Boron Influence on Defect Structure and Properties of Lithium Niobate

Review Boron Inﬂuence on Defect Structure and Properties of Lithium Niobate Crystals

Nikolay V. Sidorov *, Natalia A. Teplyakova, Olga V. Makarova, Mikhail N. Palatnikov, Roman A. Titov, Diana V. Manukovskaya and Irina V. Birukova

Tananaev Institute of Chemistry–Subdivision of the Federal Research Centre, Kola Science Centre of the Russian Academy of Sciences, 26 a, Akademgorodok, 184209 Apatity, Murmansk region, Russia; [email protected] (N.A.T.); [email protected] (O.V.M.); [email protected] (M.N.P.); [email protected] (R.A.T.); [email protected] (D.V.M.); [email protected] (I.V.B.) * Correspondence: [email protected]; Tel.: +7-81-5557-9508

Abstract: Defect structure of nominally pure lithium niobate crystals grown from a boron doped charge have been studied by Raman and optical spectroscopy, laser conoscopy, and photoinduced light scattering. An inﬂuence of boron dopant on optical uniformity, photoelectrical ﬁelds values, and

band gap have been also studied by these methods in LiNbO3 crystals. Despite a high concentration of boron in the charge (up to 2 mol%), content in the crystal does not exceed 10−4 wt%. We have calculated that boron incorporates only into tetrahedral voids of crystal structure as a part of groups 3− [BO3] , which changes O–O bonds lengths in O6 octahedra. At this oxygen–metal clusters MeO6 (Me: Li, Nb) change their polarizability. The clusters determine optically nonlinear and ferroelectric properties of a crystal. Chemical interactions in the system Li2O–Nb2O5–B2O3 have been considered. Boron, being an active element, structures lithium niobate melt, which significantly influences defect Citation: Sidorov, N.V.; Teplyakova, N.A.; Makarova, O.V.; Palatnikov, structure and physical properties of a crystal grown from such a melt. At the same time, amount of M.N.; Titov, R.A.; Manukovskaya, defects NbLi and concentration of OH groups in LiNbO3:B is close to that in stoichiometric crystals; D.V.; Birukova, I.V. Boron Influence photorefractive effect, optical, and compositional uniformity on the contrary is higher. on Defect Structure and Properties of Lithium Niobate Crystals. Crystals Keywords: lithium niobate; doping; melt; Raman spectroscopy; photoinduced light scattering; 2021, 11, 458. https://doi.org/ photoelectric fields; IR-spectroscopy; optical spectroscopy; laser conoscopy 10.3390/cryst11050458

Academic Editor: Alexander S. Krylov 1. Introduction

Lithium niobate (LN, LiNbO3) attracts attention due to its possible applications in in- Received: 26 March 2021 tegral and nonlinear optics, pure optics (generation of optical harmonics, lasing parametric Accepted: 19 April 2021 Published: 21 April 2021 generation, electro-optics, optical amplification, and conversion of optical radiation), acous- toelectronics (bandpass filters and SAW delay lines), quantum electronics, and solid state physics [1–4]. The equipment associated with modern optoelectronic and telecommunica- Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in tion technologies often includes LN crystals. Such applications claim LN crystals with high published maps and institutional affil- optical uniformity and optical damage resistance. Thus, a study of their defect structure iations. and optical characteristics in dependence on obtaining conditions are highly relevant. A LiNbO3 crystal is a non-stoichiometric oxygen octahedral ferroelectric with high −5 2 Curie temperature (1420 K), spontaneous polarization (PS = 5 × 10 C/cm ) and a wide homogeneity region on the phase diagram (44.5–50.5 mol % Li2O at 1460 K). LN should be considered as a solid solution LiNbO :Nb [5,6]. Doping by a wide spectrum of metal Copyright: © 2021 by the authors. 3 elements is possible due to an octahedral coordination of metal ions in the LN structure. At Licensee MDPI, Basel, Switzerland. + 5+ This article is an open access article this a significant however preserving symmetry distortion of MeO6 (Me: Li , Nb , dopant) distributed under the terms and octahedra can occur [1,2,7]. All these factors provide a possibility to control physical conditions of the Creative Commons characteristics of the material. Being a phase of a variable composition, LN crystal has a Attribution (CC BY) license (https:// highly developed defect structure. Optical damage (photorefractive effect) is determined creativecommons.org/licenses/by/ by defects with localized electrons; such defects form photoelectric fields. LN is in general 4.0/).

Crystals 2021, 11, 458. https://doi.org/10.3390/cryst11050458 https://www.mdpi.com/journal/crystals Crystals 2021, 11, 458 2 of 37

characterized by high values of photoelectric fields and photorefraction effect. The latter can be varied in a very wide range [1,2,8]. Optical damage resistance can be increased in congruent LN (CLN, R = Li/Nb = 0.946) crystals by their doping with non-photorefractive (Me: Zn, Mg, In, etc.) cations [2]. Unlike multiply charged photorefractive cations, they do not change their charge state in the crystal (they are not electron donors) under the action of optical radiation. The influence of such dopants on crystal properties is caused by their ability to change the amount of point defects and linked molecular complexes in the crystal cation sublattice. The molecular complexes in question can be caused by OH groups in the crystal structure [1,2,9–11]. Point 5+ + defects NbLi are Nb cations in the Li sites of a perfect stoichiometric (SLN, R = 1) LN composition. They, along with transition metal impurities (for example, Fe), are deep electron traps and influence photorefractive effect the most [1,2]. Moreover, a LN structure contains a lot of shallow electron traps besides NbLi that influence photorefractive effect [12]. The complexity of LN doping task increases provided that significant concentrations of metal dopants inevitably lead to a disorder in optical and structural uniformity of a single crystal [1,2,9–11,13]. Moreover, LN crystal grown at air always contain 1016–1018 cm−3 protons bonded with oxygen by a hydrogen bond. Hydrogen atoms form such complex defects as VLi- OH, NbLi-OH, etc., [7,14,15]. OH-groups play important role in formation of a secondary defect structure and physical characteristic of the material: it increases low-temperature conductivity, decreases photorefractive effect and coercive field value [7,14,15]. LN doping by metals is intensely studied [16]. At the same time, an influence of non-metal dopants on crystallization, structure, and optical characteristics of LN has not been paid enough attention. It has only been shown before [17–19], that significant changes in LN crystals properties occur while doped by much smaller amounts of a non-metal, than a metal. Non-metals influence mechanisms on melt-crystal system physical properties are different from those of metals. Non-metals are unable of incorporation into O6 octahedra of LN crystal structure. This is why studies of non-metal cations influence on LN structure are scarce. However, it has been determined before [19,20] that addition of B2O3 flux to LN charge leads to an increase in the crystal Curie temperature (TC) by ~47K and melting temperature by ~10K, compared to properties of a nominally pure CLN crystal. At this photorefractive effect significantly decreased even at excitation by a powerful (200 mW) laser radiation [2]. The data show that addition of boron into the charge change melt and thus LN structure. The charge contains relatively high B2O3 concentration (up to ~2.0 mol%), −5 however, the final concentration of boron in a LiNbO3:B crystal is only ≈4 × 10 through −4 ≈4 × 10 mol% B2O3, which is comparable with a basic concentrations of traces of many uncontrolled metal impurities [21–25]. Today, growing nominally pure LN crystals from under a B2O3 flux is a new and weakly studied area. Only few papers have been published on this topic yet [21–25]. Literature contains even fewer works on a secondary structure of such crystals. At the same time, it is a well-known fact that secondary structure strongly influences physical properties of oxygen octahedral phases of a variable composition, such as LN crystals. In particular, secondary structure influences photorefractive effect, coercive field strength, and concentration thresholds [2,26,27]. Addition of certain concentrations of B2O3 flux to the charge allows one to grow LN crystals with a high compositional uniformity close to that of CLN crystals. At the same time, cation sublattice units order of LiNbO3:B nears that of SLN crystals, but with much smaller photorefractive effect [21–25]. SLN and NSLN (near stoichiometric lithium niobate) crystals have low coercive field strength. It is ~3 kV/mm in SLN and ~22.3 kV/mm in CLN. Thus, SLN and NSLN crystals are perspective materials for laser radiation conversion on periodically polarized micron and submicron domain structures [28]. However, SLN crystals grown from Nb2O5–Li2O melt with 58.6 mol% Li2O have a smaller uniformity of refractive index along the polar axis and greater optical damage than CLN crystals [2]. This flaw makes SLN crystals Crystals 2021, 11, 458 3 of 37

inapplicable for optical elements manufacturing. An increase in optical uniformity and optical damage resistance of SLN and NSLN crystals is achieved by two methods. The first one is HTTSSG (High Temperature Top Seeded Solution Growth) with addition ~6 wt% of K2O flux (LN:K2O crystals) [29]. Recent papers [21–25] report the other know way: NSLN crystals with a high optical quality can be obtained from a congruent charge with a B2O3 flux (LiNbO3:B crystals). Doping LN with boron allows us to combine approaching stoichiometric composition and NbLi defects concentration decrease. As long as it is important to know technological details of obtaining of different types of highly useful LN crystals, it also is important to learn how different concentration of B exactly influence LN melt and thus structure and other properties. In this work we bring together data from optical and atomic force microscopy, optical spectroscopy, Raman spectroscopy, laser conoscopy, photoinduced light scattering (PILS), IR-spectroscopy in the region of stretching vibrations of OH groups and computer simulation of the defect structure. Methods have been applied to nominally pure NSLN crystals grown by different technologies from a charge doped by boron (0.55–1.24 mol% B2O3 in a charge). As long as grown crystals have approximately the same traces amount of boron in their structure, we consider that the designation in mol% means the B2O3 content in the charge. We also present a review of chemical interactions taking place in systems Li2O–Nb2O5 and Li2O–Nb2O5–B2O3. Such interactions determine fine features of the melt, crystallization, and crystals. Results for LiNbO3:B (0.55–1.24 mol%) crystals were compared with those of SLN and CLN crystals obtained due to a traditional technologies. IR adsorption and Raman spectra are highly sensitive to changes in a crystal structure, thus, defectivity. Sites occupied by hydrogen in LN structure are the most sensitive ones to crystal field changes. The fundamental absorption edge position and features are sensitive towards the structural uniformity of the crystal [14,18,23,24,29,30]. These two methods also allow one to evaluate Li/Nb ratio, concentration of point defects NbLi and VLi, type of complex defects that include OH-groups. PILS speckle-structure can be used to calculate photoelectric fields (photovoltaic Epv and diffuse ED) using approach offered in [31].

2. Materials and Methods 2.1. Speciﬁc Features of Obtaining Nominally Pure LN Crystals from a Boron Doped Charge and the Method of Their Experimental Studies

Studied nominally pure CLN and LiNbO3:B (0.55–1.24 mol%) crystals were grown from a congruent melt [16]. Doping was carried out both by homogeneous doping of Nb2O5 precursor [32] and direct solid-phase doping of LN charge [20,33]. Direct doping is a solid-phase synthesis of niobium pentoxide, lithium carbonate and boric acid with the subsequent production of a granular charge during annealing at pre-melting temperatures ◦ at 1240–1250 C. This method was used to grow LiNbO3:B (0.55–0.83 mol%) crystals. Nevertheless, the method itself has several disadvantages: LN crystals have articulated secondary structure and a number of macro-defects [33,34] (AppendixA, Figures A1–A12). Macro- and microdomain structure of doped LN crystals was studied by an image processing system «Thixomet». The system includes optical microscope Axio Observer D1m (Carl Zeiss, Oberkochen, Germany) connected through digital video camera Pix- eLink PL-B774U (Pixelink, Ottawa, Canada) with a computer equipped with the program ThixometPRO (Thixomet, Saint Petersburg, Russia). Studies were carried out in bright ﬁeld and differential interference contrast. Fine crystal plates of Z– and X–orientation were pre-ground, polished and selectively etched at room temperature for 18 h in the HF:HNO3 = 1:3 mixture. Nanostructures of doped crystals were studied by atomic force microscopes CMM-2000 (Zavod “Proton” MIET, Moscow, Russia) and Nano-R (Paciﬁc Nano Technology, Santa Clara, CA, USA). Earlier we have shown [19,20] that LN crystals with a high optical quality and a low photorefractive effect can be grown from a charge containing no more than ~0.1 to 0.12 wt%. For example, LiNbO3:B crystals grown from melts with ~0.12 to 0.25 wt% B2O3 contained microstructure defects absent in other LN crystals types. Crystals 2021, 11, 458 4 of 37 Crystals 2020, 10, x FOR PEER REVIEW 4 of 37

wt%. For example, LiNbO3:В crystals grown from melts with ~0.12 to 0.25 wt% B2O3 con- tainedThe microstructure melt viscosity defects greatly absent increases in other at LN high crystals boron types. content: a high complexing ability of boronThe leads melt to viscosity formation greatly of an increases anti-seeding at high viscous boron content: film on a the high melt complexing surface. Thisability results in ofgrowth boron ofleads LiNbO to formation3:B crystals of an with anti-seeding numerous viscous macro- film and on micro-defectsthe melt surface. irremovable This results by after- ingrowth growth annealing. of LiNbO Thus,3:В crystals growing withLN numerous from boron-containing macro- and micro-defects melts required irremovable the development by after-growthof new approaches annealing. and Thus, solutions growing to adapt LN fr theom boron-containing commonly used technology.melts required Changes the de- affected velopmenttechnological of new parameters approaches of growth, and solutions intrinsic to equipment adapt the ofcommonly a growth used camera technology. and synthesis of Changesinitial charge affected methods technological [19,20,25 parameters]. Papers [19 of,20 growth,] have revealedintrinsic equipment not only changes of a growth in the growth camera and synthesis of initial charge methods [19,20,25]. Papers [19,20] have revealed parameters, but also specific macrodefects, which were found only in LiNbO :B crystals: not only changes in the growth parameters, but also specific macrodefects, which were3 “channels” and deviation of optical density (optical inhomogeneity of crystals). “Channels” found only in LiNbO3:В crystals: “channels” and deviation of optical density (optical in- homogeneityare almost cylindrical of crystals). long “Channels” curved holesare almost inside cylindrical a LiNbO long3:B boulecurved with holes a inside diameter a ~1 to µ 2 LiNbO200 m.3:В We boule have with calculated a diameter the ~1 average to 200 μ densitym. We have of such calculated defects perthe average 1 mm of density the investigated of −2 sucharea, defects ~0 to 7 per mm 1 mm, Figure2 of the1 .investigated The crystals area, under ~0 to consideration 7 mm–2, Figure are 1. a The LiNbO crystals3:B under series with an considerationincrease content are ofa LiNbO boron3:B in series the melt with ~0.12 an increase to 0.25 wt%.content The of boron amount in the of “channels” melt ~0.12 to decreases 0.25up towt%. the The total amount absence of with“channels” a decrease decreases in the up boron to the concentrationtotal absence with in the a decrease melt to in ~0.1 wt%, theas paperboron concentration [20] claims. Deviationin the melt ofto ~0.1 optical wt%, density as paper due [20] to claims. deviations Deviation in the of optical melt viscosity densitywas discovered due to deviations when examining in the melt polishedviscosity was LiNbO discovered3:B plates when by examining optical microscopy polished in the LiNbOdifferential3:B plates interference by optical contrast microscopy (DIC) mode.in the DICdifferential mode isinterference actively used contrast to study (DIC) unpainted mode.transparent DIC mode objects. is actively The resulting used to image study isunpainted conventionally transparent colored objects. since The it is resulting the result of the imagepolarized is conventionally light beam interference colored since on it structuralis the result objects of the polarized with different light beam optical interfer- density. They encelook on like structural colored spotsobjects of with various different sizes opti andcal are density. usually They observed look like together colored with spots “channels”, of various sizes and are usually observed together with “channels”, Figure 2. The latter is Figure2. The latter is especially relevant for strongly doped melts. A colored with various especially relevant for strongly doped melts. A colored with various pseudocolors struc- pseudocolors structure without sharp boundaries is typical for all LiNbO3:B crystals that ture without sharp boundaries is typical for all LiNbO3:B crystals that underwent only post-growthunderwent onlythermal post-growth annealing. thermalCrystals annealing.turned to a single-domain Crystals turned state to loose a single-domain this type state ofloose a macrostructure, this type of a macrostructure,samples have uniform samples and have monochrome uniform andimage monochrome in a DIC mode, image Fig- in a DIC uremode, 2e,f Figure[19,20,25].2e,f [19,20,25].

Figure 1. (a)–shape and accumulation of “channel” macrodefects at the bottom of the LiNbO3:B Figure 1. (a)—shape and accumulation of “channel” macrodefects at the bottom of the LiNbO3:B (~3.50⋅10–5 wt% in a crystal cone) crystalline boule; (b)–a separate macrodefect of the “channel” (~3.50 × 10−5 wt% in a crystal cone) crystalline boule; (b)—a separate macrodefect of the “channel” −5 type in the LiNbO3:B (~6.20 × 10 wt% in a crystal cone) crystal; (c,d)—individual macrodefects of the “channel” type in the LiNbO :B (~6.0 × 10−5 wt% in a crystal cone) crystal; (e)—macrodefects of 3 the “channel” type in the LiNbO3:B (0.1 wt% in the charge) crystal. Crystals 2020, 10, x FOR PEER REVIEW 5 of 37

–5 Crystals 2021, 11, 458 type in the LiNbO3:B (~6.20⋅10 wt% in a crystal cone) crystal; (c), (d)–individual macrodefects5 of 37 the “channel” type in the LiNbO3:B (~6.0⋅10–5 wt% in a crystal cone) crystal; (e)–macrodefects of the “channel” type in the LiNbO3:B (0.1 wt% in the charge) crystal.

