Joint Reduction of NiO/WO 3 Pair and NiWO 4 by Mg + C Combined Reducer at High Heating Rates

: Functional features of Ni-W composite materials combined with successful performance enabled a breakthrough in their broad application. To disclose the formation pathway of Ni-W composite materials at extreme conditions of combustion synthesis in the NiO-WO 3 -Mg-C and NiWO 4 -Mg-C systems for the optimization of the synthesis procedure, the process was modeled under programmed linear heating conditions by thermal analysis methods. The reduction kinetics of tungsten and nickel oxides mixture and nickel tungstate by Mg + C combined reducer at non-isothermal conditions was studied at high heating rates (100–1200 ◦ C min − 1 ) by high-speed temperature scanner techniques. It was shown that when moving from low heating to high heating rates, the mechanism of both the magnesiothermic and magnesio-carbothermic reductions of the initial mixtures changes; that is, the transition from a solid-solid scheme to a solid-liquid scheme is observed. The strong inﬂuence of the heating rate on the reduction degree and kinetic param-eters of the systems under study was afﬁrmed. The simultaneous utilization of magnesium and carbon as reducers allowed the lowering of the starting and maximum temperatures of reduction processes, as evidenced by the synergetic effect at the utilization of a combined reducer. The effective values of activation energy ( E a ) for the reactions proceeding in the mixtures NiO + WO 3 + 4Mg, NiO + WO 3 + 2.5Mg + 1.5C, NiWO 4 + 4Mg and NiWO 4 + 2Mg + 2C were estimated by Kissinger isoconversional method and were 146 ± 10, 141 ± 10, 216 ± 15 and 148 ± 15 kJ mol − 1 , respectively. (W 2 C). The latter was not observed at the solely carbothermic reduction processes of oxides mixture and nickel tungstate. Another distinct feature of the utilization of (Mg + C) combined reducer, is the reduction of NiWO 4 after decomposition (B point, 830 ◦ C, Figures 3b and 4), in contrast to the separate utilization of Mg or C reducers.


Introduction
Nickel-tungsten composites (Ni-W) are considered useful for a vast number of industrial applications owing to their enhanced mechanical, tribological, magnetic, electrical and corrosion properties [1][2][3]. Their functional features allow the broad application of Ni-W as substrates for high-temperature superconductors, counter-balance weights, medical radiation shields, kinetic-energy penetrators, barrier layers or capping layers in micro electro mechanical systems (MEMSs) and as catalysts for hydrogen evolution from alkaline solutions [4][5][6]. These composites are recommended to protect and extend the service life of turbine blades operating at high temperature and high erosion. Electrodeposition (ED) [7], mechanical alloying (MA) [8], hydrogen reduction [9], sintering [10,11] and thermo-mechanical processes [12] are the most common processing routes for nickeltungsten composites, compacts and coatings. Recent trends illustrate the demand for new manufacturing technologies for the in situ production of a more finely dispersed and uniform composite powder for the preparation of compact specimens of improved sinterability operating at high temperature and erosion environments. Energy saving self-propagating high-temperature synthesis (SHS), known also as combustion synthesis practical interest for combustion synthesis of Ni-W composites/alloys with a finer and more homogeneous microstructure. Moreover, the considerable advantages of using nickel tungstate instead of the mixture of metal oxides for the synthesis of W-Ni composite powder has already been reported [22], contributing to enhanced chemical homogeneity of the final product, thanks to the presence of both metals in the same crystal structure. From this point of view, NiWO 4 is of particular interest with an anticipated decrease in the synthesis temperature, production of a more finely dispersed and uniform composite powder. Both of these factors, together with controlled thermal mode of SHS reaction, are of paramount importance for the preparation of compact specimens of reduced porosity.
A calcination method was utilized for the preparation of nickel tungstate from NiO and WO 3 powders' mixture (1:1 molar ratio) in air at 850 • C for 6.5 h: dark yellow product represents NiWO 4 . Figure S1a in the Supplementary Materials represents the XRD pattern of the prepared material. The SEM image of agglomerated NiWO 4 demonstrates welldefined grain boundaries with an average particle size of 5 µm ( Figure S1b).
