Crystal fields and microscopic local structures of some trigonal symmetry centres in fluorite crystals doped with trivalent rare-earth ions

The only calculation comparable to the authors' simulation of local lattice distortions in a trigonal centre is the superposition model estimate of lattice relaxation processes in the trigonal centre in the Gd3+:SrF2 system by Edgar and Newman [35].

“The only calculation with which we can compare our results appears to be the superposition model estimate of lattice relaxation processes in the trigonal centre in the Gd3': SrFz system of Edgar and Newman [35]”

• cites Edgar and Newman [35] Edgar A, 1975, J. Phys. C: Solid State Phys. sourceSupported

The results of this study, as well as analogous work on the tetragonal [15,19] and cubic [21] centres in RE3+: fluorite systems, give clear support to the view that a suitably modified electrostatic effective charge model may still be of some use in analysing rare-earth crystal field spectra.

“The results of this study, as well as analogous work on the tetragonal [IS,191 and cubic [Zl] centres in RE^': fluorite systems give clear support to the view that a suitably modified electrostatic effective charge model may still be of some use in analysing rareearth crystal field spectra.”

• cites [15] Grachev V G, 1989, Sov. Phys.-Solid StateNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [19] sourceNot checked — no full text of the source
• cites [21] Lesniak K, 1990, J. Phys.: Condens. Matter sourceSupported

At least one example, the cubic centre in the Eu3+:PbF2 system [21], clearly illustrates the limitations of the suitably modified electrostatic effective charge model.

“with at least one example (the cubic centre in the Eu3+: PbF, system [21]) clearly illustrating the limitations of such a model.”

• cites [21] Lesniak K, 1990, J. Phys.: Condens. Matter sourceSupported

At least some of these results are in accord with a superposition model estimate performed by Edgar and Newman [35] for a trigonal centre in the Gd3+:SrF2 system.

“at least some of these results are in accord with a superposition model estimate performed by Edgar and Newman [35] for a trigonal centre in the Gd3': SrF, system.”

• cites Edgar and Newman [35] Edgar A, 1975, J. Phys. C: Solid State Phys. sourceSupported

There is little reason to think that the trigonal centre observed by Jouart et al [31] in the Eu3+:BaF2 system is qualitatively different from the trigonal centre in the Eu3+:SrF2 system whose spectrum was reported in [30].

“There is, on the other hand, little reason to think that the trigonal centre observed by Jouart et al[31] in the Eu3+:BaF2 system is qualitatively different from the trigonal centreintheEu'+:SrF,system whosespectrumwasreportedin [30].”

• cites Jouart et al [31]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [30] Jouart J P, 1985, J. Phys. C: Solid State Phys. sourceSupported

For the trigonal centre in Eu3+:SrF2, the phenomenological B values obtained reproduce the energy level splitting measured by Jouart et al. with an accuracy corresponding to U = 1.5 cm-1.

“These values reproduce the energy level splitting measured by Jouart et al[30) with an accuracy corresponding to U = 1.5 cm-' (figure 6).”

• cites Jouart et al [30]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Both groups 2 and 3 had to be included in the relaxation region before reasonably close reproduction of phenomenological B6 could be achieved.

“It is, however, important to underline that both groups 2 and 3 had to be included in the relaxation region before reasonably close reproduction of phenomenological Bg could be achieved.”

The model procedure led to a reasonably close reproduction of experimentally observed crystal field splittings for trigonal centres in the Dy3+:SrF2 and Dy3+:BaF2 systems.

“Again.we see that the model procedure followed led to a reasonably close reproduction of experimentally observed crystal field splittings.”

• cites Eremin et al [32]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The procedure developed improves the phenomenological calculation of B values for the trigonal centre in the Eu3+:BaF2 system, significantly improving final fit quality.

“Finally. the procedure developed was used to improve the phenomenological calculation of 8: values for the trigonal Centre i n the Eu'* :BaF, system, demonstrating its utility in such applications by significantly improving final fit quality.”

The first type of relaxation leads to a radial collapse of the lattice around the dopant, with dopant-ligand distances reduced from 4.746 a0 to 4.42 a0 for the Eu3+:SrF2 system.

“The first type of relaxation leads to a radial collapse ofthelatticearoundthedopant, the dopant-liganddistances beingreducedfrom4.746a. to 4.42 a, for the system of interest.”

For the trigonal Eu3+:SrF2 centre, the model-predicted crystal field splittings reproduce the experimentally observed splittings of Jouart et al. very closely, usually with accuracy better than 10 cm-1.

“It is clear that the experimentally observedcrystalfieldsplittingsare reproducedveryclosely, usually withaccuracy better than lOcm-'.”

• cites Jouart et al [30]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Using the procedure of section 3 with ionic radii and lattice constant values appropriate to the Eu3+:BaF2 system and the QL, t, z, A values determined previously for the Eu3+:SrF2 system gave B values B2=+178 cm-1, B4=+1550 cm-1, B4=-1830 cm-1, B6=+1360 cm-1, B6=+821 cm-1, B6=+861 cm-1.

