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

^{*}

## Abstract

**:**

^{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.

## 1. Introduction

_{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.

- 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.

- 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.

^{2+}and Fe

^{3+}substitution for Li

^{+}. Raman spectroscopy data [35] were interpreted on the base of Fe substitution for Li. Magneto-optical and luminescence studies [36,37] identified non-paramagnetic pairs Cr

_{Li}-Cr

_{Nb}and established a correlation between optical bands and Cr

^{3+}positions.

^{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.

_{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).

_{3}) and a change of charge compensation mechanism in sLN was accompanied by a significant progress in understanding the nature and structures of intrinsic and extrinsic defects [68,69,70,71,72,73,74,75,76]. Several methods of determination of real crystal composition were developed [68,77,78,79,80]. It should be mentioned that even crystals with x

_{C}= 50% are not completely free of intrinsic defects. There is a class of intrinsic defects which break the regular order of the LN lattice without a change of x

_{C}: the permutations Nb

_{Li}and Li

_{Nb}, and cyclical permutation of Nb in Li site, Li in structural vacancy, and vacancy of Nb. Such defects can cause broadening of spectral lines.

_{res}. Depending on measurement conditions it has usual sensitivity about 10

^{12}–10

^{15}spins/cm

^{3}or higher. Equipment with wave lengths 3cm (X-band, microwave frequency ν ≈ 9.5 GHz) and 8 mm (Q-band, ν ≈ 34 GHz) are usually used. EPR lines have typical widths about 1–100 MHz. This defines the resolution ability of the EPR.

^{7}Li—92.5%,

^{93}Nb—100%,

^{181}Ta—99.99%) can be studied by NMR. Due to interactions with electron spins, nuclei in the impurity neighborhood have energy levels and resonance frequencies different from those of bulk nuclei. As their concentrations, which are about impurity concentration, are significantly smaller than concentrations of bulk nuclei, their NMR signals are too weak to be registered directly.

_{res}. ENDOR has sensitivity that is worse than EPR (about one-two orders of magnitude), but is better than NMR. Its resolution is comparable with NMR resolution. Characteristics of all nuclei (natural abundance of isotopes, their nuclear spins, magnetic and quadrupole moments) are well known and tabulated. This allows to relate observed ENDOR frequencies to interactions of impurity electrons with own nucleus and surrounding nuclei.

^{16}O has no magnetic moment and is invisible in EPR/ENDOR/NMR experiments.

## 2. Materials and Methods

_{2}O [56,57].

^{2−}ions are invisible for EPR/ENDOR. As LiNbO

_{3}and LiTaO

_{3}are isostructural crystals, all figures with lattice and structures of impurity centers are equally applicable to both LN and LT. However, dipole-dipole interactions should be calculated taking into account a difference of their lattice constants.

## 3. Basics of EPR and ENDOR Spectra Interpretation

#### 3.1. Symmetry Considerations

_{3v}

^{6}, 3m) at room temperature [8,88,89,90]. If ionic radii are taken into account, the LT/LN lattices look like consisting mainly of planar layers of closely packed oxygen ions with small voids between them, filled by Li and Nb/Ta. There are several electrically non-equivalent positions in the lattice. Some of them—the sites on the

**z**(or optical

**c**) axis of the crystal, including the sites of Li, Nb/Ta and the octahedral structural void (vacancy), v

_{oct}—have the symmetry of the point group C

_{3}. An isolated defect in any of these positions creates a C

_{3}(in the following also labeled “axial”) center. The tetrahedral structural void, oxygen sites and all other off axis positions have the lowest possible symmetry, C

_{1}.

