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Article

Investigations on Microstructures and Properties of (Fe, Cr, W)7C3 Carbides by First Principles and Experiments

1
School of Materials Science and Engineering, Jiamusi University, Jiamusi 154007, China
2
School of Mechanical Engineering, Jiamusi University, Jiamusi 154007, China
*
Author to whom correspondence should be addressed.
Coatings 2022, 12(9), 1363; https://doi.org/10.3390/coatings12091363
Submission received: 30 July 2022 / Revised: 2 September 2022 / Accepted: 16 September 2022 / Published: 18 September 2022
(This article belongs to the Special Issue Laser Cladding Coatings: Microstructure, Properties, and Applications)

Abstract

:

Highlights

  • The structural and elastic properties of (Fe, Cr, W)7C3 were investigated by first principles.
  • Tungsten doping can improve the ductility and the indentation modulus of (Fe, Cr)7C3 carbides.
  • The elastic anisotropy of M7C3 became weaker after tungsten doping.
  • A new carbide (Fe3.27Cr2.99W0.74) C3 was found to be a combination of mechanical properties.

Abstract

Tungsten doping is critical for the wear resistance and application of High-Chromium Cast Iron (HCCI). A series of investigations of (Fe, Cr, W)7C3 carbides were performed by first principles calculations and experimental analysis. The calculated results showed that with the increase in tungsten content in M7C3, the equilibrium cell volumes and the density gradually increased, and the formation energy of M7C3 carbides gradually decreased. The TEM results showed that the (Fe, Cr, W)7C3 carbides were (Fe3.27Cr2.99W0.74) C3 with a hexagonal structure after adding 2.13 wt % tungsten into laser cladding coatings of High-Chromium Cast Iron with a composition of Fe-26.8 wt % Cr-3.62 wt % C. These results from calculations and in situ nanoindentation show that tungsten doping could improve the ductility and indentation modulus of (Fe, Cr)7C3 carbides, and the composition of (Fe, Cr, W)7C3 was expected to be a high hardness and softness material. The wear test results showed that the wear resistance of tungsten-bearing HCCI was better than ordinary HCCI.

