layer near the metal droplet at samples 2 (1.539wt.% Cr) and 3 (4.990wt.% Cr). The chromium was present there as Cr2O3.

Conflicts of interest

The authors declare no conflicts of interest.


This paper was created within the frame of the project GACR reg. number 17-18668S, the project of the Institute of Clean Technologies for Mining and Utilization of Raw Materials for Energy Use Sustainability Program, reg. no. LO1406 financed by the Ministry of Education, Youth and Sports of the Czech Republic and the student projects SGS(SP2018/93 and SP2019/90).

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