Bi3TeBO9: electronic structure, optical properties

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Bi3TeBO9: electronic structure, optical properties and photoinduced phenomena

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Abstract

Footnote Information

1 July 2017 4 September 2017

Improving of the nonlinear optical properties, mainly photoinduced enhancement of effective second harmonic generation was observed in Bi3TeBO9 (BTBO) crystals under irradiation of two external UV laser beams. The effect is caused by an interaction of two coherent photoinducing beams of nitrogen laser with wavelength 371 nm near the Bi3TeBO9 fundamental edge, resulting in formation of additional anisotropy. To explain the observed phenomenon and establish the general features of the electronic structure, the band-structure calculations, as well as electronic density of states, elastic properties and principal optical functions, were simulated by means of the density functional theory approach. The comparison of the nonlinear optical properties with the conventional α-BIBO crystal shows that BTBO is a promising material for the fabrication of UV laser optical triggers.

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J Mater Sci 1

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A. Majchrowski1, M. Chrunik1, M. Rudysh2,3, M. Piasecki2,* and I. V. Kityk5

Institute of Applied Physics, Military University of Technology, 2 Kaliskiego Str., 00-908 Warsaw, Poland Institute of Physics, Jan Długosz University, 13/15 Armii Krajowej Str., 42-201 Czestochowa, Poland 3 Faculty of Physics, Ivan Franko National University of Lviv, 8 Kyrylo and Mefodiy Str., Lviv 79005, Ukraine 4 Wireless and Photonic Networks Research Centre, Faculty of Engineering, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia 5 Institute of Optoelectronics and Measuring System, Faculty of Electrical Engineering, Czestochowa University of Technology, 17 Armii Krajowej Str., 42-200 Czestochowa, Poland 2

A1

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Accepted: 4 September 2017

Improving of the nonlinear optical properties, mainly photoinduced enhancement of effective second harmonic generation was observed in Bi3TeBO9 (BTBO) crystals under irradiation of two external UV laser beams. The effect is caused by an interaction of two coherent photoinducing beams of nitrogen laser with wavelength 371 nm near the Bi3TeBO9 fundamental edge, resulting in formation of additional anisotropy. To explain the observed phenomenon and establish the general features of the electronic structure, the band-structure calculations, as well as electronic density of states, elastic properties and principal optical functions, were simulated by means of the density functional theory approach. The comparison of the nonlinear optical properties with the conventional aBIBO crystal shows that BTBO is a promising material for the fabrication of UV AQ1 laser optical triggers.

The Author(s) 2017. This

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ABSTRACT

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Received: 1 July 2017

The search for novel inorganic materials for nonlinear optics is an important direction of modern optoelectronics [1–4]. Representative applications of such materials are: second harmonic generation (SHG), optical parametric oscillation (OPO), optical parametric amplification (OPA) and self-frequency doubling (SFD). The materials should work in possibly

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Bi3TeBO9: electronic structure, optical properties and photoinduced phenomena

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COMPUTATION Computation

broadest spectral range, from near infrared (NIR) to ultraviolet (UV). Among such materials particular role belongs to borate crystals, i.e., b-BaB2O4, LiB3O5, KBe2BO3F2, CsLiB6O10, La2CaB10O19 and a-BiB3O6. In general, borates are mechanically and chemically stable, possess wide transparency range, have good optical quality and are characterized with high nonlinear optical coefficients [5]. For such materials, the main efforts are devoted to manipulation by the

Address correspondence to E-mail: [email protected]

DOI 10.1007/s10853-017-1554-z Journal : 10853 - Large 10853 Article No. :

1554

MS Code : JMSC-D-17-03998

Dispatch : 11-9-2017

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(111)

(402)

(500) (232) (501) (240) (150) (241) (502)

(123)

(203)

(132)

(113)

Z=2

(231)

(302)

a = b = 8.7546(3) [Ǻ] c = 5.8974(3) [Ǻ] V = 391.439 [Ǻ3] α = β = 90° γ = 120°

(131)

(220) (130)

(122)

(300) (121) (112) (202)

(201) (110) (101)

(100)

