3.1. Crystal Growth, the Actual Crystals Compositions and XRD Studies
The crystals were grown by the Czochralski technique in a “Kristall-2” growth machine (USSR) with RF-heating from Pt/Rh crucible (30 mm in diameter and in height) in air ambient. Prior to the start of the growth process of each crystal, the hot crucible was filled by a charge with pre-melting. This step was performed without the upper part of thermal shields.
Pre-melting behaviour of the charges appeared to be different depending on the procedure for charge preparation; all the charges, except 5 and 6, were melted easily and completely without any problems at reasonable levels of RF-heater power.
Another situation was observed during the pre-melting of the charges 5 and 6 (the only charges calcined before the UHD treatment) (see
Figure 3): after easy melting of the charges, a refractory crust was formed at the surfaces of the melts. This suggests some underheating of the melt or precipitation of a second solid phase with comparatively low density from the melt. On the other hand, under this crust, we observed the intensive melt flows through the holes in the crust. Moreover, in case of charge 6 we observed pronounced evaporation from the melt surface, meaning that the melts under the crust were considerably overheated. However, the attempts to submerge the crust by pushing it down into the melt using Pt wire have resulted in fast crystallization of a part of the melt at this wire (in case of the charge 5). Some increase of RF-heating power (within its reasonable values) resulted only in partial melting of this crust.
After pre-melting and filling the crucible with a charge, it was cooled down to room temperature. Single-crystalline seed cut from undoped MgMoO4 was mounted at the upped stock of the growth machine, and the upper set of thermal shields were installed above the crucible with a frozen melt. The construction of this shield set contains an additional active resistive heater with the temperature control by thermocouple. It allows for the smoothening of the thermal gradients inside the hot growth zone, and for the organizing of the slow (8 °C/h) cooling of the grown crystal to room temperature after finishing the growth process and switching off the main RF-heater.
Before seeding, all the pre-molten charges were completely melted, obtaining a free, mirror-smooth melt surface. We succeeded to achieve such a surface even in the cases of melts 5 and 6 because the additional active resistive heater in the upper part of the thermal shields helped the main RF-heater to heat the melts more uniformly. Only after achieving the mirror-smooth melt surface was a seeding conducted.
Rather often, at various stages of the growth processes, numerous dark, suspension-like formations appeared at the melt surfaces. These formations are most certainly conglomerates of second solid phase precipitates. From this point on, these formations are designated as “mush.” This “mush” was actively captured by the lateral surfaces of the crystals with the formation of the inclusion-containing areas (
Figure 4 and
Figure 5). This process destabilized the crystals diameters (
Figure 4). Bulk parts of the crystals were almost free from such areas. Therefore, we can conclude that the “mush” fragments were floating near the melt surface rather than distributed uniformly in the bulk of the melt. The “mush”-capturing areas microscopically looked as multiple faceted particles with an amber colour and sizes of up to 0.1 mm dispersed in the main transparent light-yellow crystallite phase (
Figure 5).
We believe that the above-noted refractory crust, formed at the surfaces of the melts 5 and 6 during pre-melting of the charges, has the same nature as the “mush.” We attempted to analyze the phase compositions of these inclusions by X-ray powder diffraction (XRD) analysis using a Bruker D8 Discover A25 DaVinci X-ray diffractometer over a 2θ range of 10–70°, with a step size of 0.02° and step exposure time of 1.5 s. In fact, some of the XRD pattern appeared to contain the reflexes that are barely recognizable as originating from the main MgMoO
4 crystalline phase (JCPDS file 21-0961
Figure 6, yellow arrows) or cannot be identified as the main phase at all (
Figure 6, red arrows).
The majority of the observed lateral reflexes are rather weak in the majority of the samples and we failed to ascribe them unequivocally to any particular second phase. Moreover, the sets of the unidentified reflexes differ from sample to sample.
We also measured the actual composition of the obtained crystals. The measurements were performed by inductively coupled plasma mass spectrometry (ICP-MS) using an Elan DRC-e mass-spectrometer (Perkin Elmer, Shelton, CT, USA). For the analysis, the samples ground into powders beforehand were dissolved in an extra-pure phosphoric acid (Suprapur, Merck, Darmstadt, Germany) at temperatures of up to 400 °C.
