How to Season A Wok & Thin-Film Interference
Why do heated woks turn blue? I asked ChatGPT, but it's still not great at physics.
Dan Dan Noodles are Too Damn Expensive
One day, my fiancée and I went out for Dan Dan Noodles (here’s a great recipe) at a local Chinese restaurant, and it cost us $47 for two (small) bowls of noodles. I know the cost of living is high in my area, but that is just absurd.
Anyway, I decided to learn how to cook various styles of Chinese food properly, so I wouldn’t spend my entire paycheck on small bowls of noodles.
Among other things, I bought a nice carbon steel wok for stir-frying.
How to Season a Wok
Carbon steel woks have to be seasoned before use, just like a cast iron pan. Here are the steps:
Wash the Wok: Wash the wok thoroughly with soap and water to remove any lingering oils from the factory
Anneal the Wok: Heat the wok over the hottest flame you can find until it turns completely blue.
Annealing the wok. You can see the blue color forming on the inside of the wok. Cool the Wok: Cool the superheated wok down and dry it off
Season the Wok: Add a thin coat of oil to the wok, heat it up until it starts smoking and develops a brown/black patina
Use the Wok: Cook with it. Lots of oil and heat will create a nonstick coating just like a cast iron.
It’s a little weird though, my wok turned a really pretty shade of blue.
Why do Woks Turn Blue When Heated?
This was a very cool effect to see in person. Naturally, I asked ChatGPT to explain why woks turn blue when you heat them.
The answer it gave is only partially correct. The blue color is due to a thermally grown iron oxide on the wok surface (not rust), but the color blue is not an inherent property of the oxide. Most of the answers you’ll read on the internet are at best partially correct, which is probably why ChatGPT doesn’t know the full answer. The best I found was makeitfrommetal, and even it gets some details wrong. So what’s really going on?
When carbon steel is heated to sufficiently high temperature (~400C in my case), iron in the steel reacts with oxygen in the air, forming a layer of “black oxide,” also known as magnetite (Fe3O4), on the surface of the steel. This black oxide is distinct from “red oxide,” or rust (Fe2O3), which naturally develops on an unprotected iron/steel surface.
The black oxide forms an extremely thin protective layer over the carbon steel, preventing rust and corrosion. But why is this layer blue, as opposed to black, or any other color?
ChatGPT has made up a plausible, but wrong answer. The color has nothing to do with absorption properties of iron oxide, and the specific iron oxide is not rust. Nor does the color have to do with impurities. The real answer is that my wok looks blue because the black oxide coating is 100 nanometers thick. The color on the wok is derived from the same effect that gives oil slicks the cool rainbow effect, called thin-film interference.
Let’s look at the principles behind thin-film interference and estimate the coating thickness on my wok.
Wave Interference
Interference is a term used in wave mechanics that basically means addition. Consider a sine wave, given by the expression:
φ is the “phase” of the sine wave. This phase is periodic, meaning that the wave repeats itself each 2π phase increment. A wave “accumulates” phase as it travels — as the wave propagates in space and time, its phase changes. Specifically, phase changes as φ = k(x-vt), where k is the wavenumber, x is position, t is time, and v is the wave speed.
When two identical sine waves are added, they are said to be “in phase” and constructively interfere.
When two sine waves shifted by one half period are added, they are said to be “out of phase” and destructively interfere.
Interference in Thin Films
Calculating the interference between two waves basically involves tracking the total phase φ accumulated by each wave, then adding the waves together with the correct phase difference. The phase accumulated by a wave traveling a distance d in a medium with index of refraction n is
where λ is the wavelength.
Light can also change phase on reflection. Phase change at an interface is actually very complicated in general, but here’s three rules that will serve you pretty well:
Light reflecting off a metal gains π phase on reflection
Light in a low-index medium reflecting off a high-index medium gains π phase.
Light in a high-index medium reflecting off a low-index medium gains 0 phase.
This will become clearer with an example.
To analyze the wok situation, first we need the refractive index of black oxide. The best website ever, refractiveindex.info, says the index of black oxide/magnetite is about 2.4 near the blue end of the spectrum. So here’s a picture of the material stack we have:
Consider two waves normally incident on the wok surface. One reflects off the oxide-wok interface, and one reflects off the air-oxide interface. Both waves gain π phase on reflection (one from the metal mirror, and one because it is traveling in air, n = 1, and reflects off oxide, n = 2.4). Since both waves gain π phase on reflection, the phase between the two waves is due entirely to the difference in distance traveled. The distance traveled by wave 1 in the oxide is 2d, so the phase difference between the two waves is
Now, the only waves we are going to see reflecting off the wok are the constructively interfering waves. When do the two waves constructively interfere? When the waves are identical, or more strictly, when their phase difference is an integer multiple of 2π.
Rearranging a bit, we derive the following condition for constructive interference in oxide thin films:
We see the “effective thickness” of the oxide is its index n times the true thickness (right-hand side). When the effective thickness of the oxide is m times half the wavelength, the two waves constructively interfere. This formula allows us to determine which wavelengths will constructively interfere for any given oxide thickness.
Thin-Film Color Charts
We can plot this equation for m = 1, 2, 3, etc. to visualize the effect of thin oxides.
Here’s a chart I made, showing oxide thickness on the x-axis, and the constructively interfering wavelength on the y-axis. The dashed black lines are the solutions to the interference equation for m = 1, 2, 3, etc. The colored lines are just a visual aid for reading y-axis.
So, looking at the blue wavelength (the blue line), we see that it intersects the black dashed line at ~100 nm. So, if our wok appears blue, then the thickness of the black oxide is probably about 100 nm!
However, there’s multiple solutions (multiple dashed lines intersecting the blue) at 200 nm, or 300 nm, etc. In this case, though, I’m pretty sure the oxide layer is 100 nm.
Let’s zoom in on the wok in the process of annealing:
The upper-right part of the wok is cooler, being farther from the fire, and is colored like normal steel. The lower-left part is hotter, and gaining color as the thermal oxide forms. You can see the gradient of colors, from a plain steel color, to tan, through a deep red-violet, to a royal blue. If the oxide was thicker than 100 nm, we would see it go through multiple rainbows before settling on blue. Seeing only purple/violet → blue indicates that the oxide is ~100 nm thick in the blue area.
Let’s see if ChatGPT can figure this out
Just out of curiosity, let’s prime ChatGPT with this approach, and see if it can figure out how thick my oxide layer is from the same information.
ChatGPT is just straight up wrong this time. In fact, color is one of the most sensitive ways of determining the thickness of an oxide. This is actually used in the semiconductor industry for thermal oxides of silicon (n ~ 1.5). Looking at the SiO2 thin-film color chart below, you can actually see the exact shades of thin-films that appear on my wok, in the correct order (tan → reddish-brown → violet → blue), albeit at slightly different thicknesses:
So there we go! The lovely shade of blue is due to a 100 nm thick layer of black oxide that I have grown on my wok by annealing it over my barbecue. And with this properly-annealed wok, I made some Cumin Lamb. It was really good.
Wow, thanks for the detail explanation for y wok turn blue.
Finally i know what to answer my hb when my wok not as evenly blue as his. 😆
Hwæt darst þu brucan "syn" ætþæt "\syn" in LATEX?
Response translated to Old English using ChatGPT.