Structures of Impurity Defects in Lithium Niobate and Tantalate Derived from Electron Paramagnetic and Electron Nuclear Double Resonance Data

: Point intrinsic and extrinsic defects, especially paramagnetic ions of transition metals and rare-earth elements, have essential inﬂuence on properties of lithium niobate, LN and tantalate, LT, and often determine their suitability for numerous applications. Discussions about structures of the defects in LN/LT have lasted for decades. Many experimental methods facilitate progress in determining the structures of impurity centers. This paper gives current bird’s eye view on contributions of Electron Paramagnetic Resonance (EPR), and Electron Nuclear Double Resonance (ENDOR) studies to the determination of impurity defect structures in LN and LT crystals for a broad audience of researchers and students. Symmetry and charge compensation considerations restrict a number of possible structures. Comparison of measured angular dependences of ENDOR frequencies with calculated ones for Li and Nb substitution using dipole–dipole approximation allows unambiguously to determine the exact location of paramagnetic impurities. Models with two lithium vacancies explain angular dependencies of EPR spectra for Me 3+ ions substituting for Li + like Cr, Er, Fe, Gd, Nd, and Yb. Self-compensation of excessive charges through equalization of concentrations of Me 3+ (Li + ) and Me 3+ (Nb 5+ ) and appearance of interstitial Li + in the structural vacancy near Me 3+ (Nb 5+ ) take place in stoichiometric LN/LT due to lack of intrinsic defects.


Introduction
Point intrinsic and extrinsic defects, especially paramagnetic ions of transition metals and rare-earth elements, belong to the most important defects in lithium niobate (LN, LiNbO 3 ) and tantalate (LT, LiTaO 3 ), because of their essential influence on properties of this material, such as domain structure, electro-optical coefficients, light absorption, refractive indices, birth and evolution of wave-front dislocations ( [1,2] and references there), and their consequences for present and potential applications [3][4][5][6][7]. A lot of effort was spent to establish a correlation between the observable data and the crystal composition, and to develop experimentally supported models of the defects: ion charges, identities, and position of the ions in the lattice, their nearest surroundings, ways of charge compensation and recharge mechanisms. Discussions about structures of intrinsic and extrinsic defects in LN/LT have lasted for decades [1]. With time, the proposed structures were evolved and detailed. Some early models were rejected. For instance, after a supposition that effective net charges are about 2.0+ [8], or 1.59+ for Nb and 1.21+ for Ta [9], it was natural to assume that divalent and trivalent impurities should preferably substitute for Nb, but not for Li. Later, numerous investigations have shown that the real picture is more complicated and richer.
In the course of the investigation of defect structures in LN/LT the following difficulties take place: • high quality conventional samples with crystal composition x C are usually grown from the congruent melt with the composition x m ≈ 48.4%, for LN and x m ≈ 48.7% for LT (x = [Li]/([Li] + [Nb/Ta]); this means that the congruent crystals with x m = x C contain many intrinsic (non-stoichiometric) defects, causing a broadening of the observable spectral lines and ambiguities in their interpretation; • the crystal composition x C of the undoped samples depends on both melt composition and growth conditions; • the most probable positions for impurity incorporation, the Li and Nb sites as well as the octahedral structural vacancy, have the same local symmetry C 3 ; this means that they are not distinguishable by many spectroscopic techniques.
Attempts to determine impurity positions by indirect methods often gave contradicting information. Direct methods also have some shortcomings. For instance,

•
Mössbauer spectroscopy demands the presence of special nuclei, • channeling investigations are more successful in the case of heavy, many-electron ions, • channeling methods are not sensitive to the charge state of the impurity and do not distinguish centers with C 3 and C 1 symmetry, • due to the relatively low sensitivity the EXAFS needs high levels of crystal dopants (about 3-5 mol.%), for which clustering and occupation of both Li and Nb positions become very probable, • EPR/ENDOR techniques are applicable to systems with non-zero spins only.
Convincing arguments of Fe 3+ substitution for Li + were obtained by ENDOR [38][39][40]: it was shown that spectrum angular dependencies calculated on the base of dipole-dipole interactions of Fe 3+ electrons with surrounding Li nuclei are qualitatively different for Li and Nb substitution; quantitative agreement calculated and experimental data was achieved for Li substitution.
The huge amount of nonstoichiometric intrinsic defects in congruent LN/LT grown by the conventional Czochralski method [41,42] (we shall call them cLN and cLT) has often undesirable effects on crystal properties. Several techniques were invented in order to reduce the concentration of these defects. Some decrease of their concentration was achieved by using melts with Li excess (with x m up to 60%) [43,44]. Thin LN/LT samples were enriched with Li by vapor transport equilibrium treatment (VTE [45][46][47][48][49][50], we shall call them vLN and vLT). Using double crucible growth [51][52][53][54][55] with excess of Li allowed one to obtain nearly stoichiometric samples (nsLN). Crystals grown by the Czochralski method from a melt to which potassium oxide K 2 O has been added ( [56][57][58][59][60][61][62][63][64][65][66][67], and references there) have composition x C ≈ 50% (LN K , stoichiometric LN, sLN). The method is scientifically called the High Temperature Top Seeded Solution Growth (HTTSSG). For centers with S = 1/2 the resonance line positions can be described using spin-Hamiltonian (1) Here μB is the Bohr magneton, B is the vector of static magnetic field, g is the tensor of spectroscopic splitting, and S is the vector of electron spin.
As an example of the multi-center spectra let's consider ion Nd 3+ in LN [91][92][93] (Figure 2). Every spectrum consists of a single dominant line labeled with the number 1 and many satellite lines of smaller intensities. The positions of the dominant line have the same value of the resonance field for B||x and B||y (φ = 90 deg), whereas positions of other lines do not coincide. We have to suppose that the single line #1 belongs to the axial C3 symmetry center, Nd1.
To make correct labeling of all observed lines a detailed study of angular dependence of EPR line positions is required. For instance, we can rotate magnetic field in xy crystallographic plane, changing azimuthal angle φ between x-axis and B. Circular diagram of measured spectra ( Figure 3) show that dominant line draw a circle, i.e., has no dependence of Bres(1) on φ. Angular patterns of other lines demonstrate the presence of all elements of the 3m group, namely, C3 symmetry and the mirror with respect to y-axis at φ = 90 deg. Measurement of such a diagram is redundant, since xy plane angular pat- For centers with S = 1/2 the resonance line positions can be described using spin-Hamiltonian Here µ B is the Bohr magneton, B is the vector of static magnetic field, g is the tensor of spectroscopic splitting, and S is the vector of electron spin.
As an example of the multi-center spectra let's consider ion Nd 3+ in LN [91][92][93] (Figure 2). Every spectrum consists of a single dominant line labeled with the number 1 and many satellite lines of smaller intensities. The positions of the dominant line have the same value of the resonance field for B||x and B||y (ϕ = 90 deg), whereas positions of other lines do not coincide. We have to suppose that the single line #1 belongs to the axial C 3 symmetry center, Nd 1 .
To make correct labeling of all observed lines a detailed study of angular dependence of EPR line positions is required. For instance, we can rotate magnetic field in xy crystallographic plane, changing azimuthal angle ϕ between x-axis and B. Circular diagram of measured spectra (Figure 3) show that dominant line draw a circle, i.e., has no dependence of B res (1) on ϕ. Angular patterns of other lines demonstrate the presence of all elements of the 3m group, namely, C 3 symmetry and the mirror with respect to y-axis at ϕ = 90 deg. Measurement of such a diagram is redundant, since xy plane angular patterns simply repeat themselves with a period 60 deg. Due to the glide mirror plane, the 30 degree dependence measured from x axis contains all information.
terns simply repeat themselves with a period 60 deg. Due to the glide mirror plane, the 30 degree dependence measured from x axis contains all information.
Usually, 90 deg of the measured dependence is plotted ( Figure 4). If spectra are measured with small angular steps (said 1 deg), it is easy to trace every line. The line tracing allows to put labels on every resonance line on Figure 2. Without doubt, at least four groups of angular branches are clearly distinguished on Figure 4: one straight branch of axial Nd1 and three sets of curved branches, which correspond to low-symmetry centers Nd2, Nd3, and Nd4. Therefore, we can conclude that Nd 3+ in Nd1 center occupies one of three possible positions on the z-axis. If Nd 3+ has additional defect or defects (charge compensators) in its neighborhood, the defect is located on the same axis. In the case of Nd2, Nd3, and Nd4 centers with the C1 symmetry, the additional defects are located off the z-axis. It is unlikely that Nd 3+ ions occupy sites with C1 symmetry (tetrahedral void or O 2− ) due to large charge misfit. Symmetry of any center reflects the symmetry of lattice sites occupied by impurity and charge compensators (if any) and their relative locations. To distinguish the C3 and C1 symmetries the measurement of angular dependence in xy plane is sufficient. However, to obtain a full set of spectroscopic characteristics of the center (like six components of g-tensor) by fitting measured angular dependence a study of spectra under three rotations in perpendicular planes (road map) is required. Symmetry of any center reflects the symmetry of lattice sites occupied by impurity and charge compensators (if any) and their relative locations. To distinguish the C 3 and C 1 symmetries the measurement of angular dependence in xy plane is sufficient. However, to obtain a full set of spectroscopic characteristics of the center (like six components of g-tensor) by fitting measured angular dependence a study of spectra under three rotations in perpendicular planes (road map) is required.  Rhombs represent experimental line positions for Q-band measurements (ν = 34.445 GHz), their sizes reflect line intensities. Horizontal whiskers near rhombs represent line widths. Cyan, lime, fuchsia, and blue curves represent simulated dependencies for axial Nd1, and low-symmetry Nd2, Nd3, and Nd4 centers, respectively. Curves for isotopes with nuclear spin I ≠ 0 are not shown.   Rhombs represent experimental line positions for Q-band measurements (ν = 34.445 GHz), their sizes reflect line intensities. Horizontal whiskers near rhombs represent line widths. Cyan, lime, fuchsia, and blue curves represent simulated dependencies for axial Nd1, and low-symmetry Nd2, Nd3, and Nd4 centers, respectively. Curves for isotopes with nuclear spin I ≠ 0 are not shown.

