We examine the region of validity of Langer's picture of homogeneous nucleation. Our approach is based on a coarse-grained free energy that incorporates the effect of fluctuations with momenta above a scale k, The nucleation rate I = A(k)exp(-S-k) is exponentially suppressed by the action S-k of the saddle-point configuration that dominates tunnelling. The factor A(k) includes a fluctuation determinant around this saddle point. Both S-k and A(k) depend on the choice of k, but, for 1/k close to the characteristic length scale of the saddle point, this dependence cancels in the expression for the nucleation rate. For very weak first-order phase transitions or in the vicinity of the spinodal decomposition line, the pre-exponential factor A(k) compensates the exponential suppression exp(-S-k). In these regions the standard nucleation picture breaks down. We give an approximate expression for A(k) in terms of the saddle-point profile, which can be used for quantitative estimates and practical tests of the validity of homogeneous nucleation theory, (C) 1999 Elsevier Science B.V. All rights reserved.
The region of validity of homogeneous nucleation theory
STRUMIA, ALESSANDRO;
1999-01-01
Abstract
We examine the region of validity of Langer's picture of homogeneous nucleation. Our approach is based on a coarse-grained free energy that incorporates the effect of fluctuations with momenta above a scale k, The nucleation rate I = A(k)exp(-S-k) is exponentially suppressed by the action S-k of the saddle-point configuration that dominates tunnelling. The factor A(k) includes a fluctuation determinant around this saddle point. Both S-k and A(k) depend on the choice of k, but, for 1/k close to the characteristic length scale of the saddle point, this dependence cancels in the expression for the nucleation rate. For very weak first-order phase transitions or in the vicinity of the spinodal decomposition line, the pre-exponential factor A(k) compensates the exponential suppression exp(-S-k). In these regions the standard nucleation picture breaks down. We give an approximate expression for A(k) in terms of the saddle-point profile, which can be used for quantitative estimates and practical tests of the validity of homogeneous nucleation theory, (C) 1999 Elsevier Science B.V. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
