Nanoscratch Experiments Research Articles

New Insights in the Nanomechanical Study of Carbon-Containing Nanocomposite Materials Based on High-Density Polyethylene

The investigation of new composite materials possessing low weight but not at the expense of their mechanical performance is of great interest in terms of reducing energy consumption in many industrial applications. This study is focused on the nanomechanical characterization of high-density polyethylene (HDPE)-based composite specimens modified with equal loadings of graphene nanoplatelets (GNPs) and/or multiwall carbon nanotubes (MWCNTs). Quasi-static nanoindentation analysis revealed the impact of the carbon nanofillers on the receiving of nanocomposites with higher nanohardness and reduced modulus of elasticity, reaching values of 0.146 GPa and 3.57 GPa, respectively. The role of the indentation size effect in elastic polymer matrix was assessed by applying three distinct peak forces. Nanoscratch experiments depicted the tribological behavior of the composite samples and inferred the influence of the carbon nanofillers on the values of the coefficient of friction (COF). It seems that the incorporation of 4 wt% GNPs in the polymer structure improves the scratch resistance of the material, resulting in a higher value of the exerted lateral force and therefore leading to the detection of a higher coefficient of friction at scratch of 0.401. A considerable pile-up response of the scratched polymer specimens was observed by means of in-situ SPM imaging of the tested surface sample area. The sway of the carbon nanoparticles on the composite pile-up behavior and the effect of the pile-up on the measured friction coefficients have been explored.

Unveiling the temperature-dependent deformation mechanisms of single crystal gallium nitride in nanoscratching

The surface grinding process of single crystal gallium nitride (GaN) is intricate, and localized high temperature generated during interactions between the workpiece and the abrasives on grinding wheel is inevitable. Elevated temperatures significantly affect the deformation mechanisms of GaN, which remains inadequately elucidated. In this study, nanoscratching experiments were systematically conducted on the (0001) plane of GaN single crystal across a temperature range up to 500 ℃, and the resultant deformation patterns were thoroughly characterized. The results indicate that temperature elevation delays the brittle-to-ductile transitions in GaN and enhance its anisotropy. Additionally, GaN exhibits increased plasticity as temperature rises, leading to distinct scratch-induced subsurface deformation patterns at varying temperatures: at room temperature, the thickness of the subsurface damaged layer is primarily influenced by the penetration depth of cross slips, whereas at 500 ℃, basal slipping predominantly defines the thickness of the subsurface damaged layer. The plastic deformation patterns at both room temperature and 500 ℃ mainly involve phase transition, polycrystal formation, slips, stacking faults, dislocations and lattice distortions. The discrepancies in deformations at varying temperatures were thoroughly investigated by transmission electron microscopy and molecular dynamics simulations, and the underlying mechanisms were elucidated.

Molecular dynamics simulation and experimental study of the material machinability characteristics and crack propagation mechanisms for fused silica double nanoscratches

Fused silica is a high-purity, hard and brittle, difficult-to-machine amorphous material that is widely used in the aerospace, optical instruments, semiconductors, microelectronics and other important fields. However, the influence of adjacent scratches on material deformation and subsurface damage during ultraprecision machining by abrasive particles is not well understood. This study aims to investigate the influence of micron-spaced double scratches on the deformation and damage for fused silica through molecular dynamics simulations and double nanoscratch experiments. An amorphous model of fused silica is created using a two-step simulated annealing method with three-directional periodic boundary conditions. Variable loaded double scratches with different nanometer distances are simulated on the surface of the model, and variable loaded double scratch experiments with varying micron-sized distances between scratches are conducted for fused silica wafers. The simulation and experimental results reveal that the deformation of fused silica during nanoscale double scratching involves both elastic and plastic deformation, and the surface and subsurface damage primarily consists of radial, lateral, Hertzian, and median cracks. The distance between the double scratches affects the load variation, surface and subsurface crack propagation, extent of material damage and removal rate, and surface roughness. Examination of the material subsurfaces using the FIB-TEM sample preparation and testing technique shows that the distance between the double scratches also influences the subsurface damage to the material.