Isotropic and Dipole-Dipole Interactions
Calculations of the ENDOR frequencies and transition probabilities (i.e., ENDOR line positions and relative intensities) for i-th nucleus is usually based on nuclear spin- where µ n -nuclear magneton, g (i) n -nuclear g-factor; A (i) , Q (i) -tensors of hyperfine and quadrupole interactions.
In many cases there are two dominant contributions to the hyperfine tensor A (i) : isotropic (contact) hyperfine interaction, a (i) SI (i) and dipole-dipole interaction of vectors of electron µ B gS and nuclear −µ n g (i) n I (i) magnetic moments. The dipole-dipole interaction can be described by where R (i) is the vector from paramagnetic impurity to the i-th nucleus. Most characteristics in Equation (3) are known: µ B , µ n , g (i) n are tabulated, g jm components of g-tensor are determined from EPR measurements. Therefore, comparison of measured angular dependences of ENDOR frequencies with calculated ones on the base of Equations (2) and (3) can be used for determination of R (i) , i.e., the position of the paramagnetic impurity relative to surrounding nuclei.
Nuclei at the same distance from impurity ions are usually called a shell. The first shell of an impurity in a Li site has six nearest Li nuclei off the z-axis at the distance R (1) (Figure 5a). Three of them are located above the impurity (the subshell 1a), other threebelow the impurity (the sub-shell 1b); if the impurity is shifted from regular Li site then R (1a) = R (1b) . The second shell consist of six Li nuclei in the xy plane of the impurity at the distance R (2) (subshells 2a, 2b).The first shell of an impurity in a Nb site has one Li nucleus on z-axis, the second shell has three Li nuclei (the nuclei are labelled 1 and 2 on Figure 5b). As directions from the impurity to the nuclei in a shell are different, their hyperfine interactions are magnetically non-equivalent, i.e., produce different branches in angular dependences of ENDOR spectra.

Isotropic and Dipole-Dipole Interactions
Calculations of the ENDOR frequencies and transition probabilities (i.e., ENDOR line positions and relative intensities) for i-th nucleus is usually based on nuclear spin-Hamiltonians Hi where μn-nuclear magneton, ( ) -nuclear g-factor; A (i) , Q (i) -tensors of hyperfine and quadrupole interactions. In many cases there are two dominant contributions to the hyperfine tensor A (i) : isotropic (contact) hyperfine interaction, ( ) ( ) and dipole-dipole interaction of vectors of electron and nuclear ( ) ( ) magnetic moments. The dipole-dipole interaction can be described by where R (i) is the vector from paramagnetic impurity to the i-th nucleus. Most characteristics in Equation (3) are known: , , ( ) are tabulated, components of g-tensor are determined from EPR measurements. Therefore, comparison of measured angular dependences of ENDOR frequencies with calculated ones on the base of Equations (2) and (3) can be used for determination of R (i) , i.e., the position of the paramagnetic impurity relative to surrounding nuclei.
Nuclei at the same distance from impurity ions are usually called a shell. The first shell of an impurity in a Li site has six nearest Li nuclei off the z-axis at the distance R (1) (Figure 5a). Three of them are located above the impurity (the subshell 1a), other threebelow the impurity (the sub-shell 1b); if the impurity is shifted from regular Li site then R (1a) ≠ R (1b) . The second shell consist of six Li nuclei in the xy plane of the impurity at the distance R (2) (subshells 2a, 2b).The first shell of an impurity in a Nb site has one Li nucleus on z-axis, the second shell has three Li nuclei (the nuclei are labelled 1 and 2 on Figure  5b). As directions from the impurity to the nuclei in a shell are different, their hyperfine interactions are magnetically non-equivalent, i.e., produce different branches in angular dependences of ENDOR spectra.   The simplest way to determine the impurity lattice site is: for the several nearest nuclei around the impurity taking lattice distances from X-ray data and g jm from EPR measurements, • to calculate ENDOR frequencies, to plot patterns of their angular dependencies, and • to compare the patterns with measured angular dependencies of ENDOR for a definite EPR line [13,38,39].
Due to different surroundings for impurities in the Li and Nb sites, the calculated patterns are completely different ( Figure 6). ENDOR frequencies for the first shell of Li nuclei for the Li site vary with rotation of magnetic field in xy plane (Figure 6a), whereas for the single Li nucleus of the first shell for Nb site two straight branches should be observed in angular dependence ( Figure 6c). As Li nuclei of the all corresponding shells are closer to the impurity ion in the Nb site than in the Li site, the range of angular variation for Nb site is larger than for Li site. The branches of the 2nd and 3rd shells for Li site practically coincide with measured angular dependencies for Nd 1 center (Figure 6b), whereas no branch for Nb site is close to observed one. The branches of the 1st shell for Li substitution also agree with observed ones after small correction due to isotropic hyperfine interaction ( Figure 6b). Based on clear agreement of hundred measured values of ENDOR frequencies for the dominant EPR line #1 with calculated frequencies for Li site and obvious disagreement with calculated ones for Nb site, we can definitely conclude that the Nd 1 line in EPR spectra ( Figure 2) belongs to Nd 3+ ion substituted for Li. The simplest way to determine the impurity lattice site is: • to calculate ( ) for the several nearest nuclei around the impurity taking lattice distances from X-ray data and gjm from EPR measurements, • to calculate ENDOR frequencies, to plot patterns of their angular dependencies, and • to compare the patterns with measured angular dependencies of ENDOR for a definite EPR line [13,38,39].
Due to different surroundings for impurities in the Li and Nb sites, the calculated patterns are completely different ( Figure 6). ENDOR frequencies for the first shell of Li nuclei for the Li site vary with rotation of magnetic field in xy plane (Figure 6a), whereas for the single Li nucleus of the first shell for Nb site two straight branches should be observed in angular dependence ( Figure 6c). As Li nuclei of the all corresponding shells are closer to the impurity ion in the Nb site than in the Li site, the range of angular variation for Nb site is larger than for Li site. The branches of the 2nd and 3rd shells for Li site practically coincide with measured angular dependencies for Nd1 center (Figure 6b), whereas no branch for Nb site is close to observed one. The branches of the 1st shell for Li substitution also agree with observed ones after small correction due to isotropic hyperfine interaction (Figure 6b). Based on clear agreement of hundred measured values of ENDOR frequencies for the dominant EPR line #1 with calculated frequencies for Li site and obvious disagreement with calculated ones for Nb site, we can definitely conclude that the Nd1 line in EPR spectra ( Figure 2) belongs to Nd 3+ ion substituted for Li. The simulation of dipole-dipole interactions for the Li and Nb sites has no fitting parameter. Therefore, the described qualitative and quantitative approach for the determination of impurity positions gives reliable results. Note that hyperfine interactions for Nb/Ta nuclei have additional contributions due to a polarization of inner electron shells of oxygen and niobium ions (transferred hyperfine interaction).
The characteristic of isotropic hyperfine interaction ( ) is related to a density of electron cloud at the location of i-nucleus R (i) . For the isotropic g-factor: The isotropic hyperfine interaction often (but not always) exponentially decreases with the distance from impurity. The largest value ( ) / ( ) should correspond to nuclei The simulation of dipole-dipole interactions for the Li and Nb sites has no fitting parameter. Therefore, the described qualitative and quantitative approach for the determination of impurity positions gives reliable results. Note that hyperfine interactions for Nb/Ta nuclei have additional contributions due to a polarization of inner electron shells of oxygen and niobium ions (transferred hyperfine interaction).
The characteristic of isotropic hyperfine interaction a (i) is related to a density of electron cloud at the location of i-nucleus R (i) . For the isotropic g-factor: The isotropic hyperfine interaction often (but not always) exponentially decreases with the distance from impurity. The largest value a (i) /g n for Li and Nb nuclei, and therefore, to find the impurity location. Impurities substituted for Li have Nb nucleus on z-axis in the nearest surrounding, whereas ions substituted for Nb have Li nucleus ( Figure 6, shell #1).
Another way to use contact and dipole-dipole interactions is: • to measure the road map of angular dependencies in three perpendicular planes (Figure 4a), • to determine all components of A (i) tensors by fitting observed angular dependencies, • to separate isotropic and anisotropic parts, • to find principal values of the anisotropic part, and finally, • to compare these principal values with calculated ones on the base of Equation (3).

