An introduction to the theory of inorganic solid surfaces

Structural, Ordering, and Magnetic Properties of PtNi Nanoalloys Explored by Density Functional Theory and Stability Descriptors

“…A third interesting descriptor is the nanoparticle surface energy which can be measured experimentally for pure metallic nanoparticles and nanoalloys. ,, In our study we define this nanoparticle surface energy (γ( N Ni , N Pt )) as the difference between the total cohesion energy of the nanocluster ( E coh NP ( N Ni , N Pt )) and the chemical potentials of Pt (μ Pt ) and Ni (μ Ni ) elements in the various Pt x Ni 1– x alloy bulks ( L 1 2 Pt 3 Ni, L 1 0 PtNi, and L 1 2 PtNi 3 ) and also in the pure Ni and Pt bulks (for x = 0 and x = 1, respectively), by using the Gibbs phase rule (see ref for more details). This excess energy is normalized to the nanoparticle surface area scriptA which is also determined approximately (see the Supporting Information for more details and ref ): γ ( N Ni , N Pt ) = E coh NP ( N Ni , N Pt ) − N Ni μ Ni normalbulk .25em normalPt x Ni 1 − x − N Pt μ Pt normalbulk .25em normalPt x Ni 1 − x scriptA Note that the strain due to the change of structure in the core of the cluster with respect to that of the FCC bulk or to the metallic coordination change at the surface is included in the calculation of the excess energy …”

“…A third interesting descriptor is the nanoparticle surface energy which can be measured experimentally for pure metallic nanoparticles and nanoalloys. ,, In our study we define this nanoparticle surface energy (γ­( N Ni , N Pt )) as the difference between the total cohesion energy of the nanocluster ( E coh NP ( N Ni , N Pt )) and the chemical potentials of Pt (μ Pt ) and Ni (μ Ni ) elements in the various Pt x Ni 1– x alloy bulks ( L 1 2 Pt 3 Ni, L 1 0 PtNi, and L 1 2 PtNi 3 ) and also in the pure Ni and Pt bulks (for x = 0 and x = 1, respectively), by using the Gibbs phase rule (see ref for more details). This excess energy is normalized to the nanoparticle surface area which is also determined approximately (see the Supporting Information for more details and ref ): Note that the strain due to the change of structure in the core of the cluster with respect to that of the FCC bulk or to the metallic coordination change at the surface is included in the calculation of the excess energy …”

Intermetallics with sp–d orbital hybridisation: morphologies, stabilities and work functions of In–Pd particles at the nanoscale

“…The stabilities of the considered systems have been computed using formation enthalpies for bulk and NP stems (Table 1 and Table S5, ESI†) and surface energies as a function of the Pd's chemical potential for slabs (see the ESI,† Section S2). 115 For NPs, historically, stabilities are evaluated through the Δ descriptor:where E NP tot is the total energy of the NP composed of M elements, E coh i is the bulk cohesive energy of the i species and N i is the number of atom i in the nanoparticle. The Δ descriptor approximates the number of surface atoms by , which is not accurate for small NPs.…”