Phase controlled synthesis of transition metal carbide nanocrystals by ultrafast flash Joule heating

Nanoscale carbides enhance ultra-strong ceramics and show activity as high-performance catalysts. Traditional lengthy carburization methods for carbide syntheses usually result in coked surface, large particle size, and uncontrolled phase. Here, a flash Joule heating process is developed for ultrafast synthesis of carbide nanocrystals within 1 s. Various interstitial transition metal carbides (TiC, ZrC, HfC, VC, NbC, TaC, Cr2C3, MoC, and W2C) and covalent carbides (B4C and SiC) are produced using low-cost precursors. By controlling pulse voltages, phase-pure molybdenum carbides including β-Mo2C and metastable α-MoC1-x and η-MoC1-x are selectively synthesized, demonstrating the excellent phase engineering ability of the flash Joule heating by broadly tunable energy input that can exceed 3000 K coupled with kinetically controlled ultrafast cooling (>104 K s-1). Theoretical calculation reveals carbon vacancies as the driving factor for topotactic transition of carbide phases. The phase-dependent hydrogen evolution capability of molybdenum carbides is investigated with β-Mo2C showing the best performance.

2 Supplementary Note 1. Simulation of the temperature distribution.
The temperature distribution was simulated based on the finite element method (FEM) using the COMSOL Multiphysics 5.5 software. The Joule heating mode in the AC/DC module was used. The geometric configuration, materials properties, and boundary conditions are listed in Supplementary Table 1. Similar to the real reaction tube, a cylinder is used as the geometric configuration with electrode radius (0.2 cm), electrode length (0.5 cm), materials length (2 cm), and materials radius (0.2 cm). The electrical conductivity (σ) and thermal conductivity (к) 1 of the carbon black are from the literature reported values.
The temperature distribution of the sample is shown in Supplementary Fig. 2a. The simulated sample temperature is up to ~3000 K at the center, while the sample temperature at the edge is slightly lower than that at the center because of thermal dissipation at the sample-electrode interface 2 . The simulated temperature values match well with the measured values by fitting the blackbody radiation (Fig. 1d). The temperature simulation further provides insight into the effects of Joule heating parameters on the available temperature. We identified that the Joule heating voltage, electrical conductivity of the materials, and thermal conductivity of the materials are critical parameters. We found that a higher voltage leads to higher temperature ( Supplementary   Fig. 2b, Supplementary Fig. 14). Also, a better sample electrical conductivity leads to higher temperature (Supplementary Fig. 2c). In contrast, a higher thermal conductivity of the sample results in lower temperature due to thermal dissipation (Supplementary Fig. 2d).

Supplementary Note 2. Removal of graphene and purification of the carbides.
There have been several post-synthesis purifications processes to remove excess carbon from carbides, including oxidization 3 , H2 etching 4,5 , and Ca metal reaction 6 . The purification process depends on the properties of the specific carbide. For example, for SiC with higher resistance to oxidation than graphene, it is possible to remove carbon by just calcination in air 3 . In contrast, the simple calcination process is not suitable for TMCs since they are oxidized prior to graphene. Hence, for TMCs, we here demonstrated a Ca metal reaction process 6 for purification.

Purification of SiC by calcination in air.
It is reported that SiC could withstand a high temperature up to 921 °C in air 3 . As shown in Supplementary Fig. 25a, the XRD pattern of the as-synthesized mixture of SiC/graphene shows a graphite peak at ~26°. The TGA curve of the mixture of SiC/graphene conducted in air shows a monotonic decrease from ~550 °C to ~750 °C (Supplementary Fig. 25b). Hence, we calcined the samples at 800 °C in air for 30 min. The XRD pattern of the product show a pure phase of SiC without any peaks from graphitized carbon or amorphous carbon ( Supplementary   Fig. 25c). The Raman spectrum of the as-synthesized mixture of SiC/graphene shows characteristic D, G, and 2D bands of graphene (Supplementary Fig. 25d). Notably, after purification, no graphene peak was identified (Supplementary Fig. 25d). Considering the excellent resolution of Raman for detecting even monolayer graphene, this result demonstrates the efficient removal of the excess carbon.

Purification of TMCs by Ca metal reaction.
4 The TMC nanocrystals were purified by a Ca metal reaction process 6 . We first used the mixture of TiC/graphene as an example to discuss the purification process in detail, and then provide the purification results for the other TMCs.
The as-synthesized mixture of TiC/graphene (~20 mg) was placed into a stainless steel crucible, and Ca metal (~80 mg) was added. Then, the crucible was loaded into a tube furnace (Thermo Scientific, Lindberg tube furnace). Ar gas with the flow of ~400 sccm was used as the inert gas under atmospheric pressure (AP). The temperature was ramped to 860 °C (ramping rate of ~40 °C min -1 ), which is somewhat above the melting point of Ca (839 °C), and maintained for 10 min. The excess carbon reacts with Ca with the following reaction, Then, the furnace was cooled to room temperature. The resulted gray solid was placed into water to remove the CaC2 and Ca residues by the following reactions, CaC2 + H2O = Ca(OH)2 + C2H2 Ca + H2O = Ca(OH)2 + H2 The undissolved TiC particles were dried for characterization (Supplementary Figs. 26-27). Supplementary Fig. 26a, the as-synthesized mixture of TiC/graphene shows a strong peak at ~26°, which is from the graphene support; after purification, no graphitized or amorphous carbon peak was identified. The Raman spectrum of the as-synthesized mixture of TiC/graphene show characteristic D, G, and 2D bands of graphene (Supplementary Fig. 26b).

