Jun Hui ?Bao-Liang Zhang?Tao Liu?Min Liu?Wen-Guan Liu

Abstract 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 theΣ5(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.

Keywords SiC.First-principles calculation.Grain boundary.Impurity atom.Co-segregation

1 Introduction

Silicon carbide(SiC)[1,2]exhibitsexcellent 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 thefact that SiCundergoesoxidation in hot water and hightemperature 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 SiCmatrix 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 overcomethelimitationsof 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 advantageousand essential for investigating thestructural defects of SiC.

GBs can serve as channels for rapid diffusion,and impurity or doping atomscan diffuse or cluster at SiCGBs.GBs are considered to be structural defects that are susceptible to corrosion.Thevacanciesat GBscan 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 isomericα-SiC which has an FCC structure[28].Tan et al.[29]observedΣ5 GBs with a tilt angle of 53°in SiC 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 inevitableimpuritiesin SiC.SiCGBsarestrongly 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[33—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,whereasnonmetallic impuritiesaredoped 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 theΣ5(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 radiusof the metal impuritiesincreased because the metal atoms could efficiently fill the excess free volume at theΣ5(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 theΣ5(210)GBs were identified,and the competing mechanismsinfluencing the impurity concentrations were analyzed.

2 Computational methods

Two types of impurity segregation are observed at the GBs of SiC:the extra-GB and intra-GB diffusion of impurities.Figure 1a,b illustrate the diffusion of impurities into and along a GB,respectively.As displayed in Fig.1a,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.1b).In addition,we considered two situations:the segregation of the same type of impurities(Sects.3.1and 3.2)and theco-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.2a 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 Fig.2b,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.2a has a thicknessof more than 10.As displayed in Fig.2b,substitutional impurities(Ni,Al,Bi,and Pb)and interstitial impurities(H,O,and N)are doped at theΣ5(210)GBs.

Fig.2 (Color online)a SiC bulkmodel,b SiCΣ5(210)GBmodeland c itsside view.A,B,C,D,and E denote differentsubstitutionalsites,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 10-5eV in the electronic self-consistency steps,and the cutoffenergy was 400 eV.The convergent atomic force was 0.01 eV/.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 VASPpotential.

Table 1 Calculated lattice constantand the Si—C bond length( )of pure SiC crystal structure,along with the previous results

Table 1 Calculated lattice constantand the Si—C bond length( )of pure SiC crystal structure,along with the previous results

SiC Results Lattice constant 4.371(Thiswork)4.348[]4.360[]4.359[]Bond length 1.892(Thiswork)1.851[] images/BZ_81_1046_1007_1081_1043.png images/BZ_81_1046_1061_1081_1096.png images/BZ_81_1046_1114_1081_1149.png images/BZ_81_1046_1220_1081_1255.png

Table 2 The electronegativity[48]of the elements and their corresponding valence electronic configurations in the VASP potential

3 Results and discussion

3.1 GBE and SE

Fig.3 (Color online)GBEs of impurities at different sites

The GBE of pure SiC was calculated to be 7.57 J/m2,which is in agreement with the experimental GBErange 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/m2was obtained for Niat site B and a maximum GBEof 1.53 J/m2wasobtained for Pb at site B.The GBEsfor thesubstitution 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 theΣ5(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 therole 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 Pbinduced 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.4a 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

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,thelarge Voronoivolume at thissiteresultsin 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].

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 SiCΣ5(210)GBs,the temperature-and concentration-induced increments in the GBE can be calculated as follows[43]:

Table 3 Radius[59]and the Voronoi volume of the impurity elements

whereμ,K,and C0represent the Boltzmann constant,the temperature,and the concentration of an impurity element,respectively.

We examined the effects of temperature on the GBE.Theinitial concentration of all the impurity elementsin 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 SEsof theimpurity elementsaredisplayed on theright of theimagesin Fig.7.First,the GBEsof 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/m2and not temperature-dependent.

Fig.7 (Color online)a—c demonstrate the effects of temperature on GBEs,respectively

The influence of the impurity concentrations on the GBEs was investigated at 1000 K.As displayed in Fig.8,the GBEdecreased 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 wasnoted 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.

