J. N. Christensen

A Mathematical Model of Stress Generation and Fracture in Lithium Manganese Oxide

Fracture of Li y Mn 2 O 4 is predicted with a numerical model that calculates the stress generated in spherical particles due to lithium intercalation along the 4-V plateau and phase change along the 3-V plateau. In the former case, fracture is probable at the rates typical of high-power applications, while in the latter case, the probability of fracture is linked not to the discharge rate or particle size, but to the LiMn 2 O 4 /Li 2 Mn 2 O 4 phase ratio. The two-phase material should fracture immediately upon lithium extraction. The effects of variation in thermodynamic factor, diffusion coefficient, and lattice parameter are examined in detail.

A Mathematical Model for the Lithium-Ion Negative Electrode Solid Electrolyte Interphase

The passivating solid electrolyte interphase (SEI) layer forms at the surface of the negative-electrode active material in lithium-ion cells. A continuum-scale mathematical model has been developed to simulate the growth of the SEI and transport of lithium and electrons through the film. The model is used to estimate the film growth rate, film resistance, and irreversible capacity loss due to film formation. We show that film growth at the negative electrode is faster for charged batteries than for uncharged batteries and that higher electron mobility in the film leads to faster growth. If electron mobility is low, the rate of film growth is limited by transport of electrons through the film, and the rate decreases as the thickness increases. We examine the dependence of film resistance upon both film thickness and defect concentration in the film. We also show that the concentration polarization in the film increases as it grows at open circuit, even though the concentration gradient may decrease.

Cyclable Lithium and Capacity Loss in Li-Ion Cells

In lithium-ion cells, there are several different classes of capacity loss, both reversible and irreversible, that limit the cells exploitable specific capacity and can lead to eventual cell failure. We attempt to clarify what is meant by capacity loss and cyclable lithium loss by defining these terms in the context of electrode state-of-charge restrictions. We define irreversible capacity loss as that associated with active material loss and define two types of reversible capacity loss associated with balanced and unbalanced side reactions. We also examine several methods of compensating for cyclable lithium loss associated with passive-film formation and calculate the effect each has on a cells specific energy. Preforming the negative electrode, adding cyclable lithium to the positive electrode, and introducing lithium powder into the negative electrode appear to be the most attractive methods in terms of specific energy, but practical constraints such as fabrication cost must be evaluated to determine which is superior.

Time scales of large volume silicic magma systems: Sr isotopic systematics of phenocrysts and glass from the Bishop Tuff, Long Valley, California

The initial Sr isotopic compositions of glass and mineral separates from the 0.74 Ma Bishop Tuff ashflow in eastern California were determined to investigate the time scales of magmatic processes in a large silicic system. It was found that there is substantial isotopic heterogeneity, both between eruptive units and between glass and phenocryst phases of individual units. The frist-erupted, lower temperature units generally have higher initial 87Sr/86Sr than later crupted, higher temperature units. Within each unit, feldspar phenocrysts have the lowest 87Sr/86Sr, associated glass has higher 87Sr/86Sr, and biotite phenocrysts have the highest 87Sr/86Sr. These isotopic differences were produced by processes in the magma chamber and not by post-eruptive alteration. Two samples were similar Fe−Ti oxide temperatures but from widely separated localities have nearly identifical Sr isotopic characteristics, indicating the existence of compositionally uniform layers of substantial volume within the chamber. Trace element data indicate that the feldspars crystallized from a liquid represented by the associated glass, and that the feldspar-glass pairs are not accidental. The rhyolitic liquids of the Bishoptuff magma chamber apparently experienced increasing 87Sr/86Sr at a rate too fast for feldspar phenocrysts to remain in isotopic equilibrium. The increasing 87Sr/86Sr is caused primarily by radioactive decay of 87Rb in the high-Rb/Sr liquids and not primarily by assimilation of radiogenic wall-rock material. A self-consistent model can be constructed to account for all of the isotopic data except for those on biotite phenocrysts. The time scale for evolution of the system is bounded on the high side at about 500 ky by observations made on precaldera lavas, and on the low side at approximately 300 ky by the time necessary to establish homogeneous layers in an actively differentiating chamber. The deduced time scale is consistent with model Rb−Sr ages, which date the differentiation of low temperature liquids from higher temperature liquids, and is compatible with the observed isotopic disequilibrium between feldspars and glass because of the low diffusivity of Sr in fieldspars (<10-16 cm2/s). The prolonged (about 500 ky) evolution of the Bishop Tuff system was facilitated by a large influx of basaltic material (about 10-2 km3/y) to the base of the system, which compensated for diffusive heat loss from the top and allowed large volumes of magma to maintain low crystal contents for >3x105 years. The silicic-magma production rate within the Bishop Tuff magma chamber is estimated to be 10-3km3/y. The growth rate of alkali feldspar is estimated to be about 10-14 cm/s based on the Sr isotopic difference between sanidine and glass of the lower Bishop Tuff. The biotite population is inferred to be partially (>50 ppm) xenocrystic, the xenocrysts being introduced to the chamber less than one year prior to eruption.

