First-principle analysis of the structural, mechanical, optical and electronic properties of wollastonite monoclinic polymorph

Accepted Manuscript First-principle analysis of the structural, mechanical, optical and electronic properties of wollastonite monoclinic polymorph Shaker J. Edrees, Majid M. Shukur, Mohammed M. Obeid PII:

S2352-2143(17)30245-9

DOI:

10.1016/j.cocom.2017.12.004

Reference:

COCOM 118

To appear in:

Computational Condensed Matter

Received Date: 25 October 2017 Revised Date:

17 December 2017

Accepted Date: 18 December 2017

Please cite this article as: S.J. Edrees, M.M. Shukur, M.M. Obeid, First-principle analysis of the structural, mechanical, optical and electronic properties of wollastonite monoclinic polymorph, Computational Condensed Matter (2018), doi: 10.1016/j.cocom.2017.12.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT First-principle analysis of the structural, mechanical, optical and electronic properties of wollastonite monoclinic polymorph

Shaker J. Edrees, Majid M. Shukur, Mohammed M. Obeid* College of Materials Engineering, University of Babylon 51002, Babylon, Iraq

* Independent Researcher

Mobile: +9647812307281

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E-mail: [email protected]

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Hilla, Babylon 51002, Iraq

Crystal structure of CaSiO3 monoclinic

ACCEPTED MANUSCRIPT First-principle analysis of the structural, mechanical, optical and electronic properties of wollastonite monoclinic polymorph

Shaker J. Edreesa, Majid M. Shukur b, Mohammed M. Obeid*c a,b,c

Department of Ceramic, College of Materials Engineering, University of Babylon 51002, Babylon, Iraq

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Abstract

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The structural, elastic, optical and electronic behavior of CaSiO3 monoclinic polymorph are estimated utilizing ultrasoft pseudo-potential technique operated in CASTEP code. The calculated lattice parameters, such as lattice constants, angle β, and unit cell volume, are in excellent agreement with the experimental data. The computed elastic constant shows that CaSiO3 monoclinic is mechanical stable according to Born criteria. In addition, the polycrystalline properties such as bulk modulus, shear modulus, Young's modulus, Poisson's ratio, elastic anisotropy, compressibility and Debye temperature are determined based on the computed values of the elastic constants. Cauchy pressure and Poisson’s ratio indicating a dominant ionic nature of the brittle CaSiO3 monoclinic. An Indirect band gap Ε (C-Г) = 5.02 eV, Ε (C-B) = 5.26 eV, and a direct gap Ε (Г-Г) = 5.06 eV were obtained. Finally, optical properties, such as dielectric function, absorption coefficient, refractive index, conductivity, loss function, and reflectivity have been predicted for polarized incident radiation with electrical vector Ε parallel to the crystalline b-axis.

1. Introduction:

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Wollastonite is an earthy occurring calcium silicate with the chemical expression of CaSiO3 [1]. Silicate minerals are generally sorted according to the manner of connection in the [SiO4] tetrahedral. Calcium silicate (CaSiO3) grows in two structurally different forms: stable high-temperature (α-wollastonite) and low-temperature (β-wollastonite) that is common CaSiO3-polymorph initiated in crusted rocks. The low-temperature wollastonite has been stated polytypes with a different packing structure of the single chains: triclinic (1T,3T,4T,5T,7T) and monoclinic parrawollastonite [2]. Due to different modes of stacking along the direction of the a-axis, wollastonite grows in triclinic and monoclinic forms. The crystal structure of parrawollastonite was primarily explained by Barnik (1936) who suggested [Si3O9]-6 rings as the essential structural property of parrawollastonite [3]. Tolliday (1958) express that monoclinic wollastonite may result from the triclinic structure by simple packing modification as shown in Fig.1 [4]. Wollastonite is remarkable ceramic material that has excellent physical, chemical, thermal and electrical properties. Therefore; it is used in various industrial applications, such as ceramic production, biomaterials, insulators, and fillers [5-12]. Insufficient studies in the literature have stated calculations on actual crystal structures, due to the large unit cell and low degree of symmetry in silicates [13]. In the current analysis, ab initio quantum mechanical computations of the structural, elastic, optical and electronic characteristic of monoclinic CaSiO3 have reported. *c corresponding author Email address: [email protected] (Mohammed M. Obeid) College of Materials Engineering, University of Babylon 51002, Babylon, Iraq

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ACCEPTED MANUSCRIPT 2. Computational Methodology:

Results and Discussion:

3.1.