The HSTS setup was utilized for the kinetic investigations of the NiO-WO 3 -Mg-C and NiWO 4 -Mg-C precursor mixtures under the programmed linear heating rates, up to 1200 • C min −1 and temperatures up to 1300 • C, which are closer to heating rates and temperatures in the combustion wave at the synthesis of alloys [17][18][19].
Note that HSTS provides the highest heating rates and involves the widest range of heating rates in existing thermal analysis devices so far. To explore the influence of heating rates and the role of each reducing agent, the mixture of raw materials (20-70 mg) was homogenized in a ceramic mortar (15 min) and placed into the central part of metallic envelope made from nickel foil (thickness of the foil is 0.1 mm), and a chromel-alumel K-type thermocouple, spot-welded directly to the foil in the center of the powder location. Measurements were conducted at 0.1 MPa argon (Ar, 99.8% purity, less than 0.1% O 2 ) pressure. The heating rate was programmed to be 100, 150, 300, 600 and1200 • C min −1 . The foil heater is heated (T max = 1300 • C) directly by the passing of an electric current with the desired temperature-time schedule provided by PC-assisted controller. The inert experiment provides linear temperature time history, which defines the heating rate and coincides with the reactive T profile in the regions when the reaction does not occur. The deviation of the reactive profile from the inert one gives information about exothermic or endothermic reactions. The reaction onset temperature (T o ), the maximum peak temperature observed during self-heating (T max ) and the temperature prescribed by linear heating, where the maximum exothermic effect is observed (T*), are determined from the heating curves. The HSTS setup allows the interruption of the process by automatically switching off the electric current at different characteristic stages, but also the continuous registration of the cooling curve by the thermocouple placed in the sample. At that point, extremely fast cooling (up to 12,000 • C min −1 ) takes place, which practically excludes further interaction during the cooling process.
The phase composition of the intermediates and final products was examined by XRD equipment (XRD; D5005, Bruker, Billerica, MA, USA) using CuKα1 radiation (λ = 1.5406 Å) with a step of 0.02 • (2θ) and a count time of 0.4 s. To identify the products from the XRD spectra, the data were processed using the JCPDS-ICDD database. Morphologies and microstructures of the samples were examined by Prisma E scanning electron microscope (SEM, Thermo Fisher Scientific, Hillsboro, OR, USA) at an accelerating voltage of 10 kV.
Kissinger's isoconversional method [31] was used to calculate the effective activation energies for the systems under study, based on the principle of temperature shift corre- sponding to the maximum advance in the heating curve at a constant heating rate. The acquired expression for the determination of the activation energy has the following form: where A is a is the pre-exponential factor, E is the effective activation energy of the process, (kJ mol −1 ), β is the heating rate (K min −1 ), T* is the reduction temperature on the inert temperature profile corresponding to the maximum advance in the reactive heating curve (K) and R is the universal gas constant (8.31 J mol −1 K −1 ). Gibbs free energies of the reactions under study were calculated by using the HSC-5 software package (Version 5, Pori, Finland).
The processes in these mixtures were interrupted at different characteristic temperatures (Figure 1a,b) and the phase composition of the quenched samples was analyzed. The intermediates were identified, the sequence of reactions was found out with the aim to disclose the reduction mechanism. The possibility of simultaneous reduction of nickel and tungsten oxides ( Figure S2a) and the decomposition of nickel tungstate during/before the reduction processes ( Figure S2b) were examined. No interaction was observed before and during the Mg melting (A point, 700 °C, Figure 1a), while the sample quenched after the exothermic peak (B point, 880 °C, Figure 1a) contained a reduced tungsten, an intermetallic compound of Ni17W3 composition, as well as MgO along with initial oxides. This circumstance shows that the simultaneous reduction of both oxides emerged in one exothermic peak. The sample cooled at 1000 °C (C point, 1000 °C, Figure 1a) contained partially reduced W (WO2.7), which was completely reduced at 1300 °C (D point, 1300 °C, Figure 1a).
