Conception and manufacture of the Avogadro Project's (nearly) perfect silicon sphere (and, what is “atomic feeling”?)

The [Avogadro Project](https://en.wikipedia.org/wiki/Alternative_approaches_to_redefining_the_kilogram#Avogadro_project), an effort prior to the [recent redefinition of Avogadro's constant](https://chemistry.stackexchange.com/questions/131315/why-was-avogadros-number-chosen-to-be-the-value-that-it-is) to design a nearly perfect sphere of silicon-28, apparently relied on the fine fingers of optician [Achim Leistner](https://en.wikipedia.org/wiki/Achim_Leistner) - at least according to the Wikipedia: 



> 
> Achim Leistner is an Australian optician of German origin.[3](https://en.wikipedia.org/wiki/Achim_Leistner) During
>  his retirement, he was asked to join the Avogadro project to craft a
>  silicon sphere with high smoothness, as automated machining does not
>  match his precision.[3](https://en.wikipedia.org/wiki/Achim_Leistner)
> 
> 
> In addition to precision instruments, Leistner uses his hands to feel
>  for irregularities in the roundness of the sphere.[3](https://en.wikipedia.org/wiki/Achim_Leistner) The research
>  team has called his extraordinary sense of touch "atomic feeling".[3](https://en.wikipedia.org/wiki/Achim_Leistner)
> 
> 
> 


I suppose this is largely a set of questions about machining and metrology, but materials science is important too. Also, because of the relevance to the redefinition of $N\_\text{A}$ I thought it appropriate for this site. With all due respect for Achim Leistner's amazing fingers:


How was this sphere conceived and crafted? For instance: how was the size of the sphere decided? How was the material selected? What is the concentration of defects in the silicon that allows assumption that the lattice is perfect? How is this degree of quality guaranteed? Why can't "automated machining" match the precision of (assuming the alternative) "machining by hand"? What is this purported "atomic feeling"? Is this PR talk, to make the manufacture of the sphere seem more mysterious?




Short answer: The success of the project benefitted from many contributors.


According to [BIPM](https://www.bipm.org/en/about-us/) and its [Avogadro project](https://www.bipm.org/en/bipm/mass/avogadro/), there are *two spheres* ([reference](https://www.bipm.org/en/bipm/mass/avogadro/)). The page equally refers to a publiction about the [2011 $\ce{^{28}Si}$ atom count](https://iopscience.iop.org/article/10.1088/0026-1394/48/2/S01) (paywall) and the report in 2017 ([here](https://iopscience.iop.org/article/10.1088/1681-7575/aa7820), open access). From the later paper, you may identify the origin of the two spheres in the Czochralski crystal obtained initially:


[![enter image description here](https://i.stack.imgur.com/2P58w.png)](https://i.stack.imgur.com/2P58w.png)


as well as where samples were taken to determine the amount of carbon, oxygen, nitrogen, and boron (*loc. cit.*, table 1), the molar mass of silicon (table 2), concentrations of point defects in the lattice (table 3). Equally, the analysis took into consideration the $\ce{SiO2}$ layer naturally formed if the sample is exposed to air, as well as adsorbed water; for both, the upper limit of layer width as well as the mass are provided. As an example, the deposit of oxygen on the spheres was mapped by X-ray photon spectroscopy (XPS):


[![enter image description here](https://i.stack.imgur.com/C5Tpg.png)](https://i.stack.imgur.com/C5Tpg.png)


The article describes that the diameter of the spheres was assessed by a sphere interferometer


[![enter image description here](https://i.stack.imgur.com/jYGPq.png)](https://i.stack.imgur.com/jYGPq.png)


in vacuum at $20\,^\circ{}\mathrm{C}$ within a tolerance of $\pm 3\,\pu{mK}$ to allow the statement



> 
> The measured diameter was the apparent diameter, which is not corrected for the phase shift due to the surface layers. The mean apparent diameter was 93 723.723 61(61) μm.
> 
> 
> 


As for imperfections, this property equally was mapped:


[![enter image description here](https://i.stack.imgur.com/JmEbS.png)](https://i.stack.imgur.com/JmEbS.png)


With papers titled like *The self-weight deformation of an x-ray interferometer* the dedicated issue of [Metrologia 48(2), April 2011](https://iopscience.iop.org/issue/0026-1394/48/2) shed some light on monitoring the quality of the samples and the used tools for the analyses.


*Additions:*
A video of channel [veritassium](https://www.youtube.com/watch?v=ZMByI4s-D-Y) is dedicated to the reference spheres, too. The section starting at 7:00 min focusses on carving and polishing them (8:11 min, at 8:19 min likely showing Leistner himself).


