Article pubs.acs.org/cm
Average and Local Crystal Structure of β‑Er:Yb:NaYF4 Upconverting Nanocrystals Probed by X‑ray Total Scattering S. Sameera Perera,† Dinesh K. Amarasinghe,† K. Tauni Dissanayake, and Federico A. Rabuffetti* Department of Chemistry, Wayne State University, Detroit, Michigan 48202, United States S Supporting Information *
ABSTRACT: The average and local structures of ∼22 nm β-Er:Yb:NaYF4 upconverting nanocrystals were probed using a dual-space approach combining Rietveld and pair distribution function analysis of X-ray total scattering. Comparison of the fits provided by the structural models derived from P6̅2m, P6̅, and P63/m space groups demonstrates that the latter yields a crystallochemically meaningful description of the nanocrystals’ average and local structures. This result is in line with those previously reported for bulk β-Na3xRE2−xF6 (x ∼ 0.45; RE = Y, Er, Tm, Yb) using powder X-ray diffraction,1 and for β-NaREF4 (RE = Y, Lu) nanocrystals using solid-state NMR;2 however, it differs from those reported in studies of βNaREF4 (RE = La, Gd, Er) single crystals, which favored the structural model derived from the P6̅ space group.3 The proposed structural model features sodium cations distributed in four translation-equivalent chains, each shifted relative to the others along the c axis. Interestingly, the structural model derived for the mineral gagarinite (NaCaREF6, P63/m), in which sodium cations are distributed in eight chains, also provides an adequate fit to the X-ray scattering data. The potential implications of this finding are discussed from the perspective of the size dependence of the crystal structure of β-NaREF4.
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INTRODUCTION Hexagonal β-NaREF4 (RE = Y, rare earth) constitutes the most extensively used host material for sensitizer−activator pairs displaying photon upconversion (e.g., Yb3+−Er3+ and Yb3+− Tm3+).4 Despite the key role of the host lattice in mediating energy-transfer processes relevant to photon upconversion (e.g., multiphonon relaxation, phonon-assisted energy migration, and cross-relaxation),5,6 the crystal structure of β-NaREF4 remains a subject of debate. The scientific problem involved in the description of the topology of β-NaREF4 is accurately establishing the cation distribution across the lattice. Structural investigations have been carried out to elucidate the distribution of cations in single-crystal3,7−9 and bulk1,9,10 βNaREF4; computational simulations have been performed as well.11 Despite the potential of β-NaREF4 upconverting nanocrystals in biophotonic applications such as imaging and sensing,12−17 investigation of their crystal structure has comparatively languished. Our work is motivated by two recent investigations of the local structure of β-NaREF4 upconverting nanocrystals, each favoring a different distribution of the cations across the lattice.2,18 Historically, three structural models derived from P6̅2m (No. 189),19 P6̅ (No. 174),7 and P63/m (No. 176)8,9 space groups have been proposed to rationalize the atomic arrangement in βNaREF4. Top and side views of the corresponding unit cells are shown in panels a−c and panels d−f of Figure 1, respectively; additional perspectives are given in the Supporting Information (Figure S1a−c). Metal atoms occupy two different crystallographic sites in the structural model derived from the P6̅2m © 2017 American Chemical Society
space group (Figure 1a). The 1a site is fully occupied by trivalent rare-earth cations (i.e., Y, Er, and Yb). The 2d site is occupied by sodium and rare-earth cations in a 3:1 ratio. Cations in both sites are located within tricapped trigonal prisms formed by nine fluoride anions. Fluoride anions occupy two different crystallographic sites, namely, 3f and 3g. The anionic framework in this space group is preserved in the structural model derived from P6̅, with fluoride anions occupying 3j and 3k sites (Figure 1b). In contrast, the cation distribution changes: metal atoms now occupy three different crystallographic sites. The 1a site is fully occupied by rare-earth cations located within tricapped trigonal prisms. The 1f site is occupied by sodium and rare-earth atoms in a 1:1 ratio. Cations in this site are also located within tricapped trigonal prisms. Finally, the 2h site