Chemistry: Magnetic Properties and Spin

Chemistry: Magnetic Properties and Spin

09/06/2012

~ Christine48

Great demo. Simple yet illustrative.

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My esteemed colleague, Professor Harman, has given me this opportunity to try to explain magnetism to you, because it happens to be my area of research. To begin our discussion I have to give you some new vocabulary words, and the first vocabulary word is diamagnetic. We say that a substance is diamagnetic when it is repelled by a magnetic field. The way that we have measured that is with a Faraday balance, among other different methods. So imagine that this system here starts out being exactly in balance, where we put our sample on the right hand side, and then we offset it with some weight, such that this bar is exactly level, and now we bring a magnet up and put it underneath our sample. If the sample tips in the direction shown, in other words, it appears to weigh less in the presence of the magnetic field, we say that the sample is diamagnetic. Furthermore, we can go as far as to say that diamagnetism results from paired electrons. So in other words, all electrons in the sample are paired up and when all the electrons are paired up, the sample behaves as though the sample were diamagnetic.
Now, in contrast, a substance is paramagnetic when it does have unpaired electrons and the way we show that is with the same Faraday balance except, again it starts out exactly balanced and now we bring up a magnet and now the sample appears to weigh more in the presence of a magnetic field rather than when there is no magnetic field there at all. Paramagnetism results from unpaired electrons, so if a sample has unpaired electrons, it is going to be paramagnetic.
Well, we have looked a fair number of compounds and ions that are paramagnetic, or at least we have talked about them. We have talked about nitric oxide and how it had an odd number of electrons, because you just couldn't satisfy the Octet Rule starting with something that had an even number of valence electrons and an odd number of valence electrons. Similarly, nitrogen dioxide has an odd electron associated with it and chlorine dioxide has an odd electron associated with it.
Two other species that turned out to have biological relevance superoxide, which is an oxygen molecule to which we add another electron, and hydroxyl radical, which is hydroxide anion from which we have removed an electron, you can convince yourself that based on the Lewis Dot structures, neither of these can satisfy the Octet Rule for all the atoms, and that no matter what, the Lewis Dot structure has to have an unpaired electron.
Now, we have also talked briefly about dioxygen and how even though Lewis Dot structures and valence bond theory don't predict that dioxygen should have an unpaired electron, in fact two unpaired electrons, Molecular Orbital Theory, which superseded Valence Bond Theory does adequately explain the result. The result is if you take oxygen it is attracted to a magnetic field, so that is another way that you can measure the magnetic properties. You can weigh it or you can just show that it is attracted to a magnetic field. Typically the way that experiment is done is to take liquid oxygen and pour it between the poles of a strong magnet and you will see that it actually sits between the two poles of the magnet.
So, the kinds of compounds that Professor Harmon has been telling you about, transition metal compounds, things like cobalt hexafluoride, which is high spin, meaning that the way electrons fill the d orbitals, you put one in each one of the three lower orbitals, and then you put one in each of the two upper orbitals, and then if you have more electrons left over, you start pairing them up. So this species has four unpaired electrons. In contrast. the cobalt hexammine is low spin, it has no unpaired electrons. Because the gap is larger here, what you do is start putting electrons in these three orbitals and then since these are too high in energy, you have to go back and put electrons in the first three orbitals that you started with, as a result, cobalt hexammine has only paired electrons and we say that it would be diamagnetic, whereas hexafloro cobalt, three minus, is going to be high spin and paramagnetic, meaning that it will be attracted to a magnetic field.
Well, could you have predicted that this should be the case? No, probably not. The point is that by measuring the magnetic properties, we can learn something about the compounds, not the other way around. We use magnetic properties as a tool to measure physical properties of about the system; in particular, we learn that the hexafloro cobalt is paramagnetic, whereas the hexammine cobalt is diamagnetic.
