Why does young’s modulus increase on lowering the temperature?

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xavi

Asked: 2021-01-04T10:50:26+05:30
2021-01-04T10:50:26+05:30In: Mechanical Metallurgy

Why does young’s modulus increase on lowering the temperature?

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You have to know the potential energy Vs distance curve which is an asymmetric parabola. What is bond length? Do you think it's an absolute distance between atoms? No it's not. Then what is it? It's the mean value of distance between the atoms. That means atoms vibrate just like springs about theirRead more

You have to know the potential energy Vs distance curve which is an asymmetric parabola. What is bond length? Do you think it’s an absolute distance between atoms? No it’s not. Then what is it?

It’s the mean value of distance between the atoms. That means atoms vibrate just like springs about their mean positions. They come very close and go very far with certain frequency. The bondlength is the average of all these distances. When there will be no vibration? At 0K. As the temperature increases the amplitude of vibration also increases and hence the bond length. This means you have different bond lengths at different temperatures. This is what manifests as thermal expansion.

See lessNow coming to your question, you now understand bond length increases with temperature. Take a look at Potential energy Vs distance curve. Initially it decreases from a very large value, hits a minimum and then increases and approach to zero asymmetrically. The minimum correspond to the 0K bond length. Now the fundamental principle is that Young’s modulus is proportional to curvature of the potential energy Vs distance curve. You pick any bondlength or distance and point the corresponding point on the curve. The maximum curvature will be at the minimum of the curve and the curvature decreases as it deviates from minimum i.e, to the right of the curve (left is not possible). You’re going right means what you’re increasing the bond length which in turn means you’re increasing the temperature. This feels confusing but final thing is radius of curvature of the U Vs distance curve is proportional to Young’s modulus.In simple terms, modulus of Elasticity corresponds to stretching of atomic bonds. When Temperature is increased, atoms vibrate which means their inter-atomic separation increases, correspondingly force between them decreases than earlier. So it is much easier to stretch the bonds (i.e modulus valueRead more

In simple terms, modulus of Elasticity corresponds to stretching of atomic bonds.

When

See lessTemperature is increased, atoms vibrate which means their inter-atomic separation increases, correspondingly force between them decreases than earlier. So it is much easier to stretch the bonds (i.emodulus value decreased). Now apply this in reverse (i.e by decreasing temperature, modulus of elasticity increases !)