Strain field

To find an upper bound on the apparent Young s modulus, E, subject the basic uniaxial test specimen to an elongation eL where e is the average strain and L is the specimen length. TRelntemal strain field that corresponds to the average strain at the boundaries of the specimen is... 

The thermal strain measurements described above have the common feature of anisotropic behaviour in a supposed isotropic state (cubic structure). These observations go well beyond the short-range, static strain fields associated with the lattice impurities responsible for Huang scattering. This then raises the question of the temperature at which the lattice symmetry changes and the implications of this for the central mode scattering. 

While there is evidence in support of a lattice impurity or defect-induced, strain-field mechanism, this model has not enjoyed wide support. 

When the polymeric material is compressed the local deformation beneath the indenter will consist of a complex combination of effects. The specific mechanism prevailing will depend on the strain field depth round the indenter and on the morphology of the polymer. According to the various mechanisms of the plastic deformation for semicrystalline polymers 40 the following effects may be anticipated ... 

In the real world the stress tensor never vanishes and so requires a nonvanishing curvature tensor under all circumstances. Alternatively, the concept of mass is strictly undefined in flat Minkowski space-time. Any mass point in Minkowski space disperses spontaneously, which means that it has a space-like rather than a time-like world line. In perfect analogy a mass point can be viewed as a local distortion of space-time. In euclidean space it can be smoothed away without leaving any trace, but not on a curved manifold. Mass generation therefore resembles distortion of a euclidean cover when spread across a non-euclidean surface. A given degree of curvature then corresponds to creation of a constant quantity of matter, or a constant measure of misfit between cover and surface, that cannot be smoothed away. Associated with the misfit (mass) a strain field appears in the curved surface. 

A set of simple physical and chemical principles can be used to understand and predict the surface reconstruction or faceting, which occurs on oxide surfaces.8,9 These include (1) autocompensation of stable surfaces, (2) rehybridization of the dangling bond charge density, (3) formation of an insulating surface, (4) conservation of near-neighbor bond lengths (which minimize the formation of surface strain fields), and (5) surface kinetic factors. We shall briefly discuss all of these factors governing the surface reconstruction of metal oxide. 

Convection of a passive scalar by a quasi-uniform random straining field. Journal of Fluid Mechanics 64, 737-762. 

However this fails to take into account the form of the strain field around the particles. If this is taken into account the modulus of a gel filled with a non-interactive filler can be written as25... 

The higher chemical energy of the elastic strain field present around a dislocation. 

The stress tensor elements a are related to the strain field Sk in the material by the equations... 

The essence of the topographic methods is that they map the interrsity of the diffracted beam over the surface of the crystal. Defects affect the diffracted intensity, so give contrast in the image. The methods are quite sertsitive enough to reveal individual dislocatiorrs, precipitates, magnetic domains and other long-range strain fields but cannot reveal point defects except in dense clusters. 

An important feature of the use of soft radiation is that both the extinction distance and the absorption distance are small, and therefore the X-rays penetrate only a veiy small distance into the crystal. We therefore examine only a small slice of the crystal close to the surface. The strain fields of dislocations deeper into the crystal do not contribute significantly to the image and, in a transmission experiment, overlapping of the images leads to an upper limit of about 10" cm on the dislocation density for individual defect imaging. With the Berg-Barrett technique this can be pushed to about 10 cm ... 

Figure 8.13 Experimental and simulated section topography images of hydrogen precipitates in silicon. All simulations were carried out using the same microscopic strain field, but the different position of the defects within the crystal results in substantially different image detail...

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