Ligand field analysis of Mn5+ in tetra-oxo coordination

Chemical Physics ELSEVIER

Chemical Physics 202 (1996) 155-165

Ligand field analysis of Mn 5÷ in tetra-oxo coordination 1 M. Atanasov a,*, H. Adamsky h, D. Reinen c " Institute of General and Inorganic Chemsitry, Bulgarian Academy of Sciences, BI.11, 1113 Sofia, Bulgaria b lnstitutffir Theoretische Chemie, Heinrich-Heine-Universit~t, Universiti~tsstrasse 1, Geb.26.32, D-40225 D'~sseldorf, Germany c Fachbereich Chemie der Philipps-Universitht und Zentrumffir Materialwissenschafien, Hans-Meerwein-Strasse, D-35043 Marburg, Germany

Received 8 June 1995

Abstract Polarized single crystal absorption and powder reflection spectra of Mn 5+ (d 2) in tetrahedral oxo-coordination of host compounds with the spodiosite and apatite structure from literature are analysed using the angular overlap model (AOM). A small number of model parameters such as the AOM parameters ecr and e~r, the interelectronic repulsion parameters B and C as well as geometric distortion angles 20 were used to fit the band positions. Covalency is pronounced, however, enforcing a treatment with varying B values for different strong field configurations e 2, elt~, t22- the C / B ratios being kept at the free ion value of 4.25. Deduced best-fit parameter values are A = 10650 cm -1 (ecr = 12000 cm - t , e t l / e l r = 4), Bee = 530 c m - I, Bet = 420 c m - 1, Btt = 340 c m - 1, showing that the central field covalency dominates over the symmetry restricted covalency. The estimated angular distortion parameters 2 0 and the A values indicate that the geometry of the tetrahedral sites is significantly modified when Mn 5+ is incorporated into positions of host ions with a smaller ionic radius (p5+).

I. Introduction The spectroscopic and structural properties of Mn 5+ and Cr 4+ ions doped into the tetrahedral sites of oxidic solids have been studied extensively [1-9]. Oxide ceramics of this type are of interest because of the possible use as pigments [ 5 - 7 ] and for laser applications [8,9]. In spite of the efforts with respect to their synthesis and optical characterization only

* Corresponding author. Mailing address: lnstitut ft~rTheoretische Chemie, Heinrich-Heine-Universit~t, D-40225 Diisseldorf, Germany. z Dedicated to Professor Dr. H.-H. Schmidtke on the occasion of his 65th birthday.

little is known about the m e t a l - o x y g e n bond, which is expected to be different from that with metals in lower oxidation states. There is convincing experimental evidence since the early papers by Milstein et al. [1,2] and Day et al. [3,4] that the d 2 configuration is well defined for MnO43- polyhedra and that the ligand field model can still be applied to interpret the multiplet structure and optical behaviour at least roughly. Single crystal EPR studies yield the zerofield splitting patterns expected for a tetrahedral d 2 system, and the powder reflection spectra of a great variety of Mn 5 +-doped oxidic host lattices confirm and extend the experimental basis for the description of the electronic structure [5-7]. Luminescence data reveal, that the I E ~ 3 A 2 transition of Mn 5+ is extraordinarily intense [8,9]. No reliable ligand field

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M. Atanasov et a l . / Chemical Physics 202 (1996) 155-165

parameters have been reported so far, however, mainly because most published optical data stem from powder samples, which usually yield rather broad and badly resolved spectra. An important feature, which will influence the ligand field analysis, is the exact geometry of the MnO43- polyhedra in the respective host lattice. Evidence has been accumulated, that Mn 5÷ will only adopt the host site geometry, if the ion to be substituted has about the same size as the doping cation [5-7]. This is the case for V 5÷, As 5+ for example, while Mn 5+ modifies the host site geometry when substituting the smaller pS+ cation. The fine structure tensor of the MnO43tetrahedra may even change its orientation in the lattice [5,6]. In this paper we report bonding parameters and coordination geometries of Mn 5+ in various oxidic lattices. The analysis of the single crystal spectra in high resolution supplemented by powder data taken from the literature is based on a ligand field treatment within the angular overlap model (AOM) [10]. It is possible within this model to factorize the ligand field problem into a geometric (angular) part and a metal-ligand bonding part allowing to estimate bond angles, interelectronic repulsion parameters and dtype antibonding energy parameters of or- and "tr-type, respectively, from a fit to the observed spectra. This will on the other hand help to understand the less resolved, but commonly reported powder spectra. We will limit ourselves to host compounds with known structures, allowing to compare the geometry of the host site in each case with that of the colour centre as deduced from the reported spectra and a ligand field analysis. Our attention will be focused on the following host compounds for which structures and polarized single crystal spectra have been already reported, namely spodiosites: A2(BO4)C1 with A;B: Ca2+,Sr2÷; PS+,VS÷ [1,2,5-9] and apatites: S r s ( P O 4 ) 3 C I [3,4]. Ligand field theory will be applied such, that in a first step an analysis is attempted in the usual way by fitting the band positions to the parameter set 20 (geometrical distortion parameter), the AOM parameters err and eTr and the Racah parameters of interelectronic repulsion B and C (see below). A further parameter affecting the Coulomb repulsion energy will also be discussed. It is connected with the operator a L 2 ( a > O) and accounts for polariza-

