The statistics of tin whisker diameters versus the underlying film grains

TL;DR

This paper analyzes the statistical relationship between tin whisker diameters and underlying film grains, revealing that whiskers often result from multiple grains rather than a single grain, and introduces a modified distribution model.

Contribution

It provides a comparative statistical analysis of whisker and grain sizes, challenging the single grain growth assumption and proposing a new distribution model for particle sizes.

Findings

Whisker and grain sizes are both lognormally distributed.

Whiskers often develop from multiple grains with similar orientations.

A modified particle size distribution clarifies dispersion characteristics.

Abstract

We compare the statistics of tin whisker diameters to that of the underlying film grains. Both are well approximated by the lognormal distributions. However, the parameters of those distributions can be rather different, not confirming the assumption that each whisker grows from a single grain. We conclude that several adjacent grains with similar crystal orientations can contribute to a whisker development. Our observations are consistent with the recent theory of multi-filament whisker structure. A modification of the particle size log-normal distribution is developed clarifying the nature of its dispersion.