FigureFigure 2. 2. OpticalOptical deviations deviations and and macrodefects macrodefects in the in theform form of “channels” of “channels” in crystals in crystals LiNbO LiNbO3:B: (a)–3:B: –5 2 –5 (~6.20(a)—(~6.20⋅10 wt%× 10[B]− in5 wt%the crystal [B] in cone, the density crystal cone,of “channels” density ~1.7 of “channels”pcs/mm ); (b ~1.7)–(~6.20 pcs/mm⋅10 wt%2); ( b[B])— 2 ⋅ –5 in(~6.20 the cone× 10 of−5 thewt% crystal,[B] in th thee density cone of of the “channels” crystal, the~3.8 density pcs/mm of); “channels”(c)–(~1.44 10 ~3.8 wt% pcs/mm [B] in 2the);( c)— cone of the crystal, the density of “channels” ~5.6 pcs/mm2), (d)–(~6.20⋅10–5 wt% [B] in the cone of (~1.44 × 10−5 wt% [B] in the cone of the crystal, the density of “channels” ~5.6 pcs/mm2), (d)— the crystal, the density of “channels” ~5.6 pcs/mm2), after heat treatment; (e)–(~6.20⋅10–5 wt% [B] in (~6.20 × 10−5 wt% [B] in the cone of the crystal, the density of “channels” ~5.6 pcs/mm2), after the cone of the crystal), after transformation into a single-domain state; (f)–(~1.1⋅10–4 wt% [B] in the −5 coneheat of treatment; the crystal), (e)—(~6.20 after transformation× 10 wt% into [B] a in single-domain the cone of the state. crystal), All images after transformation are taken in DIC into a −4 mode.single-domain state; (f)—(~1.1 × 10 wt% [B] in the cone of the crystal), after transformation into a single-domain state. All images are taken in DIC mode. We have noted that using growth parameters suitable for obtaining of pure LN, We have noted that using growth parameters suitable for obtaining of pure LN, LN:Zn LN:Zn or Mg at obtaining of LiNbO3:B leads to cellular growth in the boule bottom, Figure 3a.or MgSuch at conditions obtaining ofalso LiNbO make3 :Bthe leads crystallization to cellular growthfront more in the sensitive boule bottom,towards Figure smallest3a. thermalSuch conditions conditions also violations: make the crystallizationthe hardly notable front change more sensitive in water towards pressure smallest in the cooling thermal conditions violations: the hardly notable change in water pressure in the cooling circuit of circuit of the growth unit leads to a change in the LiNbO3:B boule diameter, Figure 3b. the growth unit leads to a change in the LiNbO :B boule diameter, Figure3b. These macro- These macro- and micro-defects decrease the 3useful volume of the crystal, suitable for and micro-defects decrease the useful volume of the crystal, suitable for manufacturing of manufacturing of optical devices units. optical devices units. Homogeneous doping essence is obtaining of Nb2O5:B precursor. Boric acid is added to a niobium strip product solution. The latter is obtained during extraction puriﬁcation of niobium hydroxide [27,33]. Doped niobium pentoxide Nb2O5:B is used as a precursor during LN charge synthesis. A crystal LiNbO3:B (1.24 mol%) was grown from such a charge. Homogeneous doping allows us to grow crystals without growth stripes and other macro- and microdefects as those characteristic of direct doping [27]. Due to mass spectrometry, concentration of boron in crystals grown by both methods is close to traces (~10−3 to 10−5 wt%). Impurities concentrations were: Pb, Ni, Cr, Co, V, Ti, Fe, and Al less than 2 × 10−4, Ca, Si less than 1 × 10−3, F less than 1 × 10−3 wt%.

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FigureFigure 3. 3. (a()–cellulara)—cellular growth growth in the in bottom the bottom of the of LiNbO the LiNbO3:B boule3:B boulegrown grown using technological using technological pa- rametersparameters typical typical for forthe thegrowth growth of LiNbO of LiNbO3:Ме3:Me (Ме (Me:: Zn, Zn, Mg) Mg) crystals; crystals; (b)–change (b)—change in the in diameter the diameter of theof theLiNbO LiNbO3:B crystalline3:B crystalline boule boule due due to changes to changes in therma in thermall conditions conditions at the at thecrystallization crystallization front. front. 2.2. The Growing and Characterization Methods of the LN Crystals Homogeneous doping essence is obtaining of Nb2O5:B precursor. Boric acid is added to a niobiumAn SLN strip crystal product was grown solution. from The a melt latter with is 58.6obtained mol% during Li2O. Growingextraction of purification stoichiomet- ofric niobium LN crystals hydroxide is a complex [27,33]. technical Doped niobium task due pentoxide to a crystal’s Nb2O wide5:В is homogeneity used as a precursor area on duringa phase LN diagram charge [ 4synthesis.,7,35]. A greatA crystal difference LiNbO between3:В (1.24 the mol%) melt andwas crystalgrown compositionsfrom such a charge.require Homogeneous a decrease in growthdoping velocityallows us V severalto grow orders crystals of magnitude.without growth This stripes suppresses and otherconcentration macro- and over-cooling microdefects that as can those lead characteristic to changes inof thedirect crystal doping composition [27]. Due atto differ-mass spectrometry,ent stages of concentration the growth. Thus, of boron even in atcrystals a very grown small by growth both method velocitys is (much close lessto traces than (~10V =–3 0.1 to mm/h10–5 wt%).), one Impurities can obtain concentrations a crystal 10 mm were: in diameter Pb, Ni, Cr, and Co, 4 mm V, Ti, long Fe, from and 200Al less g of thanmelt. 2·10 Its–4 optical, Ca, Si uniformityless than 1·10∆n–3, (where F less than n is 1 a·10 refractive–3 wt%. index) is compared with that of CLN crystals of the same diameter grown at a velocity V = 3–5 mm/h [36]. Traditional 2.2.technology The Growing provides and Characterization very little possibility Methods to of obtainthe LN SLNCrystals single crystals of a big enough diameter to create optical elements suitable in optical instrumentation, quantum electronics, An SLN crystal was grown from a melt with 58.6 mol% Li2O. Growing of stoichio- etc. metric LN crystals is a complex technical task due to a crystal’s wide homogeneity area Nominally pure CLN was grown using original ICT KSC RAS charge that allows us on a phase diagram [4,7,35]. A great difference between the melt and crystal compositions to obtain water white crystals [37]. All crystals were grown by Czochralski on Crystal-2 require a decrease in growth velocity V several orders of magnitude. This suppresses con- (Zavod Kristall Ltd, Saint Petersburg, Russian Federation) with automatic control of a centration over-cooling that can lead to changes in the crystal composition at different crystal diameter. stages of the growth. Thus, even at a very small growth velocity (much less than V = 0.1 Crystals were turned to a single-domain state by a high temperature electro-diffuse mm/h), one can obtain a crystal 10 mm in diameter and 4 mm long from 200 g of melt. Its annealing: constant current was applied to crystals during their cooling in a temperature optical uniformity Δn (where n is a refractive index) is compared with that of CLN crystals interval 1240–880 ◦C with a speed 20 grad/h. The grade of single domain state was ofdetermined the same diameter by analysis grown of at the a frequencyvelocity V = dependence 3–5 mm/h [36]. of electrical Traditional impedance technology and pro- by vides very little possibility to obtain SLN single crystals of a big enough diameter to create determining the value of the static piezomodulus (d333st). opticalSamples elements for suitable optical in experiments optical instrumentation, were cut from quantum grown boules electronics, in the etc. shape of paral- lelepipedsNominally so that pure edges CLN coincided was grown with using crystallographic original ICT KSC axes RAS X, Y, charge and Z (thethat polarallows axis) us toand obtain in the water shape white of Z-oriented crystals [37]. plane-parallel All crystals plates were ~1 grown mm thick.by Czochralski Parallelepiped on Crystal-2 samples (Zavodhad sizes Kristall ~7 × 6Ltd,× 5 Saint mm3 .Petersburg, Faces of all Russi studiedan samplesFederation) were with thoroughly automatic polished. control of a crystalRaman diameter. spectra were excited with a 514.5 nm line of laser 2018-RM (SpectraPhysics, Milpitas,Crystals CA, were USA) turned and detected to a single-domain by a spectrograph state by T64000 a high (Horiba temperature Jobin Yvon, electro-diffuse Palaiseau, annealing:France) equipped constant with current a confocal was applied microscope. to crystals Low excitationduring their power cooling (not higherin a temperature than 3 mW intervalunder the 1240–880 microscope) °С with decreased a speed an 20 inﬂuence grad/h. The of photorefractive grade of single effect domain on Ramanstate was spectrum. deter- minedSpectra by resolution analysis of was the 1 frequency cm−1. Spectra dependence were treated of electrical using Horiba impedance LabSpec and 5.0 by anddetermin- Origin ing8.1 the programs. value of Instrumental the static piezomodulus error in determination (d333st). of frequency (ν), width (S) and intensity (I) ofSamples Raman bandsfor optical was ±experiments1.0, ±3.0 cm were−1 and cut 5%, from respectively. grown boules in the shape of paral- lelepipedsPILS andso that laser edges conoscopy coincided methods with crystallographic are described in axes detail X, in Y, papers and Z[ 11(the,13 polar,38]. Cono-axis) andscopic in the patterns shape andof Z-oriented PILS patterns plane-parallel were excited plates by laser~1 mm Nd:YAG thick. Parallelepiped (MLL-100, Changchun samples 3 hadNew sizes Industries ~7 × 6 × Optoelectronics 5 mm . Faces of Tech. all studied Co. Ltd, samples Changchun, wereChina), thoroughly wavelength polished.λ0 = 532 nm Raman spectra were excited with a 514.5 nm line of laser 2018-RM (SpectraPhysics, Milpitas, CA, USA) and detected by a spectrograph T64000 (Horiba Jobin Yvon, Palaiseau,

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and power p = 1 and 90 mW. The studied sample was located on a movable two-coordinate plate, which allowed us to obtain several conoscopic patterns from different areas of a crystal. Conoscopic pattern formed on a translucent screen and was registered by a digital photo camera. Photoelectric fields studies were carried out using PILS patterns excited by argon laser 2018-RM (SpectraPhysics, Mountain View, CA, USA) lines 476.5 nm (p = 216 mW); 488.0 nm (p = 98 mW); 514.5 nm (p = 282 mW); 530.9 nm (p = 160 mW). Laser beam diameter was 1.8 mm. Scattered radiation fell on a translucent screen and was registered by a digital photo camera. PILS in both cases was registered in ee-type geometry: laser radiation that fells on the crystal and scattered radiation have the same polarization, at the same time E vector is oriented parallel to the crystals polar axis Z. PILS indicatrix parameters of studied crystals provided values of strengths of photovoltaic and diffusion electric fields. The error of our experiment calculations was 1.5–2%. The calculation of photovoltaic and diffusion field strengths was carried out in Mathcad 15.0 using approach from [31]. Refractive indexes of ordinary and extraordinary rays were determined from empirical equations from [39]. PILS indicatrix angle was calculated due to a formula θ = arctg(a/b), where a is the indicatrix size in the positive direction of the polar axis, b is the distance between the crystal and the screen. Optical absorption spectra of LN crystals were determined using spectrophotometer Varian Cary 2300 (Varian Inc., Palo Alto, CA, USA), SF-256 UVI (Granat, Saint Petersburg, Russian Federation) and monochromator MDR-41 (OKB Spectr, Saint Petersburg, Russian Federation). A deuterium lamp was used as a radiation source. Band gap was determined using crystal transmission spectrum. An invert spectrum was obtained from the latter—an absorption spectrum. The obtained absorption spectrum in the decreasing linear part of the graph was approximated by a straight line until it crossed the abscissa axis. The point of intersection of this straight line and the abscissa axis is the wavelength corresponding to the absorption edge of the crystal. A bandgap was determined due to a formula E = hc/λ, where λ is a wavelength of absorption edge, h—Planck’s constant, c—light speed in vacuum. The band gap determination error was ±1.0 nm. IR-absorption spectra were determined in vacuum by spectrometer IFS 66 v/s (Bruker, Leipzig, Germany). IR spectra treatment was carried out in programs Bomem Grammes V. 2.03, LabSpec 5.5, Origin 8.1. Differential thermal analysis (DTA) was carried out on an installation with a thermal block made of ruby single crystal, which provides a gradient-free zone, and high sensitivity and resolution [40]. Error in thermal effects temperature determination was ±0.5 ◦C. The detailed description of the method is available from [40]. Computer simulation of B3+ ion localization and electrostatic interaction of point charges in LiNbO3:B crystals was carried out by a calculation of sum energy of Coulomb interaction of point charges (U, eV) in an oxygen-octahedral cluster of a LN structure (Li+, Nb5+,O2−) with B3+ element. The chemical analysis was carried out by atomic emission spectrometry (spectrometer ICPS-9000 by Shimadzu), with an error ~1%.

3. Results 3.1. Study of LiNbO3:B Crystals Defective Structure by Raman Spectroscopy

Raman spectra of LiNbO3:B (0.55–1.24 mol%) crystals were previously studied in papers [21,22,41,42]. The papers focus on an inﬂuence of a disorder in cation sublattice on A1(TO) symmetry type phonons in Y(ZZ)Y¯ scattering geometry and on photorefractive effect manifestation in Raman spectra. Figure4 demonstrates Raman spectra of SLN, CLN and LiNbO3:B (0.55–1.24 mol%) in Y(ZX)Y¯ and Y(ZZ)Y¯ scattering geometries. These geometries correspond to fundamental vibration of the lattice of E(TO) and A1(TO) symmetry types. Spectra fragments with the most articulated changes at a crystal composition variation are given on Figure5. Table1 demonstrates main parameters ( ν—frequency, S—band width, I—band intensity) of bands appearing in studied crystals. Figure6 demon- Crystals 2020, 10, x FOR PEER REVIEW 8 of 37

А1(ТО) symmetry type phonons in Y(ZZ)Ȳ scattering geometry and on photorefractive effect manifestation in Raman spectra. Figure 4 demonstrates Raman spectra of SLN, CLN and LiNbO3:B (0.55–1.24 mol%) in Y(ZX)Ȳ and Y(ZZ)Ȳ scattering geometries. These geometries correspond to fundamental vibration of the lattice of Е(ТО) and А1(ТО) sym- Crystals 2021, 11, 458 metry types. Spectra fragments with the most articulated changes at a crystal composition8 of 37 variation are given on Figure 5. Table 1 demonstrates main parameters (ν—frequency, S— band width, I—band intensity) of bands appearing in studied crystals. Figure 6 demon- stratesstrates changeschanges inin half-widths half-widths and and intensities intensities of of 576 576 and and 630 630 cm cm−1–1 RamanRaman bandsbandsand and in in PILSPILS speckle-structure speckle-structure indicatrix indicatrix opening opening angle angleθ θ.. SLN SLN Raman Raman spectrum spectrum contains contains all all nine nine bandsbands correspondingcorresponding toto E(TO)Е(ТО) symmetrysymmetry typetypephonons phononspermitted permitted bybyselection selectionrules rules in in Y(ZX)Y(ZX)Y¯Ȳ scattering scattering geometry, geometry, Figure Figure4, 4, Table Table1. Low-intense1. Low-intense bands bands 179 179 and and 611 611 cm cm−1–1are are clearlyclearly observed observed in in SLN SLN Raman Raman spectrum. spectrum. However,However, they they dissolve dissolve by by disordering disordering effects effects inin spectra spectra of of CLN CLN and and LiNbO LiNbO3:B3:B (0.55–1.24 (0.55–1.24 mol%). mol%). Frequencies Frequencies of of all all bands bands stay stay the the same same withinwithin error,error, Figures Figures4 4and and5, Table5, Table1. This1. This indicates indicates that that secondary secondary structure structure changes changes (they(they appearappear at changes changes in in Li/Nb Li/Nb ratio ratio and and В3+ Bcation3+ cation concentration) concentration) affect affect very little very quasi- little quasi-elasticelastic lattice lattice constants constants in studied in studied LN crysta LN crystals.ls. At the Atsame the time, same Figures time, Figures 4–6 and4– 6Table and 1 Tablereveal1 reveal that width that widthand intensities and intensities of LiNbO of LiNbO3:B Raman3:B Raman bands bandschange change significantly signiﬁcantly in all Ra- in allman Raman spectra spectra areas: areas: two-particle two-particle states states of acoustic of acoustic phonons phonons (100–150 (100–150 cm–1); cm vibration−1); vibration of cat- –1 −1 ofions cations located located in oxygen in oxygen octahedra octahedra ВО6 BO(В: 6Nb,(B: Li, Nb, dopant) Li, dopant) (200–300 (200–300 cm cm); vibrations); vibrations of ox- −1 ofygen oxygen octahedra octahedra atoms atoms (500–900 (500–900 cm–1 cm). Table). Table1 shows1 shows that thatLiNbO LiNbO3:В Raman3:B Raman bands bands in the −1 −1 inarea the 150–300 area 150–300 cm–1 are cm narrowerare narrower than those than of those CLN; of 152 CLN; and 152 240and cm–1 240 widths cm ofwidths LiNbO of3:В −1 LiNbORaman3 :Bbands Raman coincide bands with coincide those with of SLN. those The of SLN.578 cm The–1 band 578 cm correspondsband corresponds to doubly de- to doublygenerate degenerate Е(TO) vibrations E(TO) vibrations of oxygen of atoms oxygen in atomsО6 octahedra. in O6 octahedra. It is much It wider is much in spectra wider in of spectraLiNbO3 of:B LiNbO(0.55–1.243:B (0.55–1.24mol%) than mol%) in SLN than and in CLN, SLN andTable CLN, 1, Figure Table 16., FigureObtained6. Obtained data show datathat showeven very that evena faint very change a faint in changeboron concentration in boron concentration in the charge in the and charge melt and(0.55–1.24 melt (0.55–1.24mol% В2О mol%3) leads B 2toO 3a) significant leads to a signiﬁcantordering of ordering cation sublattice of cation along sublattice the polar along axis the at polar both axisdoping at both methods. doping At methods. the same At time, the oxygen same time, octahedra oxygen О octahedra6 are distorted. O6 are New distorted. bands Newin the bandsarea of in Raman the area spectra of Raman corresponding spectra corresponding to oxygen to octahedra oxygen octahedra vibrations vibrations would mean would a meanchange a changein their in geometry. their geometry. However, However, the area the contains area contains no new no bands. newbands.