Table 1 Spectroscopic parameters (cm - I ) for the free d 2 ions Cr 4+, Mn 5+ and Fe 6+ a Cr 4+

Mn 5+

Fe 6+

B0

1075 1015

1228 1160

1377 1300

Co

3886 4263

4483 4930

5063 5525

~0 a

341 91

503 105

712 115

a Underlined values were obtained by a fit without taking the Trees correction ot into account.

tion effects, connected with the observation that Coulomb repulsion is underestimated for terms with high orbital momenta. Though the exact physical origin of the so-called Trees correction [11] is not known, it very probably originates from electronic correlations due to mixing with configurations outside d n. In view of the high extend of covalency of the Mn 5+ - 0 2 - bond, an approach suggested by Sch~iffer and Jorgensen [12] will be applied. Different B and C values for the various one-electron configurations I 2 (e 2 ,e I t2,t 2) are introduced, fixing the respective C / B ratio to that of the free ion, however. Finally, the obtained parameter sets will be compared with those of the isoelectronic Cr 4÷ and Fe 6÷ cations in the tetrahedral sites of oxo-compounds. Racah parameters and spin-orbit coupling constants of the free ions Cr 4+, Mn 5+ and Fe 6÷ deduced by a best-fit procedure from published term diagrams [13,14] are collected in Table 1. One set of parameters includes the Trees correction a, which considerably improves the fit.

2. Structural data and electronic spectra

The geometries of the tetrahedral sites in the spodiosite and apatite host structures can be approximately described as tetragonally compressed (D2d) and trigonally elongated (C3v), respectively. They show distinct lower-symmetry components superimposed (more pronounced in the latter case), as reflected by the true site symmetries C 2 and C s, however. Bond lengths and bond angles of the M O 4 tetrahedra (M: V,P) in spodiosite and apatite type

157

M. Atanasov et a l . / Chemical Physics 202 (1996) 155-165 Table 2 Bond lengths (,~.) and bond angles (°) of tetrahedral sites in oxidic lattices of spodiosite and apatite types Compound

Type

Bond length

Bond angle

Ref.

Ca2(PO4)C1

spodiosite

P - O I 1.548 (2 × ) P - O 2 1.534 (2 x )

[15]

Ca2(VO4)CI

spodiosite

V - O I 1.710 (2 x ) V - O 2 1.702 (2 × )

Sr2(VO4)C1

spodiosite

V - O I 1.715 (2 × ) V - O 2 1.726 (2 x )

Srs(PO4)3C1

apatite

P - O I 1.540 P - O 2 1.544 P - O 3 1.537 (2 × )

Bas(PO4)3C1

apatite

P - O I 1.548 P - O 2 1.539 P - O 3 1.536 (2 × )

Bas(MnO4)3CI

apatite

Mn-O1 1.695 M n - O 2 1.694 M n - O 3 1.702 (2 × )

O I - O 1 ' 107.5 0 2 - 0 2 ' 107.7 O 1 - O 2 113.6 (2 × ) O1-O2' 107.3 (2 × ) O1-O1' 107.0 O2-O2' 105.6 O 1 - O 2 116.3 (2 × ) O I - O 2 ' 106.0 (2 × ) O1-O1' 106.2 0 2 - 0 2 ' 105.5 O 1 - O 2 115.9 (2 × ) O 1 - O 2 ' 106.9 (2 × ) O I - O 2 111.1 O 1 - O 3 111.6 (2 × 0 2 - 0 3 107.0 (2 x 0 3 - 0 3 ' 108.6 O 1 - O 2 109.4 O 1 - O 3 111.8 (2 × 0 2 - 0 3 107.8 (2 × 0 3 - 0 3 ' 108.2 O 1 - O 2 112.6 O 1 - O 3 112.8 (2 × 0 2 - 0 3 106.0 (2 x 0 3 - 0 3 ' 106.0

[16]

[7]

[17]

[18]

[6]

Table 3 Transition energies for the MnS+-doped spodiosites Sr2(VO4)C1 and Ca2(PO4)CI as well as ligand field parameters (cm -I ) and distortion angles 20 (°), deduced from a best fit to the optical spectra " Ta

