Optical absorption spectra, crystal-field analysis, and electric dipole intensity parameters for europium in Na3[En(ODA)3]-2NaClO4·6H2O

Chemi~lPhysi~ 122 (1988) 105-124 Noah-Holland, Amsterdam

OPTICAL ABSORPTION SPECTRA, C~YST~F~~ AND ELECTRIC DH’OLE INTENSITY PA~METE~ IN Na3[Eu(ODA)3]-2NaCI04~6H20

ANALYSIS, FOR E~OPIUM

Mary T. BERRY, Charles SCHWIETERS and F.S. RICHARDSON Chemistry Department. University ofVirginia, Charlottesville, VA 22901, USA Received 2 1 September 1987

Locations and assignments of 61 crystal-field levels are reported for Eu 3+ in the trigonal Na, [Eu(oxydiacetate),]. 2NaC104]6Hz0 system. These energy levels span the o-37400 cm-’ energy region, and they were located and assigned from optical emission spectra and from axial and orthoaxial (a- and n-polarized) absorption me~umments on single crystals. The assigned crystal-fieid levels span 22 different multiplet manifolds, with principal parentages derived from seven different f6 Russell-Saunders terms (‘F, 5D, sL, SH, 5F, ‘I, and sK). The assigned levels are analyzed in terms of a 26-parameter electronic Hamiltonian in which six of the parameters are defined to represent the 4f-electron/crystal-field interactions for Et?+ ions located at sites with trigonal dihedral (D,) symmetry. Quantitative line intensities are reported for 39 individual 4f+4f (crystal-field) transitions observed in the low-temperature ( 10 K) absorption spectra, and these intensity data are analyzed in terms of a general parametric model for 4f-+4f transition intensities in lanthanide systems. The energy and intensity parameterizations provide a basis for calculating the 4f-+4f absorption spectra of Ed+ in Na3]Eu( oxydiaoetate)3] .ZNaClO,6H,O over a wide spectral range, and excellent agreement between calculated and ex~~men~lly measured spectra is obtained. Several of the intensity parameters determined to be important in this study carry information of particular significance to understanding the structural and mechanistic bases of lanthanide-ligand-radiation field interactions and 4f-+4f electric-dipole intensities.

1. Induction

The trigonal Na3 [ Ln( 0DA)3] .2NaC104+6H20 systems (where ODA denotes an oxydiacetate ligand) are excellent models for examining lanthanide 4f” electronic structure and 4f--+4f transition properties in a relatively complex (but st~~u~lly welldefined) ligand environment. At room temperature, single crystals of these systems have the space group R32, the Ln3+ ions are located at sites with D3 symmetry, and the tris-terdentate Ln( ODA):- complexes have D3 point-group symmetry [ l-31. Fu~he~ore, these crystals grow in two enantiomorphic forms which differ with respect to the absolute configuration of their constituent Ln (ODA ) :complexes and the chiral (left-handed or r&thanded) arrangement of these complexes about the trigonal axis of the crystal [ 4 1. Optical quality crystals are easy to grow and these crystals appear to retain their uniaxial symmetry down to 4.2 K, although there is evidence that at least some of the systems

undergo a second-order phase transition below 120 K in which the space group changes from R32 to P32 1 (asubgroupofR32) [5]. The Na3 [ Ln (ODA ) 3] *2NaC104*6Hz0 systems are well-suited for carrying out polarized optical absorption and emission studies, including the measurement of c~jro~~iea~properties such as circular dichroism (CD) and circularly polarized luminescence (CPL). Many optical studies of these systems have been reported in the literature [ 4,6-29 1, and in each case several aspects of the lanthanide 4fN electronic structure and optical properties were characterized. The most thorou~ly characterized system, with respect to crystal-field energy levels and 4f+4f spectroscopic properties, is the samarium ( Sm3+ ) system [ 26-301. Over 150 crystal-field energy levels have been located and assigned for this system; nearly 100 4f-+4f transition line strengths have been determined from absorption intensity data; and the rotatory strengths of 52 individual crystal-field transitions have been determined from high-resolution circular

0301-0104/88/$03.50 0 Elsevier Science Publishers B-V. ( Noah-Holland Physics Publishing Division )

106

M. T.Berry et al. / Crystal-field

dichroism measurements. Furthermore, these empirical results have been thoroughly analyzed in terms of detailed parametric models for the 4f5 energy levels and 4f+ 4f transition intensities of Sm3+ in a crystal field of trigonal dihedral ( DS) symmetry [ 26-301. The parameter values obtained from these analyses provide important insight and information about the 4f-electron/crystal-field interactions and the 4f+4f transition intensity mechanisms operative in a structurally complex ligand environment. The intensity parameters depend on the mechanistic and structural details of the lanthanide-ligand-radiation field (Ln-L-hv) interactions, and several of these parameters are diagnostic of interactions unique to complexes containing polyatomic ligands. The Na3 [ Eu ( ODA)3] *2NaC104.6H20 system has received somewhat more attention than the analogous samarium system [ 4,12-2 1 ] and its optical and chiroptical properties have been used frequently to test (or calibrate) various theoretical models of 4f+4f transition intensities and chiroptical activity [ 3 l-331. However, despite this attention, the energy levels and optical properties of the europium system are not nearly as well-characterized as those of the samarium system, and the spectroscopic analyses reported to date for the europium system are inadequate for extracting a useful set of crystal-field energy parameters and 4f-+4f transition intensity parameters. Without better knowledge about these parameters, interpretations and theoretical rationalizations of the optical properties are speculative, at best, and can lead to false conclusions regarding interaction mechanisms and spectra-structure correlations. In the present study, we report high-resolution optical absorption meaurements for single crystals of Na, [ Eu (ODA) 3] .2NaC104*6Hz0 over the 17000 -37700 cm-’ spectral region. Both axial and polarized orthoaxial absorption spectra were measured, and 50 crystal-field levels are located and assigned within the 17200-37400 cm-’ energy region. Combining these results with results obtained from emission measurements [ l&19,34], a total of 6 1 crystalfield levels are located and assigned throughout the o-37400 cm-’ region. Additionally, line strengths are quantitatively determined for 39 different crystalfield transitions originating in the ‘F,, (ground) multiplet of Eu 3+. The energy level data are analyzed in terms of a 26-parameter electronic Hamiltonian in

