Internal strain fields

A new ultrasonic technique for studying dewetting and cumulative internal damage in solid propints has been reported (Refs 17 20). This technique yields volume-dilatation data on proplnt in tension, and on damage in uniaxial compression and shear strain fields. Estimates of vacuole size and number density arising from dewetting can be made, as well as can the time dependent void growth at constant strain be observed... 

When an electric field E is applied, Eq changes by an amount proportional to E, as usually expressed by (a — 1) E/4n, where e is the dielectric constant. When a strain is applied to the film, changes in and hence changes in polarization are divided into two components 1. displacement equal to the macroscopic displacement and 2. residual displacement. The latter is the internal strain and causes the intrinsic piezoelectricity. The effect of internal strain on P is expressed by eu, where e is the intrinsic piezoelectric constant and u is the elongational strain along the x-axis. The electric displacement D can therefore be written... 

Similar to GaN Eu QDs, transitions of Tm3+ inside QDs show constant temperature behavior, a red shift, and broader line widths, resulting from the presence of large internal electric field and strain in QDs (Andreev et al., 2005a). 

The hysteresis loop of a ceramic varies according to composition and ceramic structure but is typically of the form shown in Fig. 2.46(b). The coercive field is higher and the remanent polarization is lower than for a single crystal. Changes in both 180° and 90° domain configurations take place during a cycle and are impeded by the defects and internal strains within the crystallites. 

An externally applied stress will affect the internal strain and the domain structures will respond this process is termed the ferroelastic effect. Compression will favour polar orientations perpendicular to the stress while tension will favour a parallel orientation. Thus the polarity conferred by a field through 90° domain changes can be reversed by a compressive stress in the field direction. Stress will not affect 180° domains except in so far as their behaviour may be coupled with other domain changes. 

A strain field rj in a BN lattice will tend to cause internal displacement of the B atoms (shaded) upward with respect to the N atoms. 

Finally, it has to be recalled that internal strains or crystal packing forces have to be present, in order to stabilize one of several equivalent minima so that the system is seen as statically distorted. It has been stated that even small low-symmetry perturbations can be amplified by vibronic coupling A mechanism of this kind may be more effective in lifting electronic degeneracies than low-symmetry ligand field components. The important point is whether JT contributions are greater or comparable with the low-symmetry ones if it is so, JT terms must be included in to the Hamiltonian and have to be considered before or together with the static low-symmetry crystal field. 

An internal (residual) strain field must exist around a dislocation since atoms associated with the dislocation are displaced from their equilibrium positions. The atoms near the dislocation line have substantial displacements from their normal position but outside this region the stress field will be linearly elastic. The... 

The almost horizontal portions of the hysteresis loop represent saturated states in which the crystal is a single domain during a cycle. Defects and internal strains within the crystallites impede the movement of domain walls. Domain wall mobility has been found to decrease with time (even without an applied mechanical or electrical stress or thermal changes). This is due to internal fields associated with charged defects, redistribution of lattice strains, and accumulation of defects at domain walls. 

The calculations physical properties of antiferroelectrics based on the Kittel model (i.e. with respect to antiparallel alignment of sublattices polarization vectors) can be done within the formalism of Chap. 1. The numerical calculations of phase diagrams of nanosized antiferroelectric systems of different shapes were carried out in Ref. [68] without consideration of either external or internal electric fields. Corresponding analytical calculations had been carried out in Ref. [69], However, the model used for calculations in [69] did not take into account both mechanical strains and surface piezoeffect generating built-in field. The consistent account for latter effects in Ref. [70] show that they are playing a decisive role in transformation of antiferroelectric phase into ferroelectric one in sufficiently thin Aims. With respect to the latter, the subsequent consideration will be done according to Ref. [70]. 

II. The interaction of polymer molecules with i -vortices The main part of the simplified events are the vortex rods of the yl-vortices with an internal flow field which can be described as an axysymmetric strain field with a weak vorticity field superimposed on it. The boundaries of this jetlike event are shear layers since the events have convectional velocities less than the velocity of the mean flow at their positions. 

Addition of small amount of silicon up to 0.832 mass% in very rich iron alloys (0.045 to 0.047 mass% C) reduces the peak height of die internal friction spectra which presents a maximum at around 50°C. The main reason of this drastic decrease should be due to the influence of the strain field generated by a substitutional atom due to the difference in atomic size [2004Sai]. 

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