Transformation hysteresis

Fig.3. Martensitic transformation hysteresis loops, second cycle, heating rate 30 K/min.

Figure 8. Pressure-volume relation for low-quartz ( ), coesite (A), stishovite ( ) and low-eristobalite (o) obtained by MD. Solid lines represent continuous change and broken lines discontinuous change of volume due to pressure-induced structural transformation. Hysteresis is indicated hy arrows. Pressure-volume relation obtained by an experiment is shown in the inset (from Hemley et al. Reference 45).

The hydration shell is formed with the increasing of the water content of the sample and the NA transforms from the unordered to A- and then to B form, in the case of DNA and DNA-like polynucleotides and salt concentrations similar to in vivo conditions. The reverse process, dehydration of NA, results in the reverse conformational transitions but they take place at the values of relative humidity (r.h.) less than the forward direction [12]. Thus, there is a conformational hysteresis over the hydration-dehydration loop. The adsorption isotherms of the NAs, i.e. the plots of the number of the adsorbed water molecules versus the r.h. of the sample at constant temperature, also demonstrate the hysteresis phenomena [13]. The hysteresis is i( producible and its value does not decrease for at least a week. 

This class of smart materials is the mechanical equivalent of electrostrictive and magnetostrictive materials. Elastorestrictive materials exhibit high hysteresis between strain and stress (14,15). This hysteresis can be caused by motion of ferroelastic domain walls. This behavior is more compHcated and complex near a martensitic phase transformation. At this transformation, both crystal stmctural changes iaduced by mechanical stress and by domain wall motion occur. Martensitic shape memory alloys have broad, diffuse phase transformations and coexisting high and low temperature phases. The domain wall movements disappear with fully transformation to the high temperature austentic (paraelastic) phase. 

The transformation is beHeved to occur by a diffusionless shear process (83). It is often referred to as martensitic transformation, having a thermal hysteresis between the cooling and heating cycles. The transformation is dependent on particle size finer particles transforming at a lower temperature than... 

Fig. 1. Schematic of the hysteresis loop associated with a shape-memory alloy transformation, where M. and Afp correspond to the martensite start and finish temperatures, respectively, and and correspond to the start and finish of the reverse transformation of martensite, respectively. The physical property can be volume, length, electrical resistance, etc. On cooling the body-centered cubic (bcc) austenite (parent) transforms to an ordered B2 or E)02...

Loss component of current supplying the hysteresis and eddy current losses to the voltage transformer core (it is the active component)... 

There are three major losses assoeiated with transformers and induetors hysteresis loss, eddy eurrent loss, and resistive loss. These losses are eontrolled during the transformer or induetor s design and eonstruetion. 

The a — 0 transformation has a large hysteresis in hydrogenated titanium alloys, and different thermal treatments change their phase content. Various degrees of metastability due to hysteresis are implicit for the alloys after different thermal treatments. Metastable phases undergo transformation to a more equilibrium state during deformation, which can effect the flow of the alloy. Below we consider the effect of the thermal pre-strain treatment on ductility on the strength of the Ti-6A1-2Zr-1.5V-lMo-rH alloys. ... 

The isotherms represented in Fig. 1 give a general idea of the equilibria in the Pd-H system under different p-T conditions. Most experimental evidence shows, however, that the equilibrium pressure over a + /3 coexisting phases depends on the direction of the phase transformation process p a-p > pp-a (T, H/Pd constant). This hysteresis effect at 100°... 

First-order phase transitions exhibit hysteresis, i.e. the transition takes place some time after the temperature or pressure change giving rise to it. How fast the transformation proceeds also depends on the formation or presence of sites of nucleation. The phase transition can proceed at an extremely slow rate. For this reason many thermodynamically unstable modifications are well known and can be studied in conditions under which they should already have been transformed. 

Cp is the specific heat at constant pressure, k is the compressibility at constant temperature. The conversion process of a second-order phase transition can extend over a certain temperature range. If it is linked with a change of the structure (which usually is the case), this is a continuous structural change. There is no hysteresis and no metastable phases occur. A transformation that almost proceeds in a second-order manner (very small discontinuity of volume or entropy) is sometimes called weakly first order . 

After several cycles of the compression and expansion, the dynamic jc-A curve becomes a single closed loop, somewhat distorted from a genuine ellipsoid. In order to analyze the forms of the hysteresis loop under stationary conditions, we have measured the time trace of the dynamic surface pressure after five cycles of the compression and expansion, and then Fourier-transformed it to the frequency domain. The Fourier-transformation was adapted to evaluate the nonlinear viscoelasticity in a quantitative manner. The detailed theoretical consideration for the use of the Fourier transformation to evaluate the nonlinearity, are contained in the published articles [8,43]. 

Existence of a large amount of mesopores usually results in the appearance of capillary condensation hysteresis loop. Type II AIs transform to type IV, and type III AIs transform to type V Type VI AIs are characteristic to low-temperature adsorption of some noble gases over energetically homogeneous surfaces. 

The model of Rabkin and Skripnyuk [75] seems to be quite attractive in its explanation of pressure hysteresis observed in Fig. 2.43a. Our results always show a log-normal frequency distribution of powder particles (Fig. 2.34), which points towards the possibility of the existence of large and small fractions of particle sizes. This, in turn, is compatible with the model which states that fully transformed and nontransformed particles can coexist depending on their sizes. 

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