J. CHEM. SOC. FARADAY TRANS., 1994, 90(5), 755-762 Influence of Structure on the Optical Spectra of Eu3+ in Pb(PO,), Glass :Molecular Dynamics Simulation and Crystal-field Theory G. Cormier and J. A. Capobianco" Department of Chemistry and Biochemistry, Concordia University, 1455 de Maisonneuve Blvd. W., Montreal, Canada H3G IM8 C. A. Morrison Microphotonics Division, U.S.Army Research Laboratory, Adelphi, MD, 20783,USA An investigation of the structural factors which lead to the marked differences between various spectral features of rare-earth-metal ions doped in metal metaphosphate and silicate glasses is reported. The investigation was based on a simulated structural/spectral model of an Eu3+-doped lead metaphosphate glass [Eu3+ : Pb(PO,),] that was compared to a previously reported Eu3+-doped sodium disilicate glass [Eu3+ : Na,Si,O,].The models were generated with a computational method that couples molecular dynamics simulation and point-charge crystal-field calculations. It is proposed that the marked differences in several spectroscopic features of Eu3+ ions doped in a lead metaphosphate glass are essentially due to a reduction in the width of the energetic distribution of local fields experienced by the Eu3+ ions. This distribution is shown to be influenced considerably by the presence of medium-range order in the local environment of the Eu3+ ions due to the lack of rigidity of the phosphate backbone. It is well known that optical properties of rare-earth-metal ions doped in glasses are closely related to the glass structure and composition.For the past 30 years, much emphasis has been placed on relating the chemical bonding, symmetry, and coordination within the glass network to the observed optical properties. Since the advent of the tuneable laser, energy- selective spectroscopic techniques, such as laser-induced fluo-rescence line narrowing (FLN), have been used extensively in attempts to elucidate the structural dependence of the lumi- nescent properties of rare-earth-metal doped glasses. Some insight into the rare-earth-metal local environment has been gained from such studies. Nevertheless, FLN experiments still correspond to the investigation of a macroscopic behaviour of a doped glass. Thus, any attempts to infer structural infor- mation from these experiments is complicated by the pres- ence of an overwhelming amount of accidental degeneracy.For this reason, it follows that the search for uniqueness in an atomic structural model for doped glasses, several of which have been proposed through the years,'-' might well be futile. Recently we have demonstrated"-' a new computational technique that is capable of linking experimentally deter- mined optical spectra of a doped glass and a simulated atomic structural model of the glass. This computational technique is related to ab initio crystal-field calculations, exemplified by the lattice summation technique,'3*'4 where crystal-field parameters are derived from the interaction between the impurity ion and the electrostatic potential of the surrounding lattice.In previous papers, we have used molecular dynamics (MD), an atomic-level structural simula- tion technique, to simulate a structural model of an Eu3+-doped sodium disilicate glass. Knowing the position and charge of each atom, we can calculate the electrostatic poten- tial at every individual rare-earth-metal site by summing each individual atomic contribution. Solutions to the electronic crystal-field Hamiltonian can then be calculated from the crystal-field parameters generated from the simulated glass matrix for each of the individual doped rare-earth-metal ions. Thus, we can calculate the splitting of each J manifold and the transition probabilities between all individual com-ponents of each J manifold.Once convoluted, this informa- tion permits the simulation of the optical absorption and emission spectra of rare-earth-metal ions doped in an amorphous matrix. Previously, we presented (i) an analysis of the local structure of Eu3+ ions doped into simulated amorphous silica (SO, : Eu3+) and sodium disilicate glass (Na,O -2Si0, :Eu3+)and (ii) a validation of the simulated structure of the doped sodium disilicate glass via the simula- tion of the optical spectroscopy (absorption and emission) of the Eu3+ ions doped in this glass. The aims of this research are (i) a detailed study of the local environment of Eu3+ ions doped into a lead meta- phosphate glass [Pb(PO,),], (ii) the simulation of the optical spectrum of the Eu3+ ions with the computational method outlined in the previous paragraph and (iii) a comparison between the structural/spectral models of Eu3+-doped lead metaphosphate and Eu3+-doped sodium disilicate glasses, in order to elucidate the structural factors that influence various spectral features observed in these glasses.Lead metaphosphate was chosen as the base glass because of the extensive studies of the optical and spectroscopic properties of rare-earth-metal doped metal phosphates that have been performed in the past 20 year^."-'^ The interest in such glasses lies in their ease of fabrication and the extremely wide range of compositional possibilities with which to tailor physical (optical and mechanical) properties of interest for specific technological applications.In a recent paper, we have simulated the glass structure of lead meta- phosphate using the molecular dynamics method." We pre- sented a model of the short- and medium-range structure, together with an independent confirmation of the presence of previously observed two-dimensional chain structures,20 rather than the conventional three-dimensional frame-work2'-22 postulated in other oxide (e.g. silicate, borate) glasses. Experimental The laboratory sample of Eu3+-doped lead metaphosphate glass, which is referred to in the remainder of this text, has been studied previously by absorption, emission and FLN spectros~opies.