Ce Lu Research Articles

Norm-Conserving 4f-in-Core Pseudopotentials and Basis Sets Optimized for Trivalent Lanthanides (Ln = Ce–Lu)

We present here a set of scalar-relativistic norm-conserving 4f-in-core pseudopotentials, together with complementary valence-shell Gaussian basis sets, for the lanthanide (Ln) series (Ce-Lu). The Goedecker, Teter, and Hutter (GTH) formalism is adopted with the generalized gradient approximation (GGA) for the exchange-correlation Perdew-Burke-Ernzerhof (PBE) functional. The 4f-in-core pseudopotentials are built through attributing 4f-subconfiguration 4fn (n = 1-14) for Ln (Ln = Ce-Lu) into the atomic core region, making it possible to circumvent the difficulty of the description of the open 4fn valence shell. A wide variety of computational benchmarks and tests have been carried out on lanthanide systems including Ln3+-containing molecular complexes, aqueous solutions, and bulk solids to validate the accuracy, reliability, and efficiency of the optimized 4f-in-core GTH pseudopotentials and basis sets. The 4f-in-core GTH pseudopotentials successfully replicate the main features of lanthanide structural chemistry and reaction energetics, particularly for nonredox reactions. The chemical bonding features and solvation shells, hydrolysis energetics, acidity constants, and solid-state properties of selected lanthanide systems are also discussed in detail by utilizing these new 4f-in-core GTH pseudopotentials. This work bridges the idea of keeping highly localized 4f electrons in the atomic core and efficient pseudopotential formalism of GTH, thus providing a highly efficient approach for studying lanthanide chemistry in multi-scale modeling of constituent-wise and structurally complicated systems, including electronic structures of the condensed phase and first-principles molecular dynamics simulations.

Influence of rare-earth doping on the structural and dielectric properties of orthoferrite La0.50R0.50FeO3 ceramics synthesized under high pressure

Abstract The effect of co-doping on the structural and dielectric properties of the La0.50R0.50FeO3 orthoferrites for a full number of substitutions (R = Ce–Lu) has been experimentally and theoretically studied using X-ray diffraction, SEM, EDS, and dielectric spectroscopy methods. The La0.50R0.50FeO3 ceramics with R = Nd, Sm, Gd, Dy, and Er, prepared by a solid-state reaction method under cold pressing at high pressure P = 4 GPa, have been taken as a basis. Structural parameters in the La0.50R0.50FeO3 orthoferrites have been obtained using Rietveld refinement of X-ray experimental data with their further approximation by linear dependence. Monotonic change in crystal lattice parameters, orthorhombic distortion degree, global instability index, and Goldschmidt tolerance factor have been observed for all samples doped by different R-cations. With increase in the radius of R-cation, a growth in an average grain size has been detected. The investigation of dielectric properties in a wide frequency range of 10−1–1010 Hz and their theoretical description with determining main mechanisms of dielectric polarization made it possible to establish regularities among a type of doping R-cation, crystal-chemical parameters and dielectric properties. The studied ceramic La0.50R0.50FeO3 samples demonstrate colossal dielectric constant ∼ 104 and relatively small dielectric loss tangent in a low-frequency range. The obtained results can be useful for further application of orthoferrite-based materials as sensor and switching devices.

Energies of Mixing (Interaction Parameters), Substitution Limits, and Phase Stability of Solid Solutions Lu1 − xLnxVO4 (Ln = Ce—Yb, Sc, Y)

The energies of mixing (interaction parameters) and temperature ranges of stability of solid solutions Lu1 − xLnxVO4 (where Ln is a rare-earth element (REE), scandium, or yttrium) with the zircon structure were calculated using the crystal-energy theory of isomorphous miscibility. It was shown that, with increasing atomic number of REE in the Ce—Lu series, the calculated energies of mixing and critical decomposition temperatures of the solid solutions regularly decrease. The substitution limits at various temperatures, the thermodynamic phase stability, and the temperature of transition to a metastable state were determined. The thermodynamic stability diagram of the REE vanadate solid solutions Lu1 − xLnxVO4 was presented. The results of the work can be used for searching the compositions of matrices and activators of new laser and other materials.

ChemInform Abstract: Many Metals Make the Cut: Quaternary Rare‐Earth Germanides RE4M2InGe4 (M: Fe, Co, Ni, Ru, Rh, Ir) and RE4RhInGe4 Derived from Excision of Slabs in RE2InGe2.