3 FigureFigure 4.4. RamanRaman spectraspectra of of SLN SLN (1), (1), CLN CLN (2), (2), and and LiNbO LiNbO3:B:B (0.55 (0.55 (3), (3), 0.69 0.69 (4), (4), 0.83 0.83 (5), (5), 1.24 1.24 (6) (6) mol%) inmol%) the different in the different scattering scattering geometries geometries - Y(ZX) -Y(¯ Y(ZX)a) andȲ (a Y(ZZ)) and Y(¯Y(ZZ)b). FigureȲ (b). Figure is reproduced is reproduced with the with the permission of Pleiades Publishing from the paper N. V. Sidorov et. al., Opt. Spectrosc. 2016 permission of Pleiades Publishing from the paper N. V. Sidorov et al., Opt. Spectrosc. 2016 V. 121 P. V. 121 P. 36–44, DOI: https://doi.org/10.1134/S0030400X16070195 (accessed on 26 March 2021). 36–44, DOI: https://doi.org/10.1134/S0030400X16070195 (accessed on 26 March 2021).

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Figure 5. Raman spectra fragments of the crystals SLN (1), CLN (2), and LiNbO3:B (0.55 (3), 0.69 (4), 0.83 (5), 1.24 (6) mol%) Figure 5. Raman spectra fragments of the crystals SLN (1), CLN (2), and LiNbO3:B (0.55 (3), 0.69 (4), 0.83 (5), 1.24 (6) mol%) in the scattering geometries Y(ZX)Y¯ and Y(ZZ)Y.¯ Figure is reproduced with the permission of Pleiades Publishing from the in the scattering geometries Y(ZX)Ȳ and Y(ZZ)Ȳ. Figure is reproduced with the permission of Pleiades Publishing from paperthe paper N. V. N. Sidorov V. Sidorov et al., et.Opt. al., Spectrosc Opt. Spectrosc. 2016 .V. 2016 121 P.V. 36–44,121 P. DOI:36–44, https://doi.org/10.1134/S0030400X16070195 DOI: https://doi.org/10.1134/S0030400X16070195 (accessed (ac- oncessed 26 March on 26 2021).March 2021). Table 1. Basic parameters of E(TO) bands appearing in Raman spectra of crystals SLN, CLN, Table 1. Basic parameters of E(TO) bands appearing in Raman spectra of crystals SLN, CLN, and and LiNbO :B (0.55–1.24 mol%) in the Y(ZX)Y¯ scattering geometry. Table is reproduced with the LiNbO3:B (0.55–1.243 mol%) in the Y(ZX)Ȳ scattering geometry. Table is reproduced with the per- permissionmission of Pleiades of Pleiades Publishing Publishing from from the paper the paper N. V.N. Sidorov V. Sidorov et. al., et Techn. al., Techn. Phys. 2018 Phys .V.2018 63 P.V. 1758– 63 P. 1758–1766,1766, DOI: DOI:https://doi.org/10.1134/S1063784218120198. https://doi.org/10.1134/S1063784218120198 (accessed on 26 March 2021).

LiNbO 3:B LiNbOLiNbO3:B LiNbOLiNbO3:B LiNbOLiNbO3:B SLN CLN 3 3 3 3 (0.55 mol%) (0.69 mol%)mol%) (0.83(0.83 mol%)mol%) (1.24(1.24 mol%)mol%) νν S νν SS νν SS νν SS νν SS νν SS 152 7 152 12 152 7 152 9 152 9 152 10 152 7 152 12 152 7 152 9 152 9 152 10 179 – – – – – – – – – – – 179240 –9 240 – 11 – 41– – 9 241 – –11 240 – –10 240 – –11 240268 10 9 268 240 14 11 27041 913 241271 1112 240270 1013 240270 1113 268324 10 324 268 13 14 270 325 1312 271324 1214 270324 1314 270323 1316 371 17 371 23 371 24 370 24 370 26 371 26 324 10 324 13 325 12 324 14 324 14 323 16 434 10 434 14 432 9 432 10 432 11 432 14 371578 1716 576 371 15 23 371 575 2432 370576 2433 370576 2633 371575 2624 434611 10– 434– – 14 432 – 9– 432– 10– 432– 11– 432– 14– 630578 1 1620 626 576 25 15 575 626 3241 576628 3342 576626 3346 575626 2428 876 1 20 876 30 875 25 877 25 875 26 875 31 611 – – – – – – – – – – – 1 Note. 630 and 876 cm–1 bands correspond to А1(ТО) and А1(LO) symmetry types phonons, re- 1 spectively.630 20The phonons 626 are 25 usually 626 inactive 41 in Y(ZX) 628Ȳ scattering 42 geometry, 626 in 46 our case 626 they ap- 28 pear876 due1 to20 the photorefractive 876 30 effect. 875 We do 25 not show 877 widths 25 of low-intense 875 26180 and 875 610 cm–1 31 1bands due to a great −error1 in their determination. Note. 630 and 876 cm bands correspond to A1(TO) and A1(LO) symmetry types phonons, respectively. The phonons are usually inactive in Y(ZX)Y¯ scattering geometry, in our case they appear due to the photorefractive effect. We do not show widths of low-intense 180 and 610 cm−1 bands due to a great error in their determination.

Due to selection rules [2,43], fundamental vibrations of E(TO) symmetry type should manifest in Y(ZX)Y¯ scattering geometry, A1(TO) symmetry type—in Y(ZZ)Y.¯ A1(TO) symmetry type vibrations are forbidden in Y(ZX)Y¯ scattering geometry [2]. However, due to photorefractive effect, they manifest in this scattering geometry. The bands corresponding to A1(TO) symmetry type vibrations have intensities proportional to photorefractive effect value. Papers [2,44] have shown that the 630 cm−1 band is the most suitable for photorefractive effect evaluation. The band corresponds to A1(TO) vibrations of oxygen atoms in O6 octahedra.

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θ FigureFigure 6. 6. ConcentrationConcentration dependences dependences of of (a ()a )width width (S), (S), (b (b) intensity) intensity (I), (I), and and PILS PILS opening opening angle angle (θ () ) −1 ofof 576 576 and and 630 630 cm cm−1 bandsbands of SLN, of SLN, CLN CLN and LiNbO and LiNbO3:B (0.55–1.243:B (0.55–1.24 mol%) mol%)crystals. crystals. Figure (a Figure) is re- (a) producedis reproduced with the with permission the permission of Pleiades of Pleiades Publishing Publishing from the from paper the N. paperV. Sidorov N. V. et. Sidorov al., Techn. et al., Phys.Techn. 2018 Phys. V.2018 63 P.V. 1758–1766, 63 P. 1758–1766, DOI: https://d DOI: https://doi.org/10.1134/S1063784218120198oi.org/10.1134/S1063784218120198 (accessed (accessed on 26 on March26 March 2021); 2021 Figure); Figure (b) (isb )reproduced is reproduced with with the the permission permission of Pleiades of Pleiades Publishing Publishing from from the the paper paper N.N. V. V. Sidorov etet. al.,al.,Opt. Opt. Spectrosc.Spectrosc.2016 2016V. V. 121 121 P. P. 36–44, 36–44, DOI: DOI: https://doi.org/10.1134/S0030400X160 https://doi.org/10.1134/S0030400X1607019570195 (accessed on 26 March 2021). (accessed on 26 March 2021).

DueThe to E(TO) selection 580 cmrules−1 [2,43],band doesfundamental not change vibrations with changes of E(TO) in symmetry photorefractive type should effect manifestvalue, at in least Y(ZX) in crystalsȲ scattering with geometry, a low photorefractive А1(ТО) symmetry effect. Thus,type—in photorefractive Y(ZZ)Ȳ. А1(ТО effect) sym- can metrybe evaluated type vibrations due to the are formula forbidden Irel =in (IY(ZX)630/I580Ȳ )scattering× 100%[ geometry11,13,44,45 [2].]. Structure However, disorder due to photorefractivecontributes the mosteffect, to they LN manifest Raman bands in this widening scattering during geometry. dopant The concentration bands corresponding increase toat А a1 constant(ТО) symmetry temperature type vibrations [2,43]. Structure have intensities disorder proportional and photorefractive to photorefractive effect contribute effect value.the most Papers to LN [2,44] Raman have bands shown intensity that the changes630 cm–1 [band2,43]. is Figure the most6b showssuitable that for thephotore- least −1 fractiverelative effect intensity evaluation. of the 630 The cm bandband corresponds is observed to А in1( CLNТО) vibrations and SLN crystalsof oxygen spectra, atoms the in −1 Оgreatest—in6 octahedra. LiNbO 3:B (0.55–0.83 mol%) crystals. In LiNbO3:B spectra the 630 cm band’s intensityThe Е first(ТО increases,) 580 cm–1 than band decreases does not with change an increase with changes in B3+ concentration,in photorefractive Figure effect6b. value,In addition, at least concentration in crystals with behavior a low photorefractive of 630 cm−1 band effect. intensity Thus, photorefractive and widths of effect 630 cm can−1 −1 be(A 1evaluated(TO)) and due 576 to cm the formula(E(TO)) I bandsrel = (I630 in/I580 the)⋅100% Y(ZX) [11,13,44,45].Y¯ Raman spectra Structure of LiNbO disorder3:B con- well tributescoincide the with most the to behavior LN Raman of PILSbands opening widening angle duringθ, Figure dopant6. Thus,concentration oxygen octahedraincrease at adistortions constant temperature that occur due [2,43]. to a Structure change in disord cationer sublattice and photorefractive order and photorefractive effect contribute effect the mostdepend to LN on boronRaman concentration bands intensity in the changes charge [2,43]. in studied Figure LiNbO 6b shows3:B crystals. that the least relative intensityObtained of the data630 cm allow–1 band us is to observed conclude in that CLN boron and structuresSLN crystals the spectra, melt, which the greatest— actually inmeans LiNbO that3:Вa (0.55–0.83 congruent mol%) LN crystal crystals. is growth In LiNbO from3:В aspectra boron-doped the 630charge. cm–1 band’s Such intensity a crystal firsthas noticeableincreases, than differences decreases in with fine structuralan increase features in В3+ concentration, and physical Figure characteristics 6b. In addition, from a concentrationnominally pure behavior CLN crystal, of 630 grown cm–1 band from intensity a congruent and charge. widths Obtainedof 630 cm results–1 (А1(ТО can)) haveand 576the cm following–1 (Е(ТО explanation.)) bands in the Y(ZX)Ȳ Raman spectra of LiNbO3:В well coincide with the behaviorWe believeof PILS thatopening boron angle structures θ, Figure the 6.melt Thus, so oxygen that crystals octahedra grown distortions from it havethat occur a de- duecreased to a amountchange ofin NbcationLi. Raman sublattice spectra order confirm and photorefractive this conclusion. effect Raman depend spectra on of boron both nominally pure and doped CLN crystals contain a low-intense band 120 cm−1 (A (TO)), concentration in the charge in studied LiNbO3:В crystals. 1 FigureObtained5. The banddata allow corresponds us to conclude to two-particle that boron states structures of acoustic the phonons melt, which with actually a total means that a congruent LN crystal is growth from a boron-doped charge. Such a crystal

Crystals 2021, 11, 458 11 of 37

wave vector equal to zero [2]. Due to [46], it cannot correspond to a pseudoscalar mode A2 forbidden in a point group C3v by the selection rules. This band is split in two, 105 and 118 cm−1 bands, in a spectrum of a CLN crystal, Figure5. This happens due to a refinement of the selection rules in the wave vector of two-particle states of A1(TO) acoustic phonons [2,47,48]. It is a well-known fact [2,47,48], that spectrum of a perfect SLN crystal is free of the 120 cm−1 band, Figure5. In addition, SLN crystals are characterized by the perfect order in a cation sublattice, it is free of NbLi defects. Intensity of this band first decreases, than increases in LiNbO3:B with an increase in a dopant concentration, Figure5. −1 The band is split in two components 112 and 123 cm in a spectrum of a crystal LiNbO3:B (1.24 mol%), Figure5. This indicates a high structure perfection of the crystal. A decrease in −1 the 120 cm band intensity also indicates a decrease in NbLi defects amount at its doping by B3+ ions. Cation sublattice orders (Raman bands in the area 150–300 cm−1 narrow, Table1) simultaneously with a decrease in resonant anharmonic interaction between the −1 lowest-frequency fundamental A1(TO) vibrations 254, 274 cm and two-particle A1(TO) acoustic excitations. The latter is discussed in detail in [49]. A degree of mixing between A1(TO) single-phonon and multi-phonon states depends on the value of this interaction, which also influences the spectrum in the 120 cm−1 area. Thus, LN crystals doping can effectively govern interaction between single-phonon and two-phonon states. Paper [50] has revealed that 120 cm−1 band intensity is connected with an acoustic Q-factor of LN crystal. The higher Q-factor is, the smaller the band intensity is, due to a decrease in the amount of NbLi defects. Thus, our data prove a higher structure perfection of nominally pure LN crystals grown from boron doped charge compared to that of a CLN crystal. The crystal LiNbO3:B (1.24 mol%) is the most structurally perfect one.

3.2. Study of LiNbO3:B Crystal Structure by IR Spectroscopy in the Area of OH-Groups Vibration LN single crystals obtained at air atmosphere always contain OH groups incorporated into the structure during growth [14]. Localization of hydrogen atoms in LN structure greatly influences charge distribution and polarizability of oxygen octahedra clusters MeO6 (Me: Li, Nb, dopant). Hydrogen atoms bond with oxygen of LN structure by hydrogen bonds. OH groups increase LN crystal conductivity and decrease optical damage and coercive field value [10,29]. Doping of LN crystal leads to a total restructure of the whole hydrogen bonds system. Stretching and deformation vibrations of OH groups are supposed to manifest in Raman and IR absorption spectra of LN crystals in the areas 1600–1800 and 3450–3550 cm−1, respectively. The amount of bands in these areas and their basic parameters depend on localization of hydrogen atoms in the crystal structure. The localization in its turn depends on stoichiometry, doping particularities and growth details of a single crystal [14]. A perfect strictly stoichiometric LN crystal has no site for a hydrogen atom [51]. IR spectrum of a real NSLN crystal contains only one narrow (S = 3 cm−1) 3466 cm−1 band [26,52]. A slight shift of stoichiometry leads to widening and splitting of this band in IR absorption spectrum −1 into 3466 and 3480 cm bands. This is caused by a formation of complex defects NbLi–OH, VLi, etc., in a structure of a non-stoichiometric LN crystal [51]. CLN crystal IR spectrum contains three components of the band: and intense 3466 cm−1 band, an average intense 3481 cm-1 band and a low-intense 3489 cm−1 band [53]. Papers [29,52] have demonstrated that as LN structure approaches stoichiometric composition, width of the 3466 cm−1 band and intensity of 3481 and 3489 cm−1 bands decrease. Note that SLN crystal has a ratio Li/Nb = 1, point defects, such as the same cations in the neighbor sites are absent. Thus, studies of parameters of IR absorption bands in the OH-groups vibrations area contains important information about the nature of defects and their localization in the structure; the structural rearrangements that occur in LN crystals with a change in composition; and the peculiarities of a single crystal growth. Such information is also important at refinements of technologies of growing optically and structurally perfect LN single crystals. Figure7 demonstrates IR absorption spectra of studied LN crystals in the area 3420–3550 cm−1. This area contains stretching vibrations of OH groups. Table2 demon- Crystals 2020, 10, x FOR PEER REVIEW 12 of 37

Thus, studies of parameters of IR absorption bands in the OH-groups vibrations area contains important information about the nature of defects and their localization in the structure; the structural rearrangements that occur in LN crystals with a change in composition; and the peculiarities of a single crystal growth. Such information is also important at refinements of technologies of growing optically and structurally perfect LN single crystals. Figure 7 demonstrates IR absorption spectra of studied LN crystals in the area 3420– 3550 cm–1. This area contains stretching vibrations of OH groups. Table 2 demonstrates parameters of spectral bands. It is obvious that spectra of all studied crystals are different. Crystals 2021, 11, 458 An SLN crystal spectrum contains three bands with frequencies 3465, 123480, of 37 and 3488 cm– 1, Figure 7. The bands in an SLN spectrum are much narrower than in other crystals, Table 2. It is believed that a band in the frequency range 3465–3466 cm–1 is characteristic of a highlystrates parametersperfects SLN of spectral crystals bands. with It is only obvious one that hydrogen spectra of allatom studied position crystals, [29,52]. are Figure 7 clearlydifferent. shows An SLN that crystal a CLN spectrum spectrum contains is threedifferent bands from with frequenciesthe one of 3465, an SLN 3480, crystal. and IR spectra 3488 cm−1, Figure7. The bands in an SLN spectrum are much narrower than in other of a CLN is a blurred wide absorption band consisting of several components with the crystals, Table2. It is believed that a band in the frequency range 3465–3466 cm −1 is char- –1 sameacteristic polarization of a highly perfectswith frequencies SLN crystals 3467 with ( onlyν1), one3483 hydrogen (ν2), and atom 3486 position, (ν3) cm [29 ,and52]. a weak band withFigure a 7frequency clearly shows ~3490 that acm CLN–1 (ν spectrum4). A 3480–3485 is different cm from–1 band the one is ofconsidered an SLN crystal. characteristic of a CLNIR spectra crystal of aand CLN is is attributed a blurred wide to stretching absorption vibrations band consisting of a of V severalLi–ОН componentscomplex [54]. VLi defects ν ν ν −1 arewith absent the same from polarization SLN crystal with frequencies structure. 3467 This ( 1means), 3483 ( that2), and IR 3486 spectrum ( 3) cm shouldand not contain a weak band with a frequency ~3490 cm−1 (ν ). A 3480–3485 cm−1 band is considered bands with frequencies 3480–3485 cm–14, which is confirmed experimentally [29,52]. IR characteristic of a CLN crystal and is attributed to stretching vibrations of a VLi–OH com- spectraplex [54 ].of V LiNbOLi defects3:B are (0.55–0.83 absent from mol%) SLN crystal is similar structure. to those This meansof CLN: that an IR OH-groups spectrum absorption bandshould is notsplit contain in three bands components with frequencies of the 3480–3485 same polarization cm−1, which is ~3470, conﬁrmed ~3483, experi- and ~3486 cm–1. mentally [29,52]. IR spectra of LiNbO :B (0.55–0.83 mol%) is similar to those of CLN: an Thus, hydrogen bonds in CLN and3 LiNbO3:B crystals structure should be similar. Three OH-groups absorption band is split in three components of the same polarization ~3470, components of CLN−1 crystal are considered to be connected with stretching vibrations of ~3483, and ~3486 cm . Thus, hydrogen bonds in CLN and LiNbO3:B crystals structure 4+ − OHshould groups be similar. located Three near components NbLi –V ofLi CLN defects crystal [53,55]. are considered However, to be intensities connected with of all three com- 4+ − ponentsstretching are vibrations higher ofin OH LiNbO groups3:B located than in near CLN Nb Lispectrum,–VLi defects Table [53 2.,55 At]. However,the same time widths ofintensities two bands of all are three narrower components than are higherin CLN in LiNbO spectrum,3:B than widths in CLN spectrum,of the band Table 34852. cm–1 is not At the same time widths of two bands are narrower than in CLN spectrum, widths of the narrower, Table 2. This indicates ordering of OH groups distribution in LiNbO3:B crystals band 3485 cm−1 is not narrower, Table2. This indicates ordering of OH groups distribution structure. in LiNbO3:B crystals structure.

