Phase Transitions in the Solid Elements

PHASE TRANSITIONS IN THE SOLID ELEMENTS AT ATMOSPHERIC PRESSURE... 

Phase Transitions in the Solid Elements at Atmospheric Pressure... 

The p-T phase diagram of sulfur is about the most complicated amongst the chemicd elements, and many open questions still exist with respect to phase boundaries, structures in detail, and kinetics of phase transitions in the solid as well as in the hquid state. Not only the molecular and crystalline variety of sulfur contributes to this complexity but also the metastabihty of high-pressure phases which is related to the application of different experi-mentd procedures. For example, early structural studies on the p-T phase diagram of sulfur could not be performed in-situ. Therefore, in these experiments the sulfur samples were quenched from a selected temperature-pressure point to STP conditions. The results obtained by such a procedure depend strongly on the variables AT and Ap as well as on their time derivatives (gradients), dT/dt and dp/dt, respectively. Especially, dynamic compression (shock wave) methods may introduce further complications since melting of... 

In [236], coh of FI was predicted from SR and SO-GGA-DFT solid-state calculations. The obtained value of 0.5 eV (48.2 kJ/mol), the SO-PW91 result, is in reasonable agreement with the estimates of [207, 225] (Table 16). SO effects were shown to lower and lead to structural phase transitions for the solid H (the hep structure in contrast to the fee for Pb). In a nonrelativistic world, all group-14 elements would adopt a diamond structure. An increase in the solid-state nearest-neighbor distance is found from Pb to FI, as that in their homonuclear dimers, indicating that the nature of the chemical bond in the crystal is similar to that of M2. 

Recent advances in the techniques of photoelectron spectroscopy (7) are making it possible to observe ionization from incompletely filled shells of valence elctrons, such as the 3d shell in compounds of first-transition-series elements (2—4) and the 4/ shell in lanthanides (5, 6). It is certain that the study of such ionisations will give much information of interest to chemists. Unfortunately, however, the interpretation of spectra from open-shell molecules is more difficult than for closed-shell species, since, even in the simple one-electron approach to photoelectron spectra, each orbital shell may give rise to several states on ionisation (7). This phenomenon has been particularly studied in the ionisation of core electrons, where for example a molecule (or complex ion in the solid state) with initial spin Si can generate two distinct states, with spin S2=Si — or Si + on ionisation from a non-degenerate core level (8). The analogous effect in valence-shell ionisation was seen by Wertheim et al. in the 4/ band of lanthanide tri-fluorides, LnF3 (9). More recent spectra of lanthanide elements and compounds (6, 9), show a partial resolution of different orbital states, in addition to spin-multiplicity effects. Different orbital states have also been resolved in gas-phase photoelectron spectra of transition-metal sandwich compounds, such as bis-(rr-cyclo-pentadienyl) complexes (3, 4). 

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. 

The use of a sample holder requires the sample to be reduced to a fine powder. This condition is not a problem when determining, for example, the structure of a new phase that has just been synthesized and this type of equipment is used for that purpose by solid state chemists. However, it is sometimes necessary to directly study bulk samples for which grinding could cause phase transitions. In those cases, the sample is a plane object that can be studied with the same diffractometer. Different configurations are then possible, with different paths for diffracted beams and different angular resolutions depending on the relative positions of the various elements included in the apparatus. 

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