Continuum emission at 4.9, 8.3, 78.5, 81.5, 84.9, 87.9, 106.9, and 109
.9 GHz was observed in Sgr B2. Spectral indices near 3 mm are alpha =
-0.31 +/- 0.03 and -0.2 +/- 0.2 for Sgr B2(N') and Sgr B2(W), respecti
vely, and are attributed to the optically thin free-free emission. Fre
e-free emission contributes significantly to the 3 mm continuum in Sgr
B2(M), but the positive slope of the continuum spectrum (alpha = 1.0
+/- 0.3) indicates the presence of dust grains. Sgr B2(N) is dominated
by thermal dust emission with a steep spectral index alpha = 4.6 +/-
0.5. The 3 mm continuum spectra yield the grain emissivity exponents b
eta = 1.7 +/- 1.3 and 3.7 +/- 0.7 for Sgr B2(M) and Sgr B2(N), respect
ively. The grain emissivity law derived for Sgr B2(N) is significantly
higher than most for other molecular clouds. Thus Sgr B2(N) appears t
o be a very unusual dust core. The most likely explanation is that the
region contains ice-coated core-mantle grains. The existence of ice-c
oated core-mantle grains implies the mean dust temperature in the Sgr
B2(N) dust core is less than 150 K. The short lifetime of the core-man
tle phase and the high value of n(H2) indicate that Sgr B2(N) is quite
young and in a very early stage of star formation.