Structural Properties

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3.

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Ab initio assessment was performed by means of the plane-wave psedopotential method within the framework of density functional theory (DFT) as operated in CASTEP code [14]. All assessments were treated with the local density approximation (LDA) in the scheme of Ceperley-Alder and Perdew-Zunger (CA-PZ) terms [15]. For geometry optimization, ultrasoft psedopotentials were used together with an energy cutoff of 340 eV [16]. The arrangement of valence electrons was equivalent to Ca 3s2 3p6 4s2, Si 3s2 3p2 and O 2s2 2p4. Brillouin zone (ZB) scheme integration of 3x4x4 K-point using Monkhorst-Pack grid was adequate in making the electron system to converge [17]. The convergence tolerances designated for all geometry optimization in the BFGS minimization scheme [18] were set as ultrafine quality: (energy of 0.5x10-5 eV/atom, force of 0.01 eV/A°, stress of 0.02 GPa, and atomic displacement of 0.5x10-3 A°). A tolerance of 5 x 10-7 eV/atom was used for the self-consistent estimation. It is noticeable that the increase of 100 eV in the quality of energy cut-off does not alter the first three decimal digits of the lattice parameters in LDA [19]. BZ integration of 10 irreducible kpoints with energy cut-off of 310 eV was used to estimate the elastic constant and its related properties. partial density of states and Electronic band structure were predicted. Optical properties were achieved after a single point energy run utilizing norm-conserve pseudopotentials [20] with an energy cutoff of 500 eV because CASTEP code unable to permit non-local correlation energy effects to the optical characteristic using ultrasoft pseudopotentials [21].

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The crystal structure of wollastonite is monoclinic with space group P21/A (no.14). The conventional unit cell parameters containing 60 atoms were obtained from the ICSD database operated in Findit2009. The calculated structural parameters of the experimental [22] and optimized monoclinic CaSiO3 yield an acceptable agreement between them as presented in Table 1.To make a strong basis for reliability of the elastic, electronic and optical characteristic of the considered material, one can see that the largest fluctuation between the experimental and optimized lattice parameters a,b,c does not surpass 1.3%, indicating that the utilized scheming method is trusty. The unit cell volume of the monoclinic CaSiO3 in the utilized approximation is 3.7% smaller than the experimental volume. 3.2.

Elastic constant and related characteristic

The elastic characteristics of materials give the valuable data about the bonding property between adjacent atomic planes, bonding anisotropic, stiffness and structural stability of the material. The values of these properties can be used to calculate the phonon spectra, specific heat capacity, Debye temperature, interatomic potentials and thermal expansion [23]. There are thirteen independent elastics constant Cij of the monoclinic CaSiO3 are summarized in Table 2. C22 and C33 are larger than C11 demonstrating the resistivity to compression of monoclinic CaSiO3 along the [010] and [001] directions are larger than along the [100] one. This implies that the chemical bonding property along the [010] and [001] directions are stronger than along the [100] direction. It seems that the elastic constants decline with the augment of the lattice parameters. The criteria for 2

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BV = (1/9)[C11 + C22 + C33 + 2(C12 + C13 + C23)]

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mechanical stability of low symmetry monoclinic structure are given by (supplementary) [24]. Some elastic constant Cij elements are not transformed into themselves, as required by the symmetry and the transformation operation. Instead, these elements transform into their negative values as shown for the C25 of the monoclinic phase [25]. This negative value may present that contradictory tensile alteration arises in x1x2 plane related with a shear force in the x2-x3 direction. According to the above criteria, the result shows that monoclinic CaSiO3 is mechanically stable under ambient condition. The calculated elastic constant Cij can be utilized to estimate the values of the bulk and shear modulus according the Voigt-Reuss-Hill (VRH) approximations as shown in Table 2. The bulk modulus is a degree of the resistivity against volume change executed by the applied pressure. Instead, the shear modulus represents the resistivity against the changeable distortion upon shear stress [26]. For polycrystalline aggregate, Voigt considers the strain is uniform while uniform stress was assumed by Ruess [27]. In Voigt estimation, the bulk modulus (BV) and shear modulus (GV) for the monoclinic CaSiO3 are given by [28].