D2a

3T 2

3E 3B 2 3E 3A 2 3A 2 3E IA I IB I JA I tE tB 2 IE IA~

a3Ti b3Ti IE IA I IT 2 ~T I e~ 20 e (B) t (C) f

Sr2(VO4)C1 : Mn 5+

Ca2(PO4)C1 : Mn 5 +

calculated (I)

calculated (II)

exp. [1,2,9]

calculated (1)

calculated (II)

9016 13105 13099 16600 21295 23898 8346 8509 15103 15720 19630 17350 23090 11180 118.9 0.820 0.737 29

9067 12585 13106 16371 21531 23958 8353 8518 14676 17425 20848 19073 24149 11830 117.3 (430) (2600) 150

~ 9100 13100 16600 21295 ~ 24500 8305 8560 -

9540 14236 13590 17693 22336 25448 8438 8645 15494 16116 20648 17759 24245 11960 119.5 0.823 0.729 24

9579 13622 13642 17453 22617 25499 8465 8674 15034 18063 22032 19732 25481 12670 117.8 (430) (2675) 173

Band maxima used for the fit are underlined, e ~ / e ~ = 4, see text.

-

exp. [4,9] ~ 9400 13600 17700 22330 ~ 26000 8400 8683

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M. Atanasov et al. / Chemical Physics 202 (1996) 155-165

compounds taken from literature sources [6,7,15-18] are collected in Table 2. In a first step, we will base our AOM analysis on approximate D2d and C3v molecular geometries. The tetragonal compression in the spodiosites can then be properly described by the single polar angle 20 connected with the pseudo-S 4 axis (20 > 109.47°). Similarly, the trigonal elongation in the apatites can be defined by a single angular parameter 2 0, which is the angle between the bond along the pseudo-C a axis to either one of the three other metal-to-ligand bonds (2 0 > 109.47°). The d 2 configuration in Td symmetry gives rise to three spin allowed transitions from the 3A2 ground state to 3T2, a3Tl and b 3 T 1 excited terms. Among these, the first is symmetry forbidden in To, while the third corresponds approximately to a two-electron jump which gains intensity from mixing with a3T] via interelectronic repulsion and lower-symmetry ligand field components. The symmetry allowed 3A2 --->a3Tl band is observed in the visible region and mainly responsible for the bright green, turquoise and blue colours of MnS+-doped oxide ceramics. The colour can be manipulated by varying parameters such as the chemical constitution and the structure, giving rise to changes of the ligand field param-

Table 4 Transition energies for the MnS+-doped apatite Srs(PO4)3C1, as well as ligand field parameters ( c m - i ) and the distortion angle 20 (°), deduced from a best fit to the optical spectra a Td

C3v

Calculated (II)

Expefimental[~

3T 2

3E 3A~ 3E 3A2 3A 3E 2 IE IA I ]E [A I IE IA z

10703 11139 14694 16294 23574 24179 8005 13872 18658 18949 20739 20999 12250 112.5 2350

10600, 11250

a3Ti b3Tt tE IA i iT 2 IT I e~ 20 C

e ( r / e r r = 4, B = 430 cm -~ , see text.

14250, 15000 16245

8558, 8702 13450

eter A and of the extent of tetrahedral distortion [5-7]. The lowest-energy charge transfer band appears at ~ 33000 cm-1 [3,4], but broadens into the visible region with increasing Mn 5+ concentration, presumably due to metal-metal interactions [5-7]. On symmetry lowering to D2d and C3v polyhedra, the 3T2, a3Tl and b3Tl split into orbitally nondegenerate and doubly degenerate 3E states, which depending on the extent and the symmetry of the distortion - mix with each other, thus transferring also intensity to the symmetry forbidden 3A2 ~ 3T2 transition. The compounds become strongly dichroitic, with distinct polarization effects in the single crystal spectra. Transition energies taken from literature sources are presented in Tables 3 and 4. Assignments (symmetry labelling according to D2d (spodiosites) and C3v (apatite)) as based on single crystal polarization data may be regarded as rather reliable and are strongly supported by calculations of the vibronic landscape [19]. In particular the progression lines in the region 20500-25000 cm-~ must be attributed to the 3Bl[3A2(e2)]--) 3A213T](tz2)] (rather than to the spin forbidden 3Bl[3A2(e2)]~l E[]T2(et2)] transition, see Ref. [4]) in view of the reported Huang-Rhys factors of progression lines for the stretching Mn-O mode (S = 1.5-2.0) being much larger than those reported for transitions of the et 2 type (S < 0.5 [20,21]). The single crystal data for the host compounds Sr2(VO4)C1 [1,2,9] and Ca2(PO4)C1, Srs(PO4)3C1 [4] are supplemented by low temperature powder spectral results [5], in which the spin forbidden 3A2 --->a ~E and, in the case of the apatites, even the 3A2 ~ a ~A~ transitions are nicely resolved. The latter transition is expected to overlap with the lower-energy 3A2 ~ b3E(a3T]) split band in the spodiosites, thus being smeared out. However, interferences of sharp lines with vibronically broadened bands due to spin-allowed transitions have been shown to give a dip in the absorption profile at the energy of the sharp line (Fano antiresonances [22]). Such features are indeed observed in the single crystal spectra of Sr2(VO4)CI:Mn 5+ [1,2,9] and Ca2(PO4)CI : Mn 5+ [3,4] at energies of 13100 and 13600 cm -I, respectively, which nicely match the position of the 3A2 --->a ]AI absorption in the apatite Srs(PO4)3CI :Mn 5+. The weak and rather broad 3A2 ---, b 3T 1 transition was also resolved in the powder data [5-7].

