We present new models for the evolution of stars with mass in the range 1 M _ { \odot } \leq M \leq 7.5 M _ { \odot } , followed from the pre–main–sequence through the asymptotic giant branch phase , until most of their envelope is lost via stellar winds .
The metallicity adopted is Z = 3 \times 10 ^ { -4 } ( which , with an \alpha - enhancement of +0.4 , corresponds to [ Fe / H ] = -2 ) .
Dust formation is described by following the growth of dust grains of various types as the wind expands from the stellar surface .

Models with mass M \geq 3 M _ { \odot } experience Hot Bottom Burning , thus maintaining the surface C/O below unity .
Unlike higher Z models , the scarcity of silicon available in the envelope prevents the formation of silicates in meaningful quantities , sufficient to trigger the acceleration of the wind via radiation pressure on the dust grains formed .
No silicate formation occurs below a threshold metallicity of Z = 10 ^ { -3 } .

Low–mass stars , with M \leq 2.5 M _ { \odot } become carbon stars , forming solid carbon dust in their surroundings .
The total dust mass formed depends on the uncertain extent of the inwards penetration of the convective envelope during the Third Dredge–Up episodes following the Thermal Pulses .
However , provided that a minimum abundance of carbon of X ( C ) \sim 5 \times 10 ^ { -3 } is reached in the envelope , the results turn out to be fairly independent of the parameters used .
Carbon grains have sizes 0.08 mum < a _ { C } < 0.12 \mu m and the total amount of dust formed ( increasing with the mass of the star ) is M _ { C } = ( 2 - 6 ) \times 10 ^ { -4 } M _ { \odot } .

Our results imply that AGB stars with Z = 3 \times 10 ^ { -4 } can only contribute to carbon dust enrichment of the interstellar medium on relatively long timescales , > 300 Myr , comparable to the evolutionary time of a 3 M _ { \odot } star .
At lower metallicities the scarcity of silicon available and the presence of Hot Bottom Burning even in M < 2 M _ { \odot } , prevents the formation of silicate and carbon grains .
We extrapolate our conclusion to more metal–poor environments , and deduce that at Z < 10 ^ { -4 } dust enrichment is mostly due to metal condensation in supernova ejecta .