PHASE-DIAGRAM OF VICINAL CU(111) SURFACES AS DETERMINED BY 2ND-HARMONIC GENERATION

Optical surface second-harmonic (SH) generation is used to characterize step thermodynamics on vicinal Cu(111) surfaces for 300 K < T < 700 K. The variation with temperature T of the SH intensity I(SH) generated at vicinal Cu(111) surfaces was measured for surfaces in the (110) zone at vicinal angles alpha in the range -7.5-degrees less-than-or-equal-to alpha less-than-or-equal-to 7.5-degrees. Phase transitions in the surface morphology were detected by observing discontinuities in dI(SH)/dT. The first transition, at T1 congruent-to 380 K, was only weakly dependent on the vicinal angle, while T2 ranges from 430 K at alpha = 0-degrees up to 570 K at alpha = 7.5-degrees. Low-energy-electron-diffraction results for a Cu(553) surface (i.e., alpha= -12-degrees) suggest that the surface consists of terraces separated by double-atomic-height steps at temperatures below T1, while above T2 the steps are monoatomic. Intermediate temperatures correspond to a mixed-phase region. The (alpha T1, T2) phase diagram is discussed in terms of a simple free-energy model which includes step interaction and mixing entropy contributions. The phase boundaries can be well reproduced using a step interaction potential of the form A/l2, where l is the step separation, and A = 0.155 meV angstrom2.