~~.~~The experimental details concerning the fabrication of this sample are found in ref.23 and 24. The room-temperature absorption spectrum of the experimental sample was redone with greater spectral resolution. The spec- trum was recorded in the region 380-600 nm, using a Cary 5E spectrophotometer with a 0.3 nm spectral bandwidth, a signal-averaging time of 1 s, and a step size of 0.1 nm. The fluorescence spectrum of the laboratory glass presented in this study was taken from the original spectral data gra- The reader ciously supplied by Dr. P-P. Pro~lx.~~~~~is directed to these references for experimental details. Simulation Procedures Molecular Dynamics Simulation The force law used in the molecular dynamics calculations is derived from a pairwise (two-body) ionic potential, which includes the Pauling repulsive term.It is of the same form as .~that described by Mitra et ~2 and was used by ~ us in~ previously reported The associated force 2719 law is found to be where qi and q, are the ionic charges, uiand ajare the ionic radii of the atoms i andj, n is a measure of the hardness of the repulsion, and rij is the distance between atoms i andj. The various parameters found in the force law were pre-viously published with the MD simulation of (i) undoped lead metaphosphate” (parameters for phosphorus, lead and oxygen) and (ii) Eu3+-doped in sodium disilicate10.12 (parameters for europium). Table 1 presents the ionic param- eters used with the force law. The instantaneous force, for solving the Newtonian equa- tions of motion, was determined for each ion over the set of atomic neighbours within 5.5 A using a screened Coulomb force.The length of 5.5 A is large enough to include the neighbours of importance (ca. 100 ions) and small enough that any increase will not have any effect on the structural characteristics of the glass. Once the instantaneous force on each atom was computed, at each time step (At = 1.0 x s), there was an update of the atomic coor- dinates and velocities using Verlet’s alg~rithm.~’ The composition of the simulated glass is given in Table 2, with other relevant parameters. A cubic cell was used in these calculations with periodic boundary conditions to eliminate the possibility of surface effects. The simulations were carried out at constant volume for each temperature step.The size of the cell, for the lowest-temperature steps, was adjusted to give the correct room-temperature density of undoped Pb(PO& glass, which was determined to be p = 4.74 g ern-,. For the Table 1 Force-law parameters used in the simulations element ionic radius, a/%i ionic charge, q/e 0 1.20 -1.136 P 0.15 2.840 Pb 0.99 1.136 Eu 1.oo 1.704 Hardness parameter, n = 10. Table 2 Simulation parameters for Eu3+-doped Pb(PO,), glass no. of 0 ions 420 no. of P ions 140 no. of Pb ions 67 no. of Eu ions 2 simulated density/g cmP3 4.74 oxygen molar volume/cm (mol O2-) -12.894 length of box side/%i 20.795 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 highest-temperature steps, the size of the box was increased slightly in order to simulate the effect of expansion due to temperature.The initial set of coordinates for the atomic ensemble, which contained 70 molecules of Pb(PO,), ,was derived from the unit cell of crystalline lead metaphosphate.28 This initial atomic ensemble was heated from 300 to 15000 K in a total of 25000 time steps of 1 fs. At 15000 K, we substituted three arbitrarily chosen lead atoms with two europium atoms, generating an atomic ensemble with the composition 2Eu(PO,), -67Pb(PO,), . The quenching procedure for the doped glass was as follows. The doped melt was thermalised at 15OOO K for an additional 200 0oO time steps (20 ps). The temperature of the melt was then lowered to 7500 K and then to 5000 K, each in 2000000 time steps.The melt was then allowed to thermalise at 2500 K for a duration of 18750 ~~ (75 x 250) time steps. After each 250th time-step, a configu- ration was stored for further processing. This ensured a total of 75 configurations, for a total of 150 europium ions. Each of these 75 configurations then underwent quenching from this initial temperature of 2500 to 300K in four steps at 2500, 1250, 600 and 300 K, each of 30000 time steps. Finally, each configuration was thermalised at 300 K for an additional 30000 time steps. Therefore, each of the 75 configurations of a doped glass was simulated between 750250 and 738 750 time steps for a total of 750-739 ps. The quenching rate was calculated to be ca.2 x lo1, K s-’. The simulated structure was verified throughout the run by monitoring various parameters, including average atomic dis- placements, to dispel the possibility of diffusion at the final temperatures of the quenching procedure. Pair, cumulative and bond-angle distribution functions were calculated and averaged throughout the quenching procedure for each con- figuration. However, the structural parameters presented in this paper are given for a temperature of 300 K. An averaging of the pair distribution function (PDF), cumulative distribu- tion function (CDF) and bond-angle distribution was per- formed for the last loo00 time steps of each temperature run, with a sample taken after every 10 time steps. The distribu- tion functions reported had step increments of 0.1 A for the PDF and CDF and of 1”for the bond-angle distribution and were an average of all of the 75 configurations. Optical Spectroscopy Simulation The crystal-field Hamiltonian that describes the interaction of the Eu3+ion with the host lattice can be written asz9 ZCEF = 1A,*, 1CCnm(ii) (2) nrn I where the first sum covers those values of n and m allowed by the symmetry of the site of the rare-earth metal. With n even, eqn.