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March 22, 2013

For a brief span in my career, I did research in the growth of technologically useful crystals. Crystals grow in different shapes, with facets representative of their underlying atomic structure. Sometimes, the growth rate along certain crystal directions can be quite a bit larger than others, so your crystal becomes long and extended. Adding impurities to certain crystallizing chemicals can change the resulting crystal product from an expected geometrical object to a long whisker.

Leonardo da Vinci Self-Portrait Many years ago, one of my colleagues was sent on a troubleshooting mission to a company plant that made a common household chemical. This was done by digging mineral deposits out of the Earth's crust, dissolving them in water, and crystallizing the product. For some reason, the crystal habit of the product had changed to a long whisker shape quite different from the short prism shape that had always appeared.

(Left, presumed self-portrait of Leonardo da Vinci at age 60 (circa 1512), red chalk on paper, via Wikimedia Commons.)

There was an impurity to blame, possibly appearing when raw material was mined from a different part of the mineral deposit. A recommended addition of a small amount of another chemical stopped the problem. That's another example of why companies should keep at least a few scientists employed even when industrial processes have been working without change for many years and their scientists seem redundant.

In a previous article (Tin Pest and Purple Plague, April 24, 2012), I wrote how some solder alloy compositions designed to replace leaded solder were prone to formation of whiskers. The problem started with the European Restriction of Hazardous Substances Directive (RoHS), and directives in other countries, for removal of hazardous chemicals from products, including lead in electronic devices.

The eutectic composition of the lead-tin binary alloy system has been used as an electronic solder for more than a century. The reasons for this are its low melting point (183 °C), low cost, and good electrical conductivity. One lead-free option is to use pure tin (melting point, 232 °C), but tin will form tin whiskers during repeated thermal cycling, the presence of which can lead to electrical short circuits if they dislodge from the solder ball and are deposited elsewhere in the circuitry.
Lead-Tin (Pb-Sn) Phase DiagramLead-Tin (Pb-Sn) Phase Diagram

The eutectic composition, at 61.9 wt-% tin, melts at 183 °C, quite a bit lower than the melting point of tin (232 °C).

(Author's rendition using Inkscape.)
Lead-free solders use alloying elements to both lower the melting point of tin and prevent tin whiskers. Tin with an addition of 3.5 wt-% silver has a melting point of 221 °C. A more complex alloy, Sn95.55Ag3.5Cu0.85Mn0.10 will melt at 215 ° C.

Whisker growth is not unique to tin, and it is known to occur also in silver and gold. The mechanism for whisker formation is not known, although there is evidence that it's associated with a strain gradient.[1] Such an hypothesis is supported by the fact that such whiskers grow perpendicular to the metal surface. Whisker growth is not associated with electromigration, in which material is transported by the momentum transfer of electrons in conductors subjected to high current density.

The surface roughness of metal layers produced by electroplating often increases with thickness. Surface defects will produce a locally-enhanced electric field strength which increases the growth rate at the defect. As recent research by materials scientists at Purdue University has shown, a similar mechanism may be responsible for dendrite formation in rechargeable lithium-ion batteries.[2-3]

When a lithium-ion cell is recharged, lithium ions are transported from the cathode, through a gel electrolyte, to the anode. The deposited lithium tends to form dendrites for the rapid charging cycles desired in consumer devices. These dendrites often grow large enough to bridge the cathode-anode space, causing a short-circuit which results in battery failure, and sometimes a fire.[3]

The Purdue University scientists used various resources in their investigation, including videos of dendrite growth made by Stephen Harris, a visiting scientist at Lawrence Berkeley National Laboratory.[3] Scanning electron micrographs showed that dendrite growth was in spurts, with material added as rings at each charging cycle (see photomicrograph).

Lithium dendrite showing a ring structureScanning electron micrograph of a lithium dendrite cross-section showing a ring structure.

Each ring is associated with a discharge-charge cycle.

(Purdue University Image by Quinn Horn.)

A critical radius was found, such that dendrites below that radius will shrink, and dendrites above that radius will grow.[2-3] Dendrite growth only becomes energetically favored when an overpotential barrier is overcome.[2] It appears, also, that there is a mass flow from the smaller dendrites to the larger ones.[3]

The Purdue scientists identified five regimes in the dendrite growth process; namely, a nucleation suppression regime, a long incubation time regime, a short incubation time regime, an early growth regime and a late growth regime.[2] In the early growth regime, some dendrite nuclei are energetically favored, and these reach an asymptotic growth velocity. In the late growth regime, amplification of surface irregularity is much like the electroplating roughening mentioned above.[2]

One technique that might inhibit dendrite growth is to use a charging method based on rapid pulses, rather than a constant current.[3] This research was funded by Toyota Motor Engineering & Manufacturing North America Inc.[3]


  1. Yong Sun, Elizabeth N. Hoffman, Poh-Sang Lam and Xiaodong Li, "Evaluation of local strain evolution from metallic whisker formation," Scripta Materialia, vol. 65, no. 5 (September, 2011), pp. 388-391.
  2. David R. Elyz and R. Edwin Garcıa, "Heterogeneous Nucleation and Growth of Lithium Electrodeposits on Negative Electrodes," J. Electrochem. Soc., vol. 160, no. 4 (February 12, 2013), pp. A662-A668.
  3. Analytical theory may bring improvements to lithium-ion batteries dendrites, Purdue University Press Release, March 5, 2013.

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