Failed Prediction About Variability Vs. Size Of Fragments

    Perhaps the biggest failing of the metallurgical explanation is its seriously wrong prediction for variations as a function of fragment size. The article contains this prediction, but not explicitly. The metallurgical picture predicts that the smaller the fragments, the more they will vary in antimony (because the variations are purportedly caused by "microsegregation," or differences within grains). Small fragments can come from different places within a grain, whereas larger fragments will span multiple grains and thus average out the differences within grains.
    Here are the article's actual sentences to this effect:

    General statement: "… if the sample size of a lead specimen approaches the grain size [i.e., decreasing—KAR], and the antimony and copper trace elements are segregated at the boundaries, then the variability of sample compositions will increase [as fragment size decreases—KAR]."
    Statements for small fragments: (a) "However, if the samples are only the size of, e.g., one to three grains, then each sample will likely contain different relative proportions of grain-boundary and interior grain material. This situation can result in increased compositional variability among ostensibly equivalent samples." (b) "Certainly, 5–10 mg samples should be suspect with respect to being representative of the bulk composition."
    Statement for larger fragments: "… if all samples were large enough to contain on the order of 50 or more grains [meaning grain as crystal of lead, not unit of weight—KAR], they will encompass a good average quantity of both grain-boundary material and interior grain material and will be reasonably representative of the true average composition of the alloy."

    So the prediction is clear—as fragments (samples) progress from larger to smaller, the variability of their antimony (and other minor elements) will increase. The problem is that actual measurements on WCC/MC lead show exactly the opposite—the variability of antimony decreases as fragments progress from larger to smaller.
    This clear trend can be shown on a figure that I prepared some years ago and that was well known to the authors of this article. Larry Sturdivan and I also included it as Figure 2 in the first of our two articles from 2004.

    The largest sizes, represented by samples from Guinn's 14 individual bullets, have a heterogeneity (standard deviation) of 90% for antimony. At the next-smaller scale, represented by the three individual bullets used for quarter-bullet studies, the heterogeneity was 40% (figure not shown in plot). Within each of the three bullets, the heterogeneity averaged 24%. Within the FBI's replicate analyses of the five fragments from the crime scene, it was a mere 5%. Within the two groups of fragments from the crime scene, it averaged 3%, which is just about the analytical uncertainties.
    Summarized in tabular form, the results look like this:

    In other words, the measured heterogeneities decreased from 90% from bullet to bullet down to <6% (i.e., unmeasurable) for the tiniest fragments. Since the article's metallurgical explanation predicted the opposite, it is clear that the explanation is wrong.

Possible alternative view
    It is possible to view the question of variations in an entirely different light, however. This section attempts to give the article's metallurgical standpoint its due. If you start by accepting that that grain-size variations control the variations of copper and antimony in all the WCC/MC samples, there would be no need to carefully consider their variations in the 14 test bullets and the 12 quarter-bullet samples. All the variations would just be random noise, and so you would never have to consider things like the lack of covariation and the opposite trends of variability with size than are predicted by your theory.
    But I don't think that is good enough. The quarter-bullet data were there in plain sight all the time. Any argument that purports to explain all the data needs to consider ALL the data. This paper, however, missed the critical—and fatal to its theory—variations of antimony in the three bullets that were used for the quarter-bullet samples. One bullet was systematically lower in antimony than were the other two bullets, one was intermediate in concentration, and the last was systematically the lowest in concentration. Grain-size variations alone cannot explain that pattern—something else had to be at work. (See the section "Do We Really Need To Know Metallurgy?" for a few more comments on this critical scale of variation.)
    Thus this alternative point of view cannot justify overlooking this significant piece of data against it.

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