Segmented Random Walks and Correlation Factors in Solid State Diffusion

1975 ◽  
Vol 53 (11) ◽  
pp. 1054-1059 ◽  
Author(s):  
G. V. Kidson

Hart's discussion of the measured diffusion coefficient D, for systems in which atom transport occurs via both the vacancy mechanism and along dislocation pipes, has been generalized to include any number of contributing mechanisms. The treatment introduces the concept of uncorrelated segments and shows that the correlation factor associated with each contributing mechanism contains a time independent parameter [Formula: see text] associated with the average number of jumps per segment. The analysis shows that the usual expression for the correlation factors obtained by assuming [Formula: see text] can be corrected for finite values of [Formula: see text]. The error involved in a typical case is less than 1% if [Formula: see text].

Author(s):  
I. O. Santos-Mendoza ◽  
J. Vázquez-Arenas ◽  
I. González ◽  
G. Ramos-Sánchez ◽  
C. O. Castillo-Araiza

AbstractLithium-ion batteries (LiBs) have gained a worldwide position as energy storage devices due to their high energy density, power density and cycle life. Nevertheless, these performance parameters are yet insufficient for current and future demands diversifying their range of applications, and competitiveness against other power sources. In line with the materials science, the optimization of LiBs, first, requires an in-depth characterization and understanding of their determining steps regarding transport phenomena and electrode kinetics occurring within these devices. Experimental and theoretical studies have identified the solid-state diffusion of Li+into the composite cathode material as one of the transport mechanisms limiting the performance of LiBs, in particular at high charge and discharge rates (C-rates). Nowadays, there is however ambivalence to characterize this mass transport mechanism using the diffusion coefficient calculated either by electrochemical techniques orab initioquantum chemistry methods.  This contribution revisits conventional electrochemical methodologies employed in literature to estimate mass transport diffusivity of LiBs, in particular using LiFePO4in the cathode, and their suitability and reliability are comprehensively discussed. These experimental and theoretical methods include Galvanostatic and Potentiostatic Intermittent Titration Technique (GITT and PITT), Electrochemical Impedance Spectroscopy (EIS), Cyclic Voltammetry (CV) andab initioquantum chemistry methods. On the one hand, experimental methods seem not to isolate the diffusion mechanism in the solid phase; thus, obtaining an unreliable apparent diffusion coefficient (ranging from 10–10to 10–16 cm2 s−1), which only serves as a criterion to discard among a set of LiBs. On the other hand, atomistic approaches based onab initio, density functional theory (DFT), cannot yet capture the complexity of the local environments involved at this scale; in consequence, these approaches have predicted inadequate diffusion coefficients for LiFePO4(ranging from 10–6to 10–7 cm2 s−1) which strongly differ from experimental values. This contribution, at long last, remarks the factors influencing diffusion mechanisms and addresses the uncertainties to characterize this transport mechanism in the cathode, stressing the needs to establish methods to determine the diffusion coefficient accurately, coupling electrochemical techniques,ab initiomethods, and engineering approaches based on modeling.


Author(s):  
Jeffrey S. Horner ◽  
Grace Whang ◽  
David S. Ashby ◽  
Igor V. Kolesnichenko ◽  
Timothy N. Lambert ◽  
...  

2002 ◽  
Vol 17 (1) ◽  
pp. 52-59 ◽  
Author(s):  
N.F. Gao ◽  
Y. Miyamoto

The joining of a Ti3SiC2 ceramic with a Ti–6Al–4V alloy was carried out at the temperature range of 1200–1400 °C for 15 min to 4 h in a vacuum. The total diffusion path of joining was determined to be Ti3SiC2/Ti5Si3Cx/Ti5Si3Cx + TiCx/TiCx/Ti. The reaction was rate controlled by the solid-state diffusion below 1350 °C and turned to the liquid-state diffusion controlled with a dramatic increase of parabolic rate constant Kp when the temperature exceeded 1350 °C. The TiCx tended to grow at the boundarywith the Ti–6Al–4V alloy at a higher temperature and longer holding time. TheTi3SiC2/Ti–6Al–4V joint is expected to be applied to implant materials.


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