William Hume-Rothery

Transcription

In this screencast we will be discussing the Hume Rothery Rules that refer to solid solutions So a pure crystalline metal doesn't exactly exist in reality instead structures contain impurities so alloys are materials in which impurities have been deliberately added the question is what happens when we put two solids together? We're gonna talk about miscibility which is the ability for two solid to be partially or completely soluble in each other so what are the things that that are factors in whether two solid will be miscible and these are what are known as the Hume Rothery Rules So the first one is the atomic size factor and as you might imagined the radii of the two different metals should be a similar so and in fact they must be less than 15 percent different so the second rule or factor is the crystal structure and what we mean by the crystal structure is is it face centered cubic is it body centered cubic hexagonal etc. So for complete miscibility the crystal structure has to be the same the third factor is electro negativity and these are based on the pauling electronegativity and so they should be similar and in fact if you have very dissimilar electronegativity what you'll get is a compound rather than a solid solution and finally are the valence numbers So the valence numbers should be similar. So now that we've gone over the rules let's go over an example. So we will look at aluminum and silicon and if you look at a phase diagram what you will find is that they are partially soluble. So let's see which rules they satisfy and which rules they don't So the first one let's look at atomic radii. Sol aluminum has a radius of 0.143 nanometers. Silicon has a radius of 0.117 nanometers. So they are obviously different. So let's see what the percent different is. So we look at the radius of the aluminum minus the radius of the silicon divided by the radius of aluminum and multiply that by a hundred. The percent difference is 18.2 percent which is greater than that 15 percent difference and that automatically tells you that you are going to have partial solubility. So what kind of structures do they have. So silicon has a diamond cubic structure where aluminum has an FCC structure The diamond cubic is a repeating pattern of 8 atoms so it follows the face centered cubic structure but has a much smaller packing factor. So the structures are different and they do not satisfy this second rule Thirdly let's look at the electronegativities. Aluminum has an electronegativity of 1.6 silicon has an electonegativity of 1.9 They are similar but again you'd like to see them closer and finally let's look at the valences aluminum has a plus three charges Silicon has a plus four. So all of these rules are pretty much broke and and therefore aluminum and silicon are only partially soluble.