Investigation of the nano and micromechanical performance of β-Ga2O3 epitaxial films on sapphire using nanoindentation

Beta-phase gallium oxide (β-Ga2O3) has attracted considerable attention because of its excellent properties as one of the emerging semiconductor materials. However, not only the fabrication of high quality β-Ga2O3 thin films on heterogeneous substrates is challenging, but there is also a lack of research pertaining to their mechanical properties. In this work, the mechanical properties of β-Ga2O3 epitaxial films of varying thicknesses on c-plane sapphire substrates fabricated via plasma enhanced chemical vapor deposition were investigated through nanoindentation and nano-scratch experiments. The β-Ga2O3 hetero-epitaxial thin films exhibit preferential orientation growth along the (−201) plane when deposited on the c-plane sapphire substrate. The elastic modulus, hardness, and fracture toughness of β-Ga2O3 films grown on sapphire substrates are 249.1 ± 14.1 GPa, 18.7 ± 0.9 GPa, and 1.822 MPa m1/2, respectively. The elastic-plastic behavior of β-Ga2O3 thin films with varying thicknesses is consistent. The critical loads for the elastic-plastic and plastic-brittle transitions are 9.4 ± 1.8 mN and 50.7 ± 2.7 mN respectively, while the scratch depths for the same are 91.8 ± 7.8 nm and 216.4 ± 10.1 nm, respectively. The critical adhesion and adhesive energy for the desquamation of the β-Ga2O3 film from the substrate are dependent on the thickness of the film. These results establish an experimental basis for understanding the mechanical behavior in the preparation and application of β-Ga2O3 thin films grown on sapphire substrates.

Dislocation slip mechanism and prediction method during the ultra-precision grinding process of monocrystalline silicon

Prediction of dislocation depth during ultra-precision grinding of monocrystalline silicon is a major challenge. To provide atomistic perspective, a single grain scratching molecular dynamics (MD) model of monocrystalline silicon is established to analyze the initiation and slip mechanism of dislocation. The simulation results show that the initiation of dislocations depends on the normal scratching force, and the dislocation length decreases with the decrease of scratching force and the increase of scratching velocity. Besides, the active slip system was identified by calculating Schmid factor, and the slip stress τ(111)[110],p (i.e. Peierls stress) of 2 GPa for ±1/2[110] dislocation on (1 1‾ 1) plane was obtained. Furthermore, a prediction model for dislocation depth was established based on the analysis of shear stress τ(111)[110]. Finally, a set of nano-scratch experiments were carried out, and the depth and slip direction of dislocation that close to the predicted were obtained by TEM method. This study provides a new method for predicting and controlling dislocation damage of monocrystalline silicon during ultra-precision grinding.

Comparative study of titanium and chromium transition layers on quartz substrates

As an important functional material, quartz needs to be firmly welded with electrodes through a transition layer—such as a Ti or Cr film—for practical applications. It is important to understand the microstructure of the transition layer and its interfacial structure with quartz to improve the reliability of corresponding devices. The present authors conducted a systematic comparative study on Ti and Cr thin films deposited on the surface of quartz. The distribution and valence of elements on the film–substrate interface were analyzed by X-ray photoelectron spectroscopy. The grain size and defect distribution in the films, as well as the morphology and composition distribution at the film–substrate interface, were characterized by transmission electron microscopy in combination with energy-dispersive spectrometry. The phase and preferred orientation of the films were measured by X-ray diffraction. The bonding force between the Ti and Cr films and quartz was investigated through nanoscratch experiments. Fracture analysis of the delaminated films was carried out by Auger electron spectrometry. Substantial chemical bonding was generated at the Ti–quartz interface, and there were no detectable micro-defects, resulting in high bonding strength. During deposition of the Cr film, there was substantial atomic peening, resulting in a nanoscale damage layer on the surface of quartz, facilitating delamination in scratch experiments.

Orientation-dependent plastic flow in nanoscratching of copper surfaces

The characterization of frictional behavior in ductile metals is a crucial aspect of materials science, as it relates to the plastic deformation of the material. However, due to the intricate dislocation evolution at the submicron/nanometer scale, the isolation of the basic plastic mechanisms remains challenging. In this study, nanoscratching technology is employed to investigate submicron/nanometer-level plastic deformation in individual grains of polycrystalline copper. To achieve this, a crystal plastic constitutive model for copper materials is developed by incorporating geometrically necessary dislocation effects. The calibration of the constitutive model is conducted with great precision and specificity, leveraging mechanical responses, surface accumulation morphology, and indentation size effects from nanoindentation experiments of 110-oriented single crystal copper. Through the combination of crystal plastic finite element simulation and nanoscratching experiments, the plastic flow of the material is thoroughly analyzed. The results demonstrate that the anisotropic scratching behavior is influenced by different orientations of individual grains, taking into account both statistical storage dislocations and geometrically necessary dislocations. The insights gleaned from this study offer a valuable contribution to our understanding of the plastic mechanisms of metals at a small scale, enhancing the design and performance of advanced materials for a wide range of applications.

