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Jing Wen, Hongyan Sun, Tao Jiang, Bojian Chen, Fangfang Li, and Mengxia Liu, Comparison of the interface reaction behaviors of CaO–V2O5 and MnO2–V2O5 solid-state systems based on the diffusion couple method, Int. J. Miner. Metall. Mater., 30(2023), No. 5, pp.834-843. https://dx.doi.org/10.1007/s12613-022-2564-7
Cite this article as: Jing Wen, Hongyan Sun, Tao Jiang, Bojian Chen, Fangfang Li, and Mengxia Liu, Comparison of the interface reaction behaviors of CaO–V2O5 and MnO2–V2O5 solid-state systems based on the diffusion couple method, Int. J. Miner. Metall. Mater., 30(2023), No. 5, pp.834-843. https://dx.doi.org/10.1007/s12613-022-2564-7
Research Article

Comparison of the interface reaction behaviors of CaO–V2O5 and MnO2–V2O5 solid-state systems based on the diffusion couple method

Author Affilications
  • Corresponding author:

    Tao Jiang      E-mail: jiangt@smm.neu.edu.cn

  • The formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in the reaction with vanadium are basic issues in the calcification roasting and manganese roasting process with vanadium slag. In this work, CaO–V2O5 and MnO2–V2O5 diffusion couples were prepared and roasted for different time periods to illustrate and compare the diffusion reaction mechanisms. Then, the changes in the diffusion product and diffusion coefficient were investigated and calculated based on scanning electron microscopy (SEM) with energy dispersive X-ray spectroscopy (EDS) analysis. Results show that with the extension of the roasting time, the diffusion reaction gradually proceeds among the CaO–V2O5 and MnO2–V2O5 diffusion couples. The regional boundaries of calcium and vanadium are easily identifiable for the CaO–V2O5 diffusion couple. Meanwhile, for the MnO2–V2O5 diffusion couple, MnO2 gradually decomposes to form Mn2O3, and vanadium diffuses into the interior of Mn2O3. Only a part of vanadium combines with manganese to form the diffusion production layer. CaV2O6 and MnV2O6 are the interfacial reaction products of the CaO–V2O5 and MnO2–V2O5 diffusion couples, respectively, whose thicknesses are 39.85 and 32.13 μm when roasted for 16 h. After 16 h, both diffusion couples reach the reaction equilibrium due to the limitation of diffusion. The diffusion coefficient of the CaO–V2O5 diffusion couple is higher than that of the MnO2–V2O5 diffusion couple for the same roasting time, and the diffusion reaction between vanadium and calcium is easier than that between vanadium and manganese.
  • Vanadium is an important strategic metal resource in China, which is widely used in the steel chemical industries, aerospace, and other fields due to its excellent physical and chemical properties [15]. In particular, in the presence of carbon neutrality and peak carbon dioxide emission targets, the high-tech industry of vanadium, such as vanadium–nitrogen micro-alloyed steel and all-vanadium redox flow battery, is rapidly developing [611], which opens up a broad prospect for the development of vanadium products and the utilization of vanadium resources.

    Vanadium slag, as the important intermediate product generated during the smelting process of vanadium–titanium magnetite, is the main raw material for vanadium extraction in China [1215]. Various extraction technologies of vanadium from vanadium slag have been proposed [1622]. Among them, the calcification roasting process for the treatment of vanadium slag is a hot topic because it effectively avoids many problems in the sodium salt roasting process, such as the generation of harmful gases and hazardous water-soluble vanadium and chromium with high valence state [2325]. Moreover, a production line with an annual output of 20000 t of V2O5 has been established by Xichang Steel and Vanadium Co., Ltd., China, through calcification roasting [26]. In this process, calcium salts, such as CaCO3 and CaO, are used as additives to react with vanadium in vanadium slag to form acid-soluble calcium vanadate, and around 90% of vanadium can be selectively extracted after acid leaching [27]. Furthermore, manganese vanadate and a large number of Mn2+ are also detected in roasted materials and a leaching solution, respectively, during the calcification roasting process, which is due to the reaction of vanadium and the original manganese in vanadium slag [28].

