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Write for me internet of things gartner hype cycle 2019 capstone project on nursing shortage purchase course work on gay clubs for money alik purpose of this video is to talk about ionic structures and how we describe them now we've already talked about metallic structures which are composed of hard spheres that are closely packed ionic structures are very similar again we're thinking about these things as individual ions being hard spheres however now we have an added degree of complexion that's because these spheres can either be positively charged or negatively charged so here's one example this is a material called lead zirconium titanate it's composed of lead Technium zirconium and oxygen and this is an important material cuz it has a very large piezo electric effect so change in the voltage if I compress it in one direction but in order in order to be able to talk about this and describe this and even more importantly understand why these atoms are arranged in in this specific arrangement we need to be able to understand ionic structures okay so again we talked about ionic materials having at least two different kinds of particles so there are anions negatively charged ions and we have cations positively charged ions now typically anions are going to be larger than cations because they have extra electrons but that's not always the case so there's there's an attractive force between oppositely charged particles but there's a repulsive force between similarly charged particles right two anions don't want to get too close together there's a repulsive force between them pushing them apart so really ionic structures assemble in such a way to maximize those attractive forces and to minimize the repulsive forces so we're gonna work through an example and this is sodium chloride so this is common table salt I've shown you the individual the particular structure for sodium chloride but what we want to ask our is how did we get to this particular structure and we got there by answering two questions the first question is which sites so what I mean is ionic materials we typically think of them as having n an ionic lattice so lattice anions and cations are sitting in particular locations in that an ionic lattice so which locations are they sitting and that comes down to the relative size the two different materials so the second point then is how many so how many of those sites are occupied this ultimately comes down to the stoichiometry how many anions per cation and how many available sites are there in a particular lattice so let's keep working through this example the first question I said which sites now there's a rule and that rule is that cations will occupy the largest available site that is less than or equal to their size so let's think about that with a picture first and then we'll come back to the the words so if I picture four anions here so these are negatively charged if the cation is smaller than the available site so the site is out here the cation is smaller than that that's an unstable configuration it's unstable because we have this repulsive force right those anions want to spread away from each other they're being repelled from each other so if we have a very small cation this is an unstable configuration on the other end if we have a cation that's a little bit bigger than those anions then it pushes all the anions out a little bit and remember the anion techadon interaction is attractive and so this is a more stable configuration right there's a attractive energy between that cation and that anion and the neighboring anions are being pushed apart from each other a little bit so this is a stable configuration the limit would be when it's exactly the right size and so we say that this is a stable configuration as well although it's very very rare to find a radius that's exactly the same size as that potential but this is only true to some limit right so as this cation gets larger and larger at some point now we're not going to have a stable figuration anymore because the cations will be impinging on other cations and so we come back to the rule that cations want to occupy the largest available site that is a little bit smaller than they are so let's think about this in terms of sodium chloride and we can think about this in terms of the radius ratio of the cation to the anion and we can do this because we know that if we have an anion lattice so for example if we have an FCC lattice the available size of the different sites so for example there's an octahedral site right in the middle of the FCC lattice the available size of that lattice I can calculate out the size of that interstitial position position as a function of the anion radius and so if I if I find if I look at the cation anion ratio I can I can basically look at a table and say what kind of a site those cations would like to occupy so for this case sodium plus is 116 picometer that's the radius and chlorine anion is 167 picometers so if I look at that ratio the cation over the anion I get a value of zero point six nine five and we can see that that falls within the range that's acceptable for an octahedral hole and so what that means is that that cation sodium is a little bit bigger than the size of the octahedral hole but it's a little bit smaller than the next available site so the next one would be a cubic available site and that ratio the size of that available site is 0.732 times the radius of the anion so again we found the radius ratio cation over N and we look at our table and we say that in sodium chloride lattice sodium wants to occupy octahedral sites so it's gonna sit in octahedral sites such as this one but the next question is how many of those sites is it can occupy right so for example we could occupy half of the sites remember in an FCC lattice we have 4 octahedral sites so this is one full site because it's entirely within it this one is one quarter of a site because only a quarter of that sphere is within the unit cell but if I look at all of these 4 together that adds up to 1 so these are 2 available sites that's half of the sites so that's one potential feed figuration or we could think about maybe it's occupying all the sites so how do we figure this out and that comes down to the stoichiometry of those solid so we know that we need 1 sodium for each one chlorine that we have right so let's look at the FCC lattice again in 1 unit cell we have 4 atoms 4 atoms of chlorine these are actually ions right so for chlorine ions and so essentially we need to occupy for octahedral sites with sodium and that will give us a one-to-one ratio of sodium to chlorine and that is the case if all of the octahedral sites are occupied okay so we've thought about ionic structures we've talked about how they also follow a close-packed hard sphere model but the two important things right ionic radius ratios are gonna tell you which sites are occupied are those cations sitting in cubic sites octahedral sites tetrahedral sites certain lattices do or do not have certain sites so for example the BCC lattice does not have tetrahedral sites so if you found by the ionic radius ratio that the cations want to sit in tetrahedral sites then those n ions are not going to be coordinated in a BCC structure and finally we talked about stoichiometry how many of the sites are occupied and so in FCC case for sodium chloride we know there's a one-to-one ratio and so that meant that all of those octahedral sites had to be occupied do my capstone group newport beach Hofstra University, Hempstead.