Alum (hydrous aluminum oxide) is a common mordant used for fixing in the dying of fabrics. It was widely used throughout antiquity.
Alum, along with alizarin, is found in only one corner of the Shroud and not anywhere else on the cloth. This corner is where the carbon dating sample was removed. The fact that it is found there and nowhere else forms part of the argument that the carbon dating sample was taken from a repair to the cloth.
The carbon dating samples also contain cotton fibers and spliced threads where apparently newer thread was dyed to match age-yellowed older thread.
In alum and alizarin, cotton fibers and spliced threads are NOT found elsewhere on the Shroud. As Raymond Rogers wrote in the peer-reviewed, scientific journal Thermochimica Acta:
The combined evidence from chemical kinetics, analytical chemistry, cotton content, and pyrolysis/ms proves that the material from the radiocarbon area of the shroud is significantly different from that of the main cloth. The radiocarbon sample was thus not part of the original cloth and is invalid for determining the age of the shroud.