Friday, November 24, 2017

Most Number Of...

What if, we are to use \(v_p\) instead of \(v_{rms}\) in the discussions of perovskites solar cells and superconductors,

\(T_{v\,p}=v^2_{boom}*\cfrac{molar\,mass*10^{-3}}{2*8.3144}\)

\(T_{v\,p}=\cfrac{3}{2}T_{boom}\)

In the case of \(MgO_3Ti\) with, \(Z_m=22+12+8*3=58\) a density of  \(3.36\,gcm^{-3}\) and molar mass of \(120.17\,gmol^{-1}\). Its \(T_{v\,p}\) is,

\(v_{boom}=3.4354*\cfrac{3360}{58}=199.01\)

\(T_{v\,p}=199.01^2*\cfrac{120.17*10^{-3}}{2*8.3144}=286.21\,K\) or \(13.06\,^oC\)

For \(ZnTiO_3\),

\(T_{v\,p}=\cfrac{3}{2}*354.41=531.62\,K\)  or \(258.46\,^ oC\)

For \(TiCaO_3\),

\(350.91\,K\lt T_{v\,p}\lt402.0\,K\)  or  \(77.76\,^oC\lt T_{v\,p}\lt128.85\,^oC\)

For \(FeTiO_3\),

\(458.79\,K\lt T_{v\,p}\lt476.50\,K\)  or  \(185.64\,^oC\lt T_{v\,p}\lt203.36\,^oC\)

For \(MnTiO_3\),

\(T_{v\,p}=437.01\,K\)  or  \(163.83\,^oC\)

It seems that only by reducing the density of high value \(T_{v\,p}\) perozskites can \(T_{v\,p}\) at room temperature be achieved.  For example a \(82.60\%\) \(MnTiO_3\) has a \(T_{v\,p}\) of

\(T_{v\,p}=0.8260^2*437.01=298.16\,K\)  or  \(25.01\,^oC\)

The rest of the \(100\%\), \(17.40\%\) can be with \(Fe\), \(FeTiO_3\), as long as they can form into the same crystal structure.

Reducing density can only reduce \(T_{v\,p}\); \(T_{v\,p}\) cannot be increased this way.  Density can only be reduced given a crystalline structure.

It is likely that \(v_p\) provides the most number of freed particles that will act as charge carriers.  Super-superconductor...The difference between \(v_p\) and \(v_{rms}\) is,

\(v_p=\sqrt{\cfrac{2}{3}}v_{rms}=0.667v_{rms}\)

\(v_p\) should be used instead of \(v_{rms}\); we should set \(v_{p}=\sqrt{\cfrac{2RT}{nM_m}}=v_{boom}\ne v_{rms}\) such that \(T=T_{boom}\).

And it rains again...