1. Introduction

Most likely agree that if we get to select Avogadro's constant as some number of elementary entities (e.g. atoms or molecules) that it might as well be an integer. For pedagogical purposes in discussing units for mass, it might also help (Khruschov2010) to make that integer divisible by 12 e.g. so that one gram is also to first order the mass of an integer number of 12C atoms. One strategy for doing this might be to require as few significant decimal digits as possible to specify the constant, since most humans use base-10 numbers. For example 602,214,150,000,000,000,000,000 is 

The upcoming revision of the international system of units (CGPM2014) will give the Avogadro constant NA an exact numerical value, as a mass-independent number of elementary entities and possibly (Leonard2012) as the number of grams/Dalton regardless of the precise number of Daltons associated with any elementary entity. Thus the mass M(12C)  of a 12C atom may become an experimental quantity (as always affected by neighbor binding interactions) only approximately equal to 12 Daltons (Mills2006, Hill2011, Wheatley2011a, Milton2013). Since the numeric value of the Avogadro constant will be chosen for consistency with existing values e.g. to 8 significant figures, this paper discusses physically-meaningful choices for the other 16 (or more) significant figures.

an integer divisible by 12 that would serve admirably.The other strategy is to choose the number of atoms in a relevant physical structure, to make the definition concrete. Cubes of simple-cubic and face-centered-cubic Carbon (Fox2007), and of diamond face-centered-cubic Silicon (Khruschov2010), have for example been proposed in this context.

The major problems with these choices are that: (i) simple-cubic carbon doesn't exist in nature, (ii) fcc carbon is at best rare (Konyashin2006, Tapia2005), (iii) none of these structures have naturally-occurring facets, during growth or cleavage, that lie on the (100) planes which bound these cubes, and (iv) symmetry does not dictate that the number of atoms in these structures is divisible by 12.

We show here that a good approximation (divisible by 12) is provided by hexagonal graphite prisms with m graphene-layers having m-atom armchair edges where m=51,150,060. Graphite in turn is constructed from graphene sheets whose controlled synthesis at the atomic-scale is likely to see great progress by nanotechnologists in the years ahead. The atoms in an individual graphene sheet can already be counted (Krivanek2010), and by extension these structures in tube-form may downstream allow one to generate macroscope molar-standards whose accuracy is limited primarily by one's ability to cut off a well-defined length. 

Some related references