Study on the brittle-plastic transition of YAG crystals based on nano-scratch experiments

YAG crystals are typically hard and brittle materials that are prone to be damaged during optical processing. In order to improve processing quality, it is necessary to avoid brittle damage as much as possible so that the material is removed in the plastic domain, so it is particularly important to study the critical conditions for the brittle-plastic transition of YAG crystals. The brittle-plastic transition of the (100) and (111) crystal faces of YAG crystals was investigated by variable load and constant load nano-scratch experiments. By analyzing the scratch morphology and friction-scratch distance curves, the critical load of brittle plastic transition for each crystal surface is obtained. The results show that the critical loads of (100) and (111) crystal faces for brittle-plastic transformation under variable load nano-scratch experiments are 113.575 mN and 84.05 mN, respectively, and the different critical loads of the two crystal faces are due to the discrepancy of surface energy. According to Griffith’s fracture theory, because the surface energy of (100) crystal face is higher, the energy required for brittle fracture of the crystal surface is higher, so the critical load of brittle-plastic transition is larger. Finally, the correctness of the critical load was verified by constant load nano-scratch experiments.

Study on the Removal Depth of the Surface Plastic Domain of Silicon-Modified Silicon Carbide

Silicon carbide (Sic) materials find wide-ranging applications in advanced optical systems within the aerospace, astronomical observation, and high-intensity laser fields. The silicon-modified Sic used in this study was created by depositing an amorphous silicon film on the surface of a Sic substrate using electron beam evaporation. Such hard and brittle materials often yield smooth surfaces when subjected to plastic removal. To address the issue of the removal depth of the surface plastic domain for silicon-modified Sic, we propose a method to calculate the indentation depth based on the critical load for the transition from plastic to brittle removal. We conducted a series of nanoindentation and nanoscratching experiments. The critical depth formula was validated through mechanical parameters such as hardness, elastic modulus, and fracture toughness, and the theoretical critical depth of the modified silicon layer was calculated to be 2.71 μm. The research results indicate that the critical load for obtaining the plastic-to-brittle transition point during the nanoindentation experiment is 886 mN, at which point the depth of plastic removal is 2.95 μm, closely matching the theoretical value. The measurements taken with an atomic force microscope near the critical load reveal a scratch depth of 3.12 μm, with a relative error of less than 5% when compared to the calculated value. This study establishes a solid foundation for achieving high-quality surface processing.

Feasibility and mechanism of atmospheric pressure cold plasma jet (APCPJ) assisted micro-milling of bulk metallic glasses (BMGs)

The unique microstructures of bulk metallic glasses (BMGs) provide them with excellent mechanical, physical, and chemical properties, having important applications in the fields of medical devices, military equipment, aerospace, etc. However, the superb mechanical properties also contribute to poor machinability of the BMGs. Currently, researchers have proposed to improve the machinability by single-point diamond turning, laser-assisted machining and ultrasonic vibration-assisted machining, but their plasticity and viscous flow remain unchanged, thus restraining further enhancement of surface quality. Atmospheric pressure cold plasma jet (APCPJ), which is rich in active particles, can effectively ameliorate material machinability by modulating material properties. In this paper, we propose to use the APCPJ to regulate the properties of BMGs, and carry out nanoindentation, nanoscratching, and micro-milling experiments to investigate the influence mechanisms of APCPJ on the material properties and cutting process. The results demonstrate that after modified by APCPJ, plastic deformability of the BMGs is improved due to the increase of free volume content; meanwhile, the viscous flow is inhibited. The micro-milling experiments indicate that under the conditions of feed rate Vf = 500 μm/s, spindle speed n = 30,000 rpm, and cutting depth ap = 5 μm, the improvement effect of APCPJ on the cutting process is relatively optimum. The surface roughness Ra of the Zr-based BMG and Ti-based BMG obtained by APCPJ are respectively 0.076 μm and 0.081 μm, which can be reduced by 37.7 % and 38.2 % compared with dry micro-milling. The cutting forces Fz in the direction of cutting depth are also reduced by 30.9 % and 23.3 %, respectively. The APCPJ-assisted micro-milling method proposed in this work may ameliorate the machining quality of BMGs and promote the application of BMGs and APCPJ-assisted machining technology in aerospace and precision machining.

