scholarly journals An Asymptotic Analysis of the Period-Doubling Secondary Bifurcation in a Film/Substrate Bilayer

2015 ◽  
Vol 75 (6) ◽  
pp. 2381-2395 ◽  
Author(s):  
Y. B. Fu ◽  
Z. X. Cai
Keyword(s):  
Asymptotic Analysis ◽  
Period Doubling ◽  
Secondary Bifurcation ◽  
Film Substrate

scholarly journals Multimodal Surface Instabilities in Curved Film–Substrate Structures

2017 ◽  
Vol 84 (8) ◽  
Author(s):  
Ruike Zhao ◽  
Xuanhe Zhao
Keyword(s):  
Thin Films ◽  
Mechanical Properties ◽  
Numerical Simulation ◽  
Period Doubling ◽  
Tubular Structures ◽  
Modulus Ratio ◽  
Future Design ◽  
Mismatch Strain ◽  
Curved Structures ◽  
Film Substrate

Structures of thin films bonded on thick substrates are abundant in biological systems and engineering applications. Mismatch strains due to expansion of the films or shrinkage of the substrates can induce various modes of surface instabilities such as wrinkling, creasing, period doubling, folding, ridging, and delamination. In many cases, the film–substrate structures are not flat but curved. While it is known that the surface instabilities can be controlled by film–substrate mechanical properties, adhesion and mismatch strain, effects of the structures’ curvature on multiple modes of instabilities have not been well understood. In this paper, we provide a systematic study on the formation of multimodal surface instabilities on film–substrate tubular structures with different curvatures through combined theoretical analysis and numerical simulation. We first introduce a method to quantitatively categorize various instability patterns by analyzing their wave frequencies using fast Fourier transform (FFT). We show that the curved film–substrate structures delay the critical mismatch strain for wrinkling when the system modulus ratio between the film and substrate is relatively large, compared with flat ones with otherwise the same properties. In addition, concave structures promote creasing and folding, and suppress ridging. On the contrary, convex structures promote ridging and suppress creasing and folding. A set of phase diagrams are calculated to guide future design and analysis of multimodal surface instabilities in curved structures.

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.

scholarly journals Wrinkling Phenomena in Neo-Hookean Film/Substrate Bilayers

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Yanping Cao ◽  
John W. Hutchinson
Keyword(s):  
Finite Element ◽  
Critical Strain ◽  
Full Range ◽  
Period Doubling ◽  
Modulus Ratio ◽  
Layer System ◽  
Mountain Ridge ◽  
Compliant Substrates ◽  
Film Substrate

Wrinkling modes are determined for a two-layer system comprised of a neo-Hookean film bonded to an infinitely deep neo-Hookean substrate with the entire bilayer undergoing compression. The full range of the film/substrate modulus ratio is considered from the limit of a traction-free homogeneous substrate to very stiff films on compliant substrates. The role of substrate prestretch is considered wherein an unstretched film is bonded to a prestretched substrate with wrinkling arising as the stretch in the substrate is relaxed. An exact bifurcation analysis reveals the critical strain in the film at the onset of wrinkling. Numerical simulations carried out within a finite element framework uncover advanced post-bifurcation modes including period-doubling, folding and a newly identified mountain ridge mode.

Microtomy of spherical Al2O3 powders

1983 ◽  
Vol 41 ◽  
pp. 74-75
Author(s):  
E.J. Jenkins ◽  
D.S. Tucker ◽  
J.J. Hren
Keyword(s):  
Thin Film ◽  
Size Range ◽  
Particle Aggregation ◽  
Ion Milling ◽  
Thin Sections ◽  
Α Phase ◽  
Convenient Means ◽  
Van Der Waals Attraction ◽  
Negative Feature ◽  
Film Substrate

The size range of mineral and ceramic particles of one to a few microns is awkward to prepare for examination by TEM. Electrons can be transmitted through smaller particles directly and larger particles can be thinned by crushing and dispersion onto a substrate or by embedding in a film followed by ion milling. Attempts at dispersion onto a thin film substrate often result in particle aggregation by van der Waals attraction. In the present work we studied 1-10 μm diameter Al2O3 spheres which were transformed from the amprphous state to the stable α phase.After the appropriate heat treatment, the spherical powders were embedded in as high a density as practicable in a hard EPON, and then microtomed into thin sections. There are several advantages to this method. Obviously, this is a rapid and convenient means to study the microstructure of serial slices. EDS, ELS, and diffraction studies are also considerably more informative. Furthermore, confidence in sampling reliability is considerably enhanced. The major negative feature is some distortion of the microstructure inherent to the microtoming operation; however, this appears to have been surprisingly small. The details of the method and some typical results follow.

