The PL discrete spectra (λ_exc = 488 nm) of cBN:Eu micropowders with ~0.01, ~0.05 and 0.1 at.% Eu in cBN are represented in Figures 1(a)-(c). They are originated from the consequence of the radiative electronic transitions ⁵D₀→⁷D_J (J = 0, 1, 2, 3, 4) of Eu³⁺ ions which are located in cBN crystal lattice in crystalline field of low symmetry [2]. In this work we first can obtain, that headlines of the spectra (the insets in Figures 1(a)-(c)) are visibly split into two separate main lines. It means that Eu³⁺ ions occupy two sites of

low symmetry in the cBN crystal lattice which create two luminescence centers (we called them Eu1 and Eu2). It is clear from the insets, that the Eu³⁺ ions occupy the second site in cBN crystal lattice the more expectable, the more concentration of Eu in cBN. The two-center character of Eu in cBN was suggested in our previous work [3]. The represented data here directly testify to the suggestion. The Eu1 and Eu2 centers have already figured in [3], but they were observed among four luminescence centers in PL spectra of the cBN:Eu (~0.01 at.% Eu) micropowder which was annealed at T_ann = 870 K (Figure 1(d), the inset). More likely, that the annealing effect is caused by redistribution of Eu³⁺ ions among sites in cBN crystal lattice due to activation in it of the nitrogen vacancies’ motion [4]. The PL multiband spectra (λ_exc = 488 nm) of cBN:Tb micropowders (Figure 2(a) and the inset) are related here to the ⁵D₄ → ⁷F_6,5,4,3 intra-electronic transitions of Tb³⁺ ions. The cBN:Tb spectrum considerably increases in intensity when the Tb concentration in cBN grows from ~0.05 up to ~0.1 at. %. In this case, the spectrum remains structurally unchanged. It meant, that Tb³⁺ ions continue locating in the similar crystallographic positions inside cBN crystal lattice. The ions stay in the same positions after annealing the cBN:Tb (0.1 at.% Tb) at T_ann = 870 K, in opposite to the annealed cBN:Eu (Figure 1(d)). However, the PL spectrum of the annealed

cBN:Tb is characterized with appearance of broad band in range of 700-900 nm (the gray strip in Figure 1(d) and in the inset to Figure 2(a)) of the multi-vacancy nature [5]. The PL spectrum in range of 1400-1700 nm of the cBN:Er single phase micropowder (0.05 at. % Er) is originated from the ⁴I_13/2 → ⁴I_11/2 electronic transitions (under the laser diode excitation with λ_exc = 960 nm) of the Er³⁺ions incorporated into cBN crystal lattice (Figure 2(b)). The PL spectra of the cBN:Nd micropowders reflects the two-center character of Nd³⁺ ions in cBN, referring to our work [6]. The cBN:Sm micropowders under PL analysis are described by us in [7].

XRD patterns of cBN:RE micropowders showed their single phase nature, because the patterns contained only (111), (200), (220), (311) and (331) peaks which belonged to cBN with the face-centered cubic lattice (FCC). We will not pay attention here to features of the patterns which were previously discovered by us from the comparative analysis of XRD patterns of cBN:RE and cBN standard. The features testify to the formation of disordered solid solutions of rare earth elements (Tm, Tb, Eu, Ce) on cBN basis [8]. In the present paper via analysis of shapes of peaks in XRD patterns of cBN:RE, we develop our conceptions about a possible distortions of the cBN rigid crystal lattice, which can be caused by impurities of large sizes (the RE³⁺ ions here) of various concentrations. Peaks (111), (220), and (311) in XRD patterns of cBN:RE (in particular of cBN:Eu, cBN:Nd) with the RE smallest concentrations and the RE largest concentrations are represented in Figure 3 and Figure 4. Hereinafter, a content in weight percent of any RE compound within a total mass of the precursor, is specified in parentheses next to the content in atomic percent. As seen from Figure 3 and Figure 4 when the concentration of Eu and Nd in cBN increases from less than ~0.01 at.% (0.5; 1) up to ~0.05 at.% (10), the peaks are decreased in intensity. With the concentration increasing, peaks (111), (220), (311) and (331) are displaced to the low 2Θ range, testi fying to the disordered solid solutions’ creation. We can refer to [8] as well.

As established, all peaks in XRD patterns of all cBN:RE micropowders are variously asymmetric. Mainly, because the low 2Θ-branches of peaks (111), (220) and (311) are enormously stretched towards the low 2Θ-angles, particularly, for cBN with the RE

smallest content (less than 0.01 at.%). This effect is less expressive for cBN with the RE largest content, testifying to the noninstrumental nature of the asymmetry. It is known, that Guassians, Lorenzians and Voigtians are symmetric.

