Understanding of the Elastic Constants, Energetics, and Bonding in

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Understanding of the Elastic Constants, Energetics, and Bonding in Dicalcium Silicate Using First-Principles Calculations Saravana Karthikeyan Subbiah Karuppasamy, Palanisamy Santhoshkumar, Youn Cheol Joe, Suk Hyun Kang, Yong Nam Jo, Hyeong Seop Kang, and Chang Woo Lee J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b06630 • Publication Date (Web): 19 Sep 2018 Downloaded from http://pubs.acs.org on September 25, 2018

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The Journal of Physical Chemistry

Understanding of the Elastic Constants, Energetics, and Bonding in Dicalcium Silicate Using First-Principles Calculations SKS Saravana Karthikeyan, P Santhoshkumar, Youn Cheol Joe, Suk Hyun Kang, Yong Nam Jo, Hyeong Seop Kang, and Chang Woo Lee* Department of Chemical Engineering & Center for the SMART Energy Platform, College of Engineering, Kyung Hee University, 1732 Deogyeong-daero, Gihung, Yongin, Gyeonggi, 17104, South Korea *Corresponding author: Email: [email protected] Abstract Atomistic scale modeling plays an increasingly important role in understanding the structure features, and the structure-property relationships of materials. Herein, we systematically investigate the elastic constant, thermal conductivity, phonon dispersion, Raman signature, optical constant and electronic band structure of dicalcium silicate (β-Ca2SiO4 or C2S) performed with the norm-conserving pseudopotential method based on the density functional theory (DFT). The obtained elastic constants are well consistent with experimental and other theoretical values. The lattice thermal conductivity is about 1.0 W m-1 K-1 at 300 K by using the simple Slack model, which manifests that the C2S is more likely to be a desirable thermoelectric material. The specific heat capacity at constant volume (Cv) is about 120.745 J mol-1 K-1 at 300 K from the vibrational frequency. The thermal state function of C2S such as vibrational entropy (S), vibrational enthalpy (H), and Helmholtz free energy (F) is calculated using the quasiharmonic oscillator model. The simulated Raman peaks are in an excellent agreement with the experimental results. We demonstrate the significance of coulombic interactions to understand the bonding feature and electron charge difference.

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Introduction: Dicalcium silicate (β-Ca2SiO4 or C2S) is a pivotal natural mineral named larnite or belite.1 βCa2SiO4 is an important structural component used in many applications such as the building industries,2-3 white light-emitting diodes (LEDs),4-5 energy production,6 high-density energy storage,7 environmental remediations,8 and biomedical engineering.9-10 C2S is a crucial selfsetting material exhibiting a wide range of desirable properties such as its bioactivity (nontoxic), thermoelastic martensitic properties, excellent thermal and chemical stability, good mechanical properties, low thermal conductivity, high storage capacity, and flame resistance.11-15 The lowindex surfaces of C2S exhibit higher stability because of the magnitude of the surface unwinding is less and this reveals a surface resembling bulk bonding behavior.16 According to the valencematching principle, the Lewis basicity of (SiO4)2- is 0.33 v.u. and the Lewis acidity of Ca is 0.29 v.u.; their values match up reasonably well, and C2S is a stable mineral.17 Furthermore, C2S is recognized as a polymorph exhibiting five different crystal phases.18-21 This polymorphic property affords C2S numerous crystal structures allowing its use as an active spacer and stabilizer in many applications. Hence it has been broadly utilized for its strength and stability. C2S also shows potential for hybrid practical composite materials, enhancing hydrogen production from wood decomposition, and styling tunable emitting phosphors, thus supporting a crystal phase engineering approach.22-24 Recently, mesoporous C2S with high porosity overcame an interfacial combination problem of an organic phase change material (PCM) without any leakage during the phase transition and thus increased the energy density of the PCM composite.25 In this study, we exploit first-principles calculations to determine the properties and performance of C2S β-phase for use in a wide range of applications. Quantum mechanical (QM) calculations


