MadSci Network: Physics

Re: Is there an equivalent of Brownian Movement for solid matter?

Date: Tue Sep 9 21:55:14 2003
Posted By: Matthew Buynoski, Senior Member Technical Staff,Advanced Micro Devices
Area of science: Physics
ID: 1063049515.Ph

Helloooo, Jeff!

You sort of asked two questions. The title asks whether or not a solid 
equivalent of Brownian Motion exists. The message body asks about motion of 
atoms inside a solid. They're not quite the same question, and your Mad 
Scientist will try to explain both.

Brownian motion is the random visible (in a microscope) wiggling of small 
particles because of collisions with the moving atoms in the fluid 
containing the particles.  I suppose a solid equivalent does exist (motion 
of inclusions of one solid in another) but as far as I know it has no name. 
The amplitude of motion is vastly smaller, as atoms in solid are constrained 
to moving less than the crystal lattice spacings (on the order of a few 
Angstroms or so), and so not visible in a microscope (well, possibly in a 
very sophisticated transmission electron microscope, but I doubt it).

Don't go away disappointed, though. At least two forms of atomic motion 
exist inside solids.  The first is little packets of vibrational energy 
called phonons. Think of a lattice as a bunch of solid balls (atoms)held 
together with springs (chemical bonds). Wiggle one and the whole array tends 
to jiggle. After struggling though some horrid mathematics, it turns out 
that the jiggling is constrained to occur in only certain directions and 
energies. In essence these constrained vibrations of mechanical energy, 
called phonons, are standing waves in the crystal. 1-D Analogy: a taut 
violin string will only oscillate at certain frequencies. 2-D Analogy: a 
drum head only vibrates at certain frequencies and in certain patterns.

In addition, we have point defects. A crystal with all its atoms exactly in 
place in the lattice is a very high-entropy state, and not likely to occur 
at any temperature much above absolute zero. It turns out that some of the 
atoms acquire enough thermal energy to manage to get loose, becoming what 
are called interstitials, and sit between the atoms still in the lattice. 
They leave behind "holes" in the lattice, called vacancies. At any given 
temperature, an equilibrium exists between the thermal generation of 
interstitial-vacancy pairs and their annihilation (interstitial "falling" 
back into a vacancy), causing  a specific concentration of the point defects 
to exist in the lattice. Interstitials and vacancies both move through a 
crystal lattice, fairly rapidly as these things go. 

By the way, other atomic species can enter a lattice as interstitials, too.
This is called solid-state diffusion and can change the characteristics of 
the material dramatically. For example, some metamorphic rocks are created 
when atomic species from a hot magma diffuse into the surrounding wall rocks 
and change their makeup into an entirely new set of minerals.

So, in summary, no visible equivalent to Brownian motion exists in solids, 
but yes, certainly the atoms move around, both as part of the lattice 
vibrations (phonons) and as interstitials/vacancies. Hmm, yet another yes 
and no answer. Never can get a straight answer out of these Mad Scientists 

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