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Absorption spectra of crystalline enstatite and forsterite grains and amorphous silicate grains synthesized by sol-gel reaction (size 0.1-1 μm) are measured between 0.7 and 2.9 mm wavelength (3.5-15 cm<SUP>-1</SUP>) at temperatures between 1.2 and 30 K. Some of the amorphous powders are precursors to forsterite (Mg<SUB>2</SUB>SiO<SUB>4</SUB>) and enstatite (MgSiO<SUB>3</SUB>). For the amorphous substances MgO SiO<SUB>2</SUB>, 2MgO SiO<SUB>2</SUB>, and MgO 2SiO<SUB>2</SUB> at 20 K, the millimeter-wave mass opacity coefficients are found to be up to factors of 0.9, 3.5, and 11 times the Draine & Lee values usually adopted for interstellar silicate grains. The measured coefficients are found to depend on the powder production technique. Enstatite (MgSiO<SUB>3</SUB>) is part of pyroxene [(Mg, Fe)SiO<SUB>3</SUB>] and forsterite (Mg2SiO<SUB>4</SUB>) is part of olivine [(Mg, Fe)<SUB>2</SUB>SiO<SUB>4</SUB>], both of which are thought to be principal constituents of interstellar dust particles. The frequency dependence of the absorption coefficient follows a power law with a temperature-dependent exponent for all three amorphous silicates. Depending on the precise temperature, the power-law exponent ranges between a minimum value of 1.5 and a maximum of 2.5 for 2MgO SiO<SUB>2</SUB> and MgO SiO<SUB>2</SUB>. At 20 K the index value is about 2. For the strongest absorber MgO 2SiO<SUB>2</SUB>, the power-law index has nearly a constant value of 1.2 over the entire temperature range; this value is significantly smaller than 2, the value normally adopted for interstellar dust. The frequency-dependent absorption coefficients per unit mass for Mg<SUB>2</SUB>SiO<SUB>4</SUB> and MgSiO<SUB>3</SUB> are about 4 times larger for the amorphous precursor grains than for the crystalline ones. The millimeter-wave absorption coefficient for amorphous grains first decreases with increasing temperature until about 20 K and then increases at higher temperatures. This unusual temperature-dependent property forms a significant part of the overall absorption at long wavelengths: the relative change is as large as 50% at 1 mm wavelength for 2MgO SiO<SUB>2</SUB>, 35% for MgO SiO<SUB>2</SUB>, and 14% for MgO 2SiO<SUB>2</SUB>. A weaker temperature-dependent change is observed for the crystalline forsterite and enstatite powders. The observed temperature dependence of the far-IR absorption coefficient in the powders is well described by a two-level population effect previously found for the ubiquitous low-lying tunnelling states in bulk glasses.