The isothermal, longitudinal magnetostriction of the spin-Peierls cupr
ate CuGeO3 has been measured along the three orthorhombic directions u
p to 14 Tesla by means of a high resolution capacitance dilatometer. F
or all three axes we observe anomalies at both the dimerized/incommens
urate (D/I) and the dimerized/uniform (D/U) transition whose sizes and
signs differ. A precise H-T phase diagram is determined from the fiel
d and temperature dependence of the lattice constants, which roughly a
grees with theoretical predictions. At the D/I transition the magnetos
triction shows a jumplike behavior and a hysteresis indicating a first
order transition. From the jumps of the magnetostriction at the D/I t
ransition we estimate considerable, uniaxial stress dependences of the
critical magnetic field H-c, which correlate with those of the spin-P
eierls transition temperature. A finite magnetostriction is also resol
ved within the high temperature uniform phase of CuGeO3 for all three
lattice directions. These data show a pronounced, strongly anisotropic
spin-lattice coupling in CuGeO3 and allow to derive the uniaxial pres
sure dependences of the magnetic susceptibility. Based on our findings
the relevance of different structural parameters for the magnetic exc
hange interaction is discussed.