A set of 5 samples were taken from different parts of each boule for analysis, thus, a total of 50 samples were analyzed (the results are presented in
Table 1 and discussed below). Along with that, an additional set of samples was taken from the areas of the “mush” captured at the lateral surface of crystal 6. The resulting “total” concentration of Mg
2+ ions in this additional set appeared to be 1.13 ± 0.09 f.u., whereas the “total” content of Mo
6+ ions appeared to be 0.96 ± 0.03 f.u. (
Table 1, the last separate row ‘6-mush’). The term “total” means that the ICP-MS method cannot measure separately the compositions of different crystalline (or vitreous) phases if they are jointly present in the probe. This method measures only the total amount of each chemical element in the dissolved probe, independently to the type of microparticle, from which the atom has come into the probe solution.
The typical concentrations of Mg
2+ ions in the single-phase MgMoO
4 crystalline samples are ~0.98 f.u., whereas the ones for Mo
6+ ions are ~1.005 f.u. (see
Table 1). Therefore, the “mush” capturing areas of crystal 6 contain ~15% of Mg
2+ excess and ~5% of Mo
6+ deficiency as compared to the inclusion-free areas of the crystals (including crystal 6). From this result we can conclude that “mush”-forming areas are the mixtures of the main MgMoO
4 crystalline phase and the inclusions of MgO or of a so far unknown magnesium molybdate phase with the MgO:MoO
3 molar ratio exceeding 1:1. Such phases are not mentioned in the MgO-MoO
3 phase diagram (
Figure 7).
There is an additional indirect confirmation of this conclusion: the density of MgO at room temperature is 3.58 g/cm
3 [
55], less than the density of MgMoO
4 (3.87 g/cm
3 [
56]). Unfortunately, the data on the similar values at 1322 °C, as well as on the density of MgMoO
4 melt, are unavailable. However, if the ratios between the densities at high temperatures are similar to those at room temperature, then the solid MgO (or another Mg-enriched) inclusions should float near the MgMoO
4 melt surface. This exact situation was observed.
The “mush” formation behaviour of the melts during crystal growth strongly depends on the procedure of the charges’ preparation. In the case of charges 5 and 6 (treated after the calcining), the “mush” started to form immediately after a crystal neck formation under the influence of a very slight reduction of the RF heating power, performed for starting the increase of a crystal diameter. However, after some period of growth, the “mush” disappeared without any evident additional external impact (captured by the crystal with no formation of new portions of the “mush” inside a melt), and the final stages of the crystals were grown from clear melt surfaces.
The opposite situation was observed for the crystals grown from the charges, the main components of which did not undergo any treatment (charges 7, 9 and 10), as well as for the crystal grown from charge 4, which was only mixed with standard water-alcohol solution (control). In these cases, the starting and quite substantial parts of the crystals were grown from clear melt surfaces. The “mush” started to form only after some time during the nominal growth process. However, once it appeared, the “mush” did not go away until the end of the growth.
Finally, the charges that were treated by UHD before calcining (charges 2 and 3) demonstrated no “mush” formation during the growth process.
There were only two exceptions to this regularity:
1. charge 1, which behaves like the UHD treated charges after calcining (5 and 6), although this charge was not treated at all;
2. charge 8, behaving like the charges whose main host components were treated before calcining (2 and 3), although the host components of this charge were not treated at all (only the dopant was treated);
As seen from
Table 1, the actual molybdenum concentration is almost stable all over the crystals, and it is in slight excess over the stoichiometry. On the contrary, magnesium is in a deficiency in all of the studied crystals, but the extent of this deficiency varies from sample to sample within the essential range. The highest Mg
2+ concentrations (the smallest deficiencies) are in the crystals 1 and 10, which were grown from the stoichiometric charges prepared without any treatment. All the rest of the crystals that were treated have larger Mg
2+ deficiency in their compositions.
