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If one was to quantify the shape (particularly roundness) of detrital zircon grains, would there be a correlation between the age of the detrital zircon grains and their shape? For example, if the grain is an Archaean one, would it be much more rounded than a grain that is Devonian?

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My thought is that you would not see any correlation because grain roundness has to do with how long it has been in the sedimentary system rather than its crystallisation age. That is, if one sampled a modern sediment in which a 650 Ma zircon grain from a 650 Ma granite has only recently been eroded from its granite source then one would expect this zircon to be euhedral (and this is not taking into account magmatic effects like resorption which would affect its shape!). But a 650 Ma zircon in the same sediment may have been eroded from a different Neoproterozoic granite during the Cambrian, in which case one would expect that it has been rounded by multiple cycles of sedimentation. Therefore no correlation could be made between the shape of the zircon grains and their crystallization age.

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