We investigate the quantity and composition of unburned material in the outer layers of three normal Type Ia supernovae ( SNe Ia ) : 2000dn , 2002cr and 2004bw .
Pristine matter from a white dwarf progenitor is expected to be a mixture of oxygen and carbon in approximately equal abundance .
Using near-infrared ( NIR , 0.7 - 2.5 \mu m ) spectra , we find that oxygen is abundant while carbon is severely depleted with low upper limits in the outer third of the ejected mass .
Strong features from the O i line at \lambda _ { rest } = 0.7773 \mu m are observed through a wide range of expansion velocities \approx 9 - 18 \times 10 ^ { 3 } km s ^ { -1 } .
This large velocity domain corresponds to a physical region of the supernova with a large radial depth .
We show that the ionization of C and O will be substantially the same in this region .
C i lines in the NIR are expected to be 7 - 50 times stronger than those from O i but there is only marginal evidence of C i in the spectra and none of C ii .
We deduce that for these three normal SNe Ia , oxygen is more abundant than carbon by factors of 10 ^ { 2 } -10 ^ { 3 } .
Mg ii is also detected in a velocity range similar to that of O i .
The presence of O and Mg combined with the absence of C indicates that for these SNe Ia , nuclear burning has reached all but the extreme outer layers ; any unburned material must have expansion velocities greater than 18 \times 10 ^ { 3 } km s ^ { -1 } .
This result favors deflagration to detonation transition ( DD ) models over pure deflagration models for SNe Ia .