Prediction of New Clinical Vertebral Fractures in Elderly Men using Finite Element Analysis of CT Scans

Vertebral strength, as estimated by finite element analysis of computed tomography (CT) scans, has not yet been compared against areal bone mineral density (BMD) by dual‐energy X‐ray absorptiometry (DXA) for prospectively assessing the risk of new clinical vertebral fractures. To do so, we conducted a case‐cohort analysis of 306 men aged 65 years and older, which included 63 men who developed new clinically‐identified vertebral fractures and 243 men who did not, all observed over an average of 6.5 years. Nonlinear finite element analysis was performed on the baseline CT scans, blinded to fracture status, to estimate L1 vertebral compressive strength and a load‐to‐strength ratio. Volumetric BMD by quantitative CT and areal BMD by DXA were also evaluated. We found that, for the risk of new clinical vertebral fracture, the age‐adjusted hazard ratio per standard deviation change for areal BMD (3.2; 95% confidence interval [CI], 2.0–5.2) was significantly lower (p < 0.005) than for strength (7.2; 95% CI, 3.6–14.1), numerically lower than for volumetric BMD (5.7; 95% CI, 3.1–10.3), and similar for the load‐to‐strength ratio (3.0; 95% CI, 2.1–4.3). After also adjusting for race, body mass index (BMI), clinical center, and areal BMD, all these hazard ratios remained highly statistically significant, particularly those for strength (8.5; 95% CI, 3.6–20.1) and volumetric BMD (9.4; 95% CI, 4.1–21.6). The area‐under‐the‐curve for areal BMD (AUC = 0.76) was significantly lower than for strength (AUC = 0.83, p = 0.02), volumetric BMD (AUC = 0.82, p = 0.05), and the load‐to‐strength ratio (AUC = 0.82, p = 0.05). We conclude that, compared to areal BMD by DXA, vertebral compressive strength and volumetric BMD consistently improved vertebral fracture risk assessment in this cohort of elderly men.

Optimization of Lithium Titanate Electrodes for High-Power Cells

A full-cell mathematical model is used to compare the performance of graphite (Li{sub x}C{sub 6}) and lithium titanate (Li{sub 4+3x}Ti{sub 5}O{sub 12}) negative electrodes, with a doped lithium manganese oxide (Li{sub y+0.16}Mn{sub 1.84}O{sub 4}) positive electrode. The cell designs are optimized over electrode thickness and porosity, and several particle sizes are examined for the lithium titanate/manganese oxide system. Although the graphite-based cell contains a higher specific energy than the titanate-based cell, the latter performs better at high rates (>12C) when submicrometer particle sizes are used for both the positive and negative electrode. In light of this and several life-related advantages possessed by the Li{sub 4+3x}Ti{sub 5}O{sub 12} electrode, it is recommended for development as a high-power energy storage system.

Effect of Anode Film Resistance on the Charge/Discharge Capacity of a Lithium-Ion Battery

Lithium-ion batteries are prone to failure, because both their capacity and rate capability decrease with cycling. Side reactions, which decrease the cells cyclable lithium content, can be responsible for capacity fade. An increase in cyclable lithium content is also possible, but is limited by the initial overall lithium content. Formation of a solid electrolyte interphase film on the carbonaceous anode not only consumes cyclable lithium, but also increases the anode resistance, thus reducing the rate capability of the cell, as demonstrated via computer simulation of a lithium-ion cell. Simulations also suggest that the use of cutoff potentials may not effectively prevent undesired irreversible side reactions on overcharge or overdischarge.