5.2.2.5 Trigonal system: Classes 3m (C{3v}), 32 (D{3}), (-3)m (D{3d})

2005 ◽  
pp. 59-62
Author(s):  
K. Vedam
Keyword(s):  
Trigonal System

Linear elastic eigenstates of the compliance tensor for trigonal crystals

2000 ◽  
Vol 215 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P.S. Theocaris ◽  
D.P. Sokolis
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Symmetric Tensor ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Trigonal System ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Strain Tensors ◽  
Elastic Strain Energy Density

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

Novel Red-Orange Phosphors Na2BaMg(PO4)2:Pr3+: Synthesis, Crystal Structure and Photoluminescence Performance

2018 ◽  
Vol 73 (2) ◽  
pp. 99-103 ◽  
Author(s):  
Lu Pan ◽  
Xiaozhan Yang ◽  
Chaoyue Xiong ◽  
Dashen Deng ◽  
Chunlin Qin ◽  
...  
Keyword(s):  
Crystal Structure ◽  
High Temperature ◽  
Solid State ◽  
Solid State Lighting ◽  
Photoluminescence Properties ◽  
X Ray Diffraction ◽  
Hexagonal Cell ◽  
X Ray ◽  
Trigonal System ◽  
Chromaticity Coordinates

AbstractA series of new red-orange emission phosphors Na2BaMg(PO4)2:Pr3+ were synthesised by a high-temperature solid-state reaction. The crystal structure and photoluminescence properties of these samples were characterised by X-ray diffraction and spectroscopic measurements. This compound holds P3̅m1 space group of the trigonal system with the lattice parameters of hexagonal cell a=0.5304(3) nm and c=0.6989(3) nm. The phosphor emits the strongest peak at 606 nm when excited by 449 nm. The average Commission Internationale de l’Eclairage chromaticity coordinates calculated for the phosphors are (0.52, 0.46). The results demonstrate the potential application of these phosphors in solid-state lighting and other fields.

Syntheses and crystal structures of trigonal rare-earth dioxymonocyanamides, Ln2O2CN2 (Ln=Dy, Ho, Er, Tm, Yb)

2007 ◽  
Vol 22 (1) ◽  
pp. 59-63 ◽  
Author(s):  
Min Li ◽  
Wenxia Yuan ◽  
Jingfang Wang ◽  
Cong Gu ◽  
Huaizhou Zhao
Keyword(s):  
Rare Earth ◽  
Infrared Spectroscopy ◽  
Solid State ◽  
Rietveld Method ◽  
Reaction Pathways ◽  
X Ray Diffraction ◽  
X Ray ◽  
Cell Parameters ◽  
Trigonal System ◽  
Xrd Patterns

Trigonal rare-earth dioxymonocyanamides Ln2O2CN2 (Ln=Dy, Ho, Er, Tm, Yb) were synthesized by the modified solid-state metathesis (SSM) method, in which Ln2O3 and melamine C3N6H6 were mixed and heated at 850 °C in vacuumed silica ampoules. Possible chemical reaction pathways are proposed. X-ray diffraction (XRD) patterns of Ln2O2CN2 were refined using the Rietveld method. Compounds Ln2O2CN2 crystallize in the trigonal system with space group P3m1, Z=1, and cell parameters of a and c varying from 3.7267(1) to 3.6407(1) Å and from 8.1848(3) to 8.1152(3) Å, respectively, as Ln atoms change from Dy to Yb. These compounds have stacking structures of Ln2O22+ and CN22− layers, similar to those of previously reported compounds Ln2O2CN2 (Ln=Ce, Pr, Nd, Sm, Eu, Gd). The presence of CN22− ions has been confirmed by infrared spectroscopy, with two characteristic peaks in the vicinity of 651 and 2075 cm−1.

The New Vanadoborate-supported Hexanuclear Zinc Complex [Zn(teta)]6[(VO)12O6B18O36(OH)6](H2O) · 8H2O

2011 ◽  
Vol 66 (2) ◽  
pp. 115-118
Author(s):  
Xing Liu ◽  
Jian Zhou
Keyword(s):  
Thermogravimetric Analysis ◽  
Water Molecule ◽  
Zinc Complex ◽  
Space Group ◽  
Trigonal System ◽  
Vis Spectroscopy

The new vanadoborate-supported zinc complex [Zn(teta)]6[(VO)12O6B18O36(OH)6](H2O) ・8H2O (1, teta = triethylenetetramine) was synthesized hydrothermally and characterized by elemental and thermogravimetric analysis, and IR and UV/Vis spectroscopy. Complex 1 crystallizes in the trigonal system in space group R3̄ and consists of the neutral [Zn(teta)]6[(VO)12O6B18O36(OH)6](H2O) cage aggregate that is built up from a [(VO)12O6B18O36(OH)6]12− cluster decorated with six [Zn(teta)]2+ complex groups, and a water molecule occupying the center of the cluster cage.

scholarly journals Formation of modified whitlockite-related calcium phosphates under conditions of coprecipitation from aqueous solutions

2021 ◽  
pp. 112-117
Author(s):  
N.Yu. Strutynska ◽  
◽  
M.S. Slobodyanik ◽  
Y.O. Titov ◽  
I.A. Kraievska ◽  
...  
Keyword(s):  
Room Temperature ◽  
Calcium Phosphates ◽  
Aqueous System ◽  
Molar Ratio ◽  
Mass Ratio ◽  
X Ray ◽  
Sodium Cations ◽  
Trigonal System ◽  
Optimized Conditions ◽  
Related Phase

The features of phase formation during wet coprecipitation from aqueous system Сa2+–NO3––Х (Х – NaH2PO4, Na2HPO4, Na3PO4) at the molar ratio Са2+/РО43–=1.6 and room temperature have been investigated. It was found formation of whitlockite-related calcium phosphates (trigonal system, space group R-3c). The results of elemental analysis indicated the chemical modification of calcium phosphates by sodium cations (samples contained 0.3–0.6 wt.% Na+). According to the resulta of thermogravimetry, the synthesized samples contained up to 6 wt.% of sorption water. Heating of samples to the temperature of 6000C is accompanied by water removal and an increase in particle size from 20–50 nm to 500 nm. It was shown that the use of sodium nitrate as a source of sodium cations in the formation of sodium-containing calcium phosphates allows obtaining compositions of whitlockite- and apatite-related phases. The mass ratio of phases can be adjusted by changing the content of sodium cations in the initial solution. The synthesized samples were characterized by X-ray powder diffraction, thermogravimetry, scanning electron microscopy and FTIR spectroscopy methods. Optimized conditions for preparation of whitlockite-related sodium-containing calcium phosphates as well as composites based on them with apatite-related phase can be further used in the development of materials with the required resorption rate for orthopedics.

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