Elastic properties of ice

It is interesting to make an estimate of the extent to which the elastic properties of ice are anisotropic. This can be done with the help of fig. 8.1 and the figures from table 8.i. For an isotropic material = % while for ice these quantities differ by about 10 per cent. Similarly we should have while for 

The effective Young s modulus E = is plotted as a function of orientation in fig. 8.4. 

Since it is often of practical consequence to know the elastic behaviour of polycrystalline ice, particularly under static loading. 

Most real systems, as distinct from idealized assemblies of point masses linked by two-body forces, show deviations from the simple behaviour discussed in the previous sections. One of these types of more complex behaviour is associated with the internal friction of the material which leads to the damping of free vibrations, even in the most perfectly isolated systems. We have seen that the most convenient way of determining elastic moduli is by examining the vibration frequencies of carefully shaped samples and, in the same way, internal friction or mechanical relaxation can be studied by examining the logarithmic decrement of these same vibrations when the external excitation is removed. The logarithmic decrement 8 is so defined that an oscillation of angular frequency (o is damped by a factor exp (- It is thus n times the loss 

This sort of study has been carried out on single crystals of pure ice by Kneser et al. (1955), Schiller (1958), Kuroiwa Yamaji (1959) and Kuroiwa (1964). All these workers found a simple dependence of 8 upon frequency of the form 

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The elastic properties of hydrates are important to understanding the sonic and seismic velocity field data obtained from the natural hydrates-bearing sediments. Data on the mechanical properties of CO2 hydrates are hmited. Table 10.3 shows the elastic properties of ice, CH4 hydrates, and CO2 hydrates. It should be noted that these properties may vary for different guests and occupancies. For example, Kiefte et al. [21] measured the compressional velocity of methane, propane, and hydrogen sulfide hydrates as 3.3, 3.7, and 3.35 km/s, respectively. 

Since treatments of the elastic properties of crystals are often very brief, or at best limited to a discussion of cubic crystals, let us begin by giving a short review of this subject as it applies to hexagonal crystals like ice. We shall follow the development given by Nye (1957), to whose book the reader is referred for a fuller treatment. 

ICC Termination Act of 1995, 25 331, 326 Ice. See also Water entries elastic properties, 5 614t hydrogen-bonded structure of, 26 15 properties of, 26 17t Ice wines, 26 315 Iceberg model, 23 95 Ice formation, in food processing, 72 82 Iceland, bioengineering research program, 7 702... 

In the present study, we have made X-ray diffraction, neutron diffraction with isotopic substitution, and quasi-elastic neutron scattering measurements on highly concentrated aqueous solutions of lithium halides in a wide temperature range from room temperature to below glass transition temperature, from which the microscopic behaviors of the static structure and dynamic properties of the solutions are revealed with lowering temperature. The results obtained are discussed in connection with ice nucleation, anisotropic motion of water, crystallization, and the partial recovery of hydrogen bonds. 

In continuous tests the deformation is large so the structure of the sample is destroyed. In oscillatory rheometry the deformation is small so the structure remains intact. Both viscous and elastic properties can be measured simultaneously. The elastic, solid-like component of the response (the storage modulus, G ) is in phase with the deformation and the viscous, liquid-like component (the loss modulus G") is out of phase. The ratio G /G is a measure of the relative importance of the viscous and elastic components. Thus, for example, ice cream that has a high G and a low G"/G is more solid-like than liquid-like. 

All these results apply to a completely general triclinic crystal system whose elastic properties are expressed by the twenty-one independent quantities Cy or Jy. For crystals of higher symmetry there are further relations between the Cy or 5y which reduce their number still further. For the hexagonal and cubic systems these relations are illustrated in fig. 8.1, together with similar relations for a completely isotropic, non-crystalline material. It can be seen that for a hexagonal crystal like ice there are only five non-zero independent elastic constants Jn, i3> % and 44 or the corresponding Cy. 

The presence of masses of ice in a soil means that as far as engineering is concerned, the properties of both have to be taken into account. Ice has no long-term strength, that is, it flows under very small loads. If a constant load is applied to a specimen of ice, instantaneous elastic deformation occurs. This is followed by creep, which eventually develops a steady state. Instantaneous elastic recovery takes place on removal of the load, followed by recovery of the transient creep. 

But let us turn to the "Constitution of Bodies." Dalton states "There are three distinctions in the kind of bodies, or three states, which have more especially claimed the attention of philosophical chemists namely, those which are marked by the terms elastic fluid, liquids and solids." That these three states have been recognized as different for a long time can also be derived again from our language. For the most conunon chemical compound, H2O, there are three different names steam, water, and ice, one for each of the three basic states ofinatter. One of the goals of chemistry must then be to link the existence and properties of these states with the molecular structure. 

Viscoelastic fluids possess the properties of both viscosity and elasticity. Unlike purely viscous fluids where the flow is irreversible, viscoelastic fluids recover part of their deformation. Examples include polymeric solutions, partially hydrolyzed polymer melts such as polyacrylamide, thick soups, creme frafche, ice cream, and some melted products such as cheese. 

The surface of ice shows structural transitions, such as surface roughening and surface melting, at temperature, T, below T. The occurrence of structural transitions at the surface of ice causes alterations in the dynamic, mechanical, elastic, and electric properties of the surface. Moreover, anisotropy in structural transitions among several crystallographic plane surfaces of ice is vital for understanding habit changes of snow crystals [9]. Thus, the surface ofice near is an important subject... 

A foam is a dispersion of gas bubbles in a relatively small volume of a liquid or solid continuous phase. Liquid foams consist of gas bubbles separated by thin liquid films. It is not possible to make a foam from pure water the bubbles disappear as soon as they are created. However, if surface active molecules, such as soap, emulsifiers or certain proteins, are present they adsorb to the gas-liquid interfaces and stabilize the bubbles. Solid foams, e.g. bread, sponge cake or lava, have solid walls between the gas bubbles. Liquid foams have unusual macroscopic properties that arise from the physical chemistry of bubble interfaces and the structure formed by the packing of the gas bubbles. For small, gentle deformations they behave like an elastic solid and, when deformed more, they can flow like a liquid. When the pressure or temperature is changed, their volume changes approximately according to the ideal gas law (PF/r= constant). Thus, foams exhibit features of all three fundamental states of matter. In ice cream, the gas phase volume is relatively low for a foam (about 50%), so the bubbles do not come into contact, and therefore are spherical. Some foams, for example bubble bath. 

At a typical storage temperature of —18 °C, ice cream displays solidlike properties such as elasticity, plasticity and fracture. A number of... 

Thermoplastics are elastic and flexible above a glass transition temperature T, specific for each one, and in some cases a low is useful and in other applications a high is required. A polyethylene ice box container has a very low as it is essential that it remains flexible at temperatures below -20 °C. A blood filter must retain all of its structural integrity at temperatures >37 °C and therefore polycarbonate is often the selected plastic as it has a high Tg (amongst other properties). 

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