(2) was used to calculate the crystal-field splittings; for n odd, it was used to calculate transition probabilities. The second sum is over i = 6 electrons of the 4f6 configuration of the Eu3+ ion. The simplest description of the crystal field uses the point-charge model, in which the atoms of the lattice surrounding the rare-earth-metal are described by point charges.This model neglects both the finite spatial extent of the ligand charge density and the wavefunction overlap of the optically active 4f electrons with the ligands.” For point charges, eqj located at R,, the crystal-field components, A,, , of eqn. (2) are given by (3) In eqn. (2) and (3), the irreducible spherical tensors, C,,(r), are related to the spherical harmonics Y,,(8, 4).,O J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Using the atomic positions obtained from the molecular dynamics simulation and choosing appropriate ionic charges for each atom type, we can calculate the crystal-field com- ponents, A,, .Using the three-parameter theory of crystal fields proposed by Leavitt et we can calculate the crystal-field parameters, B,, .In order to calculate the intensity of line-to-line transitions in the simulated emission and absorption spectra, we used (i) the oscillator strength between the individual components a and b,hb, for the absorption process32 and (ii) the transition probability between the individual components a and b, Azr, for the emission process.32 The individual components a and b belong to the initial and final electronic manifolds of the electronic transition studied. Both the oscillator strengths and the transition probabilities require the calculation of the radiative line strength, sob, which, according to Condon and Sh~rtely,~~is given by the square of the following matrix element: sab =I<bI Ia> l2 (4) where P is the appropriate operator (electric or magnetic dipole).Electric-dipole intensity calculations were performed using the 'full' Judd-Ofelt theory of induced electric dipole transition^.^^.^^ Within the electronic configuration 4f ",mag-netic dipole transitions are parity allowed. Thus, the calcu- lation of the line strength is more straighforward than for the electric dipole case. With the proper dipole moment operator, eqn. (4) can be directly used to calculate the magnetic dipole line strength. Finally, one must note that J-mixing of eigen- states is included in the calculation of the magnetic-dipole and electric-dipole line strengths. In order to generate a graphic representation of the simu- lated emission and absorption spectra, the calculated energies are collated and sorted.A Gaussian bandshape is assigned to each of the energies. The spectral envelope, Z(E),is given by" where the first sum is over the No =150 Eu3+ configurations and the second sum is over the 49 possible line-to-line 'Do +7F, (J =0-6) transitions for the emission spectrum or is over the (4 x 29) possible line-to-line 'L,, 5D3, 5D2, 'D1, 5D,t7F,,, transitions for the absorption spectrum, The Ek,abare the he-to-line transition energies for each of the Eu3+ ions, such that Ek,ab =IE, -Eb Ik. The width, W, Of each individual Gaussian has been chosen to be ca. 5 cm-' for the emission spectrum and ca.10 cm-I for the absorption spectrum. These widths were chosen so that the 150 Eu3+ ions of the simulated glass effectively represent the macro- scopic ensemble of doped ions found in the experimental glass. The difference in these widths stems from the fact that the two experimental spectra (absorption and emission) were taken at different resolutions. The intensity parameters, ILTrb, found in eqn. (9,where type represents either absorption or emission, are derived from the calculated oscillator strengths or transition probabilities, respectively. The intensity param- eter calculated for the emission process also includes the radi- ative branching ratio pertaining to the calculated radiative transition. Results The average short-range environment of the europium ion has been verified by (i) the calculated Eu-0 pair and cumula- tive distribution functions and (ii) the Eu-M (M =Pb and P) pair distribution functions (PDF).These distribution func- tions, obtained from the room-temperature simulated struc- ture, are shown in Fig. 1 and 2. The average Eu-0 200 225 250 575 3ffi 225 350 375 402I distance/A 20 25 30 35 40 45 50 55 60 65 70 75 80 distance/A Fig. 1 Pair distribution function of 0-Eu atomic pair for simulated Eu3+ :Pb(PO,), glass. Inset shows cumulative distribution function of the 0-Eu pair. interatomic distance, in its first coordination shell, was calcu- lated to be 2.45 A, with a full width at half maximum (FWHM) of 0.28 A. The distribution function does not return to a null value after the first peak, indicating that no clear distinction exists between the first and second coordination shells. For this reason, the average coordination number of the Eu-0 first-shell polyhedra is difficult to assess.The first minimum between the first and second coordination shells occurs at ca. 3.2 A. At this cut-off distance, the average coor- dination of the Eu polyhedra is found to be 6.2 oxygen atoms, as determined from the cumulative distribution func- tion of the Eu-0 pair, shown in the inset to Fig. 1. Fig. 2 show the P-Eu, PbEu pair distribution functions for the simulated Eu3+ :Pb(PO,), glass, together with the Si-Eu PDF for the simulated Eu3+ :Na20* 2Si0, glass that was studied previously." The P-Eu and PbEu PDFs for the simulated metaphosphate glass have maxima at 3.75 8, 3 2.0 .