Influence of Si Atoms Insertion on the Formation of the TiSiN Composite by DFT Simulation

Using Density Functional Theory (DFT) SiN and T iN structures were simulated, in order to study the influence of the silicon atoms insertion in the T iN lattice placed on interstitial and substitutional positions in a face centered cubic (FCC) crystalline lattice. Results showed that the SiN − FCC structure is pseudo-stable; meanwhile the tetragonal structure is stable with ceramic behavior. The T iN − FCC structure is stable with ceramic behavior similar to SiN − Tetragonal. 21% silicon atoms insertion in interstitial positions showed high induced deformation, high polarization and Si−N bond formation, indication an amorphous transition that could lead to the production of a material composed from T iN grains or nano-grains embedded in a Si − N amorphous matrix. When 1 Universidad del Valle, Cali, Colombia, Juan.gonzalez@correounivalle.edu.co. 2 Universidad Nacional Autónoma de México, Ciudad de México, México, johansrestrepo@hotmail.com. 3 Universidad del Valle, Cali, Colombia, carolinaortega35@gmail.com. 4 Universidad Tecnológica de Pereira, Pereira, Colombia, arudenm@gmail.com. 5 Universidad del Valle, Cali, Colombia, Federico.sequeda@correounivalle.edu.co. Universidad del Valle 11| Influence of Si Atoms Insertion on the Formation of the TiSi-N Composite by DFT Simulation including 21% of silicon atoms, substituting titanium atoms, the distribution showed higher stability that could lead to the formation of different phases of the stoichiometric T i1 −x SixNy compound.


Introduction
Titanium based structures has been studied extensively specially in hard coating applications, for example both nitrides (T iN ) and carbides (T iC) or the combination called carbo-nitride (T iCN ).These coatings are deposited on commercial substrates, because their excellent structural characteristics, mechanical and tribological properties [1], [2], [3], [4], [5], but high reactivity and low oxidation resistance limits their industrial applications in high temperatures environments (>500 • C).The addition of different atoms on the T iN lattice has shown to be a good method to improve hardness and oxidation resistance.This type of structures can be obtained by different deposition techniques like magnetron sputtering or cathodic arc [5], [6], [7], [8].The hardness and oxidation resistance increases when silicon is added to titanium nitride, due to the formation of TiN nano-crystalline/amorphous Si 3 N 4 with nanocomposite structure (T iN nanocrystals embedded on a thin silicon nitride matrix), so that the dislocations in the nanocrystal cannot propagate across the silicon nitride over the grain boundary.Cracks formed on the amorphous matrix are anchored in the titanium nitride nanocrystals boundary, so high strength is necessary to produce deformation or failure, achieving hardness and young modulus up to 45 Gpa and 400 Gpa respectively [8], [9], [10].Previously experimental and theoretical studies postulated that Ti-Si-N system stability is affected by Si atomic percent and the presence of mixed phases, reported as lateral compounds in the deposition process or by system inherent immiscibility such as Ti-Si − N (O) and T i/Si 3 N 4 [11], [12], [13].Experimentally T i 1 − x Si x N y phase has been deposited using RF magnetron sputtering by F. Vaz et all [14], showing phase separation in the stoichiometric compound.They also reported an increase of mechanical properties and oxidation temperature with low Si percent [14].The formation of binary phases indicates that is possible to obtain different configurations, resumed in four groups: 1) combination of different crystalline phases of the present elements, such as T iSi 2 or T iO x and the formation of free Si, when is present over 15%.These materials have low mechanical and tribological properties; 2) the Si homogeneous solubility in the TiN FCC lattice to form the stoichiometric compound T i 1 − x Si x N y , with low content of silicon.This material has good tribological properties, but with high Si content it becomes unstable; 3) T iN nano-crystal structures in an amorphous Si 3 N 4 matrix, with excellent properties and 4) a complete amorphous compound formed by an increase in crystal defects or decrease of the crystallite size below X ray diffraction detection limit, with high Si content [15], [16].Theoretic studies about compound stability and behavior will give a full understanding on the formation of different coexisting phases in order to find the ideal deposition parameters for needed applications.

