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We present results of experiments at the aerosol interactions and dynamics in the atmosphere (AIDA) chamber facility looking at the freezing of water by three different types of mineral particles at temperatures between -12 degrees C and -33 degrees C. The three different dusts are Asia Dust-1 (AD1), Sahara Dust-2 (SD2) and Arizona test Dust (ATD). The dust samples used had particle concentrations of sizes that were log-normally distributed with mode diameters between 0.3 and 0.5 mu m and standard deviations, sigma(g), of 1.6-1.9. The results from the freezing experiments are consistent with the singular hypothesis of ice nucleation. The dusts showed different nucleation abilities, with ATD showing a rather sharp increase in ice-active surface site density at temperatures less than -24 degrees C. AD1 was the next most efficient freezing nuclei and showed a more gradual increase in activity than the ATD sample. SD2 was the least active freezing nuclei. We used data taken with particle counting probes to derive the ice-active surface site density forming on the dust as a function of temperature for each of the three samples and polynomial curves are fitted to this data. The curve fits are then used independently within a bin microphysical model to simulate the ice formation rates from the experiments in order to test the validity of parameterising the data with smooth curves. Good agreement is found between the measurements and the model for AD1 and SD2; however, the curve for ATD does not yield results that agree well with the observations. The reason for this is that more experiments between -20 and -24 degrees C are needed to quantify the rather sharp increase in ice-active surface site density on ATD in this temperature regime. The curves presented can be used as parameterisations in atmospheric cloud models where cooling rates of approximately 1 degrees C min(-1) or more are present to predict the concentration of ice crystals forming by the condensation-freezing mode of ice nucleation. Finally a polynomial is fitted to all three samples together in order to have a parameterisation describing the average ice-active surface site density vs. temperature for an equal mixture of the three dust samples.