Lattice expansion

Impurity atoms having an ionic radius greater than that of silicon cause lattice expansion. 

At each temperature one can determine the equilibrium lattice constant aQ for the minimum of F. This leads to the thermal expansion of the alloy lattice. At equilibrium the probability f(.p,6=0) of finding an atom away from the reference lattice point is of a Gaussian shape, as shown in Fig. 1. In Fig.2, we present the temperature dependence of lattice constants of pure 2D square and FCC crystals, calculated by the present continuous displacement treatment of CVM. One can see in Fig.2 that the lattice expansion coefficient of 2D lattice is much larger than that of FCC lattice, with the use of the identical Lennard-Lones (LJ) potential. It is understood that the close packing makes thermal expansion smaller. 

In practice, thermal cycling rather than isothermal conditions more frequently occurs, leading to a deviation from steady state thermodynamic conditions and introducing kinetic modifications. Lattice expansion and contraction, the development of stresses and the production of voids at the alloy-oxide interface, as well as temperature-induced compositional changes, can all give rise to further complications. The resulting loss of scale adhesion and spalling may lead to breakaway oxidation " in which linear oxidation replaces parabolic oxidation (see Section 1.10). 

It is defined as the slope of the capacity-cycle curve, i.e., — dQ/dcycle. In order to elucidate the relationship between corrosion rate and composition it is necessary to determine lattice expansion quantita-tively.This requires the determination of VH, which is listed in Table 4 for a number of alloys. 

LaNi3 85 Co075Mn04Alt (x = 0, 0.1, 0.2, 0.3) electrodes [51] the Al-free electrode corrodes at a greatly increased rate. As illustrated in Table 7 and Fig. 16, the presence of even a small amount of A1 substantially decreases VH and n, and consequently both lattice expansion and corrosion. 

The cyclic behaviour of a series of electrodes of varying Mn content is shown in Fig. 17. It apparently increases VH (Table 8) slightly and although the correlation between lattice expansion, n, and corrosion rate is fairly strong, they are not a function of Mn content, as shown in Fig. 18. 

It is of interest to note that VH in the hydride phase is significantly less than in AB5 hydrides. Consequently, lattice expansion is also significantly reduced. However, the corrosion rate of the electrodes in Table 9 is still appreciable. Indeed, for the electrode with x - 0.25 the... 

Both factors are sensitive to alloy composition, which can be adjusted to produce electrodes having an acceptable cycle life. In AB5 alloys the effects of Ce, Co, Mn, and A1 upon cycle life in commercial AB5 -type electrodes are correlated with lattice expansion and charge capacity. Ce was shown to inhibit corrosion even though lattice expansion increases. Co and A1 also inhibit corrosion. XAS results indicate that Ce and Co inhibit corrosion though surface passivation. 

There are few systematic guidelines which can be used to predict the properties of AB2 metal hydride electrodes. Alloy formulation is primarily an empirical process where the composition is designed to provide a bulk hydride-forming phase (or phases) which form, in situ, a corrosion— resistance surface of semipassivating oxide (hydroxide) layers. Lattice expansion is usually reduced relative to the ABS hydrides because of a lower VH. Pressure-composition isotherms of complex AB2 electrode materials indicate nonideal behaviour. 

In order to reproduce the temperature variation of the lattice constants, the anisotropy of the lattice expansion has to be taken into account. For this purpose, the tensor of thermal expansion ot is introduced instead of the scalar a , and the tensor of deformation due to the HS <- LS transition is employed instead of the dilation (Fh — Fl)/Fl. Each lattice vector x T) can now be... 

The theory later developed by Spiering and co-workers [24, 196] takes as its basis changes of volume, shape, and elasticity of the lattice as the main factors influencing the cooperative interactions. This model of lattice expansion and elastic interactions has been developed further and is described in detail by Spiering in Chap. 28. 

For example, the equilibrium measurements of linear thermal expansion and X-ray lattice expansion of Simmons and Baluffi80 yield directly the total concentration of vacancies, and this is written as... 

Our development has assumed temperature independent force constants. In real liquids, however, there is a small temperature dependence of frequencies and force constants due to anharmonicities, lattice expansion, etc. The incorporation of these effects into the theory is treated in later sections. 

Subsequently, the lattice parameters of Al(Mg) were calculated as shown in Table 3.1. It is clear that the lattice parameter of Al in the powders milled for 10 h is much larger after heating in DSC up 295, 350 and 425°C than that of the sample heated up to 180°C. The lattice expansion is consistent with the magnitude of the atomic radius of Al and Mg which is equal to 0.1432 and 0.1604 nm, respectively [121]. Fossdal et al. [114] claimed the formation of the Al(Mg) solid solution during low-temperature desorption of Mg(AlH4)2 below 180°C which is not confirmed here. Mamatha et al. [117, 118] never reported the formation of the Al(Mg) solid solution although Kim et al. [119] mentioned about increase in the lattice parameter of Al most probably due to formation of the Al(Mg) solid solution. 

Aminomethylpyridine (picolylamine) is an important ligand in respect to spin cross-over, [Fe(2-pic)3]Cl2 being the key compound." Fleat capacity measurements on [Fe(2-pic)3]Cl2 EtOH gave values of 6.14kJmol and 50.59 JK moC for the spin eross-over entropy the determined entropy was analyzed into a spin contribution of 13.38, an ethanol orientational effeet of 8.97, and a vibrational contribution of 28.24 JK mol. " This compound exhibits weak cooperativity in the solid state." The heat capacity of [Fe(2-pic)3]Cl2 MeOH is consistent with very weak cooperativity." [Fe(2-pic)3]Br2 EtOH shows a lattice expansion significantly different from that expected in comparison with earlier-established behavior of [Fe(2-pic)3]Cl2 EtOH." ... 

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. 

---