Enhanced machinability of aluminium-based silicon carbide by non-resonant vibration-assisted magnetorheological finishing

Aluminium-based silicon carbides (SiCp/Al) have been widely used due to their inherent unique physical and mechanical properties. However, improving the surface quality is challenging as finishing cannot meet the requirements of removing the height differences caused by the SiC and aluminium phases. This study aims to investigate the effectiveness of non-resonant vibration-assisted magnetorheological finishing (NVMRF) in reducing the referred height differences and then to enhance the surface quality. Finite element modeling (FEM) and molecular dynamics (MD) simulations were utilized to analyze the influence of the vibration on the fragmented particles as well as the reduction of two-phase height difference. Nano scratch experiments reveal the removal mechanism of the SiC phase in NVMRF. A material removal rate (MRR) model considering the influence of the exerted forces of abrasive particles and the concept of micro-removal mechanism was established. When analyzing the machining results, it was found that the plastic removal in the SiC phase contributed to the NVMRF. Besides, it was verified that the vibration-induced tangential force effectively reduced the height difference. Although there is a slight discrepancy between the theoretical and experimental values of the finishing force within the experimental parameters, the consistent trend confirms the effectiveness of the proposed method. Finally, this research provides a valuable method for finishing the particle-reinforced metal matrix composites (PRMMCs).

Scratch-induced surface formation mechanism in C/SiC composites

Due to the extremely complex composition of C/SiC composites, their material removal mechanisms are significantly different from those of conventional single-phase ceramic materials. Therefore, the grinding removal mechanism of C/SiC composites must be investigated so that the components based on these composites can be machined efficiently and with low damage. In this paper, nano-scratch experiments with various cutting depths are carried out along different fiber orientations to simulate the material removal process in grinding and theoretically clarify the damage failure mechanism based on different cutting thicknesses. According to the assessment of surface and subsurface morphology of the various constituents in the scratch grooves regarding different fiber orientations, the multiple brittle breakage modes and surface integrity of carbon fiber are revealed. Green’s function is applied to establish a half-space anisotropic analytic elastic stress field considering the microstructural characteristics of material, and the crack nucleation and propagation principles during micro brittle fracture regime for nano-scratch experiment are elucidated based on the fracture mechanics and the maximum principal stress criterion. The formation mechanism of machined surface morphology in macro brittle removal process is investigated under the crack deflection effect at the weak interface and based on the elastic foundation beam theory. The related findings can provide a reasonable reference framework for optimizing the grinding technology, material and tool design regarding C/SiC composites.

A novel in-situ synthesized bioactive TaZrTi alloy by high energy laser beam for total knee arthroplasty application

Total knee arthroplasty is the gold standard treatment for end-stage knee osteoarthritis, which could significantly improve function and relieve pain for patients. However, the present materials and manufacturing approaches are dissatisfactory for knee implants. In the present work, a Ta60-Zr20-Ti20 (in wt%) coating was in-situ synthesized onto Ti6Al4V alloy via a high energy laser beam. The microstructure analysis indicated that α-Ta/ZrTi solid solution generated into body-centered cubic (bcc) grains in dimensions of several to hundred micrometers. The Ta-riched dendrites nucleated, grew, and expanded in the ZrTi matrix. The mechanical and biological properties of the in-situ synthesized TaZrTi sample are compared with the conventionally rolled Ti6Al4V, which is also the substrate alloy. The mean values of hardness and elastic modulus of in-situ synthesized TaZrTi tested by the nanoindenter, are 10.31 and 134.84 GPa, respectively. These results are harder than the Ti6Al4V counterpart (5.14 GPa) with a preferred slightly low elastic modulus (152.95 GPa of Ti6Al4V). Subsequently, the in-situ synthesized TaZrTi exhibits an excellent wear resistance demonstrated by nano-scratch experiments. In addition, the osteoblastic and endothelial cells were cultured in vitro to evaluate the biocompatibility of in-situ synthesized TaZrTi. The results show a comparable bioactivity and surface affinity compared with the rolled Ti6Al4V in 7 days. Briefly, this in-situ synthesized TaZrTi alloy is expected to shed light on load-bearing orthopedic applications to relieve the pain of patients, and the findings in this study provide an insightful understanding of laser additive manufactured TaZrTi alloy.

