Effects of impurity elements on SiC grain boundary stability and corrosion

NUCLEAR CHEMISTRY, RADIOCHEMISTRY, AND NUCLEAR MEDICINE

Effects of impurity elements on SiC grain boundary stability and corrosion

Jun Hui，

Bao-Liang Zhang，

Tao Liu，

Min Liu，

Wen-Guan Liu

Nuclear Science and Techniques

Vol.32, No.11

Article number 125

Published in print 01 Nov 2021

Available online 16 Nov 2021

DOI：10.1007/s41365-021-00963-2

34601

Grain boundaries (GBs) have critical influences on the stability and properties of various materials. In this study, first-principles calculations were performed to determine the effects of four metallic impurities (Ni, Al, Bi, and Pb) and three nonmetallic impurities (H, O, and N) on the GBs of silicon carbide (SiC), using the Σ5(210) GBs as models. The GB energy and segregation energy (SE) were calculated to identify the effects of impurities on the GB stability. Electronic interactions considerably influenced the bonding effects of SiC. The formation of weak bonds resulted in the corrosion and embrittlement of GBs. The co-segregation of Bi, Pb, and O was also investigated in detail.

SiCFirst-principles calculationGrain boundaryImpurity atomCo-segregation.

Introduction

Silicon carbide (SiC) [1,2] exhibits excellent irradiation stability and strength at high temperatures, which has led to its widespread application in reactor core structures, nuclear fuel, and nuclear waste disposal [3,4]. The aforementioned properties can be primarily attributed to the fact that SiC undergoes oxidation in hot water and high-temperature steam environments, which results in the formation of a protective film of silicon dioxide (SiO₂) [1,3]. However, the irradiation stability and strength of SiC may decrease in complex and extreme combustion environments. Impurities from the environment or SiC matrix may be enriched along the grain boundaries (GBs) of SiC [4], which leads to GB destabilization and problems such as corrosion, stress concentration, and cracks. In addition, the impurities at SiC GBs contribute to lattice defects that accelerate the corrosion rate of SiC [5]. Irradiation can result in the accumulation of lattice damage and accelerate SiC corrosion [6-8].

The corrosion behaviors of SiC in different environments are complex but are highly influenced by its GBs. Impurity or doping atoms can promote or suppress the intergranular corrosion of SiC. Therefore, the effects of impurities on SiC GBs and the underlying mechanisms of these effects should be investigated. Parish et al. [9] investigated the hydrothermal corrosion behavior of SiC at 603 K and 15 MPa and found that oxide additives, especially Al, were enriched at SiC GBs and induced intergranular corrosion. Doyle et al. [10] revealed that corrosion rarely occurred at the GBs of SiC in an oxygen-free atmosphere. However, in an oxygenated atmosphere, the GBs of SiC were strongly corroded, and fine SiC grains were exfoliated. Ni can improve the GB stability and corrosion resistance of SiC [11-13]. Under a static corrosion condition [14], SiC exhibits satisfactory corrosion resistance against the coolant of lead-based reactors, namely lead–bismuth eutectic (LBE) [13].

Theoretical simulations have been conducted to study the structural defects and corrosion behavior of SiC [15]. Such simulations can indicate the underlying physical mechanisms of structural defects and corrosive behavior and help overcome the limitations of experimental research (e.g., those limitations related to the irradiation facility, detection limits, and high cost) [15]. Shrader et al. [16,17] studied the diffusion of Cs, Ag, and B in SiC. By performing first-principles calculations, Zhang et al. [18] determined that the weakening of Si-O and Al-O bonds leads to the accelerated oxidation of SiC. Qing et al. [19] examined the diffusion mechanism of Ag in SiC. However, only a few studies have assessed how impurities affect GB corrosion in SiC. Thus, theoretical simulations are advantageous and essential for investigating the structural defects of SiC.

GBs can serve as channels for rapid diffusion, and impurity or doping atoms can diffuse or cluster at SiC GBs. GBs are considered to be structural defects that are susceptible to corrosion. The vacancies at GBs can capture the atoms introduced through irradiation or doping [20], which may lead to GB embrittlement or corrosion [21-23]. The Σ5 GB is frequently used to investigate the element segregation and corrosion in materials with a face-centered cubic (FCC) structure [24-27]. Rare earth (RE) elements (e.g., Lu, Er, and Ce) have been observed at the GBs of isomeric α-SiC which has an FCC structure [28]. Tan et al. [29] observed Σ5 GBs with a tilt angle of 53° in SiC by using electron backscatter diffraction.