analysisfor Eu”+

which six of the parameters are defined to represent the 4f-electron/crystal-field interactions for Eu3+ located at sites with trigonal dihedral ( D3 ) symmetry. Fifteen of the 26 parameters (including the six crystal-field parameters) are used in fitting calculated energy levels to the experimental data. The line strength (intensity) data are analyzed in terms of a 12-parameter expression for 4f+4f transition dipole strengths. The 12 parameters in this expression are related to one-electron/one-photon electric-dipole transition processes occurring within the 4f6 electronic contiguration of Eu3+ in a crystal field of D3 symmetry 121 I. The parametric models employed in this study yield excellent calculated-versus-experimental data fits for crystal-field energy levels and transition intensities. The parameter values determined from these tits provide a satisfactory basis for rationalizing the 4f-+ 4f optical spectra of Eu3+ in Na3[Eu(ODA),].2NaC104*6Hz0, and they are sufftciently well-characterized to be useful in developing and assessing general theoretical models of lanthanide-ligand-radiation field interactions [ 35-37 1. The intensity parameterization scheme employed in this study is more general than the Judd-Ofelt parameterization used in most previous analyses of 4f+4f transition intensities [ 35,361. Certain parameters found to be essential for fitting the intensity data reported here do not appear in the Judd-Ofelt parameterization scheme, and these parameters have important implications regarding the detailed nature (and mechanisms) of the lanthanide-ligand-radiation field interactions [ 35,361. The relative signs and magnitudes of the intensity parameters reported here have significance beyond the immediate objective of characterizing the Na3 [ Eu( ODA),] *2NaClO,.6H,O system. Very few complete sets of intensity parameters have been reported in the literature for lanthanide 4f-+4f (crystal-field) transitions, and such parameter sets are crucially important (if not essential) for developing and testing theoretical models of 4f+4f transition intensities.

2. Experimental Single crystals of Na3 [ Eu (ODA) 3] *2NaClO,* 6H20 were grown from aqueous solution following

107

h4.T. Berry et al. / Crystal-field analysis for Eu3+

the methods of Albertsson [ 1,2 1. All optical measurements were performed with the crystal sample mounted at the cold station in the sample compartment of a CTI-Cryogenics closed-cycle helium refiigerator/cryostat. The crystal was mounted on a onepiece copper mount using crycon grease, and the copper mount was attached to the cold head of the refiigerator, with strips of indium providing a thermally conductive interface. Cold-head temperature was controlled using a Lake Shore Cryotronics temperature controller (model DRC-70). All measurements were carried out within the lo-295 K temperature range, and the crystals appeared to maintain axial symmetry over this entire range. All absorption spectra were obtained using a Cary model 17D spectrophotometer. Both unpolarized axial spectra and polarized (o and rc) orthouxiaf spectra were measured over the 17000-37700 cm-’ spectral region at a spectral resolution of approximately 0.1 nm.

3. Optical selection rules and line assignments All crystal-field levels split out of the 4f6 electronic configuration of Eu3+ in a trigonal dihedral (D,) crystal-field potential may be classified as having A,, A*, or E symmetry in the D, point group. Therefore, all transitions between crystal-field levels may be classified (by symmetry) as Al-A,, Al-AZ, A,t*E, A2++A2,APE, or E-E. Choosing a Cartesian coordinate system in which the z axis is coincident with the C, symmetry axis of our trigonal (D3) system, the x and y components of both the electric- and magnetic-dipole moment operators (denoted here by p and m, respectively) transform as the E irrep of the D3 point group, whereas the z component of each transforms as the A2 irrep. Given these symmetry properties of the electric- and magnetic-dipole moment operators, selection rules for the A,t*A1, A,++Az,AI-E, A2~A2, AZ-E, and E-E crystal-field transitions in axial (a) and orthoaxial (o- and rc-polarized ) spectra of Na, [ Eu ( ODA) 3] +2NaC104 *6H20 may be summarized as in table 1. (Note that the Al-Al and Al-A2 transitions are both electricand magnetic-dipole forbidden in all polarizations. ) The ground multiplet of Eu3+ is ‘FO, and the only dipole-allowed crystal-field transitions originating from this level are Al +A2 and Al +E. These two types

Table 1 Transition dipole components

A,++A, Al-A2 A,wE A,++A, A,++E E-E

OLP,)

PC,

-

x

a, o a, o a, 0

x

of transitions are easily distinguished by comparing the axial and orthoaxial absorption spectra, since only the Al +E transitions will appear in the axial spectra (see selection rules given in table 1) . Comparisons of the o- versus rc-polarized orthoaxial spectra will permit an assessment of the relative electric-dipole versus magnetic-dipole contributions to the transition intensities (for both the A, +Az and A, -+E transition types). Among the transitions examined quantitatively in the present study, only those associated with the 7F,,-+5D1and ‘Fr,j5F1 transition manifolds exhibit predominantly magnetic-dipole character. All other transitions exhibit nearly pure electric-dipole character. 4. Calculations and data analysis 4. I. Energy levels

The energy levels associated with the 4f6 electronic configuration ofEu3+ are analyzed here in terms of a Hamiltonian conveniently partitioned as follows: H=H,+H,:,

(1)

where HOis defined to include only interactions that are isotropic (and spherically symmetric), and H,+, contains all the even-parity components of the nonspherically symmetric crystal-field potential experienced by the lanthanide 4f electrons. The Hs operator, defined to have D, symmetry and confined to one-electron crystal-field interactions, may be expressed as H,+f=Bh*’ U&*’+Bh4) Uh”’ +BJ4) (Us”’ - UC_“3 ) + Bh6’ Uh6’ + Bs6’ ( Us”’ - U!!j ) +B66’(Ub6)+UY~))

(2)

108

h4. T. Berry et al. / Crystal-field analysis for Eu3*

Table 2 Energy parameters (in cm-’ ) for the 4f6 electronic configuration of Eu’+ in Na,[Eu(ODA),]*2NaC10,*6H20 ‘) Parameter

Value

Parameter

Value

E avc F2 F4 Fe

63594+ 13 82458226 59293 + 40 43112+41 21.2k2.0 -608f20 1327+21 ]3701 [401 ]401 [ -3301 ]3801 13701

Lo

1332f4 [2.38] [ 1.331 [0.90] 303+24 0.75 P* 0.50 PZ -56+24 - 1007+23 -785+20 430226 1021&24 811+22

a” Y T2 T’ T4 T6 T’ T8

$ M4 P2 P4 P6 Bh2’ Bh4’ BS4’ 866’ 816’ Bj6’

a) Except for those shown in brackets, the parameter values listed

here were obtained from a tit of the experimentally observed crystal-field energy levels. The parameter values shown in brackets were held fixed in performing the calculated-versusexperimental energy level data tits. The uncertainties in the fitted parameter values are defined as the changes required to double the mean-error (tr) value of the energy level fit. For the tit reported here, u= 11 cm-‘.

