This question is related to high-pressure science. Generally, the Murnaghan Equation of state (EOS) relates the mathematical relationship between the P vs Volume (V). The equation attached in this description as jpg file(Kindly see the file).
Where K0 is the isothermal bulk modulus at room pressure and K0’ is the derivative of K0.
But I need the equation (Murnaghan EOS) for P vs. lattice parameter (a), for understanding the axial compressibility (or linear modulus) of one of my high pressure study. It will be really very useful for my research work if you are providing me the reference of the Murnaghan EOS between P vs. a.
Thanks,
Dear Rajaji,
You can use any of the available eos to determine axial compressibility. you can cube the individual lattice parameters and then it will be like volume like. fit with the desired eos as similar to the way P-V curve is fitted. then the K0 obtained from fitting the isothermal equation is one-third of the inverse of the zero-pressure linear compressibility β0 of the corresponding axis.
The following link descibes the above procedure,.
http://rimg.geoscienceworld.org/content/41/1/35
Infact i have used this procedure in one of my article. you may refer that if you wish.
Article Anomalous lattice compressibility of hexagonal Eu2O3
Also,there is a software to do all these fitting and extracting the compressibility developed by R. J. Angel named "Eosfit". you can get it from the following link...
http://www.rossangel.com/text_eosfit.htm Hope it helps...
Thank you Irshad K A. I have been using Eosfit7 software for the past 3 years. Actually i wanted to know the Murnaghan equation for P vs a. The answer given by you is precise and very useful. Especially the link http://rimg.geoscienceworld.org/content/41/1/35 is very useful.
Dear Amir Hen,
Cubing the lattice parameter individually means, take the individual lattice parameters( of any crystal system) and cube them. use any of the PV eos to fit this data to extract the linear compressibility as described in the above reference. some additional description is needed in the case of monoclinic and triclinic systems to describe the complete lattice cmpressibility, which is also clearly described in the above reference. when the unit cell volume is fitted to the eos data you will not be able to get the linear compressibility.
The equation is provided in the following article. You have to modify it for cubic case
Article Ionic layered PbFCl-type compounds under high pressure
(a/a0) = (1+K'/K*P)^(-1/3*K)
Trommer R, Muller H, Cardona M. Phys. Rev. B 1980; 21: 4889
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