D. Chrzan - Academia.edu (original) (raw)
Papers by D. Chrzan
Physical Review B, 1994
It is argued that dislocations in the L12 intermetallic compounds displaying the yield strength a... more It is argued that dislocations in the L12 intermetallic compounds displaying the yield strength anomaly undergo a stress-driven pinning-depinning transition. The transition is from a dynamic phase in which a moving dislocation becomes immobile to a dynamic phase in which a moving dislocation, in an infinite medium, remains mobile for all time. The distribution of event times and areas, where an "event" is the mobilization and subsequent immobilization of a dislocation, is related to measurements of the primary creep transient. At the critical point of the proposed transition, the distribution of events becomes scale invariant. A simple scaling hypothesis connects the scaling behavior of the transition to the time dependence of the creep tests. A simplified model of dislocation motion is presented and used to study the properties of the transition. The properties so calculated are not obviously consistent with the published interpretations of experiments, but are consistent with the published data. A reinterpretation of those experiments is proposed.
Microscopy and Microanalysis, 2003
In-situ transmission electron microscopy is particularly well suited to observing the mechanisms ... more In-situ transmission electron microscopy is particularly well suited to observing the mechanisms of dislocation nucleation, propagation and interaction in materials. We have built a novel specimen holder that mimics the now standard ex-situ characterization technique of nanoindentation, and allows us to controllably introduce deformation in a material while simultaneously observing the process in real time in the microscope. 1-3
ACS Applied Electronic Materials, 2019
A current challenge in the processing of 2D materials, or "van der Waals (vdW) solids", is the tr... more A current challenge in the processing of 2D materials, or "van der Waals (vdW) solids", is the transfer of 2D layers from source crystals and growth substrates onto target substrates. Transferas opposed to direct growth and patterning on the targetenables low-temperature processing of the target as well as the use of diverse target materials. These two attributes will allow the assembly of vdW heterostructures to realize devices exploiting the unique properties of vdW materials. Until now, however, there has been no effective method for transferring regions of monolayer material of controlled shape from a multilayer source. We introduce such a method and demonstrate its use in the spatially controlled transfer of arrays of single-layer MoS 2 and WS 2 sheets from multilayer crystals onto SiO 2 substrates. These sheets have lateral sizes exceeding 100 μm and are electronically continuous. The method offers a scalable route to parallel manufacturing of complex circuits and devices from vdW materials.
MRS Proceedings, 2005
Ion implantation into silica followed by thermal annealing is an established growth method for Si... more Ion implantation into silica followed by thermal annealing is an established growth method for Si and Ge nanocrystals. We demonstrate that growth of Group IV semiconductor nanocrystals can be suppressed by co-implantation of oxygen prior to annealing. For Si nanocrystals, at low Si/O dose ratios, oxygen co-implantation leads to a reduction of the average nanocrystal size and a blue-shift of the photoluminescence emission energy. For both Si and Ge nanocrystals, at larger Si/O or Ge/O dose ratios, the implanted specie is oxidized and nanocrystals do not form. This chemical deactivation was utilized to achieve patterned growth of Si and Ge nanocrystals. Si was implanted into a thin SiO2 film on a Si substrate followed by oxygen implantation through an electron beam lithographically defined stencil mask. Thermal annealing of the co-implanted structure yields two-dimensionally patterned growth of Si nanocrystals under the masked regions. We applied a previously developed process to obta...
The Journal of Urology, 2015
apoptosis. Treatment with N-methyl-4-isoleucine cyclosporine significantly reduced all of these e... more apoptosis. Treatment with N-methyl-4-isoleucine cyclosporine significantly reduced all of these effects. CONCLUSIONS: N-methyl-4-isoleucine cyclosporine may represent a new therapeutic agent for the prevention of kidney stone formation. This is the first report of the use of N-methyl-4-isoleucine cyclosporine as a novel therapeutic agent to prevent renal calcium crystal formation through inhibition of cyclophilin D activation.
Physical Review Letters, 1991
ABSTRACT An outstanding goal in the study of crystal growth in the theoretical determination of o... more ABSTRACT An outstanding goal in the study of crystal growth in the theoretical determination of optimal growth conditions for a specific surface morphology. We have developed a (1+1)-dimensional crystal-growth model which includes both a tunable substrate temperature and growth rate. A kinetic phase diagram, which reveals the dependence of the interface width dynamical exponent on temperature and growth rate, is constructed. The phase diagram contains two limiting phases described by different exponents. It is also demonstrated that the interface width can be minimized through a suitable choice of substrate temperature and deposition rate.