_{3}symmetry, if both are located on the crystal

**z**axis, and C

_{1}symmetry in all other cases. If the difference in positions of the nearest oxygen ions is ignored, then each unit cell has the following site sequence along the

**z**-axis: Li, Ta, v

_{oct}, Li, Ta, v

_{oct}. However, oxygen octahedrons and next neighbors for two positions of one type cation are not identical, therefore, the correct assignment of the sequence should be Li

_{L}, Ta

_{L}, v

_{oct,L}, Li

_{R}, Ta

_{R}, v

_{oct,R}. The surrounding of the “Right” (R) position can be transformed to the “Left” (L) one by a reflection

**x**⇔ −

**x**and a shift by c/2, because

**zy**is a glide mirror plane in the R3c lattice (Figure 1b). The same consideration is applicable to C

_{1}positions also. This means that each axial (C

_{3}) or low-symmetry (C

_{1}) L center has a corresponding R partner. The L and R partners are electrically identical and are not distinguishable by optical or channeling methods, but they are magnetically non-equivalent and can be resolved from each other in favorable cases (high spin value, small line width) by magnetic resonance techniques.

_{1}center in the R3c lattice has two additional magnetically nonequivalent partners, which can be transformed into each other by a rotation around the

**z**-axis of the crystal by 120° and 240°. They can be distinguished by the EPR at arbitrary orientations of the magnetic field.

**B**under rotation of the crystal sample around

**z**-axis (shortly speaking, in

**xy**plane). For a C

_{3}paramagnetic defect with electron spin S = 1/2 the EPR spectrum consists of one resonance at the same position B

_{res}at any orientation of

**B**with respect to crystallographic axes. A set of up to six lines can be observed at arbitrary orientation of

**B**for C

_{1}centers; however, some of them coincide for directions of

**B**along

**x**,

**y**, or

**z**. If two or more centers present in the sample studied, the spectrum has two or more sets of the lines. If a center has electron spin S > 1/2 multiplets of 2S lines can be observed for every center.

_{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.

^{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}.

**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.

_{1}and three sets of curved branches, which correspond to low-symmetry centers Nd

_{2}, Nd

_{3}, and Nd

_{4}. Therefore, we can conclude that Nd

^{3+}in Nd

_{1}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 Nd

_{2}, Nd

_{3}, and Nd

_{4}centers with the C

_{1}symmetry, the additional defects are located off the

**z**-axis. It is unlikely that Nd

^{3+}ions occupy sites with C

_{1}symmetry (tetrahedral void or O

^{2−}) due to large charge misfit.

_{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.

#### 3.2. Isotropic and Dipole-Dipole Interactions

_{i}

_{n}—nuclear magneton, ${g}_{n}^{\left(i\right)}$—nuclear g-factor;

**A**

^{(i)},

**Q**

^{(i)}—tensors of hyperfine and quadrupole interactions.

**A**

^{(i)}: isotropic (contact) hyperfine interaction, ${a}^{\left(i\right)}S{I}_{}^{\left(i\right)}$ and dipole-dipole interaction of vectors of electron ${\mu}_{B}gS$ and nuclear $-{\mu}_{n}{g}_{n}^{\left(i\right)}{I}_{}^{\left(i\right)}$ magnetic moments. The dipole–dipole interaction can be described by

**R**

^{(i)}is the vector from paramagnetic impurity to the i-th nucleus. Most characteristics in Equation (3) are known: ${\mu}_{B},{\mu}_{n},{g}_{n}^{\left(i\right)}$ 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.

**z**-axis at the distance R

^{(1)}(Figure 5a). Three of them are located above the impurity (the subshell 1a), other three—below 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.

- to calculate ${A}_{jm}^{\left(i\right)dd}$ 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

**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.

**R**

^{(i)}. For the isotropic g-factor:

**z**-axis in the nearest surrounding, whereas ions substituted for Nb have Li nucleus (Figure 6, shell #1).

- to measure the road map of angular dependencies in three perpendicular planes (Figure 4a),
- to determine all components of ${A}_{}^{\left(i\right)}$ 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).

#### 3.3. Charge Compensation and Intrinsic Defects

^{5+}

_{Li}

^{+}(Nb

_{Li}

^{4•}) antisite defect, v

_{Li}

^{+}(v

_{Li}

^{’}) lithium vacancy, v

_{Nb}

^{5+}(v

_{Nb}

^{5’}) niobium vacancy, Nb

^{5+}

_{v}(Nb

_{v}

^{5•}) niobium on structural vacancy, Li

^{+}

_{v}(Li

_{v}

^{•}) lithium on structural vacancy, v

_{O}oxygen vacancy. During recent years the existence of the following charge compensated complexes has been postulated most often: Nb

_{Li}+ 4v

_{Li}[90,94,95] (including three-dimensional complexes 3v

_{Li}+ Nb

_{Li}+ v

_{Li}[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.

