On the shape of wedding cakes

Journal of Statistical Physics

Volumn 87, Issue 3-4, 1997, Pages 505-518

  Krug, Joachim ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

Crystal growth; Growth instability; Hydrodynamic limit; Singular diffusion equations; Surface diffusion

Indexed keywords

EID: 0000663703     PISSN: 00224715     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02181234     Document Type: Article

References (21)

1. M. Bott, T. Michely, and G. Comsa, The homoepitaxial growth of Pt on Pt(111) studied with STM, Surf. Sci. 272:161 (1992); J. Vrijmoeth, H. A. van der Vegt, J. A. Meyer, E. Vlieg, and R. J. Behm, Surfactant-induced layer-by-layer growth of Ag on Ag(111): Origins and side effects, Phys. Rev. Lett. 72:3843 (1994) ; K. Bromann, H. Brune, H. Röder, and K. Kern, Interlayer mass transport in homoepitaxial and heteroepitaxial metal growth, Phys. Rev. Lett. 75:677 (1995).
2. M. Bott, T. Michely, and G. Comsa, The homoepitaxial growth of Pt on Pt(111) studied with STM, Surf. Sci. 272:161 (1992); J. Vrijmoeth, H. A. van der Vegt, J. A. Meyer, E. Vlieg, and R. J. Behm, Surfactant-induced layer-by-layer growth of Ag on Ag(111): Origins and side effects, Phys. Rev. Lett. 72:3843 (1994) ; K. Bromann, H. Brune, H. Röder, and K. Kern, Interlayer mass transport in homoepitaxial and heteroepitaxial metal growth, Phys. Rev. Lett. 75:677 (1995).
3. M. Bott, T. Michely, and G. Comsa, The homoepitaxial growth of Pt on Pt(111) studied with STM, Surf. Sci. 272:161 (1992); J. Vrijmoeth, H. A. van der Vegt, J. A. Meyer, E. Vlieg, and R. J. Behm, Surfactant-induced layer-by-layer growth of Ag on Ag(111): Origins and side effects, Phys. Rev. Lett. 72:3843 (1994) ; K. Bromann, H. Brune, H. Röder, and K. Kern, Interlayer mass transport in homoepitaxial and heteroepitaxial metal growth, Phys. Rev. Lett. 75:677 (1995).
4. M. Albrecht, H. Fritzsche, and U. Gradmann, Kinetic facetting in homoepitaxy of Fe(110) on Fe(110), Surf. Sci. 294:1 (1993).
5. M. Henzler, LEED from epitaxial surfaces, Surf. Sci. 298:369 (1993).
6. J. Krug, Origins of scale invariance in growth processes, Adv. Phys. 46:139 (1997).
7. G. Ehrlich and F. G. Hudda, Atomic view of surface self-diffusion: Tungsten on tungsten, J. Chem. Phys. 44:1039 (1966); R. L. Schwoebel and E. J. Shipsey, Step motion on crystal surfaces, J. Appl. Phys. 37:3682 (1966).
8. G. Ehrlich and F. G. Hudda, Atomic view of surface self-diffusion: Tungsten on tungsten, J. Chem. Phys. 44:1039 (1966); R. L. Schwoebel and E. J. Shipsey, Step motion on crystal surfaces, J. Appl. Phys. 37:3682 (1966).
9. J. Krug and M. Schimschak, Metastability of step flow growth in 1 + 1 dimensions, J. Phys. France I 5:1065 (1995).
10. P. I. Cohen, G. S. Petrich, P. R. Pukite, G. J. Whaley, and A. S. Arrott, Birth-death models of epitaxy: I. Diffraction oscillations from low index surfaces, Surf. Sci. 216:222 (1989).
11. 2, Phys. Rev. B 19:2398 (1979).
12. -2(∂u/∂x)] - (∂u/∂t) = 0. J. Math Phys. 21:1019 (1980).
13. M. A. Herrero, A limit case in nonlinear diffusion, Nonlinear Anal. 13:611 (1989); J. L. Vazquez, Nonexistence of solutions for nonlinear heat equations of fast-diffusion type, J. Math. Pures Appl. 71:503 (1992).
14. M. A. Herrero, A limit case in nonlinear diffusion, Nonlinear Anal. 13:611 (1989); J. L. Vazquez, Nonexistence of solutions for nonlinear heat equations of fast-diffusion type, J. Math. Pures Appl. 71:503 (1992).
15. P. Rosenau, Fast and superfast diffusion processes, Phys. Rev. Lett. 74:1056 (1995).
16. J. Villain, A. Pimpinelli, L. Tang, and D. Wolf, Terrace sizes in molecular beam epitaxy, J. Phys. I France 2:2107 (1992); A. Pimpinelli, J. Villain, and D. E. Wolf, Surface diffusion and island density, Phys. Rev. Lett. 69:985 (1992).
17. J. Villain, A. Pimpinelli, L. Tang, and D. Wolf, Terrace sizes in molecular beam epitaxy, J. Phys. I France 2:2107 (1992); A. Pimpinelli, J. Villain, and D. E. Wolf, Surface diffusion and island density, Phys. Rev. Lett. 69:985 (1992).
18. I. Elkinani and J. Villain, Le paradoxe de Zenon d'Elee, Solid State Commun. 87:105 (1993); Growth roughness and instabilities due to the Schwoebel effect: A one-dimensional model, J. Phys. I. France 4:949 (1994).
19. I. Elkinani and J. Villain, Le paradoxe de Zenon d'Elee, Solid State Commun. 87:105 (1993); Growth roughness and instabilities due to the Schwoebel effect: A one-dimensional model, J. Phys. I. France 4:949 (1994).
20. J. Villain, Continuum models of crystal growth from atomic beams with and without desorption, J. Phys. I France 1:19 (1991).
21. J. Krug, M. Plischke, and M. Siegert, Surface diffusion currents and the universality classes of growth, Phys. Rev. Lett. 70:3271 (1993).