Interfacial Field Research Articles

Theoretical Analysis on Thermo-Mechanical Bending Behavior of Timber–Concrete Composite Beams

In this study, an analytical approach is introduced for predicting the bending behavior of a timber–concrete composite (TCC) beam subjected to a mechanical load and a non-uniform temperature field, in which the orthotropy of timber as well as interfacial slip are taken into consideration. The analytical model addresses the non-uniform temperature field using Fourier series expansion based on the heat transport theory. The stresses and displacements of the TCC beam under the thermo-mechanical condition are governed by the thermo-elasticity theory, and the corresponding solution is derived analytically by solving a group of non-homogeneous partial differential equations. The proposed solution is in good agreement with the finite element solution and exhibits higher accuracy compared to the Euler–Bernoulli beam solution that relies on the assumption of transverse shear deformation and isotropy. An extensive investigation is carried out to analyze how the bending behavior of TCC beams is influenced by variations in interfacial shear stiffness and temperature field.

Revisiting a Cu-rich layer on the aluminum surface after twin-jet electropolishing

Twin-jet electropolishing (TJE) is a well-known method to prepare Cu-containing Al alloys for transmission electron microscopy (TEM) observation. Previous studies have reported a Cu-rich layer usually formed between Al matrix and outermost alumina layer at the electropolished Al surface. However, characteristics and formation mechanisms of the Cu-rich layer remain largely unexplored. Herein, configurations, formation process and property of the Cu-rich layer formed during TJE of Al alloys are revealed detailly employing aberration-corrected scanning TEM (STEM), STEM image simulations and first-principles calculations. The results reveal a new orientation relationship between the Cu-rich layer (θ’-Al2Cu) and Al matrix, which produces a low interfacial Al strain field. Formations of ∼2-nm-thick θ’ layer and its beneath ∼6-nm-thick Cu diffusion zone at the electropolished Cu-containing Al surface are mainly associated with traces of Cu in the electrolyte and anodization. Selective oxidation of elements, Cu-emitting alumina layer and spontaneous solute Cu segregation at the Al surface are also responsible for formations of the θ’ layer and Cu diffusion zone. Further study reveals that the θ’ layer behaves a strong self-healing ability after damaged by high-energy electron beam. The obtained results provide a potential insight into the surface modification of metals and alloys using electrochemical method.

On adhesively bonded joints with a mixed failure mode—An experimental and numerical study

Cohesive zone model (CZM) has been extensively used to study interfacial failure behaviors such as fracture of adhesively bonded joints (ABJs). Accurate and efficient identification of traction–separation law (TSL) in CZM signifies an important issue for design and analysis of adhesive structures. In this study, a modified Arcan fixture was developed and employed to investigate the mixed mode failure behaviors of ABJs for carbon fiber reinforced plastic (CFRP) substrates under a tensile-shear coupling load, in which the double cantilever beam (DCB) test was carried out to characterize fracture toughness for benchmark data. With the help of digital image correlation (DIC) technique, the interfacial displacement field was obtained. The virtual crack closure technique (VCCT) was adopted to decouple the mode mixture at different tension-shear angles of the Arcan specimens. Based on the traction–separation law for each mixed ratio of failure mode, a refined CZM was established. In this study, the Arcan and DCB specimens bonded with a flexible adhesive of 3M DP190 were prepared and tested. The experiments were carried out for the ABJs with two adhesive layer thicknesses of 0.3 mm and 1 mm, respectively, to investigate the influence of bonding thickness. Based on the extracted CZM parameters, a finite element (FE) analysis model was developed and validated with the experimental results. Unlike the traditional predetermined damage evolution law, a new CZM was established without a priori cohesive damage evolution; and the effectiveness of the proposed model for the TSL extraction was verified. By using this method, the mechanical response of the bonding interface under complex stress state was well predicted and the FE modeling of ABJ’s fracture was accurately achieved. The study is anticipated to gain new understanding and fundamental data on mixed failure mode, thereby enabling better design of ABJs for engineering applications.