where the Uik) are one-electron intraconfigurational unit-tensor operators [ 38-40 ] and the Bik’ are parameters containing all the details of the 4f-electron /crystal-field interactions. The I%,.,operator (often referred to as the “free-ion” Hamiltonian) is defined here to be identical to that described previously by Crosswhite and co-workers [ 4 l-44 ] and by Richardson and co-workers [ 27,45,46]. This operator contains 20 parameters: six two-body electrostatic interaction parameters, i.e. the Slater parameters, Fk (k=2, 4, 6), and the configuration-interaction parameters (Y,/3, and y; six three-body electrostatic parameters T’ (i=2, 3, 4, 6, 7, 8); the spin-orbit coupling parameter c,,; three spin-other-orbit interaction parameters Mk (k= 0,2,4); three electrostatically correlated spin-orbit interaction parameters Pk (k=2, 4, 6); and a parameter, I?,,,, that shifts the energy of the entire 4fN electronic configuration. A complete list of the Hamiltonian parameters used in our energy level calculations is given in table 2. Our energy level calculations were carried out in two steps. We first diagonalized the “free-ion” Ham-

iltonian (I&) in the complete Russell-Saunders (SU) basis set of the 4f6 electronic configuration, using Crosswhite’s values for the free-ion parameters [ 47 1. We then used the 387 lowest-energy JMJ levels obtained from that calculation as the basis set for performing iterative calculations of crystal-field levels. This JMJ basis spanned the o-38250 cm-’ energy range, and it included 41 different multiplet manifolds. Eleven of the 20 parameters in our freeion Hamiltonian and all six parameters in the crystalfield Hamiltonian (H$ ) were treated as adjustable parameters in carrying out least-squares calculatedversus-experimental energy level tits. The T’ and Mk parameter values were held fixed in performing these tits, and the P4 and P6 parameters were constrained according to the relationships: P4=0.75P2 and P6= 0.50P2 (with P2 being allowed to freely vary). The empirical energy level data set was not sufficient to support an analysis in which all 26 Hamiltonian parameters could be freely varied. The cr value achieved in our calculated-versus-experimental energy level fits was x 11 cm- ’ . This rr value is reduced to x 8 cm- ’ if the five crystal-field levels assigned within the 5& multiplet manifold (37200-37400 cm-‘) are excluded from consideration. The latter are relatively poorly fit by our calculations. 4.2. Transition dipole strengths Quantitative line intensities were determined for 39 different crystal-field transitions observed in the low-temperature ( z 10 K) absorption spectra of Na3 [ Eu(ODA)~] *2NaC104.6H20. All of these transitions originate in the A, (‘F,) ground level. Twentythree were observed in the axial and o-polarized orthoaxial spectra, and are assigned as A,+E transitions with predominantly electric-dipole character. Two were observed in the axial and x-polarized orthoaxial spectra, and are assigned as A1-+E transitions with predominantly magnetic-dipole character. The remaining 14 were observed only in the x-polarized orthoaxial spectra, and these are assigned as A, +A2 transitions with predominantly electric-dipole character. The axial and rr-polarized orthoaxial line intensities were converted into transition dipole strengths according to:

M. T. Serry et al. / Crystal-Jietd analysisfor Eu’+

s&~(U) =3.06x X

1o-3g

t&(F, T) dB

gA x4 t W‘4B

(esu2 cm*) ,

(3)

(esu2cm2),

(4)

A-B

X

Fa(&

7’) dF

AL

where 3ABdenotes the dipole strength of the transition A-+B, F,,s is the energy of this transition (expressed in cm- ’ ); gA is the electronic degeneracy of level A; _&(T) is the fractional thermal (Boltzmann) population of level A at temperature T, a, and .s, are molar decadic absorption coefficients measured in the axial and x-polarized orthoaxial absorption experiments, respectively; and the integrations are over the A+B transition linewidth. The expression for gAB(a) is identical to eqs. ( 3 ) and (4 ) except that EC. is substituted for e, (or Q. For all of the transitions quantitatively analyzed in this study, &= 1, T= 10 R, and/Y,% 1. The dipole strengths defined by eqs. (3 ) and (4) may be expressed in terms of their electric-dipole and magnetic-dipole contributions as follows: gABta)

=D&i,,x,+D~‘i?,x:,

>

(5)

gAB(x)

=Da”$,,ox,r+DJ.%tx;

>

(61

where x and x’ are correction factors for bulk (sample) medium effects on the electric-dipole and magnetic-dipole components of the radiation field, and

109

is the qth spherical component of a magnetic-dipole moment operator centered on the l~thanide ion (and acting only on the 4f-electron wavefunctions). As defined here, YA, and lu,, are constructed entirely within the 4fN electronic configuration but they exclude the radial parts of the 4f orbitals. The @‘t operator is defined to act only within the 4fN eigenstate manifold, but it contains (implicitly ) ail Ln-lig~d-ra~ation field (on~electron/onephoton) interactions responsible for 4f-+4f electricdipole transitions. Following Reid and Richardson [ 35,361 this operator may be expressed as

where: 2~2, 4, 6; t=A, 1+ 1; p=O, + 1, .... It t; the Uj are unit-tensor operators that operate within the 4f N electronic configuration; and the A$ are parameters that contain the structural and mechanistic details of the Ln-L-hv interactions, as well as the radial expectation values (ra) of the 4f electrons. The (A&} parameter set must reflect the site symmetry of the lanthanide ion (in its ligand or crystalline environment ) , and this places certain restrictions on the permissible pairs of (t, p) values for each value of ;t [ 35,361. In the case of D3 site symmetry, the permissible (2, t, p) combinations are 1211: (2, 2, 0), (2, 3, rt3), (493, +3), (4,4,0), (474, lt3), (435, f3), (6, 5, +3), (676, O), (6,6, *3), (676, +6), (6, 7, ?Y3), and (6, 7, Zt6). However, we also have the relationship (A&)*= (- 1 )rfP+lA&,andthe (A$) set contains just twelve independent parameters in D3 symmetry [21,35,36]. Expressions (5), (7), (8), and (9) may be combined to obtain

(8) In expressions ( 7 ) and ( 8 ) , the summations are over the degenerate com~nents of levels A and B, !&, and !& are eigenfunctions of the Hamiltoman defined by eq. ( 1 ), pgff is the qth spherical component of an “effective” electric-dipole moment operator (which acts only within the 4fNelectronic configuration), and m,

(10) with q= +I; and expressions (6)-(9) bined to obtain

may be com-

110

M. T. Berry et al. / Crystal-field analysis for Eu3+

2 +xhl

,c,

(Y*alm,

I%,>

3

(11)

in which we note that q= 0 in the electric-dipole term and q= 1 in the magnetic-dipole term. The Vi and m, matrix elements in eqs. ( 10) and ( 11) may be evaluated over the SUM, components of the Yh and YBu,, state vectors using standard techniques [ 38,391, the vector-coupling coefficients are readily calculated, and only the A$ parameters and the x and x’ correction factors remain as unknown quantities in these dipole strength expressions. Recalling that the crystal-field state vectors, YA, and YBBb, are obtained by diagonalizing the 4f-electron Hamiltonian in an SWM, basis (as described in section 4.1), we note that the Uf and m9 matrix elements in eqs. ( 10) and ( 11) have implicit dependence on the energy parameters listed in table 2. Now if we assume that xa=xX=x and J&=&=X’, expressions ( 10) and ( 11) may be combined to obtain 2&(u)

+ %a(x)

=xe* AQGJ 5 CM 1 ..