^{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

^{+}.

^{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, [D] and the total concentration of Me

^{3+}ions in the sample, [Me]. The [D] includes a dominant contribution due to a deviation of the crystal composition from stoichiometry, concentrations of H

^{+}ions and v

_{O}, as well as contributions due to non-controlled impurities (Mg, C, Si, Cl, …), which are always present in real crystal in concentrations about 1–500 ppm. If [D] >> [Me] the isolated centers with additional intrinsic defects are dominating. If [D] << [Me] then the self-compensation is preferable due to lack of charge compensators.

**g**and

**A**tensors in the case of Nd

^{3+}) and lowering of center symmetry.

#### 3.4. Di-Vacancy Models for Trivalent Impurities

_{1}centers appear in three cases:

- Impurity ion like Nd
^{3+}has an off-axis lattice defect (charge compensator) in the immediate neighborhood. - Impurity ion substitutes for O
^{2−}(this is very improbable for cations). - Impurity ion incorporates into a small tetrahedral void (this is possible, but often unlikely due to larger charge misfit than for Li substitution).

**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.

^{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.

^{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).

^{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 Figure 7 and Figure 8.

^{3+}

_{Li}.

## 4. Structures of Impurity Centers

#### 4.1. Monovalent Cations

^{+}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].

^{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]).

**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 heavily-doped 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].

#### 4.2. Divalent Cations

^{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**(3d

^{2+}^{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).

^{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].

**Cu**(3d

^{2+}^{9}, S = 1/2). Copper nuclei have two isotopes

^{63}Cu (I = 3/2, g

_{n}= 1.484, natural abundance 69.2%) and

^{65}Cu (I = 3/2, g

_{n}= 1.588, 30.8%). Hyperfine interaction of Cu

^{2+}electrons with their own nucleus leads to splitting of its single EPR line into a quartet ([110,111], and references there; [122,123,124]). As magnetic moments of

^{63}Cu and

^{65}Cu are very close, the quartets from the two isotopes overlap in cLN (Figure 11a). The Cu

^{2+}center in LN was characterized by anisotropic

**g**-tensor (g

_{1}= 2.095, g

_{2}= 2.111 and g

_{3}= 2.428; α = γ ≈ 0, β ≈ 51°) [111]. At low temperatures a static Jahn-Teller effect for 3d

^{9}ions in Cu

^{2+}O

_{6}

^{2−}complexes reduces the center symmetry to C

_{1}(Figure 11b). At room temperature, the Cu

^{2+}center has axial symmetry due to center reorientation and motional averaging. The EPR parameters of the impurity Ni

^{+}, Cu

^{2+}, and Ni

^{3+}in LiNbO

_{3}were theoretically studied from the perturbation formulas for 3d

^{9}ions [112,122].

**Ni**(3d

^{2+}^{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:

_{2}= 1/3, f

_{4}= 1/60, f

_{6}= 1/1260; ${O}_{k}^{q},{\mathsf{\Omega}}_{k}^{q}\left(S\right)$—Stevens operators, which are non-zero for k ≥ 2S. For C

_{3}symmetry only q equal to 0, 3, and 6 are allowed. For S = 1 only terms with k = 2 are present in Equation (5).

^{2+}centers in LN exhibit the EPR spectra of C

_{3}symmetry. Therefore, the sum in (5) turns into one term ${b}_{2}^{0}{O}_{2}^{0}/3.$ It was found that ${b}_{2}^{0}=$−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 v

_{Li}that is located on the C

_{3}axis or very far of Ni

^{2+}.

^{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.

^{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.

**Mn**(3d

^{2+}^{5}, S = 5/2, I = 5/2). For S = 5/2 the ZFS causes splitting into 2S = 5 components of fine structure, each of them additionally splits into 2I + 1 = 6 lines due to the hyperfine interaction of Mn

^{2+}electrons with their own nucleus (Figure 12).