Investigation of cutting depth and contact area in nanoindenter scratching

Nanostructures are widely used in various industries. Nanoscratching is an important technique for fabricating nanostructures. The cutting depth in nanoscratching is a crucial parameter that is closely related to the normal force, material properties, and tip geometry. Current prediction models are only suitable for some specific processing conditions. To extend the scope of application of prediction model, a comprehensive model is proposed. In the developed model, the indenter tip is divided into three parts: a spherical crown, transition part, and pyramid base. Accordingly, a comprehensive contact model considering elastic recovery is developed in the edge-forward, face-forward and side-forward directions based on the indenter tip geometry. The computational results indicate that face-forward nanoscratching with a conventional cube-corner indenter has the smallest contact area compared to edge-forward and side-forward nanoscratching. It is noted that the established model can reduce the prediction error by more than 10% compared with the current models when the cutting depth is lower than the tip radius. The influence of the indenter geometry is analysed based on this model. The geometric shape of the indenter has a significant influence on the contact area, and the face angle of the pyramid is the key factor. The proposed model is validated by numerous nanoscratching experiments.

Damage characteristics and material removal mechanisms of CVD-SiC in nanotests: A comparative with sintered SiC

High sensitivity to crack and damage of chemical vapor-deposited silicon carbide (CVD- SiC) restricts the high-efficiency and low-damage manufacturing of CVD-SiC components. This paper aims to reveal the damage and material removal mechanisms of CVD-SiC after being scratched by diamond abrasives. The mechanical properties, scratching force, depth of ductile-brittle transition, residual depth and material removal damages of the CVD-SiC were discussed by the indentation, nano-scratching experiments, and compared with sintered silicon carbide (SSiC) ceramics. The results demonstrated that the mechanical properties of CVD-SiC are better than SSiC. In terms of hardness and fracture toughness, CVD-SiC demonstrates a 10– 20% and 20– 30% higher level of performance than SSiC, respectively. SSiC exhibits a brittleness level approximately 30% higher than that of CVD-SiC. SSiC ceramics are prone to crack deflection, intergranular fracture and transgranular fracture during indentation, indicating a higher propensity for brittle fracture in SSiC. The crack propagation in CVD-SiC is relatively regular. Both materials undergo the ductile, ductile-brittle transition and brittle stage, and the fluctuation variability of CVD-SiC material is notably lower than that of SSiC during the brittle stage. Compared with SSiC, the residual depth, groove width and transverse force of CVD-SiC are smaller under the same normal load. The critical depth of ductile-brittle transition of CVD-SiC is about 2 times that of SSiC in experimental and theoretical, indicating that CVD-SiC easily achieves ductile grinding. The mechanical properties, crack system and crystal structure of the CVD-SiC and SSiC materials cause the divergences in brittle removal. The radial-median crack system dominates the material removal of CVD-SiC. The disparity of deformations on the inside and outside of the crystal in the brittle stage leads to significant fluctuation variability of force and depth of SSiC during the scratching.

Tribochemical insights into the carbon film formation induced by metallic species derived from layered double hydroxide nanoadditives

Layered double hydroxides (LDHs) have demonstrated excellent tribological performance in various studies. However, there remains a fundamental knowledge gap concerning the chemical composition of tribofilms across the cross-section. In this study, we seek to elucidate this question by tribologically testing various binary LDHs. It was found that five out of eight LDHs, denoted as CoAl-, CoFe-, MgAl-, NiFe-, and ZnAl-LDHs could induce hierarchical protective tribofilms due to the formation of rigid oxide layers and in situ carbon-based films. The five tribofilms helped to reduce wear loss and friction by approximately 90% and 20%, respectively. Remarkably, the Co-based tribofilms showed the best antiwear performance because of the thick carbon tribofilm formation and the strong bonding at the metallic/tribo-oxide interfaces. The formation mechanisms of the carbon tribofilm and its characteristic nature were evaluated and revealed by scanning transmission electron microscopy and electron energy loss spectroscopy. Meanwhile, the intriguing nano-scale mechanical properties, i.e., the hardness and reduced elastic modulus of different tribofilms, were well-demonstrated by nanoindentation and nanoscratch experiments. The correlation between chemical structures and mechanical properties of the tribofilms derived from LDH lubricant additives was first conducted and discussed, unveiling the tribochemical and lubrication mechanisms between the LDHs and sliding surfaces.