-_qltP)

2 =x’

,c,

(yAaImll%b)

,

(13)

from which a value for x’ may be deduced if the ml matrix elements are calculated accurately and experimental values are available for either g(a) or g(n) . Having a value forx’ permits one to estimate the value of x according to the following relationships: x’ = y1 (refractive index of the bulk sample) and x= (F?+ 2)2/9n, for optical absorption processes. In the present study, we deduce a value of z 1.3 for xl, which suggests that xx 1.2. This value of x is essentially identical to that typically assumed for aqueous solution samples of lanthanide salts. 4.3. Simulated (calculated) spectra

2

+3x1 c >

freely varying fitting) parameters. However, the x factor poses a problem because it has not been characterized for the system of interest here, and it is likely to exhibit some frequency dependence over the spectral region spanned by the transitions of interest (2 1400-37400 cm- ’ ). In practice, we ignore the frequency dependence of x and absorb this factor into the A& parameters in carrying out tits of the empirical dipole strength data (using the electric-dipole part of eq. ( 12) ). Our fitting parameters are, therefore, defined as x’/‘A”,, with x assumed to be a constant (and independent of A, t, and p). Setting xa=xX=x and assuming that x is a constant (independent of frequency) are rather crude approximations; but these approximations are not likely to have a significant effect on our calculated-versus-experimental intensity data fits and analyses [ 28 1. For the two nearly pure magnetic-dipole transitions examined in this study, A, ( ‘FO)+E( 5Di) and A,(‘F,,)-‘E(‘F,),wemaywrite

(12)

a,b

where the summation over q includes values of q= 1, 0, and - 1. For 37 of the 39 transitions analyzed here, the m4 matrix elements are calculated to be very small and magnetic-dipole contributions to their line intensities are negligible. For these transitions, the first term in eq. ( 12) may be used to fit the empirical dipole strength data, treating the A$ as adjustable (or

Quantitative line intensities could not be determined for many of the transitions occurring in the axial and orthoaxial absorption spectra obtained in this study. Several regions of these spectra are highly congested, exhibiting unresolved features whose integrated intensities cannot be determined accurately, and some of the resolved spectral features are too weak to be quantitatively analyzed (with respect to

M. T. Berry et al. / Crystal-field analysis for Eu’+

their intensities). These ill-characterized transitions and transition regions did not contribute any data to our parametric analyses of energy levels and transition intensities, but it is reasonable to expect that their qualitative spectral features could be simulated by our parametric models, if, indeed, these models are properly (and accurately) parameterized. Simulated axial and n-polarized orthoaxial absorption spectra were calculated according to

(14)

(15)

where the summations are over all transitions falling within the SpeCtrd region of inter&; g&t) and Q.&a(x ) are dipole strengths calculated from eqs. ( 10 ) and ( 11)) respectively, and expressed in units of D2 ( 1 debye’ = 1O-36 esu* cm2 ); PAB(F) is a unit-normalized lineshape function centered at DAB;and x,(T), g,& and flub are defined as in eqs. ( 3) and (4). For all of the simulated spectra reported here, Lorentzian lineshape functions were used: pt(~)=(d,/x)[(~-~~)2+d:]-1)

(16)

where A, denotes the line half-width at half-height for a transition ( t ) located at PZ.

5. Results

5.1. Energy levels Sixty-one crystal-field levels were located and assigned within the o-37400 cm-’ energy region. Fifty of these levels were located and assigned from absorption spectra obtained in this study, and the other 11 levels were located and assigned from emission measurements carried out in our laboratory [ 18,19,34]. A total of 257 crystal-field levels, spanning 40 different SW multiplets, are predicted to occur within the o-37400 cm-’ region, but only 61 of these levels could be conclusively located and assigned from our spectroscopic results. The 61 assigned levels span 22 different multiplet manifolds, derived from seven different f6 Russell-Saunders

111

terms (‘F, ‘D, 5L, ‘H, ‘F, ‘I, and ‘K), and they provide a quite adequate basis for carrying out a parametric crystal-field energy level analysis for Eu3+ in Na, [ Eu (ODA ) 3] .2NaClO,. 6H2O. The Hamiltonian (energy) parameters obtained and/or used in such an analysis are listed in table 2, and the calculated and experimentally observed energy levels are listed and characterized in table 3. Note that the crystal-field energy parameters, Bik), are defined according to eq. (2) and, therefore, have unit-tensor normalization properties [ 40 1. All of the “observed” energies listed in table 3 were obtained from room-temperature spectroscopic measurements. Some of these energies were found to shift by as much as 5- 10 cm - ’ in spectra taken at 10 K. The standard deviation (a) in our overall calculatedversus-experimental energy level fit is x 11 cm-‘, which is reduced to = 8 cm- ’ if the five crystal-field levels assigned within the 5& multiplet manifold are excluded from consideration. 5.2. Transition dipole strengths Three separate analyses of the empirical electricdipole intensity data were carried out. In each case, experimentally determined dipole strengths were fitted to eq. ( 12), treating the {~“*A&} as adjustable parameters in a nonlinear least-squares fitting procedure. However, the three analyses differed as follows: Analysis ( 1) utilized all 12 A$ parameters, but its empirical data set was restricted to line intensities measured within the ‘F0j5D2, 5Lg, and 5F4 transition manifolds. Analysis (2) utilized all 12 A& parameters, and its empirical data set included the dipole strengths for all 37 of the electric-dipole transitions whose intensities were quantitatively determined in this study. Analysis (3) was based on the same empirical data set used in analysis (2), but only sixA& parameters were used in the data tits (the t=A parameters were not used). The parameter values obtained in analyses ( 1 ), (2) and (3) are listed in table 4 (under the columns labeled set ( 1), set (2) and set ( 3 ) , respectively), along with the parameter values determined previously for Sm3+ in Na,[ Sm(ODA)3] .2NaC10,*6H,O [28]. Note that the values given in table 4 are for x’/~A$,. Calculated and experimentally determined dipole strengths are listed in tables 5 and 6, along with de-

112

h4.T. Berry et al. / Crystal-field analysis for Eu-‘+

Table 3 Calculated

and observed

Level No.

energy levels (in cm-‘) Multiplet

‘)

for ELI3+ inNax[Eu(ODA),].2NaC10,.6Hz0 l‘wl

=I

l-b’

Energy calculated

1

0

4

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52

1 0 1 2 0 3 0 1 3 2 4 0 2 3 4 3 0 1 5

E

1 4 0 3 4 3 5 3 2 6 6 1 0 0 1 0 0 2 1 0 2 1 0 3 0 1 6 6 2 5 3 3

A2 E E Al AZ A2 E Al E E Al E A2 E Al A2 E E E E A2 Al E A, E A2

E Al A2 E A, A, E A2 4

E E A2

E E A2 ‘4, ‘4,

E A, A2

E E A2 -4

-1 369 381 946 1066 1120 1814 1872 1877 1905 1949 2658 2658 2877 2910 2987 3082 3753 3795 3938 3968 4032 4051 4077 4923 4950 4954 4962 5105 5130 5131 5146 5164 17245 18982 18986 21427 21435 21471 24306 24309 24330 24332 24341 24909 24950 25000 25011 25060 25213 25241 25261

‘)

observed

Ad’

0 362 380 955 1064

-1

1879

-2

1945 2659

-1

7 1 -9 2

4

2870 2910

7 0 -3

17231 18985 18989 21438 21487 24301 24325 24352

14 -3 -3 -3 -16 8 5 -20

24950

0

25050 25210 25245

10 3 -4

Table 3 (continued) Level No.