As seen in Figures 3(b) and Figures 3(c) and Figure 4(b) and Figures 4(c), the asymmetric peaks (220) and (311) are finely structured. This allows to suggest that XRD patterns of cBN:RE contain the extra-peaks which are split from the parent peaks of cBN. When the RE concentrations in cBN increase (the peak 3 in Figure 3, the peak 2 in Figure 4), the peaks (220) and (311) change their profiles for smoothed shape and at first look loose the fine structure. However, if to decompose the peaks 3 and 2 into two Gaussians (dotted lines) or two Voigtians (not represented), the obtained doublets will not satisfy the requirements to Cu_Kά-doublet neither in intensities of their components nor in their widths. The same is related to peaks (111) and (331). Two Lorenzians absolutely are not acceptable in all cases. Thus, like the results on cBN:RE with the RE smallest concentration, the peaks of XRD patterns of the cBN:RE with the large RE concentration also possess the more complicated structure than single Cu_Kά-doublets.

It is known that a small deviation from cubic symmetry of crystal lattice leads to its distortions of different types. The perfect lattice (primitive cubic, BCC, FCC) possess the singlet lines (peaks) in its XRD pattern at the use of synchrotron monochromatic irradiation. Under the polychromatic Cu_Kά-irradiation, all lines in the XRD pattern should be represented with Cu_Kά-doublets. The singlet lines (otherwise, α₁- and α₂- component of Cu_ά-doublets) are characterized with multiplicity factor m which is the number of reflections which superimpose in the same diffraction peak and cannot be resolved in a perfect crystal lattice, satisfying the rule for the multiplicity factor m. If cubic crystal lattice is distorted, additional peaks appear in the “subcubic” XRD pattern, which are split from basic peaks in XRD pattern of the parent cubic crystal lattice, breaking the rule for the m factor. If to analyze the splitting scheme of the basic peaks, it is possible to define the type (tetragonal, trigonal and so on) of the distortions of cubic crystal lattice [9]-[11]. If the parent primitive or body centered or face centered cells of cubic crystal lattices are distorted, three different splitting schemes of basic peaks of the parent XRD patterns should be realized. In our mind, these schemes are not widely described in literature and we would refer the readers to [12] [13]. Worthy to add, that the mentioned splitting schemes are realized when all cells of a cubic crystal are uniformly distorted. The type of distortion of the FCC crystal lattice of cBN could be revealed when the number of extra-splits around each parent peak of XRD pattern of the material was known. The characteristics (relative integral intensity and angular distance from the corresponding parent peak) of the extra-splits allow to estimate the distortion quantitatively as well as to suggest a way of its creation. The relative integral intensity is directly connected with the part of the crystallographic planes from the multiplicity {hkl} which don’t participate in formation of the (hkl) basic peak. The angular distance allows to evaluate e.g. the quantitative characteristics of tetragonal and trigonal distortions Δa and Δγ where a is the parameter of cubic cell and γ is the basic angle of the cell.

In this work, peaks (111), (220), (311) of XRD patterns of all micropowders cBN:RE were deconvoluted into Voigtians. The extra-splits (as the additional ones to peaks of the parent cBN) were discovered and compared in their numbers and characteristics in dependence on the RE concentration in cBN and on sizes of the RE³⁺ ions. In correspondence with atomic numbers in the periodic table, the sizes of the RE three-charged ions should increase in the series Er³⁺, Tb³⁺, Eu³⁺, Sm³⁺, Nd³⁺. Any two lines resulted from the deconvolution were assigned with Cu_Kά-doublets if additionally to the features which were mentioned above, they possessed the similar contributions of Gaussians and Lorentzians. Making the suggestion about nonresolved Cu_Kά-doublets (broad peaks) as result of the deconvolution, we also kept in mind that a sum of two Voigtians is a Voigtian as well.

