The qualification file holds two certificates for the same natural hydroxyapatite. One reports a crystal size near 60 nanometres. The other, from an equally reputable lab, reports over a micron. Neither lab made an error, and both worked from the same X-ray diffraction data. The difference is a line of arithmetic.
How can one XRD pattern give twenty different sizes?
A 2020 study in Nanomaterials ran the comparison explicitly on natural hydroxyapatite from three sources. Using the classic Scherrer equation across all available peaks, “the sizes of crystallites obtained by the XRD patterns in each method for hydroxyapatite from cow, pig, and chicken were 1371, 457, and 196 nm.” The same patterns, run through the Halder–Wagner method, returned “4 nm for all samples.” And a corrected Scherrer model — a straight line forced through the origin — “gave 60, 60, and 53 nm, which shows much improvement.”
From 4 nm to 1,371 nm, on identical data. The authors are blunt about the worst offender: the all-peaks Scherrer fit “led to unreasonable values.” Their corrected model, by contrast, landed within a few nanometres of an independent BET surface-area cross-check (56, 52 and 49 nm) — which is what validation looks like.
Which number belongs on a certificate?
The honest answer: none of them, without the method attached. A “crystallite size” figure is not a property of the powder alone; it is a property of the powder plus a peak set, a fitting model, and a set of assumptions about strain. Quote the figure without those, and a buyer comparing two suppliers may be comparing arithmetic, not materials.
There is a second trap stacked on the first. Crystallite size is not particle size. As the paper puts it, “calculation of nanoparticle size extracted by XRD patterns is not possible because a particle has several nanoscale or microscale crystals.” A datasheet that slides from an XRD crystallite number to a “particle size” claim has changed subject mid-sentence — particle size belongs to laser diffraction, DLS or microscopy, each with its own disagreements.
None of this is exotic knowledge inside a good analytical lab — the methods are decades old and their disagreements are documented. The problem is what survives the journey from instrument to certificate: a single number, shorn of its peak set and fitting model, rounded into false precision. By the time it reaches a purchasing spreadsheet it looks as objective as a weight. Two such numbers from two suppliers get compared as if they measured the same thing, and a sourcing decision quietly inherits an assumption nobody made on purpose.
The question that sorts suppliers
So when two drums arrive with two sizes, the discriminating question is not “which number is right?” It is: which method, which peaks, which model — and was it cross-checked against anything independent? A supplier who answers with “Scherrer” and nothing else has given you a word, not a measurement. A supplier who can name the model, show the fit, and point to a BET or TEM cross-check has given you something a specification can be built on.
Consistency between lots is only detectable when the measuring stick itself holds still. The size number is where that discipline shows first.
Sources
Rabiei M, Palevicius A, Monshi A, Nasiri S, Vilkauskas A, Janusas G. “Comparing Methods for Calculating Nano Crystal Size of Natural Hydroxyapatite Using X-Ray Diffraction.” Nanomaterials, 2020;10(9):1627 (open access) — ncbi.nlm.nih.gov/pmc/articles/PMC7557758.