AbstractArc‐melting and annealing of the elements (evacuated silica tubes, 800 °C, 1 week) is used to prepare ≈50 new quaternary germanides of the series Ln4M2InGe4 (Ln: Ce—Lu except Eu and Yb; M: Fe, Co, Ni, Ru, Rh, Ir) and a different but closely related series Ln4RhInGe4.

Lattice Enthalpies of Lanthanide Orthovanadates LnVO4

Lattice enthalpies ΔLH° of lanthanide orthovanadates, LnVO4 (Ln = Ce Lu, except Pm) have been determined from the Born-Haber thermochemical cycle and compared with those calculated by an empirical equation. Two different sets of enthalpies of formation of LnVO4, from oxides (Ln2O3, V2O5) and from elements, have been used but the differences in ΔLH° are small. The Born-Haber cycle in both routes yields close values of ΔLH° to those obtained after an empirical equation proposed by Glasser and Jenkins. It has been found that the partial derivative of the lattice enthalpies to the molar volumes corresponds by magnitude and dimension to the shear moduli of these crystals. (doi: 10.5562/cca2298)

Lattice energies and polarizability volumes of lanthanide monoaluminates

Lattice energies ΔLHΘ of the entire series of lanthanide aluminum perovskites LnAlO3, Ln=Ce–Lu, have been determined for the first time by means of the Born–Haber cycle. The results have been compared for LnAlO3 obtained by other methods, with cubic lanthanide sesquioxides (C-Ln2O3) and lanthanide aluminum garnets (Ln3Al5O12). Polarizability volumes αI of LnAlO3 have been estimated by the Clausius–Mossotti equation. It has been found that the partial derivative (∂ΔLHΘ/∂αI)T corresponds by magnitude to an upper limit of elastic moduli of the same crystals.

Lattice energies and crystal-field parameters of lanthanide monosulphides

Madelung ( U M ) and experimental lattice ( U P ) energies have been determined for the series of lanthanide monosulphides (LnS, Ln=Ce—Lu, excluding Pm). Comparative crystal-field (CF) analysis has been performed for the same series in the point-charge model with inclusion of the ground 4f n and the excited 4f n–1 5d configurations. It has been found that the variations of both U M / U P and the CF parameters for the 4f n–1 5d configuration across the lanthanide series exhibit minima for the magnetic semiconductors SmS, EuS, and YbS.

Vibrational spectra and factor group analysis of lanthanide and zirconium phosphates M III0.33Zr 2(PO 4) 3, where M III = Y, La–Lu

Double anhydrous orthophosphates of zirconium and rare earth elements with general formula M III 0.33Zr 2(PO 4) 3, where M III = Y, La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm, Yb, Lu, belonging to the structure type of NaZr 2(PO 4) 3 (NZP), have been synthesized by precipitation method and characterized by Raman and infrared spectroscopy in a crystalline state. Factor group analysis has been carried out for space groups P 3 ¯ , P 3 ¯ c 1 . On the basis of the analysis of possible PO 4 unit vibrations and considering symmetry interrelations among trigonal NZP phases it was shown that due to ordered (Y, Ce–Lu) or quasiordered (La) distribution of lanthanide atoms in the structure type of NaZr 2(PO 4) 3, sp. gr. R 3 ¯ c , leads to the reduction of the symmetry to the space groups P 3 ¯ c 1 or P 3 ¯ correspondingly. The assignments of the internal and external modes of PO 4 3− ions have been made.

Eu 3F 4S 2: Synthesis, crystal structure, and magnetic properties of the mixed-valent europium(II,III) fluoride sulfide EuF 2·(EuFS) 2

Using the method to synthesize rare-earth metal(III) fluoride sulfides MFS ( M=Y, La, Ce–Lu), in some cases we were able to obtain mixed-valent compounds such as Yb 3F 4S 2 instead. With Eu 3F 4S 2 another isotypic representative has now been synthesized. Eu 3F 4S 2 (tetragonal, I4 /mmm, a=400.34(2), c=1928.17(9) pm, Z=2) is obtained from the reaction of metallic europium, elemental sulfur, and europium trifluoride in a molar ratio of 5:6:4 within seven days at 850 °C in silica-jacketed gas-tightly sealed platinum ampoules. The single-phase product consists of black plate-shaped single crystals with a square cross section, which can be obtained from a flux using equimolar amounts of NaCl as fluxing agent. The crystal structure is best described as an intergrowth structure, in which one layer of CaF 2-type EuF 2 is followed by two layers of PbFCl-type EuFS when sheeted parallel to the (001) plane. Accordingly there are two chemically and crystallographically different europium cations present. One of them (Eu 2+) is coordinated by eight fluoride anions in a cubic fashion, the other one (Eu 3+) exhibits a monocapped square antiprismatic coordination sphere with four F − and five S 2− anions. Although the structural ordering of the different charged europium cations is plausible, a certain amount of charge delocalization with some polaron activity has to take place, which is suggested by the black color of the title compound. Temperature dependent magnetic susceptibility measurements of Eu 3F 4S 2 show Curie–Weiss behavior with an experimental magnetic moment of 8.19(5) μ B per formula unit and a paramagnetic Curie temperature of 0.3(2) K. No magnetic ordering is observed down to 4.2 K. In accordance with an ionic formula splitting like (Eu II)(Eu III) 2F 4S 2 only one third of the europium centers in Eu 3F 4S 2 carry permanent magnetic moments. 151Eu-Mössbauer spectroscopic experiments at 4.2 K show one signal at an isomer shift of −12.4(1) mm/s and a second one at 0.42(4) mm/s. These signals occur in a ratio of 1:2 and correspond to Eu 2+ and Eu 3+, respectively. The spectra at 78 and 298 K are similar, thus no change in the Eu 2+/Eu 3+ fraction can be detected.