“The resulting B: values were: B i = +178cm-'. BA = +1550cm-', B! = -1830cm-', B$ = +1360cm-', B$ = +821 cm-', B$ =~+861 cm-'.”

In a modified distortion modelling procedure with t values fixed at those previously determined for the trigonal centre in Eu3+:SrF2, the sole minimum found corresponds to QL = -0.724/el and z = 0.724.

“The sole minimum found in this way corresponds to Q L = -0.724/el, z = 0.724.”

Comparing these results with the foregoing discussion of the trigonal centre in the Eu3+:SrF2 system, the present simulation produced a picture of local lattice distortions very different from that presented in table 1.

“Comparing these results with those of the foregoing discussion of the trigonal centre in the Ex3+: SrF,system, we see that the present simulation produced a picture of local lattice distortions very different from that presented in table 1.”

The authors' results agree with Edgar and Newman's assumption that the two axial ligands are equidistant from the dopant.

“our results agree with their assumption that the two axial ligands are equidistant from the dopant.”

• cites Edgar and NewmanNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The authors' calculation gives a 1% reduction in the dopant-interstitial separation.

“Our result of a 1% reduction in the dopant-interstitial separation is in accord with this picture”

This value of u = 8.5 cm-1 is significantly larger than the u = 1.5 cm-1 obtained in the analogous calculation for the Eu3+:SrF2 system.

“This value of u is significantly larger than the u = 1.5 cm-' obtained in the analogous calculation for the E d t :SrF2 system”

The crystal field splittings in the trigonal centres in Eu3+:BaF2 and Eu3+:SrF2 systems are very similar.

“Moreover, the crystal field splittings in the trigonal centres in E d + : BaF, and E d t : SrF, systems are very similar.”

The authors were able to obtain information about local lattice distortions in several centres of the type considered.

“Furthermore, we were also able to obtain information about local lattice distortions in several centres of the type considered.”

This situation is the exact opposite to that found for the trigonal centre in the Eu3+:SrF2 system, where group 5 ions moved towards the RE3+ ion and group 4 ligands moved away.

“This situation is the exact opposite to that found for the trigonal centre in the Eu3+:SrF2 system, where it was group 5 ions that moved towards the RE3+ ion and group 4 ligands that moved away.”

The data on the cubic centres in the Eu3+:BaF2 system are, at present, insufficient for phenomenological B4 determination.

“thedataonthecubiccentres in the Eu3+:BaF2 system are, at present, insufficient for phenomenological B$ determination.”

Fitting the splittings in the trigonal centre in the Eu3+:BaF2 system observed by Jouart et al from these starting values resulted in phenomenological B values that reproduce the experimental crystal field splittings with an accuracy corresponding to u = 8.5 cm-1.

“These values reproduce the experimental crystal field splittings with an accuracy corresponding to u = 8.5 cm-' (figure 7).”

• cites Jouart et alNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The authors' calculation predicts an increase in the dopant-axial ligand distance by 4%.

“the prediction of our calculation of an increase in the dopant-axial ligand distance by 4%”

The a priori calculations of section 2, in which the t values are effectively set equal to 1.00, yielded crystal field splittings close to experimental data.

“This observation helps to explain why the a priori calculations of section 2, in which the I,,, values are, in effect, put equal to 1.00, have yielded crystal field splittings that are so close to experimental data.”

The t4 and t5 values deduced from sets (I) and (II) are the same.

“Moreover, the t4 and f5 values deduced from sets (I) and (11) are the same.”

The results confirm that NNN-F' compensated centres were indeed observed in a number of experimental investigations of RE3+:fluorite systems.

“While the results obtained confirm that such centres were indeed observed in a number of experimental investigationsof these dopant : latticesystems”

Previous work on the a priori prediction of the spectra of tetragonal symmetry sites in RE3+:fluorite systems provides a model framework for investigating trigonal centres.

“Previous work on the apriori prediction of the spectra of tetragonal symmetry sites in RE'+ :fluorite systems [IS.191 appeared to provide a model framework within which suchaninvestigationcould beconducted”

• cites [IS.191]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The results provide a basis for identifying the emission observed by Eremin et al. in the Dy3+:SrF2 and Dy3+:BaF2 systems as arising from centres of the type shown in figure 1.

“The results thus provide a basis for identifying the emissionobserved by Eremin era1 [32] as arisingfrom centresof the type shown in figure 1.”

• cites Eremin et al [32]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Trigonal symmetry centres associated with F- compensation become progressively more important with increasing host lattice constant and RE3+ dopant mass.

“Moreover, the trigonal symmetry centres associated with Fcompensation were shown in a number of studies [5][6][7][8][9][10] to be progressively more important with increasing host lattice constant and RE^+ dopant mass.”

• cites [5][6][7][8][9][10]Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The reconstructed local distortions in the Eu3+:SrF2 trigonal centre are superpositions of two types of relaxation: that due to the difference in ionic radii of dopant and lattice cation, and that due to processes associated with introduction of the interstitial.

“In analysing the data in table 1, it should be remembered that the reconstructed distortions are superpositions of two types of relaxation-that due to the difference in theionicradiiofthedopant and thelatticecation,andthatdue to theprocessesassociated with introduction of the interstitial.”