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were implemented to calculate the independent elastic constants, lattice dynamics, optical constants and the electronic band structures. Moreover, we compute the overall electron density charge distribution map and chemical bond behavior analysis. The independent elastic constants are used to calculate the origin of the low thermal conductivity, Debye temperature, Poisson’s ratio, Grüneisen parameter, average sound velocity, anisotropy, bulk, Young’s and shear modulus. Also, we employ the online ELATE analysis and visualization tool to obtain systemic mechanical characterization by high-throughput calculation of elastic constants. The conspicuous lattice dynamic properties such as specific heat capacity (Cv), vibrational entropy (S), vibrational enthalpy (H), and Helmholtz free energy (F) of C2S have been obtained from the phonon calculations. We calculate the phonon dispersion relations from an empirical potential and our computed Raman signature of C2S shows excellent agreement with the experimental data.26-27 The outcome of the dielectric function, refractive index, absorption coefficient, conductivity, reflectivity, and loss function of C2S based on photon frequency via the coexistence of collective motions involving various atom groups. Finally, we depict the nature of the material, overall charge density distribution map and atomic population to represent the covalent and ionic bond behavior of C2S. All the aforementioned studies are determined from first-principles techniques using Brillouin scattering and DFT within the local density approximation (LDA) method. The results of elastic constant and phonon dispersion are compared with published experimental values. Computation Details First-principles calculations are carried out using the plane-wave basis projector augmented wave (PAW) method28 in the framework of density functional theory (DFT) with CASTEP (Cambridge Serial Total Energy Package) code.29-30 LDA functional was adopted to describe the



electronic exchange-correlation (X-C) energy.31 Around high symmetry points, the LDA approximation tends to overestimate the binding energy and underestimate the lattice parameter, saving on computational costs and it can be useful in treating larger systems. Interactions of valence electrons and ion cores are represented by norm-conserving pseudopotentials.32 The adopted pseudopotentials treat the O-2s22p4, Si-3s23p2, and Ca-3s23p64s2 shells as valence states. The plane-wave basis expansion cut-off energy and the Brillouin zone sampling were fixed at 880 eV and a 3 × 2 × 2 Monkhorst-Pack k-point grid,33 respectively. The Broyden-FletcherGoldfarb-Shanno (BFGS) minimization method was used for geometry optimization,34 where the convergence criteria for the total energy, maximum ionic Hellmann-Feynman force, maximum stress, and maximum ionic displacement were set to 5.0 × 10-6 eV/atom, 0.01 eV/Å, 0.02 GPa, and 5.0 × 10-4 Å, respectively. The calculations are performed allowing both the atomic positions and lattice parameters to find the most stable lattice configuration. C2S (P121/n1 symmetry group) polymorphs, as frequently observed in industrial applications. The unit cell for C2S has monoclinic symmetry with a, b, and c lattice parameters of 5.41265, 6.62205, and 9.13334 nm, respectively. C2S consists of 8 Ca, 4 Si and 16 O atoms (4 Ca2SiO4) as shown in Fig. 1. The computed crystal parameters agree with experimental data, showing a Ca to Si ratio of 2 to 1.35 Oxygen is covalently bound to silicon atoms forming SiO4 groups with a bonding distance of 1.59-1.63 Å. All Si atoms are part of a silicate group and all Ca atoms are ionic in character.


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Fig 1: Schematic illustration of the monoclinic crystal structure of C2S (β-phase). Ca, Si, O atom are depicted in green, yellow and red, respectively. Results and Discussions Elastic Constants The elastic constants of a solid are essential parameters for understanding the link between mechanical and dynamical behavior. Since the elastic constants are functions of the first-order and second-order derivatives of the potential, they improve the accuracy of force calculation and give valuable information for developing inter-atomic potentials. Understanding the effect of pressure on the elastic constants is essential to understand the mechanical stability, thermal properties and phase transition mechanism of the system.36-37 For isotropic polycrystalline materials, it is hard to measure their independent elastic constants (Cijs). In this case, aggregate qualities such as bulk modulus (B), shear modulus (G), Young’s modulus (E), and Poisson’s ratio (ν) are often used to denote their elastic performances. Theoretical details on elastic constants can be found elsewhere. For the monoclinic structure, the mechanical stability under ambient pressure can be approximated by:



