Erratum: An Improvement on the article Taxi Cab Geometry: History and Applications, TMME, Vol2, no.1, p. 38 - 64

As a high school student from Germany I did a Mathematics research paper entitled Taxicab Geometry: Fundamentals and Applications. During my research I found the article Taxicab Geometry: History and Applications by Chip Reinhardt which was published in the edition Vol.2, no. 1 (p. 38 – 64) of this journal. The article was very helpful for my coursework and I’d like to compliment the author and everyone who is involved in the journal on their work. In my coursework I created an application example similar to the one Chip Reinhardt used in his article. I solved my example in the same way Mr. Reinhardt solved his, but I made some improvements. In his article there were some errors in calculations which I revised. In the following article I’d like to suggest a rectified solution to Chip Reinhardt’s example

Crystal structure of lutetium disilicate, Lu2Si2O7

Lu2O7Si2, monoclinic, C12/m1 (No. 12), a 6.762(2) Angstrom, b = 8.835(3) Angstrom, c = 4.711(2) Angstrom, beta = 101.99(4)degrees, V = 275.3 Angstrom(3), Z = 2, R-gt(F) = 0.019, wR(ref)(F-2) = 0.045, T = 293 K

Darstellung und Kristallstruktur von Nd2SeSiO4

Nd2SeSiO4 has been prepared as violet rod-like single crystals by reaction of elemental neodymium, selenium and iodine in the ratio 1.0:1.0:2.5 and subsequent reaction with quartz glass powder. The compound crystallizes in the orthorhombic space group Pbcm with a = 618.2(2), b = 717.4(2), c = 1102.4(2) pm and Z = 4. The structure is built up of alternating NdSe- and NdSiO4-sheets

Ligand field density functional theory calculation of the 4f2 → 4f15d1 transitions in the quantum cutter Cs 2KYF6:Pr3+

Herein we present a Ligand Field Density Functional Theory (LFDFT) based methodology for the analysis of the 4fn → 4f n-15d1 transitions in rare earth compounds and apply it for the characterization of the 4f2 → 4f15d 1 transitions in the quantum cutter Cs2KYF 6:Pr3+ with the elpasolite structure type. The methodological advances are relevant for the analysis and prospection of materials acting as phosphors in light-emitting diodes. The positions of the zero-phonon energy corresponding to the states of the electron configurations 4f2 and 4f15d1 are calculated, where the praseodymium ion may occupy either the Cs+-, K+- or the Y3+-site, and are compared with available experimental data. The theoretical results show that the occupation of the three undistorted sites allows a quantum-cutting process. However size effects due to the difference between the ionic radii of Pr3+ and K+ as well as Cs + lead to the distortion of the K+- and the Cs +-site, which finally exclude these sites for quantum-cutting. A detailed discussion about the origin of this distortion is also described. © 2013 The Owner Societies

Ligand field density functional theory calculation of the 4f2 → 4f15d1 transitions in the quantum cutter Cs 2KYF6:Pr3+

Herein we present a Ligand Field Density Functional Theory (LFDFT) based methodology for the analysis of the 4fn → 4f n-15d1 transitions in rare earth compounds and apply it for the characterization of the 4f2 → 4f15d 1 transitions in the quantum cutter Cs2KYF 6:Pr3+ with the elpasolite structure type. The methodological advances are relevant for the analysis and prospection of materials acting as phosphors in light-emitting diodes. The positions of the zero-phonon energy corresponding to the states of the electron configurations 4f2 and 4f15d1 are calculated, where the praseodymium ion may occupy either the Cs+-, K+- or the Y3+-site, and are compared with available experimental data. The theoretical results show that the occupation of the three undistorted sites allows a quantum-cutting process. However size effects due to the difference between the ionic radii of Pr3+ and K+ as well as Cs + lead to the distortion of the K+- and the Cs +-site, which finally exclude these sites for quantum-cutting. A detailed discussion about the origin of this distortion is also described. © 2013 The Owner Societies

Zur Polymorphie von TbCl3

3 different modifications of TbCl3 were synthesized. TbCl3 (UCl3type). probably in a metastable state, crystallizes in space group P63/m with a = 737.63(2) pm, c = 405.71(2) pm and Z = 2. TbCl3(PuBr3-type) crystallizes in space group Cmcm with a = 384.71(6) pm, b = 1177.37(7) pm, c = 851.77(4) pm and Z = 4. h-TbCl3, the high temperature phase being stable above 790 K, crystallizes in space group P42/mnm with a = 642.51(4) pm, c = 1177.14(18) pm and Z = 4. © 1988, Walter de Gruyter. All rights reserved

