The 148Gd (gadolinium) power source proposal was described in NMI (1999) at http://www.nanomedicine.com/NMI/22.214.171.124.htm. The semiconductor shell structure crudely illustrated in Fig. 6.7 is intended to be an atomically precise structure. The radioactive 148Gd is kept permanently encapsulated while inside the body. The minimum radius for this powerplant is on the order of ~11 microns, so it is clearly intended for fixed-site multi-nodal (not bloodborne) use.
I haven’t yet published any detailed scaling studies specifically describing dietary-related nanorobotic systems. These proposals now exist only in rough form in my long (across 2 decades!) accumulated notes for Chapter 26 in Vol. III of my Nanomedicine book series. I hope to find time to publish NMIII sometime in this decade.
The mass of the alpha-particle is ~7000 times greater than that of an electron, so the velocity and hence the range of a-particles in matter is considerably less than for beta-particles of equal energy. Consequently the optimum radionuclide for medical nanorobots is predominantly an alpha emitter.
Among all gamma-free alpha-only emitters with t1/2 > 106 sec, the highest volumetric power density is available using Gd148 (gadolinium) which a-decays directly to Sm144 (samarium), a stable rare-earth isotope. A solid sphere of pure Gd148 (~7900 kg/m3) of radius r = 95 microns surrounded by a 5-micron thick platinum shield (total device radius R = 100 microns) and a thin polished silver coating of emissivity er = 0.02 suspended in vacuo would initially maintain a constant temperature T2 (far from a surface held at T1 = 310 K)
75-year half-life, initially generating 17 microwatts of thermal power which can be converted to 8 microwatts of mechanical power by a Stirling engine operating at ~50% efficiency. (Smaller spheres of Gd148 run cooler.) While probably too large for most individual nanorobot designs, such spheres could be an ideal long-term energy source for a swallowable or implantable "power pill" (Chapter 26) or dedicated energy organ (Section 6.4.4). A ~0.2 kg block of pure Gd148 (~1 inch3) initially yields ~120 watts, sufficient in theory to meet the complete basal power needs of an entire human body for ~1 century (given suitable nucleochemical energy conversion and load buffering mechanisms, and a sufficiently well-divided structure).
Michael highlights the cost factor:
in 1998 gadolinium cost about a dollar per two cubic microns(!) This is expensive stuff. The number of nanobots that might be used would be on the order of a billion, each with a cubic micron-sized power core, though 11 microns across due to shielding. Given the 1998 cost of Gd148, a full system would cost about $500 million for the fuel alone