On stainless steel

In Conductivity of saline solution, I talked a little about 316L stainless steel, which I bought to use as electrodes in salt water.  The main facts that I had collected there were the composition, the half-cell potential, and that stainless steel made polarizing electrodes.  I was confused by some of the information, and did a little more reading on stainless steels to try to make sense of it. I’ll repeat the information in this post, so that you don’t have to flip back to the previous one.

The 316L composition given on the Material Safety Data Sheet that came with the welding rods:

element	composition %
C	<0.03
Cr	18–20
Ni	11–14
Mo	2–3
Mn	1.0–2.5
Si	0.3—0.65
Cu	<0.75
P	<0.3
S	<0.3
Fe	balance

I believe that the “L” in the name stands for “low-carbon”, as the composition of 316 stainless steel is listed as being exactly the same except for carbon, which is given as C<0.08%, rather than C<0.03%, though both are much lower in carbon than the usual “mild steel” 0.25%

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Phase diagram for carbon steels, copied from http://www.tf.uni-kiel.de/matwis/amat/mw1_ge/kap_8/illustr/phasendiagramm_fe2.gif
This phase diagram does not really apply to stainless steels, which are iron-chromium-nickel-molybdenum-manganese mixtures, not iron-carbon mixtures. I believe that L stands for “liquid”, α for ferrite, γ for austentite, and δ for another crystal structure of iron that I couldn’t find another name for.  (Most of this information comes from a section on plain-carbon steels in a textbook by Helmut Föll, most of which is in German, but which has a few sections in English.)

An aside on non-stainless steel: A high-carbon steel has 0.8–2.11% carbon, typically around 1.5%, low-carbon C< 0.25%, and plain-carbon or mild steels in between.  The low end of the high-carbon threshold seems to be based on the “eutectoid” point at 0.8% carbon at cherry-red heat (996° K).  Cooling from that temperature results in different structure for the steel for high carbon and mild steels, with pearlite grains embedded in ferrite (for lower carbon) or cementite (for higher carbon).  Pearlite has the eutectoid composition, ferrite is pure iron, and cementite is pure Fe₃C.  Another interesting point on the diagram is the eutectic point at about 4.5%C and 1403° K, which is the composition for cast iron, the carbon and iron mixture with the lowest melting point.

Note: 6.69% carbon by weight is Fe₃C and you can’t dissolve more carbon into iron than that, so that’s why the graph stops at such a low percentage of carbon.

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The half-cell potentials for 316 stainless steel in all the “galvanic series” I found on the web always gave two disjoint ranges: an “active” range (around -0.18v) and a “passive” range (around -0.08v).  My confusion about what that meant is what sent me on the search for more information about stainless steel.  In many applications where we might use stainless steel electrodes, we’re relying on the half-cell potentials of the electrodes being the same, so that they cancel and avoid a DC bias.  If one is “active” and the other is “passive”, though the half-cell potentials will be different.

According to Dr. Anne Marie Helmenstine, in an about.com article on stainless steel, the corrosion resistance of stainless steel comes mainly from a chromium-containing oxide film that forms on steel that has at least 12% chromium content.  This layer is called the “passive film”, and when it is scratched or otherwise compromised the steel is referred to as “active”.  The passive film is self-repairing in high-oxygen environments (like air), but in salt water the chloride ions can attack the film faster than it repairs, particularly if the salt water has a low oxygen content.  I suspect that when I first put the electrodes into the 1M NaCl they had a good passive film on them, but after a few days the film was compromised and the steel should be regarded as active (which also explains the small amount of rust I saw in the cup after a few days).

The 18–20% chromium content of 316L and 11–14% Ni mean that it is most likely an austenitic steel, which means that it primarily has a face-centered cubic crystal (austenite).  Those stainless steels are not hardenable.  Indeed the Specialty Steel Industry of North America in their explanation of the stainless steel classification system puts 316 in the “300 Series Austenitic”, which it describes as

Chromium-nickel alloy can develop high strength by cold working. Non-magnetic, not heat treatable and has good formability. Additions of molybdenum can increase the corrosion resistance.

