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My idea is this: tensor stress is directly related to the internal pressure of a solid. That is to the force that the neighboring atoms exert each other in relation to a unit of surface.
When I heat a solid we can have the phenomenon of thermal expansion: this is connected to the fact that a deformation of the solid takes place which leads to an increase in the interatomic distances and therefore to a decrease in the frequencies of the phonons and a lowering of the energy of the system. For this deformation occurs. Now an increase in interatomic distances implies a decrease in internal pressure. The decrease in internal pressure is due only to the variation of the positions of the atoms in the crystal lattice with the expansion.
Given that the stress tensor is also calculated as a variation of the potential energy, it seems to me strongly linked to the internal pressure of the solid. In fact, even the potential energy depends only on the atomic positions in the lattice. I think this is the meaning of what is written in the article https://arxiv.org/pdf/2006.12867.pdf (equation (4)). Obviously, to find the correct parameters of the deformed cell I will have to apply an iterative procedure that leads me to equality between the internal pressure of the solid and the external one ("target pressure" sentence extracted from the article). This condition is necessary for the solid to be in equilibrium.
Also I don't understand why it is written that "The second term on the righthand side of equation 4 corresponds to the partial derivative of the free energy with respect to volume in the quasiharmonic approximation".
From what I know the partial derivative of the free energy with respect to the volume at constant temperature is equal to the partial derivative of the kinetic energy with respect to the volume at constant entropy. This relation contains the Gruneisen parameters that allow me to describe the dependence of frequencies on volume and therefore on temperature, since in thermal expansion a change in volume corresponds to a change in temperature.
Why did the QSCAILD method "propose a way to include pressure from kinetic energy within this static pattern"? I understood that this sentence derives from the fact that the first term can be traced back to a kinetic term through the virial theorem while the second to the derivative of Helmoltz free energy with respect to volume in the quasiharmonic approximation. Even this term if I am not mistaken is always equivalent to a kinetic term. So I wonder: maybe equation 4 in the article is just the expression for internal energy?
When I heat a solid we can have the phenomenon of thermal expansion: this is connected to the fact that a deformation of the solid takes place which leads to an increase in the interatomic distances and therefore to a decrease in the frequencies of the phonons and a lowering of the energy of the system. For this deformation occurs. Now an increase in interatomic distances implies a decrease in internal pressure. The decrease in internal pressure is due only to the variation of the positions of the atoms in the crystal lattice with the expansion.
Given that the stress tensor is also calculated as a variation of the potential energy, it seems to me strongly linked to the internal pressure of the solid. In fact, even the potential energy depends only on the atomic positions in the lattice. I think this is the meaning of what is written in the article https://arxiv.org/pdf/2006.12867.pdf (equation (4)). Obviously, to find the correct parameters of the deformed cell I will have to apply an iterative procedure that leads me to equality between the internal pressure of the solid and the external one ("target pressure" sentence extracted from the article). This condition is necessary for the solid to be in equilibrium.
Also I don't understand why it is written that "The second term on the righthand side of equation 4 corresponds to the partial derivative of the free energy with respect to volume in the quasiharmonic approximation".
From what I know the partial derivative of the free energy with respect to the volume at constant temperature is equal to the partial derivative of the kinetic energy with respect to the volume at constant entropy. This relation contains the Gruneisen parameters that allow me to describe the dependence of frequencies on volume and therefore on temperature, since in thermal expansion a change in volume corresponds to a change in temperature.
Why did the QSCAILD method "propose a way to include pressure from kinetic energy within this static pattern"? I understood that this sentence derives from the fact that the first term can be traced back to a kinetic term through the virial theorem while the second to the derivative of Helmoltz free energy with respect to volume in the quasiharmonic approximation. Even this term if I am not mistaken is always equivalent to a kinetic term. So I wonder: maybe equation 4 in the article is just the expression for internal energy?
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