Lambda anomaly

Montgomery (3) reported a lambda anomaly in the heat capacity of monocllnic sulfur with a peak at 198.3 K. The entropy change in the lambda anomaly was 0.052 0.005 cal K mol , this was interpreted as due to the disordering of the structure of monoclinic sulfur on heating (7). 

He shows that pure water at normal pressures cannot be supercooled below -40°C and that virtually all physical properties of water point to a "lambda anomaly" at -45 C [1]. 

The possible existence of an endpoint for the supercooled liquid locus is particularly Interesting in view of the experiments of Angell and coworkers (7,8,9,10). They find that pure water at ordinary pressures (even very finely dispersed) cannot apparently be supercooled below about —40 "C, and that virtually all physical properties manifest an impending "lambda anomaly at T, = —45 . The most striking features of this anomaly are the apparent divergences to infinity of isothermal compressibility, constant-pressure heat capacity, thermal expansion, and viscosity. We now seem to have in hand a qualitative basis for explaining these observations. 

Figure 2.46 Some results which establish Y2M02O7 as a spin glass material. Top left d.c. susceptibility showing a ZFC/FC cusp at T( —22 K. Top right a.c. susceptibility showing frequency dependence. Bottom left Heat capacity indicating the absence of a sharp lambda anomaly and the linear temperature dependence at low temperatures. Bottom right The build up of the nonlinear susceptibility as T approaches Reprinted with permission from Miyoshi etaL,...

An example of magnetic contributions to the specific heat is reported in Fig. 3.9 that shows the specific heat of FeCl24H20, drawn from data of ref. [35,36]. Here the Schottky anomaly, having its maximum at 3K, could be clearly resolved from the lattice specific heat as well as from the sharp peak at 1K, which is due to a transition to antiferromagnetic order (lambda peak). 

The mysteries of the helium phase diagram further deepen at the strange A-line that divides the two liquid phases. In certain respects, this coexistence curve (dashed line) exhibits characteristics of a line of critical points, with divergences of heat capacity and other properties that are normally associated with critical-point limits (so-called second-order transitions, in Ehrenfest s classification). Sidebar 7.5 explains some aspects of the Ehrenfest classification of phase transitions and the distinctive features of A-transitions (such as the characteristic lambda-shaped heat-capacity curve that gives the transition its name) that defy classification as either first-order or second-order. Such anomalies suggest that microscopic understanding of phase behavior remains woefully incomplete, even for the simplest imaginable atomic components. 

Inspection of Fig. 3.16.5, where we have set w - 2RTA, shows that as the temperature rises there is a marked increase in heat capacity, with a sharp drop off back to zero at T - TA. This figure has approximately the shape of the Greek capital letter A and hence is frequently called a A anomaly TA is known as the lambda point. What Fig. 3.16.5 once more illustrates is... 

Studies on the thermal properties of lanthanum, cerium, neodymium, and gadolinium hexaborides in the cryogenic region from 5° to 350°K. 193) have shown the presence of two types of anomalies in the latter three substances. At temperatures near 10 °K. there appears a lambda-type anomaly in each which is rather characteristic of a magnetic transformation. At slightly higher temperatures this is followed by Schottky-... 

Also other studies of type-1 EugGaigGe3o have provided evidence for a second feature at a characteristic temperature below Tc- For instance, the magnetic specific heat, in addition to the lambda-type anomaly at Tc, shows a broad shoulder at about 10 K [10]. This anomaly is more clearly revealed by the temperature dependence of the magnetic entropy change [47] that will be further discussed in the context of magnetic refrigeration in the next section. 

We performed molecular d5mamics simulations in the canonical ensemble using N = 500 particles (250 dimers) in a cubic box with periodic boundary conditions, interacting with the intermolecular potential described above. The cutoff radius was set to 5.5 length units. Pressure, temperature, density, and diffusion are calculated in dimensionless units, as detailed elsewhere (de Oliveira et al., 2010). We first compared the previous (de Oliveira et al., 2010) results, obtained with the choice of A/o" = 0.20 with a new choice /j = 0.50, in a broad range of temperatures (0.10 [Pg.393]

The phase diagram for " He is shown in Fig. 4.3. There are two liquid phases, Hel and Hell, separated in the phase diagram by a line known as the lambda line (X line) and shown dashed in Fig. 4.3. The change that occurs at the X line is marked by a very characteristic anomaly in the specific heat capacity c of the liquid the specific heat capacity rises to a very high value at the lambda... 

The heat capacity of a body is the amount of heat required to produce a temperature rise of 1°C. Specific heat is the heat capacity per unit mass, and generally decreases with lowering temperature, falling to zero at 0°K. Anomalies in the specific heat curve can be related to the molecular origins of phase transitions. Beta brass, for instance, exhibits a lambda point at 470°C due to an order-disorder transition. The specific heat anomaly is referred to as a lambda point because of the resemblance to the Greek letter A. 

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