^{2+}in both LN and LT are described by spin-Hamiltonian of axial symmetry with g ≈ 2.0, and A ≈ −0.008, ${b}_{2}^{0}$ = 0.0731 (LN), ${b}_{2}^{0}$ = 0.1694 (LT), all in cm

^{−1}, [128,129,130,131,132,133,134,135,136,137,138]. Our spectra (Figure 12) were fitted with ${b}_{2}^{0}$ = 0.074 (LN), ${b}_{2}^{0}$ = 0.175 (LT).

**g**-tensor, the principal values of dipole-dipole interaction (3) can be described by:

^{2+}ions occupy Li site [139].

#### 4.3. Trivalent Cations

^{3+}substitutes Li

^{+}there are three possibilities to compensate its 2+ excess charge: v

_{Li}, v

_{Nb}and self-compensation with Me

^{3+}

_{Nb}

^{5+}in the nearest or distant neighborhood. Every Me

^{3+}

_{Li}can be compensated by two v

_{Li}; every five Me

^{3+}

_{Li}

^{+}ions—by two niobium vacancies. The positive antisite defect Nb

_{Li}can serve as a charge compensator for Me

^{3+}replacing Nb

^{5+}(but not Me

^{3+}

_{Li}

^{+}or Me

^{3+}

_{v}). It is remarkable that one Nb

^{5+}

_{Li}

^{+}exactly compensates the excess charge of two Me

^{3+}

_{Nb}

^{5+}ions. Since v

_{Li}

^{+}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.

^{+}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}.

**Cr**(3d

^{3+}^{3}, S = 3/2). In congruent and Li-rich LN samples, the EPR lines of dominant axial Cr

^{3+}center, characterized with ZFS ${b}_{2}^{0}$≈ 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.

^{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].

_{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) and structures on Figure 7 and Figure 8 can be viable alternatives for Cr

^{3+}family.

^{5+}becomes possible. An axial Cr

^{3+}center with significantly smaller ZFS ${b}_{2}^{0}$ = 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).

**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].

^{3+}

_{Li}and small signals of non-nearest paramagnetic pairs.

^{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 ${b}_{2}^{0}$ 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 ${b}_{dd}^{\left(i\right)}$ 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.

^{3+}in cLT ${b}_{2}^{0}$ ≈ 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.

^{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**(4f

^{3+}^{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**(4f

^{3+}^{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 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].

_{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 (Figure 5a and Figure 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).

^{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].

_{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.

_{‖}= 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.

**Fe**(3d

^{3+}^{5}, S = 5/2). EPR studies have shown that the dominant iron center, Fe

_{1}in cLN has axial symmetry with the ZFS ${b}_{2}^{0}$ about 0.1680 cm

^{−1}[131,133,134,198,199,200,201,202,203,204,205,206,207,208]. Calculations of optical and EPR characteristics based on the superposition models or generalized crystal field theory gave a preference for Nb substitution [209], no definite conclusion for Li or Nb substitution [210,211,212,213] or some preference for Li site [214,215]. Mössbauer [33,34] and Raman [35] spectroscopy data, Stark effect [216] were interpreted on the base of Fe substitution for Li. Iron clusters were observed at high Fe concentration [33]. Comparison of calculated dipole-dipole interactions of Fe

^{3+}electrons with surrounding Li nuclei for Li and Nb substitution (Equation (6)) with measured ENDOR spectra [38,39,40] has shown that Fe

^{3+}is undoubtedly located in Li site in both cLN and cLT (Figure 5a). Independently, XSW [12,28], EXAFS [21,22,23,24,25,26], and ion beam/channeling [18,27] confirmed Fe

^{3+}substitution for Li

^{+}. It was concluded also that Fe

^{3+}ions can be shifted from regular Li-site; however, the obtained values for the shift were very different: 0.006 nm [21] or 0.05 nm from octahedron center [24], less than 0.012 nm [25], about 0.01 nm [26], 0.018 ± 0.007 nm [28], less than 0.005 nm [39]. Fitting observed ENDOR data in LN crystals grown from Li-rich melt (x

_{m}≈ 55%) was obtained with the shift 0.009 nm from Li site [217].

