University of Cambridge

Hard impingement: a cookie experiment to demonstrate morphological evolution

Mathew Peet and Harry Bhadeshia

When ferrite grains in iron nucleate at different locations and then grow unimpeded. However, they will eventually touch each other, a phenomenon known as hard impingement. Obviously, they cannot grow through each other so they grow in directions that eventually allow the grains to fill all space. Their shape then does not reflect the morphology during unimpeded growth.

Here is an example from X80 pipeline steel, which has a chemical composition given approximately by Fe-0.05C-1.6Mn-0.1Nb\,wt%. The carbon concentration is close to the solubility in ferrite, so during continuous cooling, all the austenite is consumed.

Transformation for a very short time of 30 s at 600oC shows beautiful plates of bainite in a transmission electron microscope. However, allowing it to complete means that the plates have to fill all space and therefore show an irregular appearance following impingement.

More details in associated publication.

TEM of bainite in X80 steel Transmission electron micrograph of X80 steel after isothermal transformation at 600oC for 30 s. Shows clear plates of bainitic ferrite.
TEM of bainite in X80 steel Transmission electron micrograph of X80 steel after completion of transformation following production. The plates of bainite have impinged and fill all space, therefore appearing irregular when compared with the neat shape of bainite. The structure therefore can confuse because this is not the shape from unrestricted growth.

The cookie experiment


This experiment was done to illustrate the fact the shape of particles during unimpeded growth is different from that expected when the touch and fill all space. Please conduct a risk assessment before attempting the task.


225 g rolled oats, 120 g flour, 5 g baking powder, 3 g teaspoon baking soda, 200 g salted butter, 250 g granulated sugar, 1 medium egg (not essential, can be replaced by ripe bananna).

The equipment is a large mixing bowl, a baking tray, grease-proof paper and an oven.


  1. Heat oven to 450 K.
  2. Prepare baking tray, use grease-proof baking paper with a small amount of butter.
  3. Mix all ingredients and make into a dough.
  4. You should now have a dough, divide this into 12 equal portions.
  5. Rolled between palms into balls and then squash to 30 mm thickness.
  6. Space the cookies on the prepared baking sheets as shown.
  7. Bake for 780 to 960 seconds rotate sheet half way through baking.
  8. Remove tray and allow cookies to cool on the sheet.

Avrami theory, Mathew Peet, cookies, hard impingementThe raw cookies laid out as if they have nucleated homogeneously but at different locations so that unimpeded lateral growth can occur. Note that the mixture flows at high temperature, which drives the lateral growth accompanied by vertical shrinkage. The driving force is gravity.
Avrami theory, Mathew Peet, cookies, hard impingement
Lateral growth eventually leads, during the 13 min and 5s heat treatment, to impingement with a balancing of forces between the cookies. This creates grain boundaries and triple junctions, a polycookie. The shape is no longer a reflection of what happened during unimpeded growth.
Avrami theory, Mathew Peet, cookies, hard impingement After eating a few cookies (note risk assessment), it is clear that the boundaries are weak interfaces, and that the triple junction particularly weak. There is clearly a greater free volume at these defects in the polycookie so diffusion or even the flow of air should be much easier from the top to bottom surfaces, or laterally.

Suggestions for future work

  1. Study the growth of a circular, single cookie in isolation. Since growth is driven by gravity, the driving force decreases as the radius (r) increases. Therefore, growth should slow down as the radius increases.
  2. Study the influence of starting shape. In the experiment above, place a square and a circular blank of the same mass, sufficiently far apart to avoid impingement, and monitor as a function of time (t). If the thickness is z and radius r, assume that dr/dtz. The volume V is a constant, equal to πr2z so we can substitute for z and integrate to obtain 3r3 - 3ro3Vt.
  3. Are there any preferred planes of fracture in the cooked cookie? How does one index such a plane? What is the appearance of the fracture surface?
  4. Is it possible to conduct this experiment while the cookie is levitated? The aim is to see whether the ridge that develops at the edges is related to friction with the grease-proof paper.
  5. Can this experiment be done in zero gravity on the space station? The aim is to prove that only the gravitational force of the earth is responsible for the growth. An alternative would be to do the work on an exoplanet which typically is ten times the size of the Earth. On second thoughts, an initial experiment on the moon would be more practical.
  6. Is it possible to get cookie coarsening when impingement is complete? If not, why not?

Jean Pomfrett's follow-up

The first scientist, according to Natalie Hayes ("comedian talks classics", BBC), was Aristotle, whose evidence based logic, the willingness to admit incorrect hypotheses, et cetra set the scene for the scientific method. After Plato's school he went to Lesbos and created biology as we know it now. His repeated observations were a key feature of his method.

Here Jean Pomfrett (who assembled a Stirling engine) now turned her hand, with the help of her grandson, to repeating the experiments described above, with some astonishing results.

The work might have answered in part, one of the suggestions made above for future work. However, further work is need to understand why the flow in her experiments was so dramatic. (nota bene: a proper piece of work finishes with unanswered queries - or as Derek Fray would say, scientists like to travel but never to reach their destination.)

Avrami theory, Mathew Peet, cookies, hard impingement,Jean Pomfrett
The raw cookies prior to heat treatment
Avrami theory, Mathew Peet, cookies, hard impingement,Jean Pomfrett
The flow during heat treatment was quite remarkable, the raw cookies appearing to coalesce into a "single crystal" analogue, with only minute vestiges of the original form visible. Those might be the analogue of "low misorientation boundaries because they could not be separated without much work (free energy)". Obviously, this object is too large for one person to eat. What is to be done?
Avrami theory, Mathew Peet, cookies, hard impingement,Jean Pomfrett
A machining operation creates the form expected but in modern jargon, instead of additive manufacturing this involves subractive manufacturing. Wonder if there is anything such as multiplicative or divsive manufacturing?

Stirling engine, by Jean Pomfrett

Banana substitution

In continuing experiments, Mathew Peet substituted the egg by a ripe banana.

This seems to have reduced the flow during heat treatment. However, Mathew points out that because of the numerous experiments, he had to limit the number of cookies made and eaten. Therefore, the ingredients were halved in quantity and the raw forms were smaller.

Furthermore, olive oil was used on grease proof paper rather than butter to enhance the vegan-ness of the recipe.

The heat treatment was interrupted for inspection to characterise the intermediate stage of the process, by removing from oven for around 30 seconds.

In summary, given that there are many variables, we propose that with the steady accumulation of data, this would be an ideal project for machine learning.

After 19 min 2 s
Avrami theory, Mathew Peet, cookies, hard impingement,Jean Pomfrett
The raw blanks.
Avrami theory, Mathew Peet, cookies, hard impingement,Jean Pomfrett
After 10 min 23 s
Avrami theory, Mathew Peet, cookies, hard impingement,Jean Pomfrett
After 10 min 23 s
Avrami theory, Mathew Peet, cookies, hard impingement,Jean Pomfrett
graph The units of cookie radius are arbitrary, with each cookie-size calibrated by the tray size. It appears as though the strict 3r3 - 3ro3Vt, where V is assumed to be proportional to ro2 is not obeyed because the size does not change after 623 s (may even show some shrinkage, perhaps evaporation of soft matter?). The initial gradient is linear (!) as expected, but then flattens out; there presumably is a limit beyond which the driving force for spreading is not sufficient. Could do with more points in the initial stages, but note that there is unexplained scatter.

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