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GV = (1/15)[C11 + C22 + C33 + 3(C44 + C55 + C66) -(C12 + C13 + C23)]

(2) (3)

In Reuss prediction, BR and GR are given in term of elastic compliance constants Sij [29] BR = 1/(S11 + S22 + S33) + 2(S12 + S23+ S13)

(4)

GR = 15/ 4(S11 + S12 + S33) – 4(S12 + S23+ S13) + 3(S44 + S55 +S66)

(5)

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The Voigt and Ruess approximations are truly valid only for isotropic materials, while it is invalid for anisotropic one. For anisotropic crystals, Hill [30] took the average result of the maximum and minimum values of the isotropic elastic moduli in the Voigt and Reuss approximations. Bulk modulus BH and shear modulus GH in Hill approximation were computed using the formula: (6)

GH = 1/2 ( GV+GR )

(7)

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BH = 1/2 ( BV +BR )

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One can see that B is larger than G for monoclinic CaSiO3 suggesting that the shear modulus is the dominant factor limiting the mechanical stability of the crystalline materials. The calculated values of the BH and GH of our LDA approximation yield an acceptable agreement with the experimental data [31,32] as shown in Table 3. Pugh's ratio G/B is a simple indicator of the correlation between the brittle/ductile characteristic of crystals and their elastic constants [33]. Brittle materials have a ratio of G/B > 0.5, while ductile is less than 0.5 [34]. Consequently, according to the Pugh’s criteria, CaSiO3 is considered brittle with a ratio of G/B > 0.5 (with Voigt, Reuss, and Hill). The values of Young's modulus E and Poisson's ratio are very significant in various applications. It is noticeable that the larger the value of Young's modulus, the stiffer the materials [35]. Young's modulus was computed using the formula:

E = 9BG/ (3B+G)

(8)

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υ = (3B-2G)/[2(3B+G)]

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Young's modulus value in our theoretical calculation agrees well with the value of the experimental one, demonstrating the dependability of suggested ab initio study as presented in Table 3. On the other hand, elastic complains were used to derive the axial components of Young's modulus: Ex= (S11)-1 , Ey= (S22)-1 and Ez= (S33)-1. One can see that the b direction Ey= 162.06 GPa, is much stiffer than a and c directions (Ex= 127.89 GPa and Ez=128.86 GPa) as shown in Table 4. The Poisson's ratio imparts essential data about the stability of the materials against shear and the nature of the chemical bonding forces. The Poisson's ratio is estimated according to the given formula: (9)

Au = 5GV/GR + BV/BR – 6

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larger the Poisson’s ratio indicating good plasticity. The value of for covalent bonding force is small (υ =0.1), and for ionic materials (υ = 0.25) or higher [36]. It is noticeable that the Poisson’s ratio is 0.26 which is indicating a dominant ionic nature of CaSiO3 phase, which agrees well with the experimental value [31] as presented in Table 3. The sign of Cauchy pressure (C12- C44) also provides essential information about the bond sorting. A negative sign of the Cauchy pressure indicating dominant covalent bond compounds while positive sign indicating dominant ionic bonds [37]. The result of Cauchy pressure (C12- C44 > 0), indicating dominant ionic bonds. This indicated the plasticity of the studied brittle material (CaSiO3). Consequently, to evaluate the chemical and physical characteristic, it is important to calculate the elastic anisotropy of crystal. The calculated values of shear anisotropic factor (A1,A2,A3), the percentage of anisotropy in compressibility, shear (AB and AG) and universal elastic anisotropy index Au are computed in Table 5. The universal elastic anisotropy index Au is estimated by [38]. ≥0