On the other hand, XRD analysis results showed that complete magnesiothermic reduction of NiWO4 already takes place at 850 °C (B point, 850 °C, Figure S2b), with the formation of tungsten and Ni17W3 at about 450 °C below the reduction temperature of the mixture (NiO + WO3). It can be assumed that, in the case of NiWO4, W and Ni are in more favorable conditions for joint reduction, being in the same crystal structure. However, in both cases, the reduced material was tungsten and intermetallic compound of Ni17W3 composition. It is worthy to note also, that the thermal decomposition of nickel tungsate into oxides was not observed before the magnesiothermic reduction.
It has been reported [30], that at low heating rates (DTA/TG studies, β = 2.5-20 °C min −1 ) the joint reduction of the both oxides by magnesium began with the NiO + Mg reaction before the magnesium melting, with a solid + solid interaction scheme, and afterwards the reduction of tungsten oxide took place followed by the formation of magnesium tungstate. However, it was not possible to achieve complete joint reduction of either oxides or NiWO4 salt at low heating rates and at a temperature below 1000 °C.
On the other hand, according to [33], only a partial reduction of nickel oxide by Mg was possible at temperatures up to 1200 °C at heating rate β = 300 °C min −1 . Therefore, the complete magnesiothermic reduction of the both metals at 1300 °C becomes possible due to the combined processing of nickel and tungsten oxides.
Moreover, for both systems the exothermic interactions (at heating rate 300 • C min −1 ) are initiated after the magnesium melting (650 • C) by a solid + liquid mechanism (T m (WO 3 The maximum temperature deviations occurring at 734 • C and 759 • C correspond to the single-stage magnesiothermic reduction of oxides and NiWO 4 , respectively. The processes in these mixtures were interrupted at different characteristic temperatures (Figure 1a,b) and the phase composition of the quenched samples was analyzed. The intermediates were identified, the sequence of reactions was found out with the aim to disclose the reduction mechanism. The possibility of simultaneous reduction of nickel and tungsten oxides ( Figure S2a) and the decomposition of nickel tungstate during/before the reduction processes ( Figure S2b) were examined. No interaction was observed before and during the Mg melting (A point, 700 • C, Figure 1a), while the sample quenched after the exothermic peak (B point, 880 • C, Figure 1a) contained a reduced tungsten, an intermetallic compound of Ni 17 W 3 composition, as well as MgO along with initial oxides. This circumstance shows that the simultaneous reduction of both oxides emerged in one exothermic peak. The sample cooled at 1000 • C (C point, 1000 • C, Figure 1a) contained partially reduced W (WO 2.7 ), which was completely reduced at 1300 • C (D point, 1300 • C, Figure 1a).
On the other hand, XRD analysis results showed that complete magnesiothermic reduction of NiWO 4 already takes place at 850 • C (B point, 850 • C, Figure S2b), with the formation of tungsten and Ni 17 W 3 at about 450 • C below the reduction temperature of the mixture (NiO + WO 3 ). It can be assumed that, in the case of NiWO 4 , W and Ni are in more favorable conditions for joint reduction, being in the same crystal structure. However, in both cases, the reduced material was tungsten and intermetallic compound of Ni 17 W 3 composition. It is worthy to note also, that the thermal decomposition of nickel tungsate into oxides was not observed before the magnesiothermic reduction.
It has been reported [30], that at low heating rates (DTA/TG studies, β = 2.5-20 • C min −1 ) the joint reduction of the both oxides by magnesium began with the NiO + Mg reaction before the magnesium melting, with a solid + solid interaction scheme, and afterwards the reduction of tungsten oxide took place followed by the formation of magnesium tungstate. However, it was not possible to achieve complete joint reduction of either oxides or NiWO 4 salt at low heating rates and at a temperature below 1000 • C.
On the other hand, according to [33], only a partial reduction of nickel oxide by Mg was possible at temperatures up to 1200 • C at heating rate β = 300 • C min −1 . Therefore, the complete magnesiothermic reduction of the both metals at 1300 • C becomes possible due to the combined processing of nickel and tungsten oxides.