Charge Compensation and Intrinsic Defects
The structure of a center, in which a lattice site is occupied by an extrinsic impurity ion having a charge different from that of the respective lattice ion (in the following labeled "non-isocharged replacement"), depends on the charge of the impurity and the mechanism of charge compensation. Because of non-stoichiometry, the real lattice of conventional congruent LN contains many intrinsic defects, the relative concentrations of which have not yet been determined reliably. The following entities have been considered (their charges with respect to the lattice being given by Kröger-Vink notation in brack-  [96,97]), 5Nb Li + 4v Nb [98,99], 2Nb Li + 2Nb v + 3v Li + 3v Nb [96] and some others [100]. Some features accompanying the crystal growth (Li 2 O evaporation, variation of oxygen deficiency in Nb 2 O 5-x [101]) and specific changes of some crystal properties after thermal oxidation and/or reduction definitely indicate that the oxygen sub-lattice is not always perfect and stable as well; therefore the oxygen non-stoichiometry has been also discussed for a long time [102][103][104][105]. The intrinsic defects by themselves or complexes of them, which are not charge compensated, can furthermore serve as local or distant charge compensators for non-isocharged extrinsic or radiation defects. Due to the high concentration of the intrinsic defects the congruent LN and LT crystals are very tolerant to substitutional or interstitial impurities, including non-controlled ones, because the necessary charge compensators (local or distant) can be easily found among the non-stoichiometric defects. Real crystals often contain H, Cu, Co, Mn, Fe, etc. in concentrations about 0.00X-0.0X.
Non-isovalent cation Me n+ (n > 1) substituted for Li + requires negative charge compensator like lithium vacancy or interstitial O 2− . If Me n+ (n < 5) substituted for Nb 5+ or Ta 5+ the n − 5 negative charge can be compensated by antisite ions, oxygen vacancies, v O or interstitial H + and Li + . In some cases, a self-compensation of impurity charges takes place. For instance, no additional charge is required if two Me 3+ ions substitute for both Li + and Nb 5+ in nearest neighbor or next neighbor sites (local self-compensation) or even relatively far one from another (distant self-compensation). There are two critical parameters, which stimulate the self-compensation: total concentration of possible charge compensation defects, then the self-compensation is preferable due to lack of charge compensators.
Distant charge compensators produce small distortions of the crystal field at the impurity site, what normally causes EPR line broadening, and an asymmetry of their shapes, but do not change the center symmetry revealed in the observed positions and splitting of EPR lines. Defects in the immediate neighborhood (local charge compensation) cause strong changes of the center characteristics (g and A tensors in the case of Nd 3+ ) and lowering of center symmetry.

Di-Vacancy Models for Trivalent Impurities
Many impurities in LN/LT crystals create a family of paramagnetic centers that includes dominant axial center and several satellite low-symmetry centers with EPR lines of smaller intensities (like presented on Figure 2). It would be reasonable to look for center models which are able to describe the whole family.
Low-symmetry C 1 centers appear in three cases: 1. Impurity ion like Nd 3+ has an off-axis lattice defect (charge compensator) in the immediate neighborhood.

2.
Impurity ion substitutes for O 2− (this is very improbable for cations).

3.
Impurity ion incorporates into a small tetrahedral void (this is possible, but often unlikely due to larger charge misfit than for Li substitution).
For axial centers, the directions of principal axes of the g-tensor are dictated by crystal symmetry: the 3rd axis of the center coincides with the crystal axis and the directions of the 1st and 2nd axes are arbitrary. For low-symmetry centers, there are no symmetry restrictions on the orientation of principal axes. However, if the symmetry lowering is related to an off-axis lattice defect, it is reasonable to expect that directions of the center axes are related to the distortion created by the off-axis defect. The 3rd axis will have some inclination from the z-axis to the defect, and projections of the 1st or 2nd axis will be close to the projection of line from the impurity ion to the defect. The distortion should decrease with the distance from the impurity ion to the defect.
ENDOR data for the dominant EPR line have confirmed that Nd 3+ substitutes for Li + and only Li and Nb nuclei were found in the neighborhood. Therefore, intrinsic defects without nuclear spin should be considered for the required 2-charge compensation. The size O 2− is comparatively large to be placed into small octahedral or tetrahedral voids. Nearly stoichiometric crystals have significantly reduced concentration of v Li . Nevertheless, their concentration often exceeds the impurity concentration. Sufficient concentration of v Li can be also created in the process of growth of samples with non-isocharged impurities.
A key to the identification of models which describe all varieties of Nd 3+ centers with minimal assumptions was obtained from the analysis of angular dependencies of the Nd 4 center. The extrema in the xy plane and, correspondingly, projections of one principal axis of the g-tensor, are close to φ values of 15, 45, and 75 degrees (Figure 4b). In the projection of the LN lattice onto the xy plane ( Figure 7, after [93]) there are no similar values of φ from Nd 3+ to any ion in the lattice: directions from the Nd 3+ site to all cation sites have azimuthal angles equal to n × 30 • . Therefore, the simplest model, that has a single lattice defect, like a Li + vacancy, v Li , cannot explain the observed angular dependencies of Nd 4 centers. However, if two Li + vacancies are located in the first and second shells of the surroundings of an Nd 3+ ion substituted for a Li + , the three defects are organized into a triangle. The longest side of the triangle connected two v Li has a perpendicular oriented in the required direction ( Figure 7).
The hypothesis that Nd 3+ substituted for Li + has two v Li as charge compensators allows for consistent models for the whole family of Nd 3+ centers in LN crystals with a low concentration of neodymium doping. After analysis of principal values and axes of g-tensors it was concluded [92,93] that Nd 3+ centers have lithium vacancies in sites described in Table 1. Some of possible structures are presented on Figures 7 and 8.
The di-vacancy models can explain EPR spectra of many other (but not all) trivalent The di-vacancy models can explain EPR spectra of many other (but not all) trivalent impurities Me 3+ Li.

Center vLi Site
The di-vacancy models can explain EPR spectra of many other (but not all) trivalent impurities Me 3+ Li.

Monovalent Cations
The most probable incorporations of Me + is the substitution for Li + . No charge compensation is required in this case. The Me Li + center should have axial C 3 symmetry.
Proton H + . This is an example of off-site position: protons occupy positions between two oxygen ions in an oxygen plane. The non-paramagnetic OH − centers were studied by infrared and NMR spectroscopies [80,[106][107][108].
A hydrogen associated paramagnetic center (g = 2.0028, A = 3 mT at 77 K) was identified as an OH 2− ion, produced because of an electron capture by a diamagnetic OH − ion, substituting the O 2− ion in LN [109].
Ni + (3d 9 , S = 1/2). Observed EPR spectra of the Ni + have axial symmetry at room temperature [110,111]. That excludes interstitial position in tetrahedral structural vacancies. However, at low temperatures the Ni + center has C 1 symmetry, as up to six lines were observed at arbitrary orientation of magnetic field (Figure 9a, after [111]). The most probable incorporations of Me + is the substitution for Li + . No charge compensation is required in this case. The MeLi + center should have axial C3 symmetry.
Proton H + . This is an example of off-site position: protons occupy positions between two oxygen ions in an oxygen plane. The non-paramagnetic OH − centers were studied by infrared and NMR spectroscopies [80,[106][107][108].
A hydrogen associated paramagnetic center (g = 2.0028, A = 3 mT at 77 K) was identified as an OH 2− ion, produced because of an electron capture by a diamagnetic OH − ion, substituting the O 2− ion in LN [109].
Ni + (3d 9 , S = 1/2). Observed EPR spectra of the Ni + have axial symmetry at room temperature [110,111]. That excludes interstitial position in tetrahedral structural vacancies. However, at low temperatures the Ni + center has C1 symmetry, as up to six lines were observed at arbitrary orientation of magnetic field (Figure 9a, after [111]). The center was characterized by anisotropic g-tensor with principal values g1 = 2.246, g2 = 2.217 and g3 = 2.061; principal axes of the g-tensor are rotated with respect to crystallographic axes by Euler angles α = γ ≈ 0, β ≈ 55°. As the 3rd principal axis is directed approximately to one of the nearest oxygen ions, the reason for the low symmetry is a static Jahn-Teller effect for 3d 9 ions in Ni + O6 2− complexes ( Figure 9b, [111,112]), and not a presence of an intrinsic defect in the neighborhood. Dynamic averaging due to center reorientation leads to the axial symmetry of observed EPR spectra at room temperatures [111].
Mg + (3s 1 , S = 1/2). Following vacuum reduction at 1000 °C, LN crystals heavilydoped with Mg exhibit an optical absorption spectrum that can be decomposed into two bands peaking near 760 and 1200 nm, and a broad EPR spectrum with gc = 1.82 [113]. The 1200-nm band and ESR signal are associated with an electron trap (identical to the one produced during the irradiations). This electron trap is suggested to be a Mg + complex. There is an alternative interpretation of this spectrum [114].

Divalent Cations
For divalent Me 2+ impurities a substitution for Li + ions and incorporation in structural vacancies has essentially less charge misfit than a substitution for Nb 5+ . Since the Li-Li distance is much larger than Li-Nb or voct-Li, voct-Nb, the Me 2+ Li + vLi centers should be slightly distorted by the presence of a local charge compensator. For vLi located on C3 The center was characterized by anisotropic g-tensor with principal values g 1 = 2.246, g 2 = 2.217 and g 3 = 2.061; principal axes of the g-tensor are rotated with respect to crystallographic axes by Euler angles α = γ ≈ 0, β ≈ 55 • . As the 3rd principal axis is directed approximately to one of the nearest oxygen ions, the reason for the low symmetry is a static Jahn-Teller effect for 3d 9 ions in Ni + O 6 2− complexes ( Figure 9b, [111,112]), and not a presence of an intrinsic defect in the neighborhood. Dynamic averaging due to center reorientation leads to the axial symmetry of observed EPR spectra at room temperatures [111].
Mg + (3s 1 , S = 1/2). Following vacuum reduction at 1000 • C, LN crystals heavilydoped with Mg exhibit an optical absorption spectrum that can be decomposed into two bands peaking near 760 and 1200 nm, and a broad EPR spectrum with g c = 1.82 [113]. The 1200-nm band and ESR signal are associated with an electron trap (identical to the one produced during the irradiations). This electron trap is suggested to be a Mg + complex. There is an alternative interpretation of this spectrum [114].