1. Introduction

Hypereutectic High-Chromium Cast Iron (HCCI) is an important wear resistance material, widely used in the mining and crushing field due to its easy production, low cost and excellent wear resistance [1,2,3]. The microstructure of HCCI primarily contains hard M7C3-type carbides (with a high hardness of 1300–1800 HV) and martensitic matrix [4]. There are three types of HCCI: hypoeutectic HCCI, eutectic HCCI and hypereutectic HCCI [5]. For hypereutectic HCCI, the M7C3 eutectic carbides solidify firstly, and could improve the hardness and the wear resistance of HCCI. HCCI could be prepared by casting [6], an Electrothermal Exial Plasma Accelerator (EAPA) [7] and so on. Heydari et al. [6] prepared HCCI with 22% Cr, 10%–12% tungsten by casting. The results showed that the coarse chromium carbides are distributed in the matrix when the carbon content was low (2.3 wt %). With the increase in carbon content, the carbides will become finer. Efremenko et al. [7] studied the effect of layered morphology and heat treatment on the microstructure and hardness after the pulsed plasma deposition of Fe-C-Cr-W coating on HCCI. Post-deposition heat treatment resulted in the precipitation of M7C3 carbides, the carbide precipitation led to a substantial increase in the coating hardness to 1240–1445 HV0.05. Thus, M7C3 carbides are important for HCCI.
M7C3 (M = Fe, Cr or other element) carbides are the main hardening phases in HCCI, showing a high hardness, a high strength, a high elastic moduli and a ductile property [8]. Furthermore, M7C3 carbides enhance the mechanical properties and oxidation resistance of HCCI at high temperatures [9]. The effect mechanism of alloy elements on the structure and mechanical properties of M7C3 has been comprehensively studied by first principles calculations [10,11,12,13,14]. Experiments from Coronado [15] showed that M7C3 carbides in HCCI were rod-like single crystals with strong anisotropy. The abrasion resistance of the M7C3 carbides in the transverse section ([0001] direction) was higher than in the longitudinal section (non-[0001] direction) [15]. Moreover, the wear resistance of ZTAP/HCCI composites with a honeycomb structure was higher than High-Chromium Cast Iron [16,17]. Therefore, the extensive application of M7C3 multi-component carbides is of great significance to future wear-resistant materials.
One method to improve the hardness and the wear resistance would be to add alloying elements in HCCI, such as vanadium, tungsten, titanium and niobium [18]. As a strong carbide-forming element, tungsten could improve the wear resistance of HCCI [19]. The extensive experiments on the effect of tungsten on microstructure and properties of HCCI have been published over the past few decades [18,19,20,21]. Cortés-Carrillo et al. [18] analyzed the effects of tungsten on the microstructure, hardness, microhardness and abrasive wear of High-Chromium Cast Iron with 17 wt % Cr. The results showed that when tungsten content was 4 wt %, the hardness of the alloys increased due to the dispersion of tungsten into the matrix and the M7C3 carbides. When the added amount of tungsten exceeded 4 wt %, M2C and M6C carbides appear in the microstructure of the alloy. The work from Lv et al. [19] found that tungsten considerably improved the wear resistance of HCCI, and the wear resistance of HCCI with 1.03 wt % W increased by 205% compared to HCCI without tungsten. Results from Anijdan et al. [20] also showed that the wear resistance of High-Chromium Cast Iron increased after adding the tungsten. The experimental results from Guerra et al. [21] verified that tungsten partially distributed in the different phases, increasing the microhardness and refining the eutectic carbides. However, the effects of tungsten on the structure and mechanical properties of M7C3 are not yet clear and should be further explored to reveal the mechanism.
First principles calculations are an effective way to reveal the mechanism. Zhang et al. [8] investigated the optimization of mechanical properties of Fe7-xCrxC3 carbides by first principles calculations, including Fe6CrC3, Fe4Cr3C3, Fe3Cr4C3 and FeCr6C3, but they ignored M7C3 carbides. Chong et al. [22] designed the anisotropic mechanical properties of M7X3 (M = Fe, Cr, W, Mo. X = C, B) by multi-alloying. The results showed that the ductility could be increased by doping of W + B and W + Mo without sacrificing the mechanical modulus of Cr4Fe3C3, and the hardness of Cr4Fe3C3 could be improved by doping of Mo + B and Mo + W + B with a finite decrease in ductility. The anisotropy of M7C3 carbides is important in the performance of High-Chromium Cast Iron [23]. However, the effect of tungsten on the anisotropy has not been researched and the mechanism is not clear to date. In addition, unfortunately, the stability, properties and electronic structure of M7C3 (M = Fe, Cr, W) carbides are seldom comprehensively investigated in the literature.
Therefore, the electronic structures, stability, chemical bonds and existing form of M7C3 (M = Fe, Cr and W) in Fe—26.8 wt % Cr—3.62 wt % C—2.13 wt % W High-Chromium Cast Iron were thoroughly investigated by first principles calculation experiments, which are helpful to improve the whole performance of HCCI.

2. Experimental Details

2.1. Calculation Details

First principles calculations are an effective way of investigating the electronic structures, stability and chemical bonds of M7C3 carbides in HCCI. The Density Functional Theory (DFT) calculation based on the pseudopotential plane-wave within the Generalized Gradient Approximation (GGA), as implemented in the Cambridge Serial Total Energy Package (CASTEP), was performed in the present work. The Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [24] was applied in the relaxation process of models to optimize the structures. In the structural optimization process, the maximal displacement was 11.0 × 10−3 Å, the largest force was 0.03 eV/Å and the energy change convergence value was less than 1 × 10−5 eV/atom. After convergence tests, the cutoff energy of 360 eV and k-point of 8 × 8 × 8 were selected for these carbides. Although Fang et al. [25] demonstrated that orthorhombic Fe7C3 is more stable than an orthorhombic or hexagonal structure, Chong et al. [22] found that the crystal structure of (Cr, Fe)7C3 carbides is hexagonal with the space group of P63mc (No. 186) by XRD and TEM analysis. Therefore, a hexagonal structure was selected in this work. Zhang et al. [8] investigated the mechanical properties of Fe7−xCrxC3 carbides based on first principles calculations, including Fe6CrC3, Fe4Cr3C3, Fe3Cr4C3 and FeCr6C3, but they neglected to calculate the other type, M7C3 carbides. Therefore, the properties of Fe5Cr2C3, Fe2Cr5C3 and Fe3Cr4C3 (the crystal structure shown in Figure 1) were calculated by first principles, and the results were compared to the calculated results from references [8,22]. To study the influencing mechanism of tungsten on the structure and mechanical properties of M7C3, different amounts of tungsten were doped into M7C3 carbides. The M7C3 structures consist of nonequivalent Fe (Cr) atoms, and the lattice parameters, elastic moduli, etc., depend strongly on the substitution sites. We calculated all the formation energy of various sites of doped atoms in the unit cell, and then the unit cell obtained by the minimum formation energy was selected as the final result. Some unit cells of M7C3 carbides with crystal structures were built, including of Fe3Cr3.5W0.5C3, Fe3Cr3W1C3, Fe3Cr2.5W1.5C3 and Fe3Cr2W2C3, as shown in Figure 1.