NiO-WO 3 -C and NiWO 4 -C Systems
The heating curves for the NiO + WO 3  XRD examinations of quenched intermediates were performed at characteristic temperatures ( Figure S3a,b). The carbothermic reduction process of nickel and tungsten oxides mixture was interrupted at the temperatures of A-850 °C, B-1000 °C, C-1080 °C, D-1150 °C and E-1300 °C. According to the XRD analysis results, the reduction begins at 1000 °C before the endothermic domain starts (Figure 2a). Interruptions for the carbothermic reduction of NiWO4 were performed at A-1050 °C, B-1100 °C, C-1200 °C and D-1260 °C, demonstrating direct reduction onset of NiWO4 at 1100 °C (by 100 °C higher compared to the reduction of the oxides mixture) without thermal decomposition (Figure 2b). Note that in contrast to the mixture (NiO + WO3), the reduction of NiWO4 proceeded completely. In contrast to the magnesiothermic reduction of the NiO + WO3 mixture, the carbothermic reduction proceeded partially at the studied temperature interval (up to 1300 °C): carbon reduced NiO up to Ni, while WO3 was endothermically reduced over WO2.7 up to WO2 (Figure 2). According to recent research carried out by our research group [33], the carbothermic reduction of nickel oxide began at 950 °C, and by 1030 °C a complete reduction had already been achieved (β = 300 °C min −1 ). At low heating rate region (β = 2.5-20 °C min −1 ), the carbothermic reduction of nickel oxide occurs with two sequential endothermic stages noticeable from the DTA, TG and DTG (Derivative Thermogravimetric) curves at 780-900 and 905-985 °C temperature ranges [30]. Therefore, with the increase of the heating rate, the conversion degree of NiO increases. However, the complete reduction was not detected in the studied temperature range (up to 1000 °C). According to [29], the carbothermic reduction of WO3 starts at 500 °C, but complete reduction was not registered at the given temperature (Tmax = 1000 °C) under identical conditions. At low heating rates in the ternary NiO + WO3 + 4 C mixture, the reduction process started with NiO and continued with WO3 reduction leading to NiWO4 formation at higher temperatures (960 °C) [29]. XRD examinations of quenched intermediates were performed at characteristic temperatures ( Figure S3a,b). The carbothermic reduction process of nickel and tungsten oxides mixture was interrupted at the temperatures of A-850 • C, B-1000 • C, C-1080 • C, D-1150 • C and E-1300 • C. According to the XRD analysis results, the reduction begins at 1000 • C before the endothermic domain starts (Figure 2a). Interruptions for the carbothermic reduction of NiWO 4 were performed at A-1050 • C, B-1100 • C, C-1200 • C and D-1260 • C, demonstrating direct reduction onset of NiWO 4 at 1100 • C (by 100 • C higher compared to the reduction of the oxides mixture) without thermal decomposition (Figure 2b). Note that in contrast to the mixture (NiO + WO 3 ), the reduction of NiWO 4 proceeded completely. In contrast to the magnesiothermic reduction of the NiO + WO 3 mixture, the carbothermic reduction proceeded partially at the studied temperature interval (up to 1300 • C): carbon reduced NiO up to Ni, while WO 3 was endothermically reduced over WO 2.7 up to WO 2 ( Figure 2).
According to recent research carried out by our research group [33], the carbothermic reduction of nickel oxide began at 950 • C, and by 1030 • C a complete reduction had already been achieved (β = 300 • C min −1 ). At low heating rate region (β = 2.5-20 • C min −1 ), the carbothermic reduction of nickel oxide occurs with two sequential endothermic stages noticeable from the DTA, TG and DTG (Derivative Thermogravimetric) curves at 780-900 and 905-985 • C temperature ranges [30]. Therefore, with the increase of the heating rate, the conversion degree of NiO increases. However, the complete reduction was not detected in the studied temperature range (up to 1000 • C). According to [29], the carbothermic reduction of WO 3 starts at 500 • C, but complete reduction was not registered at the given temperature (T max = 1000 • C) under identical conditions. At low heating rates in the ternary NiO + WO 3 + 4 C mixture, the reduction process started with NiO and continued with WO 3 reduction leading to NiWO 4 formation at higher temperatures (960 • C) [29].