Figure 7. IR absorption spectra of crystals SLN (1), CLN (2) and LiNbO3:B (0.55 (3), 0.69 (4), 0.83 (5), Figure 7. IR absorption spectra of crystals SLN (1), CLN (2) and LiNbO3:B (0.55 (3), 0.69 (4), 0.83 mol%). The ﬁgure is reproduced with the permission of Pleiades Publishing from the paper N. V. (5), mol%). The figure is reproduced with the permission of Pleiades Publishing from the paper N. Sidorov et al., Techn. Phys. 2020 V. 65 P. 627–634, DOI: https://doi.org/10.1134/S1063784220040192 V. Sidorov et. al. Techn. Phys. 2020 V. 65 P. 627–634, DOI: (accessed on 26 March 2021). https://doi.org/10.1134/S1063784220040192 (accessed on 26 March 2021).

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Table 2. Frequencies (ν, cm−1), widths (S, cm−1) and intensities (I, rel. un.) of IR bands; OH-groups − −3 4+ − concentration (C(OH ), cm ); concentration of NbLi and VLi defects in crystals SLN, CLN, and LiNbO3:B (0.55–1.24 mol%). Table is reproduced with the permission of Pleiades Publishing from papers N. V. Sidorov et al., Techn. Phys. 2020 V. 65 P. 627–634, DOI: https://doi.org/10.1134/S10637 84220040192 (accessed on 26 March 2021). and R.A. Titov et al., Techn. Phys., 2021 V. 66 №1 P. 59–66, DOI: https://doi.org/10.1134/S1063784221010217 (accessed on 26 March 2021).

IR Bands Parameters − Crystal C(NbLi), C(VLi), C(OH ), Li/Nb −3 ν IS mol% mol% cm 3465 0.14 4.28 17 SLN 3480 0.11 5.37 1 0 0 1.6 × 10 3488 0.07 8.18 3470 0.12 16.40 17 CLN 3483 0.49 24.80 0.942 0.98 3.90 3.3 × 10 3486 0.33 27.10 3466 0.14 12.50 LiNbO :B 3 0.967 0.55 2.21 × 17 (0.55 mol%) 3480 0.08 17.70 6.4 10 3485 0.33 27.70 3466 0.10 16.20 LiNbO :B 3 0.977 0.39 1.54 × 17 (0.69 mol%) 3481 0.13 20.10 3.4 10 3485 0.10 22.60 3467 0.14 12.50 LiNbO :B 3 0.970 0.50 2.01 × 17 (0.83 mol%) 3480 0.12 19.90 6.3 10 3485 0.29 27.20

A computer simulation has been carried out in a paper [56]. The paper considers possible sites of hydrogen atom in SLN crystals. The paper has shown that all hypothetical hydrogen sites on O–O bonds located near VLi defects are unstable and should be excluded from further consideration. Moreover, the hydrogen atom site on C axis has not been conﬁrmed. Analysis of possible hydrogen atoms trajectories in LN crystal structure shows that it can be associated in SLN structure only with one oxygen ion in the upper oxygen triangle of NbO6 octahedron. Dipole moment orientation of OH-group is slightly different from a direction of a short O–O bond. Thus, creation of a hydrogen bond leads not only to a cardinal change in the wave functions of the outer electron orbitals of the oxygen ion and the parameters of its electronic polarizability, but also to a strong distortion of the entire NbO6 octahedron [56]. Such changes in a crystal structure should manifest in 850–900 cm−1 area of Raman spectra. Bonds in this area correspond to stretching bridge vibrations B–O–B (B: Nb or dopant) of oxygen in NbO6 octahedra along the polar axis [2]. Table1 shows that spectra of LiNbO 3:B and nominally pure SLN, CLN crystals contain only one band in the area 850–900 cm−1. The width of this band depends on the Li/Nb value. This band width is minimal in SLN and maximal in CLN crystal spectrum, Table1. −1 An 850 cm Raman band width has an intermediate value in LiNbO3:B (0.55–0.83 mol%) crystals, Table1. The character of the Me 1-O-Me2 bridge bond is determined not only by the Me-O bridges strength in octahedra. Widening of bands in the 850–900 cm−1 area is determined by the fact that Nb cations are located in different sites in octahedra, their concentration is quite high and they interact weakly between each other [2]. Changes in LN crystals Raman spectra in the area of stretching bridge vibrations correlate with changes observed in IR spectra, Figure7. This result conﬁrms conclusions of a theoretical work [ 56] and experimental data [29,52]. Crystals 2021, 11, 458 14 of 37

Papers [57,58] have clearly indicated that the ratio Irel = I3480/I3465 between intensities of 3480 and 3465 cm−1 IR bands almost linearly decreases with an increase in −1 R = Li/Nb ratio. Note that Irel = 0 if the 3480 cm band is absent from the spectrum. Evaluation of Irel allows one to determine R with higher precision (0.01 mol% Li2O) than other methods [57,58]. For example, determination of Li2O concentration due to Curie temperature has an error 0.1 mol% Li2O. A ratio Irel = I3480/I3465 = 0.78 for an SLN crystal studied in our research. This means that R = Li/Nb = 0.98. This result is different from data obtained by Raman spectroscopy: at R = 1 a low-intense 120 cm−1 band should be absent from SLN spectrum, Figure5. Changes can be explained by the following: 120 cm −1 Raman band is sensitive only towards the R = Li/Nb ratio (which automatically include all −1 point and complex defects); 3466 cm IR band is sensitive only towards NbLi–OH complex defects. This is why R determined due to IR spectra is smaller, than that determined due to Raman spectra. A Li/Nb ratio can also be calculated with a high precision (up to 0.01 mol%) from a fundamental absorption edge [59]. However, this kind of experiment should be carried out at ﬁne plates (0.5–1.0 mm) of LN crystals. Moreover, studied samples must not have additional absorption bands in the fundamental absorption edge, as it is in crystals doped by multiply charged cations Fe, Cu, etc. Empirical formulae for Li/Nb evaluation in nominally pure LN crystals were suggested in [59]. The formulae apply data on fundamental absorption edge: 2 Li/Nb = 1 − ((λ20 − 301.5)/81.29) (1)

where λ20—fundamental optical absorption edge corresponding to a wavelength at an absorption coefﬁcient α = 20 cm−1. Knowing Li/Nb value, one can calculate concentration of point defects in LN crystal. 4+ − Due to a Li-vacancies compensation model [2], concentration of NbLi and VLi point defects in mol% in a crystal lattice of nominally pure LN crystals can be calculated due to a formula [59]: C(VLi) = ((4 − 4 × Li/Nb)/(5 + Li/Nb)) × 100 (2)

C(NbLi) = C(VLi)/4 (3) Paper [59] offers a model for determination of Li/Nb ratio in crystals that have absorption bands directly in the region of the fundamental absorption edge. Ratio of the integrated intensity of the band with a maximum at 3466 cm−1 (A ) to the total integrated in- int, II R R tensity of the IR absorption spectrum (Aint, I)(Aint, II /Aint, I = α1(ν)dv/ α(ν)dv) was determined for each crystal’s spectrum. In the formula α(ν)—absorption coefﬁcient in dependence on wavelength in cm−1. A Li/Nb ratio can be determined in crystals doped by photochrome or photorefractive cations absorbing in visible or UV spectral area due to the obtained Aint, II /Aint, I value and Li/Nb ratio [59]. This method can obviously be applied for other cases; for example, for LN crystal samples with a width >1 mm, when fundamental optical absorption edge λ20 is impossible to determine. In this paper we have used samples with a width Z = 4 mm. Our 4+ − calculations concerning Li/Nb and NbLi and VLi point defects concentration obtained due to the abovementioned formulae are demonstrated in Table2. A Klauer [60] method can be applied to calculate concentration of OH-groups:

C(OH) = Aint, I /((ln 10)·aOH) (4)

where C(OH)—concentration of OH defects in a sample, (cm−3), A —a total inte- int, I R gral intensity of IR spectrum in the OH stretching vibrations area (Aint, I = α(ν)dv, −1 α(ν)—absorption coefﬁcient in dependence on wavelength in cm ), aOH—intensity if ion absorption = (9.125 ± 1.369) × 10−18 cm [60,61]. Calculation results are demonstrated in Table2. Concentration of OH-groups is minimal in SLN and maximal in LiNbO3:B (0.55 and 0.83 mol%) crystal, Table2. CLN and LiNbO3:B(0.69 mol%) crystals have an intermediate value of OH groups, Table2. Crystals 2021, 11, 458 15 of 37

A decrease in the amount of bonded OH groups apparently leads to an increase in free protons in LN crystals, which can inﬂuence electrical conductivity of the crystals and Crystals 2020, 10, x FOR PEER REVIEWdecrease photorefractive effect. 15 of 37

3.3. Study of LiNbO :B Crystals Optical Uniformity by PILS and Laser Conoscopy 3.3. Study of LiNbO33:B Crystals Optical Uniformity by PILS and Laser Conoscopy WeWe have have studied studied optical optical uniformity uniformity of of crystals crystals by by laser laser conoscopy conoscopy at at laser laser radiation radiation (λ = 532 nm) power p = 1 and 90 mW, Figure8. When conoscopic patterns of LN crystals (λ0 0 = 532 nm) power p = 1 and 90 mW, Figure 8. When conoscopic patterns of LN crystals atat low low power power differ differ from from pattern pattern of of a a perfect perfect crystal, crystal, it it means means that that changes changes are are caused caused by by defects, mechanical stresses, or compositional heterogeneity. Conoscopic pattern distortions defects, mechanical stresses, or compositional heterogeneity. Conoscopic pattern distor- at high-power radiation are caused by laser-induced static and ﬂuctuating defects. Laser tions at high-power radiation are caused by laser-induced static and fluctuating defects. conoscopy and PILS method are unable to provide direct information about crystals Laser conoscopy and PILS method are unable to provide direct information about crystals intrinsic structure and defects type. However, they detect information on the optical intrinsic structure and defects type. However, they detect information on the optical ho- homogeneity and photorefractive properties of crystals. mogeneity and photorefractive properties of crystals.

FigureFigure 8.8. PILS speckle-structure speckle-structure ( (pp == 160 160 mW) mW) after after 60 60s of s irradiation of irradiation and and conoscopic conoscopic patterns patterns (p = 1 and 90 mW) of SLN (1), CLN (2) and LiNbO3:B (0.55 (3), 0.69 (4), 0.83 (5), 1.24 (6) mol%). The (p = 1 and 90 mW) of SLN (1), CLN (2) and LiNbO :B (0.55 (3), 0.69 (4), 0.83 (5), 1.24 (6) mol%). The figure is reproduced with the permission of Pleiades3 Publishing from the paper N. V. Sidorov et. ﬁgure is reproduced with the permission of Pleiades Publishing from the paper N. V. Sidorov et al., al., Techn. Phys. 2018 V. 63 P. 1758–1766, DOI: https://doi.org/10.1134/S1063784218120198 (accessed Techn.on 26 Phys.March2018 2021).V. 63 P. 1758–1766, DOI: https://doi.org/10.1134/S1063784218120198 (accessed on 26 March 2021).

Figure 8 shows that conoscopic patterns of studied LiNbO3:В crystals at both exciting Figure8 shows that conoscopic patterns of studied LiNbO :B crystals at both exciting radiation powers correspond to a pattern of a perfect single3 axis LN. Thus, conoscopic radiation powers correspond to a pattern of a perfect single axis LN. Thus, conoscopic patterns confirm optical single axis in LiNbO3:В (0.55–1.24 mol%) crystals, Figure 8. Slight patterns conﬁrm optical single axis in LiNbO :B (0.55–1.24 mol%) crystals, Figure8. Slight signs of anomalous optical biaxiality are observ3 ed only on a 90 mW conoscopic pattern of signs of anomalous optical biaxiality are observed only on a 90 mW conoscopic pattern a LiNbO3:В (0.83 mol%) crystal, Figure 8. A “Maltese cross” is deformed in the center, of a LiNbO :B (0.83 mol%) crystal, Figure8. A “Maltese cross” is deformed in the center, fragments 3are shifted from its center; angle between branches is not 90°; isochromes are fragments are shifted from its center; angle between branches is not 90◦; isochromes are slightly oval, however their geometry is not distorted. Appearance of anomalous biaxiality can be caused by the existence of local micro-regions and clusters with birefringence in the crystal. In addition, observed distortion in LiNbO3:В (0.83 mol%) crystal conoscopic patterns can be associated with an increase in the effect of photorefraction, Figure 8.

Crystals 2021, 11, 458 16 of 37

slightly oval, however their geometry is not distorted. Appearance of anomalous biaxiality can be caused by the existence of local micro-regions and clusters with birefringence in the crystal. In addition, observed distortion in LiNbO3:B (0.83 mol%) crystal conoscopic patterns can be associated with an increase in the effect of photorefraction, Figure8. PILS is a direct consequence of the photorefractive effect. It arises in a ferroelectric crystal on defects induced by exciting radiation with ﬂuctuating refractive index, dielectric constant, and other physical parameters [62,63]. Laser radiation scattered by such defects interferes with pumping, forming a complex pattern of minima and maxima of the scattered light intensity (speckle structure), Figure8. It causes strong laser beam destruction in the crystal; it is an interfering factor for the radiation generation and conversion [4]. The shape and features of the PILS indicatrix speckle structure depend on the crystal structure, the state of its defectiveness, as well as on the radiation polarization and the experiment geometry [62,64]. The time and opening angle of the PILS indicatrix determine the response speed of the electro-optical modulators and gates. PILS parameters are determined by the depth of traps, the mobility of electrons responsible for the magnitude of the photorefractive effect, as well as the interaction of laser radiation with a defective crystal [62]. Figure8 demonstrates PILS patterns of studied crystals. The time of full PILS indicatrix speckle structure opening for the above crystals is 60 s. According to PILS data, a crystal LiNbO3:B (1.24 mol%) possesses the highest optical damage resistance. PILS speckle structure indicatrix of this crystal does not open even at a high excitation radiation power 160 mW, despite other crystals, Figure8. Conoscopic and PILS patterns show that structure uniformity of LiNbO3:B is similar to that of a CLN crystal and is much higher than that in a SLN crystal, Figure8. Note that photorefractive effect is much higher in SLN than in ◦ CLN and LiNbO3:B (0.55–1.24 mol%) crystals. An SLN crystal PILS opening angle θ is 56 ; ◦ it does not exceed 22 in LiNbO3:B (0.55–1.24 mol%) crystals, Figure6, Table3.

Table 3. Photoelectric PILS parameters and bandgap of LN crystals at T = 25 ◦C. Table is reproduced with the permission of Pleiades Publishing from papers N. V. Sidorov et al., Techn. Phys. 2020 V. 65 P. 627–634, DOI: https://doi.org/10.1134/S1063784220040192 (accessed on 26 March 2021).

λ = 532.0 nm, I ~ 6.29 W/cm2 ◦ Crystal θ, λK, nm ∆Eg, eV Epv, V/cm ED, V/cm SLN 56 367 3.38 4055 1749 * CLN 328 3.78 5003 52

LiNbO3:B (0.55 mol%) 14 367 3.38 5458 572

LiNbO3:B (0.83 mol%) 22 368 3.37 5554 25 * PILS indicatrix does not open for CLN even at exciting radiation I ~ 6.29 W/cm2.