Surface-immobilized cross-linked cationic polyelectrolyte enables CO2 reduction with metal cation-free acidic electrolyte

Electrochemical CO2 reduction in acidic electrolytes is a promising strategy to achieve high utilization efficiency of CO2. Although alkali cations in acidic electrolytes play a vital role in suppressing hydrogen evolution and promoting CO2 reduction, they also cause precipitation of bicarbonate on the gas diffusion electrode (GDE), flooding of electrolyte through the GDE, and drift of the electrolyte pH. In this work, we realize the electroreduction of CO2 in a metal cation-free acidic electrolyte by covering the catalyst with cross-linked poly-diallyldimethylammonium chloride. This polyelectrolyte provides a high density of cationic sites immobilized on the surface of the catalyst, which suppresses the mass transport of H+ and modulates the interfacial field strength. By adopting this strategy, the Faradaic efficiency (FE) of CO reaches 95 ± 3% with the Ag catalyst and the FE of formic acid reaches 76 ± 3% with the In catalyst in a 1.0 pH electrolyte in a flow cell. More importantly, with the metal cation-free acidic electrolyte the amount of electrolyte flooding through the GDE is decreased to 2.5 ± 0.6% of that with alkali cation-containing acidic electrolyte, and the FE of CO maintains above 80% over 36 h of operation at −200 mA·cm−2.

Bio-inspired interfacial micro-electric field of FeOCl nanosheets for rapid adsorption of perfluorocarboxylic acids (PFCAs)

In this study, a FeOCl adsorbent was demonstrated to rapidly remove perfluorocarboxylic acids (PFCAs). The unique coordination environment led to preferential dissociation of the Cl− in the FeOCl lattice by hydration, forming a high-intensity interfacial micro-electric field. The interfacial micro-electric field could apply an electric driving force to increase the external diffusion flux of PFCAs, thus achieving rapid adsorption (adsorption equilibrium time ∼10 min). In addition, the interfacial micro-electric field excited synergistic adsorption of multiple interactions (complexation, electrostatic interaction, and halogen-bonding interaction), being able to reach 277.01 mg/g for perfluorooctanoic acid (PFOA). Additionally, we developed a continuous flow column using FeOCl to demonstrate its potential for decontaminating drinking water with PFCAs at environmentally relevant concentrations. The FeOCl adsorbent exhibited a bed life of 125,000 BV upon reaching breakthrough concentration of breakthrough concentration of 70 ng/L in dynamic adsorption experiment, which outperformed conventional activated carbon F400D and ion exchange resin IRA67 adsorbents. Spent FeOCl absorbent could be easily regenerated in mild regeneration conditions and maintained a high PFOA removal in subsequent usage cycles. FeOCl demonstrated great potential in the purification of PFCA-contaminated water for household or municipal applications.

(Invited) Cations at a Solid-Liquid Interface: A Second Harmonic Generation Investigation

When an electrode contacts an electrolyte, an interfacial electric field forms. This interfacial field can polarize the electrode’s surface and nearby molecules, but its effect can be reversed by applying external potential. One method for quantifying this effect is the phase-sensitive second harmonic generation (PS-SHG) technique. We present our PS-SHG investigation of the Pt/water interface, where we examine the impact of the electrolyte chemistry on the electrical double layer (EDL). We will discuss how switching cations in alkaline electrolytes can affect the solid-liquid interface, in particular, the behavior of interfacial water. Our work provides a tool for quantifying the interfacial electric field at an electrode-electrolyte interface and shows the possibility of how cations can modify the EDL.