> 0 = 1, 2, 3, 4, 5, 6 − > 0

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(1)

+ 2 > 0 − > 0

(2)

− − + − + − + > 0

(3)

2 − + − + −

= − − − + 2 + + + 2 + + > 0

(4)

The theoretical polycrystalline moduli for C2S are computed from the set of independent elastic constants. According to Hill,38 the upper and lower limits of the true polycrystalline constants are expressed via the Voigt39 and Reuss40 equations. In accordance with Hill’s observation, the value of the bulk modulus is (in GPa) B = (BV + BR)/2 (Hill’s bulk modulus), where BV and BR are the Voigt’s and the Reuss’s bulk moduli, respectively. The value of the shear modulus is G = (GV + GR)/2 (Hill’s shear modulus), where GV and GR are the Voigt’s and the Reuss’s shear moduli, respectively. The expressions for Voigt and Reuss moduli41 can be found using the four formulas: E = 9BG/(3B + G), ν = (3B - E)/6B, E/2(1 + ν), and 3G(3G-E)/9G-E, where E is the polycrystalline Young’s modulus (in GPa) and ν is Poisson’s ratio. For monoclinic C2S, five independent elastic constants are shown in the Supporting Information (Table S1). We note that the elastic constants of C2S are in a good agreement with reported experimental values.42-43 Here, we have taken the elastic constants of C2S towards a systemic mechanical characterization by high-throughput calculations of elastic constants of inorganic materials, shown in Fig. 2, as part of the Materials Project,44 linked to ELATE analyze and visualization. ELATE (version code 2017.06.27, Python 2.7.3) is open source software in Python for the manipulation of directional elastic properties such as the spatial dependence of linear compressibility, Young’s modulus, shear modulus and Poisson’s ratio module. For the input stiffness matrix (coefficients


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in GPa) of C2S, ELATE provides a 6 × 6 systemic matrix of second-order elastic constants of Cijs in Voigt notation. The elastic tensor is computed with six eigenvalues. If all of them are positive, then the material is mechanically stable. The unit vectors a (direction of the stress applied) and b (direction of measurement) were characterized by angles in spherical coordinates: 0 and 0 $ 2 ; 45

cos cos$ cos0 − sin∅ sin0 sin cos$ & = 'sin cos$, , &-. / = 'cos sin$ cos0 − cos∅ sin0, cos − sin cos 0

(5)

Fig 2: High-throughput calculations of directional elastic properties. The spatial dependence of linear compressibility (a), Young’s modulus (b), Shear modulus (c) and Poisson’s ratio (d) of C2S. Using the G. A. Slack approximation,46-47 the lattice thermal conductivity (23 ) at a temperature T is of the form



23 = 4

56 789⁄: ?

, 4 =

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.×BCD

E

F.G9H F.>>D K > IJ IJ

(6)

Where, LM is the average atomic mass, N is the volume per atom, - is the number of atoms in the

primitive unit cell, ΘP is the acoustic Debye temperature and QR is the acoustic Grüneisen

parameter. The formula has been used widely in lattice thermal conductivity evaluations.48-49 To find ΘP , the Poisson-ratio-determined acoustic Grüneisen parameter or anharmonicity of the system is calculated using the following relationships.50-52 ΘP =

9

W : V Y ZM -E⁄ , ZM TU X S

Z_ = `

aK/c d

KR

\

&-. Ze = `d

QR = [ ^,Z = ER

= [ VR : + R : Y^ c

> R E[ ]fR\ ^ > R E[ ]fR\ ^

]

E⁄

(7)

(8)

(9)

