The porosity was studied using coherent synchrotron X-ray radiography, firstly in several bulky icosahedral Al-Pd-Mn quasicrystals, grown in different laboratories by various techniques (Bridgman, Czochralski, Flux) and then in quasicrystal grains of many other alloys and structures (Part 11). In this part 1, we report a quantitative analysis which has been carried out in order to find some correlation of this porosity with some growth or after-growth cooling parameters (growth parameters). The size distribution of pores was observed to change drastically among samples grown with different growth parameters as well as in those extracted from the same ingot and no mode values were evidenced when we plotted the distribution of pores in all investigated as-grown samples. These changes point out the influence of the solidification process on the occurrence of porosity, especially the influence of the vacancy migration. These results are used to discuss the two main Current hypotheses on the origin of porosity. (c) 2005 Elsevier B.V. All rights reserved.