It is a known fact that SLN crystals have non-uniform refractive index along the growth axis, while in CLN crystals it is stable. Photorefractive effect manifests itself much stronger in SLN crystals, than in CLN crystals [2,65]. A change in the structure and properties of a melt, as well as crystal doping, adds levels in the band gap and thereby changes the photorefractive properties and electrical conductivity of the crystal. The crystal LiNbO3:B (0.83 mol%, direct doping) is photorefractive, has a pronounced PILS and is characterized by a uniform refractive index along the growth axis, as evidenced by a clear conoscopic pattern, Figure8. At the same time, the crystal LiNbO 3:B (1.24 mol%, homogeneous doping) has a reduced effect of photorefraction; a more blurred conoscopic pattern indicates the presence of ﬂuctuations in the refractive index along the polar axis. A similar, but much more diffuse conoscopic pattern is observed for SLN crystal, Figure8. At the same time, a discontinuous structure of the laser beam is observed when it propagates along the polar axis in SLN, (Figure 21 in [66]). This indicates a much higher inhomogeneity of the refractive index in SLN in comparison with the LiNbO3:B (1.24 mol%, homogeneous doping) crystal. For other crystals under study, a discontinuous structure of the laser beam has not been observed yet. Crystals 2021, 11, 458 17 of 37

A decrease in the photorefractive effect can be due to a change in the band structure and electro-optical properties of the crystal due to the structuring of the melt with boron. A low photorefractive effect value in the LiNbO3:B (1.24 mol%, homogeneous doping) Crystals 2020, 10, x FOR PEER REVIEW 17 of 37 crystal can be explained by a change in the electro-optical properties of the crystal. Due to works [67,68], a change in electro-optical coefﬁcients in nominally pure LN crystals at change in Li/Nb ratio leads to a change in ionic contribution to the magnitude of the elec- a change in Li/Nb ratio leads to a change in ionic contribution to the magnitude of the tro-optical effect. We assume that boron influence leads to such a structuring of a melt electro-optical effect. We assume that boron inﬂuence leads to such a structuring of a melt that crystals grown from the melt have a more strict crystal structure compared to CLN that crystals grown from the melt have a more strict crystal structure compared to CLN crystals, in which МеO6 octahedra have less ability to deform. crystals, in which MeO6 octahedra have less ability to deform.

3.4. Investigation of Photovoltaic Fields and Bandgap in LiNbO3:В Crystals by PILS and Optical 3.4. Investigation of Photovoltaic Fields and Bandgap in LiNbO3:B Crystals by PILS and OpticalSpectroscopy Spectroscopy

Figure9 9 demonstrates demonstrates opticaloptical absorptionabsorption spectraspectra ofof SLN,SLN, CLN,CLN, andand LiNbOLiNbO33::BВ (0.55, 0.83 mol%) crystals. The absorption edge of LiNbO3:B:B crystals crystals is is shifted shifted to to longer wavelengths compared toto thethe absorption edgeedge ofof SLN,SLN, CLN crystals. At this, absorption spectra of LiNbO3:B:B crystals crystals has has a steeper rise in comparisoncomparison with SLN.SLN. ThisThis indicatesindicates aa higherhigher optical uniformity of crystals grown fromfrom aa boron-dopedboron-doped charge.charge. ItIt isis believedbelieved thatthat NbNbLiLi defects bring the main contribution to the change in the position of the fundamental absorption edge in nominally pure CLN crystals [[2,59].2,59]. Thus, we can draw conclusions about the mechanism of non-photorefractive impuritiesimpurities incorporationincorporation intointo thethe crystalcrystal lattice.lattice.

Figure 9. AbsorptionAbsorption spectra ofof SLNSLN (1),(1), CLNCLN (2)(2) and and LiNbO LiNbO3:B3:B (0.55 (0.55 (3), (3), 0.83 0.83 (4) (4) mol%). mol%). The The figure figure is reproducedis reproduced with with the the permission permission of Pleiades of Pleiades Publishing Publishing from from the paper the paper N. V. N. Sidorov V. Sidorov et al., et.Techn. al. Phys. 2020Techn.V. Phys 65 P.. 627–634,2020 V. 65 DOI: P. 627–634, https://doi.org/10.1134/S1063784220040192 DOI: https://doi.org/10.1134/S1063784220040192 (accessed on 26(accessed March 2021).on 26 March 2021). Coincidence of the concentration dependences of NbLi defects and the Urbach parameter onCoincidence the Li/Nb of ratio the concentration in the crystal dependences has been spotted of Nb inLi adefects paper and [59]. the This Urbach agrees param- with theeter conclusionson the Li/Nb of ratio [69] in that the the crystal Urbach has absorptionbeen spotted occurs in a paper in the [59]. LN crystalThis agrees as a resultwith the of theconclusions transition of of [69] electrons that the from Urbach the ﬁlled absorption states “2p”occurs of oxygenin the LN to thecrystal empty as a states result “4d” of the of niobium.transition Aof decreaseelectrons in from the concentrationthe filled states of “2p” NbLi ofdefects oxygen as theto the Li/Nb empty ratio states approaches “4d” of unityniobium. leads A todecrease a fundamental in the concentration absorption edge of Nb shiftLi defects toward longeras the Li/Nb wavelengths ratio approaches as a result ofunity a decrease leads to ina fundamental the density of absorption local states edge associated shift toward with longer NbLi defects wavelengths near the as bottoma result of thea decrease conduction in the band. density The of transition local states of associated electrons from with the Nb valenceLi defects band nearto the these bottom states of isthe possible conduction in LN band. under The the transition light. Figure of electron9 demonstratess from the thatvalence CLN band absorption to these edgestates is is maximallypossible in shiftedLN under to short-wavelengththe light. Figure 9 region. demonstrates Table2 showsthat CLN that absorption for CLN Li/Nb edge =is 0.942,maxi- mally shifted to short-wavelength region. Table 2 shows that for CLN Li/Nb = 0.942, С(VLi) = 3.90 mol% and С(NbLi) = 0.98 mol%. It is a known fact that CLN crystals have Li deficiency near 6 mol% (Li/Nb = 0.946) [2]. According to the compensation of Li-vacancies model, the crystal lattice of a CLN crystal contains ~1 mol% NbLi4+ point defects and ~4 mol% VLi- point defects [54,70]. At the same time, NbLi4+ is completely absent from a perfect SLN crystal structure. LiNbO3:В (0.55 and 0.83 mol%) crystals have ordering of structural

Crystals 2021, 11, 458 18 of 37

C(VLi) = 3.90 mol% and C(NbLi) = 0.98 mol%. It is a known fact that CLN crystals have Li deficiency near 6 mol% (Li/Nb = 0.946) [2]. According to the compensation of Li-vacancies 4+ model, the crystal lattice of a CLN crystal contains ~1 mol% NbLi point defects and − 4+ ~4 mol% VLi point defects [54,70]. At the same time, NbLi is completely absent from a perfect SLN crystal structure. LiNbO3:B (0.55 and 0.83 mol%) crystals have ordering of structural units of the cation sublattice and the content of NbLi and VLi point defects between SLN and CLN [24]. Approximation to stoichiometry in LiNbO3:B crystals is possible by binding excess niobium in a congruent melt due to the complexing ability of boron compounds [24]. Obviously, the position of the fundamental absorption edge is determined not only by the concentration of NbLi and VLi point defects. The number of shallow electron traps depends significantly on the Li/Nb ratio [2,7,12,71]. Under laser radiation a spatial charge separation occurs and an internal electric field arises, leading to a photoinduced change in refractive indices in LN crystal as a result of photoexcitation processes (photovoltaic and diffusion current) [7,12,63,71]. Photovoltaic Epv and diffusion ED fields presented in Table3 were calculated due to formulae [31]:

λ(Γ + Γ ) = −c +c Epv h in in i (5) 3 p in θs 2 p in in θs 2π ne r33 cos θs cos 2 + nen0r51 tan θs sin θs sin 2

λ(Γ − Γ ) = −c +c ED h in in i (6) 3 p in θs 2 p in in θs 2π ne r33 cos θs cos 2 + nen0r51 tan θs sin θs sin 2

in where Epv—photovoltaic field, ED—diffusion field, λ—wavelength, θs —scattered radiation angle, Γ−c and Γ+c—amplification factors (indices “−” and “+” indicate the direction of the scattered radiation against and along the direction of the crystal polar axis, respectively), ne and no—refractive indices of the extraordinary and ordinary rays, respectively, r33 and r51—LN electro-optical coefficients. in An amplification factor Γ θs can be calculated in dependence on PILS opening angle due to a formula [31]: in 1 Is θ Γ θin = ln s (7) s in Ω in le f f θs Iso θs Ω where Is—scattered radiation intensity, Iso —primary scattering intensity (incident beam), le f f —The effective interaction interval, which is calculated depending on the scattering angle, according to the following formulas [31]:

d w = in < p le f f in , for θs arctan (8) cos θs 2d w w = p in ≥ p le f f in , for θs arctan (9) 2 sin θs 2d

where d—crystal thickness, wp—laser beam diameter. Figures 10 and 11 demonstrate angular distribution of the scattered radiation intensity at different wavelengths and dependences ED (a) and Epv (b) on the wavelengths in studied LN crystals. The band gap for the studied crystals is in the range 3.37–3.78 eV, Table3. The least band gap was observed in LiNbO3:B and SLN, Table3, the greatest—in CLN (3.78 eV). Due to [72], a pure CLN crystal band gap is 3.72 eV, which is close to the value characteristic of wide-gap semiconductors. Crystals 2020, 10, x FOR PEER REVIEW 2 of 38

characterized by high values of photoelectric fields and photorefraction effect. The latter can be varied in a very wide range [1,2,8]. Optical damage resistance can be increased in congruent LN (CLN, R = Li/Nb = 0.946) crystals by their doping with non-photorefractive (Me: Zn, Mg, In, etc.) cations [2]. Unlike multiply charged photorefractive cations, they do not change their charge state in the crystal (they are not electron donors) under the action of optical radiation. The influence of such dopants on crystal properties is caused by their ability to change the amount of point defects and linked molecular complexes in the crystal cation sublattice. The molecular complexes in question can be caused by OH groups in the crystal structure [1,2,9–11]. Point defects NbLi are Nb5+ cations in the Li+ sites of a perfect stoichiometric (SLN, R = 1) LN composition. They, along with transition metal impurities (for example, Fe), are deep electron traps and influence photorefractive effect the most [1,2]. Moreover, a LN structure contains a lot of shallow electron traps besides NbLi that influence photorefractive effect [12]. The complexity of LN doping task increases provided that significant concentrations of metal dopants inevitably lead to a disorder in optical and structural uniformity of a single crystal [1,2,9–11,13].

Crystals 2021, 11, 458 19 of 37

Crystals 2020, 10, x FOR PEER REVIEW 19 of 37

Figure 10. Angle distribution of scattered radiation intensity at excitation λ = 476.5 (a), 488.0 (b),

514.5Figure (c ),10. 530.9 Angle nm distribution (d) for the crystalsof scattered SLN radiation (1), CLN intensity (2) and LiNbO at excitation3:B (0.55 λ (3),= 476.5 0.83 ( (4)а), mol%).488.0 (b The), Moreover, LN crystal grown at air always contain 1016–1018 cm–3 protons bonded with ﬁgure514.5 ( isc), reproduced 530.9 nm (d with) for thethe permissioncrystals SLN of (1), Pleiades CLN (2) Publishing and LiNbO from3:B the(0.55 paper (3), 0.83 N. V. (4) Sidorov mol%). et The al., oxygenfigure by ais hydrogen reproduced bond. with theHydrogen permission atoms of Pleiades form such Publishing complex from defects the paper as V LiN.-OH, V. Sidorov NbLi- et. Techn. Phys. 2020 V. 65 P. 627–634, DOI: https://doi.org/10.1134/S1063784220040192 (accessed on OH, etc.,al., Techn. [7,14,15]. Phys. 2020OH-groups V. 65 P. 627–634,play important DOI: https://doi.org/10.1134/S1063784220040192 role in formation of a secondary defect(accessed 26 March 2021). on 26 March 2021).

FigureFigure 11. DependenceDependence of of EDE (Dа)( aand) and Epv E(bpv) on(b) wavelength on wavelength for the for crystals the crystals SLN (1), SLN CLN (1), (2) CLN and (2) LiNbO3:B (0.55 (3), 0.83 (4) mol%). The figure is reproduced with the permission of Pleiades Pub- and LiNbO3:B (0.55 (3), 0.83 (4) mol%). The ﬁgure is reproduced with the permission of Pleiades Publishinglishing from from the paper the paper N. V. N. Sidorov V. Sidorov et. al., et Techn. al., Techn. Phys. 2020 Phys. V. 202065 P. V.627–634, 65 P. 627–634, DOI: DOI: https: https://doi.org/10.1134/S1063784220040192 (accessed on 26 March 2021). //doi.org/10.1134/S1063784220040192 (accessed on 26 March 2021).

AA predominantpredominant photorefractionphotorefraction mechanismmechanism inin aa LNLN crystalcrystal isis photovoltaic,photovoltaic, whichwhich pv meansmeans thatthat the the value value of of the the photovoltaic photovoltaic field field (E pv(E) is) muchis much greater greater than than that that of the of diffusionthe diffu- D fieldsion (EfieldD)[ (E71].) [71]. Table Table3, Figures 3, Figures 10 and 10 11 and show: 11 show: an increase an increase in photovoltaic in photovoltaic field field in a LN in a crystalLN crystal is accompanied is accompanied with with an an increase increase in in PILS PILS scattering scattering angle angleθ θand and an an asymmetry asymmetry ofof itsits indicatrix. The The photovoltaic photovoltaic field field EpvE determinespv determines the themagnitude magnitude of the of induced the induced bire- birefringencefringence (the (the effect effect of ofphotorefraction). photorefraction). SLN SLN has has the the least least ЕEpvpv atat 476.5, 476.5, 488.0, 514.5,514.5, andand 530.9530.9 nmnm excitation.excitation. Thus,Thus, aa diffusiondiffusion chargecharge transporttransport mechanismmechanism isis manifestedmanifested inin SLNSLN strongerstronger thanthan inin otherother crystals.crystals. ThisThis picturepicture isis characteristiccharacteristic ofof crystalscrystals withwith aa largelarge numbernumber ofof shallowshallow electronelectron traps.traps. AA dependencedependence ofof EЕpvpv has a maximum at excitation by 514.5 nm for all studied crystals,crystals, butbut LiNbOLiNbO33:B:В (0.55(0.55 mol%),mol%), FigureFigure 11 11.. AtAt the the same same time, time, E Еpvpv valuesvalues ofofLiNbO LiNbO33:B:В (0.55(0.55 andand 0.830.83 mol%)mol%) crystalscrystals areare close:close: 54585458 andand 55545554 V/cm, V/cm, respectively.respectively. CuriousCurious thatthat EEDD ofof aa LiNbOLiNbO33:B:В (0.83(0.83 mol%)mol%) crystalcrystal isis closeclose toto thatthat ofof aa CLN.CLN. ThisThis maymay indicateindicate anan almostalmost equal equal numbernumber ofof shallowshallow electronelectron trapstraps inin thesethese crystals. crystals. EEDD valuevalue ofof aa LiNbOLiNbO33:B:В (0.55(0.55 mol%)mol%) crystalcrystal isis largerlarger thanthan thatthat ofof CLNCLN andand LiNbOLiNbO33:B:В (0.83(0.83 mol%)mol%) crystals;crystals; atat thethe samesame time,time, its its PILSPILS indicatrixindicatrix openingopening angleangle isis minimal,minimal, TableTable3 .3.

Crystals 2021, 11, 458 20 of 37 Crystals 2020, 10, x FOR PEER REVIEW 20 of 37

3.5. Chemical Interactions in Systems Li2O–Nb2O5, Li2O–B2O3–Nb2O5; Particularities of LN 3.5.Crystallization Chemical Interactions from Melts inwith Systems Non-Metal Li2O–Nb Dopants2O5, Li 2O–B2O3–Nb2O5; Particularities of LN Crystallization from Melts with Non-Metal Dopants Solid-phase chemical reactions with the formation of various borates occur in the Solid-phase chemical reactions with the formation of various borates occur in the process of high-temperature synthesis of the charge in the Li2O–B2O3–Nb2O5 system. To process of high-temperature synthesis of the charge in the Li O–B O –Nb O system. To evaluate the melt–crystal system, it is advisable to use the distribution2 2 3 coefficients2 5 КD and evaluate the melt–crystal system, it is advisable to use the distribution coefficients K the ∆С parameter. КD is the ratio of the impurity concentration in the crystal at the initialD andmoment the ∆ ofC growth parameter. and KtheD isimpurity the ratio concentration of the impurity in the concentration melt, ∆С characterizes in the crystal the at com- the initialpositional moment uniformity of growth of the and crystal; the impurityit is defined concentration as the difference in the between melt, ∆ Cthe characterizes dopant con- thecentration compositional at the cone uniformity and the ofend the of crystal; the crystal. it is definedA crucial as particularity the difference of between boron is the its dopant concentration at the cone and the end of the crystal. A crucial particularity of boron ability to change LiNbO3:В melt and crystal structure without incorporation to the crystal. is its ability to change LiNbO3:B melt and crystal structure−4 without incorporation to the Its effective distribution coefficient (КD) is only ~3·10 [19,20,25].− Such4 small values of the crystal. Its effective distribution coefficient (KD) is only ~3 × 10 [19,20,25]. Such small boron distribution coefficient in the Li2O-Nb2O5–B2O3 system are due to the fact [73] that values of the boron distribution coefficient in the Li2O–Nb2O5–B2O3 system are due to boron should not incorporate into the LiNbO3:В crystal, since the LN phase has no region the fact [73] that boron should not incorporate into the LiNbO :B crystal, since the LN of boron solubility in the solid state, Figure 12. The small amount3 of boron that does in- phase has no region of boron solubility in the solid state, Figure 12. The small amount of corporate into the LN structure can be either be mechanically captured or incorporate into boron that does incorporate into the LN structure can be either be mechanically captured the tetrahedral voids of the crystal structure. Note that boron В3+ has a small ion radius. or incorporate into the tetrahedral voids of the crystal structure. Note that boron B3+ Quasi-double diagrams are polythermal sections of the general quasi-ternary diagram of has a small ion radius. Quasi-double diagrams are polythermal sections of the general the state of systems Li2O-Nb2O5–B2O3: LiNbO3–LiBO2, and LiNbO3–Li3B2O4.5. These cross quasi-ternary diagram of the state of systems Li2O–Nb2O5–B2O3: LiNbO3–LiBO2, and sections have a simple form, since they contain only one two-phase eutectic transfor- LiNbO3–Li3B2O4.5. These cross sections have a simple form, since they contain only one two-phasemation each eutectic and have transformation no solubility regions, each and Figure have 12, no [73]. solubility This type regions, of phase Figure diagram 12,[73 is]. generally favorable for the quality of the growing LiNbO3:В crystal since crystallization This type of phase diagram is generally favorable for the quality of the growing LiNbO3:B crystalproceeds since from crystallization the two-phase proceeds region fromand the two-phaseonly crystallizing region andphase the is only LN.crystallizing If we disre- phasegard the is LN.radical If we change disregard in the thestructure radical of change the melt in upon the structure doping with of the boron, melt crystal upon doping grown withfrom boron,such a crystalmelt should grown chemically from such and a melt stru shouldcturally chemically correspond and to structurally a CLN grown correspond from an undoped melt. Wherein studied LiNbO3:В crystals have NbLi defects amount close to that to a CLN grown from an undoped melt. Wherein studied LiNbO3:B crystals have NbLi of an SLN crystal. Moreover, the LiNbO3:В crystal has a more ordered structure than CLN defects amount close to that of an SLN crystal. Moreover, the LiNbO3:B crystal has a more [25]. Note that NbLi are the deepest electron traps responsible for the photorefractive ef- ordered structure than CLN [25]. Note that NbLi are the deepest electron traps responsible forfect. the The photorefractive reason for this effect. is apparently The reason an elec fortronic this is structure apparently of anboron: electronic it is a strong structure com- of boron:plexing itelement is a strong due complexingto 1 electron element at a p–orbi duetal. to 1The electron electron at aprovides p–orbital. high The ionization electron providesenergies and high electronegativity ionization energies values and at electronegativitya small ionic radius, values which at aleads small to ionica significant radius, whichchange leads in the to structure a significant of the change boron-containing in the structure melt. of the boron-containing melt.