In addition to Ni, Pb, and Bi, Al is a doped in SiC ceramics. Moreover, H, N, and O are common and inevitable impurities in SiC. SiC GBs are strongly corroded in oxygenated atmospheres [30-32]. Therefore, Ni, Al, Bi, Pb, H, O, and N were selected as examples in this study to investigate the effects of impurity elements on the stability and corrosion of SiC GBs [34-36]. Moreover, the radii of metallic impurities in SiC are larger than those of nonmetallic impurities in SiC [37-40]; therefore, metallic impurities are usually doped into the GBs of SiC through substitution, whereas nonmetallic impurities are doped into the interstices at the GBs of SiC [41-44].

In summary, in this study, we employed first-principles calculations to examine the effect of metallic impurities (i.e., Ni, Al, Bi, and Pb) and nonmetallic impurities (i.e., H, O, and N) on the GB energy (GBE), segregation energy (SE), co-segregation, and corrosion of the Σ5(210) GBs in SiC. First, we calculated the GBE and SE values of the Σ5(210) GBs with metallic and nonmetallic impurities at various sites. We found that the GBE increased as the atomic radius of the metal impurities increased because the metal atoms could efficiently fill the excess free volume at the Σ5(210) GBs. Second, the effects of temperature and impurity concentration on the GBE were investigated. The GBE varied with the temperature and impurity concentration, and SE was a critical parameter. Third, the bonding mechanism between the impurity atoms and SiC was investigated by analyzing the charge density, density of states, and bond length distribution. Changes in the bond length directly affected the co-segregation of impurities. Finally, impurities that may embrittle the Σ5(210) GBs were identified, and the competing mechanisms influencing the impurity concentrations were analyzed.

Computational methods

Two types of impurity segregation are observed at the GBs of SiC: the extra-GB and intra-GB diffusion of impurities. Figures 1(a) and 1(b) illustrate the diffusion of impurities into and along a GB, respectively. As displayed in Fig. 1(a), the impurity concentration at a GB increases when the solute atoms can segregate into the GB. After impurities accumulate in the GB plane, interactions occur between them ［Fig. 1(b)］. In addition, we considered two situations: the segregation of the same type of impurities (Sects. 3.1and 3.2) and the co-segregation of different types of impurities (Sects. 3.3 and 3.4).

Fig. 1

(Color online) Schematic diagram of impurity diffusion (a) into and (b) along the GB plane

The relaxed lattice constant and Si–C bond length of pure SiC presented in Table 1 are in agreement with those obtained in Fig. 2(a) displays the model of the SiC bulk supercell used in this study [40-42]. The Σ5(210) GB model and its side view are illustrated in Figs. 2(b) and 2(c), respectively. Two substitutional sites (A and B) and one interstitial site (F) exist in the GB plane. The vacuum layer of the supercell depicted in Fig. 2(a) has a thickness of more than 10 Å. As displayed in Fig. 2(b), substitutional impurities (Ni, Al, Bi, and Pb) and interstitial impurities (H, O, and N) are doped at the Σ5(210) GBs.

Calculated lattice constant and the Si-C bond length (Å) of pure SiC crystal structure, along with the previous results

SiC	Results
Lattice constant	4.371 (This work)
	4.348[40]
	4.360[41]
	4.359[42]
Bond length	1.892 (This work)
	1.851[41]

Fig. 2

(Color online) (a) SiC bulk model, (b) SiC Σ5(210) GB model and (c) its side view. A, B, C, D, and E denote different substitutional sites, and F indicates the interstitial site. The bule and green balls represent Si and C atoms, respectively

The Vienna Ab initio Simulation Package (VASP) [45] was used to perform electronic state calculations based on density functional theory [46]. Electron–ion interactions were described using the projector-augmented plane-wave method [47]. The total energy was convergent within 10⁻⁵ eV in the electronic self-consistency steps, and the cutoff energy was 400 eV. The convergent atomic force was 0.01eV/Å. The atoms in the Σ5(210) GB model were fully relaxed during the structural optimizations; however, the coordinates of the atoms in the outermost layers of the model were fixed. Table 2 presents the atomic electronegativity [48] and corresponding electronic configuration at the VASP potential.