As seen from the MgO-MoO
3 phase diagram (
Figure 7), MgMoO
4 melts congruently at a temperature slightly exceeding 1330 °C. The precise melting point of MgMoO
4 crystal doped with a very low amount of Tm
3+ ions was determined by DTA to be 1322 °C [
32]. However, the available phase diagram does not contain any information either about the precise congruently melting composition (CMC) of magnesium molybdate or about the MgMoO
4 homogeneity field in the crystalline state. Meanwhile, based on the measured compositions of crystals and on the revealed “mush” behaviour of the melts during crystal growth, we can make some assumptions on these issues while keeping the following facts in mind:
(i) The Czochralski crystal growth process is not a phase equilibrium.
(ii) 1 at. % of Nd3+ in the melts may have some influence on the situation (on the contrary, the actual Nd3+ concentrations in the crystals are negligible from the point of view of the possibility to change anything in phase diagrams, see below);
(iii) a single-crystalline MgMoO4 seed touching the melt surface may also have some influence on the situation.
The probable assumptions are as follows (the corresponding supposed view of the vicinity of the MgMoO
4 stoichiometry point at the MgO-MoO
3 phase diagram is presented in the upper panel of
Figure 8):
1. We assume crystals 4, 7, 9 and 10 (blue points in the
Figure 8) with the actual Mg/Mo molar ratios equal to or exceeding 0.976 were grown from the melts enriched by MgO with respect to the CMC. On the other hand, the charges of these crystals have undergone very slight treatment (charge 4 was only wetted by simple, non-treated water-alcohol solution without any dilutions, whereas for charges 7 and 9, only the dopant was treated, see
Figure 3) or had no treatment at all. Thus, it is reasonable to assume that the initial compositions of the melts 4, 7, 9 and 10 are the closest ones to MgMoO
4 stoichiometry. Therefore, the CMC for MgMoO
4 crystal is in the range of slight MoO
3 excess and MgO deficiency in respect to the stoichiometric molar ratio 1:1. In this case, the melt compositions 4, 7, 9 and 10 should gradually shift from their initial values towards deeper enrichment in MgO during the crystallization process, especially taking into account that slow MoO
3 evaporation from the melt occurred both during the growth process and during the pre-melting of the charges in the crucible. Due to this shift, the melts should reach the vicinity of the MgMoO
4 + MgO eutectic point after some period of time, taking into account that this eutectic point is not very far from the MgMoO
4 stoichiometry point (see
Figure 8). This should result in the simultaneous crystallization of MgMoO
4 and MgO phases. This situation was probably observed in reality as the “mush” formation.
The actual composition of crystal 1 has larger MgO concentrations than crystals 4, 7, 9 and even 10 (see
Table 1). Similarly to sample 10, its initial charge corresponded to MgMoO
4 stoichiometry without any treatment. However, the melt of sample 1 was rather strongly overheated during pre-melting. It could lead to substantial MoO
3 evaporation. Thus, we assume that melt 1 probably had an even higher degree of MgO enrichment with respect to the CMC point than melt 10. Therefore, it should shift towards the MgMoO
4 + MgO eutectic point faster during the growth process and reach the vicinity of this point in a shorter period of time than melts 4, 7, 9 and 10. In fact, the “mush” appears almost immediately after the start of the growth of crystal 1.
On the other hand, we assume that crystals 2, 3 and 8 (green points in
Figure 8) were grown from the melts enriched by MoO
3 with respect to the CMC. Thus, the compositions of their melts should gradually shift towards even larger MoO
3 excess during the growth process. However, such a shift is unlikely to result very quickly in starting the precipitation of MoO
3-enriched secondary phases because the MgMoO
4 primary crystallization field is quite far into MoO
3 zone (see
Figure 7). This exact situation was observed in reality: neither “mush” formation in the melts nor any secondary phase precipitation in crystals 2, 3 and 8 occurred.
Therefore, the Mg/Mo atomic ratio corresponding to the CMC of MgMoO4 crystal should be slightly lower than the actual composition of crystal 4, i.e., <0.976.