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BTBO powders were synthesized by means of conventional solid-state reaction route, similarly to the procedure described by Daub et al. [6]. The molar ratio of used precursor compounds: Bi2O3 (SIAL, 99.95%), TeO2 (MERCK, 99.99%) and B2O3 (SIAL, 99.999%), was 3:2:1.1, respectively. The 5% excess of boron oxide was used to prevent non-stoichiometry due to the presence of water and possible evaporation of B2O3 at elevated temperatures. The precursor compounds were mixed and thoroughly ground in an agate mortar till the homogeneous mixture was obtained. It was initially preheated at 450 C for 12 h to evaporate the residuals of adsorbed water. In the following steps, the mixture was ground and calcined three times at 690 C for 12 h each time. After the final grounding pure, white powders of BTBO were obtained. Their phase uniformity was confirmed using the XRD analysis. The diffraction pattern of

Bi3TeBO9, hexagonal S.G. P63 (No. 173)

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Powder synthesis and XRD phase analysis

Calculations of the electronic, optical and elastic properties of BTBO crystal were performed within

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Experimental

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Methods of calculation

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synthesized BTBO powder was collected using the BRUKER D8 Discover, equipped with standard CuKa ˚ , kKa2 = 1.54439 A ˚ , Sieradiator (kKa1 = 1.54056 A mens KFL CU 2 K, 40 kV voltage and 40 mA current in operating mode). The radiator was equipped with Go¨bel FGM2 mirror. The Bragg–Brentano diffraction geometry was applied. The diffraction angle 2hB range was set to 10–70 with a step of 0.015 and acquisition time 2 s per step. The measurements were taken at 25 C in the temperature-stabilized Anton Paar HTK 1200N chamber. For the data processing, the DIFFRAC.SUITE EVA application was used. The kKa2 signal component was deconvoluted and removed, the background was subtracted and the data were smoothed using fast Fourier transform (FFT). The phase analysis was performed with support of Crystallography Open Database (COD). For crystallographic calculations, the MAUD ver. 2.32 program was used, allowing to perform the Rietveld refinement and calculate the precise unit cell parameters. The reference CIF file used for this analysis was received from the supplementary data given in Ref. [7]. The obtained BTBO powder diffraction pattern is shown in Fig. 1.

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cationic subsystem in connection with principal anionic borate clusters like [BO3], [BO4], [B3O6], [B3O7], [B2O7] or [B2O5], in order to achieve the highest second-order susceptibilities, which are determined by microscopic hyperpolarizabilities. Recently, Bi3TeBO9 (BTBO) crystal, having very large second-order susceptibilities, was discovered [6, 7]. The preliminary data indicate that its secondorder susceptibilities are, respectively, higher than in the case of the exceptional a-BiB3O6 (a-BIBO) compound [7]. Moreover, following the general considerations one can expect that the titled compound may be promising medium for the laser-operated nonlinear optical effects. For this reason, we will explore the changes of its nonlinear optical properties after illumination near the absorption edge. Additionally, the elastic properties of this material should play here crucial role. In this case, we will perform the bandstructure calculations. In the present work, we report the synthesis of BTBO powders, determine crystal structure and finally show almost 10% relative enhancement of the existing second-order susceptibilities under additional two-beam coherent UV laser light treatment with wavelength near the absorption edge of BTBO.

Int. [a.u.]

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J Mater Sci

Bi3TeBO9 (COD / No. 99-900-0001)

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30

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2θB [°]

Figure 1 Experimental powder diffraction pattern (top, purple plot) for synthesized BTBO and calculated theoretical Bragg’s positions (bottom, red markers) based on COD database CIF file. Presented precise unit cell parameters were determined using Rietveld refinement.


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Structural properties

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The crystal structure of BTBO crystal is presented in Fig. 3. BTBO belongs to hexagonal symmetry (space group P63, no. 173) with Z = 2. The experimental and theoretically calculated principal band-structure parameters using DFT–LDA and DFT–GGA exchange–correlation functionals together with NCPP after the geometry optimization of lattice constants are presented in Table 1. Following Table 1, the calculated lattice constants are in good agreement