(10)

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Au is equal to zero for isotropic crystal, while deviation from zero a degree of elastic anisotropy is reflected. The obtained result of Au = 1.34, reveals that monoclinic CaSiO3 has a certain degree of elastic anisotropy. The shear anisotropic factor used to measure the amount of the bonding anisotropy of the atoms along various crystallographic planes described in [39]. On the other hand, the percentage of anisotropy in compression and shear was calculated using [40]. (11)

AG = GV -GR/GV +GR x 100%

(12)

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AB = BV -BR/BV +BR x 100%

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The value of isotropic crystal is zero, as shown in Table 5, the values of AB and AG propose that the structure of monoclinic wollastonite is anisotropic in shear and compressibility. The Debye temperature (ӨD) is an essential parameter of materials, and it is thoroughly associated with many physical characteristics. Such as elastic constant, hardness, specific heat, melting temperature and so on [41]. ӨD can be calculated from the average velocity (υm) given by [42]. ӨD = h/k [3n/4ᴨ ( ρNa/M )] 1/3 υm

(13)

Where h is Planck’s constant, Na is Avogadro number, k is Boltzmann constant, n , M and ρ are the number of atoms in the unit cell, the molar mass, and the crystal density, respectively. The mean sound velocity, υm, was obtained using the formula [43]. υm = [1/3(2/υt3 + 1/υl3] -1/3

(14)

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ACCEPTED MANUSCRIPT where are the longitudinal wave and acoustic transverse velocity respectively. The values of υt and υl can be computed from the shear and bulk modulus using the following expressions [44]. υt = (G/ρ)1/2

(15)

υl = (3B+4G/3ρ)1/2

(16)

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By using computed results of the elastic constants presented in Table 2, we calculated υt, υl, υm , ӨD and density for CaSiO3 monoclinic as presented in Table 6 below. One can see that the sound velocities are dependent on the achieved values of the elastic moduli of a material. Materials with a large value of the elastic moduli acquiring higher sound velocity. However, no estimated data is presented in the literature for comparison. Therefore, the predicted value can be utilized as a reference for future experimental work. The values of the elastic properties of wollastonite based materials may extend its application as a matrix composite compound and is desired for the computed of strength parameters in the evolution of new materials with presenting properties [32]. 3.3. Electronic properties

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Fig.2 depicts the Kohn-Sham electronic band structure and partial density of state (PDOS) for monoclinic wollastonite along the high-symmetry points of the Brillouin zone. In Fig.2, a direct band gap equal to 5.06 eV and different indirect band gaps (5.02 and 5.26 eV) have computed. Six valence bands appear at -36 eV. A large gap of about 16 eV formed mainly from s state. Furthermore, thirty-six (36) bands can be viewed between -20 eV and -15 eV, created from s and p orbitals. The contribution of the p state is more outstanding than the contribution of s state. The same trend can be seen between the energy -9 eV and 0 eV. The conduction band is chiefly composed of d state with a minor contribution of s and p states. Fig. 3 shows the band structure near the main band gaps. Our ab initio calculation within the LDA-CAPZ at the optimized lattice parameters yield an indirect band gap of 5.02 eV between C point in the valance band and point in the conduction band. A secondary conduction band minimum formed near the B point with the energy of 5.26 eV. The values of the direct and indirect band gaps show an acceptable agreement with experimental data where the CaSiO3 has a band gap > 5 eV [13]. Furthermore, the estimated band gaps of CaSiO3 monoclinic are smaller than the predicted values of the CaSiO3 triclinic [45,46]. This may relate to differences in the shape of the crystal structure for m-CaSiO3 and t-CaSiO3. The m-CaSiO3 is denser than the t-CaSiO3 presenting more pronounced localization of 3d states at the conduction band and therefore narrower 3d states. To clarify the nature of the electronic band structure and partial density of state (PDOS), Ca, Si, and O atomic sorts are estimated as demonstrated in Fig. 4. one can see that the conduction bands are generally formed by unoccupied Ca-3d with a minor contribution of Ca-4s, Si-3p and 3s, O-2p states. The PDOS exhibit a strong p character near the fermi level (0 eV) of VB, primarily due to the O-2p orbital, with a minor contribution of Si-3p and Ca-3d orbitals. The energy level between -15 eV and -20 eV, spike mainly from Ca-3p and O-2s states. The energy of -36 eV is dominated by the Ca-3s states.

