Thick Free-standing Films Research Articles

Ferroelectric Order Evolution in Freestanding PbTiO3 Films Monitored by Optical Second Harmonic Generation.

The demand for low-dimensional ferroelectric devices is steadily increasing, however, the thick substrates in epitaxial films impede further size miniaturization. Freestanding films offer a potential solution by eliminating substrate constraints. Nevertheless, it remains an ongoing challenge to improve the stability in thin and fragile freestanding films under strain and temperature. In this work, the structure and ferroelectric order of freestanding PbTiO3 (PTO) films are investigated under continuous variation of the strain and temperature using nondestructive optical second harmonic generation (SHG) technique. The findings reveal that there are both out-of-plane and in-plane domains with polarization along out-of-plane and in-plane directions in the orthorhombic-like freestanding PTO films, respectively. In contrast, only out-of-plane domains are observed in the tetragonal epitaxial PTO films. Remarkably, the ferroelectricity of freestanding PTO films is strengthened under small uniaxial tensile strain from 0% up to 1.66% and well-maintained under larger biaxial tensile strain up to 2.76% along the [100] direction and up to 4.46% along the [010] direction. Moreover, a high Curie temperature of 630K is identified in 50nm thick freestanding PTO films by wide-temperature-range SHG. These findings provide valuable understanding for the development of the next-generation electronic nanodevices with flexibility and thermostability.

The Impact of Grain Growth on the Functional Properties in Room-Temperature Powder Aerosol Deposited Free-Standing (Ba,Ca)(Zr,Ti)O3 Thick Films

This study investigates the development of freestanding thick films (FSFs) of lead-free (Ba,Ca)(Zr,Ti)O3 and the role of grain growth on the electromechanical response. During deposition, room temperature powder aerosol deposition rapidly produces thick films with a nano-grain structure that limits the electromechanical properties. In this study, the films are removed from the substrate using a sacrificial buffering layer to avoid thermal treatment and allow for an initial as-processed state. Following this, FSFs were thermally treated at various annealing temperatures from 800 °C to 1400 °C to induce grain growth, which was characterized with scanning and transmission electron microscopy. X-ray diffraction revealed an increase in the crystallite size consistent with an increase in grain size and a decrease in internal residual stress. The temperature-dependent dielectric behavior and the large-field ferroelectric response were also characterized, revealing significant differences of the FSFs from the bulk properties.

Unleashing the potential of scalable, high-water vapor permeance graphene oxide membranes using electrospun supports

Dehumidification and dehydration technologies are projected to consume a substantial portion of the world's energy demand through the HVAC, and chemical processing industries. The development of highly permeable water-selective membranes represents a potential path to revolutionize these industries by drastically reducing their energy requirements. Selective layers based on graphene oxide (GO) have demonstrated the highest water vapor permeances to date, making GO a promising candidate for reducing the footprint and costs associated with commercial module development. However, most studies primarily focus on small-area membranes fabricated utilizing vacuum or pressure filtration, leading to either thick free-standing films or thin layers supported on model substrates such as anodic aluminium oxide. In this work, a casting approach is deployed to coat thin GO layers onto large-area membrane supports. In addition to the application of scalable methods, commonly used supports act as a significant bottleneck to the overall permeance. By designing highly porous (up to 92%) electrospun polystyrene supports, we demonstrate a 27% increase in overall permeance as compared to commercial Nylon and polyethersulfone supports even though these membranes have thicker GO selective layers. Despite the pore size in the electrospun material being larger than the GO flakes, the GO forms a selective layer via casting, and achieved water to nitrogen selectivity larger than 103.

Bubble-blowing-inspired sub-micron thick freestanding silk films for programmable electronics.

Thin film electronics that are capable of deforming and interfacing with nonplanar surfaces have attracted widespread interest in wearable motion detection or physiological signal recording due to their light weight, low stiffness, and high conformality. However, it is still a challenge to fabricate freestanding thin film substrates or matrices with only sub-micron thickness in a simple way, especially for those materials with metastable conformations, like regenerated silk protein. Herein, we developed a dip-coating method for the fabrication of sub-micron thick freestanding silk films inspired by blowing soap bubbles. Using a closed-loop frame to dip-coat in a concentrated silk fibroin aqueous solution, the substrate-free silk films with a thickness as low as hundreds of nanometres (∼150 nm) can be easily obtained after solvent evaporation. The silk films have extremely smooth surfaces (Rq < 3 nm) and can be tailored with different geometric shapes. The naturally dried silk films possess random coil dominated uncrystallized secondary structures, exhibiting high modulation ability and adaptability, which can be conformally attached on wrinkled skin or wrapped on human hair. Considering the methodological advantages and the unique properties of the obtained sub-micron thick silk films, several thin film based programmable electronics including transient/durable circuits, skin electrodes, transferred skin light-emitting devices and injectable electronics are successfully demonstrated after being deposited with gold or conducting polymer layers. This research provides a new avenue for preparing freestanding thin polymer films, showing great promise for developing thin film electronics in wearable and biomedical applications.