Anisotropy origins of coefficient of friction and scratch hardness in nano scratching monocrystalline copper

The monocrystalline Cu material mechanical properties at the micro and nano scale show complex anisotropy and size effects. However, the anisotropy of scratch hardness and coefficient of friction (COF) in micro-nano scratching monocrystalline Cu has not been well explained. In this paper, we conducted the nano-scratching experiments and corresponding molecular dynamics (MD) simulation under ramp normal force mode along two representative crystal orientations thereby investigating the anisotropy origins of scratch hardness and COF. The research results indicate that, for monocrystalline Cu materials, the scratch hardness and COF are closely related to the atomic slip resistance Fslip caused by the activated <1 1 0> {1 1 1} slip systems.

Nanoindentation and nano-scratch testing on cement paste

Carbon nanotubes are an attractive reinforcement material for several composites. This is due to their inherently high tensile strength and high modulus of elasticity. This study focused on the nanomechanical characteristics of cement paste with and without short multi-walled carbon nanotubes (MWCNTs). The objective behind studying the nanomechanical properties of cement paste is to better understand the fundamental behaviour of cement at the nanoscale level. Cement paste is a complex material that consists of various phases, including cement hydrates, unhydrated cement particles and porosity. By studying the mechanical properties of cement paste at the nanoscale, researchers can gain insights into the mechanisms that govern the behaviour of this material. Following earlier tests, the amount of MWCNTs was kept constant (0.30% by weight of cement). The nanomechanical parameters explored included the localised Young's modulus and hardness. According to the test results, short MWCNTs increased the proportion of high-density calcium silicate hydrate in the cement paste. The nanomechanical properties (localised Young's modulus and hardness) of cement paste with short MWCNTs were found to be greater than those of cement paste without MWCNTs. According to nano-scratching experiments, the cement matrix with short MWCNTs was substantially more durable than the matrix without them.

Mechanical effect of abrasives on silicon surface in chemo-mechanical grinding

To obtain high-quality surfaces and subsurfaces of ground silicon wafers, chemo-mechanical grinding (CMG) for silicon has been developed by inducing chemical reactions into grinding. Chemical reactions between abrasives and silicon during CMG process have been proved in previous studies. The mechanical effect of abrasives in CMG process is not fully understood. To investigate abrasives’ mechanical effect on material removal and subsurface damage of silicon in CMG process, silicon nanoscratching experiments with CeO2 indenter under a progressive normal load were conducted, and microtopographies of scratch surface and subsurface were observed. For comparison, silicon nanoscratching experiments with diamond indenter were also conducted. Finite element models of silicon nanoscratching with CeO2 and diamond indenters were built to investigate the relationship between stress distribution and damage evolution of silicon. Experimental investigations and simulation results indicate that no obvious material removal of silicon or serious subsurface damage is generated by CeO2 indenter's mechanical action because the wear of CeO2 indenter leads to the release of the stress on silicon. Material removal of silicon during CMG process relies on chemical reactions between soft abrasives and silicon other than stress on silicon generated by soft abrasives.

Multilayer thin film metallic glasses under nanoscratch: Deformation and failure characteristics

A nanoscratch technique to investigate the deformation and failure characteristics of multilayer thin film metallic glasses (TFMGs) is described. Nanoscratch experiments were performed on Zr-based multilayer (bilayer) TFMGs deposited over hard substrates (Si, soda-lime glass). Layer pattern and modulation ratio greatly influence the thin films failures under nanoscratch. When compared with pattern (layer-1 / layer-2) = (Zr65 / Zr55), multilayer TFMGs with layer pattern = (Zr55 / Zr65) shows better tribological performances regardless of substrate type (Si or SLG) under the considered nanoscratch conditions. This study is beneficial to find appropriate combination of layer pattern and modulation ratio to ensure good adhesion between multilayer TFMG and substrate.