    Inspired by the calcification roasting process, our group proposed manganese salt roasting, at which MnCO3, MnO2, and pyrolusite are used as additives to combine with vanadium and generate acid-soluble manganese vanadate [2931]. This process has higher separation efficiency of vanadium and chromium compared with calcification roasting and avoids the formation of insoluble sulfates. Meanwhile, calcium vanadate is detected in the roasted materials because of the existence of calcium in vanadium slag. Hence, calcium and manganese have strong abilities to combine with vanadium. However, there is no systematic study on the formation mechanism of calcium vanadate and manganese vanadate and the difference between calcium and manganese in their interaction with vanadium. These factors have a significant implication for the improvement of basic theory and process optimization during calcification roasting and manganese roasting processes with vanadium slag.

    The diffusion couple method is often used to study the mechanism of solid-state reactions. Through observation and analysis of the reaction interface, the phase transition mechanism and product formation in the solid-state reaction, along with the migration rules of essential elements, can be systematically evaluated. For example, Yue et al. [3233] studied the diffusion characteristics of vanadium and calcium in calcium vanadate through V-slag/CaO diffusion. Chen et al. [3435] researched the diffusion behavior between Cr2O3 and calcium ferrite based on the diffusion couple method at 1373 K. Ren et al. [36] investigated interdiffusion in the Fe2O3–TiO2 system through the diffusion couple method in the temperature range of 1323 to 1473 K. Hence, it is feasible to study and compare the interaction between calcium and manganese when reacting with vanadium through the diffusion couple method.

    In this work, V2O5 was used to simplify vanadium spinel in vanadium slag to avoid the interference of other impurity elements in vanadium slag. CaO and MnO2 were used as additives in calcification roasting and manganese roasting, respectively. A CaO–V2O5 diffusion couple and MnO2–V2O5 diffusion couple were roasted for different time periods to illustrate and compare the diffusion behavior of the CaO–V2O5 and MnO2–V2O5 systems. Furthermore, the diffusion mechanism was studied systematically.

    CaO, MnO2, and V2O5 used in this work were all analytical-grade reagents (Sinopharm Chemical Reagent Co., Ltd, China). CaO was roasted at 1000°C for 2 h before use to remove Ca(OH)2 and CaCO3. Fig. 1 presents the X-ray powder diffraction (XRD) patterns of CaO, MnO2, and V2O5. The observed diffraction peaks of the three raw materials are well indexed to those of the Joint Committee on Powder Diffraction Standards, which meet the requirements for the diffusion reaction of the CaO–V2O5 and MnO2–V2O5 couples.

    Fig. 1.  XRD patterns of CaO, MnO2, and V2O5.

    A molded tableting machine was used to press CaO–V2O5 and MnO2–V2O5 powders into 8 mm cylinders with two layers. 0.2 g V2O5 was first placed into the mold, and 0.2 MPa pressure was applied to ensure a smooth surface of V2O5. A drop of ethanol (C2H5OH) was dripping on the surface of V2O5. Then, 0.2 g CaO or 0.2 g MnO2 was placed into the mold. After pressing the mold at 2 MPa for 30 s, the CaO–V2O5 and MnO2–V2O5 diffusion couples were produced after demolding.

    During the process, the CaO–V2O5 and MnO2–V2O5 diffusion couples were placed into a muffle furnace at room temperature and then heated to 600°C at a constant heating rate of 10°C/min. The actual roasting temperature of calcification roasting and manganese salt roasting for vanadium slag was 850–900°C to break down the vanadium-containing spinel structure, realize the oxidation of low-valance vanadium, and promote the formation of acid-soluble vanadate [12,2930,3739]. Meanwhile, analytical-purity V2O5 was melted at above 650°C due to its low melting point. Hence, 600°C was chosen as the roasting temperature of the CaO–V2O5 and MnO2–V2O5 diffusion couples, which is sufficient for the complete reaction of V2O5 with CaO or MnO2. This conclusion has been confirmed by the powder roasting experiments with three substances in our pre-experiment [40]. During roasting, the diffusion couples were placed into a muffle furnace at room temperature. To investigate the effect of the reaction time on the diffusion reactions of the CaO–V2O5 and MnO2–V2O5 systems, the diffusion couples were held at 600°C for 0, 4, 8, 12, 16, and 20 h. After the diffusion reaction, the diffusion couples were taken out and embedded with epoxy resin. The diffusion interface was polished to be observed. Then, the product layer thickness and diffusion coefficient were measured and calculated.

