Nicolás Flores-González, Javier Castells-Gil, Bo Dong, Wilgner Lima da Silva, Alex J. Green, Shilpi Sengupta, Peter J. Baker, Ivan da Silva, Duncan Gregory, Peter Slater. “Li⁺ dynamics in LiTa₂PO₈ probed by μ⁺SR.” ChemRxiv (). https://doi.org/10.26434/chemrxiv.15007619/v1

LiTa₂PO₈
PND Rietveld refinement (GEM, room temperature), unit cell a = 9.7142(1) Å, b = 11.5329(1) Å, c = 10.6969(1) Å, β = 90.012(1)°, volume = 1198.41(2) ų
PND Rietveld structural model C2/c
PND Rietveld refinement (GEM, room temperature), fit Overall Rwp = 2.27 %, GOF = 1.22
PND and PXD, Li₃PO₄ impurity PND: observed and accounted for, < 1 wt. %; PXD: not observed
PND Rietveld refinement, Ta1 (8f) x = 0.2462(1), y = 0.0955(1), z = 0.2546(2), S.O.F = 1, Biso = 0.30(2) Ų
PND Rietveld refinement, Ta2 (4e) x = 0, y = 0.3465(1), z = 0.25, S.O.F = 1, Biso = 0.44(2) Ų
PND Rietveld refinement, Ta3 (4a) x = 0, y = 0, z = 0, S.O.F = 1, Biso = 0.47(2) Ų
PND Rietveld refinement, P1 (8f) x = 0.4976(3), y = 0.2083(2), z = 0.0601(2), S.O.F = 1, Biso = 0.51(1) Ų
PND Rietveld refinement, O1 (8f) x = 0.4432(2), y = 0.1660(2), z = −0.0675(2), S.O.F = 1, Biso = 0.87(1) Ų
PND Rietveld refinement, O2 (8f) x = 0.5440(2), y = 0.33688(2), z = 0.0501(2), S.O.F = 1, Biso = 0.87(1) Ų
PND Rietveld refinement, O3 (8f) x = 0.3789(2), y = 0.2012(2), z = 0.1520(2), S.O.F = 1, Biso = 0.87(1) Ų
PND Rietveld refinement, O4 (8f) x = 0.619(2), y = 0.1373(1), z = 0.096(1), S.O.F = 1, Biso = 0.87(1) Ų
PND Rietveld refinement, O5 (8f) x = 0.359(1), y = 0.511(1), z = 0.1291(9), S.O.F = 1, Biso = 1.10(1) Ų
PND Rietveld refinement, O6 (8f) x = 0.141(1), y = 0.2363(2), z = 0.2879(2), S.O.F = 1, Biso = 1.10(1) Ų
PND Rietveld refinement, O7 (8f) x = 0.1365(6), y = 0.0571(2), z = 0.1126(2), S.O.F = 1, Biso = 1.10(1) Ų
PND Rietveld refinement, O8 (8f) x = 0.1322(3), y = 0.4672(2), z = 0.2828(2), S.O.F = 1, Biso = 1.10(1) Ų
PND Rietveld refinement, Li1 (8f) x = 0.755(1), y = 0.622(1), z = 0.571(1), S.O.F = 0.41(1), Biso = 6.7(3) Ų
PND Rietveld refinement, Li2 (8f) x = 0.762(2), y = 0.849(2), z = 0.148(2), S.O.F = 0.59(1), Biso = 6.7(3) Ų
Raman spectroscopy (room temperature, 633 nm), PO₄ tetrahedra symmetrical and asymmetrical internal stretching modes Above 1000 cm⁻¹
Raman spectroscopy (room temperature, 633 nm), TaO₆ octahedra symmetrical and asymmetrical internal stretching modes Typically occur between 800 and 950 cm⁻¹
Raman spectroscopy (room temperature, 633 nm), TaO₆ and PO₄ bending modes Over the 500 and 700 cm⁻¹ range
Raman spectroscopy (room temperature, 633 nm), cage modes 350–500 cm⁻¹; associated with Li⁺ ions in LiO₅ trigonal bipyramid, LiO₄ tetrahedral, and LiO₄ square planar environments
Raman spectroscopy (room temperature, 633 nm), lattice modes Below 350 cm⁻¹; assigned to O–Ta–O and O–Li–O vibrations with maxima at approximately 125 cm⁻¹ and 205 cm⁻¹, respectively
DR-UV–vis spectroscopy (190–1300 nm), Tauc analysis Direct optical band gap 4.26 eV; indirect optical band gap 4.20 eV
μ⁺SR (ZF and LF 5 and 10 G), 50 K simultaneous dynamic Gaussian Kubo–Toyabe, exponential muonium-relaxation, and flat-background fit A_KT = 0.22(1), A_BG = 0.037(13), Aμ = 0.0329(1), Δ = 0.092(3), ν = 0.046(9), λ = 0.40(3)
μ⁺SR fit parameter definitions A_KT, Aμ, and A_BG are the asymmetries associated with dynamic Gaussian Kubo–Toyabe, muonium, and background contributions, respectively; Δ is the static width of the local field distribution; ν is the field fluctuation rate; λ is the muonium relaxation rate
μ⁺SR fit conditions across temperature A_BG was fixed to 0.037 while the other terms were allowed to vary freely; above 175 K, the exponential relaxation term was omitted from subsequent analyses at higher temperatures
μ⁺SR, muonium contribution Observed as an exponential decay in an early time domain from a rapidly relaxing muonium signal; progressively decreased with increasing temperature and became negligible above 175 K
μ⁺SR, static width of the local field distribution at 250 K Between 75–250 K, the magnitude did not change significantly; Δ = 0.0936(9) MHz at 250 K
TF μ⁺SR (100 G) Abragam-model inverse correlation times and ZF/LF fluctuation rates 175 K: 1/τc = 0.13(1) MHz, ν = 0.111(5) MHz; 200 K: 1/τc = 0.21(2) MHz, ν = 0.195(7) MHz; 230 K: 1/τc = 0.26(2) MHz, ν = 0.259(9) MHz; 250 K: 1/τc = 0.36(3) MHz, ν = 0.31(1) MHz
μ⁺SR fluctuation-rate fit relation ν(T) = A + B exp(−Eₐ/kBT)
μ⁺SR fluctuation-rate Arrhenius fit, approximately 150–210 K Activation energy 0.113(10) eV
μ⁺SR fluctuation-rate Arrhenius fit, 210–290 K Activation energy 0.300(25) eV
μ⁺SR, Li⁺ hopping rate at 290 K ν = 0.69 MHz