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What is the reason for anomalous expansion of water? Why doesn’t it simply expand on heating or contract on cooling? Why it shows anomalous behavior at 4 degrees Celsius? Why not on 4.6 or 10 (or whatever) degrees Celsius?

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So, the first question to ask would be: how "anomalous" is change in the thermal expansion coefficient? It turns out that for most real materials the coefficient of thermal expansion is not a constant, and takes on both positive (expansion) and negative (contraction with increasing temperature) values. For silicon as an example, see ioffe, Above room temperature Si has a positive (but not constant) CTE, below about 100K silicon's CTE is negative.

The second question is why would this occur? Taking a liquid or a solid (ignore gases for the moment), an individual atom (or molecule) sits in some kind of potential well which is what is causing the material to be bound together. At absolute zero, these atoms sit at the very bottom of the potential well. As the temperature increases, heat is added and the atom starts rattling around in the potential well, and is able to explore more of the well. There is no particularly good reason to believe that the shape of the well, across the entire temperature range of existence of the phase, will be such that a single linear coefficient will describe where the atom will most likely sit in the well at a given temperature. On top of that in a solid is the equilibrium concentration of point defects that is dependent on temperature. As an example, Google for Simmons and Balluffi and their experiments combining x-ray measurements of the lattice parameter (where the atoms sit in the potential well) and thermal expansion (change in length of a heated bar) to determine the point defect concentrations vs temperature for various solids.

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  • $\begingroup$ @OscarLanzi - well, that is not supported by experiment or theory. One place to start would be journals.aps.org/prb/pdf/10.1103/PhysRevB.94.174305 $\endgroup$ – Jon Custer Oct 5 '20 at 19:41
  • $\begingroup$ Not a place to go for me. Paywall. Can you summarize a few key points? $\endgroup$ – Oscar Lanzi Oct 5 '20 at 20:08
  • $\begingroup$ Ioffe "not found" when I click. $\endgroup$ – Oscar Lanzi Oct 5 '20 at 20:09
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    $\begingroup$ @OscarLanzi - yeah, kind of weird - my autolink at work didn't go there directly either, but going through the PRB main site got it just fine. As the abstract says, 'The phonon modes' contributions to the thermal expansion are analyzed and ... shown to be dominated by negative mode Gruneisen parameters at specific points on the Brillouin zone boundaries.' Applies to both Si and Ti. $\endgroup$ – Jon Custer Oct 5 '20 at 20:33
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The question "Why exactly 4.6 grad" has no simple answer. The question 'wtf happens with water' may have reasonably simple answer. I think about it this way: water has surprisingly low-density crystal structure with lot of holes, meaning that many defects putting a molecule into such hole would result in increase of density. Thus, the actual form of density-temperature dependency for water is result of two opposing forces: various defects, that increase its density and thermal expansion that decrease its density.

This, however, is not the only way for such dependency with extremum to occur. Another reason for negative thermal expansion coefficient would be fact, that with thermal oscillation increase and increase of mean distance between atoms, the position between mean position of some atoms may decrease. A simplistic model would be this simple physical experiment: http://youtu.be/rpnoq9hz1gw with increased speed of rotation of the chain, mean distance between its rings becomes less and less, but their mean position are slowly drageed to one point, and if chain is rotated fast enough, its vertiacal size becomes a bit more than size of one ring. IRL similar mechanism is the reason for some pulled polymers to contract at elevated temperatures. It is possible for some compounds to have negative thermal expansion for similar reason, though I can't give an example at the moment.

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When water is heated, breaking of tetrahedral structure having an ordered arrangement of H-bonds continues up to 4 degree centigrade and the contraction caused by the close proximity of water molecules is greater than thermal expansion (molecular agitation due to vibrational and kinetic energy). Consequently, volume continues to decrease up to $4 \, ^\circ$C. Therefore, water has its highest density at that temperature and it decreases with increasing temperature.

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