is occupied by sodium cations and vacancies in a 1:1 ratio. Cations in this site are located within distorted octahedra formed by six fluoride anions and show positional disorder along the c axis, a topological feature not encountered in the structural model derived from the P6̅2m space group. Positional disorder along the c axis is also observed in the 4e site of the structural model derived from the P63/m space group (Figure 1c). This site is occupied by sodium cations and vacancies in a 1:3 ratio, the former being located within distorted octahedra. Sodium cations also share a 2d site with rare-earth cations in a 1:3 ratio. Metal centers in this site are Received: April 11, 2017 Revised: July 10, 2017 Published: July 21, 2017 6289
DOI: 10.1021/acs.chemmater.7b01495 Chem. Mater. 2017, 29, 6289−6297
Article
Chemistry of Materials
Figure 1. Distribution of the sodium cations along the z direction. There is a major difference between the structural models derived from P6̅2m, P6̅, and P63/m space groups. Top (a−c) and side (d−f) views of the three models are shown; side views are depicted using the schematics first adopted in ref 8. Wyckoff positions of the metal and fluorine atoms are indicated throughout. Mirror planes are denoted with m. Site occupancies of the sodium cations are depicted with partially filled circles.
located within tricapped trigonal prisms; fluoride anions occupy site 6h. The distribution of the sodium cations along the c axis is a major difference between the three structural models described above. Sodium cations in space group P6̅2m show no positional disorder along the c axis, while they are disordered over two (four) equivalent positions in P6̅ (P63/m); side views of the corresponding unit cells are given in Figure 1d−f to illustrate this phenomenon. In this work, the nomenclature first introduced by Frank-Kamenetskaya et al. to systematically describe positional disorder of sodium cations in the P6̅ and P63/m space groups was employed.8 The distribution of the cations over a 2-fold (4-fold) position in P6̅ (P63/m) results in forbidden Na−Na distances along the z direction (∼0.96 Å in P6̅; ∼0.67, 1.09, 1.75, and 2.84 Å in P63/m). In the case of the structural model derived from the P6̅ space group, this leads to two chains of sodium cations. Each chain features cations with a Na−Na distance equals to c (∼3.5 Å). The two chains are translation-equivalent but are shifted in the z direction by a distance equal to the forbidden Na−Na distance (see Figure S2). Thus, the distribution of the sodium cations in the P6̅ space group can be described using a two-chain model. The arrangement of sodium cations in each chain consists of alternating full and empty sodium−fluorine distorted octahedra. In the case of the structural model derived from the P63/m space group, the 4-fold multiplicity of the 4e site leads to four chains of sodium cations. The four chains are shifted in the z direction by a distance equal to one of the forbidden Na−Na distances. Alternating full and empty sodium−fluorine distorted octahedra builds up a chain. Thus, the distribution of the sodium cations in the P63/m space group can be described using a four-chain model, reflecting their larger positional disorder relative to its P6̅ counterpart. In this work, the average and local structure of ∼22 nm βEr:Yb:NaYF4 upconverting nanocrystals were probed using a
dual-space approach combining Rietveld and pair distribution function (PDF) analysis of X-ray total scattering. Three competing models derived from P6̅2m, P6̅, and P63/m space groups were used to fit the experimental scattering data. Both Rietveld and PDF analysis support the four-chain model derived from the P63/m space group as an adequate description of the atomic arrangement. This finding is discussed in the context of previous structural investigations of single-crystal, bulk, and nanocrystalline β-NaREF4. The ability of the structural model derived for the mineral gagarinite (NaCaREF6, P63/m)8 to provide a meaningful description of the atomic arrangement in β-Er:Yb:NaYF4 nanocrystals was also investigated. This model features sodium cations distributed over eight chains and, based on our results, may be worth consideration when attempting to describe the atomic arrangement in ultrasmall β-NaREF4 nanocrystals (
