A NEW KIND OF PURITY (C)1995 Alan M. Schwartz For materials composed of explicit stoichiometry or discrete molecules, purity is the ratio of the right stuff to the total stuff. Purities of 99% to 99.9+% are common, one part-per- hundred to less than one part-per-thousand foreign matter. The appetites of technology make parts per million purity (99.9999%) available, and parts per billion purity (99.9999999%) available for a stiff price. We can go beyond composition and demand the structural perfection of a single crystal, its unit cell filling 3-space without taint, twinning, dislocations or other defects. Physical chemistry and solid state physics model perfection, plus approximations for imperfections. One part-per-billion is one part in 10^9. Two grams of carbon hold 10^23 atoms. Imagine the surprise echoing through academic halls when elegant theoretical frameworks elaborated over the past 100 years to model pure materials - given real world perfection - were insufficient. Nuclear technology requires isotopic purity - a single kind of atomic nucleus, not a mixture of nuclei of a single element with various numbers of neutrons. Natural uranium is 0.0055% U-233, 0.720% U-235 and 99.2745% U-238. Only the two lightest isotopes are fissionable. Volatile uranium hexafluoride diffuses through semi-permeable membranes for a per stage enrichment as the square root of the molecular mass ratio, 0.429816%. Gas centrifuge separation is proportional to the mass ratio, or 0.861480%/stage. Saddam Hussein's technicians knew 1000 stages of centrifugation would give a U-235 theoretical separation 73 times better than diffusion. Separating lighter isotopes is much easier. MAXIMUM SEPARATION RATIO/STAGE ISOTOPES COMPOUND DIFFUSION CENTRIFUGATION =============================================================== U 235/238 hexafluoride 0.429816% 0.861480% Si 28/29 silane 1.54942 % 3.12285 % C 12/13 methane 3.08187 % 6.25872 % Pure carbon-12 (98.90% naturally) and silicon-28 (92.23%) are readily available. Their enriched heavier isotopes are merely very expensive, C-13 (1.10%), silicon-29 (4.67%) and silicon-30 (3.10%). Do the properties of an isotopically pure solid differ from those of the natural mixture? HELL YES. Insulating solids transport heat via random thermal atomic vibrations, which is very slow. The conduction electron gas in metals transports heat by diffusion, which is very fast. The number-dense, tightly bonded, light atomic lattice of a diamond crystal conducts heat via quantized lattice vibrations called phonons - 5.74 times faster than pure single crystal copper at room temperature, 21.0 times faster in liquid nitrogen. The statistical thermodynamics of the solid state based upon the thermally averaged Boltzmann distribution of fundamental frequencies of lattice vibrations was worked to a theoretical fare-thee-well by Peter Debye in the 1920s. General Electric in the early 1990s grew 99.9+% C-12 diamond, rather than natural 1.10% C- 13. C-12 diamond thermal conductivity is 25% beyond theory allowing for the absence of heavier C-13 atoms which scatter propagating phonons. Something fundamental had come softly creeping. We knew not what it was. We thought some more. The 25% greater C-12 diamond thermal conductivity, while surprising if one assumes the C-13 mass defects are simple Rayleigh scatterers, is completely explainable by "Normal" 3-phonon scattering processes (which conserve phonon momentum, unlike "Umklapp" 3-phonon processes). This is the Callaway model used successfully on LiF by R. Berman. (To hear a New Age hind gut fermenter spewing astral drivel is to laugh.) The chemical bonds in C-13 diamond are 4% stronger than those in C-12 diamond. The tensile strength of diamond is 10 tons/square millimeter; a 4% increment is 800 lbs/square millimeter more. Alloy NS-355 used for highly stressed springs in jet engines, one of the strongest steel wires on Earth, has a total tensile strength of 775 lbs/square millimeter. 1.04 can be a big factor! Electrons flowing though a silicon transistor scatter off lattice impurities, like different atom isotope masses, causing energy loss (resistance) and slowed signal propagation. The advantage of isotopically pure devices for high performance is obvious, especially since each active device layer of a very large scale integrated (VLSI) circuit is grown a few atomic layers thick upon an inert silicon substrate. The incremental cost is acceptable. Much more interesting would be the growth of chemically identical but isotopically distinct circuit layers to confine and direct electron trajectory by scattering off an isotopic composition discontinuity. The problems of differential thermal expansion and crystal lattice mismatch between circuit layers of different compositions would all but disappear, because it is all silicon. To science familiar with vacuum tubes, a 1950s tiny metal top hat with three wire legs (transistor) might be fathomable as to purpose but mysterious as to mechanism. Open a VLSI chip to expose its postage stamp-sized silicon heart and, even under a good microscope, the modulated subtleties of composition and geometry evade all but cognoscenti. What wondrous subtleties of intelligent design do we ignore, evidence of life beyond Earth, because we are blind to "obvious" inflected compositions at an atomic scale?