In order to examine the quantum size effects on the properties of heavy fermion compounds, we have performed measurements of the low-temperature specific heats for T = 0.4 K - 35 K of CeAl2 nanoparticles with average particle size approximate to 80 Angstrom. The magnitude of gamma of CeAl2 changes from 150 mJ/K-2 f.u. to a magnitude as high as 1370 mJ/K-2 f.u. at T = 0.4 IC as sample size decreases to a certain extent such as nanometer scale. The anti-ferromagnetic order with T-N = 3.8 K in bulk CeAl2 is no longer shown in CeAl2 nanoparticles, whereas a Kondo anomaly with T-K approximate to 0.5 K appears at low temperatures and exhibits a large value of gamma as mentioned. Obviously the limited geometric size and the less degeneracy of the density of states of conduction electrons D((epsilon F)) in nanoparticles hinder the formation of the long-range RKKY interaction among Ce ions and thus their magnetic order. Both magnitudes of the entropy integrated from Kondo anomaly and the experimental gamma are about 40% of Rln2 and 3700 mJ/K-2 f.u. of the theoretical value respectively. The small fraction in magnitude implies incomplete Kondo interactions, indicating either a small portion of Ct ions or only a partial success of interaction involved in the heavy-fermion (Kondo) behaviour. The smaller Kondo temperature T-K approximate to JD((epsilon F)) exp(-1/JD((epsilon F))) of nanoparticles as compared to 5 K of the bulk is conceptually acceptable if D(EF) is small in nanoparticles. Clearly the quantum size effects have larger effect on the RKKY interaction than on Kondo interactions, i.e., the suppress of magnetic order reveals the heavy-fermion behavior. A conclusion is made that CeAl2 can become a very heavy fermion if its magnetic order is suppressed properly by the quantum size effects.
