Thermodynamic Geometry of the Born-Infeld-anti-de Sitter black holes

Thermodynamic geometry is applied to the Born-Infeld-anti-de Sitter black hole (BIAdS) in the four dimensions, which is a nonlinear generalization of the Reissner-Norstr\"Aom-AdS black hole (RNAdS). We compute the Weinhold as well as the Ruppeiner scalar curvature and find that the singular points are not the same with the ones obtained using the heat capacity. Legendre-invariant metric proposed by Quevedo and the metric obtained by using the free energy as the thermodynamic potential are obtained and the corresponding scalar curvatures diverge at the Davies points.Comment: Latex,19 pages,14 figure

Crystal structure and physical properties of half-doped manganite nanocrystals with size < 100nm

In this paper we report the structural and property (magnetic and electrical transport) measurements of nanocrystals of half-doped $\mathrm{La_{0.5}Ca_{0.5}MnO_3}$(LCMO) synthesized by chemical route, having particle size down to an average diameter of 15nm. It was observed that the size reduction leads to change in crystal structure and the room temperature structure is arrested so that the structure does not evolve on cooling unlike bulk samples. The structural change mainly affects the orthorhombic distortion of the lattice. By making comparison with observed crystal structure data under hydrostatic pressure it is suggested that the change in the crystal structure of the nanocrystals occurs due to an effective hydrostatic pressure created by the surface pressure on size reduction. This not only changes the structure but also causes the room temperature structure to freeze-in. The size reduction also does not allow the long supercell modulation needed for the Charge Ordering, characteristic of this half-doped manganite, to set-in. The magnetic and transport measurements also show that the Charge Ordering (CO) does not occur when the size is reduced below a critical size. Instead, the nanocrystals show ferromagnetic ordering down to the lowest temperatures along with metallic type conductivity. Our investigation establishes a structural basis for the destabilization of CO state observed in half-doped manganite nanocrystals.Comment: 11 pages, 13 Figure