Now, there is another kind of paramagnetism that is the one that is associated with unpaired electrons in a metal. So, when we were talking about the free electron model of a metal, which was the most rudimentary description, we imagine that the nuclei and the core electrons lived at lattice sites and then the valence electrons were just allowed to float around free in bulk and do whatever they wanted to do. They almost formed what we call an electron gas. Okay? Not a gas in the conventional sense, but a gas in the sense that they can sort of float around and do what ever they want and go where they want to go, just like gas in a balloon. Well these represent what should be unpaired electrons and so there is paramagnetism associated with these unpaired electrons and that's what we call, in fact, poly-paramagnetism. Not really important what it is called, but the idea is that these conduction electrons, the ones that are responsible for making a metal a metal so that it conducts electricity, can also be those that give rise to having the sample being attracted to a metal. Unfortunately, not all metals are paramagnetic. So, that that means the free electron model can't be the whole story, so here is another place where the free electron model is weak and where we have to use a more sophisticated model which is Band Theory in order to fully explain what is going on. It turns out that for really simple metals like lithium potassium sodium, which only have one valence electron, everything works great, but as soon as you evolve beyond that in a transition metals and stuff like that then it starts to breakdown and so you will have to use Band Theory in order to explain the magnetic properties.
In particular, Band Theory also gives us something else, it gives us ferromagnetism, and what a ferromagnet is, is something that is attracted to a magnetic field, but much more strongly then a paramagnet and you know what a ferromagnet is, it is the kinds of things that stick to your refrigerator door. I am taking a slight liberty with terms here, but something that would stick to your refrigerator door is a ferromagnet. So what distinguishes a ferromagnet from a paramagnet? In fact, one thing that I will tell you is that a paramagnet when you cool it down, sometimes becomes a ferromagnet, in other words, when it is in its paramagnetic state it is attracted to a magnetic field, but as you cool it down, it undergoes a phase transition until it might be really, really attracted to a magnetic field. So much so, that a refrigerator would stick to it. Okay.
So, how do we understand the distinction? The answer is, that you can imagine that a paramagnet consists of a bunch of little bar magnets so the unpaired electrons in the paramagnet behave as though they're little bar magnets. What happens when you take this sample and you apply a really large magnetic field is all the little bar magnets line up with the applied magnetic field, but when you take that applied magnetic field away, what happens in a paramagnet is the unpaired electrons go back to being somewhat random. They no longer have their little bar magnet norths pointed in one direction and all their bar magnet souths pointed in the other direction. Whereas, if you take something that it is a ferromagnet, and if you heat it up... Remember I said that, if you heat up a ferromagnet it becomes a paramagnet, okay, so if we imagine that this is the ferromagnet at really high temperature, and we put it in a magnetic field and then we take away the magnetic field, it stays aligned. So a ferromagnet stays aligned when you take the magnetic field away, whereas a paramagnet, when you take the magnetic field away goes back to being random.
Why? Well the reason is that there is an interaction between the unpaired electrons that makes them want to point in the same direction. So when one of them points in a direction, the next guy wants to point in that same direction, and the next guy, the next guy, and so they stay aligned. Here is an analogy. Suppose we take 12 people, 12 little spins, and they don't know each other, and somebody says well let's go to the movies. Well, some of them might go to the movies and some of them might not go to the movies. But if we took 12 friends who really liked each other, and one of them said, let's go to the movies, they would all go to the movies. So the idea is that because there is an interaction that makes these guys want to line up with each other, this thing stays magnetic when you remove the magnetic field, whereas this thing doesn't.
Now, to illustrate that idea, what I am going to do, is going to take a paper clip, actually two paper clips, and show you that these two paper clips are not attracted to each other. These paper clips turn out to be ferromagnets, but in the totally random state. So these are ferromagnets that are totally randomized. Now I am going to align them by putting them in a big magnetic field, and this is a big magnetic field. So we put them is this big magnetic field, and now all the spins are doing what is going on here. And now I am going to take away the big magnetic field, and now I am going to show you that they get stuck in this aligned state. And the way you can tell is they stick to each other now. So each one of these now has become a little tiny magnet and you know that magnets like to attract each north to south, so what happens is now the unpaired electrons in the little paper clip are attracted to each other and so we have made new magnets from things that weren't magnets before.
You will have to take it on faith that I have cut a lot of corners and I have been a little liberal with terminology, but the ideas is that unpaired electrons are what give rise to interesting magnetic properties, that if you have unpaired electrons, then the thing is paramagnetic. If there are interactions between the unpaired the electrons and they are strong enough, the thing is going to be ferromagnetic, and then if you have only paired electrons, then the substance is diamagnetic, and this is just a way that we can organize stuff in our world just like the way we are trying to organize things in terms of solids and liquids and gases and stuff like that.
Transition Elements
Bonding in Coordination Compounds
Magnetic Properties and Spin Page [2 of 2]