2.2. Experimental Data

In this work, Q235 carbon steel with a chemical composition of Fe-0.18% wt % C-0.22% wt % Si-0.45% wt % Mn-0.02% wt % P-0.02% wt % S was used as the substrate, and the cladding materials were High-Chromium Cast Iron powders and tungsten powders (70 wt % W and 29 wt % Fe). The diameter of the above powders was 75–105 μm. The cladding layer was made by an IPG fiber laser system (YLS-6000) with a continuous wave, with a laser beam size of 5 mm × 5 mm. The parameters were as follows: powder feeding rate k = 15 g/min, scanning speed ν = 4 mm/s, laser power P = 2000 W, flow rate of high-purity argon shielding gas = 15 L/min.
The microstructures were observed using a JEM-2100F Transmission Electron Microscope (TEM, manufacturer, city, country) with an energy-dispersive X-ray (EDX, manufacturer, city, country). TEM samples were prepared by ion milling. The wear resistance of the cladding layer was tested by a MM-200 block-on-ring wear testing machine (manufacturer, city, country, the working principle of machine can be found in reference [26]). In situ nanoindentation experiments were performed using the NanoFlip InForce 50 (manufacturer, city, country) to investigate the hardness and modulus of M7C3 carbides.
For the wear resistance of HCCI, the reported value of weight loss is the average of five results. All data graphs were drawn by Origin 8.0 software, and show the formation energy, mechanical properties, hardness and modulus and weight loss.

3. Results and Discussion

3.1. The Equilibrium Lattice Constants and Stability

To ensure the accuracy of the calculation, the optimized lattice constants were calculated, and the calculated results were compared to other calculated results and experimental values, as shown in Table 1. The optimized lattice constants of Fe3Cr4C3 were 6.8358, 6.8358 and 4.5471 Å, which are similar to other calculated values [8] and experimental values [9] (error less than 1.2%). Considering the differences in experimental equipment and calculation methods, it was proved that the parameters adopted were reliable. With the increase in Cr content, the equilibrium lattice parameter a increased and c decreased, meaning that a decreases when c increases, which is consistent with the conclusion of reference [22]. With the increase in tungsten content, the equilibrium lattice parameters a and b gradually increased. The calculated result of equilibrium cell volume (185.61 Å) for Fe3Cr4C3 was similar to the calculated values (181.09 Å) from Zhang et al. [8] (error less than 3%). With the increase in tungsten content, the equilibrium cell volumes and the density gradually increased.
In order to predict whether M7C3 (M = Fe, Cr and W) carbides were easy to compound, the formation energy was calculated by the following equation [8]:
ΔEM7C3 (M = Fe, Cr, W) = Etot(M7C3) − xEtot(Fe) − yEtot(Cr) − zEtot(W) 3Etot(C)
where Etot(M7C3), Etot(Fe), Etot(Cr), Etot(W) and Etot(C) are the total energies of M7C3 carbides, Fe, Cr, W and C systems, respectively. ΔEM7C3 (M = Fe, Cr, W) is the formation energy of M7C3 carbides. The formation energy can describe the relative stability of these carbides. If ΔEM7C3 > 0, the crystal is unstable or metastable; if ΔEM7C3 < 0, the crystal can exist stably [27]. Additionally, if the stability of carbides is better, the carbides may be synthesized easily; if the M7C3 carbides are not stable, it may not be easy to compound them in the experimental stage [28]. According to Equation (1), the formation energies of M7C3 carbides were calculated, as shown in Figure 2. Except for Fe7C3, the formation energies of other carbides are less than zero, indicating that they are stable crystal structures. With the increase in W and Cr content, the formation energy was increased gradually, indicating that the stability of carbides increased with W and Cr content.

