Remarks on the electrochemical application of optical methods for the determination of stress in electrodes

doi:10.1016/j.electacta.2005.04.006

Electrochimica Acta

Volume 51, Issue 1, 5 October 2005, Pages 93-97

https://doi.org/10.1016/j.electacta.2005.04.006 Get rights and content

Abstract

Experimental methods based on light beam deflection for the determination of surface stress change of electrodes are critically revisited. Expressions for the evaluation of data from electrochemical bending beam experiments with non-normal light incidence are derived. Consequences of neglecting the refraction at the optical window or at the air/solution boundary are discussed. It is shown that the data analysis in previous work needs revision, since neglecting the refraction may introduce severe errors in the calculations, and this can lead to inconsistencies in the interpretation of the experimental results.

Introduction

Measuring the bending of a plate to determine surface stress change or the stress in thin films is a common technique, even in electrochemistry [1], [2], [3], [4], [5], [6], [7], [8], [9]. It has been also used for instance for the investigation of the origin of electrochemical oscillations at silicon electrodes [10] or in the course of galvanostatic oxidation of organic compounds on platinum [11], [12], for the study of volume changes in polymers during redox processes [13], for the investigation of the response kinetics of the bending of polyelectrolyte membrane platinum composites by electric stimuli [14], and for the experimental verification of the adequacy of the “brush model” of polymer modified electrodes [15], etc.

Unfortunately, in many papers reporting results on electrochemical bending beam (“cantilever beam”, “bending cantilever”, “light beam deflection”, etc.) experiments, schemes of experimental arrangements can be found in which the direction of the reflected beam before and after passing the optical window or the air/solution boundary is indicated incorrectly, since the effect of refraction is ignored. In addition, no reference is made to the refractive index of the solution, or the value of the refractive index of the solution is not indicated, e.g. [3], [4], [5], [6], [7], [8], [9], [10].

However, neglecting the refraction may lead to severe problems in the interpretation of the experimental results.

For example, in a recent communication, Pyun et al. [16] reported experimental data for the stress change, Δσ, generated during lithium transport through a thin Li_1−δCoO₂ film determined as a function of the lithium stoichiometry (1 − δ), using the laser beam deflection method combined with cyclic voltammetry, and other electrochemical techniques. The thin film was deposited on the sputter-deposited Pt current collector on one side of a thin glass plate by magnetron sputtering of a LiCoO₂ target at room temperature.

For the measurements the experimental setup shown in [16, Fig. 1] was used. According to this, the light of a He–Ne laser was reflected by the free end of a cantilever electrode, and detected by a position-sensing photodetector (PSD).

For the calculation of the film stress a particular form [17] of Stoney's original equation [18] was proposed: $Δ σ = \frac{Y_{s} t_{s}^{2}}{6 (1 - v_{s}) t_{f}} \frac{Δ d}{2 D l}$ where σ is the film stress, t_f is the thickness of the film, Y_s, $ν_{s}$ and t_s are Young's modulus, Poisson's ratio and the thickness of the substrate, l represents the distance between solution level and reflection point of laser beam, D the distance between the thin glass plate and the PSD, and $Δ d$ is the change in the position of the reflected beam on the PSD, respectively.

Besides the experimental determination of Δσ, values of the stress changes generated in the Li_1−δCoO₂ film electrode during lithium transport were also determined theoretically by using an appropriate model. It is noted in the text, that there is only a slight discrepancy in the values of Δσ measured experimentally and calculated theoretically.

According to the authors, “one of the probable reasons for this slight discrepancy is the experimental error which originates from refraction of the laser beam by the electrolyte in the measurement of Δσ” [16, p. 4485].

This statement is rather surprising, since the problems caused by refraction in case of electrochemical applications of the “bending beam” method – for the special case of normal incidence at the optical window – were already discussed in [19]. It is well known, that the case of non-normal incidence, if the deflection of a light beam is measured outside the phase where the mirroring surface is located, the deflection angle should be usually corrected according to the Schnell's law of refraction. According to this law, when light travels from one medium into another the incident and refracted rays lie in one plane with the normal to the surface; are on opposite sides of the normal; make angles with the normal whose sines have a constant ratio to one another.

However, the geometrical arrangement of light source, electrode and detector used in [16, Fig. 1] differs from that discussed in [19], because the incident laser beam is not coming from a direction normal to the plane of the optical window, as assumed in [19]. It is clear that if the incident beam is perpendicular to the optical window, no refraction occurs, which makes the situation simpler, and the calculations easier. It should be noted, that in [16, Fig. 1] the directions both of the incident and the reflected laser beams before and after passing the optical window remain apparently the same. This cannot be the case in reality.

In order to estimate the error due to neglecting the effect of refraction, we have to take into account that the “original” form of Stoney's equation contains the reciprocal radius of curvature of the substrate (1/R), i.e. the change in the film stress can be expressed as $Δ σ = \frac{Y_{s} t_{s}^{2}}{6 (1 - v_{s}) t_{f}} Δ (\frac{1}{R}) = K_{i} Δ (\frac{1}{R})$ or by introducing the constant $K_{i} = Y_{s} t_{s}^{2} / (6 (1 - v_{s}) t_{f})$ : $Δ σ = K_{i} Δ (1 / R)$

Our aim is to derive an equation between the changes of the radius of curvature Δ(1/R) and the displacement of the light spot Δd on the PSD, without assuming that the incident laser beam is perpendicular to the optical window.

Section snippets

Electrochemical “bending beam” experiments: expressions for evaluation of the measured data

Fig. 1 shows the optical configuration of a typical arrangement for electrochemical bending beam experiments. Such a setup can be used mainly for the investigation of small deflections, and several details may be different in special cases. As it can be seen in Fig. 1, D is the distance between the electrode and the photodetector, b is the distance between the optical window and the reflection point (B) on the electrode, $w$ is the distance between the optical window and the detector plane, and s

Discussion of the results in [16]

On the basis of the above considerations, the expected error of Δσ, calculated in [16] from the change in the position of the reflected beam on the PSD by neglecting the effect of refraction, is about 30%. Therefore, it is quite surprising that the experimentally determined and theoretically calculated Δσ values in [16] differ only slightly. However, this contradiction can be probably resolved by taking into account, that the correct value of K_i in Eq. (3) may be uncertain. It is well known,

Conclusions

Taking into account the main points of the above considerations the following conclusions can be drawn:

1.
Many figures in the literature showing experimental setups or optical configurations for electrochemical “bending beam” (“laser beam deflection”) experiments with non-normal incidence of the light beam at the optical window or at the air/solution boundary are incorrect, since in the figures the direction of the reflected beam in the two different media adjacent to the optical window is the

Acknowledgement

Financial support from the Hungarian Scientific Research Fund (OTKA T037588, M042115) is acknowledged.

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Remarks on the electrochemical application of optical methods for the determination of stress in electrodes

Abstract

Introduction

Section snippets

Electrochemical “bending beam” experiments: expressions for evaluation of the measured data

Discussion of the results in [16]

Conclusions

Acknowledgement

Ultramicroscopy

Surf. Sci.

Surf. Sci.

Electrochem. Commun.

J. Electroanal. Chem.

J. Electroanal. Chem.

Electrochim. Acta

J. Electroanal. Chem.

Surf. Sci. Rep.

J. Electrochem. Soc.