The electronegativity [48] of the elements and their corresponding valence electronic configurations in the VASP potential

Elements	Electronegativity	Electronic configuration
Ni	1.7	3d⁸4s²
Al	1.5	3s²3p¹
Bi	1.8	4f¹⁴5d¹⁰6s²6p³
Pb	1.6	4f¹⁴5d¹⁰5s²6p³
Si	1.8	3s²3p²
H	2.1	1s¹
O	3.5	2s²2p⁴
N	3.0	2s²2p³
C	2.5	2s²2p²

Results and discussion

3.1

GBE and SE

To identify the effects of impurity or doping atoms on SiC GBs, the stability of these GBs was first determined. The tendency of SiC to form a GB can be characterized by its GBE ( $γ_{GBE}^{SiC}$ ) [43,49], which is expressed as follows:

γ_{GBE}^{SiC} = \frac{E_{GB}^{SiC} - E_{Bulk}^{SiC}}{S},

(1)

where $E_{Bulk}^{SiC}$ is the calculated energy of the bulk model in Fig. 3(a), $E_{GB}^{SiC}$ denotes the energy of the GB supercell depicted in Fig. 3(b), and S is the GB area. When an impurity X is introduced into the SiC GB plane, the corresponding GBE, namely $γ_{GBE}^{SiC - X}$ , can be calculated as follows [43,49]:

Fig. 3

(Color online) GBEs of impurities at different sites.

γ_{GBE}^{SiC - X} = \frac{E_{GB}^{SiC - X} - E_{Bulk}^{SiC - X}}{S} - γ_{GBE}^{SiC},

(2)

where $E_{GB}^{SiC - X}$ and $E_{Bulk}^{SiC - X}$ represent the total energies of the X-doped SiC GB and bulk model displayed in Fig. 3, respectively. The segregation tendencies of impurities at GBs can be indicated by the SE. A negative SE implies that an impurity is prone to segregate into a GB. The SE is defined as follows [49,50]:

E_{SE}^{SiC - X} = (E_{GB}^{SiC - X} - E_{GB}^{SiC}) - (E_{Bulk}^{SiC - X} - E_{Bulk}^{SiC}) .

(3)

The GBE of pure SiC was calculated to be 7.57 J/m², which is in agreement with the experimental GBE range of approximately 5.5–10.0 J/m² [51]. Figure 3 presents the GBEs at the substitutional sites (A and B), which were doped with metallic impurities, and interstitial site (F), which was doped with nonmetallic impurities. According to[43,49], the higher the GBE is, the more difficult is GB formation. When Si was substituted by Ni, Al, Bi, or Pb, the GBE exhibited a similar trend at sites A and B. For the metallic impurities, a minimum GBE of 0.23 J/m² was obtained for Ni at site B and a maximum GBE of 1.53 J/m² was obtained for Pb at site B. The GBEs for the substitution of Si by H, O, and N (i.e., the nonmetallic impurities) were −0.28, −1.58, and −2.27 J/m², respectively, which suggests that these atoms contributed to the formation of the Σ5(210) GBs. Figure 4 displays the correlation between the calculated GBEs and the radii of the impurity atoms. This figure indicates that the GBE is closely correlated with the radius of an impurity atom. A positive linear correlation was observed between the radius of a metallic impurity atom and the GBE, and a negative linear correlation was observed between the radius of a nonmetallic impurity atom and the GBE. Dinda et al. [52] demonstrated the role of atomic size difference between the matrix atom and the doping element in the liquid metal corrosion of steel GBs. They investigated the Sn- and Pb-induced corrosion and embrittlement of steel and found that the Fe–Sn diffusion couple was more susceptible to corrosion caused by doping than was the Fe–Pb diffusion couple . This result was attributed to the relative atomic sizes of Pb and Sn atoms. The results displayed in Fig. 4(a) are in agreement with the findings of Huang et al [24,25].

Fig. 4

(Color online) The correlation between the calculated GBE and the radius of impurity elements

A negative SE value indicates that the doped atoms are susceptible to segregation at the GBs [53]. The SEs of the different impurity elements at the Σ5(210) GBs are presented in Fig. 5. The SEs of the metal impurities at sites A and B were similar and less than 0 eV. For the metal impurities, a minimum SE of −3.83 eV was obtained for Bi at site A and a maximum SE of −0.83 eV was obtained for Al at site A. The SEs of Ni and Al were highly similar, and the SEs of Bi and Pb at site A were significantly lower than those at site B. Unfortunately, the N atoms doped into SiC ( $E_{Bulk}^{SiC - N}$ ) did not converge at the Σ5(210) GBs. The SEs of O and H were −2.63 and −0.04 eV, respectively, which implies that O is easily segregated at the Σ5(210) GBs, whereas H has a high segregation resistance at these GBs.

Fig. 5.

Calculated SEs of the impurity elements at sites A, B, and F

The SEs for Al and Ni were similar at sites A and B. Therefore, research must be conducted on why a large difference was observed in the SEs for Bi and Pb. To examine this topic, we calculated the Voronoi volume of the impurity elements. The free volume distortion of the impurity elements was quantified using the Voronoi volume (Table 3) [50]. The radius of an impurity element was proportional to its Voronoi volume (Fig. 6). The Voronoi volume of Si was larger at site A than at site B. This result indicates that impurity elements with large radii preferentially segregate at site A. The aforementioned result is also in agreement with the theory of elastic strain minimization [54]. If an impurity element with a large radius is doped into site A, the large Voronoi volume at this site results in a small local strain in the lattice [54]. This conclusion is in agreement with the results of experiments on the segregation of elements such as RE elements and Ag at GBs [55-58].