^{3+}center with small ZFS, Fe

_{2}observed in congruent LN doped with Mg [104,218,219,220,221,222], In [223], and Zn [224] was assigned to Fe

^{3+}

_{Nb}.

_{2}O, LN

_{K}samples (Figure 18a, 3) shows

^{a}:

- 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}.

_{K}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) LN

_{K}samples (see lines of Fe

^{3+}and Mn

^{2+}on Figure 18a, 3).

^{a}A brief glance on history of sLN for curios researchers. Looking for better crystals, G. I. Malovichko asked crystal growers for different samples of LN and LT. Dr. E. P. Kokanyan (at that time, one of the engineers in the group of Dr. V. T. Gabrielyan) was interested to grow crystals under various conditions (melt composition x

_{m}, growth under applied electric field, variation of temperature, etc.). He has prepared for her a set of non-stoichiometric LN samples grown from melts with x

_{m}from 43% to 60%. During her PhD research of LN and LT of different compositions, Malovichko found that EPR lines become narrower and more symmetric in samples grown with larger x

_{m}. Dr. V. G. Grachev has simulated EPR spectra with random distributions of non-axial components of ZFS, ${b}_{2}^{q}$ (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].

_{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.

_{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 ${b}_{2}^{0}$ = 0.0495 and ${b}_{2}^{0}$ = 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 ${b}_{2}^{0}$ = 0.0656 cm

^{−1}(that is very close to ${b}_{2}^{0}$ 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.

_{1}

^{3+}center in cLT has ${b}_{2}^{0}$ = 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].

_{2}

^{3+}center with ${b}_{2}^{0}$ = 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).

_{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 excessive charge compensation: distant v

_{Li}for small concentrations of Fe

^{3+}

_{Li}

^{+}, partial self-compensation of charges of Fe

^{3+}

_{Li}

^{+}by Fe

^{3+}

_{Nb}

^{5+}and partial compensation of Fe

^{3+}

_{Nb}

^{5+}by Li

^{+}in v

_{oct}for Fe

^{3+}concentrations, which exceed the concentration of v

_{Li}.

**Gd**(4f

^{3+}^{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 ${b}_{2}^{0}$ = 0.118 and ${b}_{2}^{0}$ = 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].

^{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 Figure 4b and Figure 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].

**Nd**(4f

^{3+}^{3}) First EPR spectra have shown that in cLN Nd

^{3+}creates an axial center with g

_{‖}≈ 1.43 and g

_{┴}≈ 2.95 (Nd

_{1}) [143,144,230] and second center with g

_{‖}≈ 1.33 and g

_{┴}≈ 2.95 (Nd

_{2}) [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.

^{3+}center found in LN:Mg and LN:Zn belong to Nd

^{3+}substituted for Nb [231].

**Ti**(3d

^{3+}^{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**(4f

^{3+}^{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].

**xy**plane were registered in cLN doped with 1wt.% Yb, and cLN doubly doped with 0.8 wt.% of Yb and 0.1 wt.% of Pr [243,244,245,246,247]. Some of the spectra were attributed to Yb

^{3+}pairs with the parameter of isotropic exchange interaction J = −0.0283 cm

^{−}

^{1}.

_{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 Figure 22 and Figure 23). The dominant Yb

_{1}line that represents even isotopes with I = 0 (

^{even}Yb, 69%) was described with g

_{‖}= 4.46, g

_{┴}= 2.706. Intensities of the Yb

^{3+}lines were proportional to natural abundances of isotopes and their spins: $\mathcal{I}$(even):$\mathcal{I}$(171):$\mathcal{I}$(173) = 0.69:0.144/2:0.166/6 = 0.69:0.072:0.028. It was found for Yb

_{1}that

^{171}A

_{‖}= 0.119 cm

^{−1}, and

^{171}A

_{┴}= 0.0715 cm

^{−1}. Branches of angular dependencies of the Yb

_{5}center (fuchsia lines on 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).

_{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 dipole-dipole 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.

