In the high pressure XRD, pressure versus volume data is fitted by Birch-Murnaghan equation of state (BM-EOS). The fit will yield bulk modulus (B0), derivative of bulk modulus (B0’) and volume at zero pressure (V0). Bulk modulus signifies the measure of substance resistance under pressure. Derivative of bulk modulus is a dimensionless parameter. But I am not able to the get the significance of derivative (first) of bulk modulus. Kindly help me to understand the derivative of bulk modulus.
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
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.
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