As shown in
Notably, after purification, no graphene peak is identified. Considering the excellent resolution of Note that the Ti-O could be due to the surface oxidation, and the 5 C-C peak could be from the absorbed hydrocarbon in air. The BF-TEM image shows no excess carbon on the purified TiC nanoparticles (Supplementary Fig. 27a). Moreover, the particle size is measured to be ~35.1 nm according to the TEM statistics ( Supplementary Fig. 27b), which is slightly larger than that of the as-synthesized particles ( Fig. 36).
Nevertheless, we found that the Ca reaction method is not suitable for three carbides: B4C, α-MoC1-x, and η-MoC1-x. For B4C, we found that after the same process, no residual solid remained. This is probably due to the reaction of B4C with Ca at high temperature. For α-MoC1-x and η-MoC1-x, the purification process could indeed remove the excess carbon ( Supplementary Fig. 35).
However, we found that the α-MoC1-x and η-MoC1-x phases were transformed to β-Mo2C after purification (Supplementary Fig. 35). As we discussed in detail in the manuscript (Fig. 3), β-Mo2C is the thermodynamically stable phase, while the α-MoC1-x and η-MoC1-x phases are metastable phases. The α-MoC1-x and η-MoC1-x phases are successfully synthesized and stabilized to room temperature due to the ultrafast cooling rate (~10 4 °C s -1 ) of the FJH process. For the Ca reaction purification process, we used a CVD furnace, and the cooling rate was low (~10 °C min -6 1 ). As a result, the metastable α-MoC1-x and η-MoC1-x phases were degraded to the thermodynamically stable β-Mo2C phase.
Purification of metastable molybdenum carbides by a physical process.
For the cases that the above chemical separation processes are not applicable, including α-MoC1-x and η-MoC1-x, we here applied the physical separation approach to remove excess carbon.
Experimentally, the mixture of graphene and carbides were dispersed into dimethylformamide (DMF) solvent, and cup-horn ultrasonicated for 1 h. Then, the dispersion was centrifuged to precipitate the carbide solid, while the graphene mostly remained dispersed in the supernatant. The supernatant was removed, and the precipitate was purified again by the cycle of dispersionultrasonication-centrifugation process. After 5 to 6 cycles, the supernatant was clear, indicating that all the dispersible free carbons were removed. The obtained solids were dried in an oven (~100 °C).
The results for α-MoC1-x were shown in Supplementary Fig. 37. According to the XRD ( Supplementary Fig. 37a), the graphene peak (*) intensity is greatly reduced after purification even though it is not completely removed. By using the XRD peak intensity ratio of carbide and graphene as an index, the removal efficiency of the excess carbon is ~80% by using the physical purification process. The Raman spectra similarly show the removal of carbon. Before purification, the carbides were covered by graphene and hence the carbide peaks were undetectable ( Supplementary Fig. 37b). In contrast, after purification, the carbide bands were clearly seen.
The XPS confirms the chemical states of Mo and C in α-MoC1-x (Supplementary Figs. 37c-d).
The Mo 0 and Mo 2+ are from the molybdenum carbide phase, where the Mo 4+ and Mo 6+ are from the surface oxide, as we have discussed in detail in the manuscript (Fig. 2c). The results for η-MoC1-x are shown in Supplementary Fig. 38, which is similar with that of the α-MoC1-x.
According to the change of XRD peak intensity ratio of graphene and carbide, the removal efficiency of graphene is ~60% for the η-MoC1-x. The remaining carbon might be chemically bonded with carbide and hence is difficult to remove by the physical purification process.
Improving the purity of B4C by changing the precursor feeding ratio.
B4C is another carbide that is difficult to be purified by the chemical processes. B4C is more susceptible than carbon, and hence is unable to be purified by the chemical oxidation process.
In addition, we also found that the Ca metal etching process is not suitable for B4C because it is reactive with Ca metal at high temperature. Here, we provided the strategy for the production of high-purify B4C through a synthetic modification.