Model reconstruction of the positions of the group 2 ions and the interstitial may be physically unrealistic.

“The fact that movementsof the ions in group 2 (as well as those of the interstitial) are determined mostly from leads us to expect that model reconstruction of their positions may be physically unrealistic.”

• cites [29] Lésniak K, 1986, Acta Phys. Polon.Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The J site in the Er3+:SrF2 system can be identified with a centre structurally related to the centre shown in figure 1.

“The similarity of the above two energy level schemes is sufficiently close for us to identify the J site with a centre that appears to bc structurally related to the centre shown in figure 1.”

• cites [14] sourceNot checked — no full text of the source

The local lattice arrangement shown in figure 1 is a good description of the lattice environment producing the observed level splittings in the Eu3+:SrF2 trigonal centre.

“Clearly, the local lattice arrangement shown in figure 1 appears to be a good description of the lattice environment producing the observed level splittings.”

The NNN compensation arrangement of figure 1 provides a reasonably good description of the L site in the Er3+:BaF2 system.

“The agreement between the two energy level schemes appears to be close enough to claim that the NNN compensation arrangement of figure 1 provides a reasonably good description of the L site.”

• cites [16] Kurz M D, 1977, J. Lumin.Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [17] Aizenberg I B, 1969, Sov. Phys.-Solid StateNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

The B centre in the Er3+:CaF2 system bears no direct relation, apart from symmetry, to the NNN-F' compensated centre shown in figure 1.

“While the results obtained confirm that such centres were indeed observed in a number of experimental investigationsof these dopant : latticesystems, in at least one instance (the B centre in the Er'+: CaF, system) such identification appears to be untenable.”

• Also stated in: § 3.3. Erbium · plain

  “Wearethusled toconcurwiththe authorswhothoughtthat theBsite bearsnodirect relation (apart from symmetry) to the centre shown in figure 1.”

The unrealistically large movements of the group 2 ions towards the original position of the F ligand on the trigonal axis probably reflect the limited accuracy of determination of their positions.

“The unrealistically large movements of the group 2 ions towards the original position of the Fligand on the trigonal axis probably reflect the limited accuracy of determination of their positions that was underlined in section 2.”

The initial B values do indeed seem to influence the quality of the final fit.

“indicating that the initial B: values do indeed seem to influence the quality of the final fit.”

A calculation in which B values corresponding to t = 1.00 are used as a starting point in fitting trigonal centre splittings is, at present, impossible for the Eu3+:BaF2 system.

“Thus, a calculation in which B$ valuescorresponding to t, = 1.00 are used as a starting point in fitting trigonal centre splittings is, at present.impossible for the E d + : BaF, system.”

The above arguments are strong indications that the centre in question is the NNN-compensated centre of figure 1 that was analysed in the previous sections of this paper.

“The above arguments are strong indications that the centre in question is thus theNNN-compensatedcentre of figure 1 that wasanalysedin the previoussections of this paper.”

The t4 and t5 values are particularly insensitive to the details of the modelling procedure followed.

“This is particularly significant in the case of ta and t5 values since, as was noted in section 2, these are particularly insensitive to the details of the modelling procedure followed.”

In the case of the B centre in the Er3+:CaF2 system, the present procedure clearly indicates that identification with the NNN-compensation arrangements is unwarranted, a view in accord with those of most other investigators.

“The selectivity of such identification may be seen in the case of the B centre in the Er3+:CaF2 system.where the present procedure clearly indicates that such identification is unwarranted, a view in accord with those of most other investigators.”

The authors' prediction of an increase in the dopant-axial ligand distance by 4% is in clear disagreement with the conclusions of Edgar and Newman.

“the prediction of our calculation of an increase in the dopant-axial ligand distance by 4% is in clear disagreement with the conclusions of Edgar and Newman.”

• cites Edgar and NewmanNot matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

In accordance with theoretical calculations [7,10] concerning the occurrence of NNN-compensated sites, the centre in question appears to be the dominant one in the Eu3+:BaF2 system.

“Inaccordancewith theoretical calculations [7,10] concerning the occurrence of NNN-COmpenSatedsites, the centre in question appears to be the dominant one in the Eu3+ :BaF2 system.”

• cites [7] Catlow C R A, 1976, J. Phys. C: Solid State Phys. sourceNot checked — no full text of the source
• cites [10] sourceNot checked — no full text of the source

The reported application of the modelling procedure helps to reduce significantly the deviation between calculated and measured crystal field splittings, from u = 8.5 cm-1 to u = 2.4 cm-1, underlining its utility in analysing the spectra of trigonal centres in RE3+: fluorite systems.

“We thussee that the reported application of our modelling procedure helps to reduce significantly the deviation between the calculated and measured crystal field splittings (from U = 8.5 cm-' to U = 2.4 cm-I), underlining its utility in analysing the spectra of trigonal centres in RE^+: fluorite systems.”

This is the first instance when such a complete reconstruction of these distortions has been made for the centre type of interest.

“Since this is, to our knowledge, the first instance when such a complete reconstruction of these distortions has been made for the centre type of interest”