M. Atanasov et al./ Chemical Physics 202 (1996) 155-165

3. Ligand field analysis and fitting strategy Term energies were calculated within the angular overlap model (AOM) using the computer program package AOMX described elsewhere [23]. Calculations have been made within the complete singlet and triplet basis of the d 2 configuration in the strong field scheme taking full account of configurational mixing. The basis was diagonalized under the perturbation

H = E e l r i j + V(AOM) + ~EliSi,

(1)

containing the Coulomb operator of interelectronic repulsion, the ligand field (AOM) and the spin-orbit coupling operator. The eigenvalues of H turned out to be quite insensitive with respect to the latter operator because of the rather small value of the effective spin-orbit coupling constant for Mn 5+ (see Table 1). This parameter was therefore set to zero throughout the fitting procedure, but its influence was always carefully checked, in particular in the ease of closer lying states. The matrices of the Coulomb and AOM operators were parametrized in terms of the Racah parameters B, C and the antibonding parameters e¢r and e'rr. Polar angles 2 0 were taken as free variables and fitted to the spectra which, however, exhibit additional lower-symmetry splittings superimposed on the dominant axial component. They are less pronounced in the spodiosites as compared to the apatites, in agreement with the geometries of the tetrahedral host sites (Table 2). We will consider these lower-symmetry effects in a later refining step. Limiting to an axial symmetry, we have in the D2d case to reproduce eight transition energies - those underlined in Table 3 have been used for the fit - by fitting five parameters: ecr, e'rr, B, C and 20. For this purpose we made use of the Powell parallel subspace optimization program by Hoggard [24] which was implemented into the AOMX package [23]. The function being minimized was

f = ]~wiQi2 ,

(2)

where the Q~ represents the differences between experimental and calculated triplet and singlet transition energies and the w i are weighting factors, which are approximately proportional to the inverse square of the corresponding experimental errors. Since we

159

can hardly evaluate the weight vector w from the reported spectral data it was set to unity for all transitions. In order to assess the reliability of the best-fit model parameters we have in each case calculated the standard deviations and correlation of the parameters as described in detail by Hoggard [24]. Calculated transition energies and best-fit parameter values are listed in columns 3 and 6 of Table 3. The five parameter treatment (err, e'rr, B, C, 20) follows the procedure suggested by Ferguson and Wood [25] and will be called II in the following. A more flexible approach which is particularly suitable for complexes with a more pronounced covalency (such as the systems under consideration) was proposed by Sch~iffer and Jorgensen [12]. According to this concept the reduction of B and C with respect to the free ion values B o and C O which is caused by the expansion of the metal d orbitals due to the overlap with ligand orbitals (nephelauxetic effect) - depends on the electronic configuration. Thus, in tetrahedral symmetry the cr and "rr antibonding t 2 orbitals (d~y, d~:, dy z) undergo a larger expansion than the only "rr antibonding e orbitals (dx2_y 2, dz2). Hence different B parameters Bee, Bet and Btt are used for the e 2, el t~ and t~ configurations, respectively. The C / B ratios are assumed to retain their free ion values, because covalency is thought to affect B and C to about the same extent. In order to reduce the great number of Coulomb repulsion parameters needed in a rigorous treatment, parameters e', t' and y are introduced [12], which simplify interelectronic repulsion matrix elements of the type

(d~z(1)dz2( 2)]l /r,2ldy:(1)d:.,( 2) ) = e'2t'zy(2Bo + Co) = e2t~(2Bo + Co).

(3)

While y describes the "central field covalency" (reduction of cationic charge due to electron transfer from ligands), the coefficients e' and t' reflect the "symmetry restricted covalency" caused by the different overlap between ligand and metal orbitals of e and t 2 symmetry respectively [12]. We will use in our approach parameters e and t, however (Eq. (3)), defined as containing both effects. Choosing t and e as free parameters besides e(r, e'rr and 20 the

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M. Atanasov et al. / ChemicalPhysics 202 (1996) 155-165

number of fitting parameters is the same as in the previous treatment. The reduction factors e and t are correlated with the Racah parameters B (and similarly C) in the following way: Bee = e4Bo,

Bet = e2t2no, Btt

= t4Bo .

