Hi, Mat. Thank you very much for your nice lecture. I am curious about the isosbestic points after the edge. Is there any theory to explain why these points exist? For the pre-edge features, it is easy to be explained by the absorption of core level to the empty electronic states. How about the features after the edge (0
if there are 2 varying functions (say, XANES spectra, but it could be any 2 functions) that happen to cross each other (have the same y value at a particular x value), then any weighted sum of those two functions "a*y1 + (1-a)*y2" will also have that same value no matter what the weighting value "a" is. But if you have 3 or more functions that you add together "a*y1 + b*y2 + (1-a-b)*y3", then all three have to cross each other at the same x value for that to be true. So, if you have several related functions (again, say normalized XANES for the same element/edge) and they all cross each other at multiple x/Energy values, then it is very likely that there are 2 components that are adding together, and that it is very unlikely that there are more than 2 components. OTOH, if the functions don't cross each other at multiple x/energy values, it is very unlikely that it could be only two distinct components.
Hi, Mat. Thank you very much for your nice lecture. I am curious about the isosbestic points after the edge. Is there any theory to explain why these points exist? For the pre-edge features, it is easy to be explained by the absorption of core level to the empty electronic states. How about the features after the edge (0
if there are 2 varying functions (say, XANES spectra, but it could be any 2 functions) that happen to cross each other (have the same y value at a particular x value), then any weighted sum of those two functions "a*y1 + (1-a)*y2" will also have that same value no matter what the weighting value "a" is. But if you have 3 or more functions that you add together "a*y1 + b*y2 + (1-a-b)*y3", then all three have to cross each other at the same x value for that to be true. So, if you have several related functions (again, say normalized XANES for the same element/edge) and they all cross each other at multiple x/Energy values, then it is very likely that there are 2 components that are adding together, and that it is very unlikely that there are more than 2 components. OTOH, if the functions don't cross each other at multiple x/energy values, it is very unlikely that it could be only two distinct components.