Fig.8 (Color online)a—c demonstrate the effects of impurity concentration on GBE,respectively.x indicates the impurity concentration in GB

According to White—Coghlan theory,the segregation concentration of impurity elements at GBs(CGB)can be calculated as follows[62,63]:where Cbulkisthe concentration of soluteatomsin thebulk.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 theΣ5(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 theΣ5(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.

We employed Eq.(4)to obtain insights into the GBE state at theΣ5(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 indicatesthat they exhibited low segregation at theΣ5(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 thetemperature.The GBEof Al waslower at site B than at site A,as indicated by the calculated SE values.In addition,the GBEvaried 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 theΣ5(210)GBs.

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 showsthe projection of the charge density(from doped to undoped SiC)for the Σ5(210)GBsalong the[001]plane.Theimpurity 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 hasa stronger ability to obtain electrons than Si does;thus,the electrons lost by the impurity elements were easily obtained by C.As depicted in Fig.11b—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 Fig.11g,j—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.Changesin theimpurity sitedid not affect the preferential bonding tendency of Ni and C.

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 theΣ5(210)GB supercell.As depicted inFig.13a,the electron orbitals of Siand Cwere 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 Fig.13d,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.13b)may have resulted in the strengthening of SiC GBs.?zkan 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.13c).Parish et al.[9]concluded that the enrichment of Al at GBs promotes the intergranular corrosion of SiC.Figure 13g,h illustratethe weak hybridization of Oand N with Si/C.The peak of H moved toward the lower-energy region,which weakened the hybridization of H with Si/C(Fig.13f).

Fig.9 (Color online)Calculated segregation concentration of impurity elementsin the SiCΣ5(210)GB

Fig.10 (Color online)a—c demonstrate the effects of temperature and concentration on GBEs,respectively

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

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 theΣ5(210)GBs with and without the metal impurities.Figure 14f 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:2.397for Ni＜2.488for Bi＜ 2.505for Pb ＜ 2.510for Al.The maximum a–A bond length was obtained for pure SiC(2.682);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:1.877for Ni＜ 1.938for Al＜ 2.151for Bi＜ 2.162for Pb.The lowest b—A bond length was obtained for pure SiC(1.856);thus,the Al,Bi,and Pb atoms weakened the b—A bonds by increasing their length.Although the b—A bond length of Niwasmarginally longer than that of pure SiC,the difference in their bond lengths was only 0.021.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.11a,which indicatethat theelectron cloud of Chasahigh overlap with that of Ni.

Fig.14 (Color online)The diagram shows partial bond lengths( )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 15e 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:1.118for H＜1.303for N＜1.630for O.The ascending order of the F—c bond lengths is as follows:1.602for H＜1.788for O＜1.825for N.One can assume that H may form strong bonds with Cand Si and that Omay weaken the F—b bonds.

Fig.15 (Color online)The diagram shows partial bond lengths( )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 theΣ5(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]:

To investigate the co-segregation of O,Bi,and Pb,the BE was evaluated using Eq.(6).O,Bi,and Pb were doped at thesites where they had thelowest SEs(site A for Biand Pb and site F for O;Fig.16).Table 4 presents the cosegregation of multiple impurities on theΣ5(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 tendenciesof Bi+Biand 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.

Table 4 Binding energy of Bi,Pb and O placed at its segregation sites of preferred

Fig.16 (Color online)Strongly segregatedΣ5(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.[26,70]derived the following expression for simultaneously considering multiple sites and solutes[26]:

whereαdenotes the site and Cidenotes the bulk concentration of impurity i.

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 Biat theΣ5(210)GBs were functionsof each other.As depicted in Fig.17a,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 theΣ5(210)GBs.As displayed in Fig.17b,the concentration of Bi reduced to a minimum value and was close to 0 when the concentration of Pb approached 0.5.Figure 17c,d indicate the effect of the Oconcentration on the Bi and Pb concentrations,respectively.An increase in the Oconcentration strengthened the repulsive effectsof 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 theΣ5(210)GBs.The computed SEs were substituted into Eq.(3).Figure 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 theΣ5(210)GBs,whereas low Bi and Pb concentrations resulted in the enrichment of O at theΣ5(210)GBs.An increasein temperatureinhibited theconsumption of O by Bi and Pb.