Physical Review B, 1988
ABSTRACT A full Bragg-Williams calculation of a four-sublattice face-centered-cubic ternary alloy... more ABSTRACT A full Bragg-Williams calculation of a four-sublattice face-centered-cubic ternary alloy is presented. It corresponds to elements which, similarly to Cu, Ag, and Au, form disparate binaries: one pair that strongly segregates, one pair that forms strongly ordered compounds, and a third pair that forms only weakly ordered binaries. The obtained diagrams are internally consistent, have a sensible temperature evolution towards disorder, and present a variety of behaviors which include ordered and disordered homogeneous single phases, and regions of heterogeneous two- and three-phase mixtures. Although not realistic, the calculation gives a good starting point for more sophisticated models which may include short-range correlations and a better thermodynamic treatment.
ABSTRACT A discrete model of dislocation production by a Frank-Read Source has been simulated num... more ABSTRACT A discrete model of dislocation production by a Frank-Read Source has been simulated numerically (see abstract by Tedstrom, Daw, and Chrzan). In this effectively 1-D model, an external stress acts on discrete dislocations which are emitted symmetrically from a source. The dislocations move according to a dissipative law and interact mutually with a central force that is inversely proportional to the distance between a pair of them (except for moderation at short distances). The numerical results are consistent with a scaling solution for the dislocation density of the form n(x,t) = t^a g(x/t^b) , with the numerical values for the critical exponents being a = -0.1 and b = 1.0. In this talk we transform the discrete model to a continuum form and use the theory of self-similarity and intermediate asymptotics to explain the exponents obtained numerically.
Physical Review B, 2002
The ideal strength is the minimum stress required to plastically deform an infinite defectfree cr... more The ideal strength is the minimum stress required to plastically deform an infinite defectfree crystal and is an upper bound to the strength of a real crystal. Disturbingly, however, the best available experimental estimates of the ideal strengths of tungsten and molybdenum are 25-50% above the values predicted by recent ab initio density-functional calculations. This work resolves this discrepancy by extending the theoretical calculations to account for the triaxial state of stress seen in the nanoindentation experiments and by adjusting the experimental values to account for the crystallography of loading and the nonlinearity of the elastic response at large strains. Although an implicit assumption in many discussions of mechanical properties is that the ideal strength is not experimentally observable, as the true strength of most materials is limited by lattice defects, the close agreement between corrected experimental and theoretical estimates of ideal strength suggests that the ideal strength of some materials can be observed directly using nanoindentation.
Dislocation production by a Frank-Read Source is simulated numerically. In this effectively 1-D m... more Dislocation production by a Frank-Read Source is simulated numerically. In this effectively 1-D model, an external stress acts on discrete dislocations which are emitted symmetrically from a source. The dislocations move according to a dissipative law and interact mutually with a central force that is inversely proportional to the distance between a pair of them (except for moderation at short distances). A numerical solution is obtained with a standard O(N^2) method, though other methods have been tested. The source is allowed to produce many thousands of dislocations, and the overall behavior is analyzed statistically by comparing to a scaling solution for the dislocation density of the form n(x,t) = t^a g(x/t^b). The critical exponents (a and b) are obtained numerically.
Physical Review Letters, 2006
The melting behavior of Ge nanocrystals embedded within SiO 2 is evaluated using in situ transmis... more The melting behavior of Ge nanocrystals embedded within SiO 2 is evaluated using in situ transmission electron microscopy. The observed melting point hysteresis is large (±17%) and nearly symmetric about the bulk melting point. This hysteresis is modeled successfully using classical nucleation theory without the need to invoke epitaxy.
Physical Review Letters, 2000
The core structure and stability of the 90 ± partial dislocation in diamond is studied within iso... more The core structure and stability of the 90 ± partial dislocation in diamond is studied within isotropic elasticity theory and ab initio total energy calculations. The double-period reconstruction is found to be more stable than the single-period reconstruction for a broad range of stress states. The analysis of the ab initio results shows further that elasticity theory is valid for dislocation spacings as small as 10-20 Å, thus allowing ab initio calculations to provide reliable parameters for continuum theory analysis.
