scholarly journals Phase Diagrams of Instabilities in Compressed Film-Substrate Systems

2013 ◽  
Vol 81 (5) ◽  
Author(s):  
Qiming Wang ◽  
Xuanhe Zhao
Keyword(s):  
Phase Transitions ◽  
Film Thickness ◽  
Phase Diagrams ◽  
Stability Criterion ◽  
Theoretical Study ◽  
Membrane Stress ◽  
Substrate Adhesion ◽  
Elastic Film ◽  
Quantitative Understanding ◽  
Film Substrate

Subject to a compressive membrane stress, an elastic film bonded on a substrate can become unstable, forming wrinkles, creases or delaminated buckles. Further increasing the compressive stress can induce advanced modes of instabilities including period-doubles, folds, localized ridges, delamination, and coexistent instabilities. While various instabilities in film-substrate systems under compression have been analyzed separately, a systematic and quantitative understanding of these instabilities is still elusive. Here we present a joint experimental and theoretical study to systematically explore the instabilities in elastic film-substrate systems under uniaxial compression. We use the Maxwell stability criterion to analyze the occurrence and evolution of instabilities analogous to phase transitions in thermodynamic systems. We show that the moduli of the film and the substrate, the film-substrate adhesion strength, the film thickness, and the prestretch in the substrate determine various modes of instabilities. Defects in the film-substrate system can facilitate it to overcome energy barriers during occurrence and evolution of instabilities. We provide a set of phase diagrams to predict both initial and advanced modes of instabilities in compressed film-substrate systems. The phase diagrams can be used to guide the design of film-substrate systems to achieve desired modes of instabilities.

scholarly journals Thickness-dependent electrocaloric effect in mixed-phase Pb 0.87 Ba 0.1 La 0.02 (Zr 0.6 Sn 0.33 Ti 0.07 )O 3 thin films

2016 ◽  
Vol 374 (2074) ◽  
pp. 20160056 ◽  
Author(s):  
T. M. Correia ◽  
Q. Zhang
Keyword(s):  
Thin Films ◽  
Dielectric Constant ◽  
Phase Transitions ◽  
Film Thickness ◽  
Tetragonal Phase ◽  
Sol Gel ◽  
Breakdown Field ◽  
Electrocaloric Effect ◽  
Thickness Increase ◽  
Higher Temperature

Full-perovskite Pb 0.87 Ba 0.1 La 0.02 (Zr 0.6 Sn 0.33 Ti 0.07 )O 3 (PBLZST) thin films were fabricated by a sol–gel method. These revealed both rhombohedral and tetragonal phases, as opposed to the full-tetragonal phase previously reported in ceramics. The fractions of tetragonal and rhombohedral phases are found to be strongly dependent on film thickness. The fraction of tetragonal grains increases with increasing film thickness, as the substrate constraint throughout the film decreases with film thickness. The maximum of the dielectric constant ( ε m ) and the corresponding temperature ( T m ) are thickness-dependent and dictated by the fraction of rhombohedral and tetragonal phase, with ε m reaching a minimum at 400 nm and T m shifting to higher temperature with increasing thickness. With the thickness increase, the breakdown field decreases, but field-induced antiferroelectric–ferroelectric ( E AFE−FE ) and ferroelectric–antiferroelectric ( E FE−AFE ) switch fields increase. The electrocaloric effect increases with increasing film thickness. This article is part of the themed issue ‘Taking the temperature of phase transitions in cool materials’.

scholarly journals Towards a quantitative understanding of period-doubling wrinkling patterns occurring in film/substrate bilayer systems

2015 ◽  
Vol 471 (2173) ◽  
pp. 20140695 ◽  
Author(s):  
Yan Zhao ◽  
Yanping Cao ◽  
Wei Hong ◽  
M. Khurram Wadee ◽  
Xi-Qiao Feng
Keyword(s):  
Potential Energy ◽  
Critical Strain ◽  
Deformation Behaviour ◽  
Compressive Strain ◽  
Period Doubling ◽  
Careful Examination ◽  
Deformation State ◽  
Quantitative Understanding ◽  
Surface Patterns ◽  
Film Substrate