Figure 12. Polythermal sections of the state diagram of a quasi-ternary system Li O–Nb O –B O : LiNbO –LiBO (a), Figure 12. Polythermal sections of the state diagram of a quasi-ternary system 2Li2O–Nb2 2O5 5–B2 2O33: LiNbO33–LiBO2 (a), b LiNbOLiNbO33–Li3BB22OO4.54.5 (b() )[[73].73].

Table4 demonstrates ∆C and KD for exact B, Mg, Zn, and Ce dopants concentrations Table 4 demonstrates ∆С and КD for exact B, Mg, Zn, and Ce dopants concentrations in the melt. The necessity to use KD and ∆C is substantiated in detail in the works [27,74]. in the melt. The necessity to use КD and ∆С is substantiated in detail in the works [27,74]. The distribution coefﬁcient KD for doped (B, Zn, Mg, and Ce) LN crystals is clearly a The distribution coefficient КD for doped (B, Zn, Mg, and Ce) LN crystals is clearly a func- function of the electronic structure of the dopant; the ∆C case is not so obvious, Table4. tion of the electronic structure of the dopant; the ∆С case is not so obvious, Table 4. The The ∆C parameter value is quite small for all studied dopants except Zn. In fact, the value ∆С parameter value is quite small for all studied dopants except Zn. In fact, the value is is comparable to the error of the method for determining the dopant concentration, Table4. comparable to the error of the method for determining the dopant concentration, Table 4.

Crystals 2021, 11, 458 21 of 37

Table 4. Concentration characteristics of LN doped with dopants with different electronic conﬁgura- tion. Table is reproduced with the permission of Pleiades Publishing from the paper O.V. Makarova et al., Techn. Phys. 2019 V. 64 P. 1872–1878, DOI: https://doi.org/10.1134/S1063784219120168 (accessed on 26 March 2021).

B, 0.12 wt% in Mg, 0.93 wt% in Zn, 3.04 wt% in Ce, 1.1 wt% in Element the Melt the Melt the Melt the Melt Electronic conﬁguration [He] 2s22p1 [Ne] 3s2 [Ar] 3d104s2 [Xe] 4f26s2 Ion radius, pm 23 (+3e) 66 (+2e) 74 (+2e) 103.4 (+3e) Electronegativity 2.01 1.2 1.60 1.2 First ionization potential, eV 8.29 7.64 9.39 5.65 −4 KD 3 × 10 0.9 0.77 0.32 ∆C, wt% 1.2 × 10−6 0.01 0.095 0

Table4 data reveal high concentration uniformity in dopant distribution along the polar axis at a KD coefficient strongly different from the unity. This is especially charac- −6 teristic of LiNbO3:B crystals, in which KD << 1 and ∆C ~ 10 wt%. The explanation of this fact can be the following. The initial LN charge composition ceases to be congruent with the addition of dopant, Figure 12. This, in particular, means that the spectrum of variations of ionic complexes in the melt in terms of structure and components greatly increases. The melt is trapped in a limited zone near the crystallization front, which has a constant temperature. Consequently, those ionic complexes for which this temperature is solidus (Tc1) will crystallize, naturally, taking into account some supercooling. As part of the volume of the melt is consumed, the concentration of the dopant (in our case, boron) in the remaining melt increases and the ratio of the concentrations of various ionic complexes changes. Accordingly, the fraction of ionic complexes for which the temperature Tc1 is the solidus temperature will also change, it will become noticeably less. This will continue until the system reaches a certain critical state, at which the concentration of complexes with solidus temperature Tc1 is insufficient for the growth of a crystal with a constant dopant concentration. This circumstance limits the fraction of the melt that can be crystallized to obtain a compositionally uniform LiNbO3:B crystal. Upon reaching the described critical state, the further behavior of the system can be different: from a significant change in the dopant concentration distribution along the growth axis to defects such as cellular growth and crystallization of a different composition phase, Figure3[ 19,27,74]. Many factors affect the conditions for reaching such a critical state, and hence the possible dimensions of a LiNbO3:B crystal of high optical quality with a constant dopant concentration distribution in the crystal boule volume. This is the composition of the melt, the thermodynamics of the initial components, the graphical expression of which is the phase diagram, the structure of the melt consisting of ionic complexes with different thermodynamic and kinetic characteristics, and even the technical capabilities (sensitivity and reaction time constant) of the control and monitoring system of the growth process. An important conclusion follows from the above reasoning for the technology of doped lithium niobate crystals: LN crystals with a uniform distribution of dopant can be grown by Czochralski at KD that is noticeably different from unity during crystallization of only a well-defined part of the melt. Consequently, the length and diameter of such a LN crystal boule is limited. In different systems, the limiting sizes of such structurally and compositionally uniform crystals will differ markedly. Moreover, for different systems, there may be different physical and chemical reasons for this, expressed in the difference in the thermodynamic parameters of the systems, that is, in the form of phase diagrams. LN has no regions of homogeneity with either boron or its compounds in the boron-containing system Li2O–Nb2O5–B2O3. As the crystal grows, only the pure LN phase crystallizes, Figure 12. However, at the same time, there will be a significant increase in the boron content in the melt and, as a consequence, a decrease in the crystallization temperature and a rather radical increase in the melt viscosity, which limits convective flows, Figure 12. C0, Crystals 2021, 11, 458 22 of 37

C1 and C2—the composition of the melt or the concentration of boron in the melt, T1 and T2 are the crystallization temperature corresponding to the composition of the C1 and C2. All this, most likely, limits the maximum possible boron concentration in the melt to 0.12 wt%, since an increase in the boron concentration above this critical concentration in the melt leads to cellular growth and other irreparable defects (for example, defects in the form of “channels”) in LiNbO3:B crystals, Figures1–3,[ 19,25]. Our studies have shown that the fraction of the melt, the crystallization of which leads to the production of an optically uniform LiNbO3:B crystal, does not exceed 17–18% [19,25]. The above reasoning is valid for evaluating the technological growth parameters when doping lithium niobate with any dopants. For example, the phase diagram of the Li2O– Nb2O5–MgO system is less complex than that of the system Li2O–Nb2O5–ZnO [75,76]. The Zn diagram has a greater number of phases and they are less stable; the concentration regions of existence of different phases and mixtures of phases are less extended [75]. These physical and chemical particularities of a Zn system explain a greater number of concentration thresholds at LN doping with Zn rather than Mg. The particularities also explain LiNbO3:Zn crystals tend to cracking and separation of impurity phases during growth [27]. Phase stresses in LiNbO3:Zn crystals are also a consequence of Zn system particularities. The stresses are the reason why these crystals claim special modes of after- growth treatment and turning them to a single domain state [27]. Thus, a volume of a structurally and chemically uniform boule and the fraction of the crystallized melt for LiNbO3:Zn will be less than for LiNbO3:Mg crystals. The fraction of crystallized melt in the case of Li2O–Nb2O5–ZnO system is ≤~20%, Li2O–Nb2O5–MgO system ≤~30% [16,27,74]. The fraction in the case of Li2O–Nb2O5–CeO2 system strongly depends on the initial dopant concentration in the melt; the crystallized melt fraction is significantly lower than in systems with magnesium and zinc. These facts are caused by significantly lower distribution coefficients KD, Table4. This leads to a fast increase in the dopant concentration in the melt and achieving of the critical state at which the complexes concentration with solidus temperature Tc1 is insufficient for crystal growth with a constant dopant concentration. This is why only ≤~12% fraction of the melt should crystallize to turn into a structurally and chemically uniform LiNbO3:Ce crystal [76]. Results obtained in [77] based on the analysis of the dopant electronic structure are important for predicting the technological conditions of growth and the quality control of doped LN crystals. At this, p-elements (non-metals, in our case, boron), which have a higher chemical activity due to the greater number of valence electrons than that of metals, make the melt more homogeneous at the level of ionic complexes. It is exactly this fact that allows us to grow LN crystals from a congruent melt with a defective structure close to one in SLN. Metals (s and d elements, Zn and Mg) have a similar effect on the LN melt and crystals properties. Nevertheless, Zn-doped crystals have an increased ununiformity of dopant incorporation to the crystals, tend to cracking due to phase stresses; they also are characterized by additional claims towards growth conditions and after-growth electrothermal treatment of boules. The f-element metals, due to their electronic structure, form the structure of the melt in such a way that only a relatively small fraction of the melt can be crystallized to obtain a compositionally uniform crystals, for example, LiNbO3:Ce. LN is characterized by a high melting temperature (~1526 K) and a high chemical activity of the melt, which requires platinum crucibles. This is the reason for the extremely small number of works devoted to the study of the structure of even nominally pure LN melts. In recent years, the need has arisen to obtain optically highly perfect LN single crystals (nominally pure and doped). The existence in the melt of strongly bound groups of atoms or ions (clusters) of a certain structure was considered as the main concept in the literature [78]. In [79–81], high-temperature Raman spectroscopy was effectively used to study the crystallization from a melt. In the pre-crystallization temperature of a LN melt, the Raman spectra revealed a noticeable change in the structure of the melt and a mismatch between the structure of anionic motifs in the melt and crystal. The mismatch effect near the melting point creates serious obstacles to the nucleation of equilibrium Crystals 2021, 11, 458 23 of 37

structures [79–81]. Metastable phases have an advantage in crystallization under these conditions. The phases crystal lattice is very far from the structure of the short-range order of the melt. The mismatch in the anionic structure of the melt and crystal can also affect the growth of crystal faces or the formation of structural defects [79,80]. LN structure is a framework of oxygen octahedra O6, articulated by vertices and faces, with the densest hexagonal packing. Inside the octahedra there are intrinsic (Li+ and Nb5+) or doping cations. The bonds in the octahedra occupied by niobium are pre- dominantly covalent [1]. At the same time, the lithium ion is bound to oxygen atoms only by electrostatic interaction. Due to the predominance of the covalent bond type, the niobium cation tends to form in the melt anionic motifs consisting of NbO4 tetrahedra. That is, when LN melts, anionic structure rearranges significantly: the coordination of niobium atoms changes from octahedral to tetrahedral, which is confirmed by Raman spectroscopy data [79–81]. Strong covalent bond implies the ability to preserve the structure of oxyanions in the molten state. Thus, the melt can contain not only isolated tetrahedral groups, but also complexes with a stable structure [79]. Raman studies of Li2O–Nb2O5 system melts have revealed not only bands corresponding to vibrations of terminal NbO3− −1 and middle NbO2− groups (815–870 cm ) but also bands corresponding to symmetric stretching bridge vibrations of Nb–O–Nb bonds (670–690 cm−1). Bridge bands are located at the junction of the tetrahedra [79,80]. Probably, octahedra NbO6 exist in the melt in the pre-crystallization temperature range along with NbO4 tetrahedra. Earlier paper [82] studied Raman spectra of Nb2O5, intended for charge synthesis and LN crystal growth. The study has revealed five bands 814, 845, 902, 965, and 995 cm−1 in the region of stretching bridge vibrations of oxygen atoms along the polar axis (800–1100 cm−1). This indicates a variety of island structures consisting of fragments of chains of octahedra and tetrahedra in niobium pentoxide. Boron is a highly chemically active dopant. Its fundamental properties are change in crystallization temperature, viscosity, and surface tension of melts [83]. We [19] have qualitatively revealed an increase in melt viscosity, in the melting temperature by ~10 K, and the Curie temperature by ~50 K compared to nominally pure CLN crystal during growth of studied LiNbO3:B (0.55–1.24 mol%) crystals. The crystal chemistry of boron oxide compounds is extremely diverse: it is determined by the possibility of double hy- 2 3 3− bridization of the boron atom, sp – and sp –, with the formation of [BO3] triangles and 5− 3+ [BO4] tetrahedra, respectively [84]. Boron neutral atom radius is 0.88 Å; B –0.15 Å for B(III), 0.25 Å for B(IV). In the ground state, boron atoms have the 2s22p1 configuration with one unpaired electron and two vacant p-orbitals. Due to the presence of a free orbital in a small boron atom, boron is one of the strongest acceptors of unshared electron pairs. The use of this orbital in the donor-acceptor interaction allows the coordination number of the boron atom to increase to four. The atoms and atomic groups surrounding the boron atom are located at three corners of the tetrahedron, the fourth corner of which remains free, and a positive electric field of significant intensity is created in this corner. This circumstance explains the pronounced ability of boron compounds to provide stable molecular complexes. Boron triangles and tetrahedra can be present in isolation or polymerize among themselves through a common oxygen atom [84]. The tendency towards formation of bulky polyanions explains the high viscosity of melts [85]. It is well known that alkali metal oxides are modifiers of the boron-oxygen network of the melt and transfer the boron atom to a four-coordinated state, i.e., [BO4] tetrahedra are formed [85]. When boron-oxygen triangles and tetrahedra are combined, the absolute values of specific negative charges for complex anions decrease monotonically in the series of ortho-, pyro-, meta-, and polyborates. This ensures sufficient stability of numerous condensed compounds with monovalent as well as large divalent elements. In [80], temperature changes in lithium metaborate melts were investigated from the Raman spectra. The work has shown the presence of a chain boron-oxygen anion in the melt. All these crystal-chemical laws predetermine the reaction potential of melts containing borates. Crystals 2021, 11, 458 24 of 37

The triple system Li2O–B2O3–Nb2O5 has also been studied in [73,86]. The authors analyzed over 30 different molar ratios of the components. Paper [73] has revealed in the system six different lithium borates (LiB3O5, Li2B4O7, LiBO2, Li6B4O9, Li4B2O5 and Li3BO3), one niobium borate (Nb3BO9) and three different lithium niobates (LiNb3O8, LiNbO3 and Li3NbO4). According to this work, lithium borates exhibit remarkable solubility in LN at temperatures below 1100 ◦C, and thus are suitable for crystal growth as a flux. In addition, the concentration range of LN crystallization, determined by the spontaneous nucleation method, is rather wide in the Li2O–B2O3–Nb2O5 ternary system. There is a known HTTSSG method of growing SLN single crystals with a reduced photorefractive effect from a congruent melt in the presence of K2O flux [36,87,88]. The absence of potassium in the crystal structure becomes evident from a comparison of the ionic radii of Li+ and K+ (0.68 Å and 1.38 Å, respectively). Isomorphic substitution of related elements of the alkaline group (lithium with potassium) in the cationic sublattice of the crystal seems unlikely with such a significant difference in ionic radii. Thus, potassium, like boron, does not incorporate in the crystal structure [89–91]. We assume that boron-containing polyanions, forming stable covalent bonds in the melt with niobium-containing polyanions, thereby bind the excess of niobium and increase the Li/Nb ratio in the melt. As a result, the grown crystal approaches a stoichiometric composition in terms of the cation sublattice ordering degree, in the same way as when using a K2O flux. Such a crystal is characterized by a reduced content of NbLi defects and lithium vacancies (VLi) in comparison with a CLN crystal, Table2. This is confirmed by an increase in Curie temperature (TC) by ~47 K in comparison with a CLN crystal [19]. For a comparable in magnitude change in the TC of a LN crystal doped with metallic impurities (Mg, Zn, etc.), significantly higher impurity concentrations (~2 to 3 wt%) are required. Paper [92] has shown that melts of inorganic polymers that form chain and ring structures with the inclusion of ions of a solute (B2O3, Na2B4O7, Li6B4O9, etc.), which tend to form glasses, are good solvents. For example, in [93], the formation of a high- temperature poorly soluble borate Al5BO9 is reported; a fair amount of Al2O3 is removed from the melt. It can be assumed that metal cations in the melt that incorporate into the crystal structure as uncontrolled impurities [87] will also be removed from the melt, as a result of which the LN crystal will be more perfect. Due to Raman data (Table1) oxygen octahedra are less deformed in the structure of a LiNbO3:B (homogeneous doping) than in LiNbO3:B (direct doping) crystal. This obviously happens due to an increase in the ordering of Li+ and Nb5+ cations and vacancies along the polar axis. We have concluded this because widths of 432 and 875 cm−1 bands in a LiNbO3:B (direct doping) crystal increase in the Raman spectrum. The bands correspond to deformation and stretching vibrations of oxygen atoms in the bridge Me–O–Me (Me: Li+, Nb5+). It is important to stress that 875 cm−1 band parameters are sensitive towards the magnitude of the dipole moment and, thus, the spontaneous polarization of the crystal [2]. LiNbO3:Mg crystals were studied in a paper [32]: the crystals were obtained by direct and homogeneous doping. Raman spectroscopy, optical study of macro- and microstructure have revealed higher ordering of homogeneously doped crystals compared to directly doped crystals. Magnesium incorporates directly to niobium pentoxide structure at a homogeneous doping. It has inter-polyhedra coordination with a uniform distribution in the melt volume. Clusters formed in a melt with different doping methods have different structures and sizes; therefore, melts, other things being equal, should crystallize in different ways [50,79,94]. Crystallization occurs through the attachment of the clusters to a growing crystal. 5− [BO4] tetrahedra can be both of correct and distorted form. Boron forms three covalent bonds with oxygen atoms, and the fourth bond in the tetrahedron is formed by the donor–acceptor mechanism. For this reason, the lengths of B–O bonds in the tetrahedron vary from 1.462 to 1.512 Å, the spread of angles — 104–115◦ [84]. During homogeneous LN crystal doping, the boron-containing reagent is introduced directly into the niobium stripping solution. Only one type of borates (Nb3BO9) forms Crystals 2021, 11, 458 25 of 37

initially. Thus, B–O and Nb–O are less different in the length than at direct doping, when seven different borates form [73]. Obviously, due to this, tetrahedra, and then the octahedra formed in the precrystallization region, will be less distorted during homogeneous doping. Therefore, our Raman data conﬁrmed that oxygen octahedra are less deformed in the structure of the LiNbO3:B (homogeneous doping) than in LiNbO3:B (direct doping) crystals, Table1.