The Debye temperature of C2S was calculated to be 913 K using the above equation 7 from the corresponding averaged sound velocity va = 4815m/s, which is in agreement with the phononcalculated transverse Ze , 7695m/s and longitudinal Z_ , 4327m/s sound velocities along all

directions in the Brillouin zone. The Poisson-ratio-determined Grüneisen parameter is about 1.59 and the Poisson ratio is about 0.268, as calculated from equation 9. The larger the Grüneisen parameter, the lower the thermal conductivity, eventually determining the lower limit sound velocity by the weaker interatomic interactions. According to Pugh’s criteria,53 a critical ratio of shear modulus to bulk modulus (B/G) greater than 1.75 indicates ductility; otherwise, a brittle nature is indicated. By calculation of the B/G ratio, C2S is a ductile material. Despite the fact that C2S manifests brittle characteristics, we distinguished C2S as a relatively ductile behavior at the atomic scale.54-56 This can conceivably open up new opportunities for further studies in brittle-to-


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ductile transitions to give a thorough comprehension of distortion mechanisms in silicate materials. The same can be inferred from an additional argument that designation in the brittle/ductile categories follows from the calculated Poisson’s ratio (v). For ductile metallic materials, v is typically 0.2657-58 and we interpret that v for C2S to be 0.268, suggesting a ductile nature of C2S. In a study by Ranganathan and Ostoja-Starzewski (2006),59 a universal elastic anisotropy index 4j = 5kl/km + nl/nm − 6 was proposed that was reasonable for

analyzing the development of micro cracks and the hardness of materials. The value of zero for

4j corresponds to locally isotropic single crystals. A nonzero 4j reflects the extent of a single crystal anisotropy, including both the bulk and the shear contributions. The anisotropy of compressibility of C2S is 0.264. Origin of Low Thermal Conductivity of C2S We calculated the lattice thermal conductivity of C2S using the above equation 6, as shown in Fig. 3. Our results suggest that C2S has an intrinsically low lattice thermal conductivity of 1.0 W m-1 K-1 at 300 K and 0.3 W m-1 K-1 at 1000 K. C2S is used in interior thermal insulation systems without any water vapor barriers. Due to its resistance to high temperature, it behaves as a high temperature or flame retardant insulation.60 Roels et al.,61 Hamilton and Hall et al.62 have studied its hygral properties, as well as its chemical and mineralogical compositions. A considerable amount of experimental and theoretical research of apparent thermal conductivity of calcium silicate has evolved over a range of temperature and moisture conditions.63-68 The combination of high capillary activity and low thermal conductivity enables the high moisture buffering capacity of C2S, mitigating the humidity spikes and occasional interstitial condensation by redistribution and transport out when initially saturated.69 C2S doped gadolinium primarily apatite-based material reduces thermal conductivity at high temperature. It decreases steadily with the inverse



square root of oxygen vacancies or cation vacancies or various types of point defects. Point defect and doping have proven to be a successful strategy for reducing the thermal conductivity of C2S at room temperature, and it remains to be demonstrated that it could be helpful to reduce the exceptionally low thermal conductivity.70

Fig 3: The Origin of the low thermal conductivity of C2S. Demonstration of the cumulative thermal conductivity c ontinuously decreases with the increase of temperature. Lattice Dynamics The quantitative understanding of the thermodynamic properties created from the collective atomic vibration in a crystal as a function of temperature. In particular, the lattice dynamic is one of the most important branches of condensed matter systems and the underlying issue of thermal phenomena of solids as a function of temperature.71-75 However, the lattice or total energy (Etot) is calculated from electronic and nuclear repulsion with first-principles calculations. The relative stabilities of C2S can be determined for thermodynamic properties using the Helmholtz free energy. The zero-point energy can influence the calculated relative stability of C2S. If all phonon frequencies in a unit area are positive, the crystal will be stable. If some frequencies in the unit


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area are imaginary (soft modes), then the system is unstable. Based on phonon theory, integration of phonon density of states is performed within the quasi-harmonic approximation according to the following equations:76 o = 3-pqa r sB

y|6}

~ = 3-pqa sB

y|6}

R = 3-pqa sB

y|6}

t- u2 v-ℎ [T ^z { .{ ℏy

U?

[T ?^ ℎ [T ?^ ℏy U

− t- u2 v-ℎ [

ℏy

ℏy

TU ?

U

^z { .{

[T ^ vℎ [T ^ { .{ ℏy

U?

ℏy

U?

