The electronic structures, densities of states, Fermi surfaces and elastic properties of AB(3) (A = La, Y; B = Pb, In, Tl) compounds are studied under pressure using the full-potential linear augmented plane wave (FP-LAPW) method within the local density approximation for the exchange-correlation functional and including spin-orbit coupling. Fermi surface topology changes are found for all the isostructural AB3 compounds under compression (at V/V-0 = 0.90 for LaPb3 (pressure = 8 GPa), at V/V-0 = 0.98 for AIn(3) (pressure = 1.5 GPa), at V/V-0 = 0.80 for ATl(3) (pressure in excess of 18 GPa)) apart from YPb3, although its electronic structure at zero pressure is very similar to that of LaPb3. For LaPb3 a softening of the C-44 elastic constant under pressure (equivalent to 8 GPa) may be related to the appearance of a new hole pocket around the X point. From the calculated elastic properties and other mechanical properties, all the compounds investigated are found to be ductile in nature with elastic anisotropy. The states at the Fermi level (E-F) are dominated by B p states with significant contributions from the Lambda d states. For the La compounds, small hybridizations of the La f states also occur around E-F.
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