#### 4.4. Tetra-, Penta- and Heptavalent Cations

^{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.

_{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).

^{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**(5f

^{5+}^{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.

#### 4.5. Radiation and Reduction Defects

^{4+}and hole traps like O

^{−}ions [236,255,256].

**Nb**(4d

^{4+}^{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).

_{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, 3) [238,263]. The neighboring Mg

^{2+}ion redistributes a cloud of Nb

^{4+}electrons and changes the hyperfine splitting.

**Ta**(5d

^{4+}^{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.

**Tb**(4f

^{4+}^{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].

^{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].

## 5. Impurity Identification

## 6. Conclusions

^{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.

- the compensation by nonstoichiometric defects (v
_{Li}, v_{Nb}) for small concentrations of Me_{Li}in crystals, - the partial self-compensation of charges of Me
_{Li}by Me_{Nb}mainly for the Me_{Li}concentration that exceeds the concentration of v_{Li}, - the partial compensation of Me
_{Nb}by interstitial Li^{+}in v_{oct}, - the compensation by other impurities (H, co-dopants like Mg, Zn, etc.).

^{+}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.

_{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.

_{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.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Ideal lattice of lithium tantalite (LT). To simplify the representation of the lattice and defect structures in it, the sizes of “balls” imitating ions were made intentionally different. The L (Left) and R (Right) positions are distinguished by their different oxygen surroundings. (

**b**) An illustration of local C

_{3}symmetry for the nearest surroundings of cation sites and glide mirror

**zy**plane that transforms the L center to the R partner; a projection of one Li, Ta layer between two oxygen layers on the

**xy**plane is shown.

**Figure 2.**Fragments of electron paramagnetic resonance (EPR) spectra of Nd

^{3+}impurity ions in nearly stoichiometric lithium niobate (LN) for microwave frequency ν = 34.445 GHz, T = 19 K. The numbers 1–4 correspond to four different electrically non-equivalent defects. Lines of magnetically nonequivalent partners have the same number.

**Figure 3.**(

**a**) Projection of ideal lithium niobate lattice with Nd

^{3+}impurity ion on

**xy**plane (artificial sizes of balls are used). (

**b**) Circular diagram of measured angular dependence of electron paramagnetic resonance (EPR) lines of Nd

^{3+}ions in Figure 3. Magnetic field was rotated in

**xy**plane from 0 to 360 deg. ν = 34.445 GHz, T = 19 K. Symbol sizes reflect line intensities.

**Figure 4.**(

**a**) The road map rotation corresponds to the following changes of the θ, ϕ angles: θ = 0–90° at ϕ = 0°; θ = 90°, ϕ = 0−90°; θ = 0−90° at ϕ = 90°. (

**b**) Angular dependence of the EPR spectra in

**xy**plane for nearly stoichiometric LN:Nd

^{3+}. 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 Nd

_{1}, and low-symmetry Nd

_{2}, Nd

_{3}, and Nd

_{4}centers, respectively. Curves for isotopes with nuclear spin I ≠ 0 are not shown.

**Figure 5.**Surroundings of impurity ions substituted for Li (

**a**) and Nb (

**b**) in LN crystal lattice with corresponding shell numbers. Large blue balls represent Li

^{+}ions, medium green balls—Nb

^{5+}ions, small red balls—O

^{2−}ions, and the largest magenta ball—the impurity ion.

**Figure 6.**Angular dependence of electron nuclear double resistance (ENDOR) frequencies of Li nuclei in

**xy**plane for the Nd

_{1}

^{3+}center in LiNbO

_{3}. The green, red and blue curves—calculated frequencies for Li nuclei of the 1st, 2nd and 3rd shells based on dipole-dipole interaction for Nd

^{3+}

_{Li}(

**a**,

**b**), and Nd

^{3+}

_{Nb}(

**c**). ENDOR frequencies represented on the part (

**b**) were measured at magnetic fields corresponding to the position of dominant EPR line #1 on Figure 2 (B = 820 mT for ν = 34.445 GHz, rhombs, and B = 228 mT for ν = 9.500 GHz, triangles). ν

_{Larmor}is Larmor frequency of

^{7}Li nuclei.