Physical Review Letters, 1988
ABSTRACT A calculation of the magnetic (001) surface structure of an antiferromagnetic insulator ... more ABSTRACT A calculation of the magnetic (001) surface structure of an antiferromagnetic insulator with the MnO spin arrangement is reported. The calculation is based on classical spins with Heisenberg interactions which are (a) between second neighbors throughout the bulk and surface, (b) between nearest-neighbor spins at the surface layer, and (c) between nearest-neighbor spins in the first and second layers. It is found that for a range of exchange parameters, incommensurable ground-state structures are obtained.
Physical Review Letters, 2006
Physical Review Letters, 2009
Ion beam synthesis of nanoclusters is studied via both kinetic Monte Carlo simulations and the se... more Ion beam synthesis of nanoclusters is studied via both kinetic Monte Carlo simulations and the self-consistent mean-field solution to a set of coupled rate equations. Both approaches predict the existence of a steady state shape for the cluster size distribution that depends only on a characteristic length determined by the ratio of the effective diffusion coefficient to the ion flux. The average cluster size in the steady state regime is determined by the implanted species/matrix interface energy.
Physical Review B, 2009
A model to describe the growth of nanoclusters in silica via ion-beam synthesis is introduced. Ki... more A model to describe the growth of nanoclusters in silica via ion-beam synthesis is introduced. Kinetic Monte Carlo simulations indicate that nucleation, growth, coarsening, and fragmentation occur throughout implantation, leading to a steady-state size-distribution shape that agrees with experimental observations. A set of coupled rate equations are derived and solved within a self-consistent mean-field approximation. An intermediate asymptotic scaling analysis helps to identify the important experimentally accessible parameters that control ion-beam-synthesized nanocluster size distributions. The model predicts that the shape of the asimplanted size distribution depends only on a characteristic length governed by the effective diffusivity, effective ion solubility, and the volumetric flux while the average cluster size is determined by the solute/ matrix interface energy.
Physical Review B, 2004
The ideal tensile strengths of the B2-type ͑CsCl͒ transition-metal aluminides FeAl, CoAl, and NiA... more The ideal tensile strengths of the B2-type ͑CsCl͒ transition-metal aluminides FeAl, CoAl, and NiAl have been investigated using an ab initio electronic structure total energy method. The three materials exhibit dissimilar mechanical behaviors under the simulated ideal tensile tests along [001], [110], and [111] directions. FeAl is weakest in tension along [001] whereas CoAl and NiAl are strongest in the same direction. The weakness of FeAl along [001] direction is attributed to the instability introduced by the filling of antibonding d states.
Physical Review B, 2006
ABSTRACT The elastic deformation behaviors of perfect NiAl and FeAl are investigated using an ab ... more ABSTRACT The elastic deformation behaviors of perfect NiAl and FeAl are investigated using an ab initio electronic structure total energy method. The calculated ideal shear strengths for the {112}⟨111⟩ and {110}⟨111⟩ slip show qualitatively different features between the two intermetallics. In NiAl, the shear deformation can be understood by exploring the transition among different stress-free structures on the strain paths, while in FeAl the instabilities under shear are found to be dictated by filling of the unstable anti-bonding d states. The failure modes under uniaxial ⟨100⟩ tension are also explored for NiAl and FeAl using two methods, a straightforward comparison of the resolved shear stress with the ideal shear strength and a detailed examination of the internal stability condition. Both methods yield the same conclusion: FeAl fails by tension while NiAl fails by shear. These predictions are consistent with the experimentally observed cleavage behaviors.
Physical Review B, 2005
Kinetic Monte Carlo ͑KMC͒ simulations are used to investigate the dynamics of island growth durin... more Kinetic Monte Carlo ͑KMC͒ simulations are used to investigate the dynamics of island growth during submonolayer epitaxy in the presence of anisotropic surface diffusion, and the influence of a recently hypothesized crowdion diffusion mechanism. An existing rate equation mean-field analysis of island growth is extended to include anisotropic diffusion. The mean-field analysis is found to be at odds with results from KMC simulations indicating that the details of the surface diffusion mechanism influence the nucleation rate. It is found that anisotropy in adatom hopping reduces the density of stable islands. It is also found that although the shape of the island size distribution is sensitive to island relaxation processes, it is not discernibly affected by hopping anisotropy with ratios D xx / D yy up to 16.
