Dear Rajiaji,

        The simplest way of understaing it is to think what happens changing the Kprime in the Ffplot (normalised pressure vs eulerian strain plot).

So the question you can ask yourself is what happens to you bulk bulk modulus when you have a Kprime greater than 4?

if you look it into an Ff plot you will see that your bulk modulus increases with increasing pressure (i.e. the more you compress your material the stiffer it gets). On the other hand if you have a Kprime smaller than 4 what happens is that the more you compress your material the softer it gets. It is basically the same relations that you have between velocity and acceleration. If you have a positive acceleration your speed increases with time, whereas if you have negative acceleration (eg. you are breaking) your speed decreases with time.

I hope this help. For your reference I have attached a couple of links to papers and lectures that you might be interested in watching and reading for a better understaing of EoS in general. I suggest you first watch the wideos and then you move forward to the book chapter and then to the paper. The paper is also connected to a software (named EoSFit7) that helps you in doing calculations and comfortably visualizing the results (using the GUI versions).

If you have issues in downloading the papers copies are also contained in the EoSFit7c software folder.

http://serc.carleton.edu/NAGTWorkshops/mineralogy/mineral_physics/eos.html#Lec

http://www.degruyter.com/view/j/zkri.2014.229.issue-5/zkri-2013-1711/zkri-2013-1711.xml

Dear Rajiaji,

        The simplest way of understaing it is to think what happens changing the Kprime in the Ffplot (normalised pressure vs eulerian strain plot).

So the question you can ask yourself is what happens to you bulk bulk modulus when you have a Kprime greater than 4?

if you look it into an Ff plot you will see that your bulk modulus increases with increasing pressure (i.e. the more you compress your material the stiffer it gets). On the other hand if you have a Kprime smaller than 4 what happens is that the more you compress your material the softer it gets. It is basically the same relations that you have between velocity and acceleration. If you have a positive acceleration your speed increases with time, whereas if you have negative acceleration (eg. you are breaking) your speed decreases with time.

I hope this help. For your reference I have attached a couple of links to papers and lectures that you might be interested in watching and reading for a better understaing of EoS in general. I suggest you first watch the wideos and then you move forward to the book chapter and then to the paper. The paper is also connected to a software (named EoSFit7) that helps you in doing calculations and comfortably visualizing the results (using the GUI versions).

If you have issues in downloading the papers copies are also contained in the EoSFit7c software folder.

http://serc.carleton.edu/NAGTWorkshops/mineralogy/mineral_physics/eos.html#Lec

http://www.degruyter.com/view/j/zkri.2014.229.issue-5/zkri-2013-1711/zkri-2013-1711.xml

Thank you very much for your information.

The physical significance of bulk modulus and its derivative are apparent

in a graph that shows density as a function of pressure.

This is usually the data obtained from a x-ray diffraction experiment.

The graph demonstrates that density increases with pressure, and if

temperature is constant for all data points the curve constitutes an

isothermal compression curve. Besides the actual value of density the

trends are of interest.

For this discussion, it will be useful to plot the logarithm of density

versus pressure which does not change the general shape of the curve.

We will call this the logarithmic compression curve.

The slope of this curve is equal to the isothermal compliance,

which is the inverse of the isothermal bulk modulus. So, the isothermal

bulk modulus is the inverse slope of the logartihmic compression curve.

For most materials, the bulk modulus does change with pressure and

this behavior is captured by the pressure derivative of the

bulk modulus, the so-called K' value.

The K' value is therefore the slope of the inverse slope of the

logarithmic compression curve. More precisely, K' is equal to the

curvature of the logarithmic compression curve times the bulk

modulus squared. Therefore K' is directly related to the

curvature of the logarithmic compression curve. K' only vanishes

if this curvature vanishes which also means that the logarithmic

compression curve would have to be a straight line. This behavior

is never observed, as far as I know.

Values for bulk modulus and K' are of course pressure dependent, and

many empirical formulations for equation of states use the values

for density, bulk modulus, and K' at zero pressure as parameters.