a) the potential power of interaction in between atoms in the solid is asymmetric about the equilibrium location of atoms; or

b) the frequency that vibrations of atoms increases.

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My attempt:

I did no make a huge deal out of the question, and also simply believed that that is due to the increase in frequency that vibrations, i m sorry now reasons greater oscillations around the lattice points, which consequently increases the median volume lived in by atoms, causing expansion. However the prize is a).

Can someone explain, possibly using some model (like the spring-particle version of the lattice), why this is so, and why b) is not a reason of expansion?

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edited Jun 4 "20 in ~ 16:03

asked Sep 13 "16 at 12:58

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A basic and naïve model* because that thermal growth has two surrounding atoms represented by a pair the balls connected by a spring.


Image source: basic gaianation.net (calculus based) course Notes, Dr. Rakesh Kapoor from college of Alabama in ~ Birmingham

Giving the balls much more energy (increasing the temperature that the atoms) will increase the amplitude of the spring"s oscillations, which increases the amount of an are the atoms will take up. The frequency that oscillations—how easily the balls move ago and forth—is irrelevant.

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As because that what "asymmetry the atom equilibrium positions" has to do v it, take it a look in ~ the graph below. The equilibrium distance for this atoms (spring size in the round model) is marked by the dotted heat at 74 pm. Clearly the eco-friendly potential energy line is no symmetric throughout this line. From the eco-friendly line form it have the right to be viewed that atom at equilibrium distance need less energy input to pull apart than to compress by the exact same amount, explaining why the enhancement of energy typically results in boost in distance fairly than a decrease.


Image source: Chemistry 301, college of Texas (online resource)

*From Thermal growth of Solids by C. Y. Ho and R. E. Taylor:

A famous explanation because that thermal growth assumes central forces in between pairs of connecting atoms. The asymmetry of the potential energy well causes the mean distance between the atoms to boost when they vibrate along the heat joining them. In countless texts this is the only model offered for heat expansion... Return crude and in some ways misleading for solids (it does not explain negative expansion), the reveals the most generally essential mechanism because that thermal expansion, and correctly suggests that atom vibrations give rise to thermal expansion due to the fact that of anharmonicity.