Divalent Cations
For divalent Me 2+ impurities a substitution for Li + ions and incorporation in structural vacancies has essentially less charge misfit than a substitution for Nb 5+ . Since the Li-Li distance is much larger than Li-Nb or v oct -Li, v oct -Nb, the Me 2+ Li + v Li centers should be slightly distorted by the presence of a local charge compensator. For v Li located on C 3 axis and for distant cation vacancies (local and distant charge compensation) axial centers should be observed.
Co 2+ (3d 7 , S = 1/2, I = 7/2). Dominant axial Co 2+ center with g = 2.6 and g ⊥ = 4.96 ÷ 5.04, A ≈ 0, |A ⊥ | = 0.0154 cm −1 , as well as low-intensity low-symmetry satellite centers were observed in cLN [115,116] and vLN [117]. Similar g-and A-values were reported for LiTaO 3 :Co 2+ [116]. The picture agrees with Co 2+ substitution for Li + in the dominant axial center (Co Li ) and excess charge compensation by v Li (the Co 2+ ⇔ 2Li + substitution mechanism). A small EPR line of axially symmetric cluster of Co 2+ ions appeared in sLN [118] (Figure 10a). To explain it the substitution mechanism 4Co 2+ ⇔ 3Li + + Nb 5+ [119] was considered. The four Co 2+ ions can occupy nearest possible cation sites by occupying one Nb site and three neighbor Li sites, creating a trigonal pyramid with C 3 symmetry (Figure 10b). axis and for distant cation vacancies (local and distant charge compensation) axial centers should be observed.
Ni 2+ (3d 8 , S = 1). Several additional terms, which describe zero field splitting (ZFS) of energy levels, should be added to the spin-Hamiltonian (1) for paramagnetic centers with S > 1/2: From comparison of measured and calculated characteristics it was found that Co 2+ does not occupy exactly the host Li + site but undergoes an off-center displacement 0.006 nm away from the oxygen octahedron center in LiNbO 3 (or LiTaO 3 ) [120,121].
The Ni 2+ centers in LN exhibit the EPR spectra of C 3 symmetry. Therefore, the sum in (5) turns into one term b 0 2 O 0 2 /3. It was found that b 0 2 = −5.31 cm −1 and ∆g = g − g ⊥ = 0.04 [115,125]. Since EXAFS data supports Ni 2+ substitution for Li + [24], the reasonable choice for the charge compensator is one v Li that is located on the C 3 axis or very far of Ni 2+ .
A cluster substitution 4Ni 2+ ⇔ Ta 5+ + 3Li + was considered for LT [126]. Note that an agreement of measured and calculated spin-Hamiltonian parameters [127] was obtained for Ni 2+ substitution for Nb 5+ in LN without a charge compensator.
The charge excess of one interstitial Me 2+ or two Me 2+ Li could be exactly compensated by an additional O 2− ion. However, such a compensation looks unlikely, as the ionic radius of O 2− (about 1.4 Å) is larger than the sizes of octahedral or tetrahedral vacancies. Here f2 = 1/3, f4 = 1/60, f6 = 1/1260; , Ω ( )-Stevens operators, which are non-zero for k ≥ 2S. For C3 symmetry only q equal to 0, 3, and 6 are allowed. For S = 1 only terms with k = 2 are present in Equation (5).
The Ni 2+ centers in LN exhibit the EPR spectra of C3 symmetry. Therefore, the sum in (5) turns into one term /3. It was found that −5.31 cm −1 and Δg = g∥ − g^ = 0.04 [115,125]. Since EXAFS data supports Ni 2+ substitution for Li + [24], the reasonable choice for the charge compensator is one vLi that is located on the C3 axis or very far of Ni 2+ .
A cluster substitution 4Ni 2+  Ta 5+ + 3Li + was considered for LT [126]. Note that an agreement of measured and calculated spin-Hamiltonian parameters [127] was obtained for Ni 2+ substitution for Nb 5+ in LN without a charge compensator.
The charge excess of one interstitial Me 2+ or two Me 2+ Li could be exactly compensated by an additional O 2− ion. However, such a compensation looks unlikely, as the ionic radius of O 2− (about 1.4 Å) is larger than the sizes of octahedral or tetrahedral vacancies. . Hyperfine interactions with four Li and two Nb shells of surrounding nuclei were determined by ENDOR study in LN [139]. For isotropic g-tensor, the principal values of dipole-dipole interaction (3) can be described by: Comparison of measured values of ( ) with values calculated by Equation (6) for Li and Nb substitution has definitely shown that Mn 2+ ions occupy Li site [139].