(4)

It should be noted that the treatment just described (which we will label I in the following) is only applicable to cubic and tetragonal systems with the Cartesian axes x,y, z oriented along the symmetry axes of the point group. An extension to trigonal symmetries is not easy, since the Coulomb repulsion matrices become extremely complicated in systems with C 3 as the axis of quantization (strong mixing between the basis components when the conventional tetragonal d orbitals are used). A theory for such systems has still to be elaborated. The results from the spectral fits for the spodiosites based on treatment I are listed in Table 3. It should be noted that in both treatments (I and II) the parameters err and eTr turned out to be strongly correlated. The band positions do not depend on the err/err ratio, so long as the ligand field strength, A = 9(3eo - 4 e = ) ,

-256[e~(0-

4. Discussion

4.1. Orbital energy sequences and Coulomb repulsion parameters

The d-orbital energies of the spodiosites and apatites, deduced from the values of the tetragonal and trigonal distortion angles 2 0 and the parameter err = 4err are depicted in Fig. 1.

(5)

is kept constant. The splitting (A E) of the ~E term, however, is rather sensitively influenced by e ~ (and not by err) as follows from the perturbation expression: AE=

3A 2 --->3T 2 transition. Because they are rather broad, however, they have not been used in the fitting procedure. Disregarding the lower-symmetry splittings in the spectra of Mn 5+-doped apatites, such as Srs(PO4)3Cl, by taking the average over the split components of the 3A 2 ---* IE and 3A 2 ---*3E (from 3T 2 and 3,TI) transitions, three parameters, e ~ ( = 4err), C and 20 (B = 430 cm-1 ) have been fitted to five transition energies. Calculated energies and best-fit parameter values are collected in Table 4. The inclusion of the Trees correction does not significantly improve the fit in both treatments. Hence the results do not justify to use a as an additional parameter, which is also not reasonable in regard to the small number of available experimental energies.

OTd)]2/[9(4B + C)]

12000

(6)

(0Td the tetrahedral angle). The energies of the split terms can be nicely reproduced with e~r/e'rr = 4 (Table 3). Hence the latter ratio was used in all fits. Even in this case a strong correlation between the parameters ecr, B, C and 0 was encountered in treatment II, as different to treatment I where the (err, 0, e and t) parameter correlation turned out to be rather small. In order to get more reliable values for err, C and 0 in treatment II we were forced to fix the parameter B at 430 cm -~, which is the mean value of Bee, Bet and B u (treatment I, Eq. (4)). The weak bands in the region 9000-10000 cm-1 have to be assigned to the split components of the

8000

4000

m -

bl -

&l

D2a

C3v

Fig. 1. MO energies of axially distorted MnO~- tetrahedra as calculated from the best-fit err (err = 4elf = 12000 cm -t ) and 20 values in spodiosites (20 = 117.5°) (left) and apatites (20 = ! 12.5°) (right).

M. Atanasov et al. / Chemical Physics 202 (1996) 155-165

The value of the parameter B as given by the fit in treatment I, 430 cm-1 (average of Bee, Bet and B n, see below) is considerably smaller than previously suggested (500 cm-1 [5]). The nephelauxetic ratio /3 = B / B o is very small (0.37) and indicates a pronounced M n - O covalency. A much smaller reduction is obtained for the parameter C (2540 c m - ~, average of the values in Tables 3 and 4), leading to considerably larger C / B ratios (5.9) compared to the free ion value C o / B o = 4.25 (Table 1). B and C are defined as linear combinations of the SlaterCondon parameters [26] B = F 2 - 5F4, c = 35F4.

(7)

It was pointed out earlier [25] that it is the F 2 parameter which should undergo a stronger reduction on complexation because of its greater sensitivity to the outer part of the radial distribution function, where covalency plays its major part. This is supported by the values of B and C and the C / B ratios deduced from our analysis. The rather pronounced covalency as reflected by the reduction of B and C is further manifested by our results from treatment I considering the differential expansion of the e and t 2 orbitais in terms of reduction factors e and t, respectively. From the best-fit e and t parameters (Eq. (4)) the following B values pertinent for the configurations e z, e ~t~ and t~ are calculated: host lattice Sr2(VO4)C1 Ca2(PO4)C1

Bee 524 532

Bet 424 418

Bn 342 328

The deduced order of B values: Bee > Bet > Btt is in nice support with the expected more pronounced covalency for t 2 ((r + rr-type) than for e (w-type) electrons, due to the cr contributions in the former case. Comparing the nephelauxetic effect - defining /3 as the ratio between Bet and B 0 - for Mn 5÷ (/3 = 0.36) with the reported data on Cr 4+ (/3 = 0.47, [27,28]) and Fe 6÷ (/3 < 0.3 [29]), the sequence /3(Cr 4+) > /3(Mn 5+) > /3(Fe 6+) is obtained. It nicely correlates with the observed decrease in the charge transfer energies and the metal-ligand covalency, which increase in the same sequence.

