Stress Induced Stripe Formation inPd/W(110)

Abstract

A stress-induced stripe phase of submonolayer Pd on W(110) is observed by low-energy electron microscopy. The temperature dependence of the pattern is explained by the change both in the boundary free energy and elastic relaxation energy due to the increasing boundary width. The stripes are shown to disorder when the correlation length of the condensed phase becomes comparable to its period, while the condensate to lattice-gas transition takes place at a higher temperature, as revealed by low-energy electron diffraction.PACS numbers: 64.60. Cn, 64.75.Yz, 68.37.Nq, 05.70.Jk It is well known that surface stress may give rise to periodic structural modulations [1]. The most common examples are surface recontructions on clean and adsorbatecovered crystal faces. In the presence of competing longrange and short-range interactions, restructuring of the surface can take place at mesoscopic length scales [2].Several experiments have shown the formation of mesoscopic patterns as a result of elastic interactions. Examples include (2 × 1)-O domains on Cu(110) [3], ordered two-dimensional (2D) islands of Ag on Pt(111) [4], stripes of alternating dimer direction on Boron doped Si(001) [5,6], square patterns of N/Cu(100) [7], stripe domains of Pb/Cu(111) [8], and Au stripes on W(110) [9]. In all these cases, the length scales of the periodic modulations range from a few to hundreds of nanometers, well above the atomic distances. This is understood within the analytical theory [2], which states that the period of a given stripe pattern depends exponentially on the ratio of the short-range (boundary) and long-range (elastic) interaction energies. The period D can be written aswhere a is a microscopic length, C 1 is the formation energy of the stripe boundary, and C 2 is the prefactor of the energy gained by the elastic relaxation due to the formation of stripes [2]. The prefactor of the exponent comes from a smearing of the stripe boundaries, and so is related to the boundary width. This result is identical to that obtained for magnetic layers with dipolar interactions [10,11]. We note that the correspondence between the dipolar Ising lattice and the 2D lattice gas is oneto-one, as the elastic interaction energy between lattice defects scales as 1/r 3 [12]. Studies of mesoscopic patterns show that the periodicity varies strongly with temperature. Moreover, there exists a transition temperature, at which the stripe phase disappears. This temperature dependence has been attributed to the reduction of the boundary free energy through density fluctuations as the disordering temperature is approached [13]. Earlier work on Ising spin lattices showed that the effect of fluctuations can be introduced by an entropic term, which results in a temperature dependent period for the magnetic stripes [14].The density fluctuations, which reduce the boundary free energy, also increase the boundary (or domain wall) width with increasing temperature [15]. Gehring and Keskin took this broadening into consideration, and they argued that the stripe...

Anomalous temperature dependence of antistripe width in the annealing of submonolayer Fe on Ru(0001)

“…This leads to a stripe width decrease with increasing temperature, which has been verified experimentally. 3,4 When the adlayer intermixes with the substrate, the surface stress can be released and C 2 is no longer a constant. Instead it decreases with the release of the surface stress.…”

“…Surprisingly, we find that the antistripe width increases with increasing temperature, which is in sharp contrast with other systems where the opposite behavior is commonly found. 3,4,13 To quantify the temperature dependence of the antistripe width, we average the width of the antistripes and plot the results in Fig. 3(f).…”

“…The authors further predicted its general validity for immiscible systems of adlayer and substrate. In Pd on W(110), Menteş et al 4 found that stripes behave according to the scaling laws for the two-dimensional Ising model with increasing temperature in a wide temperature range. In some systems, the adlayer can also intermix with the substrate and form a surface alloy.…”

“…Interestingly, in some systems, it can lead to the formation of various two-dimensional patterns, including dots, antidots, stripes, and antistripes, etc. [1][2][3][4][5][6][7][8] In addition to their fundamental interest, these patterns in principle offer a way to control the structure and hence functionality of surfaces such as self-assembled templates and heterogeneous catalysis. 9 The domain patterns arise from the competition between the short-range interatomic attractive interaction, which leads to phase boundary energy, and the long-range dipolar repulsive interaction between two phases due to the different surface stress.…”

C60-induced Devil's Staircase transformation on a Pb/Si(111) wetting layer

“…Pattern formation in heteroepitaxial overlayers via self-assembly at nano and mesoscale has attracted intensive research [1][2][3][4][5][6] . Among them the compressed 2-dimensional (2D) wetting layer of Pb on Si(111) has generated great interests recently because a range of experiments at low temperature (T) have shown super-fast diffusion [7][8][9][10] and explosive nucleation 11 during phase transformation in this system by fine-tuning the Pb coverage (θ).…”