3.2. Mechanical Properties

M7C3 carbides are the main hard phases in wear-resistant material, so the elastic of M7C3 compounds has an important role in the application of wear-resistant material. The elastic constants Cij depend mainly on the response of the crystal to external forces, and can be calculated by the bulk, shear and Young’s modulus, Poisson’s ratio, etc. The bulk modulus and the shear modulus can be calculated by the following method [29]:
B V = ( 1 9 )   [ 2 ( C 11 + C 12 ) + 4 C 13 + C 33 ]
G V = ( 1 30 )   [ ( C 11 + C 12 + 2 C 33 4 C 13 + 12 C 44 + 12 C 66 )
BR = [(C11 + C12) C33 − 2C132]/(C11 + C12 + 2C33 − 4C13)
G R = ( 5 2 )   [ ( C 11 + C 12 )   C 33 2 C 13 2 ]   C 44 C 66 / { 3 B V C 44 C 66 + [ C 11 + C 12 )   C 33 2 C 13 2 ]   ( C 44 + C 66 ) }
B = (BV + BR)/2
G = (GV + GR)/2
E = 9BG/(3B +G)
σ = (3B − 2G)/(6B + 2G)
where B and G are the bulk modulus and the shear modulus, respectively. E and σ are Young’s modulus and Poisson’s ratio, respectively. C11, C22 and C33 represent the uniaxial deformation along the [ 1 ¯ 2 1 ¯ 0], [2 1 ¯ 1 ¯ 0] and [0001] directions, respectively. C44, C55 and C66 represent the pure shear deformation on ( 1 ¯ 2 1 ¯ 0), (2 1 ¯ 1 ¯ 0) and (0001) crystal planes, respectively. C12 is the shear deformation on the ( 1 ¯ 100) crystal plane along the [1 1 ¯ 00] direction.
For the hexagonal phase, the mechanical stability criteria are given by [29]:
C44 > 0, C11 > |C12|, (C11 + 2C12)C33 > 2C13
The calculated elastic constants of M7C3 carbides satisfied the above formula, indicating that these M7C3 carbides were stable structures. Table 2 lists the calculated elastic constants (Cij) of different M7C3 carbides, which showed good agreement with the data of other researchers [22]. The largest C11, C12 and C13 appeared on Fe3Cr2W2C3, but the largest C66 and C44 appeared on Fe2Cr5C3. Because the hardness of M7C3 carbides is large, the relatively simple semi-empirical equation of hardness can be used, which is [30]:
HV = 1.92 K1.137G0.708, K = G/B
Figure 3 shows the mechanical properties of M7C3 carbides. The shear modulus and Young’s modulus of Fe2Cr5C3 are the largest. With the addition of tungsten, the shear modulus and Young’s modulus began to decrease, indicating that the alloying tungsten decreases the strength of M7C3. Poisson’s ratio can reflect the flexibility; the larger Poisson’s ratio is, the softer the material is. Poisson’s ratio of Fe3Cr2.5W1.5C3 is the largest, indicating that the Fe3Cr2.5W1.5C3 compound is the softest. Pugh’s modulus ratio B/G and Cauchy pressure (C11C44) can explain the ductile/brittle properties. When G/B is smaller than 0.571, the M7C3 has good ductile property [8]. With the addition of tungsten, G/B is reduced, indicating that tungsten can improve the toughness of M7C3. Cauchy pressure of M7C3 carbides increased with tungsten content, as shown in Figure 3f, which indicates that tungsten doping can improve the ductility of (Fe, Cr)7C3 carbides. The composition of (Fe, Cr, W)7C3 is expected to be a high hardness and softness material; thus, the synthesis of this carbide would be of great interest.
Anisotropy of M7C3 effects the wear resistance of HCCI [8]. Therefore, the analysis of anisotropy is important for understanding the properties of M7C3 carbides. The anisotropy of Young’s modulus for hexagonal M7C3 carbides along different directions is expounded by the 3D surface contours, following [22]:
1/E = (1 − l12)2 S11 + l14S33 + l12 (1 − l12) (2S13 + S44)
where Sij is the elastic compliance constant. Sij is the inverse matrix of Cij. l3 = cosφ is the directional cosine. The results are shown in Figure 4. In Figure 4a,b,d,e, it can be seen that Fe5Cr2C3, Fe3Cr4C3, Fe3Cr3.5W0.5C3 and Fe3Cr3W1C3 showed strong anisotropy. As the Cr content increased, the elastic anisotropy of (Fe, Cr)7C3 became weaker. Similarly, as the tungsten content increased, the elastic anisotropy of (Fe, Cr, W)7C3 became weaker, as shown in Figure 4f,g. The results indicate that alloying could weaken the elastic anisotropy of M7C3 carbides, which is in agreement with other calculated results [22].