161

In spite of the very satisfactory reproduction of the spectral data with the model of SchMfer and Jorgensen, the calculated energy of the 3A 2 --* a IA I transition seems to be too high. Although in the case of the spodiosites this transition could not be directly observed, it is expected to occur at a position similar to the one in the spectrum of Srs(PO4)3CI:Mn 5+ (13450 cm-1). This is supported by the absorption profiles exhibiting antiresonance behaviour at about the same energy, as mentioned before. A fit of the spectral data adopting a value for the 3A 2 -'~ a IA I energy as in Srs(PO4)3CI: Mn 5÷ resulted in a deterioration of the overall agreement between calculated and experimental energies and yielded rather unreasonable values of the model parameters. Apparently the 3A 2, aLE and a~A~ terms - though stemming from the same e 2 configuration - are affected by covalency to different extents and one even has to consider different B values for different many-electron terms. This argument is supported by the observation that the discussed effect is not present (within reasonable error limits) in the case of Cr 4+ [21,27] but much more pronounced for Fe 6+ [29] - in accord with the covalency increase in the sequence Cr 4+, Mn 5+ and Fe 6÷. A more explicit account of the rather anomalous behaviour of the three many-electron terms resulting from the tetrahedral e 2 configuration is discussed in a separate study [30]. 4.2. Ligand field parameters

The tetrahedral ligand field parameter A of MnO 3- in spodiosite and apatite type solids ( ~ 10650 c m - 1) may be compared with data for CrO 4( ~ 9600 cm -~ [21,27]) and FeO~- polyhedra ( ~ 13000 cm -l [29]) yielding the expected sequence A(Cr 4+) < A(Mn 5+) < A(Fe 6+) 2.The reported eo" and err values have to be regarded as effective parameters, being the sum of a covalent and an electrostatic part. The covalent contributions e(r' and

2 It should be noted that d z multiplets become strongly intermixed with charge transfer states as indicated by our ab initio calculations [28]. Therefore the interpretation of the 13000 cm- t transition as the 10Dq transition in Ref. [29] should be viewed with caution.

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M. Atanasov et al. / Chemical Physics 202 (1996) 155-165

e'tr' to the parameters eor and e'rr are related to the metal-ligand coupling matrix elements Tx(h = or,'rr) and the ligand-to-metal charge transfer energy rE. Using second-order perturbation theory one obtains e'h = Tx2/fE (h = or,w).

because the tetrahedra are well isolated from each other in these lattices. 4.3. The geometries of the MnO~- colour centres in spodiosites and apatites

(8)

It can be shown that Tx increases only slightly in the order Cr 4+, Mn 5+ and Fe 6+ [31] 3. Accordingly the rather pronounced enhancement of A in the sequence Cr 4÷, Mn 5+ and Fe 6÷ has to be interpreted as mainly due to increasing covalency connected with the drop of the charge transfer energy rE. This qualitative result is supported by ab initio calculations [28]. The spectra of Mn 5÷ in Ca2(VO4)CI [9] and Sr2(VO4)CI [2] are very similar, implying that the geometries of the MnO43- tetrahedra in the two host compounds are quite close, which is in accord with the comparable host site distortions (Table 2) and the only slightly differing ionic radii of Mn(V) (0.33 .~ [6]) and V(V) (0.355 ,~ [32]). The small increase of A by about 7% switching from Ca2(VO4)C1 and Sr2(VO4)CI to the Ca2(PO4)CI host indicates a shortening of the M n - O bonds by about fiR = 0.02 .A in the latter case, if a 1 / R 5 dependence of A on the Mn-O distance (R) is assumed. Apparently only a rather small matrix effect is present - the adaption to the PO43- host polyhedron dimension would have demanded a shrinking of the Mn-O spacing by about 0.16 .~ in regard to the ionic radius of P(V) (0.17 A [32]). As has been emphasized elsewhere [5-7], the guest cations will adopt the host site geometry, if the ionic radii of the two centres are comparable in magnitude and if the ground state of the guest cation is orbitally non degenerate and not vibronically unstable. In the case of differing ionic radii the host lattice influence is severe only if the coordination polyhedra are strongly interconnected. The geometric restrictions are expected to be small in solids with spodiosite and apatite type structures,

3 The parameter Tx which is proportional to rda/2/R 7/2 is found to vary in the order Cr, Mn, Fe as (]k- 2 ): 0.118, 0.130 and 0.138, respectively.