Trivalent Cations
Most transition metals (including iron, titanium, and chromium) and rare-earth elements enter LN in this valence. If Me 3+ substitutes Li + there are three possibilities to compensate its 2+ excess charge: vLi, vNb and self-compensation with Me 3+ Nb 5+ in the nearest or distant neighborhood. Every Me 3+ Li can be compensated by two vLi; every five Me 3+ Li + ions-by two niobium vacancies. The positive antisite defect NbLi can serve as a . Hyperfine interactions with four Li and two Nb shells of surrounding nuclei were determined by ENDOR study in LN [139]. For isotropic g-tensor, the principal values of dipole-dipole interaction (3) can be described by: has only one negative charge relative to the ideal lattice, it produces a 4-5 times weaker perturbation of the crystal field than Nb 5+ Li + or v Nb 5+ . Therefore the centers with v Li + at distances of about 6 Å should probably are not distinguishable from axial centers with non-local charge compensation.
Interstitial Li + ions should be considered as charge compensators for Me 3+ Nb 5+ in Li-rich, VTE treated, and stoichiometric crystals. The association of Me 3+ Nb 5+ with one Li + ion in the nearest vacancy (partial local charge compensation) leads to an axial center, the second Li + in the next vacancies can decrease symmetry to C 1 , if located off center axis and near the impurity. Mg 2+ or Zn 2+ ions substituted for Li + can be also suitable compensators for Me 3+ Nb . Distances between the replaced ion and shells of possible location of compensators, various configurations of Me and charge compensators, as well as the symmetries of the corresponding complexes are given in References [87,[140][141][142].
Cr 3+ (3d 3 , S = 3/2). In congruent and Li-rich LN samples, the EPR lines of dominant axial Cr 3+ center, characterized with ZFS b 0 2 ≈ 0.39 cm −1 , are accompanied with small satellite lines ( Figure 13). Initial discussion with plausible but contradictory arguments about Li + or Nb 5+ substitution [134,[143][144][145][146][147][148] should be ended after PIXE [32] and detailed ENDOR [140] studies have shown that Cr 3+ substitutes for Li + and slightly shifted from regular Li site. ENDOR measurements confirmed that Cr 3+ substitutes for Li + also in all satellite centers. Therefore, the whole family of these Cr 3+ centers can be described as Cr 3+ Li with location of charge compensator on C 3 axis for axial or off it for low-symmetry centers.
The ENDOR measurements [140] found that hyperfine interactions with Nb nuclei of the 2nd and 3rd shells (Figure 5a) are stronger than with Li nuclei (Figure 14, bottom). However, lines of Nb nuclei on the center axis (1st and 4th shells) were not identified. It can be caused by unfortunate conditions of their observation, petal distribution of electron density for the 3d 3 ion or absence of Nb ion in one of these sites, i.e., v Nb . Two v Nb can serves as the charge compensator for five Cr 3+ Li . Although the presence of v Nb in undoped LN looks unlikely, the charge compensation defects in doped crystals (especially, if dopant concentrations exceed 0.X%) can differ from dominant intrinsic defects in undoped LN or LT. During the growth process, the required compensators can organize themselves around impurities or enter from air in order to minimize the creation energy for the impurity center. This is why structures with v Nb were proposed for satellite centers of Cr 3+ Li [87].
LN looks unlikely, the charge compensation defects in doped crystals (especially, if dopant concentrations exceed 0.X%) can differ from dominant intrinsic defects in undoped LN or LT. During the growth process, the required compensators can organize themselves around impurities or enter from air in order to minimize the creation energy for the impurity center. This is why structures with vNb were proposed for satellite centers of Cr 3+ Li [87].  pant concentrations exceed 0.X%) can differ from dominant intrinsic defects in undoped LN or LT. During the growth process, the required compensators can organize themselves around impurities or enter from air in order to minimize the creation energy for the impurity center. This is why structures with vNb were proposed for satellite centers of Cr 3+ Li [87].  On the other hand, v Li are considered as dominant intrinsic defects in LN and LT. Angular dependencies of EPR spectra for the dominant (C 3 ) and satellite (C 1 symmetry) Cr 3+ centers ( Figure 15) are pretty similar to observed patterns for Nd 3+ (Figure 4). Therefore, two vacancy models for trivalent impurities (Table 1)  On the other hand, vLi are considered as dominant intrinsic defects in LN and LT. Angular dependencies of EPR spectra for the dominant (C3) and satellite (C1 symmetry) Cr 3+ centers ( Figure 15) are pretty similar to observed patterns for Nd 3+ (Figure 4). Therefore, two vacancy models for trivalent impurities (Table 1)   A lack of intrinsic defects in stoichiometric samples leads unavoidably to a change of charge compensation mechanism for trivalent impurities, and substitution for Nb 5+ becomes possible. An axial Cr 3+ center with significantly smaller ZFS = 0.0215 cm −1 (Figure 16a) was found in LNK samples [142]. ENDOR study has shown that hyperfine interactions with Li nuclei significantly larger than with Nb nuclei for this center, i.e., the nearest surrounding consist of Li nuclei. This means that Cr 3+ substitutes for Nb 5+ in this center. As lines of protons, H + , were found in the ENDOR spectra (Figure14, top), they compensate the negative charge of Cr 3+ Nb 5+ (Figure 16b).
Exchange interaction S A JS B between spins of Cr 3+ ions (S A = S B = 3/2) leads to gaps between states with values of total spin S = S A + S B equal to 0, 1, 2, and 3. The state with S = 0 is non paramagnetic. For pairs at a close distance the gaps can exceed energies of microwave quantum (36 GHz ≈ 1.2 cm −1 ). It was found by magneto-optical study that for Cr 3+ Li-Cr 3+ Nb substituted for nearest Li and Nb sites (at the distance about 0.3 nm) the exchange interaction is antiferromagnetic and J ≈ 480 cm −1 . As 1 K × kB ≈ 0.7 cm −1 the upper states of such pairs with non-zero S are not populated even at room temperatures, and the pairs are EPR silent. However, the pairs of the next orders with the isotropic exchange coupling parameter J ≈ 1.5 cm −1 were observed by EPR at relatively low concentration of chromium in LN (less than 0.1 at.%) [87,134,[148][149][150]. A lack of intrinsic defects in stoichiometric samples leads unavoidably to a change of charge compensation mechanism for trivalent impurities, and substitution for Nb 5+ becomes possible. An axial Cr 3+ center with significantly smaller ZFS b 0 2 = 0.0215 cm −1 (Figure 16a) was found in LN K samples [142]. ENDOR study has shown that hyperfine interactions with Li nuclei significantly larger than with Nb nuclei for this center, i.e., the nearest surrounding consist of Li nuclei. This means that Cr 3+ substitutes for Nb 5+ in this center. As lines of protons, H + , were found in the ENDOR spectra ( Figure 14, top), they compensate the negative charge of Cr 3+ Nb 5+ (Figure 16b). Exchange interaction S A JS B between spins of Cr 3+ ions (S A = S B = 3/2) leads to gaps between states with values of total spin S = S A + S B equal to 0, 1, 2, and 3. The state with S = 0 is non paramagnetic. For pairs at a close distance the gaps can exceed energies of microwave quantum (36 GHz ≈ 1.2 cm −1 ). It was found by magneto-optical study that for Cr 3+ Li -Cr 3+ Nb substituted for nearest Li and Nb sites (at the distance about 0.3 nm) the exchange interaction is antiferromagnetic and J ≈ 480 cm −1 . As 1 K × k B ≈ 0.7 cm −1 the upper states of such pairs with non-zero S are not populated even at room temperatures, and the pairs are EPR silent. However, the pairs of the next orders with the isotropic exchange coupling parameter J ≈ 1.5 cm −1 were observed by EPR at relatively low concentration of chromium in LN (less than 0.1 at.%) [87,134,[148][149][150]. PIXE/channeling study [32] revealed that chromium ions occupy both regular cation sites (60% on Li sites and 40% on Nb sites) in congruent LN doped with 0.1 mol.% of Cr. This means that the majority of chromium ions enter cLN as non-paramagnetic pair centers. The EPR observes only a top of iceberg in cLN: dominant Cr 3+ Li and small signals of non-nearest paramagnetic pairs. ENDOR study of Cr 3+ centers in LN heavily doped with Mg and co-doped with Cr has unambiguously shown that Cr 3+ in the dominant center has ZFS close to zero (nearly isotropic case) and substitute for Nb [151][152][153][154][155]. Measured anisotropic hyperfine interactions of Cr 3+ with for four Li shells were close to ( ) [144] is very close to the value for Cr 3+ Li in LN. EPR spectra of this center together with signals of weaker intensities of a second center [163,164] were explained in a supposition that they originate from Cr 3+ ions located at Li + sites and that two vLi play the role of a divalent charge compensator for both centers. EPR study of Cr 3+ in nsLT and superposition model analysis [165] are in good agreement with the Cr 3+ substitution for Li. The temperature dependence of b2 0 term showed a non-monotonic behavior in the region of 40 K.
