Atom placement frequency

For gemstone metamaterial on-chip factories to be able to put human scale objects together atom by atom in reasonable timespans they need to place atoms at mind boggling rates.

Example

Assuming f₀ = 1MHz atom placement frequency per mechanosynthesis core how many cores (N_core) does one need to reach the desired throughput of Q₀ = 1kg/h ?
N_core = Q₀ / (m_C * f₀) = ~1.4*10¹⁵ cores (about an 1.4 Petacore system). (m_C … mass of carbon atom.)
A core size of ~(32nm)³ = ~32000(nm³) seems to be a sensible guess for advanced APM systems.
All the cores together then take a volume of size ~45(mm³) = ~ 45microliters.
This can be spread out plenty to remove high levels of waste heat.
The effective atom placement frequency in this system is f₀*N_core = 1.4*10²¹ atoms per second (1.4ZHz – quite mind boggling) (>> 10⁹ Atoms/second).

Early mechanosynthetic systems will be several orders of magnitude lower in throughput though.

• They will have low temporal placement frequency
• they may be only two dimensional
• but they'll be already massively parallel

Related

• Mechanosynthesis core
• Mechanosynthesis
• Convergent assembly
• Pages with math

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Nanosystems chapter 8 Mechanosynthesis
=> 8.3. Solution-phase synthesis and mechanosynthesis
=> 8.3.2.a. Basic constraints imposed by mechanosynthesis
=> 8.3.2.a. Loss of natural parallelism