TY - JOUR
T1 - Continuum theory of nanostructure decay via a microscale condition
AU - Margetis, Dionisios
AU - Fok, Pak Wing
AU - Aziz, Michael J.
AU - Stone, Howard A.
PY - 2006
Y1 - 2006
N2 - The morphological relaxation of faceted crystal surfaces is studied via a continuum approach. Our formulation includes (i) an evolution equation for the surface slope that describes step line tension, g1, and step repulsion energy, g3; and (ii) a condition at the facet edge (a free boundary) that accounts for discrete effects via the collapse times, tn, of top steps. For initial cones and tn ≈ 4, we use t ∼ (g) from step simulations and predict self-similar slopes in agreement with simulations for any g=g3/g1>0. We show that for g « 1, (i) the theory simplifies to an equilibrium-thermodynamics model; (ii) the slope profiles reduce to a universal curve; and (iii) the facet radius scales as g-3/4.
AB - The morphological relaxation of faceted crystal surfaces is studied via a continuum approach. Our formulation includes (i) an evolution equation for the surface slope that describes step line tension, g1, and step repulsion energy, g3; and (ii) a condition at the facet edge (a free boundary) that accounts for discrete effects via the collapse times, tn, of top steps. For initial cones and tn ≈ 4, we use t ∼ (g) from step simulations and predict self-similar slopes in agreement with simulations for any g=g3/g1>0. We show that for g « 1, (i) the theory simplifies to an equilibrium-thermodynamics model; (ii) the slope profiles reduce to a universal curve; and (iii) the facet radius scales as g-3/4.
UR - http://www.scopus.com/inward/record.url?scp=33748319555&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33748319555&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.97.096102
DO - 10.1103/PhysRevLett.97.096102
M3 - Article
C2 - 17026379
AN - SCOPUS:33748319555
SN - 0031-9007
VL - 97
JO - Physical review letters
JF - Physical review letters
IS - 9
M1 - 096102
ER -