Synthesis, crystal structure and magnetic behaviour of dimeric and polymeric gadolinium trifluoroacetate complexes

The gadolinium(III) trifluoroacetates ((CH3)2NH 2)[Gd(CF3COO)4] (1), ((CH3) 3NH)[Gd(CF3 COO)4(H2O)] (2), Gd(CF3COO)3(H2O)3 (3) as well as Gd2(CF3COO)6(H2O) 2(phen)3 · C2H5OH (4) (phen = 1,10-phenanthroline) were synthesized and structurally characterized by X-ray crystallography. These compounds crystallize in the space group P1 (No. 2, Z = 2) (1, 2 and 4) and P 21/c (No. 14, Z = 4) (3), respectively, with the following lattice constants 1: a = 884.9(2), b = 1024.9(2), c = 1173.1(2) pm, α = 105.77(2), β = 99.51(2), γ = 107.93(2)°; 2: a = 965.1(1), b = 1028.6(1), c = 1271.3(2) pm, α = 111.83(2), β = 111.33(2), γ = 90.44(2)°; 3: a = 919.6(2), b = 1890.6(4), c = 978.7(2) pm, β = 113.94(2)°; 4: a = 1286.7(8), b = 1639.3(8), c = 1712.2(9) pm, α = 62.57(6), β = 84.13(5), γ = 68.28(5)°. The compounds consist of Gd3+ ions which are bridged by carboxylate groups either to chains (1 and 2) or to dimers (3 and 4). In addition to the Gd3+ dimers, compound (4) also contains monomeric Gd3+ units. The magnetic behaviour of 2 and 3 was investigated in a temperature range of 1.77 to 300 K. The magnetic data for these compounds indicate weak antiferromagnetic interactions. © 2006 Verlag der Zeitschrift für Naturforschung

Darstellung und Struktur von (CH3NH3)3PrCl6. 2 H20

(CH3NH3)3PrCl6 · 2 H2O has been prepared as light green, air sensitive crystals by the reaction of PrCl3·xH2O with [CH3NH3]Cl in ethanol. The compound was characterized by crystal structure determination. Crystal data: monoclinic space group I 2/a, Z = 8. Lattice constants: a = 1963.3(4), b = 925.9(3), c = 1954.3(4) pm, β = 90.56(1)°. The compound forms [PrCl4(H2O)2]--chains where two Pr3+-ions are connected via two chlorine atoms. The magnetic behaviour of (CH3NH3)3PrCl6· 2H2O has been studied

Darstellung und Kristallstruktur von NdSe1.9

NdSe1,9 has been prepared as grey, strongly reflecting platelets by reaction of elemental neodymium with selenium in the ratio 1 :2 and subsequent chemical vapour phase transport with iodine. It crystallizes in the tetragonal space group P42/n with a = 925.36(7), c = 1679.2(3) pm and Z = 20. The structure determination results in a formulation of NdSe1,9 as Nd 20(Se(I)2)8Se(I)2⃞2Se(II)20, where the defect layer built from the Se(I)22- and Se(I)2- ions corresponds to the F layer in the PbFCl substructure

The angular overlap model extended for two-open-shell f and d electrons

We discuss the applicability of the Angular Overlap Model (AOM) to evaluate the electronic structure of lanthanide compounds, which are currently the subject of incredible interest in the field of luminescent materials. The functioning of phosphors is well established by the f–d transitions, which requires the investigation of both the ground 4fn and excited 4fn−15d1 electron configurations of the lanthanides. The computational approach to the problem is based on the effective Hamiltonian adjusted from ligand field theory, but not restricted to it. The AOM parameterization implies the chemical bonding concept. Focusing our interest on this interaction, we take the advantages offered by modern computational tools to extract AOM parameters, which ensure the transparency of the theoretical determination and convey chemical intuitiveness of the non-empirical results. The given model contributes to the understanding of lanthanides in modern phosphors with high or low site symmetry and presents a non-empirical approach using a less sophisticated computational procedure for the rather complex problem of the ligand field of both 4f and 5d open she