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the framework of density functional theory (DFT) implemented in CASTEP (Cambridge Serial Total Energy Package) program—package of Biovia Materials Studio 8.0 [8]. The initial BTBO crystal structure was taken from Ref. [7]. We applied plane-wave basis set. Eigen function and eigenvalues were estimated from self-consistent solving of the one-electron Kohn–Sham equation. Exchange and correlation effects were taken into account by using local-density approximation (LDA) with Ceperley–Alder–Perdew– Zunger parameterization [9, 10] and generalized gradient approximation (GGA) together with Perdew–Burke–Ernzerhof parameterization [11]. The cutoff energy of plane-wave basis was set to be equal to Ecut = 830 eV. The Monkhorst–Pack k-points grid sampling was set at 2 9 2 9 2 points for the Brillouin zone used for electronic charge density calculations and geometry optimizations, respectively. Both the cell parameters and atomic positions were optimized (relaxed) using Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm [12] until the force on each ion was ˚ . The resulting structures smaller than 0.01 eV/A were then used as input to the electronic structures and related properties calculations. The core electron orbitals were calculated by normconserving pseudopotential (NCPP). The following electron configurations were used: B—2s2 2p1, O—2s2 2p4, Te—5s2 5p4, Bi—5d10 6s2 6p3. The convergence parameters were as follows: total energy tolerance 5 9 10-6 eV/atom, maximum force tolerance ˚, maximum stress component 1 9 10-2 eV/A ˚. 0.02 GPa and maximum displacement 5.0 9 10-4 A The band structure was calculated at the following points and along directions of high symmetry of BZ: U ? A? H ? K ?U ? M ? L ? H (see Fig. 2).

Figure 2 Brillouin zone of BTBO crystal with principal symmetry points.

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Figure 3 Visualization of BTBO unit cell crystal structure.

with experimental ones. Lattice constants calculated using the LDA functional are a bit smaller than experimental ones, while in the case of GGA functional, parameters are a bit higher. It can be explained by the renormalization of principal electronic


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Table 1 Experimental and theoretical lattice constants calculated using Rietveld refinement, DFT–LDA and DFT–GGA exchange– correlation functionals together with NCPP

Eg [eV]

Xia et al. [7] LDA GGA

2.70/3.23 (exp./calc.) 2.96 3.21

1.514 1.501 1.485 1.484

352.70 388.95 391.439 391.16

parameters within the LDA functional, which leads to underestimation of basic structural parameters.

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Electronic properties

184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199

For calculations of electronic structure and other properties, the optimized crystal structure was used. Calculated band structure of BTBO crystal using LDA and GGA functionals for exchange–correlation effects description is shown in Fig. 4. Band structure is plotted at following BZ line directions: U ? A ? H ? K ? U ? M ? L ? H. One can see that the band structure has a large dispersion. The lowest dispersion is observed for A ? H and L ? H BZ directions. Valence band maxima (VBM) and conduction band minima (CBM) are in the segment between the U and A points (Fig. 4) and are shifted in relation to each other. Thus, band gap of the titled crystal is of the indirect type. The smallest band gap value is equal to 2.96 eV for LDA and 3.21 eV for GGA, respectively (Table 2), while as previously

reported by Xia et al. [7] experimental and calculated values were 2.70 and 3.23 eV, respectively. So, using both LDA and GGA together with NCPP one can perfectly describe the model of the crystal since they give good agreement with the experimental values of the band gap and lattice constants. Density of states (DOS) and partial density of states (PDOS) charts give a quick qualitative picture of the electronic structure for a crystal. The calculated total and partial density of states for BTBO crystal are depicted in Fig. 5. In the spectral energy range within -15 to 10 eV, one can see two distinctive groups of peaks corresponding to principal electronic states of BTBO crystal. The first group corresponds to the energy states within the range of -10.6 to 0 eV. The 6s and 6p electrons of bismuth form bands in the range from -10.6 to -7 eV and from -6.5 to 0 eV. Also, a minor peak of 6s electrons is observed near 0 eV. Tellurium electrons form several peaks for 5s electrons that are situated nearby -10 eV and at -4 eV, while the 5p electrons form peak at -8 and -1 eV, respectively. In the case of B, the 2s peak at -6 eV is spectrally shifted toward relatively higher energies compared GGA

LDA

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Energy [eV]

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Energy [eV]

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Figure 4 Band energy diagrams for BTBO crystal calculated using LDA and GGA exchange–correlation functionals.