Physical Review B, 1994
It is argued that dislocations in the L12 intermetallic compounds displaying the yield strength a... more It is argued that dislocations in the L12 intermetallic compounds displaying the yield strength anomaly undergo a stress-driven pinning-depinning transition. The transition is from a dynamic phase in which a moving dislocation becomes immobile to a dynamic phase in which a moving dislocation, in an infinite medium, remains mobile for all time. The distribution of event times and areas, where an "event" is the mobilization and subsequent immobilization of a dislocation, is related to measurements of the primary creep transient. At the critical point of the proposed transition, the distribution of events becomes scale invariant. A simple scaling hypothesis connects the scaling behavior of the transition to the time dependence of the creep tests. A simplified model of dislocation motion is presented and used to study the properties of the transition. The properties so calculated are not obviously consistent with the published interpretations of experiments, but are consistent with the published data. A reinterpretation of those experiments is proposed.
Microscopy and Microanalysis, 2003
In-situ transmission electron microscopy is particularly well suited to observing the mechanisms ... more In-situ transmission electron microscopy is particularly well suited to observing the mechanisms of dislocation nucleation, propagation and interaction in materials. We have built a novel specimen holder that mimics the now standard ex-situ characterization technique of nanoindentation, and allows us to controllably introduce deformation in a material while simultaneously observing the process in real time in the microscope. 1-3
ACS Applied Electronic Materials, 2019
A current challenge in the processing of 2D materials, or "van der Waals (vdW) solids", is the tr... more A current challenge in the processing of 2D materials, or "van der Waals (vdW) solids", is the transfer of 2D layers from source crystals and growth substrates onto target substrates. Transferas opposed to direct growth and patterning on the targetenables low-temperature processing of the target as well as the use of diverse target materials. These two attributes will allow the assembly of vdW heterostructures to realize devices exploiting the unique properties of vdW materials. Until now, however, there has been no effective method for transferring regions of monolayer material of controlled shape from a multilayer source. We introduce such a method and demonstrate its use in the spatially controlled transfer of arrays of single-layer MoS 2 and WS 2 sheets from multilayer crystals onto SiO 2 substrates. These sheets have lateral sizes exceeding 100 μm and are electronically continuous. The method offers a scalable route to parallel manufacturing of complex circuits and devices from vdW materials.
MRS Proceedings, 2005
Ion implantation into silica followed by thermal annealing is an established growth method for Si... more Ion implantation into silica followed by thermal annealing is an established growth method for Si and Ge nanocrystals. We demonstrate that growth of Group IV semiconductor nanocrystals can be suppressed by co-implantation of oxygen prior to annealing. For Si nanocrystals, at low Si/O dose ratios, oxygen co-implantation leads to a reduction of the average nanocrystal size and a blue-shift of the photoluminescence emission energy. For both Si and Ge nanocrystals, at larger Si/O or Ge/O dose ratios, the implanted specie is oxidized and nanocrystals do not form. This chemical deactivation was utilized to achieve patterned growth of Si and Ge nanocrystals. Si was implanted into a thin SiO2 film on a Si substrate followed by oxygen implantation through an electron beam lithographically defined stencil mask. Thermal annealing of the co-implanted structure yields two-dimensionally patterned growth of Si nanocrystals under the masked regions. We applied a previously developed process to obta...
The Journal of Urology, 2015
apoptosis. Treatment with N-methyl-4-isoleucine cyclosporine significantly reduced all of these e... more apoptosis. Treatment with N-methyl-4-isoleucine cyclosporine significantly reduced all of these effects. CONCLUSIONS: N-methyl-4-isoleucine cyclosporine may represent a new therapeutic agent for the prevention of kidney stone formation. This is the first report of the use of N-methyl-4-isoleucine cyclosporine as a novel therapeutic agent to prevent renal calcium crystal formation through inhibition of cyclophilin D activation.
Physical Review Letters, 1991
ABSTRACT An outstanding goal in the study of crystal growth in the theoretical determination of o... more ABSTRACT An outstanding goal in the study of crystal growth in the theoretical determination of optimal growth conditions for a specific surface morphology. We have developed a (1+1)-dimensional crystal-growth model which includes both a tunable substrate temperature and growth rate. A kinetic phase diagram, which reveals the dependence of the interface width dynamical exponent on temperature and growth rate, is constructed. The phase diagram contains two limiting phases described by different exponents. It is also demonstrated that the interface width can be minimized through a suitable choice of substrate temperature and deposition rate.
