The Iraqi Ambassador to the UN has written a letter confirming this ISIS social media claim. The UK Daily Mail:
“In a letter to the United Nations, Iraq’s U.N. Ambassador Mohamed Ali Alhakim told Ban Ki-moon ‘Terrorist groups have seized control of nuclear material at the sites that came out of the control of the state,’ adding such materials ‘can be used in manufacturing weapons of mass destruction.’
‘These nuclear materials, despite the limited amounts mentioned, can enable terrorist groups, with the availability of the required expertise, to use it separate or in combination with other materials in its terrorist acts.'”
An effective dirty bomb would probably use small fragments of a radioactive metal, to disperse the effect. Smaller fragments would spread measurable radioactivity more widely. 40 Kg of uranium could be machined into thousands of radioactive pieces.