3.6. Computer Simulation of the B3+ Ion Localization in the LN Crystal Structure Calculations of the total energy of the Coulomb interaction of point charges (U, eV) were carried out for the oxygen-octahedral lithium niobate cluster (Li+, Nb5+,O2−) 3+ 2 3– with the B ion considered in the sp –hybrid state as part of the [BO3] plane triangles. Calculations were performed using the formula:

U = (k·q1·q2)/r12 (10)

where q1 and q2—charges in fractions of an electron, r12—distance between the centers of interacting charges [Å], k—constant expressed by the formula (eV·Å):

2 −10 k = e / 4·π·ε0·10 = 14.41971 (11)

where e—charge of an electron, ε0—dielectric constant. The system (cluster) consists of two Li+ cations, two Nb5+ cations, one B3+ cation, and twenty O2− oxygen anions; it is not electrically neutral. We consider only a cluster consisting of six O6 oxygen octahedra, “torn out” from a large electrically neutral system, in order to study how the energy of the B3+ interaction with the surrounding fragment of the LN crystal structure depends on the B3+ position in tetrahedral voids. Taking a larger fragment of the structure is impractical, since the electrostatic interaction of point charges strongly decreases with distance. Li+ and Nb5+ cations sites correspond in our calculations to the structure of the ferroelectric LN phase: lithium is shifted to the lower oxygen plane, niobium—to the upper oxygen plane [2]. The calculations were based on the structural data of the CLN crystal [95]. The work simulates two processes. In the first case, the energy 3+ of the Coulomb interaction of the B ion with a fragment of the CLN crystal structure (6 O6 octahedra) is calculated. In this case, we took coordinates of the cell basis with constant lattice parameters (a and c = 5.1489 and 13.8631 Å, respectively), though changing with increasing temperature [2]. In the second case, we took the same the LN structure fragment, but with different lattice parameters a and c. For this, the cell parameters were normalized to a temperature of 297 K [96]. Due to similar results obtained in the first and second cases, only experimental data with constant parameters a and c are discussed below. A fragment of the structure (six oxygen octahedra) taken for modeling is shown on Figure 13. We considered seven possible locations of the boron cation: at the centers of the tetrahedral faces of the first and second octahedral layers bordering the corresponding octahedra (lithium, niobium, and vacant), and also in the plane of the oxygen triplet separating the octahedral layers. In this case, the calculations did not take into account the replacement of lithium with niobium. The calculation results are shown on Figure 14. According to Figure 14, the maximum energy value for both cases corresponds to the 3– presence of a boron cation in the [BO3] group bordering on niobium octahedra. For other possible arrangements of boron, the sum of the energy of the Coulomb interaction is much lower, which can be considered as a theoretically possible location of B3+ cations in the crystal structure. Crystals 2021, 11, 458 26 of 37

Crystals 2020, 10, x FOR PEER REVIEW 26 of 37 Crystals 2020, 10, x FOR PEER REVIEW 26 of 37

Figure 13. Two niobium (Nb1, Nb2), two lithium (Li1, Li2), and two vacant (V1, V2) oxygen octahe- Figure 13. Two niobium (Nb , Nb ), two lithium (Li , Li ), and two vacant (V ,V ) oxygen octahedra Figuredra forming 13. Two two niobium tetrahedral (Nb11, voidsNb2), highlightedtwo lithium in(Li gr11, ey.Li2 ),The and figure two vacant is reproduced (V11, V22) oxygenwith the octahe- permis- forming two tetrahedral voids highlighted in grey. The ﬁgure is reproduced with the permission of drasion forming of Pleiades two tetrahedralPublishing voidsfrom the highlighted paper N.V. in Sidorovgrey. The et figure al. J. Struct. is reproduced Chem. 2021 with V. the 62 №permis- 2 P. sionPleiades221–229, of Pleiades Publishing DOI: https://doi.org/10.1134/SPublishing from the from paper the N.V. paper Sidorov0022476621020050 N.V. etSidorov al., J. Struct. et (accessedal. J. Chem. Struct. on2021 Chem. 26 V.March62 2021№ 2021). 2V. P. 62 221–229, № 2 P.DOI: 221–229,https://doi.org/10.1134/S0022476621020050 DOI: https://doi.org/10.1134/S0022476621020050 (accessed on (accessed 26 March on 2021). 26 March 2021).

Figure 14. The total energy of the Coulomb interaction of point charges in a cluster consisting of FigureFiguretwo Li 14. 14.+ cations, TheThe total total two energy energy Nb5+ cations, of the Coulomb one B3+ cations, interaction and oftwentyof pointpoint O chargescharges2− anions.in in a Aa cluster clusterNb1–B consisting 3+consisting pair is located of of two + + 5+ 5+ 3+ 3+ 2− 2− 3+3+ twoLiin tetrahedron cations,Li cations, two twoface Nb Nbborderingcations, cations, one with one B NbO Bcations, cations,6 of the and firstand twenty layer;twenty O a VO1anions.–B anions.3+ pair A isA Nb locatedNb1–B1–B pairin pair tetrahedron is is located located in in tetrahedron face bordering with NbO6 of the first layer; a V1–B3+3+ pair is located in tetrahedron tetrahedronface bordering face a bordering vacant octahe withdra NbO of 6theof thefirst first layer, layer; etc. aТV =1 297–B Кpair (1), 523 is located (2), 773 in (3), tetrahedron 1023 (4), 1273 face facebordering(5), bordering1473 (6). a vacant The a vacant figure octahedra octahe is reprdra ofoduced the of the first with first layer, the layer, etc.permission etc. T = Т 297 = 297 of K (1),Pl Кeiades (1), 523 523 (2), Publishing (2), 773 773 (3), (3),1023 from 1023 (4), the (4), 1273 paper 1273 (5), (5), 1473 (6). The figure is reproduced with the permission of Pleiades Publishing from the paper 1473R.A. (6).Titov The et figureal. Techn. is reproduced Phys., 2021 withV. 66the №1 permission P. 59–66, DOI: of Pleiades Publishing from the paper R.A. R.A. Titov et al. Techn. Phys., 2021 V. 66 №1 P. 59–66, DOI: Titovhttps://doi.org/10.1134/S1063784221010217 et al., Techn. Phys., 2021 V. 66 №1 P. 59–66, (accessed DOI: https://doi.org/10.1134/S1063784221010217on 26 March 2021). https://doi.org/10.1134/S1063784221010217 (accessed on 26 March 2021). (accessed on 26 March 2021). We did not take into account the influence of boron in the tetrahedral face on point chargesWe didoutside not take the intosystem account under the consideration, influence of boron since inthis the influence tetrahedral significantly face on point de- chargescreases outsidewith distance. the system It should under be notedconsideration, that the B since3+ cation, this embedding influence significantlyin the tetrahedral de- 3+ creasesvoids ofwith the distance. crystal structureIt should beduring noted the that grow the thB process cation, embeddingintroduces anin theexcess tetrahedral positive voids of the crystal structure during the growth process introduces an excess positive

Crystals 2021, 11, 458 27 of 37

We did not take into account the influence of boron in the tetrahedral face on point charges outside the system under consideration, since this influence significantly decreases with distance. It should be noted that the B3+ cation, embedding in the tetrahedral voids of the crystal structure during the growth process introduces an excess positive charge into the system. In this case, to achieve the minimum energy of the system, it will be advantageous for boron to occupy positions, first of all, in tetrahedral voids bordering lithium and vacant octahedra, or in the oxygen plane separating the oxygen-octahedral layers, Figure 14. The formation of NbLi point defects when boron is in the tetrahedral face is unlikely, since in this case it leads to an increase in the total energy due to the high localization of positive charges. Thus, according to calculations, the presence of the B3+ ion in the crystal structure can prevent the formation of a deep electron trap NbLi, at least within the considered system. The results indicate that, in contrast to the metallic K2O flux, when the potassium element does not incorporate into the crystal structure, the nonmetallic B2O3 flux has a complex effect on the LN single crystals structure. It structures the melt, changes the microscopic crystallization mechanisms, thereby, aligns and brings KLi and KNb closer to unity (the distribution coefficients of lithium and niobium in the LiNbO3:B crystal). It reduces the 3+ formation of NbLi point defects by at least the number of B cations incorporated into the tetrahedral voids of the structure, corresponding to the boron concentration in the −4 LiNbO3:B crystal (~4 × 10 mol%). As shown above, in the Li2O–Nb2O5–B2O3 system, there are no regions of homogeneity of boron and its compounds with lithium niobate, and CLN should be the only crystallizing phase. However, due to the binding of an excess of niobium in the melt with boron, the fraction of lithium in the structure of the growing crystal increases, which increases the Li/Nb ratio and brings the structure of LiNbO3:B crystals closer to that of SLN. The increase in the lithium content is additionally confirmed by the calculation of the Li2O concentration in the crystals from the increase ◦ in the Curie temperature for CLN and LiNbO3:B (0.83 mol%) crystals—1145 and 1189 C, respectively [97]. Thus, due to Raman spectroscopy, structural units of the cation sublattice are more ordered in LiNbO3:B crystals, Table1. LN crystals doped with certain concentrations of metal cations also have an increased cation sublattice order [2,98]. Metal dopants do incorporate into the crystal structure. In the case of boron, such ordering is impossible— boron incorporates into crystal tetrahedral voids and due to our data (see paragraph 3.5.) changes O–O bonds length. This changes the O6 oxygen octahedra size and the distribution of Nb5+ and Li+ cations in octahedra. As a result, a more energetically favorable distribution of cations over octahedra is established in the crystal, the arrangement of cations along the polar axis orders. Indeed, the anionic sublattice of the LiNbO3:B crystal turns out to be less distorted than of CLN crystal, Table1. At this, the polarizability of the oxygen-octahedral MeO6 clusters, which determines the nonlinear optical properties of the crystal, changes. −1 This confidently manifests in the LiNbO3:B crystals Raman spectrum. 576 and 630 cm bands correspond to doubly degenerate E(TO) and totally symmetric A1(TO) vibrations of oxygen atoms in O6 oxygen octahedra, respectively. They substantially widen ~2 times in LiNbO3:B spectrum in comparison with SLN and CLN, Table1. Changes in O–O bonds length caused by trace amounts of boron localizing in tetrahedral voids can be achieved only by a much higher concentration of metal elements Zn2+, Mg2+ [2,25,26,98]. Bands corresponding to vibrations of oxygen atoms in oxygen octahedra widen smoothly in LiNbO3:Zn and LiNbO3:Mg Raman spectra and sharply—in LiNbO3:B spectrum. This can be explained by the following: tetrahedral voids of the LN crystal structure act as a kind of “buffer”, they compensate for the deformation of the oxygen framework of the structure [99]. They compensate for various influences on the anionic sublattice, including the distortion of oxygen octahedra due to the presence of metal cations Zn, Mg, etc., in 3+ them. In the case of LiNbO3:B crystals, some of the tetrahedra are already filled with B cations, which negatively affects their “buffer” ability, which explains the sharp increase in the 576 and 630 cm−1 Raman bands widths. Crystals 2021, 11, 458 28 of 37

Table1 demonstrates that 880 cm −1 Raman band width occupies an intermediate value between the widths of this band in the spectrum of SLN and CLN crystals—25(26), 20 and 30 cm−1, respectively. The band corresponds to the oxygen atoms stretching bridge vibrations of the A1(LO) symmetry type along the polar axis in the Me–O–Me bridge (Me: + 5+ −1 Li , Nb , dopant). A decrease in the 880 cm band width in LiNbO3:B spectrum may be associated with an increase in the cation sublattice order of these crystals. Aligning k0 Li and Nb distribution coefﬁcients during crystal growth explains the approach of the Li/Nb ratio to 1 in LiNbO3:B; boron in tetrahedral voids limits the NbLi structural defect formation. Thus, the ordering of the cation sublattice of the crystal manifests itself in the Raman spectrum not only in the range 200–300 cm−1, corresponding to the vibrations of metal cations in oxygen octahedra along the polar axis, but is also indirectly traced by the parameters of the 880 cm−1 band. Due to this data, even traces amounts of B3+ cations incorporating to LN oxygen tetrahedra noticeably distort the anionic framework. This leads to a noticeable asymmetry of oxygen octahedra (compared with that in CLN crystals) and a change in their polarizability. The deformation and polarizability of oxygen-octahedral MeO6 clusters, in turn, determine the LN crystal electro-optical properties [1,2]. At this, the cationic sublattice of LiNbO3:B crystals, on the contrary, turns out to be more ordered in comparison with the that of the CLN crystal, which is also conﬁrmed by Raman data, Table1.

4. Conclusions Optical microscopy, absorption spectroscopy, Raman spectroscopy, laser conoscopy, optical spectroscopy, optical and atomic force microscopy, photoinduced light scattering, and infrared spectroscopy in the field of stretching vibrations of OH groups and computer simulation were applied to study nominally pure CLN and SLN crystals and a series of LiNbO3:B crystals grown from a charge of various genesis, doped with a non-metallic element boron. A quantitative assessment of the strengths of the photovoltaic and diffusion fields has been carried out according to the PILS characteristics for all studied crystals. It was shown that the value of the diffusion field responsible for the diffusion mechanism of charge transfer in the LiNbO3:B crystal has an intermediate value between the values CLN and SLN; it depends on the boron concentration in the charge. The PILS indicatrix opening angle also depends on the boron concentration in the charge. The angle in LiNbO3:B crystal is smaller than that in SLN crystal. A LiNbO3:B band gap corresponds to the value for a SLN crystal. At the same time, LiNbO3:B crystals have greater optical uniformity compared to SLN crystals. Positions of OH groups is more ordered in LiNbO3:B crystal structure than in CLN crystal. Thus, growing nominally pure LN crystals from a melt structured with non-metal boron makes it possible to control the features of the secondary structure, optical uniformity, the magnitude of photoelectric fields and the width of the band gap in the crystal. Macro- and micro-structure was studied in LiNbO3:B (0.55–1.24 mol%) crystal grown from a different charge. The charge contained different concentrations of boron and was prepared by solid phase synthesis-granulation and by homogeneous doping of Nb2O5:B precursor. Boron is a chemically active element; it is shown to have a strong effect on the melt structure, making it more homogeneous and viscous and changing the size and structure of clusters in the melt. This leads to a significant change in the secondary structure (defect sublattice) and properties of LiNbO3:B crystals, in comparison with nominally pure LN crystals. The melt temperature is slightly increased (1264 ◦C) compared to nominally pure CLN (1257 ◦C). Boron concentration should not exceed ~0.12 wt% in the melt for the successful growth of optically and structurally uniform LiNbO3:B crystals. At the −3 −5 same time, the boron concentration in the grown LiNbO3:B crystal is ~10 to 10 wt%, which corresponds to trace amounts of impurities. Calculations have revealed that boron can incorporate in trace amounts into the faces of oxygen tetrahedra of the LN crystal structure, bordering on the lithium or vacant oxygen octahedra, or into the oxygen plane Crystals 2021, 11, 458 29 of 37

separating the oxygen-octahedral layers. Trace amounts of boron in the LiNbO3:B structure, apparently obeys a certain mechanism of incorporation into oxygen tetrahedra, like the threshold mechanisms for doping metals. Boron introduces an additional positive charge into the system, thereby preventing the formation of NbLi point defects. On the other hand, incorporating into oxygen tetrahedra, boron noticeably distorts the anionic framework of the crystal structure, changing the O–O bond lengths and changing the polarizability of the oxygen-octahedral MeO6 clusters, which determines the nonlinear optical properties of the crystal. Moreover, when the O6 octahedra are distorted, the structural units of the cation sublattice are simultaneously ordered along the polar axis. Thus, a new approach was formulated to the preparation of nominally pure LN single crystals. Composition and structure of such crystals approach SLN. Flux in trace amounts has a multi-stage and complex effect on the structural and optical properties of LN single crystals. The results obtained make it possible to expand the concept of “doping”. Doping usually means the introduction of a noticeable amount of dopants directly into the crystal structure in order to change the physical properties of the material. Despite the high content of boron in the charge (up to 2.0 mol%), its concentration in the crystal is at the level of trace amounts, i.e., orders of magnitude is lower than the concentration of doping metals. Moreover, the B3+ ion occupies the tetrahedral voids of the structure. However, boron oxide compounds, as strong complexing agents and solvents, have a noticeable effect on the structure and physical characteristics of the melt, and, consequently, on the structure of the grown crystal. Boron structures the melt in a certain way and decreases the amount of NbLi defects. Probably, it also reduces the content of uncontrolled impurities. Thus, boron reduces the effect of photorefraction in a LN single crystal, increases its structural and optical uniformity. This approach allows one to obtain nominally pure LN crystals by directed structuring of the melt. The crystals have the same properties as doped crystals, but the ordering of the structural units of the cation sublattice and NbLi defects approach the SLN crystal. At the same time, LiNbO3:B crystal has a signiﬁcantly lower photorefractive effect than SLN crystals. In this case, the degree of the O6 octahedra distortion and the photorefractive properties of LiNbO3:B crystals can be varied using different methods of the charge doping.