Being in shortage of the paper space, we represent the characteristic XRD patterns of cBN:RE with different doping levels. Figure 5 particularly shows the deconvoluted peaks (111), (220) and (311) in XRD patterns of cBN:Er (5) and cBN:Nd (1) (less than 0.01 at. % RE in cBN). Figure 6 particularly shows the peaks in XRD patterns of cBN:Tb (12) and cBN:Sm (10) with ~0.05 at. % RE. The deconvolution is represented for the cBN:Er (20) micropowder with the RE content above 0.1 at.% (Figure 7). As seen from Figure 5, the cBN parent peaks (111), (220) and (311) are accompanied with extra-splits at the low 2Θ-position and the high 2Θ-position. When the RE concentration increased up to ~0.05 at. % RE, the parent peaks (220) and (311) lost the neighbors on the right. The extra-splits at the high 2Θ-position follow only the (111) basic peaks but lost in intensity (compare Figure 6 with Figure 5). The similarly organized XRD patterns of the cBN:Er are just redistributed in intensity (compare Figure 7 with Figure 6). As seen, the intense basic peaks of cBN are there in all XRD patterns of cBN:RE confirming the presence of the cBN parent cells. It should be reminded, that the extra-splits at the low 2Θ and the high 2Θ arise from the planes within multiplicity {hkl}, correspondingly, with the enlarged and the diminished interplanar distances, which appear in crystal lattice of cBN due to the RE ions’ incorporation. In case, the enlarged interplanar distances d_hkl in the cBN crystal lattice, appear due to large sizes of doping impurities. Possibly, that the diminished interplanar distances in the cBN crystal lattice can appear due to vacancies’ creation which have to play the role of the mechanical strains’ relaxants as well as compensators of the RE³⁺ ions' electrical charge.

It seems, that we have managed to reveal some regularities and tendencies in behavior of XRD patterns of cBN which is doped with impurities of large sizes. It means that we can foresee a state of the cBN crystal lattice and realize the doping control of cBN within the investigated concentrations and errors of the deconvolutions.

As the evaluation criteria for the latter, we selected the main characteristics of the extra-splits in XRD patterns of cBN:RE: their fixed number around each parent peak of cBN, relative integral intensity and angular distance from the corresponding parent peak.

The number of extra-splits is clearly seen from Figures 5-7. The remaining characteristics can be analyzed from Figures 8(a)-(b’) where they are mediately represented in dependence on the RE³⁺ ions’ sizes and their concentrations in cBN. The number of narrow extra-splits around the parent peaks (111), (220) and (311) in XRD pattern in Figure 5 cannot satisfy any splitting schemes [12] [13]. Thus, they only prove the nonuniformly distorted state of the cBN:RE crystal lattice with the small RE concentration. This state changes simultaneously with the RE concentration growth, but it doesn’t reach the uniformity within the RE concentrations in cBN which were used here. Formally, we got that the splitting schemes could not be applied neither to the small concentrations nor to any concentrations of the RE in cBN which are investigated in the present work. Thus, the crystal lattice of cBN:RE represents the disordered solid solution which is nonuniformly distorted. To draw conclusions, we accept that the extra-splits are resulted from the RE ions' invasion of the {hkl} planes.

The dependences in Figure 8 let us reveal some suggestions about a possible mechanism of redistribution of the RE³⁺ ions inside the cBN crystal lattice. In cBN:RE with the equal concentration of different REs, the larger is the RE ion’s size, the more number of (111) planes are occupied or “attacked” by the ions (Figure 8(a)); the planes (220) can be occupied by all ions except the largest ones. With the growth of the RE ion’s size the planes (311) can be well occupied by the smallest ions (Er³⁺ and Tb³⁺), and less with the Sm³⁺ ions and much less by the Nd³⁺ largest ions. From Figure 8(a) and Figure 8(b) follows, the more number of planes {hkl} are affected by the ions, the smaller the interplanar distances between the planes which give rise to the extra-splits around the cBN parent peaks in XRD patterns of cBN:RE. The RE³⁺ ions of one sort preferably try to occupy the planes {220} and {311} from all available planes {hkl} in crystal lattice of cBN, except the Nd³⁺ ions which go into {220)} panes.

As seen from Figures 8(a’) and Figure 8(b’), when the concentration of the RE in the cBN:RE increases, the larger number of planes {111} and the smaller number of planes {311} can be affected by all RE ions and the larger number of planes {220} will be affected by all except the Nd³⁺ largest ions. When the concentration of the RE in the cBN:RE increases, the larger number of the planes {111} and the smaller number of planes {311} with diminishing distances between the planes can be created in cBN, which give rise to the extra-splits formation. Simultaneously, the number of the planes {220} and the interplanar distances between, which give rise to the extra-splits, can vary in dependence on the RE concentration in cBN and on the ions’ size. However, at average, the different RE ions affect the larger number of planes (220) as to compare to planes (111) and (311) when concentration of the RE in cBN increases (Figure 8(a’)).