53 54-104e’ 105 106 107 108 109 110 111-152” 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192-2578’

Multiplet ‘)

I&I e’

rb)

Energy calculated c)

observed 25314

4

E

25303

3 3 2 4 0 2

Al A2 E E Al E

27557 27566 27593 27598 27599 27608

2 3 1 3 0 1 3 4 5 3 4 4 3 0 2 1 0 0 1 6 5 6 0 2 1 3 2 0 0 1 3 1 0 4 3 2 0 4 3

E Ai E A2 ‘4, E A, E E A2 E E AZ Al E E A1 A2 E Al E A2 ‘41 E E ‘% E ‘4, AZ E A2 E

31172 31176 31190 31202 31269 31293 31338 31353 31369 31384 31388 31417 31425 31425 31500 31524 31530 31535 31579 31608 31610 31614 32869 32949 32968 32977 33006 33031 33080 33100 33133 33302 33311 33404 33450 33461 33471 33507 33532

A2

E -42

E A, E ‘4,

Ad’

-11

27565

1

27594

14

31170

2

31200

-10

31290

3

31375 31376 31410 31418

9 12 7 7

31520

4

31531

4

31610 31613

0 1

32933 32955

16 13

33010

-4 4

33076

33324

-22

33409 33452 33461

-5 -2

33511

-4

0

a) Identifies the principalSL.MJ components of the crystal-field eigenvectors. b, b-rep of crystal-field level in the Ds symmetry group. ‘) Calculated using the energy parameters listed in table 2. d, Difference between calculated and observed energies. e, These levels span the 5L,, 5G2,5G3, ‘G4, 5G6, 5G5,and 5Ls multiplet manifolds, but none have been assigned from experimental results. ‘) These levels span the 5L9,5L,0, ‘Hs, and 5H, multiplet manifolds. Only one has been assigned: No. 151 at 31120 cm-‘, E( 5H,). 8, These levels span the 5F5,514,‘Is, 518,‘16,51,, 5K5,and 5& multiplet manifolds. Fourteen of these levels have been assigned, but are not listed here. The highest assigned level is No. 257 at 37341 cm-‘, E(5&).

114

M. T. Berry et al. / Crystal-field analysis for Eu’+

Table 4 Electric-dipole intensity parameters obtained from fits of empirical data Parameter b,

A:0 A:, ,449 A:0 A:9 A:9 ,423 A80 ,443 A86 A& A%

A&/X-‘/~

( IO-l2 cm) a)

set ( 1) ‘)

set (2) ‘)

1lOi -207i 51i 37i lli -314i 542i 43i 34i 36i -92i - 163i

97i -2lli 79i 106i -0.9i -298i 5831 40i 34i 29i -115i - 167i

set (3) ‘) 147i 47i

-316i 5471

-147i -130i

SmODA d, 310i -9li -30i 143i -35i - 397i 753i 189i 144i 27i -42i -162i

a) i denotes the imaginary number, ( - 1) I’*, and x is a dielectric correction factor for bulk sample refractivity. b, The parameters are defined according to eq. (9) in the text. c, Each of these parameter sets was obtained by fitting empirical intensity data for Na,[Eu(ODA)s].2NaC104.6H20 the text for a description of how fits ( 1 ), (2), and (3) differed. d, From a previous an alysis of intensity data for Nag [Sm(ODA)s] .2NaC10.,.6Hz0 [28].

scriptions of the principal multiplet parentages and IAMJI character of the various crystal-field transitions. The calculated values given in tables 5 and 6 were obtained using the parameter sets ( 1) and (2 ) listed in table 4. A comparison of the dipole strengths calculated using parameter sets (1 ), (2) and (3) is given in table 7 for all electric-dipole allowed transi. . . tions occurrmg withm the ‘F0+‘D2, 5Lg, and ‘F_, transition manifolds. These transitions were the most accurately characterized (with respect to quantitative line strengths) in our study. Analysis ( 1) was designed to yield exact calculated-versus-experimental intensity data tits for these transitions, but the intensity data for these transitions were not weighted (or treated in any preferred way) in analyses (2) and ( 3 ) . Comparing parameter sets ( 1) and (2 ), we note that only A & and A& have significantly different values, and the absolute magnitude of Ai3 is (relatively) quite small in both sets. The dipole strengths calculated from these two parameter sets exhibit similar overall agreement with the experimental data (see tables 5 and 6), even though parameter set ( 1) was determined by fitting only a subset of these data. Both qualitatively and quantitatively, parameter sets ( 1)

to eq. (12). See

and (2 ) yield calculated dipole strengths in quite good overall agreement with the experimental results. In contrast, however, the truncated parameter set (3) does not yield good agreement with experiment. Note, for example, the results shown in table 7 for transitions to excited levels 38 and 39 (within the ‘D2 multiplet), and to excited levels 46 and 49 (within the ‘L6 multiplet ). The relative dipole strengths for each of these pairs of transitions are incorrectly calculated from parameter set (3), and this same problem occurs within several other multiplet-to-multiplet transition manifolds. This problem is fmed only by including the t =I terms in eq. ( 12) and allowing the six A$, parameters to be nonzero. The t=A= 2 term and the 4 $,, parameter are especially crucial to fixing this problem and to achieving satisfactory calculated-versus-experimental intensity data fits. The t =A terms (and especially the t=A=2 term) played a similarly crucial role in our previous analysis of SmODA intensity data [ 28,291. Expression ( 12) applies to individual crystal-field transitions observed in axial and/or x-polarized orthoaxial spectra. Analogous to expression ( 12), we may write

Table 5 Calculated

and experimentally

Excited level a)

determined IA&I

No.

multjplet

38 39 41 42 46 49 50 53 107 108 110 153 155 158 160 161 163 164 167 168 171 173 176 177 179 182 186 188 190 214 217 218 220 222 224 226 229 251 253 255 257

$D* Q* SDS Q, % % % X5 SD4 % Q4 $H4 W *fG ST% SK % % SK JR? ‘H, W % % ‘F, % $F.i 5F4 5F4 %I % % %3 ‘IS % % % % % 5& %

2 1 2 1 1 2 5 4 2 4 2 2 1 1 4 5 4 4 2 1 1 5 2 1 2 1 4 2 4 5 5 4 2 1 4

1 4 1 1 4 5

dipole strengths

for A, (7F0) +E crystal-field

Energy (cm-‘)

21438 21481 24301 24325 24950 25050 25210 25314 (27593) (27598) 27594 31170 31200 31290 (31353) (31369) 31376 31410 (31500) 31520 (31579) 31610 32933 32955 33010 (33100) 33409 33461 33511 34790 34832 34857 34900 ( 34943) 34979 (35000) 35037 (37248) 37265 37316 37341

transitions

in ~&/absorption

spectra at 10 K

131(a) b’ exp. C)

talc. ( I) dt

talc. (2) ‘)

56 151 n.d. n.d. 362 589 n.d. 4480 n.d. n.d. 220 141 72 342 nd. nd. 835 672 n.d. 104 n.d. 175 n.d. n.d. 94 n.d. 160 280 18 110 262 562 291 n.d. 159 n.d. 79 n.d. n.d. nd. n.d.

