Effects of rare earth adsorption on electronic structure and optical properties in β-Si₃N₄ ceramics from first principles

Abstract

Electronic structure and optical properties of silicon nitride adsorbed by rare earths are explored by density functional theory. The fully relaxed structural parameters are found to be in good agreement with experimental data. Covalent character of polar covalent bonds by rare earth adsorption is in the order of Gd, Yb, Sc, Sm, La and Lu, which is verified by population values. Gd, Yb, Sc and La adsorption systems may exhibit longer life in applications as dielectric materials in the low energy regions because of the low static dielectric constant and loss, as well as transparent type characteristic exhibited in visible regions.

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Capturing the atomic level influences of rare earth (RE) sintering additives in the resulting crystalline/amorphous interfacial configuration has attracted numerous interests because it is the critical element that controls most of the materials' characteristics, more significantly the mechanical properties, which are dependent on the local chemical composition, atomic structure, and bonding characteristics, in silicon nitride ceramics.^1,2 Some of the RE species can segregate to grain surfaces and adsorb there according to the chemical driving force and competition with Si atoms.^3–6 After densification, these grains-boundary phases are known to greatly affect the resulting microstructure and properties of ceramics, and it is thus important to understand the underlying mechanism and effects of adsorption at internal interface, as well as the reasons for displayed discriminations among the RE series. Simultaneously, it opens a window in the application fields of microelectric and aerospace by having an insight into the dielectric and optical properties of the β-Si₃N₄ ceramics with various RE adsorption.

Considerable efforts have been taken to clearly see through bonding state and mechanism at amorphous/crystalline interface for both experimental and theoretical studies. It is well established that ultimate ceramics structure consists of elongated Si₃N₄ matrix grains embedded in an intergranular, typically amorphous, oxide phase resembling that of whisker enhanced ceramics, which are sensitive to the types of cations of the selected sintering additions.^7,8 Experimentally, the growth on the prism planes is reaction rate limited accompanying the segregation of rare-earth atoms, and thus, relatively slow compared to that along the c-axis, which belongs to diffusion control and is rapid. Grains with large aspect ratios were obtained.^9–12 Theoretically, the grain growth is found to originate from the site competition between REs and Si for bonding at β-Si₃N₄ interfaces, as well as stereochemical bonding factors.^13,14 The previous investigations of the interfaces have focused on the segregation and absorption sites of rare earths in the intergranular phase. A simple measure of the relative preference of dopant cations for bonding at interfaces is required in engineering control. However, the information about the electronic density difference, bond nature and mechanical properties after adsorption is absent. Because the principles of micrometer-scale structural design are generally employed to enhance the mechanical properties of ceramics, this work represents a step towards the atomic-level structural engineering control required for the next generation of ceramics. Our objective was to investigate the bonding characteristics of RE with N sites for a larger selection of the oxide sintering additions and to complete previous researches by analyzing their electronic configuration and optical property discrepancy.

In this paper, we capture the electronic density difference, bond nature and optical properties after adsorption using first principles calculations with regard to GGA-PW91 equations, motivated by the fact that these nanoscale structures effectively control macroscopic ceramic behaviour, in which new functional parameters are obtained by the known parameters or other accurate theoretical help. Simultaneously, the exchange–correlation energy is suitable for calculating the binding energy and elastic constants and not suitable for calculating the surface energy and oxides properties. Fig. 1 demonstrates the calculated surface configurations of β-Si₃N₄ crystal structure with RE adsorption. In the basic unit, the three outer layers of atoms can be optimized and relaxed, and the rest of the inner atoms were fixed and unchanged. Atoms in adjacent unit along the y direction (see Fig. 1b) were separated by at least 10 Å to minimize any spurious interaction between units. The initial cell sizes were a = 5.822 Å, b = 7.607 Å, c = 16.258 Å. Brillouin zone integration was performed employing a discrete 4 × 4 × 10 Monkhorst–Pack k point sampling. We used plane wave basis sets with a kinetic energy cutoff of 480 eV, in conjunction with ultrasoft pseudopotentials for describing the ion–electron interaction. However, when optical properties are calculated, norm conserving pseudopotentials are preferable. The pseudopotentials involve the following atomic orbitals in their respective valences: Si(3s2, 3p2), N(2s2, 2p2), Sc(3s2, 3p6, 3d1, 4s2), La(5s2, 5p6, 5d1, 6s2), Sm(4f6, 5s2, 5p6, 6s2), Gd(4f7, 5s2, 5p6, 5d1, 6s2), Yb(4f14, 5s2, 5p6, 6s2), Lu(4f14, 5p6, 5d1, 6s2).