-v)'I y 10 a 20 25 30 35 40 45 50 55 60 65 70 75 80 distance/A Fig.2 Eu-M [M =Pb (. ..)and P (-)I pair distribution func- tions for simulated Eu3+ :Pb(PO,), glass. Also shown is Eu-Si PDF for simulated Eu3+ :NaSi,O, glass [(---) taken from ref. lo]. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 (FWHM = 0.41 A) and 4.55 8, (FWHM = 2.32 A), respec-tively. We notice that the P-Eu PDF has sharp, surprisingly well defined, first and second coordination shell peaks, whilst the Pb-Eu PDF is quite the contrary, presenting broad, undefined peaks. This is not unexpected owing to the differ- ent function of each cation in the glass matrix, the former being a glass-former, the latter a network modifier.Fig. 3 pre-sents a comparison of the probability distribution of oxygen T 0 1 2 3 4 5 6 7 8 9 10 coordination Fig. 3 Probability distribution of oxygen neighbours about an Eu3+ ion within a coordination sphere of 3.2 A. Comparison between simulated Eu3+ :Pb(PO,), (a)and Eu3+ :NaSi,O, (0) glasses (taken from ref. 10) 0 25 scale x 10----f E 380 400 420 440 460 480 500 520 540 560 580 600 I/nm Fig. 4 Comparison between room-temperature 5L,, 'D,, ,,,,,t 7F0,absorption spectra of experimental (-) and simulated (. . .) Eu3'+:Pb(PO,), glasses Table 4 Absorption barycentres and linewidths of the experimental and simulated Eu3 + : Pb(PO,), glasses' Eu" : Pb(PO,), Eu3+ : Pb(PO,), experimental glassb simulated glass barycentre FWHM assignment /cm-' /cm -' barycentre FWHM /cm-' /cm-' 'Do t7F1 17004 253 16 957 256 'Do t7F0 17 280 42 17 279 60 'D, t7F, 18 695 206 18 730 164 'D, t7F0 19 026 47 19 024 72 'D, +'F, 'D, + 7F, 'D, t7F, 21 519 24 137 -130 208 - 21 265 21 546 24 064 z 250 72 260 'D, t'F, -- 24 377 88 'L, t7F, -- -- 'L, t7F, 25 413 84 25 388 144 a Only the electronic transitions which have been simulated are reported.Results taken from ref. 23 and 24. +neighbours about an Eu3 ion between the simulated Eu3+ : Pb(PO,), and Eu3+ : NaSi,O, glasses. The coordi- nation number represents the number of oxygen ions found surrounding a Eu3+ ion within a coordination sphere of 3.2 A.This figure shows that although average coordination numbers are similar between the doped phosphate and sili- cate glass, the overall distributions of local environments are drastically different. Table 3 summarises the structural parameters derived from the pair and cumulative distribution functions for the first and second coordination shells of the various atomic pairs present in the simulated Eu3+: Pb(PO,), glass. In this table, the average interatomic distances and their associated widths (FWHM) are shown as well as average coordination numbers. The number in brackets, found in the last column of this table, refers to the distance at which the average coor- dination number has been calculated. These distances were obtained from the position of the first minima situated between the first and second coordination shell peaks. We have given the details, in a previous paper," of the calculational steps required to obtain the simulated optical spectra.The first and most important of these, is the proper choice of partial ionic charges for all the atomic species present in the simulated glass. The charges have a direct influence on the position and the width of each of the simu- lated electronic transitions. This influence stems from the simulation of an overall covalency effect between locally bound ions. The partial charges that were used in the calcu- lation of the crystal-field parameters [eqn. (3)] have been determined empirically (under a certain set of specific conditions) and produce a proper simulation of the various spectral features found in both the absorption and emission spectra.The first of the above-mentioned conditions was to maintain strict electroneutrality of the atomic ensemble. Sec- ondly, the charge of the europium ion was kept at full value, representing a complete electrostatic interaction with its sur- rounding ligands. Thirdly, in order to simulate partial cova- lency of the Pb2+ ion interaction^,^^ the lead ion's charge was fixed at a slightly lower value than its full value. These conditions lead to the following set of partial charges: oxygen = -0.94e phosphorus = +2.4593e lead = + 1.50e europium = +3.00e which were found to yield simulated spectra, in excellent agreement with their laboratory counterparts. Table 3 Structural parameters derived from the pair and cumulative distribution functions for first and second coordination shells of the various atomic pairs present in the Eu3+ :Pb(PO,), glass atomic pair 1st peak/A FWHMIA 2nd peak/A FWHM/A 0-0 2.45 0.2 1 3.2 & 5.1 0.67 & 1.7 0-P 1.51 0.18 3.85 0.65 0-Pb 2.43 0.40 4.5 1.5 0-EU 2.45 0.28 4.5 1.22 P-P 3.04 0.25 4.95 1.2 P-Pb 3.71 0.60 5.0 1.3 P-EU 3.75 0.41 5.1 1.19 Pb-Pb ca.3.9 ca. 2.4 ca. 7.0 - Pb-Eu 4.55 2.32 ca. 7 - coordination no. (distance/A) 5.82 (3.2) 4.00 (2.1) 6.94 (3.4) 6.20 (3.2) 2.00 (3.5) 5.50 (4.3) 5.78 (4.3) 5.00 (5.5) 5.03 (5.8) J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Discussion .-c 20"i 3 > c.-gc .-580 600 620 640 660 680 700 720 A/nmFig. 