Supplementary Note 3. Electrical energy consumption for the synthesis of carbide by FJH.
The energy consumption is calculated by Supplementary Equation 4, where E is the energy per gram (kJ g -1 ), V1 and V2 are the voltage before and after flash Joule heating, respectively, C is the capacitance (C = 60 mF), and M is the mass per batch.
By using the upper bounds of V1 = 120 V, V2 = 0 V, M = 0.05 g, the energy is calculated to be, By using the lower bounds of V1 = 30 V, the energy was calculated to be, Hence, the energy used to synthesize the carbide is in the range of 2.2 -8.6 kJ g -1 .
Given that the industrial price of electric energy in Texas, USA is $0.02 kWh -1 , the cost for synthesis of carbides would be P = 0.012 -0.048 $ kg -1 .

Supplementary Note 4. Strategies for scaling up of the FJH process.
Since the reaction temperature is critical for carbide synthesis, the scaling-up of the synthesis by FJH requires that the temperature value and uniformity remain the same at different mass scale. Here, we firstly derived the key parameters of the FJH dominating the sample temperature, and then experimentally demonstrated the scaling up of the FJH process.
The charge (q) in the capacitor banks is determined by Supplementary Equation 5, where C is the total capacitance of the capacitor bank, and V is the charging voltage.

The average current (I) is calculated by Supplementary Equation 6,
where t is the discharging time, supposing that the charges in the capacitor are totally discharged in the discharge time.
As a result, the current density (j) is calculated by Supplementary Equation 7, where S is the cross-sectional area of the sample.
Since we use a cylinder-shaped tube and sample, so the mass (m) of the sample is calculated Where is the density of the sample, l is the thickness of the sample.
Above all, we get the Supplementary Equation 9, According to the Joule heating law, the heat amount (Q) per volume is determined by where is the electrical conductivity of the sample. We demonstrated the scalable synthesis of metal carbide by FJH to gram scale. As shown in Supplementary Fig. 40a, we used three quartz tubes with the diameters of 0.4 cm, 0.8 cm, and 1.6 cm for the synthesis of TiC nanocrystals with the mass of ~50 mg, ~200 mg, and ~1 g. We here used the increasing voltage strategy. As shown in Supplementary Fig. 40b (1) Enclose or carefully insulate the wire connections.
(2) All connections and wires must be suitable for high voltages and currents.
(3) Keep in mind that the system can discharge thousands of Joules in milliseconds, which could cause components such as relays to explode.
where σ is a constant of proportionality. Hence, the temperature could be evaluated based on the radiant intensity. Experimentally, we recorded the optical image of a sample during FJH using an 16 ultrafast camera (Supplementary Fig. 4a). Then, the color image was converted to a grayscale image (Supplementary Fig. 4b), and then an intensity matrix using MATLAB. The highest temperature was measured by fitting the blackbody radiation (Supplementary Fig. 2), which corresponds to the largest value (Imax) in the intensity matrix. As an example, we used a FJH voltage of 120 V with the highest temperature (Tmax) of ~3242 K. The temperature (T) of each pixel in the image was then calculated based on the Stefan-Boltzmann law using the intensity value (I) in the matrix, Then, the temperature distribution was plotted (Supplementary Fig. 4c). It is found that the temperature is very uniform throughout the whole sample. Amorphous carbon black was used as the conductive additive as well as carbon precursor for the carbothermic reduction. After FJH, the amorphous carbon black is graphitized, and the degree is related to the FJH voltages. A low FJH voltage (~30 V) cannot result in obvious graphitization ( Supplementary Fig. 6a). As the voltage increases to 60 V, a sharp peak at ~26° is observed. The peak position is related to the FJH voltage and shifted downwards with regard to the (002) peak of graphite (Supplementary Fig. 6b). This material is termed as flash graphene (FG) as shown in our previous publication 7 . In Fig. 2a, Figs. 5b-d, and Supplementary Figs. 23, 24, and 40, the peak at ~26° are attributed to the graphene support. By using a FJH voltage of 50 V, the metastable α-MoC1-x phase was formed (Supplementary Fig.   16a). The maximum temperature at FJH voltage of 50 V was recorded to be ~1173 K. In contrast, when a tube furnace was used with a much slower cooling rate of ~10 K min -1 which could be considered as thermal equilibrium, under the same synthesis temperature, only the thermodynamically stable β-Mo2C was synthesized (Supplementary Fig. 16b). This clearly demonstrated that the ultrafast cooling rate of the FJH process helps to kinetically retain the metastable carbide phases to room temperature.   The low-magnification TEM image shows only the TiC nanoparticles without excess carbon. After purification, the particle size is measured to be ~35.1 nm, somewhat larger than that of the as- After purification, no graphene peak was identified in the XRD pattern, and no graphene band was detected in the Raman spectrum, demonstrating the efficient removal of graphene. The XPS confirms the chemical states of Zr and C in ZrC. The Zr-O could be due to the surface oxidation, and the C-C peak could be from the absorbed carbon in air. After purification, no graphene peak was identified in the XRD pattern, and no graphene band was detected in the Raman spectrum, demonstrating the efficient removal of graphene. The XPS confirms the chemical states of V and C in VC. The V-O could be due to the surface oxidation, and the C-C peak could be from the absorbed carbon in air.