A now open-access publication by [Fujii *et al.*](https://iopscience.iop.org/article/10.1088/0026-1394/53/5/A19) equally briefly describes the stages to carve-out the spheres:


[![enter image description here](https://i.stack.imgur.com/SqvS0.png)](https://i.stack.imgur.com/SqvS0.png)


Starting from the ingot, a section is cut. A lathe is used to obtain a sphere already with an shape accuracy of $1\,\pu{mm}$. To smoothen the surface, these spheres are lapped with alumina particles in water with finer and finer grains; eventually (fine lapping) within a margin of $100\,\pu{nm}$. To polish the surface, collodial alumina and eventually titanium dioxide yielded a shape deviation of less than $50\,\pu{nm}$ and a surface roughness below $0.2\,\pu{nm}$. This publication explicitly refers to Leistner's work including publications authored by him ([example](https://www.osapublishing.org/ao/abstract.cfm?uri=ao-26-4-600), [example](https://www.spiedigitallibrary.org/conference-proceedings-of-spie/2536/1/High-precision-large-diameter-single-crystal-silicon-spheres--their/10.1117/12.218436.short)) and then established protocols easing to manufacture such samples reliably.


PTB continues both further development of the interferometers ([here](https://www.ptb.de/cms/en/ptb/fachabteilungen/abt5/fb-54/ag-541/kugelinterferometer541.html)) and the deployment of these spheres as substitute of the old standards ([example](https://www.youtube.com/watch?v=pouZ3oWIQCk)). (As of writing, the [mass standard's](https://www.ptb.de/cms/en/ptb/fachabteilungen/abt1/fb-11/ag-111.html#maincontent_forschung_header) group seeks collaborators for Si spheres ([reference](https://www.ptb.de/cms/en/about-us-careers/careers/bms-stellen/bms-stelle.html?tx_jobmodul_pi1%5Bjob%5D=3223&tx_jobmodul_pi1%5BlistBackPid%5D=11489&cHash=d5af8c68fa533e496032881c998a6720), [perma](https://web.archive.org/web/20200409000000*/https://www.ptb.de/cms/en/about-us-careers/careers/bms-stellen/bms-stelle.html?tx_jobmodul_pi1%5Bjob%5D=3223&tx_jobmodul_pi1%5BlistBackPid%5D=11489&cHash=d5af8c68fa533e496032881c998a6720)).) Comments by Maurice and GM suggest the advancement of mechanical engineering and this new definition of the kilogram might offer smaller mass references which do not need to be as large and heavy as $1\,\pu{kg}$.


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First thing I think we have to differentiate between checking the **roundness** and the **roughness** (that in the article seems it is called smoothness) these two properties of the surface necessitate different tools. Regarding the roundness I doubt that the atomic feeling of Leistner can do much in fact if you look at this [video](https://youtu.be/RkT3L3hL2Ps) it is clear that the roundness is measured with a [CMM](https://en.wikipedia.org/wiki/Coordinate-measuring_machine) machine (even though in the publications is reported a special interferometer). 


Regarding the roughness, indeed the human tactile sense has a great sensitivity to roughness in an article appeared in [Nature](https://www.nature.com/articles/srep02617) the authors found that humans can distinguish patterns with a wavelength of 760 nm and amplitude of only 13 nm. But [from the new scientist article it seems](https://www.newscientist.com/article/dn14229-roundest-objects-in-the-world-created/#ixzz6J6y93tSO) that “rough spots” in the sphere stick out no more than 0.3 nanometres so basically I don't think that his atomic touch, in the sense of measuring roughness, was enough for this task. Working in surface metrology I would guess that is not so easy to measure the roughness at a nanometric level in the whole sphere in a curved surface! So if we want to take "the atomic feeling" literally what we could suppose is that he used his tactile sense to guide the roughness sampling with more accurate instruments, for instance, some interferometric technique. 



> 
> Why can't "automated machining" match the precision of (assuming the
>  alternative) "machining by hand"?
> 
> 
> 


In the polishing phase is not only a matter of precision but rather on adapting to the changes of surface. Expert polishers are incredibly well paid, they know how to modulate the polishing pattern and force to solve the specific problem of the surface (e.g. scratches valleys etc. etc.) nowadays automated polishing still can not adapt quickly to the chaotic behaviour of the surface. 


I quote the article [Towards an automated polishing system: capturing manual polishing operations](https://pdfs.semanticscholar.org/6ccd/6b90240e5b765dd580d9080507666edc1fde.pdf):



> 
> Some automated solutions have already been proposed to assist or
>  replace human operator. However, these solutions typically lack
>  flexibility and dexterity that are provided by human operators. For
>  example, some of the polishing skills that are particularly
>  challenging to automate include rapid reasoning and decision making
>  based on visual inspections, and fast adjustment of the polishing
>  patterns, e.g. when a surface defect is identified
> 
> 
> 


So I would rather think that with "atomic feeling" they are just referring to the impressive, not well-defined skills set that an expert polisher has matured in his career to reach "atomic" polishing results! 


Or maybe not?
=============


Looking at the answer of @Buttonwood it seems that the roundness error was +- 28 nm and the diameter around 10 cm that would be a signal with an amplitude of 56 nm and very long wavelength of around let's say 2 cm, that would fit into the range in the Nature article that I linked (even if so long wavelength would indeed necessitate another study...)so maybe somehow he was able to detect this imperfection on the roundness as well for guiding the polishing? In the meanwhile, at PTB it seems they found a way to replace the atomic feeling of Achim, as shown in this [video](https://www.youtube.com/watch?v=pouZ3oWIQCk). 


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