56 151
65 148 to.1 2.1 451 567 2.3 4966 25 7.6 140 149 102 158 218 420 471 539 2.0 72 28 209 46 63 28 1.2 169 178 62 112 266 119 133 2.9 84 3.5 37 18 69 136 81

*) See table 3. b, Dipole strengths are given in units of lo-* D*, where D*= debye* = 1O-36 em2 cm*. ‘) Determined from eq. (3). n.d. 3 not determined. d, Calculated using parameter set ( 1) of table 4. ‘) Calculated using parameter set (2 ) of table 4.

116

M. T. Berry et al. / Crystal-field analysis for Eu’+

Table 6 Calculated and experimentally determined dipole strengths for A, (‘F,,) -+A2crystal-field transitions in x-polarized orthoaxial absorption spectra at 10 K ‘) Excited level a) No.

Energy (cm-‘)

IAWl

9(a)b’

multiplet 6 3 3 3 3 3 0 6 0 3 3 6 3 6 6 3

48 51 106 156 162 165 170 174 181 183 187 21s 219 228 249 256

(25011) 25245 27565 31185 31375 31418 31531 31613 33076 (33133) 33452 34811 34900 35037 37248 37328

exp. c’

talc. (l)d)

talc. (2) e,

n.d. 7060 256 215 1180 1500 639 373 72 n.d. 670 188 645 370 255 338

1.1 7060 195 219 649 1187 466 361 29 0.2 670 162 583 118 98 281


‘) See table 3. b, Dipole strengths are given in units of 10-s D’, where D* = debye’= 1O-36 esu’ cm*. ‘) Determined from eq. (4). n.d. G not determined. d, Calculated using parameter set ( 1) of table 4. ‘) Calculated using parameter set (2 ) of table 4. 2 +x’

5

,c,

(yhlmqlyBb)

(17)

7

where 9.B R.preSt?ntS the totu/ (electric and magnetic) dipole strength of the crystal-field transition A+B. Now if we ignore crystal-field-induced mixTable 7 Comparison of dipole strengths calculated using the intensity parameter sets ( 1 ), (2) and (3) Excited level e) No. 38 39 46 48 49 50 51 53 186 187 188 190

Multiplet

IAWl r E E E A2 E E A2 E E A2 E E

gb’ expt. ‘)

2 1 1 6 2 5 3 4 4 3 2 4

56(a) 151(a) 362(a) n.d. 589(a) n.d. 7060(x) 4480(a) 160(a) 670(r) 280(a) 18(u)

talc. ( 1) d,

talc. (2) Cl

talc. (3) f,

56 151 362 1.1 589 1.7 7060 4480 160 670 280 18

65 148 451 co.1 567 2.3 8701 4966 169 736 178 62

74 10 549 6.0 385 4.9 9421 3355 130 710 320 23

‘) See table 3. b, Dipole strengths are given in units of 10-s D*. ‘) Determined from either eq. (3) or eq. (4). n.d. = not determined. d, Calculated using parameter set ( 1) of table 4. ‘) Calculated using parameter set (2) of table 4. f, calculated using parameter set (3) of table 4.

M. T. Berry et al. / Crystal-fieldanalysisfor Eu 3+

ings between different J (multiplet ) levels, eq. ( 17 ) may be used to obtain an expression for the total dipole strength of a pure multiplet-to-multiplet (VJ-, W’J’) transition: 9 vJ,,r,J=xe2A~p