Incommensurately modulated lanthanide coinage-metal diarsenides. I. CeAu1−δAs2 [δ = 0.015 (2)] – a new distortion variant of the HfCuSi2 type with irregularly stacked cis–trans chains of arsenic atoms

Rare-earth metal coinage-metal diarsenides LnTAs2 (Ln = Y, La, Ce-Lu; T = Cu, Ag, Au) are known to crystallize in structures closely related to the HfCuSi2 type, which comprises a stacking sequence of puckered TAs layers and planar square As nets, separated by the Ln atoms. CeAu(1-delta)As2, with delta = 0.015 (2), shows an incommensurate positional modulation of the arsenic atoms in the planar As nets. Based on X-ray diffraction data on a twinned crystal, a structure model in the monoclinic superspace group P12(1)/m1(alpha0gamma)00 (No. 11.1) with basic unit-cell parameters of a = 5.804 (1), b = 5.814 (1), c = 10.179 (1) A and beta = 90.09 (8) degrees is presented. The components of the modulation wavevector q = alphaa* + 0b* + gammac* are alpha = 0.08 (1) and gamma = 0.39 (1). The structure comprises cis-trans chains and rectangles of As atoms and displays an intricate stacking sequence of the modulated arsenic nets. Rod groups and layer groups of the respective arrangements are identified and the arrangement of different motifs of the modulated As net is discussed.

Ab initio calculation of the total energy and elastic properties of Laves phase C15 Al 2RE (RE = Sc, Y, La, Ce–Lu)

Ab initio calculations for the total energy and elastic properties of the C15-type Al 2RE (RE = Sc, Y, Lanthanide) at T = 0 K have been performed by using the projector augmented-wave (PAW) method within the generalized gradient approximation (GGA). The lattice constants, formation enthalpies, elastic constants, bulk modulus and its pressure derivatives of the C15-type Al 2RE are obtained. Poisson’s ratios, Young’s modulus, shear modulus and the ratios of elastic anisotropy are also estimated in the present work. By using the Debye–Grüneisen model, the Debye temperatures, Grüneisen constants and the coefficients of thermal expansion at T = 300 K are obtained for the C15-type Al 2RE. The present calculated results are in good agreement with reported experimental values and with other theoretical calculations available as well.

Calculation of the thermodynamic properties of B2 AlRE (RE=Sc, Y, La, Ce–Lu)

First-principles calculations for the total energy and elastic constants of the B2-type AlRE (RE=Sc, Y, lanthanide) have been performed at T=0 K by using the projector augmented wave (PAW) method within the generalized gradient approximation (GGA). The Debye temperatures, Grüneisen constants, the temperature dependences of the Gibbs free energy, coefficients of thermal expansion, heat capacities are obtained for the B2-AlRE within the Debye–Grüneisen model. The activation energy of self-diffusion, Poisson's ratio, Debye sound velocities are also evaluated for the B2-AlRE in the present work.

