Hill limit

Apart from d- and 4f-based magnetic systems, the physical properties of actinides can be classified to be intermediate between the lanthanides and d-electron metals. 5f-electron states form bands whose width lies in between those of d- and 4f-electron states. On the other hand, the spin-orbit interaction increases as a function of atomic number and is the largest for actinides. Therefore, one can see direct similarity between the light actinides, up to plutonium, and the transition metals on one side, and the heavy actinides and 4f elements on the other side. In general, the presence or absence of magnetic order in actinides depends on the shortest distance between 5f atoms (Hill limit). 

When An is small (well below the Hill limit) and the corresponding 5f-5f overlap is large and/or when the 5f-ligand hybridization is strong, one expects that a relatively broad 5f band is formed, intersected by EF. A relatively low density of the 5f states at EF is reflected in a modest value of the specific heat coefficient y. The magnetic susceptibility x is practically temperature independent, but the values can be somewhat enhanced with respect to the specific heat data if the formula... 

Besides the compounds with non-metallic or semi-metallic elements possessing the NaCl-type structure, a number of UX intermetallics adopt a variety of lower-symmetry structures (table 3.3). The 1 1 binaries are the first compounds (when proceeding from An-rich compounds to lower An concentrations) that can exhibit magnetic ordering. This is consistent with the development of the interatomic distances dAn An, which in some cases slightly exceed the Hill limit, and with the lower An-An coordination. Basic magnetic characteristics of the compounds reported below are given in table 3.4. 

The An-An spacing in the Laves phases of the light actinides, with exception of AnAl2 compounds, is far below the Hill limit. Therefore the overlap of the 5f wave functions must be regarded as the main delocalizing mechanism. This provides the justification for the application of the band approach, at least in a first approximation. 

The An-An spacing of these compounds by far exceeds the Hill limit (for structural data see table 3.7). Therefore, the 5f-ligand hybridization is the main mechanism controlling the localization of the 5f states. The behaviour of UX3 compounds can be roughly classified as belonging to three qualitatively different groups ... 

Discussion Since dv v exceeds the Hill limit in these materials the hybridization with ligand states dominates the mechanisms of the 5f electron delocalization. The d-states are situated well below EF in AnUX3 compounds and therefore they do not hybridize with the 5f states of the actinide atoms. If d-states with relatively high N(E) are present in the valence band (which is undoubtedly the case in UT3 compounds) the strength of the 5f-d hybridization becomes a very critical parameter. It depends mostly on details of the mutual position (overlap) of the d-states and the 5f-states which remain pinned at (or near) EF. 

Chemical and Procese Engineering, Leonard-Hill Limited, London. 

UAI2 is a cubic Laves phase with lattice parameter a = 7.776 A (Katz and Jacobs 1962). From this an U-U distance of 3.375 A follows, which is close to the Hill limit for the appearance of localization of the 5f moments. 

We turn now to the isomer shift. Its variation for NpX2 intermetallics (X = nonmagnetic) indicates a continuous change of electronic structure with lattice constant (or df p). The slope AS/Ad p on the right-hand side of fig. 36 is practically the same as the one found as a function of applied pressure in NpAl2- In essence, the systematics of isomer shift supports the continuous change of f electron structure outlined just above. As expected, the Hill limit is not noticeable in the isomer shift. It does not constitute a break in electron structure. 

Although in the NpX series is well above the Hill limit, the expected simple localized lanthanide-like f electron structure is not observed as was already pointed out on occasion of the high-pressure data for NpAs. If lanthanide-like behavior were present no correlation between hyperfine parameters and lattice constant and/or... 

Straub, Hans. A History of Civil Engineering An Outline from Ancient to Modem Times. Translated by E. Rockwell. London Leonard Hill Limited, 1952. 

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