I am performing uniaxial pressure to a tetragonal oxide by reducing one of their cell parameters and relaxing the other two in a computational way. I found that the material is squeezed, suffering an elongation in two cell parameters as I reduce the third one. At certain point there is an insulator-metal transition.
Could I quantify the pressure needed to achieve this transition?? which is driven by the reduction of one cell parameter (that I understand as an uniaxial pressure). Would be enough to check the components of the stress tensor?
I get energies, volumen reduction (which is small), stress tensor, ...
Thank you very much
The hydrostatic pressure P which given by negative trace of the stress tensor Sigma.
For isotropic elastic material one has following relationships: For Xtal systems the connection between stress and strain tensors is represented by 6x6 Matrix if one uses Cauchy vector notation for Sigma and Epsilon in 6D space. Because of symmetry properties of tetragonal lattice, 36 elements may be reduced into 6 distinct constants......
P=- Trace Sigma. Satisfies the following connection: P=- K DelV /V , where Del V decrease in the volume V, and V is the volume before straining. K is Coefficient of Bulk Modulus. That means one has to know the Bulk modulus to calculate the applied pressure. One can also show the following connection:
Del V / V = (1 - 2 Nhu ) Epsilonzz, where Epsilonzz= relative extension along z axis alon which stress applied. Nhu is the Poissons ratio, which defined as
Nhu= - Epsilonxx / Epsilon zz = - Epsilonyy / Epsiionzz.
Unfortunately, for tetragonal system Poisson's ratio may be different for tetragonal and basal axis. That means there are two different Poisson's Ratios.
NOTE: In cubic system there is following connection between bulk modulus K and the Young modulus E through Poisson's ratio: E= 3K(1-2 Nhu) or = 2G(1+Nhu), where G is the shear modulus.
NOTE: Tetragonal System: There are 6 independent elastic constants.
C11 =C22, C33 , C44, C66, C12=C21 , C!3=C31
The hydrostatic pressure P which given by negative trace of the stress tensor Sigma.
For isotropic elastic material one has following relationships: For Xtal systems the connection between stress and strain tensors is represented by 6x6 Matrix if one uses Cauchy vector notation for Sigma and Epsilon in 6D space. Because of symmetry properties of tetragonal lattice, 36 elements may be reduced into 6 distinct constants......
P=- Trace Sigma. Satisfies the following connection: P=- K DelV /V , where Del V decrease in the volume V, and V is the volume before straining. K is Coefficient of Bulk Modulus. That means one has to know the Bulk modulus to calculate the applied pressure. One can also show the following connection:
Del V / V = (1 - 2 Nhu ) Epsilonzz, where Epsilonzz= relative extension along z axis alon which stress applied. Nhu is the Poissons ratio, which defined as
Nhu= - Epsilonxx / Epsilon zz = - Epsilonyy / Epsiionzz.
Unfortunately, for tetragonal system Poisson's ratio may be different for tetragonal and basal axis. That means there are two different Poisson's Ratios.
NOTE: In cubic system there is following connection between bulk modulus K and the Young modulus E through Poisson's ratio: E= 3K(1-2 Nhu) or = 2G(1+Nhu), where G is the shear modulus.
NOTE: Tetragonal System: There are 6 independent elastic constants.
C11 =C22, C33 , C44, C66, C12=C21 , C!3=C31
For uniaxial stress component please see attached file. I hope that it will be of your interest.
- Badges
- Science topic
- Similar topics
- Physics
- Condensed Matter Physics