5 Comparison between room-temperature 5D0+ 7F0,,.2, ,, emission spectra of experimental (-) and simulated (. . -) Eu3+ : Pb(PO,), glasses Fig. 4 shows a comparison between the absorption spec- trum of the laboratory glass to the spectrum of the computer- generated Pb(PO,), : Eu3+ glass, in the region between 380 and 600 nm. The relative population of the 7F0and 7F1man-ifolds was taken into account in the simulated absorption spectrum by calculating the Boltzmann distribution at a tem- perature of 300 K for each of the Eu3+ ions and incorpor- ating the results in eqn. (5). Assignments, band positions and widths of the measured and simulated absorption spectra for the Pb(PO,), : Eu3+ glass are presented in Table 4.We observe, in Fig. 4, that an excellent agreement exists between the barycentre positions, widths, and overall shapes of the optical transitions, for the two spectra (simulated and labor- atory glass). The 'Do -+ 7F, (J = 0-4) simulated and experimental emission spectra are shown in Fig. 5. The spectral region investigated is between 570 and 720 nm. Although the simu- lated 'Do -+ 7FS,6 transitions were calculated, they are not shown because no emission was detected in these regions for the laboratory glass. Table 5 presents a comparison of the emission barycentres and their associated linewidths for the simulated and laboratory sample of the Eu3+ : Pb(PO,), glass.Although the comparison between the experimental and the simulated absorption and emission spectra is more than qualitatively adequate, certain discrepancies can be found in both simulated spectra, especially regarding the simulations of the hypersensitive transitions 5Do-,7F2 and 'D, t7F0. These discrepancies have been discussed previously,' ',3 and since no attempt has been made to alleviate the problems presented by the absence of dynamic coupling in the crystal- field calculations, the problem and its solution remain essen- tially the same. Table 5 Emission barycentres and linewidths of the experimental and simulated Eu3+ : Pb(PO,), glasses Eu3+ : Pb(PO,), experimental glass Eu3+ : Pb(PO,), simulated glass assignment barycentre/cm- FW HM /cm - barycen tre /cm - FWHM /cm - 5D0+ 7F0 17 283 48 17 282 68 'Do + 7F,5DO+7F2 16 900 16244 300 368 16 901 16 283 316 268 5D0+ 'F,5D0+ 7F, 15295 14292 188 112 15 335 14 316 122 218 Extensive investigations of the luminescent properties of Eu3+ ions (or any other trivalent rare-earth-metal ion for that matter) doped into oxide glasses have shown that absorption and emission spectra can be affected by varying the glass composition.This phenomenon is exemplified by the wide range of physically different local environments experienced by Nd3+ ions in various oxide, fluoride and mixed anion glasses, which leads to extensive variations in barycentre positions and widths as shown by their respective absorption3* and emission39 spectra.A more specific example is the difference in position and width exhibited by the 5D0--+ 7F0transition of the Eu3+ ion doped into a sili- cate glass and a phosphate glass. In a europium-doped mag- nesium aluminosilicate glass of the cordierite stoichiometry (MgO . AI2O3* 2.5Si02),40 the previously mentioned tran-sition is situated at 17 314 cm- ' and has a room-temperature FWHM of 119 cm-'. In the case of a europium-doped lead metaphosphate glass,23 the same room-temperature tran-sition is positioned at 17283 cm-' and has an FWHM of 48 cm-l. This leads to a difference of 31 cm-' (ca. 1 nm) between the positions of the barycentres and to a factor of nearly 2.5 between linewidths.The difference in the position of the barycentres has tradi- tionally been attributed to a difference in the overall crystal- field strength of the average local rare-earth-metal en~ironment.~'As for the widths, it is normally assumed that the smaller the value of width of a given transition, the less disturbed are the local environment^.^^ According to these premises, there would be an increase in the order of the local structure surrounding the rare-earth-metal ions present in the doped metaphosphate glass when compared with the doped silicate glass. Thus, it would be worthwhile to examine in greater detail the differences in the chemical surroundings of the doped europium ions as presented by both structural models, i.e.the doped sodium disilicate" and lead meta- phosphate glasses simulated by the MD technique. Our first concern was to verify the possibility of an increase in the overall symmetry of the individual configu- rations while comparing a silicate to a metaphosphate glass. Although for a glass, an increase of the symmetry might not be significant since there still remains a distribution of differ-ent local environments ; the increase could still be construed as an indication of ordering in the glass. The following two analogies, although divergent in views, examine the possible significance of the results. First, one can imagine a rare-earth- metal doped crystal having the dopant ions situated in a site of C1 point symmetry.Although the site itself does not exhibit any order, translational symmetry from one unit cell to another still remains, and an optical spectrum will neces- sarily show crystalline characteristics. The importance of this analogy resides in the presence (or rather the absence, within the limits of inhomogeneous broadening, in the case of the crystal) of a distribution of local environments. Secondly, a comparison could be made with the microscopic processes occurring during ceramitisation or during nucleation. These processes