Coherency strain and the kinetics of phase separation in LiFePO4

A theoretical investigation of the effects of elastic coherency on the thermodynamics, kinetics, and morphology of intercalation in single LiFePO4 nanoparticles yields new insights into this important battery material. Anisotropic elastic stiffness and misfit strains lead to the unexpected prediction that low-energy phase boundaries occur along {101} planes, while conflicting reports of phase boundary orientations are resolved by a partial loss of coherency in the {100} direction. Elastic relaxation near surfaces leads to the formation of a striped morphology, whose characteristic length scale is predicted by the model and yields an estimate of the interfacial energy. The effects of coherency strain on solubility and galvanostatic discharge are studied with a reaction-limited phase-field model, which quantitatively captures the influence of misfit strain, particle size, and temperature on solubility seen in experiments. Coherency strain strongly suppresses phase separation during discharge, which enhances rate capability and extends cycle life. The effects of elevated temperature and the feasibility of nucleation are considered in the context of multi-particle cathodes

Theory of Nucleation in Phase-separating Nanoparticles

The basic physics of nucleation in solid \hl{single-crystal} nanoparticles is revealed by a phase-field theory that includes surface energy, chemical reactions and coherency strain. In contrast to binary fluids, which form arbitrary contact angles at surfaces, complete "wetting" by one phase is favored at binary solid surfaces. Nucleation occurs when surface wetting becomes unstable, as the chemical energy gain (scaling with area) overcomes the elastic energy penalty (scaling with volume). The nucleation barrier thus decreases with the area-to-volume ratio and vanishes below a critical size, and nanoparticles tend to transform in order of increasing size, leaving the smallest particles homogeneous (in the phase of lowest surface energy). The model is used to simulate phase separation in realistic nanoparticle geometries for \ce{Li_XFePO4}, a popular cathode material for Li-ion batteries, and collapses disparate experimental data for the nucleation barrier, with no adjustable parameters. Beyond energy storage, the theory generally shows how to tailor the elastic and surface properties of a solid nanostructure to achieve desired phase behavior.Comment: 7 pages, 4 fig

A Characterization of Four Prairie Grasses

Even though native range forages have been available a long time, there is little research data concerning the specific grasses characterized as native forage or browse. Little research has been done to study these forages because of their natural habitat far from research laboratories, the task of collecting enough forage for adequate sample testing, and sparse yet hardy existence and questionable known vegetative growth with each year\u27s different climate and environmental conditions. Certainly it seems logical that at some future time the knowledge of their nutritive value will become important. Perhaps then with adequate management the rancher can improve upon native grasses he already has or the grass breeder can use the knowledge to his advantage to breed a desirable characteristic into a new grass variety. Two warm season grasses, blue grama (Bouteloua gracilis) and prairie sandreed (Calamovilfa lonizifqlia), and two cool season grasses needle and thread (Stipa comata) and threadleaf sedge (Carex filifolia) were studied. Samples of the grasses were collected throughout the 1968 growing season at the Antelope Range Field Station in northwestern South Dakota. The research undertaken had the following objectives: 1. To characterize range grasses by analysis of the components cellulose, acid-detergent fiber, acid-detergent lignin, dry matter digestibility, protein, holocellulose, hemicellulose, neutral sugar an uronic sugar content. 2. To study comparative composition of the various grasses at different cutting dates. 3. To give special emphasis to any comparative differences between cool and warm season grasses. All comparisons in this study centered largely on fibrous carbohydrates and the components closely associated with them