NiO-WO 3 -Mg-C and NiWO 4 -Mg-C Systems
The heating curves for the reduction processes of the mixture (NiO + WO 3   To clarify the sequence of oxides' reduction and the role of reducers in each stage, the process was interrupted at different characteristic temperatures (NiO + WO3 + 2.5Mg + 1.5C; A-725 °C, B-800 °C, C-1060 °C and D-1300 °C / NiWO4 + 2Mg + 2C; A-720 °C, B-830 °C and C-1000 °C) and cooled samples were examined by XRD analysis (Figure 4). It was revealed that complete reduction of NiWO4 had already taken place at 1000 °C, while in the case of oxides mixture, the complete reduction of WO3 was not achieved at the studied temperature range (1300 °C) (Figures 3 and 4) at 300 °C·min −1 . Note that the sample quenched immediately after the exothermic peak contained tungsten carbide (W2C). The latter was not observed at the solely carbothermic reduction processes of oxides mixture and nickel tungstate. Another distinct feature of the utilization of (Mg + C) combined reducer, is the reduction of NiWO4 after decomposition (B point, 830 °C, Figures  3b and 4), in contrast to the separate utilization of Mg or C reducers.  To clarify the sequence of oxides' reduction and the role of reducers in each stage, the process was interrupted at different characteristic temperatures (NiO + WO 3 + 2.5Mg + 1.5C; A-725 • C, B-800 • C, C-1060 • C and D-1300 • C / NiWO 4 + 2Mg + 2C; A-720 • C, B-830 • C and C-1000 • C) and cooled samples were examined by XRD analysis (Figure 4). It was revealed that complete reduction of NiWO 4 had already taken place at 1000 • C, while in the case of oxides mixture, the complete reduction of WO 3 was not achieved at the studied temperature range (1300 • C) (Figures 3 and 4) at 300 • C min −1 . Note that the sample quenched immediately after the exothermic peak contained tungsten carbide (W 2 C). The latter was not observed at the solely carbothermic reduction processes of oxides mixture and nickel tungstate. Another distinct feature of the utilization of (Mg + C) combined reducer, is the reduction of NiWO 4 after decomposition (B point, 830 • C, Figures 3b and 4), in contrast to the separate utilization of Mg or C reducers.

NiO-WO3-Mg-C and NiWO4-Mg-C Systems
The heating curves for the reduction processes of the mixture (NiO + WO3) and (Figure 3a) NiWO4 (Figure 3b) by combined (Mg + C) reducer at β = 300 °C min −1 are depicted in Figure 3. Strongly peaked exothermic stages correspond to the magnesiothermic reduction of nickel and tungsten oxides (Figure 3a) and nickel tungstate (Figure 3b). The maximum shifts for the mixture of oxides and salt were observed at very close temperatures, 712 °C ( Figure 3a) and 728 °C (Figure 3b), respectively. To clarify the sequence of oxides' reduction and the role of reducers in each stage, the process was interrupted at different characteristic temperatures (NiO + WO3 + 2.5Mg + 1.5C; A-725 °C, B-800 °C, C-1060 °C and D-1300 °C / NiWO4 + 2Mg + 2C; A-720 °C, B-830 °C and C-1000 °C) and cooled samples were examined by XRD analysis (Figure 4). It was revealed that complete reduction of NiWO4 had already taken place at 1000 °C, while in the case of oxides mixture, the complete reduction of WO3 was not achieved at the studied temperature range (1300 °C) (Figures 3 and 4) at 300 °C·min −1 . Note that the sample quenched immediately after the exothermic peak contained tungsten carbide (W2C). The latter was not observed at the solely carbothermic reduction processes of oxides mixture and nickel tungstate. Another distinct feature of the utilization of (Mg + C) combined reducer, is the reduction of NiWO4 after decomposition (B point, 830 °C, Figures  3b and 4), in contrast to the separate utilization of Mg or C reducers. By combining the results obtained for the mixture of oxides and NiWO 4 , it can be assumed that the reduction reactions of NiWO 4 by Mg and (Mg + C) combined reducer started earlier and that the complete reduction was achieved at comparatively lower temperatures. In addition, the magnesio-carbothermic reduction reactions of nickel and tungsten oxides and nickel tungstate began by~20 and 30 • C earlier than magnesiothermic ones, and about~300 and 370 • C earlier than carbothermic processes, evidencing the synergetic effect at utilization of combined reducer in the ternary and quaternary mixtures.