Compression of a stiff film on a soft substrate may lead to surface wrinkling when the compressive strain reaches a critical value. Further compression may cause a wrinkling–folding transition, and the sinusoidal wrinkling mode can then give way to a period-doubling bifurcation. The onset of the primary bifurcation has been well understood, but a quantitative understanding of the secondary bifurcation remains elusive. Our theoretical analysis of the branching of surface patterns reveals that the wrinkling–folding transition depends on the wrinkling strain and the prestrain in the substrate. A characteristic strain in the substrate is adopted to determine the correlation among the critical strain of the period-doubling mode, the wrinkling strain and the prestrain in an explicit form. A careful examination of the total potential energy of the system reveals that beyond the critical strain of period-doubling, the sinusoidal wrinkling mode has a higher potential energy in comparison with the period-doubling mode. The critical strain of the period-doubling mode strongly depends on the deformation state of the hyperelastic solid, indicating that the nonlinear deformation behaviour of the substrate plays a key role here. The results reported here on the one hand provide a quantitative understanding of the wrinkling–folding transition observed in natural and synthetic material systems and on the other hand pave the way to control the wrinkling mode transition by regulating the strain state in the substrate.

Some Remarks on Phase Transitions Generated by the Superposition of Multifractals

1997 ◽  
Vol 11 (24) ◽  
pp. 2961-2974
Author(s):  
H. J. Chen ◽  
H. C. Tseng ◽  
W. Y. Lai ◽  
W. D. Chen
Keyword(s):  
Phase Transitions ◽  
Phase Diagrams ◽  
Second Order

Emergence of novel second-order phase transitions by sums of multifractals was found by Radons and Stoop.1,2 Using the same method as Radons and Stoop but different support, we have found that the second-order phase transitions are suppressed.3 In this paper, we continue to extend the method to three multifractals, with the effect of the sums of the three multifractals being the sums of two identical multifractals and those of two different multifractals combined together. We have found that the resulted phase diagrams are more complicated, with second-order phase transitions either partially or completely suppressed.

scholarly journals Thermodynamics at the nanoscale: phase diagrams of nickel–carbon nanoclusters and equilibrium constants for phase transitions

Nanoscale ◽  
2014 ◽  
Vol 6 (20) ◽  
pp. 11981-11987 ◽  
Author(s):  
Yannick Engelmann ◽  
Annemie Bogaerts ◽  
Erik C. Neyts
Keyword(s):  
Molecular Dynamics ◽  
Phase Transitions ◽  
Molecular Dynamics Simulations ◽  
Phase Diagrams ◽  
Equilibrium Constants ◽  
Melting Behavior ◽  
Reactive Molecular Dynamics ◽  
Carbon Nanoclusters ◽  
Dynamics Simulations

Using reactive molecular dynamics simulations, the melting behavior of nickel–carbon nanoclusters is examined.

scholarly journals Enhanced Ionic Conduction at the Film/Substrate Interface in LiI Thin Films Grown on Sapphire(0001)

1993 ◽  
Vol 318 ◽  
Author(s):  
D. Lubben ◽  
F. A. Modine
Keyword(s):  
Thin Films ◽  
Film Thickness ◽  
Ionic Conduction ◽  
High Vacuum ◽  
Dislocation Motion ◽  
Ultra High Vacuum ◽  
Vacuum System ◽  
Substrate Interface ◽  
Interdigital Electrodes ◽  
Film Substrate

ABSTRACTThe ionic conductivity of LiI thin films grown on sapphire(0001) substrates has been studied in situ during deposition as a function of film thickness and deposition conditions. LiI films were produced at room temperature by sublimation in an ultra-high-vacuum system. The conductivity of the Lil parallel to the film/substrate interface was determined from frequency-dependent impedance measurements as a function of film thickness using Au interdigital electrodes deposited on the sapphire surface. The measurements show a conduction of ∼5 times the bulk value at the interface which gradually decreases as the film thickness is increased beyond 100 nm. This interfacial enhancement is not stable but anneals out with a characteristic log of time dependence. Fully annealed films have an activation energy for conduction (σT) of ∼0.47 ± .03 eV, consistent with bulk measurements. The observed annealing behavior can be fit with a model based on dislocation motion which implies that the increase in conduction near the interface is not due to the formation of a space-charge layer as previously reported but to defects generated during the growth process. This explanation is consistent with the behavior exhibited by CaF2 films grown under similar conditions.

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