English: Cross View of a Battery with a Polymer Separator (Photo credit: Wikipedia)
The Note 7's lithium-polymer battery is a flattened "jelly-roll" consisting of a positive layer made of lithium cobalt oxide, a negative layer made of graphite, and two electrolyte-soaked separator layers made of polymer. The separator layers allow ions (and energy) to flow between the positive and negative layers, without allowing those layers to touch. If the positive and negative layers ever do touch, the energy flowing goes directly into the electrolyte, heating it, which causes more energy to flow and more heat - it typically results in an explosion. Compressing the battery puts pressure on those critical polymer separator layers that keep the battery safe.
Samsung stated that these separator layers may have been thin to start with due to aggressive manufacturing parameters. Add some pressure due to normal mechanical swell from the battery or accumulated stress through the back cover (e.g. from being sat on in a back pocket), and that pressure could be enough to squeeze the thin polymer separator to a point where the positive and negative layers can touch, causing the battery to explode.
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