Radius [59] and the Voronoi volume of the impurity elements

Impurities	Radius(Å)	Voronoi volumes (Å³)
		Substitutional		Interstitial
		Site A	Site B	Site F
Ni	1.149	11.29	12.89	N/A
Si	1.173	10.31	10.04	N/A
Al	1.248	12.41	12.82	N/A
Bi	1.520	14.76	14.62	N/A
Pb	1.538	14.84	14.62	N/A
H	0.320	N/A	N/A	7.560
O	0.660	N/A	N/A	11.61
N	0.700	N/A	N/A	10.66

Fig. 6

(Color online) The correlation between the Voronoi volume and the radius of impurity elements.

When impurity elements are introduced at different sites of the SiC Σ5(210) GBs, the temperature- and concentration-induced increments in the GBE can be calculated as follows [43]:

γ_{GBE}^{SiC - X} (K, C_{0}) = \frac{E_{SE}}{(1 + \exp (\frac{E_{SE}}{μK} - ln (\frac{c_{0}}{1 - c_{0}}))) S},

(4)

where μ, K, and C₀ represent the Boltzmann constant, the temperature, and the concentration of an impurity element, respectively.

We examined the effects of temperature on the GBE. The initial concentration of all the impurity elements in this study was 1.3%. SiC has satisfactory stability at low temperatures and exhibits a phase change at 2000 K [60]. Therefore, the temperature range was set as 1000–2000 K. The GBE of SiC is a function of the temperature (Fig. 7). The SEs of the impurity elements are displayed on the right of the images in Fig. 7. First, the GBEs of Ni, Bi, Pb, and O were positively correlated with the temperature. However, the GBEs of Al and H were not temperature-dependent because of their large SEs. Second, as illustrated in Fig. 8, the GBEs of the impurity elements were positively correlated with their SEs. Moreover, the GBEs were relatively independent of the temperature when the SEs tended to be positive. Fan et al. [49] found that the GBEs of Y and Sr are positively correlated with their SEs. Shao et al. [61] observed that the GBEs of H doped on stack faults were close to 0 J/m² and not temperature-dependent.

Fig. 7.

(Color online) (a), (b), and (c) demonstrate the effects of temperature on GBEs, respectively

Fig. 8.

(Color online) (a), (b), and (c) demonstrate the effects of impurity concentration on GBE, respectively. x indicates the impurity concentration in GB

The influence of the impurity concentrations on the GBEs was investigated at 1000 K. As displayed in Fig. 8, the GBE decreased with an increase in the concentration of a metal impurity. This result is mainly attributed to the negative SEs of Ni, Al, Bi, and Pb, and a similar phenomenon was noted in our previous Ref. [43,44]. The GBE of H was not concentration-dependent because of its large SE. Similarly, Shao et al. [61] reported that the GBE of H is not affected by the doping concentration when its SE is close to 0 eV. Fan et al. [49] also found that the GBE (Σ3) is unaffected by the doping concentration when the SE of the doped atoms is close to 0 eV.

According to White–Coghlan theory, the segregation concentration of impurity elements at GBs (C_GB) can be calculated as follows [62,63]:

C_{GB} = \frac{1}{1 + (\frac{1 - C_{bulk}}{C_{bulk}}) exp (\frac{E_{SE}^{SiC - X}}{K T})},

(5)

where C_bulk is the concentration of solute atoms in the bulk. Notably, the entropy term neglected in Eq. (5) may qualitatively modify the temperature dependence of the solute concentration at a GB [64]. This aspect was not considered in the current study.

Figure 9 illustrates the prediction curves for the segregation concentrations of the impurity elements at the Σ5(210) GBs. When the SEs of Ni, Bi, and Pb were negative at 0 K, these impurity elements tended to segregate into the Σ5(210) GBs. As the temperature increased, the segregation concentrations of the aforementioned impurity elements decreased and they were more easily enriched at the substitutional sites without significant segregation. When the SEs of Al and H were only a little negative at 0 K, the segregation resistance of these impurity elements was high at the Σ5(210) GBs. As the temperature increased, the concentrations of the aforementioned impurity elements was consistently close to 0, which indicates that their segregation concentration was saturated at 0 K and that changes in temperature did not increase their segregation concentration.

