Mean Amplitudes of Vibration of the
نویسنده
چکیده
Although salts of the PBr4 and PC14 anions are well-known [1-3], a salt of the corresponding fluoroanion could only recently be prepared by reaction between N(CH3)4F and PF3 using either CH3CN, CHF3 or excess PF3 as a solvent [4], and the novel PF4 anion is stabilized in the form of its tetramethylammonium salt, N(CH3)4PF4. It possesses a pseudo-trigonal bipyramidal structure with two longer (1.74 Ä) axial bonds and an equatorial plane containing two shorter P-F bonds (1.60 Ä) and a sterically active free electron pair. As a continuation of our studies concerning vibrational and bond properties of simple novel inorganic species, we have now calculated the mean amplitudes of vibration of this interesting anion in order to attain a wider insight into its bond characteristics and peculiarities. For comparative purposes we have also undertaken a recalculation for the isoelectronic SF4 molecule. The calculations were performed with the method of the characteristic vibrations of Müller and co-workers [5-7]. The necessary vibrational and structural data for PF4 were taken from [4]. For SF4, the structural parameters were taken from [8] and the vibrational data from [9]. The obtained values, in the temperature range between 0 and 1000 K, are shown in Table 1 for PF4 and in Table 2 for SF4. A comparison of the results obtained for SF4 with those previously calculated for this molecule [10] shows Table 1. Calculated mean amplitudes of vibration (in A) for the PF4 anion.
منابع مشابه
Exact analytical approach for free longitudinal vibration of nanorods based on nonlocal elasticity theory from wave standpoint
In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus, it can be used to describe the vibration behavior. Boundaries reflect the propagating waves after incident. Firstly, the governing quation of nanoro...
متن کاملSimulation-based Vibration Sensor Placement for Centrifugal Pump Impeller Fault Detection
In this paper, a simulation-based method is proposed for optimal placement of vibration sensors for the purpose of fault detection in a centrifugal pump. The centrifugal pump is modeled to investigate the effect of vane tip fault on fluid flow patterns numerically. Pressure pulsations are investigated at different locations at the inner surface of the pump before and after the presence of the f...
متن کاملMean Amplitudes of Vibration of the Halogen Molecules
During the last years, we have performed systematic calculations on the vibrational properties of simple molecules and ions containing interhalogen bonds. Surprisingly, during our literature searches we found that detailed information on the mean amplitudes of vibration of the halogen molecules themselves ar not available. In the classic work of Cyvin [1] only a brief mention of these values fo...
متن کاملThe Response of Two-Degree of Freedom Self-Sustained Systems with Quadratic Nonlinearities to a Parametric Excitation (RESEARCH NOTE)
In this study the interaction between self-excited and paramet rically excited oscillations in two-degree-of-freedom systems with quadratic nonlinearities is investigated. The fundamental parametric resonance of the first mode and 3:1 internal resonance is considered, followed by 1:2 internal and parametric resonances of the second mode. The method of multiple time scales is applied to derive f...
متن کاملFree Vibration Analysis of a Nonlinear Beam Using Homotopy and Modified Lindstedt-Poincare Methods
In this paper, homotopy perturbation and modified Lindstedt-Poincare methods are employed for nonlinear free vibrational analysis of simply supported and double-clamped beams subjected to axial loads. Mid-plane stretching effect has also been accounted in the model. Galerkin's decomposition technique is implemented to convert the dimensionless equation of the motion to nonlinear ordinary differ...
متن کاملبکارگیری مدل های مختلف کوپل شدگی سیال - جسم برای بررسی مشخصه های ارتعاشی در ناحیه قفل شدگی
In this paper, several models of structure-fluid coupling are employed to investigate on the vibration behavior of the structure. Using basic equations of vibration and employing a mathematical model, a single degree of freedom system is analyzed. Some parameters of the mathematical model are obtained from test. To examine structure-flow interaction, coupled system of nonlinear second-order dif...
متن کامل