3.3. The Electronic Structures

As is known, the properties of carbides are associated with electronic states [31]. In order to gain some insight into the nature of bonding in M7C3 carbides, the band structure and the Partial Density of States (PDOS) were calculated. Figure 5 shows the band structure of M7C3, and the dashed line indicates the Fermi level. All calculated M7C3 carbides in this work exhibited metallic properties. Figure 6 shows the Total Density of States (TDOS) and the Partial Density of States (PDOS). PDOS can analyze the electronic hybridization states quantitatively with chemical bonding. Fe5Cr2C3, Fe3Cr4C3, Fe2Cr5C and Fe3Cr3W1C3 carbides show large shifts, because the up and down spin channels are not symmetric. However, Fe3Cr3.5W0.5C3, Fe3Cr2.5W1.5C3 and Fe3Cr2W2C3 are symmetric, which may indicate non-magnetic characteristics of these carbides. In Figure 6, the DOS on both sides of the Fermi level were determined mainly by the Fe-d and Cr-d. From −15 to −10 eV, TDOS mainly consists of C-s orbit, but from −7.5 to 10 eV, TDOS of M7C3 mainly consists of W-d, Fe-d, Cr-d and C-p orbit, as shown in Figure 6d–g. From −7.5 to −2.5 eV, TDOS mainly consists of Fe-d, W-d and Cr-d orbit, and their peak shape and peak intensity are similar, indicating that there is orbital hybridization. The d orbit of Cr, Fe, W and the p orbit of carbon have strong hybridization, suggesting a covalent bond between the Cr, Fe, W atom and carbon atom. The total electron density distribution is shown in Figure 7. For an ideal single crystal, the magnitude of the mechanical modulus is related to the chemical bond strength. In Figure 7a, Fe-C-Cr and Fe-C-Fe covalent chains can be observed in Fe3Cr4C3 carbides, which is in agreement with other calculated results [8]. In Figure 7b, Cr-W-C, Fe-C-Cr and Fe-C-W covalent chains can be observed in Fe3Cr2W2C3 carbides, explaining the decrease in formation energy after adding tungsten.

3.4. TEM Analysis

To study the existence form of carbides after adding tungsten to HCCl, the microstructures of High-Chromium Cast Iron with a composition of 3.44C-26.7Cr-1.25Mn-2.3 wt % W was characterized by TEM. Figure 8a shows the bright-field TEM micrographs, and Figure 8b shows the Selected Area Diffraction Pattern (SADP) of M7C3. The results show that the carbides are M7C3 phase with a hexagonal structure, and the space group is P63mc (No. 186). According to the accurate measurement using EDX at 10 different areas of M7C3, the calculated analysis suggests that (Fe, Cr, W)7C3 has a stoichiometry of (Fe3.27Cr2.99W0.74) C3. Moreover, the lattice constant of (Fe3.27Cr2.99W0.74) C3 carbides is a = 0.6833 nm, b = 0.6833 nm, c = 0.4796 nm.

3.5. Nanoindentation Experiments

The hardness and modulus of carbides were investigated by a NanoFlip InForce 50. Figure 9a,b shows the indentation hardness HIT and the indentation modulus EIT of M7C3 carbides, respectively. With indentation depths larger than 100 nm, EIT and HIT of M7C3 phase reached a constant level, which indicated that the intrinsic material properties of the hard phases were measured in this experiment. Furthermore, the crack formation was not observed at an indentation depth of 200 nm, and the triangular indentations could be observed on M7C3 carbides, indicating that the credibility of the data is high. The indentation hardness values of (Fe, Cr)7C3 and (Fe, Cr, W)7C3 were 17.55 and 17.39 GPa, respectively. The indentation modulus values of (Fe, Cr)7C3 and (Fe, Cr, W)7C3 were 367.87 and 385.48 GPa, respectively.