Finally, a lot of studies were devoted to various properties of Cr 3+ in LN and LT crystals of different compositions in order to clarify relations of optical characteristics with structures of chromium centers [166][167][168][169][170][171][172][173][174][175] etc. Dy 3+ (4f 9 ). The observed Zeeman splitting [143] was described with g-tensor of axial symmetry: g∥ = 8.7 and g^ = 1.3. The single EPR line had width about 8-10 mT at B||z and became broader at B^z. Such a behavior can be related to unresolved splitting due to satellite centers, if Dy 3+ occupies Li position and its charge is compensated by vLi. Two Dy 3+ centers with gxx(1) = 2.56(1), gzz(1) = 4.43 (1), and gxx(2) = 6.67(1), gzz(2) = 1.23 (1) and linewidth about 20 mT were registered in LN after γ-irradiation [176]. Both centers were attributed to Dy 3+ Li. A broad line of the third center with gzz(3) ≈ 1.2 appeared only at B close to the z-axis. Weak hyperfine lines due to isotopes 161 Dy (natural abundance 19%), 163 Dy (2.49%) was observed in single crystal of LN [177]. PIXE/channeling study [32] revealed that chromium ions occupy both regular cation sites (60% on Li sites and 40% on Nb sites) in congruent LN doped with 0.1 mol.% of Cr. This means that the majority of chromium ions enter cLN as non-paramagnetic pair centers. The EPR observes only a top of iceberg in cLN: dominant Cr 3+ Li and small signals of non-nearest paramagnetic pairs. ENDOR study of Cr 3+ centers in LN heavily doped with Mg and co-doped with Cr has unambiguously shown that Cr 3+ in the dominant center has ZFS b 0 2 close to zero (nearly isotropic case) and substitute for Nb [151][152][153][154][155]. Measured anisotropic hyperfine interactions of Cr 3+ with for four Li shells were close to b (i) dd for Nb site. From comparison of data obtained by EPR, ENDOR, optical absorption, fluorescence, fluorescence line narrowing, selective excitation and radiative lifetime measurements [156][157][158][159][160][161][162] it has been concluded that the addition of Mg 2+ ions to LN does not create new Cr 3+ complexes, but changes the relative concentrations of the Cr 3+ Li and Cr 3+ Nb centers. The measured value of ZFS for dominant Cr 3+ in cLT b 0 2 ≈ 0.444 cm −1 [144] is very close to the value for Cr 3+ Li in LN. EPR spectra of this center together with signals of weaker intensities of a second center [163,164] were explained in a supposition that they originate from Cr 3+ ions located at Li + sites and that two v Li play the role of a divalent charge compensator for both centers. EPR study of Cr 3+ in nsLT and superposition model analysis [165] are in good agreement with the Cr 3+ substitution for Li. The temperature dependence of b 2 0 term showed a non-monotonic behavior in the region of 40 K. Finally, a lot of studies were devoted to various properties of Cr 3+ in LN and LT crystals of different compositions in order to clarify relations of optical characteristics with structures of chromium centers [166][167][168][169][170][171][172][173][174][175] etc. Dy 3+ (4f 9 ). The observed Zeeman splitting [143] was described with g-tensor of axial symmetry: g = 8.7 and g ⊥ = 1.3. The single EPR line had width about 8-10 mT at B||z and became broader at B⊥z. Such a behavior can be related to unresolved splitting due to satellite centers, if Dy 3+ occupies Li position and its charge is compensated by v Li . Two Dy 3+ centers with g xx (1) = 2.56(1), g zz (1) = 4.43(1), and g xx (2) = 6.67(1), g zz (2) = 1.23 (1) and linewidth about 20 mT were registered in LN after γ-irradiation [176]. Both centers were attributed to Dy 3+ Li . A broad line of the third center with g zz (3) ≈ 1.2 appeared only at B close to the z-axis. Weak hyperfine lines due to isotopes 161 Dy (natural abundance 19%), 163 Dy (2.49%) was observed in single crystal of LN [177].
Er 3+ (4f 11 ). Due to fast spin-lattice relaxation, the EPR signals of Er 3+ are observable at low-temperatures only. Earlier studies claimed that Er 3+ ions in cLN create an axial  [143,178] or g zz ≈ 15.5 and g xx ≈ g yy ≈ 0.8 [179]. A proposed model with lithium vacancies statistically distributed around Er 3+ Li [179] supposed that the center with no vacancies in surrounding, i.e., the center with axial C 3 symmetry, should give a dominant (54%) line in the EPR spectra. Note that angular dependences of EPR spectra in xy-plane were not measured in these studies. Later measurements in all three principal planes [180][181][182][183] have shown that there is no line without angular dependence in the xy-plane, i.e., dominant Er 3+ center in cLN has C 1 symmetry. This does not agree with statistically distributed v Li around Er 3+ Li [179]. Significant narrowing of EPR lines in LN K (Figure 17a) allowed us to trace two different Er 1 3+ and Er 2 3+ centers with extrema at about 15, 45 and 75 degrees in xy plane (Figure 17b) [184,185]. The divacancy model (Figure 7) gives a possible explanation if a shift of Er 3+ Li from regular Li site is taken into account: RBS, XSW and ion-beam/channeling studies have determined that Er occupies Li sites, but is shifted from the ferroelectric Li position by 0.03 [186], 0.046 [187], and 0.02 nm [188]. In this case, distances from Er Li to the v Li in the 1a and 1b shells (Figures 5a and 7b) are completely different, and these centers have one charge compensating v Li in the nearest neighborhood (the shell 1a for Er 1 , and 1b for Er 2 ), and the second v Li in the next nearest neighborhood (shells 2a, 2b, Figure 7). Er 3+ (4f 11 ). Due to fast spin-lattice relaxation, the EPR signals of Er 3+ are observable at low-temperatures only. Earlier studies claimed that Er 3+ ions in cLN create an axial center with g∥ ≈ 15.1-15.4 and g^ ≈ 2.1 [143,178] or gzz ≈ 15.5 and gxx ≈ gyy ≈ 0.8 [179]. A proposed model with lithium vacancies statistically distributed around Er 3+ Li [179] supposed that the center with no vacancies in surrounding, i.e., the center with axial C3 symmetry, should give a dominant (54%) line in the EPR spectra. Note that angular dependences of EPR spectra in xy-plane were not measured in these studies. Later measurements in all three principal planes [180][181][182][183] have shown that there is no line without angular dependence in the xy-plane, i.e., dominant Er 3+ center in cLN has C1 symmetry. This does not agree with statistically distributed vLi around Er 3+ Li [179].
Significant narrowing of EPR lines in LNK (Figure 17a) allowed us to trace two different Er1 3+ and Er2 3+ centers with extrema at about 15, 45 and 75 degrees in xy plane (Figure 17b) [184,185]. The divacancy model (Figure 7) gives a possible explanation if a shift of Er 3+ Li from regular Li site is taken into account: RBS, XSW and ion-beam/channeling studies have determined that Er occupies Li sites, but is shifted from the ferroelectric Li position by 0.03 [186], 0.046 [187], and 0.02 nm [188]. In this case, distances from ErLi to the vLi in the 1a and 1b shells (Figures 5a and 7b) are completely different, and these centers have one charge compensating vLi in the nearest neighborhood (the shell 1a for Er1, and 1b for Er2), and the second vLi in the next nearest neighborhood (shells 2a, 2b, Figure 7).
Magnetic moments for both Er 3+ centers are very large and strongly anisotropic. At low temperatures their interactions lead to magnetic ordering for Er concentration about 0.5 at.% in sLN [189]. Various models with two vLi were also extensively discussed in papers devoted to site-selective spectroscopy [190][191][192][193][194][195][196] and references there. Note that models with one of two vLi on z-axis (Figure 8) do not agree with the EPR spectra for dominant lines and hyperfine satellites on Figure 17a. However, such centers can probably be associated with weaker lines or may have no EPR lines at all, if they are non-paramagnetic.
EPR spectra detected in cLN heavily doped with Mg or Zn and co-doped with Er were described with g∥ = 4.3, g⊥ = 7.6 for the Mg-doped samples and g∥ = 4.26, g⊥ = 7.8 for the Zn-doped ones [197]. The spectra can be attributed to Er 3+ located at the Nb 5+ site of LN, as they are compared to additional centers observed for some trivalent transition metal ions (particularly Cr 3+ ) in LN: Mg or LN:Zn. Magnetic moments µ B gS for both Er 3+ centers are very large and strongly anisotropic. At low temperatures their interactions lead to magnetic ordering for Er concentration about 0.5 at.% in sLN [189].
Various models with two v Li were also extensively discussed in papers devoted to site-selective spectroscopy [190][191][192][193][194][195][196] and references there. Note that models with one of two v Li on z-axis (Figure 8) do not agree with the EPR spectra for dominant lines and hyperfine satellites on Figure 17a. However, such centers can probably be associated with weaker lines or may have no EPR lines at all, if they are non-paramagnetic.
EPR spectra detected in cLN heavily doped with Mg or Zn and co-doped with Er were described with g = 4.3, g ⊥ = 7.6 for the Mg-doped samples and g = 4.26, g ⊥ = 7.8 for the Zn-doped ones [197]. The spectra can be attributed to Er 3+ located at the Nb 5+ site of LN, as they are compared to additional centers observed for some trivalent transition metal ions (particularly Cr 3+ ) in LN: Mg or LN:Zn.