2. The range of retrograde solubility exists in the MgO-enriched boundary of the MgMoO
4 homogeneity field (solidus line) and the actual compositions of crystals 5 and 6 (red points in
Figure 8) are located in this range. The initial melt compositions of these samples are probably quite strongly enriched in MgO (more so than melt 1) and are already in the vicinity of the MgMoO
4 + MgO eutectic at the starting stage of the growth. That is why the “mush” appears just at the start of the growth of these crystals. After some time, the continuous capturing of “mush” by the crystal leads to the removal of some MgO from the melt, a shift of the total melt composition away from the vicinity of the MgMoO
4 + MgO eutecti, and, therefore, to the cessation of the formation of new “mush” portions. However, due to the retrograde solubility, the actual compositions of crystals 5 and 6 have lesser MgO concentrations compared to crystal 1 and, even, compared to crystals 4, 7, 9 and 10, despite fact that the melts 5 and 6 had larger concentration of MgO, at least at the first stages of the growth.
3. The MoO
3-enriched boundary of the MgMoO
4 homogeneity field probably has also rather complicated shape, as tentatively indicated in
Figure 8 (upper panel). That is why the actual compositions of crystals 2 and 3 have very minor differences with the ones for crystals 4 and 7 (see
Table 1), whereas the composition of crystal 8 is even slightly MgO-enriched in respect to those of crystals 4 and 7, despite the initial melt compositions for crystals 2, 3 and 8 being (as we assume) MoO
3-enriched in respect to the CMC.
Another possible explanation is that the actual composition of crystal 8 is shifted towards the MoO
3-enriched side, whereas the actual compositions of crystals 4 and 7 are, on the contrary, shifted towards the MgO-enriched side from the corresponding average values given in
Table 1 within the limits of the measurement errors (see
Figure 8 lower panel). The measurements of the unit cell parameters support this version, as can be seen below. In this case, we can build the supposed MoO
3-enriched boundary of the MgMoO
4 homogeneity field with a much simpler and traditional shape, whereas the Mg/Mo atomic ratio corresponding to the CMC should be ~0.977–0.978 in this version.
We have performed an additional XRD analysis to reveal the unit cell parameters of the crystals. For these measurements we ground six pieces taken from different defect-free areas of each sample. TOPAS (Total Pattern Analysis Solutions) software Version 8 was used for the calculations by the Rietveld method. The file with the theoretical structure model of MgMoO
4 crystal from the Crystallography Open Database [
57] was used as the starting approximation. The revealed unit cell volumes of all the crystals are presented in
Figure 9. The samples on the chart are arranged along the horizontal axis sequentially as their unit cell volume increases.
The values of the unit cell volumes appear to correlate with the “mush” behaviour of the melts during the growth and (to some extent) with the Mg/Mo atomic concentration ratios in the actual measured compositions of the crystals. The largest and rather stable values of the unit cell volume were revealed for crystals 2, 3 and 8, during the growth of which no “mush” appeared at all (green diamonds,
Figure 9). Along with that, the actual compositions of crystals 2 and 3 are among the most deficient in MgO, as shown in
Table 1. Moreover, according to our assumption (see above), the actual composition of crystal 8 is shifted towards the MoO
3-enriched side from the average value given in
Table 1 (see
Figure 8 lower panel) and in fact, this composition is also among the most MgO-deficient.
As can also be seen from
Figure 9, the statistical errors in the unit cell parameters determination are comparatively small for the “mush”-free samples, labeled by green points in
Figure 8 and
Figure 9. This may be evidence of the high uniformity of chemical compositions of the crystals. It means that the MoO
3-enriched boundary of the MgMoO
4 crystal homogeneity field lies almost vertically in the MgO-MoO
3 phase diagram (
Figure 8). Therefore, the crystals grown from MoO
3-enriched melts (with respect to the CMC) have nearly the same actual compositions and, correspondingly, very close unit cell parameters, independent of the particular amount of MoO
3 excess in the melt.
Samples 5 and 6, red diamonds (during the growth of which the “mush” appeared at the starting stage and then disappeared by itself, see above) can also be tentatively assigned to this group. The actual compositions of these crystals are also among the most MgO-deficient (see
Table 1) although, according to our assumptions, their compositions lie at the MgO-enriched boundary of the MgMoO
4 homogeneity field (
Figure 8). These crystals also have the largest unit cell parameters, comparable with those for crystals 2, 3 and 8. Thus, we can certainly conclude that the largest MgO deficiency in the MgMoO
4 crystal composition provides the largest unit cell parameters of the crystal.
