  In this work the problem of characterizing matrix material structure from
embedded electron spin decoherence is studied both theoretically and
experimentally. Theoretical calculation using nuclear spin bath model and
cluster correlation expansion method shows that the positions of decoherence
time scale extremums among single crystal orientations of the matrix material
coincide with those of the nearest neighbour proton dipolar couplings. This
finding is confirmed by single crystal pulsed EPR experiment performed on
$\gamma$-irradiated malonic acid (MA). Electron spin decoherence decay profile
in polycrystalline matrix material is obtained from the orientation dependence
as an average over sampled orientations on a Fibonacci grid. In addition, it is
pointed out theoretically that a further removal of crystal ordering in the
nuclear spin bath can reduce decoherence time scale from the polycrystalline
value. This prediction is verified experimentally by the Hahn echo time decay
scale in a new amorphous polymorph of MA, obtained for the first time by
mechanical milling. Thus the embedded electron spin decoherence can be viewed
as a quantitative indicator for studying structures and/or structure changes of
the matrix material.