    The phases of raw materials were detected using an X-ray diffractometer (X’Pert Pro, PANalytical B.V., Netherlands). Then, a scanning electron microscope (SEM, Ultra plus, Zeiss, Germany) equipped with an energy-dispersive X-ray spectroscope was employed for analyzing the microstructure of diffusion interfaces and the element distribution of vanadium, calcium, and manganese among the roasted CaO–V2O5 and MnO2–V2O5 diffusion couples. The experimental process of this work is shown in Fig. 2.

    Fig. 2.  Experimental process of this work. P―Pressure; t―Time; T―Temperature.

    Fig. 3 shows the SEM images and element distribution of the CaO–V2O5 and MnO2–V2O5 diffusion couples holding at 600°C for 0 h. The micrographs with different magnifications show that the particles on the right side are denser than those on the left side in the CaO–V2O5 couple, as shown in Fig. 3(a) and (b). Combined with the distribution of calcium and vanadium elements in Fig. 3(c) and (d), CaO and V2O5 are on the left and right sides in the field of vision, respectively. Furthermore, according to the EDS analysis of points A and B in Fig. 3(e) and (f), the two sides of the diffusion couple are still CaO and V2O5 after raising the temperature to 600°C and holding for 0 h.

    Fig. 3.  (a, b) SEM images of the CaO–V2O5 diffusion couple at 600°C for 0 h; (c, d) element mapping of (b); (e, f) EDS analysis of points A and B in (b). (g, h) SEM images of the MnO2–V2O5 diffusion couple at 600°C for 0 h; (i, j) element mapping of (h); (k, l) EDS analysis of points C and D in (h).

    In Fig. 3(g)–(l), similar phenomena occur in the MnO2–V2O5 diffusion couple. The phase containing vanadium on the right side of the diffusion couple is denser than that containing manganese on the left side, as shown in Fig. 3(g)–(j). Meanwhile, as shown in Fig. 3(k), the atomic ratio of oxygen to manganese at point C is 1.45, which is closer to the atomic ratio of oxygen to manganese in Mn2O3 of 1.5, rather than the value of MnO2 of 2. Hence, MnO2 has been decomposed into Mn2O3 after roasting from room temperature to 600°C. The reaction equation is shown in Eq. (1):

    4MnO2=2Mn2O3+O2(g) (1)

    This conclusion has also been further verified by the XRD results. Mn2O3 and V2O5 are on the left and right sides, respectively. Moreover, no obvious product layer can be observed on the interface of the CaO–V2O5 and MnO2–V2O5 diffusion couples without keeping at 600°C for a period of time. There is also no coincidence of the element distributions of vanadium and calcium, along with vanadium and manganese, confirming that diffusion reactions did not take place among the CaO–V2O5 and MnO2–V2O5 couples.

    Figs. 4 and 5 show the changes in the micromorphology of the CaO–V2O5 and MnO2–V2O5 diffusion couples under the same magnification after roasting at 600°C for different time periods, respectively. In Fig. 4, the diffusion interface of the CaO–V2O5 diffusion couple is clear. Moreover, the diffusion product in the center of the visual field can easily be identified, whose grayscale is notably different from that of CaO and V2O5. Moreover, the product layer is denser than CaO and V2O5. The thickness of the product layer gradually increases with the extension of the roasting time, which does not significantly increase after 16 h.

    Fig. 4.  SEM images of the CaO–V2O5 diffusion couples after roasting at 600°C for different time periods: (a) 0 h; (b) 4 h; (c) 8 h; (d) 12 h; (e) 16 h; (f) 20 h.
    Fig. 5.  SEM images of the MnO2–V2O5 diffusion couples after roasting at 600°C for different time periods: (a) 0 h; (b) 4 h; (c) 8 h; (d) 12 h; (e) 16 h; (f) 20 h.

    For the MnO2–V2O5 diffusion couple in Fig. 5, in the diffusion reaction progress of manganese oxide and V2O5, the micromorphology of V2O5 greatly changes. At 0 h, V2O5 is shown as small particles. With the extension of the roasting time, V2O5 particles are like slender needle-like dendrites, and the gap between V2O5 particles at the interface is large. This phenomenon is further reflected intuitively in the diffusion couple after roasting for 8 h. V2O5 with the above two morphologies are reflected in parts A and B, respectively. When the roasting time exceeds 16 h, there is no V2O5 layer in the field of vision, but it is replaced by a wide fault zone.