Lanthanoid(III) oxide chloride oxoselenates(IV): A fascinating class of multinary compounds

Compounds in the systems M 3+–O 2−–Cl −–Se 4+ are more than just quaternaries, for they can offer both oxygen that is bonded to selenium(IV) to form discrete [SeO 3] 2− ψ 1-tetrahedra ([SeO 3 E] 2− with E: non-bonding electron pair as pseudo-ligand) and oxygen that is only bonded to the trivalent lanthanoid (M = Ce–Lu) to form regular [OM 4] 10+ tetrahedra. The latter share edges and vertices in most cases to build up cationic chains ([OM 2] 4+ in Cl −-free Tb 2O[SeO 3] 2: a = 1064.57(7) pm, c = 521.56(4) pm, Z = 4, tetragonal, P4 2/ ncm), double strands ([O 2M 3] 5+ in Tb 3O 2Cl[SeO 3] 2: a = 535.16(4) pm, b = 1530.51(9) pm, c = 1081.72(7) pm, Z = 4, orthorhombic, Pnma; Er 3O 2Cl[SeO 3] 2: a = 1498.23(9) pm, b = 1102.04(7) pm, c = 547.95(4) pm, β = 105.515(6)°, Z = 4, monoclinic, C2/ c) or layers ([O 3M 4] 6+ in Yb 4O 3Cl 2[SeO 3] 2: a = 853.87(6) pm, b = 1145.92(8) pm, c = 1195.46(8) pm, α = 68.132(6)°, β = 78.113(6)°, γ = 85.748(6)°, Z = 2, triclinic, P 1 ¯ , [O 4M 5] 7+ in Tb 5O 4Cl 3[SeO 3] 2: a = 1229.13(8) pm, b = 546.17(4) pm, c = 978.79(6) pm, β = 90.485(6)°, Z = 2, monoclinic, C2/ m; [O 8M 9] 11+ in Gd 9O 8Cl 3[SeO 3] 4: a = 680.17(5) pm, b = 882.86(7) pm, c = 960.18(7) pm, α = 97.241(6)°, β = 95.539(6)°, γ = 96.265(6)°, Z = 1, triclinic, P 1 ¯ ; [O 3M 3] 3+ in CsEu 4O 3Cl 3[SeO 3] 2: a = 545.09(4) pm, b = 879.98(7) pm, c = 1597.45(9) pm, α = 81.036(6)°, β = 89.992(6)°, γ = 71.925(6)°, Z = 2, triclinic, P 1 ¯ ). On the other hand and much like in the pure lanthanoid(III) oxoselenates(IV) M 2[SeO 3] 3 themselves, segregation of the stereochemically active non-bonding electron pairs (one per Se 4+ cation) of the pyramidal [SeO 3] 2− units occurs, such that “lone-pair” channel or layer structures emerge. Sometimes even the “lone-pair” electrons of the chloride anions help to construct these structural features as also observed in the O 2−-free chloride oxoselenates(IV) MCl[SeO 3].

First-principles electronic structure calculations of [formula omitted] (R being the rare-earth elements Ce–Lu)

The paramagnetic electronic structure calculations of the R 3 Al 5 O 12 ( R = Ce – Lu , the rare-earth elements) systems by substituting Y atoms in Y 3 Al 5 O 12 ( YAG ) with R atoms, using the tight-binding linearized muffin-tin orbital (TB-LMTO) method within local density approximation (LDA) have been reported. Our calculated band structure and density of states (DOS) for the doped systems clearly show that the ground state of the R = Ce – Yb systems are metallic while the R = Lu system (it has completely filled 4f states) is insulating. This insulating phase of Lu 3 Al 5 O 12 is in very good agreement with the experimental results. Our calculations correctly brings out the narrow bandwidth feature of 4f states. Our studies clearly show that the position of the O-2s/p in YAG remains intact while substitution, the O-2p and R-4f energy gap remains almost the same up to near half filling of 4f states ( R = Ce – Pm ) , from then it decreases continuously up to R = Yb and finally it becomes zero for R = Lu (insulator) due to a strong hybridization between the O-2p and Lu-4f states. Our calculated cohesive energy ( E coh ) per molecule for these systems decreases from R = Ce – Sm (up to half filling of 4f bands) then increases from R = Sm – Tb , decreases from R = Tb – Yb (more than half filling) and finally increases for R = Lu , which is an insulator. This decreasing and increasing trend of E coh is exactly similar to that of the rare-earth elemental solids, indicating that the rare-earth elements in the YAG system plays crucial role in deciding the physical properties of the doped systems. However, there are no experimental results available to our knowledge to compare our results.

Peculiarities of the growth of disordered Na, R-fluorite (R=Y, Ce–Lu) single crystals

Single crystals of rare-earth ions doped over a wide concentration range Na 0.4R 0.6F 2.2 (R=Y, Lu) have been grown by the Bridgman technique. Temperature fields in the growth zone were investigated and modified for obtaining high optical quality crystals of this type. Vacuum ultraviolet absorption spectra were measured for the undoped crystal hosts. Some spectroscopic features of the Ce 3+-doped Na 0.4Lu 0.6F 2.2 crystals were determined.