(10)

(11)

(12)

Where, kB is the Boltzmann constant, ωmax is the largest phonon frequency, n is the number of atoms per unit cell, N is the number of unit cells, and g(ω) is the normalized vibrational density y|6}

of states (VDOS) with sB

{.{ = 1. The term ‘quasiharmonic approximation’ arises

from the approach that for a given volume, Helmholtz free energy as a function of volume and temperature is calculated under the harmonic approximation, and the anharmonic effects are included solely through the volume dependence of the phonon frequency. In this work, we focus on the phonon dispersion and thermodynamic properties of C2S. In statistical thermodynamics, a phonon represents a quantized vibrational mode characterized by a frequency. A Low or imaginary phonon frequency at a given reciprocal wave-vector point may reveal structural instabilities. The calculated phonon dispersion curves along several symmetry directions and VDOS of C2S are shown in Fig. 4. The phonon dispersion and VDOS from LDA methods are generated using density functional perturbation theory.77-78 Herein, no soft modes are observed in the phonon dispersion curves. The dynamical stability calculations were computed at 36 wave vectors (q) in the Brillouin zone of the crystal and interpolated to obtain



the bulk phonon dispersions. The wave-vector grid spacing for interpolation was 0.05 Å–1 representing the average distance between the Monkhorst-Pack k-points.

Fig 4: The phonon dispersion curve (a) and vibrational density of states (b) of C2S. Thermodynamic Quantities The thermodynamic quantities such as vibrational entropy, vibrational enthalpy, Helmholtz free energy, and specific heat capacity at constant volume of C2S have been systematically predicted by the quasi-harmonic approximation as shown in Fig. 5. Considering only harmonic zero-point energies, the heat capacity at constant volume of C2S tends to the limit value of 120.745 J mol-1 K-1 at 300 K and 160.362 J mol-1 K-1 at 1000 K. Fig. 5a shows the Cv increases quickly from 0 to 132 J mol-1 K-1 when the temperature increases from 0 to 400 K. When the temperature increases from 0 to 800 K, as shown in Fig. 5b, the Helmholtz free energy decreases from about 0 to -5 eV, the enthalpy increases from 0 to 4 eV and the entropy increases from 0 to 9 eV. Our calculated results are comparable with heat capacity measurements by Zhihua Xiong (2016).79 Our results coordinate with a relative difference quickly decreasing from 1.285% for the temperature range of 10 to 1000 K, as shown in the Supporting Information (Table S2). The specific heat capacity at constant pressure (Cp) can be calculated by the well-known thermodynamic function Cp = Cv +


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α2BVT, where α is the coefficient of volumetric thermal expansion, V is the unit cell volume, B is the bulk modulus and T is the temperature for the solid material. For the solid materials, Cp and Cv are comparable at the temperature below 300 K.

Fig 5: Calculated total heat capacity curve (a) and thermodynamic function curves (b) of C2S at 0-1000 K. Raman Signature The vibrational modes from the VDOS of lattice crystal are used to measure Raman scattering. An ultraviolet region of ~363.8nm was used for C2S. In addition, Raman spectroscopy is used to characterize the electronic state,80 probe crystallinity,81 lattice temperature,82 doping,83-84 and strain.85 Calculations of the irreducible representation of the monoclinic structure yield 84 fundamental normal modes of vibration whose symmetry species are: Γvib = 21 Ag + 21 Bg + 21 Au + 21 Bu. However, g mode is Raman-active and u mode is IR active with Ag polarized and Bg depolarized. Au and Bu modes are acoustic. Here, 42 Raman active modes have been observed in the spectra of the β phase: 9Ag + 9Bg (internal modes); 9Ag + 9Bg (translational modes); and 3Ag + 3Bg