Structural and electronic properties of defects in semiconductors

1995 ◽  
Vol 53 ◽  
pp. 4-5
Author(s):  
J.L. Batstone
Keyword(s):  
Semiconductor Device ◽  
Chemical Vapor ◽  
Misfit Strain ◽  
Organic Chemical ◽  
Extended Defects ◽  
Transmission Electron ◽  
Semiconductor Thin Films ◽  
Wide Range ◽  
Metal Organic ◽  
Film Substrate

The development of growth techniques such as metal organic chemical vapor deposition (MOCVD) and molecular beam epitaxy during the last fifteen years has resulted in the growth of high quality epitaxial semiconductor thin films for the semiconductor device industry. The III-V and II-VI semiconductors exhibit a wide range of fundamental band gap energies, enabling the fabrication of sophisticated optoelectronic devices such as lasers and electroluminescent displays. However, the radiative efficiency of such devices is strongly affected by the presence of optically and electrically active defects within the epitaxial layer; thus an understanding of factors influencing the defect densities is required.Extended defects such as dislocations, twins, stacking faults and grain boundaries can occur during epitaxial growth to relieve the misfit strain that builds up. Such defects can nucleate either at surfaces or thin film/substrate interfaces and the growth and nucleation events can be determined by in situ transmission electron microscopy (TEM).

Microstructural investigation of surface roughness in MBE-grown AlAs

1995 ◽  
Vol 53 ◽  
pp. 454-455
Author(s):  
R. Rajesh ◽  
R. Droopad ◽  
C. H. Kuo ◽  
R. W. Carpenter ◽  
G. N. Maracas
Keyword(s):  
Thin Film ◽  
Real Time ◽  
Growth Control ◽  
Native Oxide ◽  
Effusion Cell ◽  
Surface Oxide Layer ◽  
Microstructural Investigation ◽  
Mbe Growth ◽  
Film Substrate ◽  
And Control

Knowledge of material pseudodielectric functions at MBE growth temperatures is essential for achieving in-situ, real time growth control. This allows us to accurately monitor and control thicknesses of the layers during growth. Undesired effusion cell temperature fluctuations during growth can thus be compensated for in real-time by spectroscopic ellipsometry. The accuracy in determining pseudodielectric functions is increased if one does not require applying a structure model to correct for the presence of an unknown surface layer such as a native oxide. Performing these measurements in an MBE reactor on as-grown material gives us this advantage. Thus, a simple three phase model (vacuum/thin film/substrate) can be used to obtain thin film data without uncertainties arising from a surface oxide layer of unknown composition and temperature dependence.In this study, we obtain the pseudodielectric functions of MBE-grown AlAs from growth temperature (650°C) to room temperature (30°C). The profile of the wavelength-dependent function from the ellipsometry data indicated a rough surface after growth of 0.5 μm of AlAs at a substrate temperature of 600°C, which is typical for MBE-growth of GaAs.

Microstructure of YBa2Cu3O7-x thin films deposited by dc sputtering

1989 ◽  
Vol 47 ◽  
pp. 172-173
Author(s):  
O. Eibl ◽  
G. Gieres ◽  
H. Behner
Keyword(s):  
Thin Films ◽  
Cross Sections ◽  
Intermediate Layer ◽  
Amorphous State ◽  
Critical Currents ◽  
Dc Sputtering ◽  
State Process ◽  
Diffraction Patterns ◽  
Film Substrate ◽  
Substrate Temperatures

The microstructure of high-Tc YBa2Cu3O7-X thin films deposited by DC-sputtering on SrTiO3 substrates was analysed by TEM. Films were either (i) deposited in the amorphous state at substrate temperatures < 450°C and crystallised by a heat treatment at 900°C (process 1) or (ii) deposited at around 740°C in the crystalline state (process 2). Cross sections were prepared for TEM analyses and are especially useful for studying film substrate interdiffusion (fig.1). Films deposited in process 1 were polycristalline and the grain size was approximately 200 nm. Films were porous and the size of voids was approximately 100 nm. Between the SrTiO3 substrate and the YBa2Cu3Ox film a densly grown crystalline intermediate layer approximately 150 nm thick covered the SrTiO3 substrate. EDX microanalyses showed that the layer consisted of Sr, Ba and Ti, however, did not contain Y and Cu. Crystallites of the layer were carefully tilted in the microscope and diffraction patterns were obtained in five different poles for every crystallite. These patterns were consistent with the phase (Ba1-XSrx)2TiO4. The intermediate layer was most likely formed during the annealing at 900°C. Its formation can be understood as a diffusion of Ba from the amorphously deposited film into the substrate and diffusion of Sr from the substrate into the film. Between the intermediate layer and the surface of the film the film consisted of YBa2Cu3O7-x grains. Films prepared in process 1 had Tc(R=0) close to 90 K, however, critical currents were as low as jc = 104A/cm2 at 77 K.

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