Video instructions and help with filling out and completing Where 8850 Form Certification

Instructions and Help about Where 8850 Form Certification

Their coffee or tea or bagel or cookies okay good morning everybody we have dealt with reciprocal space in the last couple of lectures today we will go a little bit further in that we will be talking about structure practice and you've seen that already on one of the handouts somewhere I think I promise you that we will get back to them so here we are structure factors are really a thing that allows you to get more than just a unit size the unit cell size or shape from your diffraction data so these are very important when it comes to actually getting a crystal structure once again we need to explain some convenient concepts but the good news is this is the last time that we have to do that okay so we're almost there originally we introduced the concept of reflection of excess from lattice planes right it was a nice concept because it allowed us to might come up with a very simple drawing and derive Bragg's law which describes to us where we see diffraction right so we could derive Bragg's law and we could actually explain where we saw the fraction the next thing that we introduced was we said okay it's not really a lattice plane right we get scattering from all of the atoms and what we kind of then did was we made a simplified view of things by saying okay we can consider all of those atoms kind of accumulated in the lattice point which is how we draw bright lettuces right where we have the dots at the corners at the Centers it doesn't mean that the atom has to sit at 0 0 0 just much easier for us to see what the relationship between essences once again that allowed us to figure out where the diffraction spots where the spots and refraction hadn't won but who says that all the atoms have to sit on a certain lattice plane that I described who says that all the atoms have to sit very tall reciprocal lattice where I draw lattice points in a prevalence most cases they won't write to think about a real life materials most case there will be atoms throughout the unit cell and if I draw any given plane what are our chance of having all the atoms on there zero right it's not going to happen so what we do know is any anthem will scare the x-rays right so we have to worry about those atoms that are not on one of those planes that we draw and what we need to address is what does that do to our scattering amplitude now what we did derive in the last couple of lectures was a general scattering crater that equation did not make any assumptions in the end we only dealt with a certain part of it which was a summation part which goes back to the unit cell repetition however there was a term in there that really applied to everything that's what we'll be looking at a little bit today now to put it back into something that we can draw and that we can envision let's just assume we are drawing our lattice planes but there are some atoms there are not on a lattice plane they are between lattice planes okay it's simple enough drawing isn't it here's one of your planes here's your next plane space d HK all apart and there is this atom a that is sitting at a distance da from the original plane now as long as all the atoms carry x-rays if atoms on this plane and on that plane with Kara in face which means the path difference will be equal to a multiple of lambda right then an atom sitting here in this plane a has to be partially out of phase with the other ways right now on this drawing they actually say out of phase what they mean is partially out of phase it's not going to be exactly out of phase in which case we would get an extinction okay so we have an atom that is sitting between the lattice planes that show constructive interference so we get some kind of reduction in intensity that's what we can already guess right now how can we describe this mathematically well it all comes back to how do you describe a plane I know not everybody here likes lectures okay but the easiest way to describe a plane is one vector which is a normal to the plane that describes the entire plane if you want to describe a plane by points you need at least three points right so here's a little drawing it shows you a plane with respect to an XYZ axis system okay and here's a vector P to a point P which is in the plane as you can see by this little symbol here the vector P is perpendicular to this plane we could of course describe this point with reference to the XY and z axis right they will basically say we take the projections along XY and Z and that gives us the coordinates of that point that is probably what most of you are more familiar with right because that is how we describe things all the way up through school now there are several ways to describe the plane okay and one of them is a so called intercept equation and that may be one that you may not be that familiar with here's the intercept equation of a plane okay now we will do a very simple derivation in two dimensions so that would be an intercept equation of a line that will hopefully make clear where these things come from okay your work in two dimensions X&Y we get what you don't get a plane right we get a lot in two dimensions