Bending Force Constant of the Carbon Tetrafluoride Molecule

1955 ◽  
Vol 23 (8) ◽  
pp. 1563-1564
Author(s):  
Eiko Aihara
Keyword(s):  
Force Constant ◽  
Carbon Tetrafluoride ◽  
Bending Force

Kinematical evaluation of force constants: application to trihalides of phosphorus and arsenic

1970 ◽  
Vol 23 (5) ◽  
pp. 881 ◽  
Author(s):  
SN Rai ◽  
SN Thakur
Keyword(s):  
Force Constant ◽  
Vibrational Frequencies ◽  
Force Constants ◽  
Arbitrary Parameter ◽  
Two Dimensional ◽  
Matrix Elements ◽  
Bending Force ◽  
Symmetry Species

The F-matrix elements for the two-dimensional symmetry species are dependent on one arbitrary parameter in addition to the vibrational frequencies. This parameter has been chosen as an angle � (0 ≤ � ≤ 2π) and the F-matrix elements for the A1- and the E-species of trihalides of phosphorus and arsenic have been studied as functions of �. It is found that the best values of the force constants obtained from Coriolis 1; constants can be correlated with those values of the angle ξ for which the bending force constant exhibits a minimum.

scholarly journals INTERATOMIC INTERACTIONS AND ZONE CENTRE PHONONS IN MULTIFERROIC BiFeO3 CERAMICS

2013 ◽  
Vol 22 ◽  
pp. 134-139 ◽  
Author(s):  
M. M. SINHA ◽  
RUBY ◽  
H. C. GUPTA
Keyword(s):  
Force Constant ◽  
Ferroelectric Properties ◽  
Compressive Strain ◽  
Potential Energy Distribution ◽  
Bending Force ◽  
Short Range Force ◽  
Multiferroic Bifeo3 ◽  
Zone Centre ◽  
Range Force ◽  
Good Agreement

The existence of an epitaxially stabilized tetragonal-like (“T -like”) monoclinic phase in BiFeO 3 thin films with high levels of compressive strain has been reported recently. While their structural and ferroelectric properties are different from those of rhombohedral-like (“R-like”) films with lower levels of strain, little information exists on magnetic properties. In this study we have applied a short range force constant model by using normal coordinates to investigate the Raman and the infrared wavenumbers in tetragonal BiFeO 3 having space group P4mm (C4v1). The calculation of zone center phonons has been made by using three stretching and six bending force constants. The calculated Raman and infrared wavenumbers are in very good agreement with the observed ones. The potential energy distribution has also been investigated for determining the significance of contribution from each force constant toward the Raman and the infrared wavenumbers.

Vibrational, mechanical and thermodynamical properties of RE2Ti2O7 (RE = Sm, Gd, Dy, Ho, Er and Yb) pyrochlores

2017 ◽  
Vol 31 (21) ◽  
pp. 1750145
Author(s):  
A. K. Kushwaha
Keyword(s):  
Bond Strength ◽  
Bulk Modulus ◽  
Force Constant ◽  
Present Calculation ◽  
Neighbor Interaction ◽  
Thermodynamical Properties ◽  
Bending Force ◽  
Young’S Moduli ◽  
Bond Bending ◽  
The One

Vibrational, mechanical, thermodynamical properties and thermal conductivities of RE2Ti2O7 (RE = Sm, Gd, Dy, Ho, Er and Yb) pyrochlores have been calculated using a proposed eight-parameter bond-bending force constant model. The main outcome of present calculation is that the first neighbor interaction (Ti–O) is stronger than the second neighbor interactions (RE–O). This means that the bonding between Ti and O is more ionic than the one between RE and O. It is also found that the bond strength of RE–O and the bulk modulus decrease in the sequence Sm [Formula: see text] Gd [Formula: see text] Dy [Formula: see text] Ho [Formula: see text] Er [Formula: see text] Yb. The bulk moduli and Young’s moduli of RE2Ti2O7 also decrease when RE changes from Sm to Yb.

Comparison of ring bending strain with infrared bending vibrations

1969 ◽  
Vol 22 (12) ◽  
pp. 2575
Author(s):  
IJ Miller
Keyword(s):  
Force Constant ◽  
Empirical Formula ◽  
Reasonable Agreement ◽  
Bending Vibrations ◽  
Bending Force ◽  
Bending Strain ◽  
Pendulum Dynamics ◽  
Good Agreement

An empirical formula which has been shown to give good values for ring bending strain in small rings has been applied to infrared bending vibrations. The derived dynamics are of a ?pendulum? character, and reasonable agreement is obtained in calculating the C-C-C bending force constant from the empirical formula constant. Resultant anharmonicities are calculated from the ?pendulum? dynamics, and good agreement is obtained with experimentally determined levels up to the 060 level of CO2 and 040 for HCN.

Zero-Point Energy Shifts in Hydrides of the Elements upon H/D Isotope Substitutions and Their Periodicity

1988 ◽  
Vol 43 (5) ◽  
pp. 511-516
Author(s):  
Takao Oi ◽  
Makoto Aikawa ◽  
Hidetake Kakihana ◽  
Takanobu Ishida
Keyword(s):  
Linear Function ◽  
Force Constant ◽  
Periodic Table ◽  
Zero Point ◽  
Type A ◽  
Square Root ◽  
Molecular Type ◽  
Zero Point Energy ◽  
Point Energy ◽  
Bending Force

Periodicities are established among the zero-point energy shifts, δ (ZPE), of AHn (n =1-4) type hydrides of the elements upon mono H/D isotope substitutions. δ (ZPE) for diatomic hydrides is correlated with the position of the element A in the periodic table. The contribution of the A-H stretching force constant to δ (ZPE) is to a good approximation a linear function of the square root of the force constant, irrespective of the molecular type. A similar correlation is also found between the square root of the H-A-H bending force constant and its contribution to δ (ZPE).

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