1,

W+1)-‘L4&12

~~~~ll~‘lllv/‘J’>*+X’I~WJll~ll~‘~~l*~

(18)

where the reduced matrix elements are evaluated over the intermediate-coupling eigenvectors of the y/Jand y/J’ multiplets. Expression ( 18) derives directly from

so long as the A crystal-field levels are assumed to be of pure VJ-multiplet parentage, and the B crystal-field levels are of pure r/J’-multiplet parentage. The electric-dipole part of eq. ( 18 ) may be expressed in terms of the familiar Judd-Ofelt intensity parameters, QA (1~2, 4, 6), by use of the relationship [ 35,361 C&=(212+1)-’

c IA&I2. GP

(20)

From this relationship and the A;I, values listed in table 4 under set (2), we may estimate values for the Cn, intensity parameters: Q2= 1.65 x 1O-” cm*, 52,= 1.89~ lo-*’ cm*, and 8,=4.92x lo-*’ cm* (assuming that xx 1.2). Spectroscopic studies of Eu( ODA):- in aqueous solution yield values of 82=1.68~10-20cm2andQ~=2.06x10-20cm2,with the value of Q6 undetermined [ 48 1. 5.3. Spectra

A survey absorption spectrum obtained over the 17850-41600 cm-’ spectral range is shown in fig. 1. This is an axial spectrum obtained at 10 K, and it shows the locations and relative intensities of the most prominent (intense) multiplet-to-multiplet transitions occurring between 17850 and 4 1600 cm- ‘. The identities of these transitions can be deduced from the energy level data given in table 3. All transitions observed in the 10 K spectrum originate in the ‘F. (ground) multiple& whereas several “hot” transitions originating from the ‘Fr or ‘F2 multiplet levels are observed in the corresponding room-temperature spectrum. Several of the multiplet-to-multiplet transitions falling within the 17850-41600 cm-’ region are too weak to appear on the absorbance scale used

117

in fig. 1. Among the multiplet-to-multiplet transition regions examined in this study, the most intense features are observed within the 7Fo+5L6 transition manifold (in both the axial and polarized orthoaxial spectra). Axial and x-polarized orthoaxial absorption spectra are shown in figs. 2-7 for six different transition regions. The experimental spectra were obtained on crystal samples at x 10 K, and each spectrum shows at least partial resolution of individual crystal-field transitions. The calculated spectra were computed according to eqs. ( 14) and ( 15), using dipole strengths calculated from eqs. ( 10) and ( 11). All dipole strength calculations were based on the {x’/*,4~,}parameter set (2) (see table 4)) and it was assumed that xa=xn=x= 1.2 and x;=x;=x’ = 1.3. Each of the transitions (A+B) included in eqs. ( 14) and ( 15 ) was centered at its calculated transition energy ( PAAB ). Values for the linewidth parameter, dt, were chosen rather arbitrarily in calculating the simulated spectra, but all crystal-field transitions within any given spectral region were assigned the same A, value (see figure captions). All of the crystal-field transitions contributing to the spectra shown in figures 2-7 originate in the A, ( ‘Fo) ground level, and each may be classified as having either AI+A2 or A,-+E symmetry (in the DJ point group). Only two of these transitions occur by a predominantly magnetic-dipole mechanism: A1(7Fo)+E(5F1) andA,(7Fo)~A2(5F,),locatedat 33324 and a33333 cm-‘, respectively. All of the other transitions are predominantly electric-dipole in character, and among these the A,-+E transitions should be observed only in the axial spectra and the A, -+A2 transitions should be observed only in the 7cpolarized orthoaxial spectra. Except for some small “polarization leakages” in a few transition regions, the observed axial and n-polarized orthoaxial spectra are distinct, and they permit differentiation between the A, -+E and A, +A2 electric-dipole transitions. Only half of the crystal-field transitions contributing to the spectra shown in tigs. 2-7 have been quantitatively analyzed (with respect to intensity), and, therefore, only half have contributed data to our parametric analysis of transition intensities. However, we note that the calculated and experimental spectra shown in figs. 2-7 match up quite well in all the transition regions represented, which suggests that our intensity parameterization has general applicability

M. T. Berry et al. / Cptal-field analysisfor Eu’+

118

r

r 17650

22620

27390

I 32160

I 36930

I 41700

WAVENUMBER (CM-‘) Fig. 1. Survey axial absorption spectrum obtained at a sample temperature of 10 K.

PI(CALC)

1

WA”EN”MBER

(CM-‘)

WAVENUMBER

(CM-‘)

Fig. 2. Axial and n-polarized orthoaxial absorption spectra, calculated and experimentally observed, in the ‘F,, + 5Lbtransition region at a sample temperature of 10 K. Simulated spectra were calculated from eqs. ( 14) and ( 15) using the linewidth parameters: A,= 10 cm-’ for the axial spectrum and d,= 20 cm- ’ for the pi spectrum.

119

M. T. Berry et al. / Crystal-field analysis for Eu ‘+

PI(EXPT)

PI(CALC) h

w

..--I:I;

n

f

Fig. 3. Axial and z-polarized orthoaxial absorption spectra, calculated and experimentally observed, in the 7F0-5L7, 5GJ (J= 2, 3,4, 6, and 5) transition region at a sample temperature of 10 K. Simulated spectra were calculated from eqs. (14) and (15) using a linewidth parameter, A,= 10 cm-‘.

PI(CALC)

I- AXlAL(RXPT)

AXIAL(CALC)

‘F, - “D,

J

2,100

1

27P””

WAVENUMBER

(CM”)

WAVRNUMBER

(CM-‘)

Fig. 4. Axial and n-polarized orthoaxial absorption spectra, calculated and experimentally observed, in the ‘F0-‘D4 transition region at a sample temperature of 10 K. Simulated spectra were calculated from eqs. ( 14) and ( 15) using a linewidth parameter, A,=2.5 cm- ‘.

M. T. Berry et al. / Crystal-Jeld analysis for Eu’+

120 2 _

PI(CALC)

PI(EXPT) ‘F, - =H,

:: n

AXlAL(CALC)

//

WAVENUMBER

(CM-‘)

Fig. 5. Axial and r-polarized orthoaxial absorption spectra, calculated and experimentally observed, in the ‘F,,-P~H., (J= 3, 7,4, 5, and 6) transition region at a sample temperature of 10 K. Simulated spectra were calculated from eqs. (14) and (15) using a linewidth parameter, A,=73 cm-‘.

PI(CALC)

x o

1

II

AXIAL(BXPT)

AXIAL(CALC)

WAVENUMBER

(CM-‘)

1

WAVENUMBER

(CM”)

Fig. 6. Axial and x-polarized orthoaxial absorption spectra, calculated and experimentally observed, in the ‘F&FJ (J=2,3,1, and 4) transition region at a sample temperature of 10 K. Simulated spectra were calculated from cqs. ( 14) and ( 15) using a linewidth parameter, A,= 12.5 cm-‘.

121

A4.T. Berry et al. / Crystalzfield analysis for Eu ‘+ _ ‘0 n

PI(CALC)

PI(BXPT)

“,

r; z_ ;

AXIAL(CALC)

AXIAL(EXPT)

I

‘F, - ‘1,

WAVENUMBER

(CM”)

Fig. 7. Axial and x-polarized orthoaxial absorption spectra, calculated and experimentally observed, in the ‘FO-‘IJ (J=4,5,8,6, and 7) transition region at a sample temperature of 10 K. Simulated spectra were calculated from eqs. ( 14) and ( 15) using a linewidth parameter, A,=7.5 cm-‘.

(and validity) over all the transition regions examined in this study.

6. Discussion This is the first study of Na3 [ Eu (ODA),] .2NaC104*6Hz0 in which sufficient experimental data were obtained to permit reasonably reliable parametric analyses of crystal-field energy levels and 4f-+ 4f transition intensities. Furthermore, this is only the second study in which a complete set of generalized electric-dipole intensity parameters, {A&}, for the 4f+4f transitions of a lanthanide system has been characterized from an analysis of empirical intensity data. The only previous study in which a complete set of A& parameters was determined was reported by May et al. [ 281 for Sm3+ in Na, [ Sm( 0DA)3 ] *2NaC104.6H20. For both the SmODA and EuODA systems, the A$, members of the {A$} set are found to be essential to fitting (and rationalizing) the experimentally observed electric-dipole intensity data for transitions between crystal-field levels

(see table 4). This is a significant finding because these t=A (A$,) parameters have no counterparts in the Judd-Ofelt-Axe [ 49-5 1 ] parameterization scheme often applied to the electric-dipole intensities of 4f+4f crystal-field transition, and their apparent importance implies significant intensity contributions from lanthanide-ligand-radiation field (Ln-L-hv) interactions not accounted for in the Judd-Ofelt intensity model [ 35,361. The Judd-Ofelt-Axe intensity parameters, {A&t, A)}, are contained as a subset of the Reid-Richardson parameters, {A$}, according to [ 35,361: A;,=-