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ACCEPTED MANUSCRIPT 3.4. Optical properties

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It is necessary to analyze the optical functions because it provides all-important information about the electronic structure of materials [34]. The optical characteristics of materials are usually distinguished by the complex dielectric function ε(ω) = ε1(ω) + iε2(ω), which is referred to the electronic band structure [47]. The momentum matrix elements between the occupied and unoccupied electronic states can be utilized to estimate the imaginary part ε2(ω)[48]. The Kramers-Kronig equation can bes utilized to compute the real part ε1(ω) from the imaginary one [49]. Refractive index, reflectivity, absorption spectrum, electron loss function and the conductivity can be calculated from real and imaginary parts [50]. Fig.5 depicts the optical function of CaSiO3 monoclinic estimated from photon energy up to 44 eV for [010] polarized vector. When an electric field is applied, a material is polarized because of the electric dipoles that created in that material, this represented by the real part. Instead, the imaginary part is an indication of absorption in a material. The transparency of a material can be indicated by the zero value of imaginary part. It is observed that the imaginary part become zero at the range of 16.1-23.3 eV and above 28.8 eV, indicating that CaSiO3 monoclinic becomes transparent at that range. The imaginary part in CaSiO3 monoclinic has four bands located at 5.3, 6.02, 7 and 7.9 eV, due to the transition from occupied O-2p to the unoccupied Ca-3d. The static dielectric constant ε1(0) which depends on the band gap can be calculated from the zero frequency of the real part. A wide band gap represents a smaller static dielectric constant value [35,49]. The estimated value of the static dielectric constant for CaSiO3 is 1.47 at low energy and augmented gradually to make its highest value of 2.16 at 5.77 eV. The absorption coefficient starts at 4.02 eV and gradually increased, which accords well with the estimated value of the band gap. Four absorption bands can be seen from Fig. 5: one broad band starting at 4.02 eV and ending near 12.5 eV, two small bands between 13.5 and 25.2 eV and a narrow band at 27 eV. It is noticeable that the absorption coefficient is nearly linked to the imaginary part of the dielectric function. The estimated value of refractive index for monoclinic wollastonite increase with energy increment in the 0-7.5 eV range and then decrease abruptly for energy level higher than 7.5 eV. The upper limit value of the refractive index is 1.5 at 7.6 eV (ultraviolet region). The estimated results for the static dielectric constant and refractive index satisfy the equation n(0)= (ε1(0))1/2 [47] at low frequency. The energy loss function is specified by the bulk plasma frequency ωp which takes place at ε2 < 0 and ε1= 0. In the energy-loss spectrum, it can be determined that the effective ωp is equal to 9.5 eV, which is corresponding to the rapid drop of reflectivity. Due to the absorption of the electromagnetic wave, the electric conductivity of materials may augment (optoelectronic phenomenon). Since the CaSiO3 monoclinic has a broad band gap, the photoconductivity starts at 4.3 eV as shown in Fig. 5. The electrical conductivity of the monoclinic phase becomes higher at 8.5 eV. Above 12 eV, photoconductivity is diminished. This confirms the insulating characteristic of CaSiO3 monoclinic.