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5.621 5.842 5.8974 (3) 5.898

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˚ 3] V [A

a/c

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8.512 8.768 8.7546 (3) 8.751

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Table 2 Band energy gap value of BTBO crystal calculated using DFT–LDA and DFT–GGA functionals, compared to referred ones

0

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J Mater Sci

0 100

B

2p 2s

O

-10

-5

0

5

10

Energy, eV

Figure 5 Total and partial density of states of BTBO crystal calculated using LDA and GGA exchange–correlation functionals.

264

The optical properties of solids are described by their 265 dielectric function e = e1 ? ie2, which real part e1 266 corresponds to the refractive indices of the material, 267 while its imaginary part e2 describes the absorption 268 coefficients in material which are directly related to 269 the absorption spectra. The imaginary part of com- AQ2270 plex dielectric function e2, which corresponds to the 271 absorption, can be obtained from inter-band transi- 272 tion by numerical integration in k-space of elements 273 of dipole matrix operator between the filled VB states 274 and empty CB levels (Eq. 1): 275 2 X 2pe wc ur wv 2 d Ec Ev E ; e2 ðx Þ ¼ ð1Þ k k k k Xe0 k;v;c

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to the peak formed by tellurium. Wide band originating from -6.3 to -1 eV is formed by 2p B electrons. The electrons of oxygen atoms, originating from bands that are situated in the range from -10.3 to 0 eV, correspond to 2p subshell. As shown in Fig. 5, the top of the valence band originates from oxygen 2p states, bismuth 6s and tellurium 5p states. The bottom of the conduction band is formed by p states of oxygen and s states of tellurium. It can be assumed that the optical transitions in absorption spectra are likely formed by O 2p to Bi 7s or 7p states. Additional important information can be obtained from atomic charge bond population. In contrast to plane-wave basis, a linear combination of atomic orbitals (LCAO) basis set provides a natural way of specific quantities such as atomic charge, bond population and charge transfer. Population analysis in CASTEP is performed using a projection of the PW states onto a localized basis using a technique described by Sanchez-Portal et al. [13]. Population analysis of the resulting projected states is then performed using the Mulliken formalism [14]. This technique is widely used for the analysis of electronic structure calculations performed within a framework of LCAO basis sets. Calculated atomic populations in units of the proton charge for BTBO crystal are presented in Table 3. One can see that the obtained charges calculated using LDA functional are close to the calculated using GGA. The shortest bond lengths between constituent atoms in BTBO crystal calculated using LDA and GGA functionals together with overlap populations

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Optical properties

2p

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5p

256 257 258 259 260 261 262 263

O

0 20

5s

5s 5p

7s7p

6s

are collected in Table 4. As can be seen, the calculated bond lengths and population values are in good agreement between one to another. All bonds of the titled crystal are of covalent type. It is easy to see that B–O bonds possess the highest degree of covalency, while Bi–O—the lowest one. From these results, we can conclude that BTBO crystal possesses covalent type of chemical bonding.

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s states p states 6p

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PDOS [e/eV]

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Bi

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100 90 10 5 0 6


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where E—energy of probing optical beam; u—incident photon polarization vector; wck and wvk —wave functions of the conduction and valence bands in kspace, respectively; X—unit cell volume; e—electron charge; e0 —dielectric permittivity of vacuum; r—operator of electron position; and x—frequency of incident radiation. Using Kramers–Kronig relation (Eq. 2) [15] from the imaginary part of dielectric function, its real part can be estimated as follows: 2 e1 ðxÞ ¼ 1 þ p

Z1

e2 ðx0 Þx0 dx0 x02 x2

277 278 279 280 281 282 283 284 285 286

ð2Þ

0

Figure 6 depicts the dispersion of real e1 and imaginary e2 parts of dielectric functions calculated using GGA functional. The crystals of hexagonal symmetry have two principal directions that correspond to the direction along polar z-axis and direction perpendicular to z. In Fig. 6, we present the calculated dielectric function, which corresponds to photon polarization E || z and E ? z. The dielectric function shows insignificant anisotropy for BTBO crystal. The real part of dielectric function in the


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s

p

d

Total

Charge [e]