(2i1+1)(2t+l)-“*A,qt,~))

(21)

with t restricted to values of If 1. This t = 1 f 1 subset of AtP parameters would be entirely sufficient if all lanthanide-ligand (Ln-L) pairwise interactions were cylindrically symmetric and independent [ 3536,521. However, if either one or both of these conditions are not met, the t =A parameters may assume some importance. Given the complexity of the ligand environment about the lanthanide ions in the

122

M. T. Berry et al. / Crystal-fieldanalysisfor Eu’+

SmODA and EuODA systems, it is not surprising that complete sets of A$, parameters are required for rationalizing their 4f+4f intensity data. Few of the ligand entities within the Ln(ODA):complexes would be expected to interact with the lanthanide 4f electrons via cylindrically symmetric (and independent) interaction potentials. Each of the donor atoms in the ODA ligands is involved in chemical bonding to adjacent atoms, and these chemical bonds have anisotropic charge distributions. Furthermore, the non-coordinated parts of the ligands also have anisotropic charge distributions which are sufficiently close to the metal ion to make non-negligible contributions to the crystal-field potential. The A$ parameters contain all the mechanistic details of the 4f-electron interactions with the odd-parity components of the crystal field and with the electric-dipole components of the radiation field (within the one-electron/one-photon approximation ) . As introduced in expression ( 9 ) for the “effective” electric-dipole moment operator, pff, these intensity parameters are formally independent of the Hamiltonian parameters used in our energy level calculations (and listed in table 2). However, the values of the A$ parameters deduced from fits of empirical intensity data to eq. ( 12) can be quite sensitive to the values of the energy parameters, since the latter determine the SWM, compositions of the crystal-field state vectors and, therefore, the relative signs and magnitudes of the Uj and m4 matrix elements appearing in eq. ( 12). If the crystal-field state vectors are ill-determined, the A& parameters obtained from empirical data fits to eq. ( 12) will also be illdetermined. The energy level data reported here far exceed those available from previous studies on the EuODA system [ 12-2 11. These data include locations and assignments for 6 1 crystal-field levels whose major SLJ parentages span 22 different multiplets derived (principally) from seven different f6 Russell-Saunders terms. These data are sufficient to support a parametric energy level analysis based on the Hamiltonians defined by eqs. ( 1) and (2 ), and the parameters listed in table 2. Using the parameter values listed in table 2, diagonalization of our 26-parameter electronic Hamiltonian produced crystal-field eigenvalues in quite good agreement with the experimental data (see table 3 for a comparison ). This

strongly suggests (but does not prove) that the eigenvectors obtained from that diagonalization will give accurate representations of the crystal-field state vectors required in our intensity calculations. The generally very good agreement between our calculated and experimentally observed energy levels (table 3), transition dipole strengths (tables 5 and 6 ), and absorption spectra (figs. 2-7 ) indicates that the energy parameters listed in table 2 and the intensity parameters given in table 4 (excluding set (3 ) ) provide a quite satisfactory basis for describing the 4f6 electronic states and 4f+4f transition intensities of Eu3+ in Na3 [ Eu(ODA)~] .2NaC104*6H20. A comparison of the even-parity crystal-field parameters, Bik), determined for SmODA [ 271 and EuODA (past and present) is given in table 8. Note that the values of the rank-two and rank-four parameters obtained in the present study for EuODA are quite similar to those deduced in previous studies [ l&19,2 11. However, the rank-six parameters are somewhat different. The previous crystal-field analyses of EuODA were based on a relatively small number of assigned energy levels confined to multiplet manifolds of J< 4, and values for the rank-six parameters had to be estimated rather than obtained from empirical data tits. The SmODA parameter values were obtained from a fit of 144 crystal-field energy levels spanning 20 different Russell-Saunders terms within the 4f5 electronic configuration of Sm3+. The analyses carried out in this study assume a trigonal dihedral ( D3) crystal-field symmetry. We found no evidence for a reduction of this symmetry in any of the absorption spectra obtained on crystal samples down to x 10 K. However, Banerjee et al. [ 16 ] have reported some evidence that the actual site symmetry at the Eu3+ ions is CZ at low temperatures, and they suggested that this reduction in site symmetry (from D3 at room temperature) is due to the movement of a Na+ ion off the three-fold axis of the crystal. In their picture, the crystal retains macroscopic trigonal symmetry at low temperatures (but with space group P321 rather than R32), and the Eu(ODA):- complexes retain D3 symmetry, with their trigonal axes remaining nearly parallel to the crystal three-fold axis. Banerjee et al. [ 16 ] measured absorption and magnetic circular dichroism spectra in the ‘FO+ ‘D , and ‘FO+ ‘Dz transition regions, and at 5 K they observed splittings of the AM,= f 1 and AM,= f 2 crystal-field

M. T. Berry et al. / Crystal-fieldanalysisfor Eu 3+

123

Table 8 Comparison of crystal-field parameters (in cm-‘) for Sm3+ and Eu’+ in Na3[Ln(ODA),].2NaC10&H20 Parameter a)

B&Z’ Bh4’ Bs4’ B&@ Bj6’ BA6’

Value SmODA b,

EuODA (present ) c,

EuODA (previous) d,

-19rt22 -941 zk26 -837+20 606+27 1112+23 794rt24

-56f24 - 1007+23 -785f20 43Oi26 1021+24 811+22

-70 - 1020 -660 320 285 220

*) Defined according to eq. (2). b’ Fro& ref. [27]. ‘) See table 2. d, From refs. [ 18,19,21].

components. However, these splittings were < 3 cm- ’ in each case, suggesting that the “effective” crystalfield symmetry is essentially D3.

dent of any mechanistic assumptions (except that the Ln-L-hv interactions be one-ele~tron/one-photon in nature ) .

7. Conclusion

Acknowledgement

The energy and intensity parameterizations (and parameter values) reported here provide a remarkably good description of the 4f+4f optical spectra of Eu3 + in Na3 [ Eu (ODA ) 3] -2NaC104*6H20. The energies, polarizations, and intensities of transitiorrs between crystal-field levels are well accounted for over a wide spectral range spanning many multiplet-tomultiplet transition manifolds. Mechanistic and structural inte~retations of the energy and intensity parameters are beyond the scope of the present study. However, it is clear that the electric-dipole intensity parameters, {A$), obtained in this study cannot be satisfactorily explained by any model that represents the 4f-electron crystal-field Hamiltonian as a superposition of Ln-L pairwise independent and cylindrically symmetry interactions. Either the pairwise independent condition or the cylindrical symmetry assumption must be discarded if the t=l parameters are to be explained. The possible importance of noncylindrically symmetric Ln-L interactions for rationalizing 4f+4f electric-dipole intensities has been considered previously by Mason and co-workers, [ 13,14,53], Stewart [54], and Richardson and coworkers [21,35,36,55,56] within the context of a pur~icu~ar 4f-+4f intensity mechanism (or model). However, it is important to point out again that the A& parameters obtained in this study are indepen-

Luminescence data obtained by Dr. David Metcalf and several discussions with Dr. Michael F. Reid were valuable in carrying out this study. This work was supported by a grant from the National Science Foundation (NSF Grant CHE-82 158 15) to FSR.

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M. T. Berry et al. / Crystal-field analysis for Eu”

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