Physical Review B, 1988
ABSTRACT A full Bragg-Williams calculation of a four-sublattice face-centered-cubic ternary alloy... more ABSTRACT A full Bragg-Williams calculation of a four-sublattice face-centered-cubic ternary alloy is presented. It corresponds to elements which, similarly to Cu, Ag, and Au, form disparate binaries: one pair that strongly segregates, one pair that forms strongly ordered compounds, and a third pair that forms only weakly ordered binaries. The obtained diagrams are internally consistent, have a sensible temperature evolution towards disorder, and present a variety of behaviors which include ordered and disordered homogeneous single phases, and regions of heterogeneous two- and three-phase mixtures. Although not realistic, the calculation gives a good starting point for more sophisticated models which may include short-range correlations and a better thermodynamic treatment.
ABSTRACT A discrete model of dislocation production by a Frank-Read Source has been simulated num... more ABSTRACT A discrete model of dislocation production by a Frank-Read Source has been simulated numerically (see abstract by Tedstrom, Daw, and Chrzan). In this effectively 1-D model, an external stress acts on discrete dislocations which are emitted symmetrically from a source. The dislocations move according to a dissipative law and interact mutually with a central force that is inversely proportional to the distance between a pair of them (except for moderation at short distances). The numerical results are consistent with a scaling solution for the dislocation density of the form n(x,t) = t^a g(x/t^b) , with the numerical values for the critical exponents being a = -0.1 and b = 1.0. In this talk we transform the discrete model to a continuum form and use the theory of self-similarity and intermediate asymptotics to explain the exponents obtained numerically.
Physical Review B, 2002
The ideal strength is the minimum stress required to plastically deform an infinite defectfree cr... more The ideal strength is the minimum stress required to plastically deform an infinite defectfree crystal and is an upper bound to the strength of a real crystal. Disturbingly, however, the best available experimental estimates of the ideal strengths of tungsten and molybdenum are 25-50% above the values predicted by recent ab initio density-functional calculations. This work resolves this discrepancy by extending the theoretical calculations to account for the triaxial state of stress seen in the nanoindentation experiments and by adjusting the experimental values to account for the crystallography of loading and the nonlinearity of the elastic response at large strains. Although an implicit assumption in many discussions of mechanical properties is that the ideal strength is not experimentally observable, as the true strength of most materials is limited by lattice defects, the close agreement between corrected experimental and theoretical estimates of ideal strength suggests that the ideal strength of some materials can be observed directly using nanoindentation.
Dislocation production by a Frank-Read Source is simulated numerically. In this effectively 1-D m... more Dislocation production by a Frank-Read Source is simulated numerically. In this effectively 1-D model, an external stress acts on discrete dislocations which are emitted symmetrically from a source. The dislocations move according to a dissipative law and interact mutually with a central force that is inversely proportional to the distance between a pair of them (except for moderation at short distances). A numerical solution is obtained with a standard O(N^2) method, though other methods have been tested. The source is allowed to produce many thousands of dislocations, and the overall behavior is analyzed statistically by comparing to a scaling solution for the dislocation density of the form n(x,t) = t^a g(x/t^b). The critical exponents (a and b) are obtained numerically.
Physical Review Letters, 2006
The melting behavior of Ge nanocrystals embedded within SiO 2 is evaluated using in situ transmis... more The melting behavior of Ge nanocrystals embedded within SiO 2 is evaluated using in situ transmission electron microscopy. The observed melting point hysteresis is large (±17%) and nearly symmetric about the bulk melting point. This hysteresis is modeled successfully using classical nucleation theory without the need to invoke epitaxy.
Physical Review Letters, 2000
The core structure and stability of the 90 ± partial dislocation in diamond is studied within iso... more The core structure and stability of the 90 ± partial dislocation in diamond is studied within isotropic elasticity theory and ab initio total energy calculations. The double-period reconstruction is found to be more stable than the single-period reconstruction for a broad range of stress states. The analysis of the ab initio results shows further that elasticity theory is valid for dislocation spacings as small as 10-20 Å, thus allowing ab initio calculations to provide reliable parameters for continuum theory analysis.
