Physicists may finally have an answer for a seemingly simple question that has remained unanswered for about a century: when does a substance melt?
at Queen Mary University of London found it mysterious that 鈥渋n this age of scientific and technological development鈥�, physicists do not always know how to predict at what temperature and pressure a material will melt. He has now derived an equation that can be used to make such predictions for a vast range of substances.
He focused on 鈥渕elting lines鈥�, or formulae that capture the relationship between temperature and pressure when an object is just beginning to melt. Similar formulae for vaporisation and sublimation (the changing of a substance from a solid into a gas) are well established, but prominent physicists throughout history have decried the transition from solid to liquid as too mathematically complex to understand. This is because the final state is a liquid where atoms interact with each other and move around in a more complicated way than they do in solids or in gases.
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Trachenko says he had previously worked out laws for how much energy and heat a liquid can contain. He has now discovered how to combine these laws with a 200-year-old equation that shows how two phases, like solid and liquid, can coexist. The result is his new melting line equation, which reveals that the pressure at which a substance melts depends on the square of its temperature. The new equation also contains fundamental physical constants like the charge and mass of an electron, which implies that it can be applied very generally.
鈥淏efore this paper, it was not at all expected or thought that this might be the case,鈥� says Trachenko.
He says he has tested his equation against experimental melting data for many different substances and so far found only good agreement.
鈥淚t鈥檚 very nice that this work is open to comparison with future data. It can be easier to say, 鈥榣ook, my theory agrees with [past] experiments鈥�, than to be more bold and rigorous and say, 鈥榟ere鈥檚 my theory, go test it against experiments that haven鈥檛 been performed yet鈥�,鈥� says at the University of Salford in the UK.
at the German Aerospace Centre says that while the new equation is 鈥渁 remarkable result鈥�, its derivation still involved a number of approximations based on 鈥減hysical intuition鈥�, so such future comparisons will be crucial for further verifying its accuracy.
Physical Review E