Production of thick Gd freestanding films for energy conversion applications

The use of magnetocaloric material in microelectromechanical energy conversion devices requires freestanding films with smooth surfaces to allow fast and efficient heat transfer. We present and discuss a mechanical method to produce freestanding thick Gadolinium films showing excellent magnetic properties, and high-quality surfaces on both sides. Polycrystalline Gd films have been prepared by sputtering on a silicon substrate with a thermally oxidized layer with different thicknesses. Films have been grown at 543 K. Tantalum and Tungsten have been used as buffer layers because of their corrosion resistance and of their thermal conductivity. The magnetic and surface properties of the freestanding films are presented, with special focus on the role of using different capping layers. Full characterizations of the three freestanding Gd films, including AFM measured surface roughness, XRD patterns, Curie temperature, thermo-magnetic curves, and maximum entropy change, are presented and discussed.

Manufacturing Poly(3,4‐Ethylenedioxythiophene) Electrocatalytic Sheets for Large‐Scale H2O2 Production

AbstractProducing thick films of conducting polymers by a low‐cost manufacturing technique would enable new applications. However, removing huge solvent volume from diluted suspension or dispersion (1–3 wt%) in which conducting polymers are typically obtained is a true manufacturing challenge. In this work, a procedure is proposed to quickly remove water from the conducting polymer poly(3,4‐ethylenedioxythiophene:poly(4‐styrene sulfonate) (PEDOT:PSS) suspension. The PEDOT:PSS suspension is first flocculated with 1 m H2SO4 transforming PEDOT nanoparticles (≈50–500 nm) into soft microparticles. A filtration process inspired by pulp dewatering in a paper machine on a wire mesh with apertures dimension between 60 µm and 0.5 mm leads to thick free‐standing films (≈0.5 mm). Wire mesh clogging that hinders dewatering (known as dead‐end filtration) is overcome by adding to the flocculated PEDOT:PSS dispersion carbon fibers that aggregate and form efficient water channels. Moreover, this enables fast formation of thick layers under simple atmospheric pressure filtration, thus making the process truly scalable. Thick freestanding PEDOT films thus obtained are used as electrocatalysts for efficient reduction of oxygen to hydrogen peroxide, a promising green chemical and fuel. The inhomogeneity of the films does not affect their electrochemical function.

X-ray ptychographic mode of self-assembled CdSe/CdS octapod-shaped nanocrystals in thick polymers

This work describes the application of X-ray ptychography for the inspection of complex assemblies of highly anisotropic nanocrystals embedded in a thick polymer matrix. More specifically, this case deals with CdSe/CdS octapods, with pod length L = 39 ± 2 nm and pod diameter D = 12 ± 2 nm, dispersed in free-standing thick films (24 ± 4 µm) of polymethyl methacrylate and polystyrene, with different molecular weights. Ptychography is the only imaging method available to date that can be used to study architectures made by these types of nanocrystals in thick polymeric films, as any other alternative direct method, such as scanning/transmission electron microscopy, can be definitively ruled out as a result of the large thickness of the free-standing films. The electron density maps of the investigated samples are reconstructed by combining iterative difference map algorithms and a maximum likelihood optimization algorithm. In addition, post image processing techniques are applied to both reduce noise and provide a better visualization of the material morphological details. Through this process, at a final resolution of 27 nm, the reconstructed maps allow us to visualize the intricate network of octapods inside the polymeric matrices.