2θ/° 2θ/°
At low heating rates (β = 20 • C min −1 , DTA/TG studies), the reduction process in the NiO + WO 3 + Mg + 2C mixture started by Mg reduction of nickel oxide (T max = 615 • C; solid + solid mechanism), at first, and then of tungsten oxide (T max = 660 • C; solid + liquid mechanism). Later, the reduction process was continued by carbon (DTG min = 927 • C). Note that at higher temperatures (T > 927 • C) the MgWO 4 formation took place by the interaction of remaining (non-reacted) WO 3 and obtained MgO [30].
The heating rate has a decisive effect not only on the interaction pathway, but also on the reduction degree. XRD analysis of the products of the NiO + WO 3 + 2.5Mg + 1.5C mixture treated at 100 • C min −1 and higher (300-1200 • C min −1 ) heating rates revealed that, at 100 • C min −1 , the reaction proceeded completely up to W, Ni 17 W 3 and MgO formation, while higher heating rates (>300 • C min −1 ) hinder the complete reduction; partially reduced WO 2 remained.
Microstructural images of the initial mixture, intermediate and final products of the NiWO 4 + 2Mg + 2C ( Figure 5) reaction cooled down at different temperatures (A-initial mixture, B-720 • C, C-830 • C and D-1000 • C) are presented in Figure 5.
By combining the results obtained for the mixture of oxides and NiWO4, it can assumed that the reduction reactions of NiWO4 by Mg and (Mg + C) combined redu started earlier and that the complete reduction was achieved at comparatively lower te peratures. In addition, the magnesio-carbothermic reduction reactions of nickel a tungsten oxides and nickel tungstate began by ~20 and 30 °C earlier than magnesiotherm ones, and about ~300 and 370 °C earlier than carbothermic processes, evidencing t synergetic effect at utilization of combined reducer in the ternary and quaterna mixtures.
The heating rate has a decisive effect not only on the interaction pathway, but a on the reduction degree. XRD analysis of the products of the NiO + WO3 + 2.5Mg + 1. mixture treated at 100 °C min −1 and higher (300-1200 °C min −1 ) heating rates revealed th at 100 °C min −1 , the reaction proceeded completely up to W, Ni17W3 and MgO formatio while higher heating rates (>300 °C min −1 ) hinder the complete reduction; partially duced WO2 remained.
Microstructural images of the initial mixture, intermediate and final products of t NiWO4 + 2Mg + 2C ( Figure 5) reaction cooled down at different temperatures (A-init mixture, B-720 °C, C-830 °C and D-1000 °C) are presented in Figure 5. According to the results obtained, agglomerated NiWO4 with an average particle s of 5 μm along with black carbon and magnesium powder with well-defined grain boun aries were present in the initial mixture, without significant microstructural changes, to 720 °C (Figure 5a,b). During the exothermic reduction process (quenched at 830 °C), t According to the results obtained, agglomerated NiWO 4 with an average particle size of 5 µm along with black carbon and magnesium powder with well-defined grain boundaries were present in the initial mixture, without significant microstructural changes, up to 720 • C (Figure 5a,b). During the exothermic reduction process (quenched at 830 • C), the newly formed submicron particles of partially reduced product (NiO, WO 2 , W, etc.) underwent partial sintering and crystallization (Figure 5c). Further increases in temperature up to 1000 • C did not cause a change in particle size, but contributed to the homogenization of the final product, comprising submicron sized particles of completely reduced W, Ni 17 W 3 and MgO mixture (Figure 5d).

