The effect of clamped and free boundaries on long range strain coupling in structural phase transitions

In ferroelastic structural phase transitions, the atomic ordering in one cell creates a local strain field which is propagated elastically throughout the material, resulting in an effective or indirect coupling J(R _ij ) between the ordering in cells i and j. With free boundaries on the sample, the J(R _ij ) contains a Zener-Eshelby term J _Z of infinite range, which largely determines the transition temperature T _c. The present paper shows what happens when the boundaries are clamped. On cooling from a high temperature an anomaly takes place at more or less the same temperature as the phase transition for free boundaries. Cooling results in an irregular pattern of domains with positive and negative order parameter whose long range strains cancel. Two cases are distinguished. In the “tweed” case coherent domain boundaries form easily and result in fine lamellar domains. When coherent domain boundaries are not possible (the “non-Sapriel”) case, larger less regular domains are formed. In either case the macroscopic net strain adds up to zero.     

Herringbone and triangular patterns of dislocations in Ag, Au, and AgAu alloy films on Ru(0 0 0 1)

We have studied the dislocation structures that occur in films of Ag, Au, and Ag_0.5Au_0.5 alloy on a Ru(0 0 0 1) substrate. Monolayer (ML) films form herringbone phases while films two or more layers thick contain triangular patterns of dislocations. We use scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED) to determine how the film composition affects the structure and periodicity of these ordered structures. One layer of Ag forms two different herringbone phases depending on the exact Ag coverage and temperature. Low-energy electron microscopy (LEEM) establishes that a reversible, first-order phase transition occurs between these two phases at a certain temperature. We critically compare our 1 ML Ag structures to conflicting results from an X-ray scattering study [H. Zajonz et al., Phys. Rev. B 67 (2003) 155417]. Unlike Ag, the herringbone phases of Au and AgAu alloy are independent of the exact film coverage. For two layer films in all three systems, none of the dislocations in the triangular networks thread into the second film layer. In all three systems, the in-plane atomic spacing of the second film layer is nearly the same as in the bulk. Film composition does, however, affect the details of the two layer structures. Ag and Au films form interconnected networks of dislocations, which we refer to as “trigons.” In 2 ML AgAu alloy, the dislocations form a different triangular network that shares features of both trigon and moiré structures. Yet another well-ordered structure, with square symmetry, forms at the boundaries of translational trigon domains in 2 ML Ag films but not in Au films.     

The influence of chain stretching on the phase behavior of multiblock copolymer and comb copolymer melts

The subject of this paper is inspired by microphase-separated copolymer melts in which a small-scale structure is present inside one of the phases of a large-scale structure. Such a situation can arise in a diblock copolymer melt, if one of the blocks of the diblock is in itself a multiblock copolymer or a comb copolymer. Due to the presence of the large-scale structure, the chains are stretched. The aim of this paper is to investigate the influence of this chain stretching on the formation of the small-scale structure. To gain insight we study infinite melts of infinitely long copolymer chains that are subjected to a stretching force. For melts of monodisperse multiblock copolymers we find that the stretching destabilizes the homogeneous phase. If the stretching is strong, the lamellar structure is the only stable structure. The periodicity increases with the degree of stretching. For melts of monodisperse comb copolymers the chain stretching has no influence on the stability of the homogeneous phase. If the stretching is strong, the lamellar structure and the hexagonal structure are the only stable structures. The periodicity is independent of the degree of stretching. For the multiblock copolymer we investigated the influence of block length polydispersity. For small polydispersity the period of the structure increases monotonically with the degree of stretching. For intermediate polydispersity, the period initially decreases before it starts to increase. For large polydispersity, the mean-field period at the spinodal is infinite, becoming finite once the stretching force exceeds some critical value. For very large polydispersity the mean-field period at the spinodal remains infinite for any value of the stretching force. Received: 14 February 2002 / Accepted: 24 March 2003 / Published online: 29 April 2003 RID="a" ID="a"e-mail: hindrik.angerman@abp.nl     

The dense α-√3 × √3Pb/Si(1 1 1) phase: A comprehensive STM and SPA-LEED study of ordering, phase transitions and interactions

The T-θ phase diagram for the system Pb/Si(1 1 1) was determined in the coverage range 6/5 ML < θ < 4/3 ML from complementary STM and SPA-LEED experiments. This coverage is within the range where a “Devil’s Staircase” (DS) has been realized. The numerous DS phases answer conflicting information in the Pb/Si(1 1 1) literature and update the previously published phase diagram. The measurements reveal the thermal stability of the different linear DS phases with the transition temperature found to be a function of phase period. Because of additional complexity in the experimental system (i.e. two-dimensionality and 3-fold symmetry) the linear DS phases transform at higher temperature into commensurate phases of 3-fold symmetry HIC (historically named “hexagonal incommensurate phase”). Different types of HIC phases have been discovered differing in the size of the supercell built out of √3 × √3 domains separated by domain walls of the √7 × √3 phase. The detailed structures of these HIC phases (coverage, binding site, twist angle, etc.) have been deduced from the comparison of STM images and diffraction patterns. After heating the system to even higher temperature the HIC phase transforms into the disordered phase. For sufficiently high coverage a SIC (“striped incommensurate phase” which is also built from √3 × √3 domains but meandering √7 × √3 domain walls) is observed which also disorders at high temperatures.