Experimental setup
In this paper the influence of the insertion of silicon atoms in the TiN lattice is studied, with the objective of determining the T i − Si − N formation mechanism.The composite simulations were performed using Gaussian 03 software with 6-311G/6-31G databases, Single Point Energy method (SPE), with the unrestricted Hartree Fock approximation to find spin functions and electrostatic multipolar expansion.Local Density Approximation (LDA) energy functions were used for short range correlations and General Gradient Approximation (GGA) functions for long range.Dummy atoms were included in order to complete the periodicity of the crystalline lattice and avoid edge discontinuities in the total electrostatic potential.A 1x10 −2 convergence values were achieved for the density functions and energy between 150 cycles [17], [18].Computational time for all the simulations was superior to 12 hours.Obtained data was summarized by Mulliken charge distribution and electron total density mapped to the highest occupied molecular orbital (HOMO).For a simpler representation, 75% of the Van deer Walls radius was used.Experimental studies indicate that Si atoms insertion over 7% increases the probability of nano-composite formation composed of T iN nano-crystals in an amorphous SiN matrix (nc − T iN/a − SiN ) [16], in order to overcome this experimental limit, 21% of Si atoms were inserted to the structures.Simulated structures corresponds to a face center cubic titanium nitride (T iN −F CC), tetragonal silicon nitride (SiN −tet), face center cubic silicon nitride (SiN − F CC), face center cubic titanium silicon nitride with 21% interstitial silicon (T i−Si−N −interstitial) and face center cubic titanium silicon nitride with 21% substitutional silicon (T i−Si−N −substitutional) (Figure 1).Table 1 shows the total energy obtained from the simulated structures.|14

