Generation of Internal Stress During Hydrogen and Lithium Transport
Atomic diffusion in insertion electrodes such as hydride-forming metals and transition metal oxides may induce structural deformation due to a volume change, modifying the physical properties of the electrode. Also, the strain or stress field induced by a
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Generation of Internal Stress During Hydrogen and Lithium Transport
6.1
Relationship Between Diffusion and Macroscopic Deformation
Atomic diffusion in insertion electrodes such as hydride-forming metals and transition metal oxides may induce structural deformation due to a volume change, modifying the physical properties of the electrode. Also, the strain or stress field induced by an external force, for example, elastic bending, may influence the diffusion process in the electrode, because of the resulting inhomogeneous distribution of the atoms. The relationship between the diffusion and macroscopic deformation of the electrode can be classified into the elasto-diffusive and diffusion-elastic phenomena as schematically illustrated in Table 6.1 [1].
6.1.1
Elasto-Diffusive Phenomenon
The elasto-diffusive phenomenon is presented in Fig. 6.1, which shows the variation of the hydrogen pressure within a Pd81Pt19 tubular membrane with time from the initial, virtual value, po [1]. The hydrogen pressure was initially kept constant within the tubular membrane and the hydrogen gas was in equilibrium with the hydrogen distributed over the tubular membrane. A subsequent increase of hydrogen concentration at the outer surface caused by the increase of the outer hydrogen pressure results in an initial decrease of the hydrogen pressure within the tube (B in Fig. 6.1a). This phenomenon is known to occur by the outward bending of the tubular membrane, as illustrated in Fig. 6.1b. The outward bending of the tubular membrane causes hydrogen to diffuse from the inner surface toward the outer surface, which is referred to as the elasto-diffusive phenomenon or “Gorsky effect.”
S.-I. Pyun et al., Electrochemistry of Insertion Materials for Hydrogen and Lithium, Monographs in Electrochemistry, DOI 10.1007/978-3-642-29464-8_6, # Springer-Verlag Berlin Heidelberg 2012
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6
Generation of Internal Stress During Hydrogen and Lithium Transport
Table 6.1 Elasto-diffusive and diffusion-elastic phenomena (Reprinted from Han and Pyun [1], Copyright #2001 with permission from Korean Electrochemical Society) Original Primary Direction of Phenomenon state cause Consequence flux (final state) Elastic Inhomogeneous hydrogen Elastobending distribution diffusive
Diffusionelastic
Fig. 6.1 (a) Variation of the hydrogen pressure within a Pd81Pt19 tubular membrane, and (b) the shapes of the tubular membrane at A and B (Reprinted from Han and Pyun [1], Copyright #2001 with permission from Korean Electrochemical Society)
Diffusion flux
Inhomogeneous elastic deformation
6.2 Theory of Stress Change Measurements
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It is known that the relative magnitude of this phenomenon is related to the initial hydrogen concentration. The stress field developed in tubular membranes of Pd and Pd alloys during the Gorsky effect was determined by several researchers using hydrogen permeation techniques [2, 3].
6.1.2
Diffusion-Elastic Phenomenon
The diffusion-elastic phenomenon refers to the situation where stress or strain fields are generated by di
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