necessarily start with ordering in the short-range domain (<8 A), where a reorganisation of the local environ- ments leads to the formation of the proper unit cell for a doped crystal. This reorganisation would then proceed through the medium- and long-range domains.The distribu- tion of possible local environments exists at the onset of the process, but this distribution diminishes with time. In order to quantify the spatial arrangement of the oxygen ligands about the Eu3 + ions, we calculated the quadrupole moment for each of the individual configurations. This pro- cedure has been delineated in ref. 10, where we have found 760 that none of the 150 individual Eu3+ configurations, of the simulated Eu3+-doped sodium disilicate glass, had a point- group symmetry higher than C,. The same analysis of the quadrupolar moments on the simulated Eu3+ : Pb(P03), also shows that none of the simulated local environments show any elements of symmetry.That is to say that the point-group symmetry of the Eu3+ ions doped in a lead metaphosphate glass is rigorously C,. It is important to note that this determines only the presence of symmetry elements in the spatial distribution of the oxygen ligands that were identified to be directly connected to the europium ions at a maximum distance of 3.2 A. Obviously, this does not give any indication of ordering in the surrounding matrix; yet it still dispels the postulate that because of the nature of the rare- earth-metal dopant, its ligand shell would have a regular arrangement very similar to its crystalline ~ounterpart.'-~ Returning to the two analogies that we have previously dis- cussed, it is then necessary to propose at this point that the possible ordering experienced by the Eu3+ ions in the lead metaphosphate glass is not due to an increase of symmetry (ordering in the short-range domain, leading to an eventual- ity of ceramitisation) but, rather, would be due to a substan- tial decrease of the distribution of possible local fields experienced by the Eu3+ions. Our second concern was to identify if the Eu3+ ions were situated in specific regions of the Pb(P03), glass matrix.Before discussing this point, let us briefly review the salient structural features of the lead metaphosphate base glass. Pre- vious have postulated the presence of phosphate chains of varying lengths that were connected to each other uia the metal cations bonded with the non-bridging oxygen atoms of the phosphate tetrahedra.This structural organis- ation differs markedly with the typical three-dimensional backbone of network-forming cations with a random dis- tribution of network-modifying cations as postulated by Zachariasen, in oxide glasses, and exemplified by modified silicate glasses. A connectivity study of the phosphate back- bone of a molecular dynamics simulated lead metaphosphate glasslg essentially showed the presence of primary and sec- ondary phosphate chains together with smaller amounts of phosphate ring structures. Furthermore, this study showed the presence of a secondary network made up of the modifier lead cations linked by non-bridging oxygen atoms, as postu- lated by the modified random network theory.,, Table 6 presents the results of an analysis of the connec- tivity of the oxygen atoms found in the first coordination shell of the Eu3+ ions (Eu-0 interatomic distance G3.2 A).An identification of the number of metal cations bonded to these oxygen atoms shows the following results. First, nearly all (ca. 98%) of the first coordination shell oxygen atoms are non-bridging oxygen atoms (NBO) of the phosphate tetra- hedra. The amount of non-bridging oxygen atoms, in metal metaphosphate glasses, is substantial since the presence of long chains ensures two NBO per phosphate tetrahedra, three NBO for terminal phosphate groups, and four for ortho- phosphate groups. Although there is no empirical way of cal- culating precisely the amount of NBO, as is the case for silicate glasses,43 the HPLC experiments of Sales et aL2' and Table 6 Percentage of first coordination shell oxygen ions having x bonded M cations (M = Pb2+ or P5+) X Pb2+ P5+ 23 0.84 0.00 2 7.79 0.42 1 52.42 98.21 0 38.95 1.37 J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 the MD simulation of Cormier et ~1.'~indicate the amount of various species present in the glass. The value of the NBO : BO ratio, determined from the simulated undoped lead metaphosphate glass," was found to be 2. The very high percentage of NBO connected to the Eu3+ ions clearly indi- cates that the rare-earth-metal ions are essentially connected to the phosphate backbone but are not an intrinsic part of it. Secondly, we observe that ca.60% of the oxygen atoms sur- rounding the Eu3+ are also shared by one or more Pb2+ ions. This prompted us to calculate the number of Eu3+ ions that are directly bonded (through one non-bridging oxygen) with a lead ion. The result obtained showed that all of the Eu3+ ions have at least one lead ion in their second coordi- nation shell. These points confirm the fact that the Eu3+ ions are situated amongst the secondary Pb2 + ionic network, a network which has been clearly identified in undoped lead metaphosphate g1a~s.l~ This secondary network acts as a 'buffer' zone between adjacent phosphate chains, and should therefore be substantially amorphous. Any degree of organis- ation present in the metaphosphate glass will arise from an ordering of the phosphate chains (primary and secondary). This ordering should occur much more readily than in the case of the three-dimensional framework of