Role of stress in thin film alloy thermodynamics: competition between alloying and dislocation formation

Phase transition driven discontinuity in thermodynamic size selection

We show how an order-disorder phase transition in a two-dimensional system can discontinuously alter the shape and size of stress-stabilized self-assembled nanostructures. Low energy electron microscopy was used to study the dealloying of the Cu(111)-sqrt[3]×sqrt[3]-R30°-Bi surface alloy. The gradual expulsion of embedded bismuth from the alloy with increasing temperature induces a hard-hexagon-type order-disorder transition in the surface alloy. Our low energy electron microscopy results demonstrate how the loss of long-range order induces enormous changes in the domain patterns that the alloy forms with a Bi overlayer phase. We propose that the occurrence of phase transitions in one of the two surface phases that constitute a self-assembled domain pattern, provides a general, largely unexplored, mechanism that can be used to influence the morphological details of two-dimensional nanostructures.

Phase-field crystal modeling of compositional domain formation in ultrathin films

Bulk-immiscible binary systems often form stress-induced miscible alloy phases when deposited on a substrate. Both alloying and surface dislocation formation lead to the decrease of the elastic strain energy, and the competition between these two strain-relaxation mechanisms gives rise to the emergence of pseudomorphic compositional nanoscale domains, often coexisting with a partially coherent single phase. In this work, we develop a phase-field crystal model for compositional patterning in monolayer aggregates of binary metallic systems. We first demonstrate that the model naturally incorporates the competition between alloying and misfit dislocations, and quantify the effects of misfit and line tension on equilibrium domain size. Then, we quantitatively relate the parameters of the phase-field crystal model to a specific system, CoAg/Ru(0001), and demonstrate that the simulations capture experimentally observed morphologies.

In situ thin film growth stresses during chemical ordering

The in situ growth stress and postgrowth stress relaxation during the L1(0) chemical ordering of Fe0.54Pt0.46 thin films have been characterized. The compressive stress is reduced with an increase in order parameter. The postgrowth stress relaxation rate increased with the order parameter and is rationalized in terms of an increase in the interfacial energy contribution at the grain boundaries because of chemical order. Density functional theory calculations were performed to quantify possible diffusion pathways and binding energies for Fe and Pt that may mitigate surface migration.

Ordered surface alloy of bulk-immiscible components stabilized by magnetism

Using scanning tunneling microscopy and a diffraction experiment, we have discovered a new ordered surface alloy made out of two bulk-immiscible components, Fe and Au, deposited on a Ru(0001) substrate. In such a system, substrate-mediated strain interactions are believed to provide the main driving force for mixing. However, spin-polarized ab initio calculations show that the most stable structures are always the ones with the highest magnetic moment per Fe atom and not the ones minimizing the surface stress, in remarkable agreement with the observations. This opens up novel possibilities for creating materials with unique properties of relevance to device applications.

Nanoscale "Quantum" Islands on Metal Substrates: Microscopy Studies and Electronic Structure Analyses

Confinement of electrons can occur in metal islands or in continuous films grown heteroepitaxially upon a substrate of a different metal or on a metallic alloy. Associated quantum size effects (QSE) can produce a significant height-dependence of the surface free energy for nanoscale thicknesses of up to 10–20 layers. This may suffice to induce height selection during film growth. Scanning STM analysis has revealed remarkable flat-topped or mesa-like island and film morphologies in various systems. We discuss in detail observations of QSE and associated film growth behavior for Pb/Cu(111), Ag/Fe(100), and Cu/fcc-Fe/Cu(100) [A/B or A/B/A], and for Ag/NiAl(110) with brief comments offered for Fe/Cu₃Au(001) [A/BC binary alloys]. We also describe these issues for Ag/5-fold i-Al-Pd-Mn and Bi/5-fold i-Al-Cu-Fe [A/BCD ternary icosohedral quasicrystals]. Electronic structure theory analysis, either at the level of simple free electron gas models or more sophisticated Density Functional Theory calculations, can provide insight into the QSE-mediated thermodynamic driving force underlying height selection.

Thermal motion and energetics of self-assembled domain structures: Pb on Cu(111)

Low energy electron microscope measurements of the thermal motion of 50-200 nm diameter Pb islands on Cu(111) are used to establish the nature and determine the strength of interactions that give rise to self-assembly in this two-dimensional, two-phase system. The results show that self-assembled patterns arise from a temperature-independent surface stress difference of approximately 1.2 N/m between the two phases. With increasing Pb coverage, the domain patterns evolve in a manner consistent with models based on dipolar repulsions caused by elastic interactions due to a surface stress difference.

Linking surface stress to surface structure: measurement of atomic strain in a surface alloy using scanning tunneling microscopy

Annealed submonolayer CoAg/Ru(0001) films form an alloy with a structure that contains droplets of Ag surrounded by Co [G. E. Thayer, V. Ozolins, A. K. Schmid, N. C. Bartelt, M. Asta, J. J. Hoyt, S. Chiang, and R. Q. Hwang, Phys. Rev. Lett. 86, 660 (2001)]. To understand how surface stress contributes to the formation of this structure, we use scanning tunneling microscopy to extract atomic displacements at the boundaries between regions of Co and Ag. Comparing our measurements to Frenkel-Kontorova model calculations, we show how stress due to lattice mismatch contributes to the formation of the alloy droplet structure. In particular, we quantitatively evaluate how competing strain and chemical energy contributions determine surface structure.

Elastic relaxations in ultrathin epitaxial alloy films

Elastic interactions responsible for the stability of nanometer-scale patterns in ultrathin, bulk-immiscible-alloy films are analyzed within the context of a hybrid atomistic-continuum model. Two apparently different descriptions of alloy film behavior, a continuum elasticity theory describing a deformable substrate and a rigid substrate atomistic scheme, emerge naturally as limiting cases on long and short length scales, respectively. Quantitative first-principles calculations explain the origin of recently observed nanoscale patterns in Co-Ag/Ru(0001), and reveal a surprising failure of the continuum model.