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I've recently come across one of the methods to form tungsten carbide($\ce{WC}$) from wolframite ($\ce{(Fe,Mn)WO4}$) by using carbothermic reduction which was supposedly one of the first methods for extracting tungsten from its ores developed in 1783. But I wanted to know the particular temperature at which the reduction occurs, so I've searched online for the Ellingham diagram of wolframite but I've found no sources for that. There were Ellingham diagrams for many metals except for wolfram. I just want to know if anyone can cite a place where I can find it?

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Wendel [(1)] studied the oxidation of tungsten and produced this diagram for the free energy of formation of various tungsten oxides:

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Each of the lines represents free energy per mole of $\ce{O2}$, and $\ce{WO3}$ appears lower than any lower oxide (red, lowest line in the graph). Therefore $\ce{WO3}$ is the only thermodynamically stable oxide and the only one that would appear in an Ellingham diagram. Fitting that line onto the diagram we find that it crosses the $\ce{C/CO}$ line at about 1200°C.

This equilibrium termperature of 1200°C assumes the carbon monoxide is generated at one atmosphere partial pressure. The reaction could take place at somwhat lower temperature using a lower $\ce{CO}$ pressure. In practice, the reduction conditions are more likely driven by kinetics instead of thermodynamics. Wang et al.[2] report that carbothermic reduction at 1100°C gives a mixture of tungsten metal and carbides, which are then purified to ultrafine $\ce{WC}$ By reacting with more carbon at 1200°C:

In the current study, ultrafine and high-purity tungsten carbide (WC) powders are successfully prepared by a two-step process: carbothermic reduction of WO3 followed by carbonization reaction. The effects of the C/WO3 molar ratio, reaction temperature and reaction time on the phase transition and morphology evolution of the products are investigated. During the carbothermic reduction process, all the oxygen in yellow tungsten trioxide (WO3) is removed by carbon to generate a mixture of W, W2C and WC at 1100 °C; and then the as-prepared powder is mixed with an appropriate content of carbon black and carbonized at 1200 °C. The carbon content in the finally obtained WC powders is almost equal to the theoretical value. Furthermore, it is found that a high C/WO3 molar ratio at the first stage is beneficial for decreasing the particle size of the WC powders. When the C/WO3 molar ratio is 3.5, the single phase WC with a particle size of about 200 nm can be obtained. Therefore, this carbothermic reduction–carburization process may provide a simple, low-cost, and high efficiency route to prepare the WC powders in a large-scale.

References

1. J. Wendel. Thermodynamics and Kinetics of TungstenbOxidation and Tungsten Oxide Sublimation in the Temperature Interval 200°–1100°C. MS thesis submitted to Lund University (Sweden). (Lund, Sweden: European Spallation Source ESS AB, 2014), p. 14.

2. Kai-Fei Wang, Guo-Dong Sun, Yue-Dong Wu, Guo-Hua Zhang (2019). "Fabrication of ultrafine and high-purity tungsten carbide powders via a carbothermic reduction–carburization process". Journal of Alloys and Compounds 784, 362-369, ISSN 0925-8388, https://doi.org/10.1016/j.jallcom.2019.01.055.

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