New Complexes of Rare Earth Elements with 3-Methyladipic Acid

Rare earth element 3-methyladipates were prepared as crystalline solids with general formula Ln2(C7H10O4)3⋅nH2O, where n=6 for La, n=4 for Ce,Sm–Lu, n=5 for Pr, Nd and n=5.5 for Y. Their solubilities in water at 293 K were determined (2⋅10–3–1.5⋅10–4 mol dm–3). The IR spectra of the prepared complexes suggest that the carboxylate groups are bidentate chelating. During heating the hydrated 3-methyladipates lose all crystallization water molecules in one (Ce–Lu) or two steps (Y) (except of La(III) complex which undergoes tomonohydrate) and then decompose directly to oxides (Y, Ce) or with intermediate formation of oxocarbonates Ln2O2CO3 (Pr–Tb) or Ln2O(CO3)2 (Gd–Lu). Only La(III) complex decomposes in four steps forming additionally unstable La2(C7H10O4)(CO3)2.

The ab initio model potential method: Lanthanide and actinide elements

In this paper we present relativistic core ab initio model potentials based on atomic Cowan–Griffin calculations, together with Wood–Boring spin-orbit operators and optimized Gaussian valence basis sets, for the lanthanide elements Ce to Lu and for the actinide elements Th to Lr. This completes the chemically relevant part of the Periodic Table. A [Kr,4d] core was chosen for Ce–Lu and a [Xe,4f,5d] core was chosen for Th–Lr. Minimal (14s10p9d8f )/[2s1p1d1f] and (14s10p11d9f )/[2s1p1d1f] valence basis sets were, respectively, optimized for Ce–Lu and Th–Lr, and a [6s5p5d4f] contraction is recommended for all these 28 elements in molecular calculations. The atomic and molecular results show the same good quality already observed for the main-group elements and the transition metal elements.

Spectral and thermal studies of rare earth complexes with 2,4,6-trimethylbenzoic acid

The rare earth element 2,4,6-trimethylbenzoates were prepared as solids with the general formula Ln(C10 H11 O2 )3 ×n H2 O, where n =2 for Ln =Y, La–Nd, and n =1 for Ln =Sm–Lu. The IR spectra of the complexes prepared were recorded and their solubilities in water and thermal decomposition in the air were investigated. During heating the hydrated complexes lose all the crystallization water molecules in one (Y, Ce–Lu) or two steps (La) and then the anhydrous complexes decompose either directly to oxides (Y, Ce, Pr, Sm–Lu) or with intermediate formation oxocarbonates Ln2 O2 CO3 (La, Nd). The carboxylate groups in the complexes prepared act probably as mono- and bidentate.

Spectroscopic and Thermal Studies of Y(III) and Lanthanide(III) Complexes with 3,4-Dichlorobenzoic Acid

The tris(3,4-dichlorobenzoate) complexes of Y(III) and (La-Lu)(III) were prepared. Their solubilities in water at 293 K were determined (6.57×10−4–3.04×10−4 molċdm−3). The IR spectra suggest that the carboxylate ligand is bidentate. The dihydrated complexes (Y, Ce–Lu) are dehydrated in one step, the tetrahydrated La complex in two steps. The anhydrous compounds decompose to oxides Ln 2O3, Pr6O11, and Tb4O7 (Y, La, Pr–Lu) with intermediate formation of LnOCl or directly to the oxide in the case of Ce (CeO2)

Solution enthalpies of hydrates LnCl 3· xH 2O (Ln=Ce–Lu)

Trichlorides of the lanthanide elements Ln=Ce–Lu form: (a) isotypic hexahydrates LnCl 3·6H 2O with a coordination number (CN) 8 for the Ln 3+ ions. (b) Two isotypic groups of trihydrates LnCl 3·3H 2O, in the first group Ln=Ce-Dy the CN is 8; the structure of the second group Ln=Er–Lu is unknown. With Ho no trihydrate exists; a dihydrate is formed. (c) Two isotypic groups of monohydrates LnCl 3·H 2O with unknown structure – Ln=Ce–Dy and Ln=Ho–Lu. For all compounds and for anhydrous chlorides LnCl 3 solution enthalpies were measured with an isoperibolic calorimeter. The Δ sol H 0 values do not depend only on the difference (lattice enthalpies/hydration enthalpies), but also on the state in solution. According to Spedding the CN of the Ln 3+ ions against water changes from 9 to 8 between Nd and Sm, causing minima in the series of solution enthalpies. Dihydrates LnCl 3·2H 2O are found for Ln=Ce, Pr, Nd, Sm and presumably for Eu and Gd. They are not yet well characterised.