The Role of Surface and Interface Energy on Phase Stability of Nanosized Insertion Compounds

Adv. Mater. 2009, 21, 2703–2709 2009 WILEY-VCH Verlag G T IO N The exploration of nanoscale materials during the past decade has led to great advances in both sciences and technology. Recent developments in the field of nanoionics is offering new possibilities and challenges for the much required future energy-storage and conversion devices. When particle sizes approach the nanoscale, the influence of surfaces and interfaces can no longer be neglected in the rationalization and prediction of a material thermodynamic and kinetic properties. Recent observations in crystalline battery materials and hydrogenstorage materials that undergo a first-order phase transition upon ionic insertion indicate that a reduction in particle size causes a change of the equilibrium compositions, leading to a decrease or a shift of the miscibility gap. Surprisingly, such nanoscale effects already set in at particle sizes as large as 100 to 150 nm. This has direct consequences for the voltage profile during battery charging or the equilibrium pressure during hydrogen loading, which for large particles are constant during a two-phase reaction. Generally, a reduced voltage or increased pressure plateau is observed in a two-phase reaction within nanoparticles, indicating a lower stability of the Li/H rich phase. Changes in thermodynamic properties at the nanoscale can also impact kinetic behavior. It has for example been proposed that increases in vacancy concentration due to altered equilibrium compositions at the nanoscale enhances ionic mobilities to render reversibility of hydrogen loading possible in metal hydrides and to enable Li-insertion in otherwise inactive electrode materials. Nanoscaling has also been identified as playing an important role in enhancing (dis)charge rates in LixFePO4, as it seems to increase equilibrium compositions and thereby reduce the lattice mismatch between coexisting phases, which is responsible for large energy barriers to two-phase decomposition due to coherency strains. In this paper, we derive general equilibrium criteria for two-phase coexistence within insertion compound nanocrystallites, explicitly accounting for surface and interface free-energy contributions. For typical values of surface and interface energies estimated from first principles for LixFePO4, [17] we find that interface contributions in particular can have a pronounced effect on equilibrium compositions for two-phase coexistence in nanocrystallites. Not only do the solubility limits and equilibrium compositions depend on the particle size, they appear surprisingly sensitive to the particle shape, rationalizing recent inconsistent observations of solubility limits in nanosized LiFePO4. The derived equilibrium criteria for two-phase coexistence in nanocrystallites also shows that the equilibrium compositions are not constant, but depend on the overall concentration of the particle. This prediction implies that equilibrium compositions measured electrochemically (based on concentrations coinciding with the onset of two-phase coexistence) will not necessary produce the same values as those measured using diffraction techniques (such as neutron diffraction). We also provide simple graphical construction methods to assess the role of surface and interface free energies on two-phase coexistence within insertion compound crystallites. We consider crystalline host materials that undergo a first-order phase transformation upon insertion of interstitial Li ions from a Li poor phase (a) to a Li rich phase (b). We denote the bulk Gibbs free energies at constant temperature (T) and pressure (P) of the a and b phases by ga(xa) and gb(xb),defined per interstitial site. The concentrations xa and xb refer to the fraction of filled interstitial sites in the a and b phases. For small crystallites, surface and interfacial free energies, s and gab, become important. If the crystallite consists of a single phase, its free energy can be written as