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ACCEPTED MANUSCRIPT 4.Conclusion

Supplementary material

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In summary, ab initio analysis using LDA approximation to understand in details the structural, mechanical, optical and electronic behavior of CaSiO3 monoclinic. The small deviation of the calculated lattice parameters indicating the reliability of the chosen theoretical approach. The bulk modulus, shear modulus, Young's modulus, elastic anisotropy, Poisson's ratio, compressibility and Debye temperature are determined based on the calculation elastic constant. Ab initio analysis shows that the compound is mechanically stable and possess large anisotropy along b-axis with brittle behavior. The electronic structure of CaSiO3 indicated that the compound is an insulator with indirect band gap of 5.02 eV. The calculated value of the static dielectric constant for CaSiO3 is 1.47 at low energy and increased gradually to reach its highest value of 2.16 at 5.77 eV. The maximum value of the refractive index is 1.5 at 7.6 eV. The results are in good agreement with experimental and theoretical available data. Based on the predicted values of the bulk modulus, band gap structure and some optical properties, the studied monoclinic phase can be utilized as a promising coating material for electronic, bioelectronic applications and to develop true solar-blind photodetectors.

See supplementary material which represent the criteria for mechanical stability of low symmetry monoclinic structure.

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Acknowledgments

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We acknowledge the continuous support and encouragement of the college of materials engineering/University of Babylon.

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ACCEPTED MANUSCRIPT Figure Captions

Fig. 1: Crystal structure of wollastonite monoclinic: (a) optimized unit cell and (b) Polyhedral model of the crystal structure of wollastonite-2M along a-axis [2]

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Fig.2: The electronic band structure and density of state (DOS) for CaSiO3 monoclinic Fig. 3: Band structure near the main band gap for monoclinic CaSiO3

Fig. 4: electronic partial density of states (PDOS) of monoclinic CaSiO3

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Fig. 5: The optical functions (a) reflectivity, (b) absorption, (c) refractive index, (d) dielectric function, (e) conductivity and (f) loss function of CaSiO3 monoclinic for polarization vector [010] using 0.15 smearing

ACCEPTED MANUSCRIPT Table 1 Comparison between experimental [22] and theoretical calculated parameters for the CaSiO3 monoclinic unit cell Experimental data 15.426 7.320 7.066 95.404 795.434

Calculated (this work) 15.252 7.224 6.978 95.971 764.834

Relative deviation (%) 1.1 1.3 1.2 +0.005 3.7

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Parameter a b c β V

Table 2 Calculated elastic constant Cij (in GPa) of CaSiO3 monoclinic C11

C22

C33

C44

C55

C66

C12

C13

C15

C23

C25

C35

C46

CaSiO3

164.02

195.92

191.61

53.94

34.68

68.41

65.26

61.74

15.4

38.38

-4.33

40.32

2.65

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Phase

Phase

BV

BR

CaSiO3

98.04

87.17

Exp. [31, 32]

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Table 3 summarize the bulk modulus B, shear modulus G, young's modulus E, and Poisson’s ratio υ (all in GPa, except for the non-dimensional Poisson's ratio). BH

GV

GR

GH

E

υ

92.6

57.15

45.92

51.53

130.4

0.26

102.1

‫ـــــ‬

‫ـــــ‬

50.3

129.5

0.23

TE D

Table 4 summarize the axial components of young's modulus Eii (GPa) and non-dimensional Poisson’s ratio υij υij Ei Ey

127.89

162.06

Ez

128.86

υ xy

0.29

υ yx

υ xz

0.29 0.21

υ yz

υ zx

υ zy

0.37

0.18

0.14

EP

Ex

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Table 5 Universal anisotropy factor (AU), The shear anisotropic factors (A1, A2, and A3), percent anisotropy factors of bulk (AB) and shear (AG) moduli. AU

A1

A2

A3

AB (%)

AG (%)

1.34

0.92

0.44

1.19

5.5

10.8

Table 6 Theb calculated density ρ, transverse sound velocity υt, longitudinal sound velocity υl, sound velocity υm and Debye temperature ӨD for monoclinic CaSiO3. ρ (Kg/m3)

υt (m/s)

υl (m/s)

υm (m/s)

ӨD (k)

3020

4130.72

7308.4

4593.84

133.97

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Highlights

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Poisson’s ratio and Cauchy pressure indicating a dominant ionic nature of the brittle CaSiO3 monoclinic. The highest degree of anisotropy is along the b-axis this related to the high bonding strength between atoms along that axis. Wide Indirect band gap indicating insulating characteristic of the studied phase

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