B O Te Bi

0.52/0.50 1.89/1.88 1.23/1.14 1.91/1.94

1.65/1.71 5.12/5.14 2.06/2.04 1.38/1.40

0.00/0.00 0.00/0.00 0.00/0.00 10.00/10.00

2.17/2.20 7.02/7.01 3.28/3.19 13.28/13.34

0.83/0.80 -1.02/-1.01 2.72/2.81 1.72/1.66

Bond population

˚] Length [A

B-O Te–O Bi-O

0.79/0.80 0.43/0.44 0.19/0.16

1.37743/1.36047 1.91535/1.89254 2.13786/2.16634

Re(ε ) E z Im(ε ) E z Re(ε ) E||z Im(ε ) E||z

ð3Þ

where E(V0, 0) is the energy of the unstrained system with equilibrium volume V0, s0 is an element in the stress tensor and ni is a factor to take care of Voigt index. For the hexagonal crystal, its elastic properties can be described by asymmetric 6 9 6 matrix of elastic coefficients. In case of hexagonal symmetry, we get the following relation between elastic constants: C11 = C22; C13 = C23; C44 = C55; C66 = 1/2(C11-C12); it is known that for practical application it is important to obtain a stable crystal structure. Knowing of the elastic constants and Young’s modulus is important for technological aims, in the manufacturing process and crystal preparation. For crystal structure stability of hexagonal symmetry, the obtained elastic constants should satisfy the requirements of mechanical stability criteria [17], which are: C33 [ 0; C44 [ 0; C12 [ 0; C11 [ |C12|; (C11 ? 2C12)C33 [ 2C213). Following Table 5, the calculated elastic constants completely satisfy the mechanical stability criteria. Unfortunately, according to already published data concerning the BTBO crystal, the experimental results of its mechanical properties are still unknown. The values of C11 and C33 differ one from another, indicating the anisotropy of elastic properties. The universal anisotropy index for BTBO crystal is equal to AU = 0.412/0.254 from the calculation using GGA/

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Re(ε), Im(ε)

6

! 1 si ni di þ Cij di ni dj nj ; 2

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EðV; dÞ ¼ EðV0 ; 0Þ þ V0

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-2 5

10

15

Energy [eV]

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Table 4 Inter-atomic lengths and overlap populations of the shortest atomic bonds in BTBO crystal (GGA/LDA functionals)

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Table 3 Atomic populations (in units of the proton charge) of the constituent atoms of BTBO crystal (GGA/LDA functionals)

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Figure 6 Calculated real Re(e) and imaginary Im(e) parts of the dielectric functions dispersion for the BTBO crystal using GGA functional.

region from 7.5 to 18 eV has inversion of sign that can correspond to metallic reflection.

300

Elastic properties

301 302 303 304 305 306 307 308 309

In terms of crystal anisotropy studies, elastic properties of the crystal can be of special interest. The optimized crystal structure of investigated compound as input for the elastic constant simulations was used. The elastic constants are defined by means of the Taylor expansion of the total system energy E(V, d), with respect to a small strain d of the lattice primitive cell volume V. The energy of a strained system is expressed as follows [16]:

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Table 5 Elastic constants Cij and bulk modulus B (in GPa) of the BTBO crystal Source

