© 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 ~10²⁷ sec at 0 K, ~10⁴ 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 N₂ ), ~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 exception²⁹³⁸). 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 N₂ has witnessed the temperature sensitivity of materials strength.

Last updated on 24 February 2003