Polyester-amide hyperbranched polymer as an interfacial modifier for graphene oxide nanosheets: Mechanistic approach in an epoxy nanocomposite coating

Graphene Oxide nanosheets (GO) are synthesized through modified Hummer’s method using expandable graphite. Consequently, the synthesized GO is surface functionalized by the aid of a polyester-amide hyperbranched polymer (HB) possessing hydroxyl end-groups. The characteristics of the surface modified GO are assessed by Fourier transform infrared spectroscopy (FT-IR), X-ray diffraction (XRD), UV-VIS spectroscopy and thermo-gravimetric analysis (TGA). The results show that HB molecules have been adsorbed on the GO surface and the d-spacing of the GO lamellae has been increased from 11.058 Å to 13.763 Å. Subsequently, the modified GOs are impregnated into an epoxy resin at various loadings and dispersed utilizing mechanical agitation and complementary sonication process. The dispersions are mixed and cured with stoichiometric amount of a polyamidoamine-based curing agent and applied on glass substrates to form 75–100 μm thick free-standing films. Viscoelastic behavior are then evaluated by dynamic mechanical analysis (DMA). The results show that storage (E’) modulus is enhanced and the glass transition temperatures (Tg) increases as GO and its modified counterparts are impregnated. Also, among the nanocomposites, coatings prepared by HB/GO = 0.5 and HB/GO = 1 show better improved properties indicating there exists an optimum ratio of GO/HB in which maximum surface modification has occurred.

Studies on ferroelectric and nanomechanical response of single-layered PZT thick film for energy harvester applications

We have made an attempt to fabricate free standing warpage free PZT thick films of 100 µm thickness by tape casting method. The poly crystalline nature and nanoscale polarization switching of free standing thick film were confirmed using X-ray diffraction technique and piezo force microscopy, respectively. The piezoelectric coefficient (d33) of 100 µm free-standing Pb(Zr0.56Ti0.44)O3 [PZT] thick film was calculated using double beam laser interferometer and found to be 400 pm/V. From the results, it indicates that free-standing PZT thick films are suitable candidate for miniaturization of harvesting device by directly bonding them on microsystem components for microelectromechanical systems (MEMS) applications.

Hydration States and Blood Compatibility of Hydrogen-Bonded Supramolecular Poly(2-methoxyethyl acrylate).

The practical use of the viscous liquid polymer, poly(2-methoxyethyl acrylate) (PMEA), was expanded from thin films with excellent blood compatibility to thick coatings and free-standing films without essentially sacrificing its blood compatibility. This was undertaken by creating multiple hydrogen-bonding polymer networks by introducing a functional methacrylic monomer bearing a 6-methyl-2-ureido-4[1H]-pyrimidone group in the PMEA backbone via free radical copolymerization. The hydrogen-bonded PMEA (H-PMEA) contained about 6 mol % of the functional monomer in the copolymer. These functional monomers as physical cross-links are distributed in the PMEA matrix with a Tg of -35 °C, making H-PMEA a solid rubber-like material with recoverable tensile strain. Additionally, mechanical tests revealed its tensile strength, and thermogravimetric analyses confirmed its higher thermostability. The dry and hydration states of H-PMEA were assessed by differential scanning calorimetry, contact angle, and atomic force microscopy measurements. Comparison with viscous PMEA was made. For the first time, we included PVC alongside PET, the surface we usually use as a negative control, in the platelet adhesion test with human blood, and found out that 1.5 times more platelets adhered onto the PVC surface than onto the PET surface, while H-PMEA proved to have a clear edge. Thus, H-PMEA may serve as a suitable replacement for polymers in products contacting blood as it shows potential for making free-standing films, thick coatings, implants, and articles with various geometries for the medicinal industry.

Synergy of elastic strain energy and electron wind force on thin film grain growth at room temperature

Grain growth in polycrystalline materials is commonly achieved with thermal annealing. Here, we explore an alternate athermal route through a synergy of electrical current and tensile strain at or near room temperature. Our experimental approach involves passing electrical current in 100 nm thick freestanding palladium films with about 5 nm initial grain size. The resulting Joule heating increases the temperature up to 470 K (homologous temperature of 0.25) at the middle section of the specimen. The massive heatsinks at the two ends of the specimen constrain them at the room temperature. At current density of 7 × 105 A/cm2, in-situ transmission electron microscopy shows more than two orders of magnitude grain growth in the high temperature regions and little growth at the room temperature regions. However, application of elastic strain (about 0.1%) dramatically increased the grain size to about 100 nm in a few seconds at the room temperature regions. Our finding suggests that the synergy of elastic strain energy and electrical current density may achieve grain growth in metallic materials even at the room temperature. Molecular dynamics simulation of this phenomenon reveals that the externally applied strain is localized at the grain boundaries in nanocrystalline metals, which promotes the effects of electron wind force on the grain boundary atoms. We conclude that a synergy of two or more stimuli can achieve grain growth at room or even lower temperatures.