(vibrational modes). The range 100-1200 cm-1 covers Raman scattering for C2S as depicted in Fig. 6. The Raman spectrum permits detachment of two gatherings of vibrations which are situated in β-Ca2SiO4 at 470 to 1080 cm-1 with an overwhelming line at 846 cm-1, 520 cm-1 for O-Si vibrations and underneath 450 cm-1 for O-Ca vibrations, respectively.86 The correspondences established in Supporting Information (Table S3) matching with the simulated Raman spectrum demonstrates that the gross features are very similar: this shows that our calculation is sufficiently precise. The Raman spectrum is a continuous distribution of phonon modes; along these modes, the structure is well-ordered.87-88 The spectrum mainly shows the internal and external bands υ2, υ4, (υ1 or υ3), and υ3 in order of increasing frequency. The internal vibration bands are related to isolated tetrahedral [SiO4]4- anion cluster vibration in the lattice. The isolated tetrahedral [SiO4]4- anions has a cubic point symmetry.89 The most intense band occurs at 850 cm-1 (υ1 [SiO4]-4) and a shoulder at 905 cm-1 (υ1 or υ3 [SiO4]-4) allowing identification of the β-phase. The highest frequency band at 981 cm-1 (υ3 [SiO4]-4) can be assigned to an asymmetric stretching vibration of C2S. In the frequency range from 800 to 981 cm-1, all the vibrations involve large energy changes and therefore dispersion interactions play a minor role in these vibrations. The peaks below 550 cm−1 correspond to phonons (or lattice vibrations), i.e., vibrations involving intermolecular motion. The bands at 311, 361, 418, 522, and 549 cm-1 probably correspond to the modes derived from the υ2, υ2, υ4, υ4, and υ4 internal modes of the isolate silicate tetrahedral [SiO4], respectively.90-93 The bands at 260, 236 and 205 cm-1 are very similar and derived from the relative motion of the calcium cations since they are involved in external lattice modes. The same holds for the lowest wavenumber signal observed at 169 cm-1. According to reference 20, most of these low-frequency modes correspond to intermolecular translations and vibrations.


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Fig 6: Raman signature of C2S at 0~1000 cm-1. Optical Constants The understanding of the quantum mechanical models under the perturbation of classical electrical fields, a huge interest is dedicated to the study of collective optical phenomena for the design of optoelectronic devices. C2S inspires the more profound study of light-matter interactions with its high value static dielectric constant (B ) and wide use in technological applications.94-97 Optical properties consist of an optical absorption coefficient, complex dielectric function, complex refractive index, extinction coefficient and optical conductivity. These optical functions serve to give a better understanding of exotic collective and excitation behavior of the electronic band structure under an interacting with light. The value of complex permittivity determines the degree of miniaturization of electronic circuits. The complex dielectric function is calculated within the linear response range, usually described by a complex

permittivity of { = { + { or complex refractive index N{ = -{ + q{ with real and imaginary components. The imaginary component {, which can be deduced

by a direct evaluation, mainly characterizes the electron transition from occupied states to



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unoccupied states. The real component { is calculated using the Kramers-Kronig transform obtained by integration over a fairly wide frequency range using a differential

coefficient of {. From equation 10 and 11,98 the absorption coefficient and the optical conductivity can be inferred. Here, we calculate the optical constants of C2S related to the polarizability α, in particular to the dipole polarizability, which arise from structures with a permanent electric dipole which can change orientation in an applied electric field. =

9

y>

∑, sa . 2 .

X

= 1 + ∑, sa . 2 .

{ = √2{V = B { {

{

|. L 2| N 2 − 2 − ℏ{

(13)

>

|P.5 | ℏ: E > > > E X Eℏ y

−

{

(14)

9 >

− {Y

(15)

(16)

C and V are the conduction and valence bands, respectively, { is the angular frequency, and

are constants, BZ is the first Brillouin Zone, K is the electron wave vector, |. L 2| is the

momentum transition matrix element, 2 and 2 are the intrinsic energy levels of the conduction and valence bands, respectively, { is the absorption coefficient, B is the static

dielectric constant, and is the optical conductivity. The above relationships form the

theoretical basis of the optical properties of crystals. Fig. 7 represents the dielectric function, refractive index, absorption coefficient, optical conductivity, reflectivity, and loss function spectrum of C2S for photon frequency up to 45 eV. The dotted and solid lines represent the imaginary and real components of the optical functions, respectively. The dielectric function and complex refractive index are shown in Fig. 7a-b, which


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can be obtained from equation 13 and 14. In low-energy areas, the real component of the dielectric function increases with energy to achieve a maximum value of 3.47 when the energy reaches about 6.159 eV. It is associated with the electronic transition from Ca 3d to the 2p states

of O in the valence band. The real component, , reaches its maximum and minimum values at the maximum slope of when rising or declining, respectively. In the second peak, the value

increases from 0.025 to 1.49 over the energy range of 10-24 eV followed by a sharp decrease with increasing energy as shown in Fig. 7a.