However, in contrast to “green” samples 2, 3 and 8, “red” crystals 5 and 6 are characterized by substantial variations in the unit cell volumes at different areas of a sample. We assume that this reflects the fact that beginning parts of these samples were crystallized from quite strongly magnesium-enriched melts. However, then the “mush” was captured by the crystal surface and a significant part of MgO has left the melts. Therefore, the further portions of the crystals were already solidified from the melts with another less MgO-enriched composition, which should lead to changes in the actual crystal compositions. Thus, the actual compositions of different parts of crystals 5 and 6 are slightly different from each other. These differences also reflect a rather strong spread in the unit cell parameters.
Finally, the crystals 4, 7, 9 and 10 (blue diamonds) grown from the initially clear melts with the appearance of “mush” after some period of time, as well as crystal 1 (red diamond), are characterized by essentially lower unit cell parameters than the rest of the samples. Substantial variations in the unit cell volumes are observed for this group. The variations occur both from sample to sample and within different areas of each sample.
According to our assumptions, all these crystals were solidified from the MgO-enriched melts with respect to the CMC, but within a normal (not retrograde) solubility range. The actual compositions of these samples have the least Mg
2+ deficiency with respect to the stoichiometry, and obviously, they have the least content of magnesium vacations compared to other crystals. Thus, we can conclude that the size of Mg
2+ ion is smaller than the “size” of Mg vacancy. A similar situation was earlier found for Scheelite-like molybdate crystals [
58,
59,
60].
Furthermore, we suppose that the solidification of crystals 1, 4, 7, 9 and 10 was accompanied by a comparatively strong shift of the melt compositions and, obviously, of the crystal compositions, like in the case of crystals 5 and 6. Thus, rather strong spreads in the unit cell parameters inside each sample of this group are explainable.
Note that the unit cell volumes of crystals 1 and 10, grown from the same stoichiometric charge completely without any treatment, coincide with each other within the measurement error limits. Moreover, they are very close to the literature data for MgMoO
4 (the JCPDS file 21-0961) and for MgMoO
4:0.1 at. % Tm crystal [
32] (
Figure 9, violet and pink lines, correspondingly).
It is clear from the results presented above that the different procedures for the charge preparation (different sequence of the procedures of UHD treatment and calcining) result in different shifts of the starting melt compositions towards different sides from the MgMoO4 CMC. This leads to different “mush” behaviour of the melts and to crystals with slightly different actual compositions and unit cell parameters.
We have also grouped the crystals by the type of components that were treated by UHD and by sequence of the procedures of UHD treatment and calcining (whole charge treatment before calcination 2, 3, 4; whole charge treatment after calcination 5, 6; Nd2O3 treatment 7, 8, 9) and then checked for statistically significant differences in unit cell parameters within each a group. Comparisons within the groups were carried out using analysis of variance followed by pairwise comparison of groups using Student’s t-test with the Kruskal–Wallis correction followed by Dunn’s test. The comparison has resulted in the following pairs: samples 2 and 4 (control) differ in parameters a, b and V; sample 7 differs from sample 8 (control) in a, β, V as well as from 9 (control) in a and V. No other differences were found to be statistically significant between those groupings. These results show that only UHD-treated charges have statistically different unit cell parameters of the grown crystals, which underlines the possible modifying effects of UHDs of charges.
The observed changes may have the same explanation, as suggested by others [
16]: after the technical preparation of UHD solution, aggregates of highly diluted initial substances connected to gas nanobubbles may form, which can be retained after repeated dilutions due to the flotation effect [
18].
3.2. Actual Nd3+ Concentration and Optical Absorption Spectra
Along with the measurements of the actual Mg and Mo concentrations in the samples, the contents of Nd3+ and of some accidental impurities in the crystals was also measured. For the majority of the impurities, the measurements were performed by ICP-MS simultaneously with the measurements of Mg and Mo concentrations. For some impurities (e.g., potassium) the refining measurements were also carried out by atomic emission spectroscopy with inductively coupled plasma (ICP-AES) using an of iCAP 6300 duo spectrometer (Thermo Fisher Scientific, Waltham, MA, USA). A set of the multi-element standards (High-Purity Standards, Charleston, SC, USA) was used for calibration.
The measured Nd concentrations are presented in
Figure 10. Among the revealed accidental impurities, one should especially mention potassium. Its concentrations are also given in
Figure 10.