    To further investigate the difference between calcium and manganese in the diffusion reaction process with vanadium, the CaO–V2O5 and MnO2–V2O5 diffusion couples roasted for 16 h are compared in detail. The results show that after the roasting process, the thickness of the product layers does not increase obviously. The morphology and element distribution at the interface of the CaO–V2O5 diffusion couple after roasting the CaO–V2O5 and MnO2–V2O5 diffusion couples at 600°C for 16 h are shown in Fig. 6. In Fig. 6(a) and (b), the diffusion product of CaO and V2O5 in the center of the visual field is obvious, and the product layer is denser than those of CaO and V2O5. According to the element mapping of Fig. 6(c) and (d), the distribution regions of vanadium and calcium are partly coincident, which is due to the diffusion reaction of CaO and V2O5 and the formation of calcium vanadate. Based on the line-scan analysis of calcium and vanadium in Fig. 6(e), the distribution of calcium and vanadium shows a three-stage change. On the CaO side, the content of calcium reaches a high level, but there is no vanadium. In the diffusion product layer, the content of vanadium significantly increases with the reaction between CaO and V2O5, and the content of calcium decreases due to the formation of reaction products, as shown in Fig. 6(e). On the V2O5 side, calcium cannot be easily detected, whereas the content of vanadium reaches a high level. The EDS analysis in Fig. 6(f) shows that the atomic ratio of vanadium and calcium is 1.85, and the atomic ratio of oxygen and calcium is 6.41, close to the values of CaV2O6. Hence, the diffusion-layer product is supposed to be calcium metavanadate (CaV2O6).

    Fig. 6.  SEM images and corresponding EDS results the CaO–V2O5 diffusion couple roasted at 600°C for 16 h: (a, b) morphologies with different magnifications; (c, d) element mapping images of (b); (e) line-scan analysis; (f) EDS analysis of point A).

    Fig. 7 shows the morphology and element distribution at the interface of the MnO2–V2O5 diffusion couple after roasting for 16 h. MnO2 on the left side of the MnO2–V2O5 diffusion couple is further decomposed into Mn2O3. As shown in Fig. 7(a), the whole visual field can be divided into five parts. Combined with the element mapping and line-scan analysis in Fig. 7(b)–(d), part I is V2O5. With the gradual diffusion of V2O5 to Mn2O3, a fault exists in the V2O5 side, as shown in part II, which is attributed to the fact that the diffusion ability of vanadium to the product layer and the Mn2O3 side is far stronger than that of manganese to the product layer and V2O5. This condition results in the gradual diffusion of vanadium near the diffusion couple interface into Mn2O3. Moreover, an obvious fault zone appears on the V2O5 side away from the diffusion couple interface. After the fault zone, a dense area including part III and part IV appears on the Mn2O3 side. Due to many pores in the Mn2O3 side, vanadium is easily diffused and entered the inside of Mn2O3. Meanwhile, only part of the vanadium can combine with manganese to form manganese vanadate and form the diffusion production layer, as shown in part III. Hence, the existence of pores in the Mn2O3 side makes the diffusion of vanadium easy and accelerates the diffusion reaction of vanadium and manganese. In part IV, although vanadium has diffused into the Mn2O3 side, it only fills the pores on the manganese side. The low concentrations of vanadium and manganese make the kinetic conditions of their reaction poor and make it difficult for them to continue the reaction and form the product layer. Moreover, almost no vanadium is detected, indicating that part V is Mn2O3.

    Fig. 7.  SEM images and corresponding EDS results of the MnO2–V2O5 diffusion couple roasted at 600°C for 16 h: (a, e) morphology with different magnifications; (b, c) element mapping images of (a); (d) line-scan analysis of line 1 in (a); (f, g) element mapping images of (e); (h, i): line-scan analysis of lines 2 and 3 in (e); (j, k) EDS analysis of points A and B.

    The diffusion reaction between V2O5 and Mn2O3 is further verified, as shown in Fig. 7(e)–(g). A clear fault zone is observed due to differences in the diffusion ability of vanadium and manganese. Only manganese is detected in the area surrounded by the dotted line, which is considered to be Mn2O3. In the area around Mn2O3, vanadium and manganese simultaneously exist. Meanwhile, the EDS results show that points A and B are not the same substance. Point A is located inside the diffusion product layer of vanadium and manganese, where the atomic ratio of vanadium to manganese is close to 2, and the atomic ratio of oxygen to manganese is close to 6. The value is close to the values of manganese metavanadate MnV2O6. Hence, the diffusion-layer product is supposed to be MnV2O6. Point B is located inside Mn2O3, where the atomic ratio of vanadium to manganese is not like that in the product layer. Point B is the simple diffusion of vanadium into the gap of Mn2O3. The above studies show obvious differences in the reaction between CaO and Mn2O3 with V2O5.