We considered the impurity concentrations of SiC bulk andΣ5(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 potencyλ as the reduction of O at theΣ5(210)GBs if 5%of impurity i is added at theΣ5(210)GBs[26].

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

Asdisplayed in Fig.19a,thehighestλvalue,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.18a.When the temperature was increased,λbecame lessthan 0,which indicatesthat Bidid not compete with O;thus,the consumption of O by Bi and Pb was weak at high temperatures.Thisresult is consistent with the results displayed in Fig.18b,d.Bi and Pb had similar effectson the Oconcentration;therefore,thecurves displayed in Fig.19a,b are similar.

Fig.18 (Color online)Competing relationships between the concentrations of Bi,Pb and O

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,Bior Pb wasdoped at site A and Owasdoped at site F.The following pairsof doped atomswerepresent at theΣ5(210)GBs:Bi+Bi,Pb+Pb,Bi+Pb,and O+O.Unfortunately,when Owasdoped at site F and Bior Pb wasdoped at site A,Odeviated from itsinitial 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 theΣ5(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 20d 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 depictsthe partial bond lengthsat theΣ5(210)GBs with and without the metal impurities.Figure 21e displaysthe locations of theatomic 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:2.486for Bi(Fig.21b)＜ 2.501for Pb(Fig.21d)＜ 2.502for Pb(Fig.21c).The maximum a–A bond length was obtained for pure SiC(2.682);thus,the Bi and Pb atoms strengthened the a–A bondsby reducing thelength of these bonds.The ascending order of the b–A bond lengths is as follows:2.153for Bi(Fig.21b)＜ 2.162for Pb(Fig.21d)＜ 2.160for Pb(Fig.21c).The minimum b–A bond length was obtained for pure SiC(1.856);thus,the Biand Pb atomsweakened the b–A bondsby increasing the length of thesebonds.The a–A and b–A bond lengthsof Bi and Pb displayed in Figs.14 and 21 are approximately equal.The a–A and b–A bond lengths displayed in Fig.21c,d arealso approximately equal.Thus,thebonding of Pb or Bi was not strongly influenced by the other impurities at theΣ5(210)GBs.The ascending order of the A–B bond lengths is as follows:2.666for Pb(Fig.21c)＜ 2.728for Bi(Fig.21d)＜ 2.729for Bi(Fig.21b).The minimum A–B bond length was obtained for pure SiC(2.600).The ascending order of the d–A bond lengths is as follows:2.504for Bi(Fig.21b)＜2.505for Bi(Fig.21d)＜ 2.526for Pb(Fig.21c).The minimum d–A bond length was obtained for pure SiC(2.006).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 Fig.21b,d are approximately equal.

Fig.21 (Color online)The diagram shows partial bond lengths( )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 22c 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.22b,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.20d and the mutual repulsion of O+O(Table 4).

Fig.22 (Color online)The diagram shows partial bond lengths( )on Σ5(210)GB with and without nonmetallic impurities.a Pure SiC,b O+O,c Numbering of atomic sites

4 Conclusion

First-principlescalculationswereemployed in thisstudy to determinethe GBEsand SEsat theΣ5(210)GBsof 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 theΣ5(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 theΣ5(210)GBs,whereas low concentrationsof Biand Pb result in an enrichment of Oat these GBs.An increase in temperature also inhibits the consumption of Oby Biand Pb.In addition,thebonding of Pb or Bi is not strongly influenced by other impurities at theΣ5(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.

Author contributionsAll authors contributed to the study conception and design.Material preparation,data collection and analysis were performed by Jun Hui,Wen-Guan Liu,Bao-Liang Zhang,Tao Liu,and Min Liu.The first draft of the manuscript was written by Jun Hui and Wen-Guan Liu,and all authors commented on previous versions of the manuscript.All authors read and approved the final manuscript.