Fig. 9

(Color online) Calculated segregation concentration of impurity elements in the SiC Σ5(210) GB

We employed Eq. (4) to obtain insights into the GBE state at the Σ5(210) GBs. The computed SEs were substituted into Eq. (4); the temperature was set as 1000–2000 K; and the concentrations of the impurity elements were set as 0%–10 %. Al and H had high SEs, which indicates that they exhibited low segregation at the Σ5(210) GBs. The reasons for this result should be explored. Figure 10 displays the GBE of SiC as a function of the temperature and impurity concentration. At site A, the GBE of Al increased from −573.5 to −312.5 J/m². At site B, the GBE of Al increased from 800.0 to −450.0 J/m². The concentration of Al was positively correlated with the GBE. By contrast, the GBE of H exhibited a low dependence on the temperature. The GBE of Al was lower at site B than at site A, as indicated by the calculated SE values. In addition, the GBE varied between the impurity elements but exhibited only a very weak dependency on the concentration of H. This weak influence of the H concentration on the GBE can be attributed to the weak segregation tendency of H at the Σ5(210) GBs.

Fig. 10

(Color online) (a), (b), and (c) demonstrate the effects of temperature and concentration on GBEs, respectively

3.2

Atomic bonds

To determine the mechanisms of the effects of impurity elements on the GBE, we investigated the charge density and bond length at site A. Figure 11 shows the projection of the charge density (from doped to undoped SiC) for the Σ5(210) GBs along the ［001］ plane. The impurity elements in SiC only affected the local doping location. Accordingly, neither charge redistribution nor charge transfer occurred in the bulk material [63,65,66]. C and Si are nonmetallic elements that belong to the IVA group, and C has a stronger ability to obtain electrons than Si does; thus, the electrons lost by the impurity elements were easily obtained by C. As depicted in Figs. 11(b)–11(i), the electron clouds of Ni, Al, Bi, and Pb almost did not overlap with that of Si and tended to be close to that of C. As displayed in Figs. 11(g) and 11(j)–11(l), the electrons lost by H were easily obtained by C. O and N consistently captured the electrons lost by C, which implies that Ni and the interstitial elements preferentially bonded to C. Three doping methods were adopted (Fig. 12): site A + H, site B + H, and site A + site B + H. Changes in the impurity site did not affect the preferential bonding tendency of Ni and C.

Fig. 11

(Color online) Calculated charge density (e/Bohr³) of the GB which contains Sites A and B, and interstitial atom.

Fig. 12

(Color online) Calculated charge density (e/Bohr³) of the GB which contains sites A+H, B+H, and A+ B+H.

Figure 13 displays the calculated densities of various SiC states and the doped atoms (Ni, Al, Bi, Pb, H, O, and N) at site A of the Σ5(210) GB supercell. As depicted in Fig. 13(a), the electron orbitals of Si and C were hybridized. Moreover, the calculated indirect band gap of SiC was 1.90 eV, which was close to the experimental value of approximately 2.20–2.35 eV [67]. As illustrated in Figs. 13(d) and 13(e), the p orbitals of Bi or Pb and C were hybridized, which implies that Bi, Pb, and C formed strong bonds with each other. This result also indicates that SiC has satisfactory corrosion resistance against LBE [13]. The p-orbital hybridization of Ni and C/Si ［Fig. 13(b)］ may have resulted in the strengthening of SiC GBs. Özkan and Zarghami et al. [11,12] observed that SiC GBs were strengthened by Ni doping. The peak of Al moved toward the lower-energy region, which resulted in the weakening of the hybridization between Al and C ［Fig. 13(c)］. Parish et al. [9] concluded that the enrichment of Al at GBs promotes the intergranular corrosion of SiC. Figures 13(g) and 13(h) illustrate the weak hybridization of O and N with Si/C. The peak of H moved toward the lower-energy region, which weakened the hybridization of H with Si/C ［Fig. 13 (f)］.

Fig. 13

(Color online) Calculated density of states of SiC, and the impurity elements at site A of the GB

To determine the regularity of the bonding of the impurity elements, the impurities at site A were investigated. Figure 14 displays the partial bond lengths at the Σ5(210) GBs with and without the metal impurities. Figure 14(f) depicts the locations of the different atomic sites. As displayed in Fig. 14, Ni, Al, Bi, and Pb only affected the bond lengths at sites a, b, and c. When impurities were doped at site A, the ascending order of the a–A bond lengths was as follows: 2.397 Å for Ni < 2.488 Å for Bi < 2.505 Å for Pb < 2.510 Å for Al. The maximum a–A bond length was obtained for pure SiC (2.682 Å); thus, the Ni, Al, Bi, and Pb atoms strengthened the a–A bonds by reducing the length of these bonds. Ni exhibited the highest bond strengthening effect, and this result is in agreement with the experimental results [11,12]. The ascending order of the b–A bond lengths is as follows: 1.877 Å for Ni < 1.938 Å for Al < 2.151 Å for Bi < 2.162 Å for Pb. The lowest b–A bond length was obtained for pure SiC (1.856 Å); thus, the Al, Bi, and Pb atoms weakened the b–A bonds by increasing their length. Although the b–A bond length of Ni was marginally longer than that of pure SiC, the difference in their bond lengths was only 0.021 Å. Thus, Ni doping did not lead to a significant weakening of the b–A bonds. This finding is consistent with the results displayed in Fig.11(a), which indicate that the electron cloud of C has a high overlap with that of Ni.

