What is the explanation for this discrepancy?

In summary, the free electron model for calculating Bulk modulus in a metal results in a value that is twice the experimental value. This is because the model does not take into account the contributions from the ion cores and bound electrons, which have a negative contribution to the bulk modulus. This is surprising considering that the magnetic susceptibility, which also has contributions from free electrons and bound electrons, has a positive and negative contribution respectively. The discrepancy between the model and reality is unexpected but the model still provides a good estimate of the compressibility.
  • #1
JohanL
158
0
When I calculate the Bulk modulus for a metall with the free electron model
I get a value that is twice the experimental value.

I find this strange.
With the free electron model i don't get the contribution from the ion cores and the bound electrons, right?
Do these have a negavite contribution to the bulk modulus.
If so, why?

The magnetic suceptibility has a positive contribution from the free electron paramagnetism and a negative from the diamagnetism. Where the diamagnetism comes from the ion cores and the bound electrons. This i can understand...but how can the bulk modulus have a negative contribution??
 
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  • #2
I never worried about this difference before. To me, it is surprising that this estimate of the compressibility is so good. After all, in equilibrium the real metal does not exert any outward pressure at all, because the positive ions keep the electrons inside.
 

1. What is the definition of bulk modulus for a metal?

The bulk modulus for a metal is a measure of its resistance to volume change under pressure. It is a material property that describes the stiffness of a metal when subjected to external forces.

2. How is bulk modulus calculated for a metal?

Bulk modulus is calculated by dividing the applied stress by the resulting strain in the material. It is usually expressed in units of gigapascals (GPa).

3. What factors affect the bulk modulus of a metal?

The bulk modulus of a metal is affected by factors such as the crystal structure, atomic bonding, and temperature. Metals with a higher stiffness or stronger bonding tend to have a higher bulk modulus.

4. What is the significance of bulk modulus for a metal in engineering applications?

Bulk modulus is an important factor in determining the compressibility and elasticity of a metal. It is used in engineering applications to design structures that can withstand external forces and pressure without deforming or breaking.

5. How does bulk modulus differ from other modulus values for a metal?

Bulk modulus measures the stiffness of a metal in response to changes in volume, while other modulus values such as Young's modulus and shear modulus measure the stiffness in response to changes in length and shape, respectively. Bulk modulus is also typically higher than other modulus values for metals.

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