B

C11

C12

C13

C33

C44

LDA GGA

76.717 48.238

139.58 108.86

28.80 15.34

58.05 30.27

123.28 71.51

42.84 29.04


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ð5Þ

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Effective SHG measurements Following the performed band-structure calculations and the elastic features, one can expect that the titled crystal may be operated by external laser light near the fundamental band edge. For this reason, we used two coherent nitrogen 371 nm 9 ns laser pulses with frequency repetition about 10 Hz in order to study the possible changes of the effective second-order susceptibilities. As a probing beam, an Er:glass 20 ns laser (at k = 1540 nm) was used. The detection was performed using interferometric filter at 770 nm and the photomultiplier connected to the oscilloscope. In order to monitor the possible photoluminescence near 371 nm laser treatment, the additional control of the spectral lines and their time dependences were performed in the range of 330–905 nm by spectrometer. There was no any wider spectral photoluminescence in this spectral range. Additionally, the time shift between the excitation and the induced nonlinear signals did not exceed few nanoseconds, while for the fluorescence it should be an order higher. The use of two coherent beams interacting at different angles should stimulate the occurrence of additional birefringence [20], which also changes the nonlinear optical susceptibilities. Moreover, during the photoinduced changes in the common borate crystals, the contributions of anharmonic phonons begin to play an additional role [21, 22]. They may be responsible for the different degrees of the photoinduced second-order susceptibility changes versus the cationic content, as shown in Fig. 9. It is crucial that, contrary to the well-studied aBIBO crystal, for the titled BTBO there exists a huge opportunity to operate the output SHG using external photoinducing UV coherent nanosecond laser pulses. The arrow indicates an excitation of the prevailing number of anharmonic phonons by the nitrogen pulsed laser beams. Because they are anharmonic, their symmetry is the same as for the second-order optical susceptibility. As a consequence, it is manifested in Fig. 9 and the optical functions are changed significantly. The effect disappears immediately after the switching off the photoinducing beam treatment.

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where B is the bulk modulus and E is the value of Young’s modulus, in the direction determined by l1 ; l2 and l3 —the direction cosines of [uvw] directions and Sij are the elastic compliance constants, which are inverse to the matrix of elastic constants Cij calculated for BTBO crystal. The surface of directional dependence of bulk modulus B and Young’s modulus E of BTBO crystal, plotted in spherical coordinates, is depicted in Fig. 7. The surfaces of directional dependence of bulk and Young’s modulus (Fig. 7) show that the BTBO crystal possesses low anisotropy. Both surfaces have the similar shape. In order to receive additional information and a better understanding of bulk modulus and Young’s modulus relation along different directions, the projections of the moduli at ab and ac crystal plane are plotted (see Fig. 8).

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360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376

ð4Þ

377 378 379 380 381

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1 ¼ ðS11 þ S12 þ S13 Þ ðS11 þ S12 S13 S33 Þl23 ; B 1 ¼ 1 l23 S11 þ l43 S33 þ l23 1 l23 ð2S13 þ S44 Þ; E

It is easy to see that at ab plane both bulk modulus and Young’s modulus are of a spherical shape, which means in this plane the BTBO crystal is almost isotropic. In the case of ac plane, some anisotropy of mechanical properties is shown.

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LDA functionals. Calculated elastic compliance matrix Sij for BTBO crystal is presented in Table 6. The Young’s modulus components Ex , Ey and Ez can be estimated from elastic compliance Sij using following relations: Ex ¼ S111 , Ey ¼ S221 , Ez ¼ S331 . The axial compressibilities ka, kb and kc for hexagonal BTBO crystal are also calculated in the following way [18]: ka ¼ S11 þ S12 þ S13 , kb ¼ S12 þ S22 þ S23 , kc ¼ S13 þ S23 þ S33 . Both Young’s modulus E and compressibility k calculated using GGA/LDA functionals are collected in Table 7. Additional useful method to show mechanical anisotropy can be given by visualization of a threedimensional dependence of the bulk modulus and Young’s modulus as a function of direction. For hexagonal crystal class, the directional dependence of bulk modulus and Young’s modulus is given by the following relation [19]:

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339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356

Table 6 Calculated elastic compliance matrix (Sij) for hexagonal BTBO crystal (in GPa-1)

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J Mater Sci

Source

S11

S12

S13

S33

S44

LDA GGA

0.00891 0.01042

-0.00012 -0.00027

-0.00414 -0.00429

0.01201 0.01762

0.02334 0.03442


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J Mater Sci

Table 7 Calculated averaged compressibility (bH in GPa-1), Young’s modulus components (Ex, Ey and Ez in GPa), and axial compressibility (ka, kb and kc in GPa) for hexagonal BTBO crystal bH

Ex

Ey

Ez

ka

kb

kc

LDA GGA

0.013 0.020

112.223 95.985

112.223 95.985

83.245 56.762

0.00465 0.00586

0.00465 0.00586

0.00373 0.00904

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Source

90

(a) 120

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ab ac

30

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Figure 7 Surface of directional dependence of bulk modulus B (a) and Young’s modulus E (b) of BTBO crystal plotted in spherical coordinates.