Fig. 14

(Color online) The diagram shows partial bond lengths (Å) on Σ5(210) GB with and without metal impurities. (a) Pure SiC, (b) Ni, (c) Al, (d) Bi, (e) Pb, (f) Numbering of atomic sites.

Figure 15 illustrates the partial bond lengths at the Σ5(210) GBs with and without the nonmetallic impurities. Figure 15(e) illustrates the locations of the atomic sites. The nonmetallic impurities affected the bond lengths of all the atoms and caused an irregular distribution of bond lengths. Therefore, we only examined the F–b and F–c bonds of the interstitial impurities. The ascending order of the F–b bond lengths is as follows: 1.118 Å for H < 1.303 Å for N < 1.630 Å for O. The ascending order of the F–c bond lengths is as follows: 1.602 Å for H < 1.788 Å for O < 1.825 Å for N. One can assume that H may form strong bonds with C and Si and that O may weaken the F–b bonds.

Fig. 15

(Color online) The diagram shows partial bond lengths (Å) on Σ5(210) GB with and without nonmetallic impurities. (a) Pure SiC, (b) H, (c) O, (d) N, (e) Numbering of atomic sites.

3.3.

Co-segregation

Figure 5 indicates that Bi, Pb, and O segregation was preferred at the Σ5(210) GBs. Therefore, we investigated the co-segregation of Bi, Pb, and O. To investigate the effects of co-segregation, we calculated the binding energy (BE) as follows [26]:

E_{BE}^{i, j} = (E_{GB}^{SiC - i} + E_{GB}^{SiC - j}) - (E_{GB}^{SiC - i . j} + E_{GB}^{SiC}),

(6)

where $E_{GB}^{SiC - i . j}$ , $E_{GB}^{SiC - i}$ , and $E_{GB}^{SiC - j}$ represent the total energies of the Σ5(210) GBs where some Si atoms were substituted by the atoms of both solutes i and j, solute j only, and solute i only, respectively. A positive BE implied that the interaction between solutes i and j was attractive. The interactions between the atoms at the GBs were mostly weakly attractive; however, some strong repulsive interactions were also noted [68-72].

To investigate the co-segregation of O, Bi, and Pb, the BE was evaluated using Eq. (6). O, Bi, and Pb were doped at the sites where they had the lowest SEs (site A for Bi and Pb and site F for O; Fig. 16). Table 4 presents the co-segregation of multiple impurities on the Σ5(210) GBs. The BEs of the interactions between Bi and Bi, Bi and Pb, and Pb and Pb were 0.14, 0.13, and 0.11 eV, respectively (i.e., attractive interaction). By contrast, the interaction between O and O was repulsive. According to Scheiber et al. [26], the co-segregation energy of an impurity is equal to the value obtained by subtracting its BE from its SE. If the BE has a high positive value, the SE is low. The interaction of Bi (Pb) with Bi or Pb increased the segregation tendencies of Bi + Bi and Bi + Pb. However, when O was doped at site F and Bi or Pb was doped at site A, O deviated from its initial position, which resulted in the nonconvergence of the model energy; thus, the BE was a failure.

Binding energy of Bi, Pb and O placed at its segregation sites of preferred.

Impurities	Binding energy (eV)
Bi+Bi	0.14
Pb+Pb	0.11
Bi+Pb	0.13
O+O	-2.23
O+Bi	-
O+Pb	-

Fig. 16

(Color online) Strongly segregated Σ5(210) GBs with sequence of segregation given by numbers (site 1, 2 for Bi, Pb, site 3, 4 for O)

To analyze the interrelationship among multiple impurities at different temperatures, Scheiber et al. [26,72] derived the following expression for simultaneously considering multiple sites and solutes [26]:

C_{i, α}^{GB} = \frac{C_{i} exp (- \frac{E_{SE}^{i, α}}{K T})}{1 + Σ_{j} C_{j} (\exp (- \frac{E_{SE}^{j, α}}{K T}) - 1)},

(7)

where α denotes the site and C_i denotes the bulk concentration of impurity i.