Pine Needle (Pinus ponderosa) Abortive Factor and its Biological Determination

A study was conducted to develop a reliable method to measure presence and quantity of the toxic factor in ponderosa pine (Pinus ponderosa) needles that interferes with normal maintenance of pregnancy in cattle. Special emphasis was given to biological assay sensitivity during embryo implantation and gestation in laboratory animals. The detrimental component was found to be present in both aqueous and acetone fractions prepared from ponderosa pine needles. There was a reduction in average rat litter size from bred rats fed either the aqueous or acetone pine needle extracts throughout pregnancy. Rats fed pine needle extracts from the winter pine needles delivered smaller litters at term than did those fed summer and fall pine needle extracts and the unidentified detrimental component in winter pine needles was more toxic to both dam and fetus. Reduction in viable embryos was observed 5 to 7 days post coitum from mice fed aqueous or acetone pine needle extracts from any of six collection dates. Adrenal weight obtained during the implantation study reflected a time x treatment x age interaction but failed to provide definite conclusions abo·.t ponderosa pine needle toxicity. Gestation study verified results from the implementation experiment as very few mice fed pine needle extracts delivered normal litter. Mice receiving the concentrated aqueous extract suffered diarrhea and inadequate feed intake. It appeared evident that a biological assay at implantation could be used to estimate injury from feeding ponderosa pine needle extracts to bred laboratory animals throughout gestation. Both dried needles and branches collected throughout the year were analyzed for moisture, ash, crude protein, ether extract, acid-detergent fiber, acid-detergent lignin and in vitro dry matter digestibility. In general, chemical components and in vitro dry matter digestibility changed very little on a month to month basis but low protein content and low digestibility would hinder long term maintenance of an animal on ponderosa pine needles and branches. The use of biological assay in early gestation should serve as a useful screening tool for eventual isolation of the “active ponderosa pine needle abortive factor.

Thermodynamic phase-field model for microstructure with multiple components and phases: the possibility of metastable phases

A diffuse-interface model for microstructure with an arbitrary number of components and phases was developed from basic thermodynamic and kinetic principles and formalized within a variational framework. The model includes a composition gradient energy to capture solute trapping, and is therefore suited for studying phenomena where the width of the interface plays an important role. Derivation of the inhomogeneous free energy functional from a Taylor expansion of homogeneous free energy reveals how the interfacial properties of each component and phase may be specified under a mass constraint. A diffusion potential for components was defined away from the dilute solution limit, and a multi-obstacle barrier function was used to constrain phase fractions. The model was used to simulate solidification via nucleation, premelting at phase boundaries and triple junctions, the intrinsic instability of small particles, and solutal melting resulting from differing diffusivities in solid and liquid. The shape of metastable free energy surfaces is found to play an important role in microstructure evolution and may explain why some systems premelt at phase boundaries and phase triple junctions while others do not.Comment: 14 pages, 8 figure

Building Demand and Reaching for Capacity

In this case study, the authors describe a classroom redesign at Dartmouth College. The classroom was redesigned as a way to seed innovations in teaching and new ideas on how space influences learning through a partnership incubator for working with faculty. This paper outlines the campus context for how the classroom was redesigned, data collected on its use, and the support structure for faculty

Size-dependent phase morphologies in LiFePO4 battery particles

Lithium iron phosphate (LiFePO$_4$) is the prototypical two-phase battery material, whose complex patterns of lithium ion intercalation provide a testing ground for theories of electrochemical thermodynamics. Using a depth-averaged (a-b plane) phase-field model of coherent phase separation driven by Faradaic reactions, we reconcile conflicting experimental observations of diamond-like phase patterns in micron-sized platelets and surface-controlled patterns in nanoparticles. Elastic analysis predicts this morphological transition for particles whose a-axis dimension exceeds the bulk elastic stripe period. We also simulate a rich variety of non-equilibrium patterns, influenced by size-dependent spinodal points and electro-autocatalytic control of thermodynamic stability

The development and validation of a teacher-reported low-level classroom disruption scale (LLCD-S)

Low-level classroom disruption (LLCD) is characterised by pupils swinging on chairs, whispering or fidgeting in class. This paper provides initial data on the development and validation of the teacher-rated Low-Level Classroom Disruption Scale (LLCD-S), with two samples of primary school pupils. Exploratory factor analysis in Study 1 (N= 120) revealed one factor accounting for 61% of the variance; supported by confirmatory factor analysis in Study 2 (N= 274), with one factor accounting for 63% of the variance. Both studies reported high Cronbach’s alpha values of.82 and.93 respectively. The evidence supports LLCD being a unidimensional construct, measured by the eight item LLCD-S. Weak convergence validity was found between the LLCD-S and the Strengths and Difficulties Questionnaire’s (SDQ) externalising behaviours: conduct problems and hyperactivity. This preliminary evidence indicates that LLCD-S is a valid and reliable measure of low-level classroom disruption. Further research is needed to test the utility of the LLCD-S across different levels of education, cultures and as a pupil-reported measure