Plastic crystal-incorporated magnesium ion conducting gel polymer electrolyte for battery application

Studies on a novel composition of magnesium ion conducting gel polymer electrolyte (GPE), comprising a solution of Mg-salt, magnesium trifluoromethanesulfonate (Mg-triflate or \(\hbox {Mg(Tf)}_{2})\) in a plastic crystal succinonitrile (SN), entrapped in a host polymer poly(vinylidenefluoride–hexafluoropropylene) (PVdF–HFP) was reported. Small amount of an ionic liquid, 1-ethyl-3-methylimidazolium trifluoromethanesulfonate (EMITf) was added to stabilize the GPE composition. The electrolyte possesses excellent dimensional integrity in the form of free-standing thick film, which offers the ionic conductivity of \(4 \times 10^{-3} \hbox { S } \hbox {cm}^{-1}\) at room temperature \({\sim }26{^{\circ }}\hbox {C}\). The electrochemical potential window of the electrolyte, observed from the linear sweep voltammetry, is determined to be \({\sim }4.1 \hbox { V}\). The magnesium ion conduction in the GPE film is confirmed from cyclic voltammetry, electrochemical impedance spectroscopy and dc polarization techniques. Different structural, thermal and electrochemical studies demonstrate the promising characteristics of the polymer film, suitable as electrolyte in rechargeable magnesium batteries. The potential of the GPE as electrolyte/separator was ascertained by fabricating a prototype magnesium battery of the configuration Mg:graphite composite \(\hbox {anode}/\hbox {GPE}/\hbox {MnO}_{2}\)-cathode. The specific discharge capacity of \(40 \hbox { mAh g}^{-1}\) (with respect to the \(\hbox {MnO}_{2}\) cathode material) was obtained at the first discharge. The cell shows charge–discharge performance for eight cycles with a substantial fading in capacity.

Improved ferroelectric and piezoelectric properties of tape casted free standing PSLZT thick films

We have synthesized Sr and La substituted Pb(1-x-3y/2)SrxLay(Zrz, Ti(1−z))O3 ceramics with x = 0.06, y = 0.01, 0.03, 0.05, z = 0.56 by solid-oxide route. Compacted discs were sintered at optimized temperature of 1280 °C for 2 h and its phase formation was confirmed by XRD analysis. Rietveld refinement confirmed that for the composition with y = 0.03 coexistence of tetragonal and rhombohedral phases comparatively closer to MPB. Dielectric and ferroelectric properties of discs were investigated thoroughly as a function of La content. Among the three compositions, ceramics with y = 0.03 (PSLZT) exhibit higher piezoelectric voltage coefficient (g33) of 30 mV.m/N which is relatively high compared to commercial PZT compositions. This composition was further utilized to fabricate free-standing piezoelectric thick films of 100 μm thickness using tape casting method with optimized slurry formulation. Warpage free PZT thick films with Pt electrodes were achieved with better density by co-sintering at 1060 °C for 2 h. Free standing thick films were characterized for their structural, microstructural, ferroelectric and piezoelectric properties and compared with bulk ceramic properties. The relative dielectric constant of 1250 with loss tangent of 0.02–0.03, remnant polarization of about 19 μC cm−2, piezoelectric charge coefficient of 300–325 pC/N and piezoelectric voltage coefficient up to 27 mV.m/N have been observed. These results indicate piezoelectric voltage coefficient of PSLZT free standing thick films is comparable to that of its bulk ceramic counterpart.

Incorporation of pervasive impurities on HVPE GaN growth directions

High crystallinity thick films with low free carrier concentration (≤1×1015/cm3) and low compensation are required for many GaN-based electronic device applications. It has been demonstrated that low pressure chemical vapor and molecular beam epitaxy techniques can reproducibility deposit homoepitaxial films with low residual impurity concentrations. However, their typical slow growth rates prevent their utilization for thick film growth. Presently, hydride vapor phase epitaxy is the sole method that can deposit films with residual impurity concentrations ≤5×1016/cm3 at hundreds of microns per hour growth rate. It is crucial to verify if this method can reproducibly deliver thick free-standing GaN films of high crystalline quality with exceptionally low and uniform free carrier concentration. X-ray diffraction, Raman scattering, and low temperature photoluminescence experiments were carried out on a number of samples prepared by dicing a free-standing wafer into several pieces perpendicular and parallel to the major growth directions; namely, c-plane {0001}, a-plane {11−20}, and m-plane {1−100}. SIMS depth profiles were employed to identify and quantify the concentration of the pervasive impurities. Spatial maps of a Raman line sensitive to free-carrier concentration were measured to determine the spatial distribution of the net impurity concentration. The reduced concentration of un-compensated shallow donors was also verified by low temperature electron paramagnetic resonance.