3.6. Wear Resistance

The wear resistance of HCCI was tested by a MM-200 block-on-ring wear testing machine. It was apparent that the wear resistance of HCCI after adding tungsten exceeds that of HCCI without tungsten. With the increase in wear load, the wear loss increased, as shown in Figure 10. The wear resistance of HCCI was closely related to the hardness of carbides, but also to the hardness of the matrix. Therefore, the abrasion resistance slightly increased after tungsten was added.
To better reflect the wear resistance of HCCI after the addition of tungsten, the worn surface was characterized by a JSM-6510 Scanning Electron Microscope (SEM) and a VK-9710 color 3D laser scanning microscope. Figure 11a,b is the SEM images of ordinary HCCI and HCCI with tungsten, respectively. Figure 11c,d is the 3D laser morphologies of the worn surfaces of ordinary HCCI and HCCI with tungsten, respectively. Some obvious scratches were found on the specimen surface, and the wear surfaces of both HCCIs were consistent [32]. However, the groove scratches and fine wear of ordinary HCCI were obviously deep, indicating that the wear resistance of HCCI is better after adding tungsten.

4. Conclusions

In this work, we added tungsten to High-Chromium Cast Iron to investigate the microstructures and properties of M7C3 carbides by first principles and experiments.
(a) With the increase in W and Cr content in M7C3 carbides, the formation energy of M7C3 carbides gradually decreased. Tungsten doping can improve the ductility of (Fe, Cr)7C3 carbides, and the composition of (Fe, Cr, W)7C3 is expected to be a high hardness and softness material.
(b) TEM results showed that the (Fe, Cr, W)7C3 carbides are (Fe3.27Cr2.99W0.74) C3 with a hexagonal structure after adding 2.13 wt % W into Fe—26.8 wt % Cr—3.62 wt % C High-Chromium Cast Iron.
(c) Wear test results showed that the wear resistance could be improved after adding tungsten to HCCI.

