Magnetic resonance in a cubic Ґ 3 (E) doublet system IV. Improved theory of the nuclear interactions

1982 ◽  
Vol 382 (1782) ◽  
pp. 61-74 ◽  
Keyword(s):  
Magnetic Resonance ◽  
Experimental Studies ◽  
Electronic States ◽  
Electric Quadrupole ◽  
Zero Magnetic Field ◽  
Electric Quadrupole Interaction ◽  
Arbitrary Direction ◽  
Substantial Agreement ◽  
Special Cases ◽  
Octahedral Crystal Field

In previous papers of this series, a study has been made of the theory of magnetic resonance in a Ґ 3 doublet (paper I), together with experimental studies of Cs 2 NaHoCl 6 by n. m. r. (paper II) and by e. s. r. (paper III). In this substance the Ho 3+ ion, 4f 10 , 5 I 8 , is in an octahedral crystal field which gives a Ґ 3 doublet as the ground electronic state. The results, both from enhanced n. m. r. of the 165 Ho nucleus ( I = 7/2) and from e. s. r., provide evidence of fast motional averaging, ascribed to interactions between the ions. The measurements are in substantial agreement with the theory of I; however, though the theory is correct for the electronic levels and transitions, and for the nuclear electric quadrupole interaction in zero magnetic field, it needs improvement in the treatment of the nuclear terms when a field B is applied. In this paper a general theory is developed for the case when B is in an arbitrary direction, together with some special cases that are analytically simpler. These include B along [111], the spectrum of an isolated ion, and the spectrum of a concentrated compound where there are fast flip-flops between the electronic states.

Nuclear Magnetic Resonance in Solid Zinc

1979 ◽  
Vol 34 (8) ◽  
pp. 1029-1030 ◽  
Author(s):  
H. Herberg ◽  
J. Abart ◽  
J. Voitländer
Keyword(s):  
Nuclear Magnetic Resonance ◽  
Magnetic Resonance ◽  
Spin Echo ◽  
Relaxation Times ◽  
Lattice Relaxation ◽  
Electric Quadrupole ◽  
Quadrupole Coupling Constant ◽  
Spin Lattice Relaxation ◽  
Electric Quadrupole Interaction ◽  
Nuclear Magnetic

AbstractThe nuclear magnetic resonance of 67Zn in hexagonal close-packed Zn metal has been observed at 4.2 K by pulsed NMR with three different frequencies. The spin echo profile showed a well resolved powder pattern due to electric quadrupole interaction. The quadrupole coupling constant was determined to be e2 q Q/h = 12.0 (4) MHz. The spin-spin and spin-lattice-relaxation times were measured to be T2 = 58 ± 2 ms and T1 = 0.45 ± 0.2 s, respectively. The isotropic Knight shift is found to have the value Kiso = 0.1 ± 0.05%.

Theoretical and experimental studies of the electronic states of the diatomic cationCl22+

1986 ◽  
Vol 34 (3) ◽  
pp. 1657-1666 ◽  
Author(s):  
P. G. Fournier ◽  
J. Fournier ◽  
F. Salama ◽  
D. Stärk ◽  
S. D. Peyerimhoff ◽  
...  
Keyword(s):  
Experimental Studies ◽  
Electronic States

scholarly journals Nuclear electric-quadrupole interaction of ion-implantedHg203andZn69min graphite

1992 ◽  
Vol 46 (14) ◽  
pp. 8818-8827 ◽  
Author(s):  
B. Kastelein ◽  
M. W. J. Prins ◽  
J. Andriessen ◽  
H. Postma ◽  
L. Klostermann ◽  
...  
Keyword(s):  
Quadrupole Interaction ◽  
Electric Quadrupole ◽  
Electric Quadrupole Interaction

scholarly journals EN The wave model of secondary flows and coherent structures in pipes

2020 ◽  
Vol 55 (5-6) ◽  
pp. 273-281
Author(s):  
S. Surkov
Keyword(s):  
Wave Equation ◽  
Stream Function ◽  
Coherent Structures ◽  
Large Scale ◽  
Experimental Studies ◽  
Viscous Friction ◽  
Orthogonal Decomposition ◽  
Secondary Flows ◽  
Friction Forces ◽  
Special Cases

In this article, a theoretical analysis of the flows arising in the cross sections of fluid and gas flows is performed. Such flows are subdivided into secondary flows and coherent structures. From experimental studies it is known that both types of flows are long-lived large-scale movements (LSM) stretched along the flow. The relative stability of the vortices is traditionally explained by the fact that the viscous friction forces that inhibit the rotation are compensated by the intensification of the swirl when moving slowly rotating peripheral layers to the center of the vortex due to longitudinal tension. An analysis of this mechanism made it possible to develop a relatively simple model of vortex structures in which the viscous friction forces and axial expansion are considered to be infinitesimal. Under these assumptions, one can use the equations of motion of an ideal fluid in the variables “stream function - vorticity”. It is shown that under certain assumptions these equations take the form of a wave equation, and the boundary conditions are the condition that the stream function on the solid walls of the flow equals zero. The obtained solutions of the wave equation describe the following special cases: Goertler’s vortices between rotating cylinders, secondary flows in a pipe with a square cross section, swirling flow in a round pipe, paired vortex after bend of the pipe. The physical sense of more complex solutions of the wave equation has become clear relatively recently. Very similar structures were found in experimental studies using orthogonal decomposition (POD) of a turbulent pulsations field. This may mean that the eigenfunctions in the POD correspond to coherent structures that really arise in the flow. The results obtained confirm the hypothesis that secondary flows and coherent structures have a common nature. The solutions obtained in this paper can be used in processing the experiment as eigenfunctions for the orthogonal decomposition method. In addition, they can be used in direct numerical simulation (DNS) of turbulent flows

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