Modulus in Metals versus Sound Vibration

[Kaiera Ai Tanay]

So I'm trying to understand how the modulus works in metals. I understand that when the temperature rises, that means that the modulus decreases. But I do not understand exactly what it is or how it affects the way that the molecules would vibrate for instance, as kinetic sound energy moved through them.

I get that it has to do with elasticity, but is it saying that the elasticity also goes down? The molecules aren't capable of moving as far from equilibrium? And if that's so, why are heated metals more likely to bend? Or is that a density-based issue and not a modulus issue?

 

[Sonderval]

So I'm trying to understand how the modulus works in metals. I understand that when the temperature rises, that means that the modulus decreases. But I do not understand exactly what it is or how it affects the way that the molecules would vibrate for instance, as kinetic sound energy moved through them.

I get that it has to do with elasticity, but is it saying that the elasticity also goes down? The molecules aren't capable of moving as far from equilibrium? And if that's so, why are heated metals more likely to bend? Or is that a density-based issue and not a modulus issue?

Young's modulus increases with tempretaure. If you strain a material, you can imagine that you strain the bonds between the atoms. Nor consider the energy between two atoms. At temperature zero in the unstrained case, the atoms are at the lowest.energy position. Straining the bonds means that you have to add energy, this is how Hookes law comes about.

If you increase the temperature, the atoms move higher inside the potential well, making it effectively less deep. This reduces the force you need to strain a bond and thus reduces the elasticity.

Sound waves are nothing but elastic waves, they also astrain the material, so they are directly related to this.

Plastic deformation of metals is a different thing, because this is deformation that causes atoms to actually shift over larger distances (so that the deformation is irreversible). Plasticity is due to the movement of faults in he metal, called dislocations. Their movement is also aided by the additional energy available at higher temperature. In some metals (some steels), this movement gets strongly restricted at low temperatures, making them become very brittle. (Google for "liberty ship fracture" to seean impressive example.)

 

[Mapes]

Young's modulus increases with tempretaure

It generally decreases with temperature. (I think maybe you made a typo?) The fundamental reason is that the stiffness or Young's modulus corresponds to the negative second derivative of the pair potential energy between atoms, and this interaction is not perfectly symmetric. This asymmetry is also the http://www.mtarr.co.uk/courses/topics/0197_cte/images/ch_cte_imga.gif in metals and ceramics, in which stiffness has an enthalpic origin (as opposed to polymers, in which stiffness can be primarily entropically driven).

If the potential energy well between atoms were perfectly symmetric, the Young's modulus would be temperature independent. Try it yourself; take an https://www.researchgate.net/publication/279359555/figure/fig59/AS:268062939152390@1440922593765/Figure-3-3-Force-and-potential-energy-diagrams-for-a-diatomic-molecule-with-respect-to.png (as a function of atomic distance) and sketch the slope, also as a function of distance. This is the interatomic force, and its negative value is the resistance to stretching. Sketch the slope of that resistance, and you'll get the Young's modulus, which clearly decreases with increasing interatomic distance and thus with increasing temperature.

 

[Sonderval]

@Mapes
Yes, that was a typo - the explanation in the next paragraph explains why it decreases.