By using Eq. (7), we determined the relationships among the concentrations of Pb, Bi, and O at temperatures of 500, 1000, 1500, and 2000 K (Fig. 17). The concentrations of Pb and Bi at the Σ5(210) GBs were functions of each other. As depicted in Fig. 17(a), when the concentration of Bi was close to 0.5, the concentration of Pb was 0. Thus, the concentrations of Pb and Bi exhibited a negative correlation at the Σ5(210) GBs. As displayed in Fig. 17(b), the concentration of Bi reduced to a minimum value and was close to 0 when the concentration of Pb approached 0.5. Figures 17(c) and 17(d) indicate the effect of the O concentration on the Bi and Pb concentrations, respectively. An increase in the O concentration strengthened the repulsive effects of O on Bi and Pb. However, when the concentrations of the aforementioned three impurities were close to 0.1, the repulsion was reduced and perfect co-segregation was achieved. Thus, when the concentrations of the aforementioned impurities were low and close to 0.1, these impurities were attracted to each other and could coexist.

Fig. 17

(Color online) Competing relationships between the concentrations of impurities

We employed Eq. (3) to obtain insight into the perfect co-segregation state of multiple impurities at the Σ5(210) GBs. The computed SEs were substituted into Eq. (3). Fig. 18 displays the variations in the O concentration with the Bi and Pb concentrations. At 500 K, the O concentration decreased from 0.63% to 0.19% as the Bi and Pb concentrations increased. At 1000, 1500, and 2000 K, the O concentration gradually decreased with increasing Bi and Pb concentrations. The O concentration gradually increased with an increase in the temperature but was negatively correlated with the Bi and Pb concentrations. High Bi and Pb concentrations resulted in the consumption of O at the Σ5(210) GBs, whereas low Bi and Pb concentrations resulted in the enrichment of O at the Σ5(210) GBs. An increase in temperature inhibited the consumption of O by Bi and Pb.

Fig. 18

(Color online) Competing relationships between the concentrations of Bi, Pb and O.

We considered the impurity concentrations of SiC bulk and Σ5(210) GBs to be equal, and the concentrations of impurities at different temperatures were calculated using Eq. (5). To quantify the effect of an impurity i (Bi or Pb) on O enrichment, we introduce the replacement potency λ as the reduction of O at the Σ5(210) GBs if 5% of impurity i is added at the Σ5(210) GBs [26].

λ (T, O : i) = C_{GB}^{O} (T, C_{GB}^{i} = 0) - C_{GB}^{O} (T, C_{GB}^{i} = 5 %)

(8)

For impurities that exhibit weak competition with O, λ has a value close to 0, whereas for impurities that do not compete with O, λ has a value of less than 0.

As displayed in Fig. 19(a), the highest λ value, which was close to 0, was obtained when the temperature was lower than 500 K, which indicates that the competition between Bi and O was weak. This result is consistent with the results shown in Fig. 18(a). When the temperature was increased, λ became less than 0, which indicates that Bi did not compete with O; thus, the consumption of O by Bi and Pb was weak at high temperatures. This result is consistent with the results displayed in Figs. 18 (b)–18(d). Bi and Pb had similar effects on the O concentration; therefore, the curves displayed in Figs. 19(a) and 19(b) are similar.

Fig. 19.

The O replacement potency of Bi and Pb for different temperatures

3.4

Bonding of co-segregation impurities

According to the doping principle depicted in Fig. 16, Bi or Pb was doped at site A and O was doped at site F. The following pairs of doped atoms were present at the Σ5(210) GBs: Bi + Bi, Pb + Pb, Bi + Pb, and O + O. Unfortunately, when O was doped at site F and Bi or Pb was doped at site A, O deviated from its initial position, which resulted in the nonconvergence of the model energy; thus, the charge density was a failure.

Figure 20 shows the charge densities of Bi + Bi, Pb + Pb, and Bi + Pb at the Σ5(210) GBs along the ［001］ plane. The electron clouds of Bi and Pb exhibited a tendency to be close to the electron cloud of C only. This tendency is similar to the electron cloud distribution of Bi and Pb in Fig. 11, which indicates that no strong interactions existed between the metal impurities co-doped at the Σ5(210) GBs. Figure 20(d) indicates that the O atom on the left side was bonded to three C atoms and that the O atom on the right side was bonded to one C atom. A careful observation of the bonding of these O atoms indicated that they repelled each other. This phenomenon can be quantified by the bond length.