I note that 316L does have a high molybdenum concentration.  Their Design Guidelines for the Selection and Use of Stainless Steel gives a chart for several of the common stainless steel alloys, showing 316L as deriving from the common 304 type, but with more Mo for higher corrosion resistance and lower carbon for easier welding.  (The 317 and 317L have still more Mo for even higher corrosion resistance.)  The steels in the 316 series, including 316L, are among the few stainless steels suitable for reducing environments.  According to Wikipedia, 316L is commonly used for surgical implants, because of its corrosion resistance and low brittleness (though reactions to the nickel content may still be a problem).

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Stainless steel electrodes, unlike the Ag/AgCl electrodes used in the EKG labs, are polarizable—that supposedly means they behave more like capacitors than resistors.  I think that the insulating layer comes from depletion of ions in a thin layer around the stainless steel, but I don’t really understand electrochemistry.  The electrodes are not perfectly polarizable—there is some leakage current through the insulating layer.

I described in Conductivity of saline solution my experiments to measure and model a pair of electrodes.  The resistances were not high (on the order of a hundred ohms), but the capacitance was quite large (around 60µF), implying a very thin insulating layer, given that the area of each electrode is only about 2.72 cm². (Side note: it is very convenient that 1/8″ rod has a circumference of 1cm to an accuracy of about ¼%.)

The electrical modeling was not very satisfying, though, as it needed 4 parameters to get a not-very-good fit to the data and no intuition about what the parameters corresponded to physically.  The problem is that simple low-pass RC models will have an impedance change that falls off as the inverse of frequency, and the impedance of the electrodes seems to fall off as f^-0.6.

A simple 2-parameter power-law fit seems as good as the 4-parameter (C2 || (R2 + (C1 || R1)) model that I used before, but I have no physical explanation for either model.

The classification of electrodes into “polarizable” and “nonpolarizable” seems to be a simplification of the chemistry. So far as I can tell (I don’t quite understand this yet), the electrical behavior of an electrode is best described by a voltage difference that is linear with current density for low currents and logarithmic with current density for higher currents. (Equivalently, the current density is linear or exponential with voltage difference from equilibrium.) The high-current formula is known as the Tafel law, and the low-current formula as the Stern Geary equation. A more general form that covers both low and high current density is the Butler-Volmer equation, which applies as long as the ions are mobile enough that the current is not limited by mass transfer.

I think that electrodes are “nonpolarizable” if  a large current is needed to move them far from equilibrium potential: that is if the exchange current density in the Butler-Volmer equation is large.  Supposedly, the Ag/AgCl reaction has a high exchange current density as does hydrogen evolution on platinum.  I know that stainless steel electrodes in salt water are considered polarizable, but I don’t know even what the redox reaction is for them, so I don’t know how to look up the exchange current density.  It is undoubtedly complicated by the mix of metals in the alloy and highly affected by the oxide films that provide corrosion resistance, since even the equilibrium voltage (the half-cell potential) is affected by the passive oxide film.

On the other hand, the Butler-Volmer equation is just talking about DC current flow, but what we are interested in is the dynamic behavior of electrodes.  It seems like there we may be more interested in the Cottrell equation, which basically says that current density is proportional to the square root of the derivative of voltage (due to diffusion of the reactants). But that doesn’t look exactly like what is happening if I do I vs. V curves on my scope. What I would expect from the Cottrell equation is a rounded-corner square with a sine-wave input, and a simple square with triangle-wave input.  I sort of get that at low frequencies, but at high frequencies the I vs V curve is a nice straight line, perhaps because there is no time for products to diffuse away before the reverse reaction, and so the Cottrell equation is not really relevant.

Maybe I should set up something to do a much slower sawtooth to see the curves for the Butler-Volmer equation, though I’d have to record the voltage and current numerically and plot the result with gnuplot instead of my scope. Since I have 2 identical electrodes, I should see a symmetric curve, with the minimum current at 0V.  But maybe I should look at some lower salt concentrations first, since that doesn’t need as much change to the setup.

I’m not convinced that the simple (R2+ (R1||C1)) model that Neuman presented in Chapter 5 of  Medical Instrumentation: Application and Design (or, using essentially the same text and pictures, in Chapter 48 of The Biomedical Engineering Handbook: Second Edition) is applicable to stainless steel electrodes in high salt concentration, but I’m not sure how to construct a model that from the Butler-Volmer equation and the Cottrell equation (and maybe others) that would work any better.  Any such model would non-linear, as both the Butler-Volmer equation and the Cottrell equation are non-linear, so the model would not be very useful for a beginning circuits class anyway.