Results and discussion
Figure 1a shows TiN-FCC structure simulated, generating an interstitial nitride with lattice parameter of 0.424 nm; the array corresponds to a free stress structure reported by A. Devia et al [19].This lattice parameter was used for all simulations in order to eliminate intrinsic variations caused by system sintering or deposition [2]. Figure 2a, shows Mulliken charges population analysis for T iN − F CC.The structure showed a neutral, stable behavior ( q 1 = 0) and spatial distribution depends on the element electronegativity.There is a high probability for other compounds to be formed, produced by chemical reactions after material sintering or thin film deposition, such as T iO 2 and T iO, Meanwhile nitrogen produces N H 2 .However, N H 2 formation needs more energy, for that reason is expected that nitrogen stabilization is produced by association of N + ions to N 2 [13].Figure 2b, shows total electron density of the T iN lattice mapped to the highest occupied molecular orbital (HOMO).The surface is continuous with polarizations produced by charge separation, as observed in the Figure 2a.This is agreement with the sp hybridization morphology that have been observed experimentally by X Ray Photoelectron Spectroscopy (XPS) [20].The charge ranges from −57.72x10 −4 up to 57, 72x10 −4 a.u, showing symmetry, continuity and stability.Initial discussion regarding the composition and crystalline structure of silicon nitride included the formation of two phases (α and β), both appearing to be hexagonal, with the c-axis dimension as principal difference between each other [21].However, further research proved that silicon atoms were at the center of a tetrahedron, each nitrogen in trigonal and approximately planar coordination by three silicon (Figure 1b) [22].Procedures to obtain the α and β structures of silicon nitride have been reported to be successful at high temperatures (above 1800K), due to the high intrinsic stress generated between the elements.Meanwhile the formation of tetragonal or amorphous silicon nitride is reported in low temperatures using high energy techniques, such as PVD and hybrid methods [23], [24].
Mulliken population analysis (Figure 3a) shows high polarization due to the high electronegativity of nitrogen atoms that attracts charges; meanwhile silicon atoms shoed reduced charge distributions.However the structure is stable ( q 1 = 0).High polarization of the atoms in the structure could indicate a polar bond between the elements; nevertheless orbital formed strongly indicates a covalent bond formation that has been confirmed both theoretically and experimentally [11], [13].Figure 3b shows SiN-Tetragonal electron total density mapped to the HOMO orbitals.As discussed above, an intrinsic polarization due to compound ceramic characteristics is observed.This phenomenon stabilizes with lattice expansion as studied by R.F.Zhang et al [11] and E.V. Shalaeva et al [13].Charge range from −1.05x10 −2 to 1.05x10 −2 a.u.Face Center Cubic (FCC) silicon nitride has raised particular interest since the late 90's due to the theoretical prediction that the mechanical properties of several compounds with A3N4 stoichiometry (A: C, Si and B among others) may be comparable, of even higher to diamond.However Si3N4-FCC has shown to be metastable in air, returning to the α and β phase, oxidizing or becoming amorphous by a pressure increase [24].
SiN − F CC simulated structure is shown in the Figure 1c.Mulliken charges population analysis (Figure 4a) showed a complete system polarization with high instability for the phase formation; however Mulliken charges sum is equal to cero [1].High values in the change population analysis could indicate the absence of Si − N bonds, tending to increase in energy with the number of atoms in the system as observed from Table 1, leading to instability for the 6 coordination number of the FCC structure.As the Mulliken population analysis explicitly depends on the basis set choice, the use of two different data bases reduced the uncertainty and comparable results were obtained [25].Si − Si or N − N bond creation was discarded, indicating lateral compound formation after sintering; resulting in oxidation to SiO and SiO 2 .The tetragonal SiN structure is predomiing.cienc., vol.12, no.23, pp.11-23, enero-junio.2016.
nant at the nano-composite interface.Control in the formation of lateral compounds will improve adherence between the matrix and the nano-grain [13].Total electron density mapped to the HOMO orbitals (Figure 4b), shows polarization in the total density surface, this instability is related to absence of charge compensation on the center of the face.Charge ranges from −1.564x10 −2 to 1.564x10 −2 a.u.)â.The lattice parameter used (a=0.424nm) correspond to the standard α − T iN in equilibrium [13], [16], [17].Figure 5a shows the Mulliken population analysis of the simulated structure.Distribution shows low Charge separation between the elements, with an increase in the charge in T i and N atoms.Titanium oxidation states indicate that there is a minimum probability of charge gain when an atom is a close neighbor with higher electronegativity, such as silicon.This observation could indicate an increase in probability of bond formation between Si − T i and Si − N .These bonds will lead to the amorphous phase of SiN with triple bond Si − N .While Si − T i bonds, indicates the formation of different phases T i − Si − N , possiblyβ − T i − Si − N , or a combination of α and β phases in meta-equilibrium [13].The electron total density mapped to the HOMO orbitals (Figure 5b) shows low polarization on the opposite sites of the interstitial Si, which could confirm system instability.The polarizations observed on simulated T iN , that are due to sp hybridization, are nearly absent in the interstitial

