Quantitative local structures of trivalent rare-earth ions in glasses: testing and setting the limits of the ionic 'crystal-chemistry' (radius-ratio / modified-random-network) model

When trivalent rare-earth (RE$^{3+}$) ions such as Er$^{3+}$, Nd$^{3+}$ or Tm$^{3+}$ are dissolved in oxide and fluoride glasses, their luminescence properties — and the doping levels at which concentration quenching sets in — depend on the ions' local atomic environments. In 1993, Wang, Brocklesby, Lincoln, Townsend and Payne proposed a qualitative 'crystal-chemistry' model that predicts RE$^{3+}$ coordination numbers from ionic radius ratios within a modified-random-network picture of glass structure. The model presumes predominantly ionic, non-directional RE–ligand bonding and yields only semi-quantitative predictions. The open problem is the quantitative determination and validation of RE$^{3+}$ local structure in glasses: coordination-number distributions, bond-length and bond-angle distributions, and site-type multiplicity, their dependence on glass composition and RE concentration, the validity of the radius-ratio and modifier-partitioning predictions in hosts where bonding is significantly covalent or directional, and the quantitative connection of these structural quantities to spectral inhomogeneity, fluorescence-decay kinetics and concentration-quenching thresholds. Later EXAFS, NMR and molecular-dynamics studies have quantified RE environments in several specific host families, but no validated general composition-to-local-structure model with a quantitative link to quenching exists, and work remains composition-by-composition.

Background

Rare-earth-doped glasses are the active media of fiber lasers and optical amplifiers (most famously the erbium-doped fiber amplifier operating near 1.5 $\mu$m). Because the $4f$ energy levels of a trivalent rare-earth (RE$^{3+}$) ion are split and shifted by the electrostatic field of its ligand anions (the crystal field), and because non-radiative decay and energy transfer between ions depend on inter-ionic distances, the optical performance of a doped glass is controlled by the dopant's local atomic environment: its first-shell coordination number (CN, the number of nearest ligand anions), the distribution of RE–ligand bond lengths and bond angles, the number of distinct site types the ion occupies, and the spatial correlation between RE ions.

Two competing pictures of glass structure frame the question. In the continuous-random-network (CRN) picture, network modifiers (cations such as alkalis, alkaline earths, or RE$^{3+}$ that depolymerize the network) are treated as spatially and coordinationally highly disordered, implying broad, essentially random RE coordination. EXAFS (extended X-ray absorption fine structure) spectroscopy — which measures the absorption spectrum just above an element's X-ray absorption edge and yields element-specific inter-atomic distances and coordination numbers — instead showed that modifier cations in glasses retain well-defined, crystal-like coordination and medium-range order extending to roughly 1 nm, motivating the modified-random-network (MRN) picture of Greaves, in which modifier-rich channels coexist with a polymerized network-former framework and local coordination polyhedra remain approximately invariant despite long-range disorder.

Building on the MRN picture and on Pauling's classic ionic crystal-chemistry rules (which relate the ratio of cation to anion ionic radii to the preferred coordination geometry), Wang, Brocklesby, Lincoln, Townsend and Payne proposed in 1993 a compact predictive model for RE$^{3+}$ sites in glasses. Its ingredients are: (i) radius-ratio thresholds — with an effective oxygen radius of about 1.40 Å, a ratio $R_{\mathrm{RE^{3+}}}/R_{\mathrm{O^{2-}}}$ between 0.414 and 0.732 favors six-coordination, while ratios above 0.732 allow seven- to nine-coordination — so that smaller RE$^{3+}$ (Er, Tm, Yb) sit predominantly in six-coordinated, more regular sites and larger RE$^{3+}$ (Nd, Pr, Eu) in multiple seven- to nine-coordinated site types; (ii) site regularity (narrowness of bond-length and angle distributions) increasing with network depolymerization (abundance of non-bridging oxygens) and with RE field strength; and (iii) modifier partitioning — RE$^{3+}$ co-locates with other modifiers in MRN channels, so added modifier species (for example six-coordinated Al$^{3+}$ in alumina-doped silica) form mixed Al–O–RE linkages in place of RE–O–RE linkages, increasing RE–RE spacing and, by Pauling's rule of parsimony (the preference for few distinct structural unit types), delaying concentration quenching. Applied to heavy-metal-fluoride (HMF) glasses such as ZBLAN (a Zr–Ba–La–Al–Na fluoride glass), the model predicts more regular RE sites and higher tolerable RE concentrations than in oxides. The model thereby rationalizes observed host-dependent spectroscopy, e.g. near-exponential Er$^{3+}$ fluorescence decay versus strongly non-exponential, inhomogeneous Nd$^{3+}$ decay in oxide glasses.

The authors themselves delimited the model's open issues: it presumes predominantly ionic, non-directional RE–ligand bonding and may fail where bonding is significantly covalent or directional; it is qualitative to semi-quantitative, providing no detailed predictions of coordination-number distributions, bond-length distributions, or concentration-dependent structural evolution; the influence of medium-range ordering, local distortions, and concentration-induced changes (edge-sharing motifs, local phase separation, clustering) on the radius-ratio predictions remained to be determined experimentally for specific host chemistries; and the model's applicability across multicomponent glass families, and its quantitative connection to measured quenching thresholds, were left as tasks for targeted EXAFS/scattering/fluorescence-line-narrowing (FLN, a site-selective laser spectroscopy that resolves the inhomogeneously broadened Stark sublevels of dopant ions) studies and for atomistic simulations.

Problem Statement

Determine, quantitatively, the local atomic environments of trivalent rare-earth (RE$^{3+}$) ions in glasses and thereby establish the validity, predictive power and quantitative limits of the ionic 'crystal-chemistry' model proposed by Wang, Brocklesby, Lincoln, Townsend and Payne (1993). Concretely, one must establish: (1) the first-shell coordination-number distributions, RE–ligand bond-length and bond-angle distributions, and the number and regularity of distinct RE$^{3+}$ site types in specific glass hosts, rather than only average coordination; (2) how these quantities depend on glass composition — degree of network polymerization, identity and content of co-modifier cations, ligand type (oxygen versus fluoride), and RE–ligand ionicity — addressing each of these axes, and including at least one host in which RE–ligand bonding is significantly covalent or directional and the ionic radius-ratio thresholds (six-coordination for $0.414 \le R_{\mathrm{RE^{3+}}}/R_{\mathrm{O^{2-}}} \le 0.732$, seven- to nine-coordination above 0.732) may fail or require modification; (3) how they evolve with RE concentration, including clustering, medium-range ordering, edge-sharing motifs and local phase separation, and how they are modified by co-dopants such as Al$^{3+}$; (4) whether the modified-random-network modifier-partitioning and parsimony predictions of RE–RE spacing hold quantitatively; and (5) the quantitative relationship between these local-structural distributions and the measured optical observables — spectral inhomogeneity, non-exponential fluorescence decay, and the concentration-quenching threshold — across multicomponent glass families, including mixed-alkali, strongly covalent oxide, and halide or oxyhalide compositions. The determination must connect glass composition and RE concentration to RE local structure and to its optical consequences across at least one host in each of the composition classes named in (5), establish the boundaries within which the ionic crystal-chemistry predictions remain reliable, and compare each predicted coordination-number, bond-length and bond-angle distribution with independent experimental or simulation data for that host, reporting the resulting level of agreement quantitatively.

References

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