**Figure 7.**A projection of lithium niobate crystal lattice on

**xy**plane (

**a**) and 3D model (

**b**) with shell numbers for an impurity substituted for Li

^{+}ion (sizes of all ions were artificially changed in order to make clear positions of cation ions). Hatched circles represent two vacancies of Li

^{+}ions for Nd

_{4}center.

**Figure 8.**Divacancy models for an impurity substituted for Li

^{+}ion in LN crystal lattice. Hatched circles represent two v

_{Li}. (

**a**) Axial center, (

**b**) nearly axial center, (

**c**) low-symmetry center.

**Figure 9.**(

**a**) X-band EPR spectra of Ni

^{+}in LiNbO

_{3}at θ = 25 deg in

**zy**plane at various temperatures T: 1–40 K, 2–90 K, 3–151 K, 4–206 K, 5–244 K, 6–300 K. The spectrum 7 was measured at θ = 0 deg, T = 300 K. (

**b**) Distortion of oxygen octahedron due to the Jahn-Teller effect.

**Figure 10.**(

**a**) Measured EPR spectra of Co

^{2+}, X-band, T = 5 K. 1—sLN,

**B||z**; 2—sLN,

**B||x**; 3—cLN,

**B||x**. The red arrow indicates an additional line assigned to clusters of Co

^{2+}ions. (

**b**) Possible model for a cluster of four Co

^{2+}ions substituted for one Nb

^{5+}and three Li

^{+}ions.

**Figure 11.**(

**a**) Measured EPR spectrum of Cu

^{2+}in LN, X-band, T = 7 K. (

**b**) Distortion of oxygen octahedron due to Jahn-Teller effect.

**Figure 12.**(

**a**) Measured EPR spectrum of Mn

^{2+}in LN

_{K}, ν = 34.45 GHz. (

**b**) Model of axial Mn

^{2+}

_{Li}center with v

_{Li}.

**Figure 13.**Measured EPR spectrum of Cr

^{3+}in LN grown from the melt with x

_{m}≈ 60% and 0.1 wt.% of Cr (room temperature, ν = 9.84 GHz). Black braces indicate lines of dominant Cr

^{3+}center, red arrows—lines of satellite centers.

**Figure 14.**The ENDOR spectra of Cr

^{3}

^{+}

_{Li}(high-field EPR transition) and Cr

^{3}

^{+}

_{Nb}(central EPR transition) at

**B**||

**x**, T = 5 K. To facilitate a comparison of the spectra, they were shifted to the

^{93}Nb Larmor frequencies.

**Figure 15.**The angular dependencies of EPR spectra in the

**xy**plane for LN:Cr

^{3+}grown from the melt with x

_{m}≈ 60%, ν = 9.26 GHz. Rhombs represent line positions; their sizes are proportional to line intensities. Horizontal whiskers near rhombs represent line widths. Cyan, lime, fuchsia, and blue curves represent simulated dependencies for axial Cr

_{1}, and low-symmetry Cr

_{2}, Cr

_{3}, and Cr

_{4}centers, respectively.

**Figure 16.**(

**a**) Measured EPR spectra of Cr

^{3+}in LN grown from the melt with addition of K

_{2}O and 1 wt.% of Cr; room temperature, ν = 9.445 GHz. (

**b**) Model of Cr

^{3+}

_{Nb}center.

**Figure 17.**(

**a**) EPR spectra of Er

^{3+}in congruent and stoichiometric LN at

**B**||

**z**, X-band. (

**b**) Calculated angular dependence of EPR spectra in

**xy**plane for the Er

_{1}

^{3+}(green lines) and Er

_{2}

^{3+}(fuchsia lines) centers in sLN. Symbols with horizontal whiskers represent line position and widths.