210

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240

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180

0

330

90

(b) 120

150

30

180

0

210

300

330

240

300

270

270

Figure 8 Projection of bulk modulus B (a) and Young’s modulus E (b) of BTBO crystal on ab and ac planes.


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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licen ses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

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Figure 9 Dependence of the effective nonlinear coefficient of BTBO (red plot) at fundamental wavelength 1540 nm versus the power density of the 371-nm pulsed 9 ns laser. The latter is incident under the optimal angle between photoinducing beams equal to about 20 degrees. The arrow corresponds to the critical photoinducing power density at which it gets maximal changes of the second-order susceptibility. The measurement was taken with comparison to a-BIBO (black plot).

Conclusions

426 427 428 429 430 431 432 433 434 435 436 437 438 439 440

An opportunity to influence the second-order susceptibility of BTBO powder using two coherent beams treatment of 371 nm laser near the absorption edge was established. The performed band-structure calculations and the related elastic properties show that BTBO possesses relatively improved elastic features with respect to other borates. This may favor laser operation with the output second-order susceptibilities due to changes in microscopical hyperpolarizability. This phenomenon may be a consequence of both the elastooptical photoinduced anisotropy and possible contribution of the phonon anharmonicities. The comparison with the conventional a-BIBO crystal shows that BTBO is a promising material for the fabrication of UV laser optical triggers.

441

Acknowledgements

442 443 444 445

Calculations were carried out using resources provided by Wroclaw Centre for Networking and Supercomputing (http://wcss.pl), Grant Nos. WCSS#10106944 and WCSS#10106945.

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Kogut Y, Khyzhun OY, Parasyuk OV, Reshak AH, Laksh455 minarayana G, Kityk IV, Piasecki M (2012) Electronic 456 spectral parameters and IR nonlinear optical features of 457 novel Ag0.5Pb1.75GeS4 crystal. J Cryst Growth 354:142–146 458 [2] Piasecki M, Lakshminarayana G, Fedorchuk AO, Kushnir 459 OS, Franiv VA, Franiv AV, Myronchuk G, Plucinski KJ 460 (2013) Temperature operated infrared nonlinear optical 461 materials based on Tl4HgI6. J Mater Sci Mater Electron 462 24:1187–1193 463 [3] Chung I, Kanatzidis MG (2014) Metal chalcogenides: a rich 464 source of nonlinear optical materials. Chem Mater 465 26:849–869 466 [4] Ghotbi M, Sun Z, Majchrowski A, Michalski E, Kityk IV 467 (2006) Efficient third harmonic generation of microjoule 468 picosecond pulses at 355 nm in BiB3O6. Appl Phys Lett 469 89:173124 470 [5] Chen C, Sasaki T, Li R, Wu Y, Lin Z, Mori Y, Hu Z, Wang J, Aka AQ3471 G, Yoshimura M, Kaneda Y (2012) Nonlinear optical borate 472 crystals: principals and applications. Wiley-VCH, New York 473 [6] Daub M, Krummer M, Hoffmann A, Bayarjargal L, Hille474 brecht H (2017) Synthesis, crystal structure, and properties 475 of Bi3TeBO9 or Bi3(TeO6)(BO3): a non-centrosymmetric 476 borate–tellurate (VI) of bismuth. Chem Eur J 23:1331–1337 477 [7] Xia M, Jiang X, Lin Z, Li R (2016) All-three-in-one: a new 478 bismuth–tellurium–borate Bi3TeBO9 exhibiting strong sec479 ond harmonic generation response. J Am Chem Soc 480 138:14190–14193 481 [8] Clark SJ, Segall MD, Pickard CJ, Hasnip PJ, Probert MJ, 482 Refson K, Payne MC (2005) First principles methods using 483 CASTEP. Z Kristallogr 220:567–570 484 [9] Ceperley DM, Alder BJ (1980) Ground state of the electron 485 gas by a stochastic method. Phys Rev Lett 45:566–569 486 [10] Perdew JP, Zunger A (1981) Self-interaction correction to 487 density-functional approximations for many-electron sys488 tems. Phys Rev B 23:5048–5079 489 [11] Perdew JP, Burke K, Ernzerhof M (1996) Generalized gra490 dient approximation made simple. Phys Rev Lett 491 77:3865–3868 492 [1]

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