The Al-Rich Part of the Fe-Al Phase Diagram

The Al-rich part of the Fe-Al phase diagram between 50 and 80 at.% Al including the complex intermetallic phases Fe$_{5}$Al$_{8}$ (ε), FeAl$_{2}$, Fe$_{2}$Al$_{5}$, and Fe4Al$_{13}$ was re-investigated in detail. A series of 19 alloys was produced and heat-treated at temperatures in the range from 600 to 1100 °C for up to 5000 h. The obtained data were further complemented by results from a number of diffusion couples, which helped to determine the homogeneity ranges of the phases FeAl$_{2}$, Fe$_{2}$Al$_{5}$, and Fe$_{4}$Al$_{13}$. All microstructures were inspected by scanning electron microscopy (SEM), and chemical compositions of the equilibrium phases as well as of the alloys were obtained by electron probe microanalysis (EPMA). Crystal structures and the variation of the lattice parameters were studied by x-ray diffraction (XRD) and differential thermal analysis (DTA) was applied to measure all types of transition temperatures. From these results, a revised version of the Al-rich part of the phase diagram was constructed

Another approach to the Gibbs-Thomson equation and the melting point of polymers and oligomers

The common Gibbs–Thomson equation, widely used to explain the melting temperature of lamella crystals, is based on a given heat of fusion and a given surface free energy and the size (thickness) of the crystal. With this equation it is not possible to explain the, compared to the thickness of the crystals, very high melting temperature of cyclic alkanes and ultra-high molar mass polyethylene (UHMMPE). Another thermodynamic approach to the Gibbs–Thomson equation, starting from an incremental composition of enthalpy and entropy of the chain molecule, is presented. This describes the melting temperature of (lamella) crystals of linear, folded and cyclic alkanes as well as UHMMPE, all forming crystals of the same lattice type, with only one set of parameters. The essential variable turns out to be the number of CH2-groups of the respective molecule, incorporated into the crystallite, rather than its thickness. This may be explained if we assume the melting process caused by conformation dynamics which are more restricting the greater number of CH2-groups that are involved in the chain movement. In a lamella crystal of a certain thickness, a cyclic alkane ‘feels’ longer than an n-alkane, as well as a linear molecule with adjacent or tight folds feels longer than one with randomly distributed chains and large loops in the amorphous. This approach helps to understand the melting behavior of polymers forming folded-chain crystals. It enables the cyclic and folded ultra-long alkanes to serve as model substances for the folded-chain crystals of polyethylene without further assumptions concerning the surface energy and fits all findings smoothly into one picture

Melting kinetics in polymers

In polymers, it is possible to obtain single chain forming single crystals. It is feasible to melt these crystals by simple consecutive detachment of chain segments from the crystalline substrate and its diffusion into the melt. However, complication in the melting process occurs when the chain in the process of detachment from the surface is shared between different crystals. Experimentally, a clear distinction in different melting processes is observed, by the differences in the activation energies required for the consecutive detachment of chain segments or of segments having topological constraints. The consecutive detachment of free chain segments starts at the melting temperature predicted from the Gibbs-Thomson equation, whereas higher temperature or time is required if the chain has to overcome the constraints