A theoretical analysis of the mechanical relaxation of single-crystalline ice

1958 ◽  
Vol 247 (1251) ◽  
pp. 462-464 ◽  
Keyword(s):  
Relaxation Time ◽  
Loss Factor ◽  
Mechanical Deformation ◽  
Lattice Defects ◽  
Mechanical Relaxation ◽  
Hydrogen Atoms ◽  
Maximum Loss ◽  
Maximum Value ◽  
Modes Of Vibration ◽  
Characteristic Maximum

Kneser, Magun & Ziegler (1955) have found a mechanical relaxation of single crystals of ice. Torsional vibrations of cylindrical specimens, cut parallel to the c -axis, were employed and the logarithmic decrement showed the characteristic maximum associated with a single relaxation time. Similar results have since beer obtained by Schiller (yet unpublished) for various modes of vibration and various crystallographic orientations. The frequency for maximum loss factor and the energy of activation are approximately equal for the mechanical and dielectric relaxation. It seems obvious to associate both relaxations with movements of the hydrogen atoms. In the mechanical case, this may be done in two different ways. As a first possibility I have assumed that an equilibrium exists between a large number of possible hydrogen arrangements and that this equilibrium is disturbed by and mechanical deformation of the crystal lattice. The rearrangement of the hydrogen atoms throughout the lattice then gives rise to the observed relaxation. A second possible mechanism is connected with the distribution of lattice defects such as doubly occupied and vacant bonds between neighbouring oxygen atoms. Normally the probability of finding a given type of defect on a given bond would be approxi­mately the same for all bonds. In the deformed lattice, bonds with a certain orientation would be preferred and the resulting rearrangement of the defects would cause the observed relaxation. With the first mechanism, lattice defects can serve as catalysts in bringing about configurational changes and their presence (in small numbers) will thus affect the relaxation time, but not the magnitude of the decrement. With the second mechanism, however, the magnitude of the decrement is proportional to the number of defects present. I have calculated the maximum value of the decrement for the first mechanism, which implies a general rearrange­ment of the hydrogen atoms, and shall show that the result agrees well with the measurements. On the other hand, estimates based on the second mechanism are clearly inconsistent with the experimental evidence.

Pressure dependence of iodine nuclear relaxation in rubidium iodide

1978 ◽  
Vol 56 (10) ◽  
pp. 1386-1389
Author(s):  
Marie D'Iorio ◽  
Robin L. Armstrong
Keyword(s):  
Relaxation Time ◽  
Lattice Relaxation ◽  
Low Pressure ◽  
Lattice Relaxation Time ◽  
Lattice Defects ◽  
Spin Lattice Relaxation ◽  
Polymorphic Phase Transition ◽  
Spin Lattice Relaxation Time ◽  
Spin Lattice ◽  
Pressure Phase

The pressure-induced polymorphic phase transition at about 4 k bar in rubidium iodide was studied using nuclear magnetic resonance. The signature of the structural transition is a loss of echo intensity which presumably is due to an increase in the number of lattice defects as a result of the transition. The ratio of the spin–spin relaxation times of the iodine nuclei in the two phases is in agreement with the ratio predicted by a second moment calculation. The actual experimental values, however, are considerably smaller than the theoretical predictions signifying the migration of lattice defects. Estimates of the iodine spin–lattice relaxation time at atmospheric pressure indicate the necessity to include both an anharmonic Raman contribution and a covalency factor. The change in spin–lattice relaxation time with pressure as measured in the low pressure phase is dominated by the change in the lattice parameter. At the critical pressure the spin–lattice relaxation time decreases by a fractional amount which is approximately equal to the fractional volume change characterizing the transition. The pressure derivative of the spin–lattice relaxation time in the high pressure phase is nearly equal to that in the low pressure phase.

The two coefficients of viscosity for an incompressible fluid containing air bubbles

1954 ◽  
Vol 226 (1164) ◽  
pp. 34-37 ◽  
Keyword(s):  
Relaxation Time ◽  
Incompressible Fluid ◽  
Small Proportion ◽  
Incompressible Fluids ◽  
Air Bubbles ◽  
Maximum Value ◽  
Volume Viscosity ◽  
Coefficient Of Viscosity ◽  
Surrounding Fluid

Incompressible fluids possess only one coefficient of viscosity because, by definition, no changes in volume can occur. If such a fluid contains air bubbles it becomes compressible, and any changes in volume involves a contraction or expansion of the bubbles which is resisted by the ordinary viscosity of the surrounding fluid. The resulting second coefficient of viscosity is found to be 4μ/3v, where μ is the viscosity of the incompressible fluid and v the (small) proportion of the total volume which is occupied by the bubbles. The effect of compressibility in the fluid is discussed in Notes by Sir Geoffrey Taylor and Dr R. O. Davies. In the second of these it is shown that a relaxation time must exist and in the first the volume viscosity of water containing air bubbles is calculated. This is found to reach a maximum value of 6700 times the viscosity of water when v = 5 x 10 -5 .

