Capacity allotrope

Many substances exist in two or more solid allotropic fomis. At 0 K, the themiodynamically stable fomi is of course the one of lowest energy, but in many cases it is possible to make themiodynamic measurements on another (metastable) fomi down to very low temperatures. Using the measured entropy of transition at equilibrium, the measured heat capacities of both fomis and equation (A2.1.73) to extrapolate to 0 K, one can obtain the entropy of transition at 0 K. Within experimental... 

Entropy of Methylammonium Chloride. Heat capacities for this solid in its various crystalline modifications have been determined [10] precisely down to 12 K. Some of these data are summarized in Figure 11.3. There are three crystalline forms between OK and 298K. One can calculate the entropy by integrating Equation (11.21) for each allotrope in the temperature region in which it is most... 

Figure 11.3. Heat capacities of the three allotropic forms, a, (3, and y, of methylammonium chloride [10]. The dashed curve represents the heat capacity of the metastable, supercooled y form.

There has been much controversy over the structure of jS-sulfur, and the question of whether it is a true allotrope. It has been suggested that it constitutes merely a thermally distorted lattice expansion of orthorhombic sulfur. Furthermore, phase transition, at 101°C, has been described by various authors (S2), but it has been shown that this eJffect was due to traces of water in the lattice (65). However, recently a true anomaly in the heat capacity has been found (7i) at —75°C. 

Sulphur has two solid allotropes Monoclinic sulphur can readily be supercooled to very low temperatures, completely bypassing the phase transformation at 368.5K. The temperature dependence of the heat capacities of both allotropes can be determined experimentally. It has been found that... 

To illustrate the type of analysis that is involved we exhibit a representative set of heat capacity data in Fig. 1.20.2 for oxygen, as a plot of CP versus log T this representation is useful for the direct calculation of the entropy of oxygen from the area under the curves. Note that the element exists in three allotropic modifications in the solid state, with transition temperatures near 23.6, 43.8, and 54.4 K, the last being the melting point of solid phase I. The boiling point of liquid oxygen is near 90.1 K. An extrapolation procedure was used below 14 K. 

By way of illustrations we display in Fig. 1.17.2a plot of the molar heat capacity of oxygen under standard conditions. The plot of Cp vs. In T is then used to determine the entropy of oxygen from the area under the curves. Note that the element in the solid state exists in three distinct allotropic modifications, with transition temperatures close to 23.6 and 43.8 K the melting point occurs at 54.4 K, and the boiling point is at 90.1 K. All the enthalpies of transition at the various phase transformations are accurately known. An extrapolation procedure was employed below 14 K, which in 1929 was about the lower limit that could conveniently be reached in calorimetric measurements. 

Farr (109)y of the Tennessee Valley Authority, has compiled a resume of the physical and thermodynamic properties of the allotropic forms of phosphorus. Based on entropy calculations from low temperature heat capacity measurements, Stephenson (318) believes that red crystalline triclinic phosphorus (T.V.A. designation V) is the most stable form at room temperature. This point of view is buttressed by the x-ray work of Roth, DeWitt, and Smith (376). Consequently we have selected red phosphorus V as the reference state up to its sublimation point at 704° K. 

Detailed calorimetric data have been reported for M2Cli0 and AMC16 (A = Rb, Cs).417 Enthalpy contents and molar heat capacities were measured as functions of temperature. The ionic compounds underwent allotropic solid-solid transformations. 

From measurements of the molar heat capacity of Sa,2(=S2) in the temperature range 5-370 K this allotrope was suspected to undergo a transition to a more stable phase above 310 K, the structure of the new phase being unknown [146]. 

Thermodynamic Functions of Three Carbon Allotropes [19]. Low temperature heat capacities of three allotropes of carbon are shown in Fig. 4.46. The data were derived from adiabatic calorimetry. Based on the discussion of heat capacities of Sect. 2.3 and the known chemical structure of the allotropes given in Fig. 2.109, the thermal behavior can be easily understood. Fullerene, Cgg, is a small molecule. All strong bonds he in the surface of the almost spherical molecule. The low-temperature heat... 

The heat capacity measurement of essentially allotropically pure /3-Ce was first made by Koskimaki and Gschneidner (1974). These authors claimed that their sample was 99.5% or greater pure /3-phase, but more recent studies by Burgardt et al. (1976a) revealed that K and G s sample might have contained an additional 0.8% a-Ce due to the transformation of some /3-Ce to a-Ce between 15 and 50 K (see Tsang et al., 1976). A redetermination of the low temperature... 

Antimony and phosphorus react very easily with lithium to form Li2Sb and LisSb (allotropic forms a and y), and LiP and LisP phases, respectively. The theoretical capacities range from 2,596 to 660 mAh/g for P and Sb, respectively, but these high capacities cannot usually be sustained for more than a few cycles. As for silicon, many methods have been developed to address the issue of the loss of contact between the grains of the AM (X = Sn, Sb, P...) in the electrode, which is a consequence of strong volume variations (100-200%). The preparation of X/carbon composites, X Xt, (X and X forming alloys with Li), or IV X , compounds (M, transition metal. 

If we consider a substance undergoing an allotropic transformation in the solid state at temperature T, which melts at temperature 7> and boils at temperature Tsb, to integrate expressions [4.4] and [4.6], it is necessary to divide the temperature interval between the initial temperature To and the temperature T into slices. Each slice is characterized by a phase and therefore a function of the molar specific heat capacity at constant pressure with changing temperature. Thus, integration of equation [4.4] involves two t3 es of terms ... 

Elements from column V studied for their potential use in Li-ion batteries are essentially P, Sb and Bi. Data relative to As are relatively scarce in the literamre, probably because of its high toxicity and also its relatively high atomic mass, which limits the gravimetric capacity. The most common allotrope of arsenic is grey or metallic As, which crystallizes in the rhombohedric system. In a small paragraph of their paper on Li intercalation in ZnSb, Park and Sohn have reported a capacity of 330 mAh/g (1300 mAh/cm ) and 100 % capacity retention after 300 cycles for an As/C composite anode [106]. 

Phosphorus reacts with lithium to form Li3P at complete lithiation, corresponding to a volume increase of 300 % and a maximum capacity of 2595 mAh/g. However, among the three main phosphoras allotropes [107], the white variety tends to be unstable above 30 °C and only red and black phosphorous have been tested as anode materials. Red phosphorous (rP), which is commercially available, is usually amorphous and exhibits a low electrical conductivity, which induces a poor reversibility for the lithiation reaction [108]. Mixing rP with carbon (30.56 wt% of... 

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