Novel low-temperature fabrication process for integrated high-aspect ratio zinc oxide nanowire sensors

The authors present a new low-temperature nanowire fabrication process that allows high-aspect ratio nanowires to be readily integrated with microelectronic devices for sensor applications. This process relies on a new method of forming a close-packed array of self-assembled high-aspect-ratio nanopores in an anodized aluminum oxide (AAO) template in a thin (2.5 μm) aluminum film deposited on a silicon substrate. This technique is in sharp contrast to the traditional free-standing thick film methods, and the use of an integrated thin aluminum film greatly enhances the utility of such methods. The authors have demonstrated the method by integrating ZnO nanowires onto the metal gate of a metal-oxide-semiconductor (MOS) transistor to form an integrated chemical field-effect transistor (ChemFET) sensor structure. The novel thin film AAO process uses a novel multistage aluminum anodization, alumina barrier layer removal, ZnO atomic layer deposition (ALD), and pH controlled wet release etching. This new process selectively forms the ZnO nanowires on the aluminum gate of the transistor while maintaining the remainder of the aluminum film intact for other integrated device components and interconnects. This self-assembled high-density AAO template was selectively formed in an ultrasmooth 2.5 μm thick aluminum layer deposited through e-beam evaporation without the electropolishing required in AAO template formation in traditional 100 μm thick free standing films. The resulting nanopore AAO template consists of nanopores of 90 nm in diameter and 1 μm in height at an aerial density of 1.3 × 1010 nanopores/cm2. This thin film AAO template was then filled with ZnO using ALD at 200 °C, forming polycrystalline ZnO nanowires inside the pores. The alumina template was then removed with a buffered NaOH solution, leaving free standing ZnO nanowires of 1 μm height and 90 nm diameter, offering an increase in 38× the surface area over a standard flat ZnO film for sensing applications. The aluminum film remains intact (unanodized) in nonselected regions of the device as well as underlying the ZnO nanowires, acting as the gate of the MOS transistor. The ZnO nanowires were characterized by scanning electron microscopy, energy-dispersive x-ray spectroscopy, and transmission electron microscopy to verify stoichiometry and crystal structure. Additionally, the response of a ZnO nanowire ChemFET was measured using ammonia as a target gas. I-V characterization and transient response to ammonia in the range of 25–200 ppm were examined. The ammonia response to the threshold limit value concentration of ammonia (25 ppm) shows a 56 mV shift in threshold voltage, an overall sensitivity of 14%, an 8 min response time, and a 27 min recovery period. The ZnO nanowire fabrication sequence that the authors present is accomplished at low-temperature (&amp;lt;200 °C) and can be accomplished selectively, making it readily amenable to integration with standard metal-oxide-semiconductor field-effect transistor processing as well as other microelectronic sensors such as surface acoustic wave devices. This new process has initially been demonstrated using ZnO, but is also adaptable to a variety of nanowire materials using appropriate deposition methods as well as selective nanowire release methods. This allows the potential to conveniently fabricate a variety of high-aspect ratio nanowire based microelectronic sensors for a range of applications.

Growth of free-standing wurtzite AlGaN by MBE using a highly efficient RF plasma source

Ultraviolet light emitting diodes (UV LEDs) are now being developed for various potential applications including water purification, surface decontamination, optical sensing, and solid-state lighting. The basis for this development is the successful production of AlxGa1−xN UV LEDs grown by either metal-organic vapor phase epitaxy (MOVPE) or molecular beam epitaxy (MBE). Initial studies used mainly sapphire as the substrate, but this result in a high density of defects in the epitaxial films and now bulk GaN or AlN substrates are being used to reduce this to acceptable values. However, the lattice parameters of GaN and AlN are significantly different, so any AlGaN alloy grown on either substrate will still be strained. If, however, AlGaN substrates were available, this problem could be avoided and an overall lattice match achieved. At present, the existing bulk GaN and AlN substrates are produced by MOVPE and physical vapor transport, but thick free-standing films of AlGaN are difficult to produce by either method. The authors have used plasma-assisted MBE to grow free-standing AlxGa1−xN up to 100 μm in thickness using both an HD25 source from Oxford Applied Research and a novel high efficiency source from Riber to provide active nitrogen. Films were grown on 2- and 3-in. diameter sapphire and GaAs (111)B substrates with growth rates ranging from 0.2 to 3 μm/h and with AlN contents of 0% and ∼20%. Secondary ion mass spectrometer studies show uniform incorporation of Al, Ga, and N throughout the films, and strong room temperature photoluminescence is observed in all cases. For films grown on GaAs, the authors obtained free-standing AlGaN substrates for subsequent growth by MOVPE or MBE by removing the GaAs using a standard chemical etchant. The use of high growth rates makes this a potentially viable commercial process since AlxGa1−xN free-standing films can be grown in a single day and potentially this method could be extended to a multiwafer system with a suitable plasma source.