Author Contributions: Conceptualization, N.V.S., N.A.T., and R.A.T.; methodology, N.A.T., O.V.M., R.A.T., and I.V.B.; software, O.V.M., R.A.T.; validation, O.V.M. and R.A.T.; investigation, O.V.M., R.A.T., and I.V.B.; data curation, R.A.T.; writing—original draft preparation, N.V.S., N.A.T., R.A.T., and D.V.M.; writing—review and editing, M.N.P. and D.V.M.; visualization, O.V.M., R.A.T., and D.V.M.; supervision, N.V.S. and M.N.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was supported by the Ministry of Science and Higher Education Russian Federation scientific topic No 0186-2021-0022 (registration AAAA-A21-118022190125-2) and by RFBR grant № 19-33-90025. Data Availability Statement: Raw data of this paper will be available from corresponding author, N.V., on a reasonable request. Acknowledgments: Authors would like to thank Vadim Efremov from Tananaev Institute of Chemistry—Subdivision of the Federal Research Centre «”Kola Science Centre of the Russian Academy of Sciences” (ICT RAS) for providing Figures A2 and A12. Authors would like to thank Vyacheslav Voskresenskiy from ICT RAS for advice on computer modeling. Conflicts of Interest: The authors declare no conflict of interest.

Appendix A The appendix presents possible secondary structure elements in LN crystals: cracking if the dopant concentration is too high (Figure A1), after-growth thermal stresses (Figure A2), growth stripes (Figures A3 and A4), separation of the second phase (Figures A5–A7), macro-cellular (Figure A8) and mosaic (Figures A9 and A10) structure, Crystals 2021, 11, 458 30 of 37

appearance of micro- (Figure A11) and nanodefects (Figure A12). The crack on Figure A1 developed in accordance with the symmetry of the crystal at angles between the individual branches of ~120 degrees. Probably, the second phase on Figure A7a can be in a quasicrys- talline state since the spatial regions of its separation contain 5th-order symmetry axes. Crystals 2020, 10, x FOR PEER REVIEW 30 of 37 Crystals 2020, 10, x FOR PEER REVIEW 30 of 37 Crystals 2020, 10, x FOR PEER REVIEW 30 of 37

FigureFigure A1.A1.Cracking Cracking inin heavilyheavily dopeddoped LiNbO3 crystals: ( (aa)–LiNbO)—LiNbO3:Mg3:Mg ([MgO] ([MgO] ≈ 4≈ mol%4 mol% in the in the Figure A1. Cracking in heavily doped LiNbO3 crystals: (a)–LiNbO 3:Mg ([MgO] ≈ 4 mol% in the crystal); (b)–LiNbO3:Zn (direct doping, [ZnO] ≈ 5.19 mol% in the crystal). crystal); (b)—LiNbO3:Zn (direct doping, [ZnO] ≈ 5.19 mol% in the crystal). crystal);Figure A1. (b)–LiNbO Cracking3:Zn in heavily(direct doping,doped LiNbO [ZnO]3 ≈ crystals: 5.19 mol% (a)–LiNbO in the crystal).3:Mg ([MgO] ≈ 4 mol% in the crystal); (b)–LiNbO3:Zn (direct doping, [ZnO] ≈ 5.19 mol% in the crystal).

Figure A2. (a)–AFM image of the region of mechanical stresses in the form of a fragment of the Figure A2. (a)–AFM image of the region of mechanical stresses in the form of a fragment of the Figurenetwork A2. of( adislocations)—AFM image in the of theLiNbO region3:Mg of crystal mechanical ([MgO] stresses ≈ 5.59 in mol% the form in the of melt); a fragment (b)–manifesta- of the net- networkFigure A2. of (dislocationsa)–AFM image in the of theLiNbO region3:Mg of crystal mechanical ([MgO] stresses ≈ 5.59 inmol% the formin the of melt); a fragment (b)–manifesta- of the worktion of of the dislocations nanostructure in the in LiNbO the LiNbO3:Mg crystal3:Zn crystal ([MgO] ([ZnO]≈ 5.59 = 5.84 mol% mol% in the in melt);the melt) (b)—manifestation at the boundary tionnetworkof the of positive the of nanostructure dislocations and negative in in the the macrodomains. LiNbO LiNbO3:Mg3:Zn crystal crystal ([MgO] ([ZnO] ≈= 5.595.84 mol% in the melt)melt); at(b the)–manifesta- boundary of the nanostructure in the LiNbO3:Zn crystal ([ZnO] = 5.84 mol% in the melt) at the boundary of the oftion the of positive the nanostructure and negative in themacrodomains. LiNbO3:Zn crystal ([ZnO] = 5.84 mol% in the melt) at the boundary positive and negative macrodomains. of the positive and negative macrodomains.

Figure A3. Growth bands in heavily doped LiNbO3:Mg crystals (direct doping): (a )–X-cut; (b)–Z- Figurecut. A3. Growth bands in heavily doped LiNbO3:Mg crystals (direct doping): (a)–X-cut; (b)–Z- cut. 3 FigureFigure A3.A3. GrowthGrowth bands bands in in heavily heavily doped doped LiNbO LiNbO3:Mg:Mg crystals crystals (direct (direct doping): doping): (a)—X-cut; (a)–X-cut; (b)—Z-cut. (b)–Z- cut.

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Figure A4. (a)–growth bands in a plane parallel to the growth axis of a LiNbO3:Mg crystal ([MgO] Figure A4. (a)—growth bands in a plane parallel to the growth axis of a LiNbO3:Mg crystal ≈Figure 5.3 mol% A4. in(a )–growththe melt), bands X-cut; in (b a)–domain plane parallel structure to the fixed growth by growth axis of bandsa LiNbO in 3a:Mg LiNbO crystal3:Gd ([MgO] crystal ([MgO] ≈ 5.3 mol% in the melt), X-cut; (b)—domain structure ﬁxed by growth bands in a LiNbO3:Gd (directFigure≈ 5.3 mol% doping,A4. (ina)–growth the [Gd melt),2O3] bands≈ X-cut; 0.44 inwt% (b a)–domain plane in a crystal), parallel structure Z-cut.to the fixed growth by growth axis of bandsa LiNbO in 3a:Mg LiNbO crystal3:Gd ([MgO] crystal crystal (direct doping, [Gd2O3] ≈ 0.44 wt% in a crystal), Z-cut. (direct≈ 5.3 mol% doping, in the [Gd melt),2O3] ≈X-cut; 0.44 wt% (b)–domain in a crystal), structure Z-cut. fixed by growth bands in a LiNbO3:Gd crystal (direct doping, [Gd2O3] ≈ 0.44 wt% in a crystal), Z-cut.

Figure A5. Isolation of the interstitial phase with incoherent boundaries on Z-cuts of crystals: (a)–

FigureLiNbOFigure A5.3A5.:ZnIsolation Isolation([Zn] = 4.74 ofof thethemol%); interstitialinterstitial (b)–LiNbO phasephase3:Mg withwith (joint incoherentinco solid-phaseherent boundariesboundaries synthesis, onon Z-cuts[MgO]Z-cuts ofof= 5.6 crystals:crystals: mol% (ina)—)– FigureLiNbO 3A5.:Zn Isolation([Zn] = 4.74 of themol%); interstitial (b)–LiNbO phase3:Mg with (joint inco solid-phaseherent boundaries synthesis, on Z-cuts[MgO] of = 5.6crystals: mol% ( ain)– LiNbOthe melt).3:Zn ([Zn] = 4.74 mol%); (b)—LiNbO3:Mg (joint solid-phase synthesis, [MgO] = 5.6 mol% in theLiNbO melt).3:Zn ([Zn] = 4.74 mol%); (b)–LiNbO3:Mg (joint solid-phase synthesis, [MgO] = 5.6 mol% in the melt). the melt).

Figure A6. Crack formed in the crystal LiNbO3:Zn ([ZnO] ≈ 3.95 mol% in the crystal), Z-cut, at the

interfaceFigure A6. between Crack formedthe matrix in the and crystal the seco LiNbOnd phase3:Zn ([ZnO]with inco ≈ 3.95herent mol% boundaries. in the crystal), Z-cut, at the FigureinterfaceFigure A6.A6. betweenCrack Crack ( a,bformedthe) matrix formed in the and in crystal the the crystal seco LiNbOnd LiNbO phase3:Zn3 ([ZnO]:Znwith ([ZnO] inco ≈ 3.95herent≈ mol%3.95 boundaries. mol% in the in crystal), the crystal), Z-cut, Z-cut, at the at theinterface interface between between the the matrix matrix and and the the seco secondnd phase phase with with inco incoherentherent boundaries. boundaries.

Crystals 2021, 11, 458 32 of 37

Crystals 2020Crystals, 10 ,2020 x FOR, 10 ,PEER x FOR REVIEW PEER REVIEW 322 of 3738 Crystals 2020, 10, x FOR PEER REVIEW 32 of 37 characterized by high values of photoelectric fields and photorefraction effect. The latter can be varied in a very wide range [1,2,8]. Optical damage resistance can be increased in congruent LN (CLN, R = Li/Nb = 0.946) crystals by their doping with non-photorefractive (Me: Zn, Mg, In, etc.) cations [2]. Unlike multiply charged photorefractive cations, they do not change their charge state in the crystal (they are not electron donors) under the action of optical radiation. The influence of such dopants on crystal properties is caused by their ability to change the amount of point defects and linked molecular complexes in the crystal cation sublattice. The molecular complexes in question can be caused by OH groups in the crystal structure [1,2,9–11]. Point defects NbLi are Nb5+ cations in the Li+ sites of a perfect stoichiometric (SLN, R = 1) LN composition. They, along with transition metal impurities (for example, Fe), are deep

electron traps and influence photorefractive effect the most [1,2]. Moreover, a LN struc- Figure A7. (a)–precipitation of the second phase with semi-coherent boundaries in the LiNbO 3:Zn ture Figurecontains A7. a(a lot)—precipitation of shallow ofelectron the second traps phase besides with semi-coherentNbLi that influence boundaries photorefractive in the LiNbO 3:Zn crystalFigurecrystal (directA7.(direct (a)–precipitation doping, [Zn] [Zn] = of =4.68 the 4.68 mol% second mol% in phase the in thecr ystal)with crystal) semi-coherent Z-cut, Z-cut, after afterthe boundaries high-temperature the high-temperature in the LiNbO elec- 3:Zn electrod- effecttrodiffusion [12]. The complexityannealing; (b )–separationof LN doping of the task second increases phase with provided partially that coherent significant boundaries concen- in iffusioncrystal (direct annealing; doping, (b )—separation[Zn] = 4.68 mol% of in the the second crystal) phase Z-cut, with after partiallythe high-temperature coherent boundaries elec- in the trationstrodiffusionthe LiNbOof metal3:Zn annealing; dopants crystal ([ZnO] ( binevitably)–separation = 5.84 mol%lead of the toin secondathe disorder melt), phase Z-cut. in with optical partially and coherent structural boundaries uniformity in LiNbO3:Zn crystal ([ZnO] = 5.84 mol% in the melt), Z-cut. of a singlethe LiNbO crystal3:Zn crystal[1,2,9–11,13]. ([ZnO] = 5.84 mol% in the melt), Z-cut.

FigureFigure A8.A8. MacrodefectMacrodefect cellular cellular structure structure in a in heavily a heavily doped doped LiNbO LiNbO3:Zn crystal:Zn crystal(direct doping): (direct doping): 3 (Figurea(a)—At)–At theA8. the bottomMacrodefect bottom of of a a large largecellular boule, boule, structure observation observation in a heavily in ina bright a brightdoped field; ﬁeld;LiNbO (b)–On (b3:Zn)—On the crystal Z the surface Z(direct surface through doping): through the the X X surface, observation in a bright field; (c)–observation in the DIC mode. surface,(a)–At the observation bottom of a in large a bright boule, ﬁeld; observation (c)—observation in a bright in field; the DIC(b)–On mode. the Z surface through the X surface, observation in a bright field; (c)–observation in the DIC mode.

Figure A9. Accumulation of triangular domains against the background of an uneven mosaic structure in a LiNbO3:Mg crystal (joint solid-phase synthesis, [MgO] ≈ 4.7 mol% in the crystal), Z- FigureFigureMoreover, A9.A9. Accumulation LN crystal grownof of triangular triangular at air domains domainsalways against againstcontain the the 10 background background16–1018 cm of–3 of protonsan an uneven uneven bonded mosaic mosaic with structure structurecut. in a LiNbO3:Mg crystal (joint solid-phase synthesis, [MgO] ≈ 4.7 mol% in the crystal), Z- oxygenin a by LiNbO a hydrogen:Mg crystal bond. (joint Hydrogen solid-phase atoms synthesis, form [MgO] such≈ complex4.7 mol% defects in the crystal), as VLi-OH, Z-cut. NbLi- cut. 3 OH, etc., [7,14,15]. OH-groups play important role in formation of a secondary defect

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FigureFigure A10. A10. MosaicMosaic structure: structure: (a)–with (a)—with cells of cellsdifferent of different sizes, located sizes, near located the macrodomain near the macrodomain wall Figure A10. Mosaic structure: (a)–with cells of different sizes, located near the macrodomain wall inwall the LiNbO in the3 LiNbO:Zn crystal3:Zn ([ZnO] crystal ≈ ([ZnO]4.77 mol%≈ 4.77In the mol% crystal); In the(b)–In crystal); a LiNbO (b)—In3: Mg crystal a LiNbO ([MgO]3: Mg ≈ crystal in the LiNbO3:Zn crystal ([ZnO] ≈ 4.77 mol% In the crystal); (b)–In a LiNbO3: Mg crystal ([MgO] ≈ 4.7 mol% in a crystal); with equiaxed cells in the LiNbO3:Ce crystal (direct doping, [Ce] = 0.5 mol% ([MgO] ≈ 4.7 mol% in a crystal); (c)—with equiaxed cells in the LiNbO3:Ce crystal (direct doping, in4.7 the mol% crystal), in a Z-cut.crystal); with equiaxed cells in the LiNbO3:Ce crystal (direct doping, [Ce] = 0.5 mol% [Ce]in the = crystal), 0.5 mol% Z-cut. in the crystal), Z-cut.

Figure A11. Defective micro-structure in heavily doped crystals: (a)–A “network” of triangular Figure A11. Defective micro-structure in heavily doped crystals: (a)–A “network” of triangular microdomainsFigure A11. Defectivein a LiNbO micro-structure3:Zn crystal ([ZnO] in heavily= 6.5 mol% doped in the crystals: melt); (b ()–Ana)—A accumulation “network” of tri- triangular microdomains in a LiNbO3:Zn crystal ([ZnO] = 6.5 mol% in the melt); (b)–An accumulation of tri- angularmicrodomains microdomains in a LiNbO against3 :Znthe backgr crystalound ([ZnO] of a =mosaic 6.5 mol% “grid” in in the a LiNbO melt);3 (:Znb)—An crystal accumulation ([ZnO] = of angular microdomains against the background of a mosaic “grid” in a LiNbO3:Zn crystal ([ZnO] = 4.69triangular mol% melt); microdomains (c)–An accumulation against the of background triangular domains, of a mosaic a sign “grid” of inhomogeneity in a LiNbO :Znof the crystal ([ZnO] 4.69 mol% melt); (c)–An accumulation of triangular domains, a sign of inhomogeneity3 of the chemical= 4.69 mol% composition, melt); (inc)—An the LiNbO accumulation3:Mg crystal of ([MgO] triangular ≈ 4.4 domains, mol% in the asign crystal); of inhomogeneity (d)–Poorly of the chemical composition, in the LiNbO3:Mg crystal ([MgO] ≈ 4.4 mol% in the crystal); (d)–Poorly formed mosaic structure in a LiNbO3:Mg crystal (direct doping, [MgO] ≈ 4.77 mol% in the crystal), chemical composition, in the LiNbO :Mg crystal ([MgO] ≈ 4.4 mol% in the crystal); (d)—Poorly Z-cut,formed with mosaic shapeless structure structural in a LiNbO formations,3:Mg3 crystal probably (direct crystallization doping, [MgO] centers ≈ 4.77 of themol% second in the phase. crystal), formedZ-cut, with mosaic shapeless structure structural in a LiNbO formations,3:Mg crystalprobably (direct crystallization doping, [MgO] centers≈ of4.77 the mol%second in phase. the crystal), Z-cut, with shapeless structural formations, probably crystallization centers of the second phase.

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FigureFigure A12. A12. NANO-RNANO-R ATF ATF image image of a of hexagonal a hexagonal microdomain microdomain in a LiNbO in a LiNbO3:Mg crystal3:Mg crystal (joint solid- (joint phasesolid-phase synthesis, synthesis, [MgO] [MgO] ≈ 5.59 mol%≈ 5.59 in mol% the melt), in the after melt), the after high-temperature the high-temperature electrodiffusion electrodiffusion annealing,annealing, Z-cut. Z-cut.

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