the modified sili- cate glasses, because of the greater degree of freedom of the chain structure.Under the premise of the modified random network theory,22 this secondary ionic network exists in counterpart to the crystalline structure. In crystalline lead metaphosphate, individual phosphate chains are infinite in length and parallel to each other, separated by columns of lead oxide. The bonding of the Eu3+ polyhedra to the glass matrix was shown to be essentially through non-bridging oxygen atoms (Table 6). As such, the degree of organisation of the local environment of the europium-oxygen polyhedra will be necessarily dependent on the degree of organisation of the phosphate backbone.This degree of organisation can be investigated by analysing the metalkeuropium pair distribu- tion function, where the metal corresponds to either lead or phosphorus. These pair distribution functions have been presented in Fig. 2. What is remarkable about this figure is the surprisingly well defined first and second coordination shell peaks of the Eu-P PDF. A comparison with the Eu-Si PDF of the simulated Na20 * SiO, :Eu3+ glass" imme-diately shows the difference in ordering of the local frame- work surrounding the Eu-0 polyhedra. Several factors provide evidence for this. First, the values of the associated widths for the first and second coordination peaks are sub- stantially smaller in the case of the phosphate glass.Specifi- cally, for the phosphate glass, they are A, = 0.41 A and A, = 1.19 A, whereas we find for the silicate glass, Al = 0.72 A, whilst the width of the second coordination peak is not dis- tinct enough to be accurately measured. Secondly, the ratio between the maxima of the first and second coordination peak is significantly greater in the lead metaphosphate glass in comparison to the corresponding ratio of the sodium dis- ilicate glass. These ratios are 3.3 and 1.9, respectively. This indicates that the first coordination shell of phosphorous atoms, as seen by the europium atoms, is clearly more dis- tinct than the second coordination shell.In the case of the doped sodium disilicate glass, the corresponding shells tend to be more indistinguishable. This is also observed for the height of the minima between the first and second coordi- nation peaks. In the case of a network-former-ligand pair, the minimum between the first and second peak is necessarily a null value, indicating a high degree of short-range order. A network-modifier-ligand pair will show a distinct increase in the height of this minimum, yet will not attain the height of a network-modifier-network-modifier or anionic ligand- J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 anionic ligand pair. Fig. 2 shows that, in the case of the europium-phosphorus pair, this height is comparable with that of a network-modifier-ligand pair.All these factors are directly linked to the substantial degree of short-range order in the local environment of the europium-oxygen polyhedra as a result of the presence of medium-range order of the phosphate backbone. In Table 6, we notice in the simulated glass the presence of a small quantity of oxygen atoms that are determined to be 'free'. These oxygen atoms, previously observed in other simulated doped are not connected to the phos: phate backbone and are shared between modifying lead cations and doped europium ions. The formation of free oxygen atoms has been ascribed to the presence of neigh- bouring cations with large field strengths, such as Pb2+ and Eu3+. As mentioned at the start of this section, rare-earth-metal doped lead metaphosphate glasses show exceptional behav- iour in their spectral features.We have argued that this is due to the presence of substantial ordering in the local environ- ment of the rare-earth-metal dopant compared to that found in a more conventional type of glass, such as a doped sodium silicate glass. This should lead, as suggested previously, to a noticeable decrease in the energetic distribution of possible local fields experienced by the doped rare-earth-metal ions. This ordering of the phosphate backbone and its influence on the local environment of the europium-oxygen polyhedra should be observed in the spectroscopic features of the simu- lated europium-doped lead metaphosphate glass. The last section of the Discussion will deal with such spectroscopic evidence.Since we are not restricted by the direct study of an experi- mental spectrum, it is possible to establish an indirect link between the MD-generated structural model of europium- doped lead metaphosphate glass and the experimental spec- trum of the corresponding laboratory glass. This link is established through a proper duplication of the experimental spectrum of the laboratory doped glass, by the calculated spectrum generated from the structural information (atomic positions, partial charges) obtained from the MD simulated model. As such, the knowledge of the exact local atomic con- figurations surrounding each of the doped ions, together with the possibility to identify and isolate individual structural contributions to the simulated spectra, allows for the pos- siblity of spectra/structure correlations.In order to investigate the postulated reduction in the dis- tribution of local field in doped lead metaphosphate glass, we calculated the crystal-field ~trength,~' S,, , using the follow- ing equation : (6) where the B,, are crystal-field parameters3' and the sum over n covers the values of 2, 4, 6. The crystal-field strength was plotted vs. the excitation wavelength (the