    Fig. 8 shows the atomic ratios of vanadium to calcium or vanadium to manganese in the product layers when the CaO–V2O5 and MnO2–V2O5 diffusion couples are roasted at 600°C for different time periods. In Fig. 8(a), the atomic ratios of vanadium to calcium in the product layers are approximately 2 under different roasting times, which indicates that the diffusion product of the CaO–V2O5 couples is CaV2O6. The atomic ratios of vanadium to manganese in the product layer shown in Fig. 8(b) are also approximately 2 when the roasting time ranges from 0 to 20 h. Hence, MnV2O6 is supposed to be the diffusion product of the MnO2–V2O5 couples. These results show that the diffusion reaction products are stable and do not change with the extension of the reaction time.

    Fig. 8.  Effect of the roasting time on the diffusion products of the CaO–V2O5 and MnO2–V2O5 couples.

    When the roasting temperature is kept at 600°C, the diffusion reactions gradually proceed among the CaO–V2O5 and MnO2–V2O5 diffusion couples with the extension of the roasting time, and the thicknesses of the product layers increase. Based on the micromorphology and line scanning results of the CaO–V2O5 diffusion couples at different roasting times, the image of the product layers is supposed to be divided into 24 regions at an equal distance (∆H) along the vertical direction of the sample cross section. The diffusion-layer thicknesses between L1 to L25 are measured according to the image scale. Then, the average value L is taken according to Eq. (2), which is considered to be the thickness of the diffusion layers of the CaO–V2O5 diffusion couples [36,41].

    L=L1+L2+...+L2525 (2)

    The diffusion-layer thicknesses of the MnO2–V2O5 diffusion couples at different roasting times are also measured and calculated by this method. The results of the product layer thickness are shown in Fig. 9.

    Fig. 9.  Relationships between the product layer thickness and roasting time of two diffusion couples.

    The results show that the thicknesses of the product layer (L) increase with the extension of the roasting time, which remarkably increase from 0 to 16 h and remain stable after 20 h among the CaO–V2O5 and MnO2–V2O5 diffusion couples. The L values of the CaO–V2O5 and MnO2–V2O5 diffusion couples are 39.85 and 32.13 μm at 16 h, respectively. Accordingly, the relationships between the product layer thickness and roasting time of the two diffusion couples are fitted at 0–16 h, as shown in Eqs. (3) and (4).

    CaO–V2O5 diffusion couple:

    L=2.40t (3)

    MnO2–V2O5 diffusion couple:

    L=2.00t (4)

    where L is the thickness of the product layer of the two diffusion couples, μm, and t is the roasting time of diffusion reaction, h. The relationships between the diffusion-layer thickness and roasting time are basically linear at 0–16 h, as shown in Fig. 9. The determination coefficient R2 values of the CaO–V2O5 and MnO2–V2O5 diffusion couples are both 0.99, which illustrates that the fitting equations are suited for describing the relationships between the product layer thickness and roasting time. The reaction coefficient of the CaO–V2O5 diffusion couple is 2.40, which is higher than that of the MnO2–V2O5 diffusion couple (2.00). This finding confirms that the reaction between vanadium and calcium is easier than that between vanadium and manganese at the same roasting temperature and roasting time.

    Furthermore, the activation of the diffusion reaction of CaO and V2O5 or MnO2 and V2O5 is expected to be constant due to the linear relationship between the product layer thickness and roasting time. Then, the diffusion coefficients D of the CaO–V2O5 and MnO2–V2O5 diffusion couples can be calculated by Eq. (5) [34,42], as shown in Fig. 10.

    Fig. 10.  Relationships between the diffusion coefficient and roasting time of CaO–V2O5 and MnO2–V2O5 diffusion couples.
    L2=4Dt (5)

    The results show that with the extension of the roasting time, the diffusion coefficients (D) basically increase first and then decrease among the CaO–V2O5 and MnO2–V2O5 diffusion couples. The maximum values are achieved at 16 h, which are 6.89 × 10−11 and 4.48 × 10−11 cm2·s−1. Hence, prolonging the roasting time is beneficial to the diffusion reactions of the CaO–V2O5 and MnO2–V2O5 diffusion couples. After 16 h, the diffusion reactions reach the equilibrium states on the whole, and the diffusion coefficients decrease. Furthermore, the diffusion coefficient D of the CaO–V2O5 diffusion couple is higher than that of the MnO2–V2O5 diffusion couple at the same roasting time, which further confirms that calcium is slightly stronger than manganese in terms of the reaction ability with vanadium.

