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We present low-temperature volume thermal expansion, $\beta$, and specificheat, $C$, measurements on high-quality single crystals of CeNi2Ge2 andYbRh2(Si$_{0.95}$Ge$_{0.05}$)$_2$ which are located very near to quantumcritical points. For both systems, $\beta$ shows a more singular temperaturedependence than $C$, and thus the Grueneisen ratio ${\Gamma \propto \beta/C}$diverges as T --> 0. For CeNi2Ge2, our results are in accordance with thespin-density wave (SDW) scenario for three-dimensional criticalspin-fluctuations. By contrast, the observed singularity inYbRh2$(Si$_{0.95}$Ge$_{0.05}$)$_2$ cannot be explained by the itinerant SDWtheory but is qualitatively consistent with a locally quantum critical picture.Comment: 11 pages, 4 figure

Divergence of the Grüneisen Ratio at Quantum Critical Points in Heavy Fermion Metals