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T i − Si − N simulated.This indicates that lateral reactions have high probability, leading to the formation of different compounds.All this leads to the conclusion that interstitial silicon in the T iN lattice is unlikely (at least in these atomic sites), due to the formation of other compounds, by the absence of balance and the amount of energy needed to keep this particular system stability [15].Charge ranges from −1.221x10 −2 to 1.221x10 −2 a.u. Figure 1e shows T i − Si − N structure, with 21% of titanium atoms substituting silicon in the positions (0, 0, 0), (1, 0, 1) and ( 12 , 1, 1 2 ), with α − T i 1 − x Si x N (FCC) crystalline structure and a=0.424 nm.The Mulliken charges distribution (Figure 6a), showed a stable system compared to interstitial silicon (Figure 5a).Charges are distributed according to elements electronegativity, nitrogen as high electronegative followed by silicon and titanium.Anomalies are not observed, as presented in the first structure and the same configuration is retained when charge symmetry is not forced between the elements.Creation and destruction of atomic bonds was observed and high state energy of T i − Si bond indicates the existence of different allotropic phases, β − phase or an α/β combination.Some Si − N and T i − N bonds disappear, probably due to unbalances between atoms, by electronegativity differences and absorption of charges by silicon atoms, which have oxidation states between −4 and +4 (without passing through zero) [11], [13], [15], [16].Creation of double or triple bonds between the elements was not observed.
The electron total density (Figure 6b) is continuous.There is an improbable orbital overlap in the left front corner, generated by electrons in the titanium atom, due to the location of silicon in the vicinity.The same phenomenon is observed in all the titanium atoms near the silicon but to a lesser extent.In general, the structure is stable, but low formation probability is observed, due to T i − Si bond formation and T i − N and Si − N bond destruction.It is possible that lateral structures are formed, as α ,β or γ (cubic) SiN and α and β T iN or other phases of the compound (α, β, α−βT i−Si−N ) in meta-stable equilibrium [13].Charge range from −9, 173x10 −3 to 9, 173x10 −3 a.u.

Conclusions
Computational methods allow determination, with a good range of certainty, of crystal structures behavior in terms of energy and stability.The use of DFT, to determine the influence of 21% Si in the F CC − T iN showed that the T i − Si − N stoichiometric phase is at metastable equilibrium and there is high probability that the compound formed corresponds to an interstitial T iN alloy where Si atoms form Si 3 N 4 as an amorphous matrix for T iN stable crystals.According to population analysis, there is a high probability of alternative compounds formation, due to nitrogen atoms migration and absence of Si − N bonds with sp 2 hybridization, creating |20 another reaction path for the amorphous compound or other crystalline phases.Except for the separated compounds, there are anomalies in the total electron density, confirming the meta-equilibrium phase T i − Si − N .The F CC − SiN Mulliken charges population analysis showed a complete system polarization with high instability on the compound phase formation.This result may lead to the generation of amorphous silicon nitride in the nanocomposite material.

Figure 2 :
Figure 2: a) TiN-FCC Mulliken charges population analysis, charge range from -1.784 up to 1.784 a.u (atomic units).b) Electron total density mapped to the HOMO orbitals.

Figure 3 :
Figure 3: a) SiN-tetragonal Charge distribution, charge ranges from -1.542 to 1.542 a.u.b) Electron Total density mapped to the HOMO orbitals.

Figure 4 :
Figure 4: a) SiN-FCC Mulliken charges, range is from -2,194 up to 2,194 a.u.b) Electron total density mapped to the HOMO orbitals.

Figure
Figure1dshow T i−Si−N with 21% of interstitial silicon atoms located on the vectors (1,1  4 , 1 4 )â, ( 1 4 , 3 4 , 1 4 )â and ( 1 4 , 3 4 , 3 4 )â.The lattice parameter used (a=0.424nm) correspond to the standard α − T iN in equilibrium[13],[16],[17]. Figure5ashows the Mulliken population analysis of the simulated structure.Distribution shows low Charge separation between the elements, with an increase in the charge in T i and N atoms.Titanium oxidation states indicate that there is a minimum probability of charge gain when an atom is a close neighbor with higher electronegativity, such as silicon.This observation could indicate an increase in probability of bond formation between Si − T i and Si − N .These bonds will lead to the amorphous phase of SiN with triple bond Si − N .While Si − T i bonds, indicates the formation of different phases T i − Si − N , possiblyβ − T i − Si − N , or a combination of α and β phases in meta-equilibrium[13].The electron total density mapped to the HOMO orbitals (Figure5b) shows low polarization on the opposite sites of the interstitial Si, which could confirm system instability.The polarizations observed on simulated T iN , that are due to sp hybridization, are nearly absent in the interstitial

Figure 5 :
Figure 5: a) Mulliken population analysis, charge range is from -1.948 up to 1.948 a. u. b) Electron total density mapped to the HOMO orbitals.

Table 1 :
Total energy of the systems simulated.