    Based on the above analyses, the diffusion reaction mechanisms of the CaO–V2O5 and MnO2–V2O5 diffusion couples are summarized in Fig. 11. For the CaO–V2O5 diffusion couple, the diffusion ability of vanadium to the product layer and CaO side is close to that of calcium to the product layer and V2O5 side. With the extension of the roasting time, vanadium and calcium continue to contact and react to form CaV2O6, and their thicknesses gradually increase. After roasting for 16 h, it is difficult for vanadium or calcium molecules to pass through the product layer, which may be related to the molecular diffusion ability of vanadium and calcium or the thickness and density of the product layer. Thus, vanadium and calcium cannot easily contact each other, and the diffusion reaction would not be continued.

    Fig. 11.  Diffusion reaction mechanisms of the CaO–V2O5 and MnO2–V2O5 diffusion couples.

    For the MnO2–V2O5 diffusion couple, the diffusion ability of vanadium to the product layer and Mn2O3 side is far stronger than that of manganese to the product layer and V2O5. With the extension of the roasting time, the diffusion-layer thickness increases mainly due to the reaction between vanadium and manganese on the Mn2O3 side. Even when the roasting time reaches 16 h, an obvious fault zone appears on the V2O5 side away from the diffusion couple interface. At this time, vanadium diffuses into the Mn2O3 side has reached the reaction equilibrium with manganese, whereas vanadium on the V2O5 side cannot easily diffuse to the Mn2O3 side and break the reaction equilibrium due to the existence of the fault zone. Therefore, the thickness of the product layer no longer increases after 16 h.

    In this work, the reaction mechanism of calcium and manganese in the reaction with vanadium was investigated and compared through the diffusion couple method. V2O5 was used to simulate and simplify vanadium slag to avoid the interference of other impurity elements. The CaO–V2O5 and MnO2–V2O5 diffusion couples were roasted for different time periods to illustrate the diffusion interface, diffusion products, and diffusion coefficient of the CaO–V2O5 and MnO2–V2O5 systems. Accordingly, the following conclusions can be drawn.

    (1) During the diffusion reaction of the CaO–V2O5 couple, calcium and vanadium always exist in the form of CaO and V2O5. The product layer and boundaries of calcium and vanadium are obvious. For the MnO2–V2O5 couple, MnO2 is gradually decomposed into Mn2O3. Vanadium can diffuse into the interior of manganese, whereas only part of vanadium combines with manganese to form the diffusion production layer. The particles of V2O5 are stretched, and a fault even appears in the V2O5 side with the extension of the diffusion time, which is attributed to the fact that the diffusion ability of vanadium to the product layer and Mn2O3 side is far stronger than that of manganese to the product layer and V2O5.

    (2) The atomic ratios of calcium to vanadium or manganese to vanadium in the product layers of the CaO–V2O5 and MnO2–V2O5 diffusion couples are approximately 2 for different roasting times, confirming that the diffusion products of the CaO–V2O5 and MnO2–V2O5 diffusion couples are CaV2O6 and MnV2O6, respectively.

    (3) The thickness of the product layer gradually increases with the extension of the roasting time, which does not significantly increase after 16 h. The diffusion product layer thickness of the CaO–V2O5 and MnO2–V2O5 diffusion couples are 39.85 and 32.13 μm at 16 h. After 16 h, the two diffusion couples reach the reaction equilibrium due to the limitation of diffusion. Moreover, the diffusion coefficient of the CaO–V2O5 diffusion couple is higher than that of the MnO2–V2O5 diffusion couple at the same roasting time. Hence, the diffusion reaction between vanadium and calcium is easier than that between vanadium and manganese.

    This work was financially supported by the National Natural Science Foundation of China (Nos. 52174277 and 51874077), the Fundamental Funds for the Central Universities, China (No. N2225032), the China Postdoctoral Science Foundation (No. 2022M720683), and the Postdoctoral Fund of Northeastern University, China.

    The authors have no relevant financial or non-financial interests to disclose.

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