I’m excused from interpreting this talk, Nanometers, Femtoseconds, and Yoctomoles: Molecular-Dynamics Simulations of Diffusion in Garnet, which means I can take notes and play!
The professor is highly billed: Dr. Bill Carlson from UT at Austin. You think I’m kidding about “play”? No way, Jose!
Scale: plates, rocks in the field, mineral grains, atoms….
Geologic Time:
Sizes from macro to nano…..
Diffusion gives direct qualitative information on rates and duration of metamorphic processes. Garnet is present in a wide range of bulk compositions, is stable, and has a wide array of diffusive behaviors that can be monitored to help us understand rates of diffusion and the mechanisms behind them. You know my parallel? Groups (of people) and knowledge/understanding (disseminated via language).
Main topic: Molecular dynamics simulations…. (microdynamic intergroup relations?)
Problem: existing theories for diffusion at atomic scale don’t explain the phenomena we observe…(sounds like social science to me!)
Novel systematics emerge from recent synthesis…
Elastic Strain Theory (EST) – diffusion by vacancy mechanism: work is required to move atoms apart and squeeze this atom in-between them….larger atom = more strain which slows down diffusion. Like all theory (!) “sometimes it works…sometimes it doesn’t.”
There’s a “misfit parameter” (!) = “how badly an atom fits in its new site.” If a good fit, then the number is small; if the atom is too big you get a positive misfit parameter, if the atom is too small you get a negative misfit parameter. (No speculation, thanks, on the size or charge of my misfits!)
Observation: a fundamental gap in our knowledge, sometimes smaller sizes diffuse more slowly (instead of faster, which is what theory predicts).
How else can observable systematics be explained if EST doesn’t do it? Perhaps – molecular dynamics (MD) …EST relies on a visualization based on Hooke’s Law ;MD takes into account all of the binary potential fields (imagine: all 756 (?) potential dyads we calculated as the total combination of interpersonal pairings (28 individuals, each with 27 unique relationships – except I don’t know how to do this math!) in the current course on Group Dynamics).
Comparison of Potential Barriers for Atoms of Different Size: take potential energy, over time, and compare it to optimal diffusion (and yield (?) energy barriers to diffusion). EST predicts well for larger atoms…..for smaller atoms….start with lower energy well because more tightly bound….then a smaller atom has a larger energy barrier to cross than the optimum size….
MD: Newtonian mechanics at the atomic scale…. with forces as sum of pairwise interactions: interatomic potential, interatomic distance.
Interaction potentials:
- ionic charges (same = repel; different = attract)
- Born-Mayer repulsion – atoms can’t get too close to each other, will begin to push each other away = gives an indication of how hard the atom is (large value = billiard ball, small value = nerf ball)
- dipole attraction (van der Waal) – an induced dipole, if the force is strong it leads to a large value, if the force is small then it leads to small value.
Interaction parameters are determined by fitting MD models to data on static properties, eg…molar volumes, expansivities, compressivities (ah, no static properties in human relations – although social science (and basic prejudice) TRIES to make “identity” static/stereotypical…)
You have to select time steps that are a function of atomic motion…durations long enough to obtain many diffusive jumps… (time…always time! not to mention timing!)
Assign initial positions (“groups” never simply “begin” they are a convergence in time of dynamics already in motion, already historical), throw in random velocity (intensity/emphasis of attention to the storming phase of group development?)….
Diffusive Jump – Dr. Carlson shows an animation of atoms in motion…..cute!!! I wanna link to it! Could we model interpersonal relations in some kind of analogue? I’ve envisioned forever – do we have the technology?
Einstein relates diffusivity to time using a mean-square displacement…..average over all atoms, average over all possible times….get tau….then see how it changes, the slope is the diffusion quotient…
Vacancy concentrations are crucial – but how do we figure this out? One method comes up with a physically impossible result (100% vacancy) which indicates some of the physics is still being missed in the calculations. The standard MD simulations…. tend to significantly underestimate…. (something crucial. Kinda like social science, language, social construction of reality, you know what I mean).
Tracer diffusion simulations: replace 10% of the atoms with some other elements and examine the rate of diffusion of that element. (Can I just say, as if anything only ever goes in one way?!!!!!?)
Failure to generate (via simulation) the relationships that match measured behavior in strain relationships but the gaps/discrepancies point us to what we’re missing… STATIC properties all MATCH up But the DYNAMICS do not!!! (Same as with social science?!)
Failing to account for what’s happening to atoms when there are other atoms in the vicinity. Different cases pending varying polarizability. (I swear this is group relations jargon!)
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