Throughout this course we have come across a couple of examples where a metal possessing defects actually leads to some pretty interesting features, most notably the quantum Hall Effect. Chapter 30 goes into a bit more detail about these, but as it's not required reading I shall summarise a few key points here.
Firstly, whilst any disruption from the perfect crystal state is a defect, only two are considered in this chapter. They are:
1) Vacancies and Interstitials
2) Dislocations
The first are known as point defects, as the imperfection bounds this one point in three dimensions (as opposed to a line or surface). Examples of these are the addition of removal of additional ions from the crystal structure, the former of these known as a Schottky Defect. This particular defect can arise naturally without disrupting any thermodynamic laws as long as the number of vacancies n is given by
n = N*exp(-(E+Pv)/kT)
Here N is the total number of ions, E is the derivative of (U-TS) with respect to n, where U is the potential energy, T is Temperature and S Entropy, P is pressure, v velocity and k is the boltzmann constant!
Consequences of this type of defect include changes in the electrical conductivity and optical properties. Similar consequences arise if an additional ion was at the lattice point, if particular ions were polarons or excitons (polarised or excited state ions).
Dislocations, on the other hand, refer to line defects, where the imperfection is bounded in two dimensions. This defect is important as it helps explain why a much smaller force is necessary to deform a crystal than predicted by all the previous theories. There are two kinds, screw and edge dislocations, and the diagram for these is on page 632. The basic requirements for this type of dislocation are (from page 634)
1) Everywhere else in the crystal except at the point of dislocation the crystal can be described as perfect
2) In the region around the dislocation the atomic positions differ substantially to that predicted by a pure crystal
3) There exists a nonvanishing Burgess Vector, defined as a loop of vectors that when mapped out in the perfect lattice return one to their starting point, but when the same vectors are traversed in the dislocation region one ends up at a different lattice.
As well as describing the weakness of crystals, these dislocations also affect the rate at which a crystal can grow.
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So, I guess it's kind of a fuzzy area, but I was wondering at what point an impure metal becomes an alloy? My first thought was that it would be some kind of arbitrarily defined point, but upon further thought, I figure it's really when you deliberately mix the two metals.
ReplyDeleteDefinition a vacancy or dislocation in an alloy would see like the first thing that needs to be defined.
DeleteIs an alloy really a crystal?
Crystals are periodic, thus a gap or something in the wrong place (or just something that doesn't fit the periodic pattern) could be spotted.
I would have imagined that an alloy could be modelled as a bravais lattice with a basis, so I see no reason why an alloy couldn't be classified as a crystal (assuming it met all other requirements).
DeleteAs for the difference between alloys and impure metals, I would probably say it's a mixture of the two points you made. Because you can create sources where you deliberately made the material impure (ie, doped semiconductors), but they're definitely not alloys. So perhaps it is a percentage thing, or maybe scientists are just creatures of whim?
Thanks for the summary, Dale!
ReplyDeleteI suppose we do need to consider defects, particularly dislocations, as they contribute greatly and in reality, we're probably not going to create a perfect crystal.
The division between the two types of impurities seems to be on the micro and macro levels?
Sidenote: Schottky has an interesting pedigree.
His advisors were Max Planck and Heinrich Rubens, but he has no listed descendants. His siblings include Gustav Hertz and Max von Laue.
Also interesting, Schottky's work includes the ribbon microphone and loudspeaker.
Just another defect that I've been reading about, actually relates directly to my talk I'll be giving on Monday.
ReplyDeleteThe Kondo effect is the scattering of conduction electrons in a metal due to magnetic impurities. At low temperatures, this effect is actually the primary source of electrical resistance which counter-intuitively increases with decreasing temperature! When this term is balanced against the electrical resistance due to phonons, then a certain minimum resistivity results, which depends on the initial material and concentration of impurities.
How this relates to my talk, all shall be revealed monday!!!