Structure, phase transitions and ionic conductivity of K_3NdSi_6O_(15)·xH_2O. I. α-K_3NdSi_6O_(15)·2H_2O and its polymorphs

Hydrothermally grown crystals of α-K_3NdSi_6O_(15)·2H_2O, potassium neodymium silicate, have been studied by single-crystal X-ray methods. The compound crystallizes in space group Pbam, contains four formula units per unit cell and has lattice constants a = 16.008 (2), b = 15.004 (2) and c = 7.2794 (7) Å, giving a calculated density of 2.683 Mg m^(−3). Refinement was carried out with 2161 independent structure factors to a residual, R(F), of 0.0528 [wR(F^2) = 0.1562] using anisotropic temperature factors for all atoms other than those associated with water molecules. The structure is based on highly corrugated (Si_2O_5^(2−))_∞ layers which can be generated by the condensation of xonotlite-like ribbons, which can, in turn, be generated by the condensation of wollastonite-like chains. The silicate layers are connected by Nd octahedra to form a three-dimensional framework. Potassium ions and water molecules are located in interstitial sites within this framework, in particular, within channels that extend along [001]. Aging of as-grown crystals at room temperature for periods of six months or more results in an ordering phenomenon that causes the length of the c axis to double. In addition, two phase transitions were found to occur upon heating. The high-temperature transformations, investigated by differential scanning calorimetry, thermal gravimetric analysis and high-temperature X-ray diffraction, are reversible, suggesting displacive transformations in which the layers remain intact. Conductivity measurements along all three crystallographic axes showed the conductivity to be greatest along [001] and further suggest that the channels present in the room-temperature structure are preserved at high temperatures so as to serve as pathways for easy ion transport. Ion-exchange experiments revealed that silver can readily be incorporated into the structure

Structure, phase transitions and ionic conductivity of K_3NdSi_6O_(15)·xH_2O. II. Structure of β-K_3NdSi_6O_(15)

Hydrothermally grown crystals of β-K_3NdSi_6O_(15), potassium neodymium silicate, have been studied by single-crystal X-ray methods. Under appropriate conditions, the compound crystallizes in space group Bb2_1m and has lattice constants a = 14.370 (2), b = 15.518 (2) and c = 14.265 (2) Å. There are 30 atom sites in the asymmetric unit of the basic structure. With eight formula units per unit cell, the calculated density is 2.798 Mg m^(-3). Refinement was carried out to a residual, wR(F^2), of 0.1177 [R(F) = 0.0416] using anisotropic temperature factors for all atoms. The structure is based on (Si_2O_5^(2-))∞ layers, connected by Nd polyhedra to form a three-dimensional framework. Potassium ion sites, some of which are only partially occupied, are located within channels that run between the silicate layers. The silica-neodymia framework of β-K_3NdSi_6O_(15), in particular the linkages formed between the silicate layers and Nd polyhedra, bears some similarities to that of the essentially isocompositional phase α-K_3NdSi_6O_(15)·2H_2O. In both, the silicate layers are corrugated so as to accommodate a simple cubic array of NdO_6 octahedra with lattice constant 7.5 Å. Furthermore, the Si_2O_5 layers in β-K_3NdSi_6O_(15) are topologically identical to those of the mineral sazhinite, Na_2HCeSi_6O_(15). Although β-K_3NdSi_6O_(15) and sazhinite are not isostructural, the structures of each can be described as slight distortions of a high-symmetry parent structure with space group Pbmm

Structure, phase transitions and ionic conductivity of K_3NdSi_6O_(15)·xH_2O. I. α-K_3NdSi_6O_(15)·2H_2O and its polymorphs

Hydrothermally grown crystals of α-K_3NdSi_6O_(15)·2H_2O, potassium neodymium silicate, have been studied by single-crystal X-ray methods. The compound crystallizes in space group Pbam, contains four formula units per unit cell and has lattice constants a = 16.008 (2), b = 15.004 (2) and c = 7.2794 (7) Å, giving a calculated density of 2.683 Mg m^(−3). Refinement was carried out with 2161 independent structure factors to a residual, R(F), of 0.0528 [wR(F^2) = 0.1562] using anisotropic temperature factors for all atoms other than those associated with water molecules. The structure is based on highly corrugated (Si_2O_5^(2−))_∞ layers which can be generated by the condensation of xonotlite-like ribbons, which can, in turn, be generated by the condensation of wollastonite-like chains. The silicate layers are connected by Nd octahedra to form a three-dimensional framework. Potassium ions and water molecules are located in interstitial sites within this framework, in particular, within channels that extend along [001]. Aging of as-grown crystals at room temperature for periods of six months or more results in an ordering phenomenon that causes the length of the c axis to double. In addition, two phase transitions were found to occur upon heating. The high-temperature transformations, investigated by differential scanning calorimetry, thermal gravimetric analysis and high-temperature X-ray diffraction, are reversible, suggesting displacive transformations in which the layers remain intact. Conductivity measurements along all three crystallographic axes showed the conductivity to be greatest along [001] and further suggest that the channels present in the room-temperature structure are preserved at high temperatures so as to serve as pathways for easy ion transport. Ion-exchange experiments revealed that silver can readily be incorporated into the structure