Fig 7: Optical properties of C2S; dielectric function (a), refractive index (b), absorption coefficient (c) in wavelength, optical conductivity (d), reflectivity and loss function spectrum of C2S as a function of energy (eV).


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Here, the high energy peaks are associated with the electronic transition between the 3d states of

Ca and 2p states of O. In insulators, the charge is localized and > 0, silicon nitrides with a

dielectric constant greater than 7 are classified as high dielectric constant materials.99 The complex refractive index of C2S is illustrated in Fig. 7b. It shows 1.90 in the energy range of 6.32 eV, which is very close to the experimental value 1.72,100 and gradually increases from 0.48 - 1.24 over the energy range from 11 to 24 eV. Especially, the refractive index is tuned round the visible range between 1.65 to 3.2 eV for the clear semiconducting applications. Fig. 7c shows the light absorption coefficient spectrum of C2S. It indicates the attenuation of light intensity per unit of distance travelled in the system. In the absorption coefficient spectrum, there are two emission peaks at 48.73 nm and 150.74 nm in wavelength, which are identical to the imaginary component of the dielectric function of C2S. Fig. 7d shows the high optical conductivity of C2S with a maximum light absorption rate of 3 in the energy range from 20.8 to 25 eV and minimum light absorption rate of 2.74 in the energy range of 7.5 eV. The electrical conductivity will also increase as a result of photon absorption due to the increase in the number of free carriers generated.101 In Fig. 7e, the spectrum shows that C2S is a perfect reflector over the energy ranges 0.01 - 16.7 eV and 21 - 33 eV. At the energy of 0.01 eV the reflection is about 0.022, and the energy of 16.7 eV the reflection decreases to 0.001. The electron energy function describes the energy loss of a fast electron traversing a material with a change in plasma frequency. Fig. 7f shows two prominent peaks for the energy loss function of 2.72 and 1.67 in the energy range of 11 eV and 26.3 eV, and these peaks are associated with the plasma resonance as well as the reflectivity spectrum of C2S. Band Structure



Since the electronic structure is crucial to understanding the physical properties of C2S. The electronic structure including band structure and partial density of states (PDOS) was obtained from the transitions in occupied and unoccupied states around the Fermi level.102-104 The calculated band structure along with the high symmetry direction in the Brillouin zone is shown in Fig. 8. Both the covalence band maximum and the CB minimum are located at the Γ-point with a band gap of 5.127 eV and its electronic structure is a direct band gap insulator. A flattopped VB is speculated below the Fermi level. The experimental band gap in a series of Dy3+activated Ca2SiO4 phosphors was found to be in the range of 5.10–5.44 eV.105 From the absorption spectrum of the β-Ca1.999Ce0.0005Na0.0005SiO4 host material, the band gap energy was estimated to be approximately 7.7 eV.106 The experimental band gap of γ-Ca2SiO4 is about 5.3 eV.107

Fig 8: Calculated band structure of C2S. In Fig. 9, the PDOS of C2S, we discover that the lower part of the VB is from O 2s orbitals and the upper part is from O 2p orbitals, whereas the lower CB originates mostly from Ca 3d orbitals. There is a significant contribution from Si 3p orbitals to the upper part of the VB as well. The


