Contains reports on six research projects.Joint Services Electronics Program (Contract DAAG29-80-C-0104

Andelman, David

Berker, A. Nihat

Blankschtein, Daniel

Caflisch, Robert G.

Goldstein, Raymond E.

Kardar, Mehran

Walker, James S.

DSpace@MIT

Phase Transitions in Chemisorbed Systems6. Phase Transitions in Chemisorbed SystemsAcademic and Research StaffProf. A.N. Berker, Dr. D. Blankschtein, Dr. J.S. WalkerGraduate StudentsD. Andelman, R.G. Caflisch, M. Kardar, S.R. McKayUndergraduate StudentsR.E. Goldstein, R.J. LenkSurfaces and interfaces abound in our physical environment, and as systems which are lowdimensional and therefore fluctuation dominated, embody fundamental problems of many-bodyphysics. Our research group is studying a variety of low-dimensional and fluctuation-dominatedsystems. Such studies start with microscopic descriptions, such as the interactions of an overlayer inthe presence of a constraining substrate, or the configuration energies and entropies of a helix-coilpolymer immersed in an electrolyte. The eventual outcome is macroscopic, measured or measurableproperties. Another important outcome is the understanding of mechanisms generic to many-bodyphysics.Through the discovery and development of the renormalization-group method, extraordinaryadvance has been achieved in recent years in phase transitions and critical phenomena. Thisapproach successfully deals with a large number of coupled degrees of freedom in a stepwisemanner, by thinning out a fraction of the degrees of freedom, and repeating this operation over andover. Thus, our program utilizes the renormalization-group method, but also any other theoreticaltool as may be necessary. Important technical advances have been achieved in this respect.6.1 Oxygen on Nickel and other Chemisorption Phase DiagramsJoint Services Electronics Program (Contract DAAG29-80-C-0104)Robert G. Caflisch, A. Nihat BerkerEpitaxial adsorption onto a square substrate is studied with a Hamiltonian includingnearest-neighbor exclusion, second and third-neighbor pair and trio interactions. The resultingphase diagrams1 exhibit 2x2, V2x'2, and 2x1 ordered phases and a disordered phase. Thus, allthree ordered structures observed with oxygen on nickel (100) are obtained for the first time withinthe same phase diagram in the coverage and temperature variables. The 2x1 phase has an importantentropy content and appears only at intermediate temperatures. Simple ground-state energy analysisRLE P.R. No. 125Phase Transitions in Chemisorbed Systemsor classical mean-field calculations, therefore, completely miss this phase. Other cross-sections ofour global phase diagram should be applicable to chemisorbates such as oxygen, sulfur, selenium, ortellurium, on substrates such as nickel, copper, tungsten, or platinum (100). First- and second-orderphase boundaries are evaluated, punctuated by tricritical, critical-end, bicritical, and tetracriticalpoints. Reentrant tricriticality is found, yielding closed-loop coexistence regions. The possibility oftwo distinct 2x2 phases, with uniaxial order or a novel biaxial order, is raised for the first time. We usea Migdal-Kadanoff approximation on a cell system, with renormalization-group flows in sixteenenergy levels.in a separate work 2 in collaboration with Prof. J.D. Joannopoulos' group, total-energy ground statecalculations are combined with renormalization-group analysis to predict the surface reconstructionof Si (100).6.2 Commensurate-Incommensurate Phase Transitions, DomainWalls, and Helicity in Two-Dimensional SystemsJoint Services Electronics Program (Contract DAAG29-80-C-0104)Mehran Kardar, A. Nihat BerkerUpon increased adsorption, registered overlayers become incommensurate with their substrate byforming high-density domain walls, which results in interactions (between domains) of a helicalcharacter. For this phenomenon, we introduced the helical Potts model, which successfullyreproduced several experimental observations with krypton on graphite, from Prof. Birgeneau'sgroup, and with krypton and deuterium coadsorbed on graphite. A q-state generalization of thismodel has been studied on the square lattice.3 At low temperatures, this model can be mapped ontothe six-vertex model of Baxter in direct fields. This mapping indicates the presence of a modulatedincommensurate phase. This phase exhibits a virtual ordering, in the sense that the correlations overlarge separations neither go to a non-zero constant, as in a truly ordered phase, nor do they decayexponentially to zero, as in a disordered phase. Instead, a weak algebraic decay of correlationsoccurs, with a critical exponent -r = 2/q2 at low temperature. A Lifshitz-like multicritical point islocated where the registered, modulated, and disordered phases meet.6.3 Multicritical Phenomena in Cubic Symmetry SystemsJoint Services Electronics Program (Contract DAAG29-80-C-0104)Robert G. Caflisch, Daniel BlankschteinPhase transitions which are predicted to be first-order by the classical Landau theory can in fact bedriven second-order by critical fluctuations. This fluctuation-induced criticality occurs in cubicRLE P.R. No. 125Phase Transitions in Chemisorbed Systemssystems which are almost tricritical. Application of symmetry-breaking perturbations suppressesfluctuations and may restore first-order behavior via tricritical points. We are currently studying theeffect of off-diagonal, quadratic symmetry-breaking perturbations on cubic systems undergoingfluctuation-induced transitions. We expect a wide variety of bicritical and tetracritical-like phasediagrams, also featuring tricritical, critical and critical-end points. Our approach combinesmean-field theory, large-anisotropy