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), respectively, and are attributed to the optically thin free-free emission. Free-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 beta = 1.7 +/- 1.3 and 3.7 +/- 0.7 for Sgr B2(M) and Sgr B2(N), respectively. The grain emissivity law derived for Sgr B2(N) is significantly higher than most for other molecular clouds. Thus Sgr B2(N) appears to be a very unusual dust core. The most likely explanation is that the region contains ice-coated core-mantle grains. The existence of ice-coated 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-mantle 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.