The special interest in potassium accidental impurity is due to the fact that the substitution of Mg
2+ ion for Nd
3+ is heterovalent in the MgMoO
4 lattice and the effective excess positive charge appears in the crystal during such a substitution. It requires a compensation of charge. If no special charge compensator is introduced into the lattice along with Nd
3+ (as in our case), such compensation occurs in the crystal via the formation of some own non-stoichiometry charged defects—probably magnesium vacancies—according to the following quasi-chemical equation (Kröger-Vink notations):
where Mg
Mg× is magnesium ion in its regular site without any effective excess charges, Nd
Mg• is neodymium ion in the magnesium site with the effective excess positive charge and V
Mg″ is magnesium vacancy with a double effective excess negative charge.
The formation of additional point defects (like magnesium vacancies) in crystals is an energetically unfavorable process that occurs with difficulty and brings additional internal energy into a lattice. It partially explains the very low distribution coefficient of Nd
3+ between MgMoO
4 crystal and the melt (see below). However, if a monovalent cation (like K
+) enters into magnesium lattice simultaneously with trivalent neodymium, these two cations compensate the effective excess charges of each other in the frame of the mechanism of conjugate isomorphism, according to the equation:
where K
Mg′ is the potassium ion in the magnesium site with the effective excess negative charge.
In this case there is no necessity for the formation of magnesium vacancies, and neodymium entry into the lattice should be facilitated to some extent. That is why it is very important to monitor the existence of such accidental impurities as potassium in the Nd:MgMoO4 crystal.
As can be seen from Equation (2), the mechanism of conjugate isomorphism efficiently works only if the concentrations of the mutually compensating impurities are comparable, which is the case for potassium in our samples (
Figure 10). All other revealed accidental impurities that could, in principle, participate in this process with Nd
3+ in the Nd:MgMoO
4 the crystal (other alkali metal ions, or small pentavalent ions that could enter into the Mo
6+ lattice) appeared to be in too low concentrations in the crystals. Thus, we do not consider these impurities.
An indicator of functioning of the mechanism of conjugate isomorphism between Nd
3+ and K
+ in the Nd:MgMoO
4 crystal should be the correlation between the concentrations of these two ions in the crystals. However, as shown in
Figure 10, the correlation is not very strong. At least 3 of 10 samples (5, 7 and 10) apparently do not follow this correlation. It means, at least, that there are some additional factors a having a strong influence on the entry of Nd
3+ and K
+ into the crystal.
In order to search for these factors, we used different colour pattern to mark experimental points in
Figure 10. Marks indicating Nd
3+ concentrations in the samples (squares) have the same colours as in
Figure 8 and
Figure 9, i.e., they reflect the “mush” behaviour of melts. Marks indicating potassium concentrations in the samples (triangles) have the same colours as the blocks in
Figure 3, i.e., they reflect the type and order of treatment of the charges. It is seen that the Nd
3+ concentrations rather close to each other, 0.0027–0.0032 wt. % in the majority of the samples (except 5 and 6). This corresponds to the segregation coefficients of 0.0034–0.0041. This is substantially lower than the earlier determined segregation coefficient of the Tm
3+ and Cr
3+ ions in MgMoO
4 crystal, which are equal to 0.02 [
31] and 0.24 [
40], respectively. Neither the type of treatment nor the “mush” behaviour of the melt (its position in respect to the CMC) nor the fluctuations of K
+ concentration from sample to sample had any pronounced effect onto the actual Nd
3+ content in these samples.
However, samples 5 and 6 contain about 1.5 times larger Nd3+ concentrations as compared to the other 8 samples. These samples were grown from the charges that have undergone UHD treatment before calcining (in contrast to all the rest samples) and the growth of these crystals was most likely run from the most MgO-enriched melt, see above. Thus, it is likely that these factors are the main reason for the increased Nd3+ content in crystals 5 and 6 and the corresponding segregation coefficients. However, the particular mechanism of such influence is still unclear and requires additional investigation.
The unpolarized optical absorption spectra of all samples in the range of 550–850 nm were measured using a Cary 5000 spectrophotometer (Varian, France) with a measurement step of 0.2 nm at 300 K. The obtained spectra after subtraction of the background of the own host absorption [
31] are presented in
Figure 11.