expansion, and renormalization-group analysis. The relevanceof cubic models to oxygen chemisorbed on nickel (111) has been noted by other workers. The cubicphase diagrams may also be realizable experimentally by applying uniaxial stresses or magnetic fieldsto systems exhibiting structural or magnetic phase transitions, such as KMnF 3, RbCaF 3, BaTiO 3,MnO, TbP, etc.6.4 Crossover to Equivalent-Neighbor Multicritical BehaviorJoint Services Electronics Program (Contract DAAG29-80-C-0104)Mehran Kardar, A. Nihat BerkerExact solutions of models of many-body systems, though difficult to achieve, are of crucialimportance to our understanding of physical phase transition phenomena. Our recently introducedcentral-limit minimization method, based on a new statistical mechanical proof, yields new classes ofexactly solvable Hamiltonians. Using this method, systems with both short- and long-rangeinteractions are solved exactly.4 Such situations could occur, for example, in chemisorption orsurface reconstruction systems with short-range covalent bond formation and long-range dipolarcouplings. Crossover from fluctuation-dominated to mean-field criticality is described in arbitraryspatial dimension. Phase diagrams are derived, with lines of classical and non-classicalsecond-order transitions and first-order transitions, meeting at multicritical points and exhibiting newtypes of critical behavior.6.5 Hydrogen-Bonding and Helix-Coil TransformationsJoint Services Electronics Program (Contract DAAG29-80-C-0104)Raymond E. Goldstein, A. Nihat BerkerThe conformational changes undergone by certain biological macromolecules, such aspoly-y-benzyl-L-glutamate in ethylene dichloride + dichloroacetic acid, are proposed to arise fromthe same interplay of energy versus entropy that causes lower critical-solution points in [iquidmixtures, which have been studied extensively in this group. In these mixtures, hydrogen bondsbetween unlike molecules are responsible for the reappearance of a miscible (substitionallylong-range disordered) phase below a lower critical temperature, but concurrently with increasedshort-range orientational order, so that entropy is decreased according to the third law. This resultsRLE P.R, No. 125Phase Transitions in Chemisorbed Systemsin closed-loop coexistence regions. Note that we have also predicted closed-loop coexistenceregions in chemisorbed systems. In certain macromolecular solutions, an ordered helical stateevolves into a random-coil state with decreasing temperature. This reversal from the expectedordering trend is explained by associating to the polymer-solvent hydrogen bonds, the role played byunlike-molecule bonds in liquid mixtures. A Potts model is used to carry out the statistical mechanicsof these macromolecular solutions. Experiments to clarify the relationship outlined above areproposed.6.6 Improved Renormalization-Group TransformationsJoint Services Electronics Program (Contract DAAG29-80-C-0104)David Andelman, Raymond E. Goldstein, James S. Walker, A. Nihat BerkerIn its rapid evolution to an everyday calculational tool, the renormalization-group methodincorporates correlated fluctuations, but yet has become more amenable than classical approachesto many problems. This is certainly the case, for example, for the calculation of the multicritical,multistructure phase diagrams of chemisorbed systems described above. One approach which wehave introduced is to map, by a so-called prefacing transformation, a system with complicatedfurther-neighbor interactions onto one with complicated local degrees of freedom coupled bynearest-neighbor interactions, and readily renormalizable. This renormalization is most easily doneby a Migdal-Kadanoff procedure. We have also investigated replacing the ad hoc bond-movingprescription of this approximation by a systematic procedure. The free energy is required to bepreserved by matching perturbative series expansions. The approach is characterized by a smallparameter, and can be order-by-order extended. A significant improvement is obtained over thestandard Migdal-Kadanoff calculation, with little increased effort. A detailed application to q-statePotts models in two and three dimensions has been presented. 5,6 In a most recent development, thebond-moving procedure is fixed by an exact finite-lattice calculation. The resultingrenormalization-group transformation is applied to infinite, thermodynamic systems. This newmethod is most promising in that it produces quantitative results for three-dimensional systems.References1. R.G. Caflisch and A.N. Berker, "Oxygen Chemisorbed on Ni(100): Renormalization-Group Study ofthe Global Phase Diagram," Phys. Rev. B, submitted for publication.2. J. Ihm, D.H. Lee, J.D. Joannopoulos, and A.N. Berker, "Structural Phase Diagrams for the Surfaceof a Solid: A Total Energy/Renormalization-Group Approach," Phys. Rev. Lett., submitted forpublication.3. M. Kardar, "Phase Boundaries of the Isotropic Helical Potts Model on a Square Lattice," Phys. Rev.B 26, 2693 (1982).RLE P.R. No. 125Phase Transitions in Chemisorbed Systems4. M. Kardar, "Crossover to Equivalent-Neighbor Multicritical Behavior in Arbitrary Dimensions,"Phys. Rev. B 28, 244 (1983).5. J.S. Walker, "Exact Preservation of the Free Energy in a Modified Migdal-KadanoffApproximation," Phys. Rev. B 26, 3792 (1982).6. D. Andelman and J.S. Walker, "Preserving the Free Energy in a Migdal-Kadanoff Approximation forthe q-State Potts Model," Phys. Rev. B 27, 241 (1982).RLE P.R. No. 125RLE P.R. No. 125 30

Phase Transitions in Chemisorbed Systems

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Phase Transitions in Chemisorbed Systems

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