**Figure 18.**Normalized spectra of Fe

^{3+}in LN (

**a**) and LT (

**b**), X-band. (

**a**) Congruent (1), grown with x

_{m}= 0.545 (2), undoped sample grown from congruent the melt with 6 wt% of K

_{2}O (3),

**B||z**. (

**b**) Congruent (1), vapor transport equilibrium (VTE) treated sample (2),

**B**||

**x**.

**Figure 19.**Possible structures of Me

^{3+}

_{Nb}

^{5+}(large magenta ball) centers in LN. Structure with one (

**a**) and two (

**b**) additional Li ions in v

_{oct}(marked with red crosses). Axial (

**c**) and low-symmetry (

**d**) structures with two Mg

^{2+}

_{Li}

^{+}ions.

**Figure 20.**Angular dependence of ENDOR frequencies of Li nuclei in

**xy**plane for the Fe

_{2}

^{3+}center in LiTaO

_{3}. The green, magenta, blue and lime curves—calculated frequencies for Li nuclei of the 1st, 2nd, 3rd and 4th shells based on dipole-dipole interaction for Fe

^{3+}

_{Li}(

**a**), and Fe

^{3+}

_{Nb}(

**b**). Fuchsia lines on (

**b**)—calculated frequencies for the additional Li nucleus in the nearest v

_{oct}on the axis of Fe

^{3+}

_{Nb}center. ENDOR frequencies represented by rhombs were measured on the EPR line at B = 1162 mT (ν ≈ 34.5 GHz).

**Figure 21.**The angular dependencies of EPR spectra in

**xy**plane for Li-rich LN:Gd

^{3+}, ν = 9.26 GHz. Rhombs represent line positions; horizontal whiskers—line widths. Cyan, lime, fuchsia, and blue curves are simulated dependencies for axial Gd

_{1}, and low-symmetry Gd

_{2}, Gd

_{3}, and Gd

_{4}centers, respectively.

**Figure 23.**Angular dependence of EPR spectra of Yb

^{3+}in stoichiometric LN,

**xy**plane, ν = 9.86 GHz. Red arrows—lines of hyperfine structure for Yb

_{5}centers.

**Figure 24.**(

**a**)

**E**PR spectra of Nb

^{4+}centers in cLN (1) and cLN doped with 6 mol.% Mg (2) and 10 mol.% Mg (3), X band. (

**b**) Model for axial Nb

^{4+}

_{Nb}– Mg

^{2+}

_{Li}center.

**Figure 25.**Models for Nb

^{4+}

_{Li}(large green ball) centers with three v

_{Li}in LN. Hatched circles represent lithium vacancies. (

**a**) Axial center. (

**b**) Low-symmetry center. (

**c**) The center with O

^{−}near Mg

^{2+}substituted for Nb

^{5+}.

**Table 1.**Sites for lithium vacancies, v

_{Li}in the surroundings of Me

^{3+}

_{Li}centers in LiNbO

_{3}.

Center v _{Li} Site | Me_{1} | Me_{2} | Me_{3} | Me_{4} | Me_{5} | Me_{6} | Me_{7} | Me_{8} |
---|---|---|---|---|---|---|---|---|

First | 5a/5b | 1a/1b | 2a/2b | 1a | 1b | 1a/1b | 2a/2b | 5a |

Second | distant | 5a/5b | 5b/5b | 2a | 2b | 3a/3b | 3a/3b | 5b |

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## Share and Cite

**MDPI and ACS Style**

Grachev, V.G.; Malovichko, G.I.
Structures of Impurity Defects in Lithium Niobate and Tantalate Derived from Electron Paramagnetic and Electron Nuclear Double Resonance Data. *Crystals* **2021**, *11*, 339.
https://doi.org/10.3390/cryst11040339

**AMA Style**

Grachev VG, Malovichko GI.
Structures of Impurity Defects in Lithium Niobate and Tantalate Derived from Electron Paramagnetic and Electron Nuclear Double Resonance Data. *Crystals*. 2021; 11(4):339.
https://doi.org/10.3390/cryst11040339

**Chicago/Turabian Style**

Grachev, Valentin G., and Galina I. Malovichko.
2021. "Structures of Impurity Defects in Lithium Niobate and Tantalate Derived from Electron Paramagnetic and Electron Nuclear Double Resonance Data" *Crystals* 11, no. 4: 339.
https://doi.org/10.3390/cryst11040339