Mechanical Relaxation Studies of Sub-Rouse Modes in Amorphous Polymers

2012 ◽  
Vol 184 ◽  
pp. 52-59 ◽  
Author(s):  
Xue Bang Wu ◽  
Hua Guang Wang ◽  
Chang Song Liu ◽  
Zhen Gang Zhu
Keyword(s):  
Relaxation Time ◽  
Coupling Model ◽  
Amorphous Polymers ◽  
Large Temperature ◽  
Mechanical Relaxation ◽  
Segmental Motion ◽  
Mechanical Spectroscopy ◽  
Segmental Dynamics ◽  
Frequency Scale ◽  
Segmental Relaxation

Mechanical spectroscopy is a powerful tool for the investigation of molecular dynamics of amorphous polymers over a large temperature range and frequency scale. In this work, by using high precision shear mechanical spectroscopy tool, we have investigated the segmental dynamics from local segmental relaxation to sub-Rouse modes in a series of amorphous polymers. We have demonstrated the existence of sub-Rouse modes slower than the local segmental motion in amorphous polymers. The sub-Rouse modes exhibit a similar change of dynamics at the same temperature TB ~1.2 Tg, as the local segmental relaxation through the temperature dependence of relaxation time and relaxation strength. Furthermore, the crossover relaxation time of the sub-Rouse modes at TB is almost the same for all the polymers investigated, i.e. τα'(TB) = 10-1±0.5 s, which is independent of molecular weight and molecular structure. This remarkable finding indicates that solely the time scale of the relaxation determines the change in dynamics of the sub-Rouse modes. According to the coupling model, the crossover is suggested to be caused by the onset of strong intermolecular cooperativity below TB. Hence the results suggest that the sub-Rouse modes and their properties are generally found in amorphous polymers by mechanical spectroscopy, and reveal the cooperative nature of the sub-Rouse modes.

scholarly journals Structural optimization to maximize loss factor of embedded co-cured damping composite

2019 ◽  
Vol 11 (11) ◽  
pp. 168781401989212
Author(s):  
Shaoqing Wang ◽  
Sen Liang ◽  
Qiang Li
Keyword(s):  
Loss Factor ◽  
Strain Energy ◽  
Stress Component ◽  
Ritz Method ◽  
Present Formulation ◽  
Total Thickness ◽  
The Finite Element Method ◽  
Maximum Loss ◽  
Structure Thickness ◽  
Optimal Value

The purpose of this study is to obtain the maximum loss factor of the embedded co-cure damping composite structure with the boundary condition of four edges clamped. To achieve this goal, the strain energy of each stress component is deduced using the Ritz method, and the loss factor of the structure is calculated. The present formulation is validated based on the results obtained using the finite element method. Finally, the law of loss factor variation with the change in structure thickness and layup angle is obtained. The results obtained show that the loss factor of the structure increases as the thickness of the structure increases; when the total thickness of the structure is constant, the loss factor increases first and then decreases, and there is an optimal value for the design; the optimal lay angle is pi/4.

scholarly journals Spin-Gitter-Relaxationszeit T1 von Nitrilkohlenstoffen / Spin-Lattice-Relaxation Time T1 of Nitrile Carbon-atoms

1979 ◽  
Vol 34 (3) ◽  
pp. 375-379 ◽  
Author(s):  
H. Sterk ◽  
J. Kalcher ◽  
G. Kollenz ◽  
H. Waldenberger
Keyword(s):  
Relaxation Time ◽  
Correlation Time ◽  
Lattice Relaxation ◽  
Relaxation Mechanism ◽  
Lattice Relaxation Time ◽  
Spin Rotation ◽  
Spin Lattice Relaxation ◽  
Hydrogen Atoms ◽  
Spin Lattice ◽  
Almost All

Abstract It is shown that in almost all nitrile carbon-atoms T1 depends first of all on the inter-and/or intramolecular dipol-dipol-relaxation mechanism. Only acetonitrile, as is already known, shows a remarkable dependence on the spin-rotation-relaxation mechanism. This influence is strongly decreasing with an increasing number of atoms, specially hydrogen atoms, in the molecule. The significance of the correlation time r is discussed extensively and the experimental results are verified by calculation of T1 using the viscosity and the inertial moments as parameters.