4.3.1. Axial distortions The best-fit 2 0 angles of the MnO43- tetrahedra in the spodiosites listed in Table 3 compare well with the geometry of the distorted host sites in Sr2(VO4)C1 (Table 2 : 2 0 = 115.9) in the treatment II (117.3°), but are somewhat larger for the treatment I fit (118.9°). Apparently, Mn 5+ induces a comparable or even larger distortion when replacing V 5+ which has a similar ionic radius. The best-fit 20 angle of treatment II (117.8 °) for MnS+-doped Ca2POaC1 is distinctly larger than that of the PO43- polyhedra in the host compound (Table 2: 113.6°), but similar to that for Ca2VOaCI (Table 2:116.3 °) or Sr2VO4CI (115.9°). Apparently the MnO43- tetrahedra in the former compound adopt an angular geometry close to the one of the VO43- polyhedra in Ca2(Sr2)VO4CI, which was proposed on the basis of the powder spectra [5] and was discussed in the preceding section already. While it is difficult to assess the geometrical differences resulting from treatments II and I in view of the limitations of the model (vide supra) the trends when switching from PO43- to VO 3- do not depend on the model under consideration. The luminescence data [9], in particular the splitting of the ~aE term, very sensitively mirror even finer details of the tetragonal MnO 3- polyhedron distortion. This splitting is 255 cm-1 for Sr2VO4CI and 361 cm -~ for Ca2VO4C1, paralleling to the 20 angles for the VO43- tetrahedra of 115.9 ° and 116.3 °, respectively (cf. Eq. (6)). However, the a IE term splitting amounts to 283 cm -~ in the case of Ca2PO4CI, although the PO 3- host polyhedra are only little compressed (2 0 = 113.6°). When substituting the trigonally elongated PO43polyhedra in the apatite Srs(PO4)3CI by MnO43- the best-fit 2 0 angle (treatment II: 112.5 °) is - similar to the situation in the spodiosites - larger than the angular distortion of the PO 3- tetrahedron in the host compound (Table 2 : 2 0 = 111.4°), and also in Bas(PO4)3C1 (20 = 111.0°), but very close to the one of the MnO 3- polyhedra in Bas(MnO4)3C1 (20---

112.7°).

163

M. Atanasov et al./ Chemical Physics 202 (1996) 155-165 4.3.2. Lower-symmetry distortions 4.3.2.1. Spodiosites. Lower-symmetry distortions re-

ducing the pseudo-D2d to a C 2 site symmetry in the spodiosites may lead to splittings of the 3A2 ~ BE transitions and to changes in the absorption profiles [1-5,9]. The symmetry lowering to C 2 (the two-fold axis being perpendicular to the crystallographic c and the molecular pseudo-S 4 axis) leads to inequivalent atoms O t and 0 2 with slightly different bond lengths to the central ion (Table 2). Overlap integrals have been used together with the relation ex(1)/ex(2) = Sx(1)2/Sx(2) z,

(9)

in order to approximate the effect of the bond length variations on the ecr and e-rr values. The splittings of the tetragonal 3E terms resulting from the 3T2, a3Tl and b 3T 1 tetrahedral parent states of Mn 5+ in Sr2VO4CI are calculated to be small (70, 65 and 140 cm -~, respectively) and cannot be resolved experimentally. As already mentioned we prefer to interpret the dip in the BA2 ~ 3E(a3T1) absorption profile [1-9] as due to resonance with an overlapping 3A 2 a ~Al transition rather than to a lower-symmetry splitting. One may hence conclude that the absorption spectra of the MnS+-doped spodiosites are satisfactorily described within the pseudo-Dzd symmetry. 4.3.2.2. Apatites. Adopting a MnO 3- site geometry

as in Bas(MnO4)3C1 and the bonding parameters from Table 4, but corrected for small variations in the bond lengths according to Table 2 the energy splittings of the trigonal 3E states originating from the 3T2, a3T~ and b 3T) parent terms are calculated to be 94, 64 and 165 cm -1, respectively, while the 3A2 ~ 1E transition does not split even when spinorbit coupling is taken into account. No significant enhancements of the triplet splittings are calculated when angular geometries of the PO 3- polyhedra in Srs(PO4)3C1 and Bas(PO4)3C1 with more pronounced lower-symmetry distortion components (Table 2) are taken into account (see below). In contrast, the spectral data in Table 4 indicate splitting effects larger than those according to the host site distortions in the various apatites (Table 2). One reason for the enhanced lower-symmetry distortion of the