Fig. 1 The surface configurations of β-Si₃N₄ crystal structure with RE adsorption. N: white atoms; Si: green atoms; RE: red atoms. (a) Atomic cluster model viewed slightly off normal to the basal plane. (b) The local amplification model surface. (c) Top view of atom cluster model of surface.

To obtain the stable adsorption systems, we first conducted the optimization by relaxing both the internal coordinates and the lattice constants by calculating the ab initio forces on the ions with the Born–Oppenheimer approximation, until the absolute values of the forces were converged to less than 0.01 eV Å⁻¹. Calculated equilibrium adsorption sites in the cluster are illustrated in Fig. 2 and relevant parameters, such as covalent radius (CR), total energy (TE), band gap (BG), band angle (BA), D and d, are listed in Table 1. It was found that all the adsorption sites were located near A point in Fig. 1b, which was similar to that reported by Gayle.¹⁴ The calculated TE values predict that Yb adsorption system is more stable than other systems. The BG gradually decreased in the order of Sc > Lu > La > Sm > Yb > Gd, indicating that the distance between the valence band and the conduction band became narrow in Ga adsorption system. The D values (the distance of RE with N atom in one unit), in experimental measurements and theoretical calculations, were obtained by the Pythagorean theorem from the reported values, which were used to compare the calculated D values in this present work. With the reported theoretical values, the calculated values have a maximum deviation of 0.27 Å. With the experimental values, the calculated values were within the experimental errors reported in literature, and hence, are reliable. The calculated d_RE–N values (the bond length of RE and N atoms) decreased in the order of La > Lu > Sm > Ga > Yb > Sc, which was in accordance with the configuration exhibited in Fig. 2. This may be because of the two reasons, namely, atomic radius and electronegativity. The atomic radius is in the order of La > Sm > Gd > Yb > Lu > Sc, which is in accordance with the order of the d values except Lu element. The reason was attributed to higher electronegativity of Lu element, leading to the larger bond length by polarization action.

Fig. 2 Surface configuration patterns of RE atoms adsorbed on the prismatic plane.

Table 1 The covalent radius and calculated total energy (TE), band gap (BG), band angle (BA), D and d values. Theoretical and experimental values come from ref. 14 and 15

RE	CR (Å)	TE/eV	BG/eV	BA (θ)/degree	DRE–N/Å	Expt. DRE–N/Å	Theor. DRE–N/Å	dRE–N/Å
Sc	1.44	−2.9587 × 10^3	0.498	99.229	2.10	—	—	1.97
Lu	1.56	−7.4502 × 10^3	0.154	83.503	2.38	2.20 [±0.2]	2.11	2.25
Gd	1.62	−4.7163 × 10^3	0.100	89.440	2.33	2.33 [±0.2]	2.21	2.13
Sm	1.62	−3.8808 × 10^3	0.104	87.404	2.38	—	—	2.17
La	1.69	−2.5417 × 10^3	0.110	79.772	2.41	2.40 [±0.3]	2.29	2.34
Yb	1.74	−8.0741 × 10^3	0.102	90.671	2.28	—	—	2.12

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For the purpose of clarifying the nature of the bonds that a RE forms with N atoms, the description of adsorption state is illustrated in Fig. 3, where charge density difference^16,17 (the change in charge density owing to RE adsorption bond) is shown. Blue and red parts displayed in maps refers to the electron deficiency and enrichment, respectively. The changes in electron density were obvious when the RE atoms adsorb on prismatic plane. Compared to the original system, blue area around Sm atom decreases, i.e. electron deficiency weakens, indicating that covalent character of adsorption bond reduces. Moreover, blue areas around La and Lu atoms almost disappear, clearly stating the great decrease in electron deficiency and it illustrates that covalent character of adsorption bond dramatically attenuates and the covalent–ionic transition occurs. For the systems of Yb, Gd and Sc adsorption, except the reduction in the blue area, one can see that the red area is present, indicating that electron density increases around RE atoms accompanying the uneven distribution of electron cloud, resulting in the lighter reducing amplitude of electron deficiency compared to the first three RE elements. This makes clear that the Yb, Gd and Sc adsorption bonds retains some covalent character. In the study, the degree of inhomogeneous distribution of electron cloud in Gd adsorbed system is larger than that in other two systems, revealing that polar covalent bond with N atom formed by Gd adsorption is stronger in all three systems, and the next element is Yb. Combined with the above analysis, covalent caused by RE adsorption is in the order of Gd > Yb > Sc > Sm > (La, Lu).

Fig. 3 Charge density difference maps of RE adsorption systems character of polar covalent bonds. The figures are projected along cylindrical surfaces (cutting along (0001) surface).