Three characteristic optical absorption bands of Nd3+ are seen in the spectra, peaking near 815, 750 and 590 nm. All the bands are very weak due to the very low actual Nd3+ concentrations in the samples. The following conclusions can be drawn from the analysis of the observed optical absorption bands:
1. The shapes and peak positions of the bands corresponding to the particular transitions are equal for all the studied samples within the measurement error. The only exception is the additional local peak at ~576.5 nm observed for crystals 9 and 10 but absent for the rest of samples. This difference can be easily explained by different probe beam directions with respect to the crystallographic axes for these two groups of samples (
Figure 11 caption).
2. The absorption band with the maximum near 590 nm probably corresponds to the overlapped bands of the 4I9/2→2G5/2 and 4I9/2→2G7/2 transitions of Nd3+ ion. According to the theory, for a single kind of Nd3+ ion located in a low-symmetry crystal field, the total number of Stark components should be equal to seven for these two transitions (in sum). However, except for the above-noted additional local peak at 576.5 nm in samples 9 and 10, no local Stark components are distinguishable at 300 K. Obviously, this is the result of too large a number of strongly overlapped elementary lines being located within a rather narrow spectral range.
3. The absorption band near 750 nm should be attributed to the 4I9/2 → 4F7/2 transition of Nd3+ ion. Four local maxima at the wavelengths of ~742,5~745,2~750 and ~755 nm can be clearly distinguished for all samples in this spectral range. Obviously, these maxima correspond to the transitions between the lowest Stark component of the 4I9/2 ground state and all four Stark components of the 4F7/2 excited state. According to the theory, just this number of Stark components should exist for this transition in the case of a single kind of Nd3+ ion located in a low-symmetry crystal field.
4. The absorption band near 800 nm belongs to the 4I9/2→4F5/2 transition of neodymium. Similarly, three local maxima at the wavelengths of ~802, ~809,2 and ~815 nm can be distinguished for all samples. These maxima correspond to the transitions between the lowest Stark component of the 4I9/2 ground state and all three Stark components of the 4F5/2 excited state. Again, according to the theory, just this number of the Stark components should be observed for the 4I9/2→4F5/2 transition in the case of a single kind of Nd3+ ion located in a low-symmetry crystal field.
Therefore, within the experimental error, only one kind of Nd3+ optical center was revealed in Nd:MgMoO4, regardless of the peculiarities of the sample growth or treatment of the charges. These centers are probably located in the low-symmetry crystal field of the Mg1 4g site. No additional Nd3+ centers (located in either the Mg2 4i site or in any disturbed site, for example, associates of Nd3+ ions with charge compensating point defects) were revealed by optical absorption spectroscopy analysis at 300 K. Further attempts to search for these centers should be conducted with the help of more sensitive methods such as optical absorption spectroscopy at 4.2 K or EPR spectroscopy.
On the other hand, the absorption intensities vary from sample to sample. We believe these variations are caused by differences in the actual Nd
3+ concentrations in the crystals. According to the Lambert–Booger–Behr law, the peak optical absorption cross-section was calculated for this transition for each Nd:MgMoO
4 crystal. The average value appeared to be 1.9 ± 0.3 × 10
−20 cm
2. It is less than for monoclinic molybdate Nd
3+:KY(MoO
4)
2 (
E‖
Nm (3.8 × 10
−20 cm
2),
E‖
Ng (7 × 10
−20 cm
2) and
E‖
Np (4 × 10
−20 cm
2) [
58] or for tetragonal Scheelite-like tungstate Nd
3+:PbWO
4 (2.75 × 10
−20 cm
2 and 4.75 × 10
−20 cm
2 for σ-(
E⊥
c) and π-(
E‖
c) polarizations, respectively [
59].
Note that quite close values of Nd3+ optical absorption coefficients for samples 1–4 and 7–10 reproduce/confirm rather small variations in the actual neodymium concentrations in the crystals revealed by ICP MS analysis. Meanwhile, the increased Nd3+ optical absorption coefficients for samples 5 and 6 reflect the increased actual neodymium concentrations in the latter samples although, unfortunately, with substantial measurement errors.