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​Colored pigments seem to have a farily consistent particle size; for example, titanium white is listed as .5 microns, viridian generally listed as 2.5 microns, etc.  Filler or extender pigments (white or transparent solids) seem to come in a very wide range of particle sizes depending on use (from industrial to artist grade).  My questions are…
1.  Do synthesized colored pigments generally – or always – have a consistent, predictable particle size?
2.  How much can the particle size of artist grade, natural earth pigments vary?  Or are there standard, predictable sizes used within the paint industry?   

3.  Are filler/extender pigments mostly dervied from natural minerals? (The only synthesized filler/extender I can think of is glass powder…)  ​
4. Are artist grade filler/extender pigments ground/sieved to specfic sizes (are there industry standards)?  Or can they range all over the place?  For example, if I buy a “fine grade” chalk from two companies, can I expect them the same particle size?  If not, how much might “fine grade” particle sizes vary? 

Thanks

Organic pigments have much finer particles, typically. A few inorganic pigments, like zinc oxide (PW 4) also are produced with small particles. Zinc oxide is even sold in nanoparticle​ form for sunscreens.
Because organic pigments have much finer particles they need more oil when made into oil paint. This comes with the drawbacks of the additional oil, especially for underpainting when using the indirect painting method (fat over lean). However, they can also be better for glazing, due to higher transparency than many inorganic pigments (although some organics are not so transparent).
Pigment codes for organic pigments can be misleading, too. Some forms of the same “PY 83” are opaque and some are transparent.
Some organic pigments are produced to have larger particle sizes, such as PR 151, used in the high-end automotive industry. The larger particle sizes generally (not always — it depends on the specific organic pigment molecule) have better lightfastness. However, a large-particle pigment (let’s say pigment A) can have lower lightfastness than an entirely different organic pigment  (let’s say pigment B), so particle size differences only point toward lightfastness.
Overall, organic pigments are less lightfast than the most lightfast inorganic pigments. However, some organic pigments are much more lightfast than some inorganic pigments that have been used in art.
Some pigments are described as losing color saturation and becoming lighter as they are more finely ground. Copper greens that don’t contain arsenic (such as malachite) are an example. Finer inorganic pigment grinds/particles can also require more oil, such as with synthetic barium sulfate (aka blanc fixe) versus natural barium sulfate (aka baryte).
Some artists argue that watercolorists are better-served by fine grinds, although highly granulating saturated pigments (such as coarse ultramarine) have become trendy in watercolor painting. 
Very coarse pigments can be unpleasant to paint with, like painting with sand. I don’t know for certain but I imagine that they are also harder for a binder to hold, as there is less surface area for the binder to bind.

Finer grinds tend to have more tinting strength.

In oils, the ideal base pigment is extremely opaque, extremely saturated, finely ground, highly tinting, totally lightfast (inorganic), totally chemically/molecularly stable, very lean (not needing much oil for the grind), non-stringy, donates the right metal ions to stabilize a paint film, and free of rare expensive elements such as yttrium and indium. The ideal glazing pigment is transparent and needs more oil for its full saturation (CPVC — critical pigment volume concentration) but has most of those other qualities.
— SRS

I mistyped the pigment code. It should have been PR 251 not PR 151.​

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Modern precipitated pigments tend to have a more predictable particle size. Natural products like chalk, azurite, earth colors, etc. can vary in particle size.

Historical natural pigments were generally much larger in particle size than their modern counterparts. Modern earth pigments made for the mass market are generally going to be much finer.

Larger particle sized earth pigments are probably only available to the average customer through specialty art suppliers like Kremer and Natural Pigments. There are others and this is not intended as an endorsement nor a complete list.

Fillers and extenders can come from a variety of sources. One of the most common is aluminum stearate which is a synthetically produced half inorganic half organic compound. Chalk can be natural or precipitated and is available in a large number of grind sizes for different uses.

There are likely industry standards in the commercial paint industry, but I would imagine that each tailors their product for a specific purpose. You can order products with a specific range of particle size.

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​​Thanks for those clarifications, Brian.  

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