Calculation of Activation Energy
To reveal the influence of the heating rate on the kinetic features of NiO + WO 3 + 4Mg (1), NiO + WO 3 + 2.5Mg + 1.5C (2), NiWO 4 + 4Mg (3) and NiWO 4 + 2Mg + 2C (4) mixtures, the HSTS studies were performed in a wide range of heating rates: from 100 up to 1200 • C min −1 . As can be seen from Figure 6, with the increase in the heating rate the exothermic peaks of magnesiothermic reduction of (NiO + WO 3 ) mixture ( Figure 6a) and NiWO 4 (Figure 6b) were shifted to the higher temperature area. newly formed submicron particles of partially reduced product (NiO, WO2, W, etc.) underwent partial sintering and crystallization (Figure 5c). Further increases in temperature up to 1000 °C did not cause a change in particle size, but contributed to the homogenization of the final product, comprising submicron sized particles of completely reduced W, Ni17W3 and MgO mixture (Figure 5d).

Calculation of Activation Energy
To reveal the influence of the heating rate on the kinetic features of NiO + WO3 + 4Mg (1), NiO + WO3 + 2.5Mg + 1.5C (2), NiWO4 + 4Mg (3) and NiWO4 + 2Mg + 2C (4) mixtures, the HSTS studies were performed in a wide range of heating rates: from 100 up to 1200 °C min −1 . As can be seen from Figure 6, with the increase in the heating rate the exothermic peaks of magnesiothermic reduction of (NiO + WO3) mixture ( Figure 6a) and NiWO4 (Figure 6b) were shifted to the higher temperature area. Using the data of the temperatures of the exothermic peaks' maximum deviation at different heating rates (T*), the values of the effective activation energies for magnesiothermic reduction stages were calculated by Kissinger's isoconversional method [31] according to Equation (1).
Thus, the effective activation energy value for the NiO + WO3 + 4Mg reaction is calculated to be 146 ± 10 kJ·mol −1 . The addition of carbon to the mixture (NiO + WO3 + 2.5Mg + 1.5C) had no notable influence on the effective activation energy value, as it was derived for the magnesiothermic stage of the process (141 ± 10 kJ mol −1 ). In comparison with NiO + WO3 + 4Mg reaction, the activation energy value for the magnesiothermic reduction of nickel tungstate (NiWO4 + 4Mg) is higher: 216 ± 15 kJ·mol −1 , and when carbon is added to this mixture (NiWO4 + 2Mg + 2C), the activation energy of the magnesiothermic reduction stage of the reaction decreases almost 1.5 times, reaching 148 ± 10 kJ·mol −1 (Figure 7, Table 1). Using the data of the temperatures of the exothermic peaks' maximum deviation at different heating rates (T*), the values of the effective activation energies for magnesiothermic reduction stages were calculated by Kissinger's isoconversional method [31] according to Equation (1).
Thus, the effective activation energy value for the NiO + WO 3 + 4Mg reaction is calculated to be 146 ± 10 kJ mol −1 . The addition of carbon to the mixture (NiO + WO 3 + 2.5Mg + 1.5C) had no notable influence on the effective activation energy value, as it was derived for the magnesiothermic stage of the process (141 ± 10 kJ mol −1 ). In comparison with NiO + WO 3 + 4Mg reaction, the activation energy value for the magnesiothermic reduction of nickel tungstate (NiWO 4 + 4Mg) is higher: 216 ± 15 kJ mol −1 , and when carbon is added to this mixture (NiWO 4 + 2Mg + 2C), the activation energy of the magnesiothermic reduction stage of the reaction decreases almost 1.5 times, reaching 148 ± 10 kJ mol −1 (Figure 7, Table 1).  Note that at low heating rates (2.5-20 °C min −1 ) in the 575-662 °C temperature interval, the Ea value for the NiO + WO3 + 4Mg reaction was determined to be 152 kJ·mol −1 ; for the magnesiothermic stage of the NiO + WO3 + Mg + 2C reaction, in the 605-662 °C temperature interval, to be 149 kJ mol −1 [31]. Despite the fact that the reduction process in the NiO-WO3-Mg-C system at low heating rates started before Mg melting, no notable difference was observed in Ea values. The behaviour of NiWO4-Mg-C and NiO-WO3-Mg-C systems are quite similar according to Ea values, whereas the complete conversion was observed only in the first system. The reduction of the WO3 and WO3 + NiO mixture by combined reducers started at the same temperature (~660 °C). However, the Ea value