Fig. 20

(Color online) Calculated charge density (e/Bohr³) of the GB which contains substitutional and interstitial atoms

Figure 21 depicts the partial bond lengths at the Σ5(210) GBs with and without the metal impurities. Figure 21(e) displays the locations of the atomic sites (i.e., sites A, B, C, a, b, and c). Bi + Bi, Pb + Pb, and Bi + Pb only affected the bond lengths of the atoms at sites a, b, d and B. When impurities were doped at site A, the ascending order of the a–A bond lengths was as follows: 2.486 Å for Bi ［Fig. 21(b)］ < 2.501 Å for Pb ［Fig. 21(d)］ < 2.502 Å for Pb ［Fig. 21(c)］. The maximum a–A bond length was obtained for pure SiC (2.682 Å); thus, the Bi and Pb atoms strengthened the a–A bonds by reducing the length of these bonds. The ascending order of the b–A bond lengths is as follows: 2.153 Å for Bi ［Fig 21(b)］ < 2.162 Å for Pb ［Fig 21(d)］ < 2.160 Å for Pb ［Fig 21(c)］. The minimum b–A bond length was obtained for pure SiC (1.856 Å); thus, the Bi and Pb atoms weakened the b–A bonds by increasing the length of these bonds. The a–A and b–A bond lengths of Bi and Pb displayed in Figs. 14 and 21 are approximately equal. The a–A and b–A bond lengths displayed in Figs. 21(c) and 21(d) are also approximately equal. Thus, the bonding of Pb or Bi was not strongly influenced by the other impurities at the Σ5(210) GBs. The ascending order of the A–B bond lengths is as follows: 2.666 Å for Pb ［Fig. 21(c)］ < 2.728 Å for Bi ［Fig 21(d)］ < 2.729 Å for Bi ［Fig 21(b)］. The minimum A–B bond length was obtained for pure SiC (2.600 Å). The ascending order of the d–A bond lengths is as follows: 2.504 Å for Bi ［Fig 21(b)］ < 2.505 Å for Bi ［Fig 21(d)］ < 2.526 Å for Pb ［(Fig. 21(c)］. The minimum d–A bond length was obtained for pure SiC (2.006 Å). The aforementioned results indicate that the Bi and Pb atoms weakened the A–B and d–A bonds by increasing the lengths of these bonds. The A–B and d–A bond lengths displayed in Figs. 21(b) and 21(d) are approximately equal.

Fig. 21

(Color online) The diagram shows partial bond lengths (Å) on Σ5(210) GB with and without metal impurities. (a) Pure SiC, (b) Bi+Bi, (c)Pb+Pb, (d) Bi+Pb, (e) Numbering of atomic sites.

Figure 22 illustrates the partial bond lengths at the Σ5(210) GBs with and without the nonmetallic impurities. Figure 22(c) displays the locations of the atomic sites. The nonmetallic impurities affected the bond lengths of all the atoms, which resulted in an irregular distribution of bond lengths. In Fig. 22(b), the c–F bond length is smaller on the left than on the right. This phenomenon is consistent with the charge density distribution of O displayed in Fig. 20(d) and the mutual repulsion of O + O (Table 4).

Fig. 22

(Color online) The diagram shows partial bond lengths (Å) on Σ5(210) GB with and without nonmetallic impurities. (a) Pure SiC, (b) O+O, (c) Numbering of atomic sites.

Conclusion

First-principles calculations were employed in this study to determine the GBEs and SEs at the Σ5(210) GBs of FCC SiC. Four metallic impurities and three nonmetallic impurities were doped at two substitutional (sites A and B) and one interstitial site (site F) at the Σ5(210) GBs of SiC.

First, the GBE had a positive and negative linear correlation with the radius of a metallic and nonmetallic impurity, respectively. The atoms with large radii (Bi and Pb) preferentially aggregated at site A. The impurities that formed strong bonds with C were Ni, H, O, and N, and the lengths of these bonds varied.

Second, electronic interactions played a dominant role in the bonding effects. The charge and state densities of the impurities were explored to determine the underlying electronic interactions in the bonding.

Finally, the conclusions of the co-segregation investigation suggest that high concentrations of Bi and Pb result in the consumption of O at the Σ5(210) GBs, whereas low concentrations of Bi and Pb result in an enrichment of O at these GBs. An increase in temperature also inhibits the consumption of O by Bi and Pb. In addition, the bonding of Pb or Bi is not strongly influenced by other impurities at the Σ5(210) GBs.

In summary, a comprehensive investigation was conducted in this research on the structure and energy of the Σ5(210) GBs of doped SiC from the atomic and electronic perspectives. The current results may be valuable for the development of new ceramics with high corrosion resistance.

Reference

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Shi X., Li B., Liu H. et al.,

The corrosion resistance mechanisms of the Cr-coated SiC in molten Na2SO4 salt: strengthened boundaries and protective scales

. Corros. Sci. 185, 109421 (2021). doi: 10.1016/j.corsci.2021.109421