position of the 'Do manifold representing the 'Do + 'F, transition) for each of the 150 Eu3+ configurations of (i) the simulated Eu3+ : +Pb(P03), glass and (ii) simulated Eu3 :Na,O. 2Si02 glass" (Fig. 6). Since the crystal-field parameters are essen- tially geometric in nature, directly influenced by the nature and the position of each atom in the surrounding lattice, SCF is seen to be a quantitative measure of the strength of the electrostatic interaction between the rare-earth-metal ion and the surrounding lattice.In Fig. 6 we observe the same general trends for both simu- lated glasses. First, a somewhat linear decrease of the crystal- 00 --.5 574 575 576 577 578 579 580 581 A/nm Fig. 6 Crystal-field strength, S,,, as a function of simulated 5D,t 'F, transition wavelength. Comparison between simulated Eu3+ : Pb(PO,), (0)and Eu3+ : NaSi,O, (0)glasses (taken from ref. 10) fielA ctr-nnth ic ceon hmtxirmen Z7A Z cant4 Z70 Z nm ffir tho LlllJ (1bLCI IJCU c ..oy a sumranrial vertical spreaa or tne possiue values OI tne crystal-field strength for a given excitation energy. Secondly, this decrease is followed by a sharp fall to an asymptotic value which is known as the zero-field energy.Thirdly, the overall spread in possible excitation energies reflects the broadness of the 'Do +7F0transition in both glasses, i.e. it is much smaller in the case of the phosphate glass. Lastly, we observe that for a given value of excitation, the vertical spread in possible crystal-field strengths is much greater in the silicate glass than in the phosphate glass. The average values with their standard deviations of the crystal-field strengths were found to be 282.7 cm-' (a = 69.0 cm-') and 350.2 cm-' (a = 98.0 cm-') for the phosphate and silicate glasses, respectively.This vertical spread is a consequence of the widespread presence of accidental degeneracies in the doped glasses. Accidental degeneracy represents cases where a substantial difference in the local environment leads to a difference in crystal-field strength, yet gives the same value of the difference in position between the 'Do excited state and 'F, ground state of the Eu3+ ion. All these points are clear spectroscopic indications of the considerable influence that the local environment, provided by the glass, has on the electronic levels of the rare-earth- metal dopant. As postulated from the MD-generated struc- tural model, the phosphate glass shows greater ordering in the local environment of the rare-earth-metal dopant.Conclusions We have presented an investigation of the structural factors which lead to the marked differences between various spectral features of rare-earth-metal ions doped into metal meta-phosphate and silicate glasses. The investigation was based on a simulated structural/spectral model of an Eu3+-doped lead metaphosphate glass [Ed + : Pb(PO,),] which was compared to a (previously reported) Eu3+-doped sodium dis- ilicate glass (Eu3+ : Na,Si,O,). The models were generated 762 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 with a computational method that couples molecular dynamics simulation and point-charge crystal-field calcu- lations. The structural model of the Eu3+ : Pb(P03) glass, shows that the doped Eu3+ ions are bonded in their first coordi- 13 14 N.Karayianis and C. A. Morrison, Rare Earth lon-Host Crystal Interactions 1. Point charge lattice sum in Scheelites, Harry Diamond Laboratories, Adelphi MD, 1973, HDL-TR-1648. N. Karayianis and C. A. Morrison, Rare Earth Ion-Host Crystal Interactions 2. Local distortion and other efects in reconciling lattice sums and phenomenological B,, , Harry Diamond Labor- nation shell to approximately six non-bridging oxygen atoms. The non-bridging oxygen atoms are themselves an intrinsic part of the phosphate backbone. The point group for the local environment of the Eu3+ ions was found to be C,.Fur-thermore, the Eu3+ ions are situated in the secondary network, which is made up of the modifier lead cations linked 15 16 17 atories, Adelphi MD, 1975, HDL-TR-1682. 0.K.Deutschbein, C. Pautrat and I. M. Svirchevsky, Rev. Phys. Appl., 1967, 1,29. V. B. Kravchenko and Yu P. Rudnitskii, Sov. J. Quantum Elec- tron., 1979,9, 399. N. E. Alekseev, V. P. Gapontev, M. E. Zhabotinskii, V. B. Krav- chenko and Yu P. Rudnitskii, Laser Phosphate Glasses, Nauka, by non-bridging oxygen atoms. Finally, substantial medium- range order was observed in the local environment of Eu3+ ions. We attribute this to the ordering of the phosphate back- bone. It was previously shown that europium ions doped in a sodium disilicate glass are influenced to a greater degree by their bonding and energetic requirements than by the topol- ogy of the silicate framework. Although the bonding and ene- getic requirements have a substantial influence on the local rare-earth-metal environments in the phosphate glass, we have shown that the topology of the phosphate backbone has a much greater influence.We propose that the marked differ- ences in several spectroscopic features of Eu3+ ions doped into a lead metaphosphate glass are essentially due to a reduction in the width of the energetic distribution of local fields experienced by the Eu3+ ions. This is due to the pres- ence of medium-range order in the Eu3+ environments, which is a direct result of the lack of rigidity of the phosphate backbone (comprised essentially of chains and large ring structures). 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Moscow, 1980. M. J. Weber, D. C. Ziegler and C.A. 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