Physical Review Letters, 1988
ABSTRACT A calculation of the magnetic (001) surface structure of an antiferromagnetic insulator ... more ABSTRACT A calculation of the magnetic (001) surface structure of an antiferromagnetic insulator with the MnO spin arrangement is reported. The calculation is based on classical spins with Heisenberg interactions which are (a) between second neighbors throughout the bulk and surface, (b) between nearest-neighbor spins at the surface layer, and (c) between nearest-neighbor spins in the first and second layers. It is found that for a range of exchange parameters, incommensurable ground-state structures are obtained.
Physical Review Letters, 2006
Physical Review Letters, 2009
Ion beam synthesis of nanoclusters is studied via both kinetic Monte Carlo simulations and the se... more Ion beam synthesis of nanoclusters is studied via both kinetic Monte Carlo simulations and the self-consistent mean-field solution to a set of coupled rate equations. Both approaches predict the existence of a steady state shape for the cluster size distribution that depends only on a characteristic length determined by the ratio of the effective diffusion coefficient to the ion flux. The average cluster size in the steady state regime is determined by the implanted species/matrix interface energy.
Physical Review B, 2009
A model to describe the growth of nanoclusters in silica via ion-beam synthesis is introduced. Ki... more A model to describe the growth of nanoclusters in silica via ion-beam synthesis is introduced. Kinetic Monte Carlo simulations indicate that nucleation, growth, coarsening, and fragmentation occur throughout implantation, leading to a steady-state size-distribution shape that agrees with experimental observations. A set of coupled rate equations are derived and solved within a self-consistent mean-field approximation. An intermediate asymptotic scaling analysis helps to identify the important experimentally accessible parameters that control ion-beam-synthesized nanocluster size distributions. The model predicts that the shape of the asimplanted size distribution depends only on a characteristic length governed by the effective diffusivity, effective ion solubility, and the volumetric flux while the average cluster size is determined by the solute/ matrix interface energy.
Physical Review B, 2004
The ideal tensile strengths of the B2-type ͑CsCl͒ transition-metal aluminides FeAl, CoAl, and NiA... more The ideal tensile strengths of the B2-type ͑CsCl͒ transition-metal aluminides FeAl, CoAl, and NiAl have been investigated using an ab initio electronic structure total energy method. The three materials exhibit dissimilar mechanical behaviors under the simulated ideal tensile tests along [001], [110], and [111] directions. FeAl is weakest in tension along [001] whereas CoAl and NiAl are strongest in the same direction. The weakness of FeAl along [001] direction is attributed to the instability introduced by the filling of antibonding d states.
Physical Review B, 2006
ABSTRACT The elastic deformation behaviors of perfect NiAl and FeAl are investigated using an ab ... more ABSTRACT The elastic deformation behaviors of perfect NiAl and FeAl are investigated using an ab initio electronic structure total energy method. The calculated ideal shear strengths for the {112}⟨111⟩ and {110}⟨111⟩ slip show qualitatively different features between the two intermetallics. In NiAl, the shear deformation can be understood by exploring the transition among different stress-free structures on the strain paths, while in FeAl the instabilities under shear are found to be dictated by filling of the unstable anti-bonding d states. The failure modes under uniaxial ⟨100⟩ tension are also explored for NiAl and FeAl using two methods, a straightforward comparison of the resolved shear stress with the ideal shear strength and a detailed examination of the internal stability condition. Both methods yield the same conclusion: FeAl fails by tension while NiAl fails by shear. These predictions are consistent with the experimentally observed cleavage behaviors.
Physical Review B, 2005
Kinetic Monte Carlo ͑KMC͒ simulations are used to investigate the dynamics of island growth durin... more Kinetic Monte Carlo ͑KMC͒ simulations are used to investigate the dynamics of island growth during submonolayer epitaxy in the presence of anisotropic surface diffusion, and the influence of a recently hypothesized crowdion diffusion mechanism. An existing rate equation mean-field analysis of island growth is extended to include anisotropic diffusion. The mean-field analysis is found to be at odds with results from KMC simulations indicating that the details of the surface diffusion mechanism influence the nucleation rate. It is found that anisotropy in adatom hopping reduces the density of stable islands. It is also found that although the shape of the island size distribution is sensitive to island relaxation processes, it is not discernibly affected by hopping anisotropy with ratios D xx / D yy up to 16.