•
Lines of allowed transitions in LN K become symmetric-intensities of left (up) and right (down) wings become equal.

•
Lines of forbidden transitions (see yellow box on Figure 18) disappear in LN K .
Comparison of EPR spectra of congruent (Figure 18a, 1), near-stoichiometric grown from Li enriched melts (Figure 18a, 2) and grown from congruent melt with the addition of K2O, LNK samples (Figure 18a In LNK the EPR lines become narrower (up to dozen times at some magnetic field orientation). The narrowing strongly increases spectral resolution. This allows to register even trace impurities in undoped (nominally pure) LNK samples (see lines of Fe 3+ and Mn 2+ on Figure 18a, 3).  EPR spectra with random distributions of non-axial components of ZFS, b q 2 (q = 0) for Cr 3+ and Fe 3+ and confirmed that line width and asymmetry, as well as intensities of forbidden transitions are related to intrinsic defects in non-stoichiometric samples [43]. In 1991, on Malovichko's request Dr. Kokanyan has grown several congruent samples with 2, 4, and 6% of K 2 O in the melt (LN K ). First EPR measurement has surprisingly shown narrow symmetrical lines in LN K with traces of Fe 3+ (Figure 18a, 3). Based on the experience of studies of Li-rich samples, it was concluded that the concentration of intrinsic defects in LN K is smaller than in LN grown from the melt with x m = 60%, and that K 2 O may serve as a catalyst in electrochemical reaction of crystal growth [56]. As abilities of research techniques in Ukraine were limited, Dr. Malovichko asked Prof. O. F. Schirmer (Osnabrueck University, Germany) for an international collaboration. Prof. Schirmer was very enthusiastic and has quickly managed to involve many of his colleagues in the investigation of LN K properties. K. Betzler, B. Faust, B. Gather, F. Jermann, S. Klauer, U. Schlarb, M. Wesselmann, M. Woehlecke and others participated in the LN K study by different techniques resulting in publications [57,69,77].
All these features are the result of significant reduction of intrinsic defects in LN K samples. Estimations of crystal composition x C made by different methods [59,68,77,79] have shown that x C can exceed 49.8-49.9%, i.e., LN K is really a stoichiometric crystal.
As for other impurities, the lack of intrinsic defects in LN K :Fe has led to the appearance of centers where impurities substitutes for Nb. Two additional axial Fe 3+ centers named Fe 3 and Fe 4 were observed in LN K [69]. Their ZFS are b 0 2 = 0.0495 and b 0 2 = 0.0688 cm −1 . Compared with Fe 2 , the Fe 3 and Fe 4 centers were also assigned to Fe 3+ in Nb sites with different charge compensation. The Fe 3+ center with b 0 2 = 0.0656 cm −1 (that is very close to b 0 2 for Fe 4 ) was observed in VTE treated stoichiometric LN [76]. Therefore, Fe 4 , Fe 3 , and Fe 2 were attributed to Fe Nb with different charge compensator ions in nearest structural vacancy v oct : Fe 4 -non-regular, interstitial Li + v (Figure 19a), Fe 3 -K + v , and Fe 2 -Mg 2+ v . Two Li + v (Figure 19b), or interstitial Mg 2+ v or two Mg 2+ Li + are required for full charge compensation of Fe 3+ Nb 5+ . Our measurements of EPR in LN:Mg show angular patterns with extrema at 15, 45 and 75 degrees in xy plane. It is why we think that models with two differently located Mg 2+ Li + (Figure 19c,d) are more suitable for Fe Nb (similar to models with two v Li for Fe Li ). ENDOR measurements could confirm some of these reasonable assignments.
Dominant Fe 1 3+ center in cLT has b 0 2 = 0.33 cm −1 [38,225] (Figure 18b, 1), and according to ENDOR data [38] it is definitely Fe 3+ Li . Line narrowing in nsLT grown by double crucible Czochralski method from an Li rich melt composition (about 60 mol.% Li 2 O) allowed to determined b 2 0 more accurately [226]. The main features of the spectra in sLT obtained by VTE treatment are strong line narrowing, higher resolution, and a clear presence of the second axial Fe 2 3+ center with b 0 2 = 0.205 cm −1 (Figure 18b, 2) [75]. Comparison of calculated angular dependences of ENDOR frequencies for Li and Nb substitution using Equation (6) with measured ones (Figure 20) obviously shows that in the case of Fe 2 center the Fe 3+ ion substitutes for Nb. Both Fe 1 and Fe 2 centers in sLT have C 3 symmetry. No foreign nuclei in the nearest neighborhood were detected for Fe 1 . As sLT still have some residual concentration of v Li , the charge compensators for Fe 1 centers are one v Li on center axis (shells 5a, 5b on Figure 7) and probably one other distant v Li (any vacancy cannot be directly detected by ENDOR).  A pair of ENDOR lines for Fe2 (fuchsia line on Figure20b) were attributed to the additional Li + v in the nearest voct at the distance about 0.277 nm from Fe 3+ Nb. It is difficult to make a choice between two models on Figure 19a,b as lines of the second Li + i in the next or next-next voct are not identified yet. The ratio of concentrations of Fe2 and Fe1 centers changed from less than 0.2 for Fe concentrations 1.1 × 10 19 cm −3 to about 1 for 6.7 × 10 19 cm −3 in the crystals. Therefore, there are three different mechanisms for excessive   A pair of ENDOR lines for Fe 2 (fuchsia line on Figure 20b) were attributed to the additional Li + v in the nearest v oct at the distance about 0.277 nm from Fe 3+ Nb . It is difficult to make a choice between two models on Figure 19a,b as lines of the second Li + i in the next or next-next v oct are not identified yet. The ratio of concentrations of Fe 2 and Fe 1 centers changed from less than 0.2 for Fe concentrations 1.1 × 10 19 cm −3 to about 1 for 6.7 × 10 19 cm −3 in the crystals. Therefore, there are three different mechanisms for by Li + in v oct for Fe 3+ concentrations, which exceed the concentration of v Li . Gd 3+ (4f 7 , S = 7/2). The EPR spectrum for every Gd 3+ center consists of 2S + 1 = 8 strong lines of fine structure and many low intensity lines of so called forbidden transitions due to nearly equal values of Zeeman splitting and ZFS. Results of the first EPR study [227], were interpreted as a presence of two axial Gd 1 and Gd 2 centers with b 0 2 = 0.118 and b 0 2 = 0.126 cm −1 . From the viewpoint of charge compensation, a preference was given to Gd 3+ substitution for Nb 5+ . A small rhombic distortion (b 2 2 ≈ 0.004) determined for Gd 2 [228] was attributed to an off axis charge compensator, while for Gd 1 the charge compensator may either be absent or must lie on the same threefold axis as Gd 3+ . However, no decision on whether Gd 3+ substitutes for Li + or Nb 5+ or for both was made. Similar results with slightly smaller b 2 2 ≈ 0.002 were also reported [229]. At least four different Gd 3+ centers were identified in our study of Li-rich LN doped with 1 wt.% Gd 2 O 3 in the melt. As patterns for every EPR transition in xy-plane ( Figure 21) are very similar to presented on Figures 4b and 15, the divacancy model is suitable for Gd 3+ in LN. Gd 3+ substitutes for Li + in all centers. The dominant axial Gd 1 center and low-symmetry Gd 2 , Gd 3 , and Gd 4 centers have v Li in positions described in Table 1. This assignment agrees with the Gd substitution for Li found by RBS and PIXE channeling [31]. Gd 3+ (4f 7 , S = 7/2). The EPR spectrum for every Gd 3+ center consists of 2S + 1 = 8 strong lines of fine structure and many low intensity lines of so called forbidden transitions due to nearly equal values of Zeeman splitting and ZFS. Results of the first EPR study [227], were interpreted as a presence of two axial Gd1 and Gd2 centers with = 0.118 and = 0.126 cm −1 . From the viewpoint of charge compensation, a preference was given to Gd 3+ substitution for Nb 5+ . A small rhombic distortion ( ≈ 0.004) determined for Gd2 [228] was attributed to an off axis charge compensator, while for Gd1 the charge compensator may either be absent or must lie on the same threefold axis as Gd 3+ . However, no decision on whether Gd 3+ substitutes for Li + or Nb 5+ or for both was made. Similar results with slightly smaller ≈ 0.002 were also reported [229]. At least four different Gd 3+ centers were identified in our study of Li-rich LN doped with 1 wt.% Gd2O3 in the melt. As patterns for every EPR transition in xy-plane ( Figure  21) are very similar to presented on Figures 4b and 15, the divacancy model is suitable for Gd 3+ in LN. Gd 3+ substitutes for Li + in all centers. The dominant axial Gd1 center and low-symmetry Gd2, Gd3, and Gd4 centers have vLi in positions described in Table 1. This assignment agrees with the Gd substitution for Li found by RBS and PIXE channeling [31]. Nd 3+ (4f 3 ) First EPR spectra have shown that in cLN Nd 3+ creates an axial center with g∥ ≈ 1.43 and g^ ≈ 2.95 (Nd1) [143,144,230] and second center with g∥ ≈ 1.33 and g^ ≈ 2.95 (Nd2) [143]. EPR/ENDOR studies in sLN [91][92][93] has established that Nd 3+ substitutes for Li + , and resolved eight different Nd 3+ centers. Divacancy models explain angular dependencies of EPR spectra for the whole family of Nd 3+ centers [93], and Section 3.1 of this paper.
It is supposed that Nd 3+ center found in LN:Mg and LN:Zn belong to Nd 3+ substituted for Nb [231].
Ti 3+ (3d 1 , S = 1/2) EPR spectrum of Ti 3+ consist of one line with g ≈1.961 and g ⊥ ≈ 1.840 in LN [232][233][234], and g = 1.948, and g ⊥ = 1.827 in reduced LT [235]. An axial EPR signal observed in vacuum annealed LiNbO 3 single crystals doped with 8 mol.% Mg and 0.05 mol.% Ti has g = 1.760 and g ⊥ = 1.786 for T = 5 K and g = g ⊥ = 1.893 for T = 74 K. The signal has been attributed to Ti 3+ on Nb site [236][237][238][239][240]. The g tensor components of these centers were explained by a model calculation involving a dynamic pseudo Jahn-Teller effect. Spin-orbit coupling, lattice vibration, pseudo Jahn-Teller interaction, and the Zeeman term were treated on equal footing. Electron transfer from the observed Ti 3+ Nb center to lattice niobiums, resulting in Nb 4+ trapped polarons, has been stimulated by illumination in the near UV region.
Yb 3+ (4f 13 ) The EPR lines of Yb 3+ in congruent LN are very broad (Figure 22a,c) [241]. The axial center Yb 1 with g ≈ 4.7-4.86 and g ⊥ ≈ 2.7 was observed in cLN with 0.5-1.2 wt.% Yb 2 O 3 in the melt [144,230,241]. The second Yb 2 3+ center with g ≈1.9 and g ⊥ ≈ 2.8 was found in LN:Mg [241]. By comparison of these observations with EPR data for Cr 3+ , Er 3+ , Fe 3+ , and Ti 3+ in LN and LN:Mg the Yb 1 center was tentatively assigned to Yb 3+ Li and Yb 2 center to Yb 3+ Nb . A variation of lattice parameters found in cLN:Yb supported Yb 3+ substitution for Li compensated by Li + vacancy [242].
Our study of LN K crystals doped with 0.02 wt.% Yb 2 O 3 has shown that the broad line observed in cLN belongs in reality to a family of at least 8 different centers (Figure 22b,d) [92,248,249]. Hyperfine structures from isotopes 171 Yb (I = 1/2, natural abundance 14.4%) and 173 (I = 5/2, 16.6%) that are barely distinguished in cLN, were well resolved in LN K (see Figures 22 and 23). The dominant Yb 1 line that represents even isotopes with I = 0 ( even Yb, 69%) was described with g  Figure 22) were described with spin-Hamiltonian for S = 1 and anisotropic S A JS B interaction (J ik ≈ 0.012-0.066 cm −1 ). They were assigned to low-symmetry Yb 3+ -Yb 3+ pairs. The presence of additional lines of hyperfine structure with similar angular dependence (indicated by red arrows in Figure 23) supports the assignment, as their intensities are proportional to probabilities to meet two even Yb, or one even Yb and one 171 Yb, or one even Yb and one 173 Yb in such pairs. A self-compensated pair consisted of Me 3+ Li and Me 3+ Nb in the nearest sites (Nb shell 1 at a distance 0.3 nm on the crystal axis, Figure 5a) creates an axial center with rather strong exchange interaction (Jiso > 300 cm −1 ). Therefore, the observed low-symmetry pairs were attributed to the Yb 3+ -Yb 3+ ions in next neighbor or next-next neighbor positions (shells 2 and 3 on Figure 5a). One of the satellite centers (Yb 6 ) has axial symmetry; all others are low-symmetry centers. ENDOR measurements has revealed that Yb 3+ substitutes for Li: at the first, comparison of measured angular dependencies with calculated ones on the base of dipoledipole interactions (Equation (3)) gave undisputable preference for Li site, and at the second, the strongest axial hyperfine interaction was found for 93 Nb on the z-axis (the first shell on Figure 5a). The most reasonable explanation for the existence of the whole family of ytterbium centers is that Yb 3+ Li is compensated by one or two v Li in different configurations.  One of the satellite centers (Yb6) has axial symmetry; all others are low-symmetry centers. ENDOR measurements has revealed that Yb 3+ substitutes for Li: at the first,  One of the satellite centers (Yb6) has axial symmetry; all others are low-symmetry centers. ENDOR measurements has revealed that Yb 3+ substitutes for Li: at the first,

Tetra-, Penta-and Heptavalent Cations
The non-paramagnetic tetravalent impurities (C and Si) are always present in LN in rather high concentrations (about 50-500 ppm). Since determined concentrations of chlorine Cl (50-500 ppm) and manganese Mg (1-100 ppm) have the same order of magnitudes, no other charge compensators are necessary if C or Si substitutes for Nb creating C 4+ Nb -Cl − O 2− or C 4+ Nb -Mg 2+ Li . The additional possibilities for the charge compensation supply H + and Li + v ions. It is supposed that Ti 4+ substitutes for Nb 5+ ; however, at present a mechanism of its charge compensation is not well established.
Due to the lithium deficiency of congruent lithium niobate crystals, v Li have been considered as possible charge compensators for Nb 5+ Li + or Ta 5+ Li + antisites for a long time. Models with plane and space configurations of v Li for non-stoichiometric defects were proposed [96,97] and used for calculations of stability of intrinsic defects and defect clusters in LN [250][251][252][253] and LN:Mg [254]. The antisites become paramagnetic ions Nb 4+ Li + or Ta 4+ Li + after irradiation (see Section 4.5 below). The Ta 5+ substitution for Nb 5+ in LN causes minor lattice distortions only. The heptavalent ions (Mo, W) probably substitute for Nb 5+ having lithium vacancies as charge compensators.
U 5+ (5f 1 ). EPR spectra of U 5+ were studied in LiNbO 3 powders doped with natural U 3 O 8 and 233 U 3 O 8 . A hyperfine sextet of EPR line for 233 U (I = 5/2) was described with A = 0.0145 and A ⊥ = 0.0128 cm −1 . g = 0.71, g ⊥ = 0.724 were determined for the line of natural U 5+ (even isotopes with I = 0 have total natural abundance about 99%). It was observed that U 5+ takes part in photoinduced valence change which is the basic mechanism for photorefraction.