of the first process was significantly lower, indicating a difference in product composition (W, MgO vs Ni17W3, W, MgO). Interesting phenomena were observed in the comparative overview of the NiWO4-Mg and NiWO4-Mg-C systems, where solely magnesiothermic reduction starts at higher temperature and is characterized by an approximately 70 kJ mol −1 higher Ea value, clearly demonstrating the beneficial influence of combined reducers on the reduction process of nickel tungstate. Comparing both reduction reactions of NiO + WO3 mixture and NiWO4 by combined reducers, the insignificant difference in Ts and  Note that at low heating rates (2.5-20 • C min −1 ) in the 575-662 • C temperature interval, the E a value for the NiO + WO 3 + 4Mg reaction was determined to be 152 kJ mol −1 ; for the magnesiothermic stage of the NiO + WO 3 + Mg + 2C reaction, in the 605-662 • C temperature interval, to be 149 kJ mol −1 [31]. Despite the fact that the reduction process in the NiO-WO 3 -Mg-C system at low heating rates started before Mg melting, no notable difference was observed in E a values. The behaviour of NiWO 4 -Mg-C and NiO-WO 3 -Mg-C systems are quite similar according to E a values, whereas the complete conversion was observed only in the first system. The reduction of the WO 3 and WO 3 + NiO mixture by combined reducers started at the same temperature (~660 • C). However, the E a value of the first process was significantly lower, indicating a difference in product composition (W, MgO vs Ni 17 W 3 , W, MgO). Interesting phenomena were observed in the comparative overview of the NiWO 4 -Mg and NiWO 4 -Mg-C systems, where solely magnesiothermic reduction starts at higher temperature and is characterized by an approximately 70 kJ mol −1 higher E a value, clearly demonstrating the beneficial influence of combined reducers on the reduction process of nickel tungstate. Comparing both reduction reactions of NiO + WO 3 mixture and NiWO 4 by combined reducers, the insignificant difference in T s and E a values might be attributed to the complete reduction of salt, in contrast to the oxides mixture. On the other hand, the separate reduction of nickel and tungsten oxides by combined reducer illustrated the same starting temperature (conditioned by the fact that both processes started after Mg melting), while having double the E a values.
In Table 1 the activation energy values obtained in this work and compared with similar thermite type mixtures obtained earlier [29,32,33]. It can be deduced that the influence of the heating rate is mainly notable on T s but not on the E a values. In particular, for the NiO-WO 3 -Mg system, despite the change from solid-solid mechanism to solidliquid, E a values are practically the same, attributed to the conversion degree and phase composition, i.e., to the formation of Ni 17 W 3 , W and MgO.

Conclusions
The stepwise nature of complex reactions in the multicomponent NiO-WO 3 -Mg, NiO-WO 3 -C, NiO-WO 3 -Mg-C, NiWO 4 -Mg, NiWO 4 -C and NiWO 4 -Mg-C systems was successfully examined by HSTS technique to reveal the phase and microstructure transformations at high heating rates (up to 1200 • C min −1 ) and determine the effective activation energy values.
The results showed that: • simultaneous utilization of magnesium and carbon as reducers allowed the reduction of the starting and maximum temperatures of reduction processes, evidencing the synergetic effect of the utilization of combined reducers; • complete magnesiothermic reduction of NiWO 4 had already taken place at 850 • C, which is about 450 • C below the magnesiothermic reduction temperature of the mixture (NiO + WO 3 ); • complete magnesio-carbothermic reduction of NiWO 4 took place at 1000 • C, while the reduction of oxide mixtures by (Mg + C) combined reducer at the same conditions proceeded partially; • unlike the magnesiothermic and carbothermic reduction, magnesio-carbothermic reduction of nickel tungstate proceeded through thermal decomposition of the NiWO 4 into oxides. The effective (apparent) activation energies reported in this work characterize macroscopic kinetics of the exothermic interaction in heterogeneous mixtures taking place by solid + solid or solid + liquid mechanisms.