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contribution from 0 to -6 eV and small features emerging at -15.8 eV belongs to the VB of the Ca 3d orbital. The large features are emerging to VBs with -36.7, -5.5 and -15.8 eV result mainly from the Ca 4s orbital, Si 3s orbital and O 2s orbital. The small features emerging to the VBs at 5.5, -4.1 and -2.6 eV result mainly from the Ca 4s orbital. The moderate features emerging to the VBs at -19.3 and -17.1 eV result mainly from the Si 3s orbital. The small features emerging to the VBs at -19.2, -17.1, -15.8, -4.5, and 3.7 eV are mainly from the O 2s orbital. The large features emerging to the VBs at -18.4 and -3.8 eV result mainly from Ca and Si 3p orbitals. The small features emerging to the VBs at -17.1, -15.8, and -18.9 eV result mainly from Ca and Si 3p orbitals. The moderate features emerging at -15.8 eV result mainly from the Si 3p orbital. The VBs between 0 to -4.8 eV mainly result from the O 2p orbital. The electronic densities near the Fermi surface and the bottom of the CB are mainly due to the contributions of Ca 3d and Si 3p orbitals. Hence, accurate theoretical computations based on density functional theory provide reliable properties for C2S.



Fig 9: Partial density of states (PDOS) of C2S as a function of energy (eV). The electronic density near the Fermi surface and the bottom of the CB are mainly due to the contributions of Ca 3d and Si 3p orbitals. In order to understand the charge transfer of C2S in more detail, the electron density has been investigated. Fig. 10 depicted the contour plot of charge densities of C2S. The potentials were generated from self-consistent charge densities obtained from plane-wave PAW method with the CASTEP code. The charge distribution of oxygen is deformed towards the silicon atom. It is also confirmed that Si and O atoms are bonding covalently; this bonding feature resembles well that of the isolated silicate tetrahedral molecule [SiO4]-4. The charge distribution of the Ca atom is almost spherical and the density magnitude is small, indicating that the bond is mainly ionic.108 Here, the monoclinic C2S contains 96 orbitals, visualized in the Supporting Information.


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Fig 10: Overall electron charge distribution map of inbound C2S crystal with an isosurface. The chemical bond analysis109 scheme is a useful tool for evaluating the bonding character in a material. It is recognized that a positive estimation of the bond population shows a covalent bond, and a negative estimation demonstrates an anti-bonding state, while a zero estimation suggests an immaculate ionic bond. However, this method is more qualitative than quantitative, giving results that are sensitive to the atomic basis. All the bond populations of Si-Ca and O-O bonds have a negative quality, which reveals the anti-bonding state originates from the electronegative difference as shown in Table (S4-5). In addition, charge transfers from Ca to O atom are observed, because of the small contribution of the Ca orbit for occupied states and the relatively high charge density distribution around the O atoms existing near the Ca atom. Consequently, it is normal that Ca atoms are ionized as Ca2+ cations and O atoms like O- anions. However, bond populations of Si-O bonds are positive, so covalent bonds amongst Si and O atoms, in concurrence with the investigation of the electron density difference maps.110 Conclusion



We studied the elastic constants, thermal conductivities, and lattice dynamic, optical and electronic properties of C2S by first-principles calculations. Studies on its elastic constants reveal that C2S behave in a ductile manner. It has a bulk modulus of 120.09 GPa and a shear modulus of 65.68 GPa. Using calculated Cijs, the acoustic Debye temperature (ΘP ) of C2S is derived. At 300 K, the predicted thermal conductivity is about 1.0 W m-1 K-1 by using the simple Slack model, which manifests that the C2S is more likely to be a desirable thermoelectric material. The polycrystalline elastic properties and lattice thermal conductivities was compared with the available experimental data. Computed phonon dispersion curves indicate that C2S is dynamically stable. The specific heat capacity at constant volume is about 120.745 J mol-1 K-1 at 300 K from the vibrational frequency. The thermal state function of C2S is reported for the full temperature range. Our calculations well trace the experimental Raman mode. Ca atom plays an important role in the modulation of the static dielectric constant and the static refractive index. Moreover, the band structure reveals that C2S is an insulator with a direct band gap of 5.127 eV. From the charge density distribution, it is confirmed that Si and O atoms are bonded covalently.

Supporting Information Identification of computing independent elastic constants, heat capacity at the constant volume at a selected temperature, electron charge distribution, and chemical bond behavior of C2S by using first-principles calculations is presented. Acknowledgment: This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (No. 2017R1A2B4010157).


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