Radiation and Reduction Defects
A radiation usually recharges of regular lattice, interstitial and impurity ions or produces interstitial ions. Two kinds of recharged defects were observed in LN: electron traps like Nb 4+ and hole traps like O − ions [236,255,256].
Nb 4+ (4d 1 ). Hyperfine interaction of the unpaired 4d 1 electron with the 93 Nb nuclear spin I = 9/2 splits its EPR line into ten components. The ten-line EPR spectrum (g = 1.90 and g ⊥ = 1.72) has been described for congruent LiNbO 3 after ionizing radiation [257]. Later this spectrum has been reproduced in vacuum-reduced and UV bleached crystals [258][259][260][261] (Figure 24, 1) and ascribed to antisite Nb [255]). It is remarkable that at least part of the Nb 4+ centers has C 1 symmetry [262], although the main possible positions for Nb (regular Nb and Li site, v oct ) have C 3 symmetry. It means that compensating defects for Nb 4+ , most probably lithium vacancies, are located in the nearest neighborhood (Figure 25a,b).
Similar spectra were observed in LiNbO 3 doped with 6 mol.% Mg (Figure 24, 2) after X-irradiation or vacuum reduction treatments and were related to Nb 4+ centers on niobium sites [104,113,114], obviously with nearby defects. The Nb 4+ center in LiNbO 3 doped with 10 mol.% Mg belongs to Nb in regular position, but with Mg 2+ Li in neighborhood (Figure 24 Ta 4+ (5d 1 ). The isotope 181 Ta has I = 7/2 and 100% natural abundance. The eight-line axial EPR spectrum with g∥ = 1.503 and g^ = 1.172, A∥ = 0.0023, and A^ = 0.0234 cm −1 has been observed in LiTaO3 after reduction in argon and attributed to axial Ta 4+ Li [257]. Other ways to obtain Ta 4+ are an irradiation of as-grown crystals with X-rays or optical bleaching of crystals that had been previously reduced [264]. A possible model for axial Ta 4+ center is similar to the presented on Figure 25a. Tb 4+ (4f 7 ). EPR study at 15 K revealed a signal of g ≈ 2.0 appearing after UV irradiation with a simultaneous decrease in the Fe 3+ signal intensity in near-stoichiometric LiNbO3:Tb and LiNbO3:Tb:Fe [265]. This implies that the Fe 3+ ions act as electron traps. Irradiation by UV light induced an absorption band extending from λ ≈ 650 nm to the Ta 4+ (5d 1 ). The isotope 181 Ta has I = 7/2 and 100% natural abundance. The eight-line axial EPR spectrum with g = 1.503 and g ⊥ = 1.172, A = 0.0023, and A ⊥ = 0.0234 cm −1 has been observed in LiTaO 3 after reduction in argon and attributed to axial Ta 4+ Li [257]. Other ways to obtain Ta 4+ are an irradiation of as-grown crystals with X-rays or optical bleaching of crystals that had been previously reduced [264]. A possible model for axial Ta 4+ center is similar to the presented on Figure 25a. Ta 4+ (5d 1 ). The isotope 181 Ta has I = 7/2 and 100% natural abundance. The eight-line axial EPR spectrum with g∥ = 1.503 and g^ = 1.172, A∥ = 0.0023, and A^ = 0.0234 cm −1 has been observed in LiTaO3 after reduction in argon and attributed to axial Ta 4+ Li [257]. Other ways to obtain Ta 4+ are an irradiation of as-grown crystals with X-rays or optical bleaching of crystals that had been previously reduced [264]. A possible model for axial Ta 4+ center is similar to the presented on Figure 25a. Tb 4+ (4f 7 ). EPR study at 15 K revealed a signal of g ≈ 2.0 appearing after UV irradiation with a simultaneous decrease in the Fe 3+ signal intensity in near-stoichiometric LiNbO3:Tb and LiNbO3:Tb:Fe [265]. This implies that the Fe 3+ ions act as electron traps. Irradiation by UV light induced an absorption band extending from λ ≈ 650 nm to the Tb 4+ (4f 7 ). EPR study at 15 K revealed a signal of g ≈ 2.0 appearing after UV irradiation with a simultaneous decrease in the Fe 3+ signal intensity in near-stoichiometric LiNbO 3 :Tb and LiNbO 3 :Tb:Fe [265]. This implies that the Fe 3+ ions act as electron traps. Irradiation by UV light induced an absorption band extending from λ ≈ 650 nm to the absorption edge caused by the charge transfer from UV-sensitive absorption centers to Fe 3+ ions via the conduction band.
Other electron and hole traps. A trapped-hole center with S = 1/2 was produced in LiNbO 3 by ionizing radiation [266]. Its ESR spectrum contains at least 26 equally spaced lines with 1.54 mT separation at B||z. This hyperfine pattern was explained as one "hole" interacting equally with three 93 Nb nuclei (I = 9/2 and 100% abundant). The hole is equally shared by three equivalent oxygen ions adjacent to a cation vacancy. A center with 25 lines of hyperfine interaction with two 7 Li and two 93 Nb nuclei was ascribed to O − in regular O 2− site with unclear stabilizing factor for the hole trap [236].
An OH 2− ion was identified in undoped and weakly doped with Mg LN samples after γ-irradiation and subsequent partial UV bleaching [109]. Specific hyperfine structure with 93 Nb was observed for a hole trap in LN doped with 6-8 mol.% Mg. The center was attributed to O − near Mg 2+ ion substituted for Nb 5+ (Figure 25c) [263].

Impurity Identification
At an investigation of a sample grown from a melt with an addition of a paramagnetic spice in concentration 0.00X-0.X at.%, which warrants that EPR signal significantly exceeds noise, it would be reasonable to expect EPR signal from this spice. Often, studied samples (especially, commercial ones) contain so-called non-controlled or trace impurities like Cr, Mn, Fe, Cu etc. in a slightly smaller or comparable concentration. Fortunately, most paramagnetic impurities are already investigated by EPR/ENDOR techniques and their characteristics-electron and nuclear spins, zero-field splitting, hyperfine and quadrupole interactions, kinds of charge compensators and their locations, i.e., "passports" of the impurities-are known. Comparison of published and observed spectra (see, for instance, figures with EPR spectra and their angular dependencies above) allows to identify the impurities in films, epitaxial layers, and fibers, or to evaluate profile of impurity distribution in bulk samples. Spectra of LN/LT powders and ceramics can be simulated using determined spin-Hamiltonian parameters.

Conclusions
Very detailed information about structures of impurity defects (charge state, point symmetry, hyperfine interactions with neighbor nuclei, charge compensation mechanisms etc.) was obtained with the help of EPR and ENDOR.
The necessity of a charge compensation for non-isovalent substitution usually leads to the creation of families of electrically and magnetically non-equivalent impurity centers. The families of satellite centers exist due to the different relative locations of the impurity ion and its charge compensator. Two or more different centers were observed for Co 2+ , Cr 3+ , Cu 2+ , Er 3+ , Fe 3+ , Gd 3+ , Mn 2+ , Nd 3+ , Yb 3+ , and other ions. Since the relative concentrations of satellite centers are comparable with the concentration of the main center, both kinds of centers generally are equally responsible for many of the properties of LN/LT crystals, and they should both be taken into consideration, especially in non-stoichiometric crystals.
Several different mechanisms for a compensation of excessive charge of Me impurity were found: The presence of non-stoichiometric defects is one of the reasons why LN tolerates a strong incorporation of dopants non-isovalent to Li + and Nb 5+ . As long as the impurity concentration [Me] is smaller than δx C = |50% − x C |, the number of intrinsic defects is large enough to compensate the corresponding charge excess. However, for stoichiometric or nearly stoichiometric samples with high impurity concentrations (when [Me] > δx C ) and with the lack of charge compensators a decrease of the distribution coefficient of impurities is observed in comparison with congruent material. A further increase of the [Me]/δx C ratio up to [Me] >> δx C can result in a change of the charge compensation mechanism. This can reveal itself in the appearance of new impurity centers.
The charge compensation by v Li works well for most of the non-isovalent ions. Vacancies in the nearest neighborhood of Me Li decrease symmetry of centers from C 3 to C 1 , whereas distant vacancies cause spectral line broadening. For Me 3+ Nb/Ta in stoichiometric LN/LT the charge compensation by interstitial H + and Li + v ions was found. The interstitial Li + v should be considered as a concurrent charge compensation mechanism in VTE treated samples. The compensation of Me Nb by Mg Li , Zn Li and other impurities occurs when the co-dopant concentration exceeds some threshold that depends on δx C . Typically, the threshold is about 6-8% for congruent samples, but it is lower than 1% for nearly stoichiometric samples.
The use of stoichiometric or nearly stoichiometric crystals with δx C ≈ 0 presents many advantages for the investigation of impurity centers by spectroscopic techniques. The decreased concentration of intrinsic defects causes a tremendous narrowing of the spectral lines. This is accompanied with the increase of spectral resolution and sensitivity, facilitates the analysis of the spectra, and simplifies the interpretation of the data. However, together with the disappearance of intrinsic defects the satellite centers disappear also. For a detailed investigation of such additional centers, the crystals with high x C ≈ 49.5-49.85% are more suitable than others: they have more narrow spectral lines than congruent samples, but the satellite centers are still present. Further study of nearly stoichiometric and stoichiometric LN and LT samples should help to eliminate some disagreements in published data and to clarify intimate details of structures of impurity defects in materials, which are important for both physics and applications.
Derived structures and obtained by EPR/ENDOR characteristics of Zeeman and zerofield splitting, quadrupole and hyperfine interactions of impurity electrons with own and surrounding nuclei can be reliable corner stones for modelling of the structures.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.

Conflicts of Interest:
The authors declare no conflict of interest.