MnO43- polyhedra in Srs(PO4)3C1 compared to the geometric situation in Bas(MnO4)3CI is presumably the misfit in the ionic radii of Mn 5÷ and pS+ (vide supra), increasing not only the axial but also the lower-symmetry distortion components. Similar lower-symmetry effects not reflected by the host site geometries seem to be present in cra+-doped olivines (Mg2SiO 4, forsterite [33] and Ca2GeO 4 [21,27]). Another possible cause might be excited state vibronic Jahn-Teller coupling. It should be noted in this context that the double-humped distribution of Franck-Condon factors in the range 10000-12000 cm-1 in the case of Srs(POa)3Cl:Mn 5+ (indicated by a single progression of as much as 18 vibronic lines) was interpreted as caused by vibronic effects of this kind [34]. A discussion of the sharp line spectra and the possible Jahn-Teller coupling in the excited 1E state of MnO43- in apatites and pseudoJahn-Teller coupling between the IA l and ~B 1 (l E) split levels in spodiosites will be published separately [ 19].

5. Conclusions 1. Using a newly developed program package based on the angular overlap model and published data from polarized absorption spectra of Mn 5+ doped into the distorted tetrahedral sites of various spodiosites and apatites, for the first time reliable ligand field and electron repulsion parameters were deduced. Two different approaches (II,I) were applied to account for the influence of covalency on the Racah parameters B and C. The following best-fit values are obtained: A -- 10650cm -1 (e,~ = 12000cm -1 , e~/e~ = 4), C = 2540cm -l ( B = 430cm -1,

(ix)

or, with C / B = C o / B o = 4.25, Boe ~ 530 cm- 1, Bet _ 420 cm- l B, ~ 340cm -I .

(I)

Taking the Trees correction into account additionally did not essentially improve the fit. Thus a was not

164

M. Atanasov et al. / Chemical Physics 202 (1996) 155-165

considered, also in order to avoid overparametrization. The pronounced covalency of the Mn-O bond as indicated by the strongly reduced B values compared to the B 0 parameter of the free Mn 5+ ion (1160 cm- 1) is - in the argumentation of treatment I - mainly due to central field covalency. The still distinct variation of B when changing the electronic configuration (e 2, emt~ and t22), however, shows that symmetry restricted covalency is important as well. Following the trends of the B parameters for CF 4+, Mn 5+ and Fe 6+, doped into the tetrahedral sites of oxidic host compounds, we conclude that the metal-oxygen covalency increases in this sequence. This explains why the ligand field model is found to work quite well for Cr 4+, with moderate success for Mn 5+, but is seemingly not applicable to Fe 6÷, where metal-based d 2 multiplets become strongly intermixed with ligand-to-metal charge tranfer states. It should be noted finally, that the obtained ligand field and electron repulsion parameters provide information only on those Mn-O bonding contributions, which involve the metal 3d orbitals. It seems reasonable to assume, however, that the indicated trends are typical for the Mn-O bond itself, including the even more significant interactions between the metal 4s, and 4p and ligand LCAOs. 2. The fitting procedure allowed to estimate the angles of axial distortion 20 of the MnO43- tetrahedra in spodiosites (tetragonal compression) and apatites (trigonal elongation). The spectra of MnO43in spodiosite type host lattices are reasonably well described by a Dza host site geometry, low-symmetry splittings being small or negligible. The distortions of the MnO43- polyhedra in Ca2(PO4)C1 and Sr2(VO4)C1 resemble those of the VO43- tetrahedra in Ca2(VO4)C1 and Sr2(VO4)CI, respectively, the reason being the comparable ionic radii of V 5+ and Mn 5+. In lines with earlier qualitative results [5-7] it is found, however, that the extent of distortion of the tetrahedral sites is significantly modified if Mn 5+ occupies positions of host ions with smaller ionic radii such as (pS+). The lower-symmetry splittings of Mn 5+ in apatites are rather large and cannot be understood solely on the basis of the tetrahedron geometries in the respective host compounds. Apparently, they are significantly enhanced when Mn 5+ replaces ions

with smaller ionic radii. Jahn-Teller coupling in the excited states may further contribute to the observed splittings. The results convincingly demonstrate that the newly developed AOM program (AOMX) we have used is well suited to deduce at least approximate information about the polyhedron geometry of d" cations, doped into oxidic matrices, from the optical spectra.

Acknowledgements The authors are grateful to the Deutsche Forschungsgemeinschaft and to the Volkswagen Stiftung for financial support. One of us (MA) owes thanks to Dozent Dr. J. Degen, Heinrich-Heine University, Diisseldorf for his hospitality and support during the final state of this investigation. Discussions with Dr. M, Hazenkamp and Professor Dr. H. Giidel (Bern, Switzerland) are gratefully acknowledged.

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M. Atanasov et al. / Chemical Physics 202 (1996) 155-165

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