1 / 17

Surface Structures of Growth Models with Constraints From the Surface-Height Distribution

Surface Structures of Growth Models with Constraints From the Surface-Height Distribution. 허희범 , 윤수연 , 김 엽 경희대학교. 1. 1. Motivation. In equilibrium state, Normal restricted solid-on-solid model : Edward-Wilkinson universality class Two-particle correlated surface growth

posy
Download Presentation

Surface Structures of Growth Models with Constraints From the Surface-Height Distribution

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Surface Structures of Growth Models with Constraints From the Surface-Height Distribution 허희범, 윤수연, 김 엽 경희대학교

  2. 1 1. Motivation • In equilibrium state, • Normal restricted solid-on-solid model • : Edward-Wilkinson universality class • Two-particle correlated surface growth • - Yup Kim, T. S. Kim and H. Park, PRE 66, 046123 (2002) • Dimer-type surface growth • J. D. Noh, H. Park, D. Kim and M. den Nijs, PRE 64, 046131 (2001) • - J. D. Noh, H. Park and M. den Nijs, PRL 84, 3891 (2000) • Self-flattening surface growth • -Yup Kim, S. Y. Yoon and H. Park, PRE(RC) 66, 040602(R) (2002)

  3. 2 Steady state or Saturation regime , Partition function, nh: the number of columns with height h 1. Normal RSOS (z =1) Normal Random Walk (1D) (EW) 2. Two-particle correlated (dimer-type) growth (z = -1) nh=even number, Even-Visiting Random Walk (1D)

  4. 3 Phase diagram (1D) ? ? ? z z= 1 z= 0 z=-1 Normal Random Walk Even-Visiting Random Walk Self-attracting Random Walk 3. Self-flattening surface growth (z = 0) Self-attracting random walk (1D)

  5. 4 2. Generalized Model 크기가 L인 1차원 substrate의 한 column 를 임의로 선택한다. 확률p (1-p)로 deposition (evaporation)을 결정한다. Height distribution 중, 주어진 높이 h에 있는 column의 개수 nh를 계산한다. Weight를 ( nh : 높이 h를 갖는 column의 개수 ) 로 정의하고, 만일 에서 deposition (evaporation)이 일어났다고 가정했을 때, 새로운 configuration에 대하여 weight 을 구한다. 이때, 이 과정을 허용할 확률을 다음과 같이 정의한다.

  6. 5 (여기서는d-dimensional hypercubic lattice에서의 nearest-neighbor bond vectors 중, 한 site를 말한다.) p =1/2 L = 10 z = 0.5 hmax hmin w w´ n´+2 = 2 n´+1 = 2 n´0 = 2 n´-1 = 2 n´-2 = 2 n+2 = 1 n+1 = 3 n 0 = 2 n-1 = 2 n-2 = 2 만약 확률 P가 P1 일 경우, deposition (evaporation)의 과정을 무조건 허용한다. 반대로 P<1 이면, 임의의 random number R을 발생시켜 P  R일 경우에만 이 과정을 허용한다. (Metropolis algorithm) 모든 과정은 restricted solid-on-solid constraint를 만족하여야 한다. P  R

  7. 6 3. Simulation Results  Equilibrium model (1D, p=1/2)

  8. 7 z 1.5 1.1 1 0.9 0.5 0 -0.5 -1  (L)  0.33 0.33 1/2 0.33  0.33  0.33  0.34  0.33   0.22 0.22 1/4 0.22  0.22  0.22  0.22  0.19

  9. 8

  10. 8-1 Phase diagram in equilibrium (z =1/2) z = 1 -1/2 1/2 3/2 z = 0 z =-1 z = 0.9 z = 1.1 2-particle corr. growth Self-flattening surface growth Normal RSOS

  11. 9 • Growing (eroding) phase (1D, p=1(0) ) z  0 : Normal RSOS model (Kardar-Parisi-Zhang universality class)

  12. 10 z  0 Normal RSOS Model (KPZ)

  13. 11 z  0 z=-0.5 p=1 L=128

  14. 11-1 z  0 morphology z = 0.5 , L=256

  15. 11-2 z < 0 morphology z = - 0.5 , L=256

  16. 12 4. Conclusion  Equilibrium model (1D, p=1/2) z 3/2 0.9 1.1 1 1/2 0 -1 -1/2 2-particle corr. growth (EVRW) Normal RSOS (Normal RW) Self-flattening surface growth (SATW) • Growing (eroding) phase (1D, p= 1(0) ) 1. z  0 : Normal RSOS model (KPZ universality class) 2. z  0 : Groove phase ( = 1) Phase transition at z=0 (?)

  17. Scaling Collapse to in 1D equilibrium state. ( = 1/3 , z = 1.5) 12-1

More Related