scholarly journals On the Region for the Application of Passive Damping Treatment and Loss Factor Enhancement

2019 ◽  
Vol 24 (4) ◽  
pp. 693-700
Author(s):  
Thomas K. Joseph ◽  
K. Renji ◽  
Kartik Venkatraman
Keyword(s):  
Energy Distribution ◽  
Viscoelastic Material ◽  
Loss Factor ◽  
Strain Energy ◽  
Significant Loss ◽  
Efficient Design ◽  
Modal Strain Energy ◽  
Damping Material ◽  
Modes Of Vibration ◽  
Constrained Damping

The loss factor of a structure is significantly improved by using constrained damping treatment. For a mass efficient design, the damping material is to be applied at suitable locations. The studies reported in literature use the modal strain energy distribution in the viscoelastic material or the strain energy distribution in the base structure as tools to arrive at these suitable locations for the damping treatment. It is shown here that the regions identified through the above criteria need not be suitable for certain bending modes of vibration. A new approach is proposed in which the strain in the viscoelastic material and the angle of flexure are shown to be more reliable in arriving at the locations for the damping treatment. Providing damping layers at identified locations using these parameters results in significant loss factors with minimal added mass.

scholarly journals Investigations of infra-red spectra. Determination of C-H frequencies (~3000 cm. -1 ) in paraffins and olefins, with some observations on “polythenes”

1940 ◽  
Vol 175 (961) ◽  
pp. 208-233 ◽  
Keyword(s):  
Double Bond ◽  
Carbon Tetrachloride ◽  
General Type ◽  
The Other ◽  
Hydrogen Atoms ◽  
Wave Numbers ◽  
Infra Red ◽  
Modes Of Vibration ◽  
Single Bonds

In a previous communication (1938) we described the results of an investigation into the infra-red absorption in the region of 3 µ of a number of hydrocarbons dissolved in carbon tetrachloride, with special reference to the absorption of ⟩CH 2 groups in different molecules. It was found that in many simple compounds the CH 2 group gave rise to two frequencies, essentially C-H valency vibrations, about 2857 and 2927 cm. -1 , and that from one compound to another these frequencies varied by only a few wave numbers. The lower frequency was identified with the mode of vibration in which the hydrogen atoms move in phase, while the other frequency was taken as the unsymmetrical mode of vibration. This assignment was substantiated by calculations with potential functions for molecules of the general type CH 2 — X , where X represents the rest of the molecule and is attached to the CH 2 group by single bonds. It was found that the CH frequencies of a CH 2 group are but little affected by the nature of X in saturated compounds, but that when the CH 2 group is attached to X by a double bond the CH frequencies are some 150 cm. -1 higher. In ethylene each CH 2 group has two CH valency modes of vibration, and since the CH 2 groups themselves can vibrate in or out of phase with one another, four CH frequency modes are possible for the C 2 H 4 molecule, two being Raman active and two infra-red active. In many molecules containing several CH 2 groups, similar coupling effects are important, and frequently four infra-red CH frequencies are observed.

Mechanical Deformation of Leadframe Assemblies in Plastic Packages During Molding

1991 ◽  
Vol 113 (4) ◽  
pp. 421-425 ◽  
Author(s):  
E. Suhir ◽  
L. T. Manzione
Keyword(s):  
Process Parameters ◽  
State Of The Art ◽  
Mechanical Deformation ◽  
Flow Front ◽  
Transfer Molding ◽  
Plastic Packages ◽  
Maximum Value ◽  
Significant Difference ◽  
The Difference ◽  
Maximum Stresses

We evaluate the maximum stresses and deflections in electric leads subjected to flow induced forces during transfer molding of plastic packages. It is found that lead deflection is proportional to the fifth power of the lead length and the inverse third power of lead thickness. These dependencies explain why it is more difficult to mold high pin count packages which have significantly longer and thinner leads to accommodate the higher interconnection density. In addition we find that the maximum value of the elastic lead deformation is about 0.9 mm (35 mils) for large state-of-the-art packages; exceeding this value causes permanent (plastic) lead distortion that compromises the symmetry of the package. We find also that minimizing the difference in flow front locations through careful gate design, and lowering the velocity over the leads by using balanced mold filling can make a significant difference in lead deformation. The results obtained are useful in establishing the appropriate geometry of the leads, as well as in choosing the materials and process parameters, so that excessive stresses and lead deflections can be avoided.

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