**Nanomedicine,
Volume I: Basic Capabilities**

**©
1999 Robert A. Freitas Jr. All Rights
Reserved.**

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

**10.5.1 Dimensional Stability
and Strength**

At high applied stress, covalent bonds cleave much more readily
at higher temperatures. For example,^{10}
at an applied stress of 8 nN/bond a C=C double bond cleaves in ~10^{27}
sec at 0 K, ~10^{4} sec at 300 K, and ~10^{-3} sec at 500 K.
The positional uncertainty is somewhat less problematic in design -- the mean
classical thermal longitudinal displacement of a diamondoid logic rod varies
only as ~T^{1/2}.^{10} The endpoint
of such a rod 1 nm wide and 100 nm long displaces ~0.05 nm at 77 K (liquid N_{2}
), ~0.10 nm at 300 K, and ~0.14 nm at 600 K (liquid lead). Mechanical elements
thus become more reliable at lower temperature -- e.g., the probability of error
in a force sensor (Section 4.4.1) scales as ~exp(1/T),
so a 1% error in a sensor at 310 K increases to a 10% error at 600 K, but falls
to just 10^{-6} % error at 77 K.

Most materials contract when cold and expand when hot (although
zirconium tungstate is a well-known exception^{2938}).
Thus a 1000-nm long diamondoid rod at 310 K contracts to ~999 nm at 77 K and
expands to 1001 nm at 600 K. However, the coefficients of thermal expansion
and various other thermophysical parameters are themselves temperature-dependent.
The coefficients of volumetric thermal expansion at ~298 K (~25°C) are 3.5 x
10^{-6} K^{-1} for diamond, 15.6 x 10^{-6} K^{-1}
for sapphire, 1.2 x 10^{-6} K^{-1} for vitreous silica and 36
x 10^{-6} K^{-1} for crystalline silica or quartz.^{567}

Young's modulus (modulus of elasticity) and the other moduli
are also temperature-sensitive, especially and most obviously near phase changes
-- e.g., sapphire melts at 2310 K but "softens" at 2070 K.^{1602}
At ~1773 K, diamond plastically deforms at just ~1 atm pressure, but >60,000
atm are required to deform diamond at ~1300 K.^{2041}
At the cold extreme, anyone who has seen the hammering of a nail using a piece
of banana cooled in liquid N_{2} has witnessed the temperature sensitivity
of materials strength.

Last updated on 24 February 2003