The Effect of Lattice Vibrations on Substitutional Alloy Thermodynamics

A longstanding limitation of first-principles calculations of substitutional alloy phase diagrams is the difficulty to account for lattice vibrations. A survey of the theoretical and experimental literature seeking to quantify the impact of lattice vibrations on phase stability indicates that this effect can be substantial. Typical vibrational entropy differences between phases are of the order of 0.1 to 0.2 k_B/atom, which is comparable to the typical values of configurational entropy differences in binary alloys (at most 0.693 k_B/atom). This paper describes the basic formalism underlying ab initio phase diagram calculations, along with the generalization required to account for lattice vibrations. We overview the various techniques allowing the theoretical calculation and the experimental determination of phonon dispersion curves and related thermodynamic quantities, such as vibrational entropy or free energy. A clear picture of the origin of vibrational entropy differences between phases in an alloy system is presented that goes beyond the traditional bond counting and volume change arguments. Vibrational entropy change can be attributed to the changes in chemical bond stiffness associated with the changes in bond length that take place during a phase transformation. This so-called ``bond stiffness vs. bond length'' interpretation both summarizes the key phenomenon driving vibrational entropy changes and provides a practical tool to model them.Comment: Submitted to Reviews of Modern Physics 44 pages, 6 figure

Seasonal variation of photosynthetic model parameters and leaf area index from global Fluxnet eddy covariance data

This is the publisher’s final pdf. The published article is copyrighted by American Geophysical Union and can be found at: http://sites.agu.org/.Global vegetation models require the photosynthetic parameters, maximum carboxylation capacity (V[subscript cm]), and quantum yield (alpha) to parameterize their plant functional types (PFTs). The purpose of this work is to determine how much the scaling of the parameters from leaf to ecosystem level through a seasonally varying leaf area index (LAI) explains the parameter variation within and between PFTs. Using Fluxnet data, we simulate a seasonally variable LAI(F) for a large range of sites, comparable to the LAI[subscript M] derived from MODIS. There are discrepancies when LAI[subscript F] reach zero levels and LAI[subscript M] still provides a small positive value. We find that temperature is the most common constraint for LAI[subecript F] in 55% of the simulations, while global radiation and vapor pressure deficit are the key constraints for 18% and 27% of the simulations, respectively, while large differences in this forcing still exist when looking at specific PFTs. Despite these differences, the annual photosynthesis simulations are comparable when using LAI[subscript F] or LAI[subscript M](r² = 0.89). We investigated further the seasonal variation of ecosystem-scale parameters derived with LAI[subscript F]. V[subscript cm] has the largest seasonal variation. This holds for all vegetation types and climates. The parameter alpha is less variable. By including ecosystem-scale parameter seasonality we can explain a considerable part of the ecosystem-scale parameter variation between PFTs. The remaining unexplained leaf-scale PFT variation still needs further work, including elucidating the precise role of leaf and soil level nitrogen