Calculations of Solid Properties Using Wien2k Package
Would you like to react to this message? Create an account in a few clicks or log in to continue.

Role of symmetry and energy in structural phase transitions

Go down

Role of symmetry and energy in structural phase transitions Empty Role of symmetry and energy in structural phase transitions

Post by Algerien1970 Tue 16 Jun - 0:14

[You must be registered and logged in to see this link.]

To download the lecture clik on the link below :


[You must be registered and logged in to see this link.]
Algerien1970
Algerien1970
Forum Manager
Forum Manager

Messages : 485
Date d'inscription : 2015-05-14

https://wien2k.forumalgerie.net

Back to top Go down

Role of symmetry and energy in structural phase transitions Empty Re: Role of symmetry and energy in structural phase transitions

Post by Algerien1970 Tue 16 Jun - 0:28

Thermodynamic order of the phase transition (Ehrenfest’s classification): 

smallest order of the derivatives of the Gibbs free energy G (with respect to the relevant 
variable, T or p) which are discontinuous across the transition

First-order transitions:  

the first-order derivatives (entropy S and volume V) are discontinuous, leading to enthalpy 
(latent heat) ∆H and volume ∆V jumps

dG = -SdT + Vdp (1)

Second-order transitions:  

the second-order derivatives (heat capacity Cp and compressibility β) are discontinuous, 
whereas the first-order ones are continuous (no heat or volume effects):

∆S = 0, ∆H = 0, ∆V = 0

d2G = - (Cp/T)dT2 -Vβdp2 -VαdTdp (2)

Phase α stable for T < Tc,   phase β stable for T > Tc →

∆G = Gβ -Gα > 0 for T < Tc,   ∆G = Gβ -Gα < 0 for T > Tc ?
Algerien1970
Algerien1970
Forum Manager
Forum Manager

Messages : 485
Date d'inscription : 2015-05-14

https://wien2k.forumalgerie.net

Back to top Go down

Back to top

- Similar topics

 
Permissions in this forum:
You cannot reply to topics in this forum