Highly conductive freestanding graphene films as anode current collectors for flexible lithium-ion batteries.

The electrodes in lithium-ion batteries (LIBs) are typically films that are arranged on metal foil current collectors with a thickness of several tens of μm. Here, we report on the preparation of a thick free-standing graphene film synthesized by CVD as an alternative to Cu foil as an anode current collector. As a model system, MoS2 anodes with a flower-like morphology were anchored onto the surface of the thick graphene film. A hybrid and binder free anode without a conventional metal current collector exhibited an excellent capacity value of around 580 mAh/g (@50 mA/g) and reasonable charge/discharge cyclability. The work presented here may stimulate the use of graphene films as replacements for conventional current collectors and additive free electrode in LIBs.

OS1113 自立銅ナノ薄膜における疲労き裂発生の力学条件

The mechanical conditions of fatigue crack initiation were evaluated on roughly 500 nm thick freestanding copper films. Fatigue experiments and fatigue damage observations by using field emission scanning electron microscope (FESEM) and electron backscatter diffraction (EBSD) analysis revealed that an intrusion/extrusion formed parallel to a Σ3 twin boundary, and fatigue crack then initiated from this intrusion/extrusion. On the basis of these results, anisotropic elastic finite element method (FEM) analysis considering grain shape and crystal orientation around the fatigue crack initiation sites was conducted in order to evaluate local stress distribution near fatigue crack initiation sites. FEM analysis results indicated that fatigue crack initiation occurred at the slip system which penetrated the film in thickness direction. Moreover, number of cycles to fatigue crack initiation showed a tendency to increase as resolved shear stress decreased.

Low temperature viscoelasticity in nanocrystalline nickel films

Metals typically do not exhibit viscoelastic deformation. However, grain size effects can render grain boundaries in nanocrystalline metals viscous. Modeling the nanocrystallites as linear elastic elements embedded in a viscous network of grain boundaries, the overall response of nanocrystalline metals can be viscoelastic even at lower temperatures. To investigate this hypothesis, we measured viscoelastic response of 100nm thick freestanding nickel films at temperatures up to 425K. Experimental results show about two orders of magnitude lower viscosity compared to the bulk, suggesting that diffusion enhanced mobility of grain boundary atoms may be responsible for such pronounced viscoelasticity.

Effects of stress ratio on fatigue crack propagation properties of submicron-thick free-standing copper films

The dominant mechanics and mechanisms of fatigue crack propagation in ca. 500nm thick free-standing copper films were evaluated at the submicron level using fatigue crack propagation experiments at three stress ratios, R=0.1, 0.5 and 0.8. Fatigue cracking initiated at the notch root and propagated stably under cyclic loading. The fatigue crack propagation rate (da/dN) vs. stress intensity factor range (ΔK) relation was dependent on the stress ratio R;da/dN, increases with increasing R. Plots of da/dN vs. the maximum stress intensity factor (Kmax) exhibited coincident features in the high-Kmax region (Kmax⩾4.5MPam1/2) irrespective of R, indicating that Kmax is the dominant factor in fatigue crack propagation. In this region, the fatigue crack propagated in tensile fracture mode irrespective of the R value. The region ahead of the fatigue crack tip is plastically stretched by tensile deformation, causing necking deformation in the thickness direction and consequent chisel-point fracture. In contrast, in the low-Kmax region (Kmax<4.5MPam1/2), the da/dN vs. Kmax function assumes higher values with decreasing R; in this region, the fracture mechanism depends on R. At the higher R value (R=0.8), the fatigue crack propagates in the tensile fracture mode similar to that in the high-Kmax region. On the other hand, at the lower R values (R=0.1 and 0.5), a characteristic mechanism of fatigue crack propagation appears: within several grains, intrusions/extrusions form ahead of the crack tip along the Σ3 twin boundaries, and the fatigue crack propagates preferentially through the intrusions/extrusions.