Three-Dimensional Analysis of Wakefields Generated by Flat Electron Beams in Planar Dielectric-Loaded Structures

An electron bunch passing through dielectric-lined waveguide generates $\check{C}$erenkov radiation that can result in high-peak axial electric field suitable for acceleration of a subsequent bunch. Axial field beyond Gigavolt-per-meter are attainable in structures with sub-mm sizes depending on the achievement of suitable electron bunch parameters. A promising configuration consists of using planar dielectric structure driven by flat electron bunches. In this paper we present a three-dimensional analysis of wakefields produced by flat beams in planar dielectric structures thereby extending the work of Reference [A. Tremaine, J. Rosenzweig, and P. Schoessow, Phys. Rev. E 56, No. 6, 7204 (1997)] on the topic. We especially provide closed-form expressions for the normal frequencies and field amplitudes of the excited modes and benchmark these analytical results with finite-difference time-domain particle-in-cell numerical simulations. Finally, we implement a semi-analytical algorithm into a popular particle tracking program thereby enabling start-to-end high-fidelity modeling of linear accelerators based on dielectric-lined planar waveguides.Comment: 12 pages, 2 tables, 10 figure

Structure of Na_3NdSi_6O_(15)._2H_2O - A Layered Silicate with Paths for Possible Fast Ion Conductor

Hydrothermal investigations of the high silica region of the Na₂0-Nd₂0₃-SiO₂ system, carried out in the search for new fast-ion conductors (FIC's), yielded the compound Na₃NdSi₆O₁₅.2H₂0 (sodium neodymium silicate). Single-crystal X-ray methods provided lattice constants of a=7.385(2), b=30.831(7) and c= 7.1168 (13)Å, space group Cmm2, and 22 atoms in the asymmetric unit. With four formula units per unit cell, the calculated density is 2.68gcm⁻³. Refinement was carried out with 1113 independent structure factors to a weighted residual wR(F) of 2.63% [8.09% for wR(F²)] using anisotropic temperature factors for all atoms. The structure, based on corrugated Si₆O₁₅ layers containing four-, five-, six- and eight-membered rings, is related to that of a model previously reported for a compound assigned the composition NaNdSi₆O₁₃(OH)₂.nH₂0. Our structure differs in the placement of sodium ions and water molecules, and contains no hydroxyl groups. We believe that both studies examined the same phase

Structure of Na_3YSi_6O_(15) - a Unique Silicate Based on Discrete Si_6O_(15) Units, and a Possible Fast-Ion Conductor

Hydrothermal investigations in the high silica region of the Na₂O-Y₂0₃-Si₆O₁₅ system, carried out in a search for novel fast-ion conductors (FIC's), yielded the new compound trisodium yttrium hexasilicate, Na₃YSi₆O₁₅. Single-crystal X-ray methods revealed that Na₃YSi₆O₁₅ crystallizes in space group Ibmm, has lattice constants a=10.468 (2), b=15.2467 (13) and c=8.3855 (6) Å, Z=4, and 11 atoms in the asymmetric unit. Refinement was carried out to a weighted residual of 3.53% using anisotropic temperature factors for all atoms. The structure is unique in that the silica tetrahedra form isolated SiSi₆O₁₅⁶⁻ double dreier-rings, rather than layers as might be expected from the Si to O ratio of 0.4. No isomorphs to Na₃YSi₆O₁₅ have been reported

Calculation of wakefields in a 17 GHz beam-driven photonic band-gap accelerator structure

We present the theoretical analysis and computer simulation of the wakefields in a 17 GHz photonic band-gap (PBG) structure for accelerator applications. Using the commercial code CST Particle Studio, the fundamental accelerating mode and dipole modes are excited by passing an 18 MeV electron beam through a seven-cell traveling-wave PBG structure. The characteristics of the longitudinal and transverse wakefields, wake potential spectrum, dipole mode distribution, and their quality factors are calculated and analyzed theoretically. Unlike in conventional disk-loaded waveguide (DLW) structures, three dipole modes (TM[subscript 11]-like, TM[subscript 12]-like, and TM[subscript 13]-like) are excited in the PBG structure with comparable initial amplitudes. These modes are separated by less than 4 GHz in frequency and are damped quickly due to low radiative Q factors. Simulations verify that a PBG structure provides wakefield damping relative to a DLW structure. Simulations were done with both single-bunch excitation to determine the frequency spectrum of the wakefields and multibunch excitation to compare to wakefield measurements taken at MIT using a 17 GHz bunch train. These simulation results will guide the design of next-generation high-gradient accelerator PBG structures.United States. Dept. of Energy. High Energy Physics Division (Contract DEFG02- 91ER40648)China. Fundamental Research Funds for the Central Universities (Contract ZYGX 2010J055