Author Contributions

C.C.: Investigating, Methodology, Formal analysis, Writing, Review, Editing. J.W.: Supervision, Funding acquisition, Writing, Review, Editing. Y.G.: Investigation, Experiments, Data curation. L.M.: Software, Writing, Review, Editing. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the National Natural Science Foundation of China (grant 51875252), the Natural Science Foundation of Heilongjiang Province (LH2020E026) and the Basic Scientific Research Business Fee Project of Heilongjiang Provincial Department of Education (2020-KYYWF-0266).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Unit cells of M7C3 carbides with crystal structures: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d)Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
Figure 1. Unit cells of M7C3 carbides with crystal structures: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d)Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
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Figure 2. Calculated formation energy of M7C3 carbides (ΔE for, eV/cell).
Figure 2. Calculated formation energy of M7C3 carbides (ΔE for, eV/cell).
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Figure 3. The mechanical properties of M7C3: (a) the bulk modulus (B); (b) the shear modulus (G); (c) Young’s modulus (E); (d) Poisson’s ratio (σ); (e) Pugh’s modulus ratio G/B; (f) Cauchy pressure C12C44; (g) calculated hardness.
Figure 3. The mechanical properties of M7C3: (a) the bulk modulus (B); (b) the shear modulus (G); (c) Young’s modulus (E); (d) Poisson’s ratio (σ); (e) Pugh’s modulus ratio G/B; (f) Cauchy pressure C12C44; (g) calculated hardness.
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Figure 4. Surface constructions of Young’s modulus of M7C3 carbides: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d)Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
Figure 4. Surface constructions of Young’s modulus of M7C3 carbides: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d)Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
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Figure 5. Calculated band structure: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d) Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
Figure 5. Calculated band structure: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d) Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
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Figure 6. Calculated PDOS: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d)Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
Figure 6. Calculated PDOS: (a) Fe5Cr2C3; (b) Fe3Cr4C3; (c) Fe2Cr5C3; (d)Fe3Cr3.5W0.5C3; (e) Fe3Cr3W1C3; (f) Fe3Cr2.5W1.5C3; (g) Fe3Cr2W2C3.
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Figure 7. The valence electron density for (a) Fe3Cr4C3 and (b) Fe3Cr2W2C3.
Figure 7. The valence electron density for (a) Fe3Cr4C3 and (b) Fe3Cr2W2C3.
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Figure 8. Bright-field TEM micrographs and corresponding Selected Area Diffraction Patterns (SADPs): (a) bright-field TEM micrographs; (b) corresponding SADPs of M7C3.
Figure 8. Bright-field TEM micrographs and corresponding Selected Area Diffraction Patterns (SADPs): (a) bright-field TEM micrographs; (b) corresponding SADPs of M7C3.
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Figure 9. Indentation hardness and indentation modulus of M7C3 phase: (a) indentation hardness; (b) indentation modulus.
Figure 9. Indentation hardness and indentation modulus of M7C3 phase: (a) indentation hardness; (b) indentation modulus.
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Figure 10. The wear resistance of HCCI.
Figure 10. The wear resistance of HCCI.
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Figure 11. The worn surfaces of HCCI: (a,c) ordinary HCCI; (b,d) tungsten-bearing HCCI.
Figure 11. The worn surfaces of HCCI: (a,c) ordinary HCCI; (b,d) tungsten-bearing HCCI.
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Table 1. The lattice parameters of different M7C3 carbides.
Table 1. The lattice parameters of different M7C3 carbides.
SpeciesSpace Groupa (Å)b (Å)c (Å)Volume (Å3)Density (g/cm3)
Fe5Cr2C3P63mc (186)7.00547.00544.3188183.007.61
Fe2Cr5C3P63mc (186)6.77956.77954.6500187.217.23
Fe3Cr4C3P63mc (186)6.83586.83584.5471185.617.37
Fe3Cr4C3 [11]P63mc (186)6.82586.82584.4948180.07.48
Fe3Cr4C3 [8]P63mc (186)------181.09--
Fe3Cr4C3Exp. [11]P63mc (186)6.9--4.52----
Fe3Cr3.5W0.5C3P63mc (186)6.75566.75584.8070190.128.34
Fe3Cr3W1C3P63mc (186)6.86096.86094.8098195.459.23
Fe3Cr2.5W1.5C3P63mc (186)6.89986.97214.7962199.9810.12
Fe3Cr2W2C3P63mc (186)6.98186.98184.8382203.7811.00
Table 2. The elastic constants (Cij, GPa) of different M7C3 carbides.
Table 2. The elastic constants (Cij, GPa) of different M7C3 carbides.
SpeciesC11C33C44C12C13C66
Fe5Cr2C3534.6560.8123.8193.5255.4152.3
Fe2Cr5C3562.1559.2157.9159.2258.3193.0
Fe3Cr4C3549.2531.6122.5179.6248.1179.6
Fe3Cr4C3 [9]550.7532.8110.6185.2229.0182.7
Fe3Cr3.5W0.5C3546.1523.6100.9251.5246.0166.5
Fe3Cr3WC3543.2504.999.1236.8243.6155.8
Fe3Cr3WC3 [9]565.5415.487.8252.0249.2156.8
Fe3Cr2.5W1.5C3578.9403.492.3276.5279.5149.1
Fe3Cr2W2C3581.5377.590.9300.1288.1166.9
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Chen, C.; Wang, J.; Ge, Y.; Ma, L. Investigations on Microstructures and Properties of (Fe, Cr, W)7C3 Carbides by First Principles and Experiments. Coatings 2022, 12, 1363. https://doi.org/10.3390/coatings12091363

AMA Style

Chen C, Wang J, Ge Y, Ma L. Investigations on Microstructures and Properties of (Fe, Cr, W)7C3 Carbides by First Principles and Experiments. Coatings. 2022; 12(9):1363. https://doi.org/10.3390/coatings12091363

Chicago/Turabian Style

Chen, Chao, Junfa Wang, Yiyuan Ge, and Lili Ma. 2022. "Investigations on Microstructures and Properties of (Fe, Cr, W)7C3 Carbides by First Principles and Experiments" Coatings 12, no. 9: 1363. https://doi.org/10.3390/coatings12091363

APA Style

Chen, C., Wang, J., Ge, Y., & Ma, L. (2022). Investigations on Microstructures and Properties of (Fe, Cr, W)7C3 Carbides by First Principles and Experiments. Coatings, 12(9), 1363. https://doi.org/10.3390/coatings12091363

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