To verify the deductive results, population values were calculated with regard to various adsorption systems. The distributions of electron charges in terms of different atoms can be illustrated by the atomic population analysis. Owing to atomic charges being sensitive to the used set, the calculated population values has no absolute meaning, but only relative one. In a majority of methods, Milliken population analysis was extensively employed because it provides a method for evaluating partial atomic charges from calculations conducted by the computational chemistry methods, and particularly those based on the linear combination of atomic orbital method, and were routinely used as variables in linear regression procedures. Simultaneously, the overlap degree of the electron cloud of two bonding atoms, as well as covalent and ionic nature of a chemical bond, may be explained by the bond population. Chemically, the positive and negative Mulliken population values correspond to a bonding and an anti-bonding character, respectively. The highest and lowest values for the bond population represent the strong covalent and ionic chemical bond nature, respectively. Table 2 shows the calculated population distribution results. It was found that the values gradually decrease in the order of Gd > Yb > Sc > Sm > La > Lu, which is in agreement with the analysis results of charge density difference.

Table 2 The calculated population values of bonds by RE adsorption

	Gd	Yb	Sc	Sm	La	Lu
RE–N	0.25	0.20	0.19	0.17	0.14	−4.73

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The optical properties are of essential importance because they not only embody the occupied and unoccupied parts of the electronic structure, but also convey the information about the characteristic of bands. The optical properties may be obtained from the dielectric function ε(ω) = ε1(ω) + iε2(ω), which is calculated from the momentum matrix elements between the occupied and unoccupied wave functions by Ehrenreich.¹⁸ Fig. 4 illustrates the dielectric constant of photon energy changes for various RE adsorption systems. It can be seen that dielectric constant decreased gradually with photon energy increasing and remained steady finally. The static dielectric constants located in the low energy region were 10.05 and 9.76, respectively, for Lu and Sm adsorption systems, larger than that of the other four systems (see Fig. 4a), caused by higher bond dipole moment and polarizability. Correspondingly, the change was similar to that of imaginary part shown in Fig. 4b. In summary, with the increasing of covalent radius, the static dielectric constant and dielectric loss increased firstly and then decreased and finally became unchanged (see Fig. 4c). This reveals that Gd, Yb, Sc and La adsorption systems can exhibit longer life in applications as dielectric materials in the low energy regions because of the low static dielectric constant and loss. The Lu- and Sm-adsorbed cases show plasma response.

Fig. 4 Dielectric constant curves of various RE adsorption systems. (a) Real part; (b) imaginary part; (c) covalent radius dependence.

Fig. 5 shows the adsorption coefficient and reflection spectrum curves of various RE adsorption systems. One can see that for Sm, Lu, La, Sc, Yb and Gd adsorptions, the adsorption coefficients come to the maximum values at 166, 165, 186, 165, 174 and 182 nm, respectively, and simultaneously for Gd, Sm and Yb adsorption, the second peak values are present at 47, 43 and 43 nm, respectively (see Fig. 5a), indicating that in the ultraviolet regions the adsorption systems may emerge “Barrier Type” properties. In the visible regions that the wavelength was in the range of 390 to 780 nm, the adsorption systems represent lower adsorption coefficients, explaining that all the systems except Lu and Sm adsorption may exhibit “Transparent Type” characteristic. From the reflection spectrums (see Fig. 5b), it is observed that the values of Lu and Sm adsorption systems were higher than that of the other four systems in visible regions, showing that part energy loss occurs. Combined with the analysis results of Fig. 5a, it is concluded that light spreads more easily in the systems of Gd, Yb, Sc and La adsorption ones.

Fig. 5 Adsorption coefficient and reflection spectrum curves of various RE adsorption systems.

Conclusions

In summary, we conducted the study on the first principles of electronic structure and optical properties of rare earth adsorption at β-Si₃N₄ interface. The fully relaxed structural parameters are found to be in good accordance with experimental data. Charge density difference results illustrate that covalent character of polar covalent bonds by RE adsorption is in the order of Gd > Yb > Sc > Sm > (La, Lu), which was verified by calculated population values. Gd, Yb, Sc and La adsorption systems may exhibit longer life in applications as dielectric materials in the low energy regions due to low static dielectric constant and loss, as well as “Transparent Type” characteristic exhibited in visible regions.

Acknowledgements

The authors gratefully acknowledge the financial support provided by the National Natural Science Foundation of China (51272206, 51472198), Program for Changjiang Scholars and Innovative Research Team in University (IRT1280), National Key Laboratory Functional Composite (9140C560109130C56201) The Fundamental Research Funds for the Central University (xkjc2014009) and State Key Laboratory for Mechanical Behavior of Materials (20121207).

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