(Invited) Towards a Mechanistic Understanding of the Oxygen Evolution Reaction on Hematite: Operando Characterization of Band Bending and Interfacial Chemical Speciation Using Sum Frequency Generation Spectroscopy

Hematite is an attractive photoanode for the oxygen evolution reaction (OER) due to its cheap price, relatively small band gap, stability in alkaline solution and a valence band energy suitable for OER catalysis. However, insight into the OER mechanism, and thus the capability to rationally modify this material to optimize performance, is limited by the challenge in relating band bending, surface state population and chemical reactivity operando. Conventionally these issues are addressed by some combination of electrochemical impedance spectroscopy (EIS), photocurrent/voltage kinetics, and linear optical spectroscopies in the visible. While important, all of these approaches suffer from significant limitations: e.g. EIS and related techniques integrate over all charge transfer processes in the device while only those at the hematite/water interface are of interest (and thus require a challenging to validate model to quantify) and UV/Vis absorption measurements (whether steady-state or time resolved) are bulk-sensitive and probe spectrally broad features that are challenging to relate to surface structure.Sum Frequency Generation (SFG) spectroscopy is interface-specific by its symmetry selection rules, can straightforwardly probe interfacial chemical speciation if one of the two incident fields is in the infrared, and is sensitive to the amplitude of interfacial electric fields. These attributes make the technique particularly suitable for characterization of interfacial chemical speciation, double layer and space charge layer structure at the working electrode/electrolyte interface within thin-film spectroelectrochemical cells. Here I describe our recent efforts to characterize chemical speciation and interfacial field at a hematite/electrolyte interface, in the presence and absence of external illumination, as one moves from the Hematite flat band potential through the onset of the OER. Using vibrationally resonant SFG spectroscopy, at infrared wavelengths > 10 micron, we quantify the population of surface holes, i.e. Fe(IV)=0 groups, as the OER turns on. Concurrently we quantify the development of the space charge potential using non-resonant SFG. Recent work has argued, largely from current or optical transients in the visible under chopped illumination, that the OER on Hematite proceeds by a multi-hole mechanism. Because our approach allows for the simultaneous quantification of interfacial field and chemical speciation we directly address this mechanism and the circumstances under which it is expected to apply. More generally, the role of interfacial field in oxidation catalysis has been an object of much current interest. The approach described here – in which interfacial speciation and field can be quantified operando – offers an ability to explore this relationship not possible via any other combination of experimental approaches.

Research on AZ31 Mg alloy/22MnB5 steel pinless friction stir spot welding process and interfacial temperature field simulation

This paper discusses the successful welding of AZ31 Mg alloy to 22MnB5 high-strength steel using pinless friction stir welding (P-FSSW) to join dissimilar metals and reduce vehicle weight while maintaining strength and stiffness. P-FSSW eliminates fusion welding defects, ensuring good performance of Mg/steel welds. An orthogonal experimental design was adopted to comprehensively analyze welding parameters for determining the optimum P-FSSW process conditions. The study provides an in-depth examination of the interfacial layer formation between AZ31 Mg alloy and 22MnB5 steel, emphasizing the importance of Al for effective bonding in Mg alloys. Numerical simulation of the welding process's temperature field is verified by thermocouple measurements, confirming result accuracy. The study aims to optimize bonding of dissimilar materials and facilitate interfacial reactions for achieving high-performance welded joints. This comprehensive understanding of the P-FSSW process and interfacial layer formation holds great significance for lightweight construction in the automotive industry, contributing to reduced emissions and improved fuel efficiency.

Micro-/nano- bubbles ozonation for effective industrial wastewater remediation: From lab to pilot-scale application

Herein, micro-nano bubbles (MNBs) assisted ozonation process (O3/MNBs) was developed to enhance interfacial reactions for pollutant degradation. Notably, the removal of organic contaminants in O3/MNBs system was ultrafast over a wide pH range, much faster than that of macrobubbles ozonation process (O3/MaBs). Experimental observations suggested that MNBs can effectively accelerate O3 interfacial mass transfer and enrich abundant OH− from a bulk solution, thus inducing high concentrations of O3 and hyperaccumulation of OH− ions at gas-liquid interface. These interfacial characteristics of MNBs resulted in formation of a special interfacial reaction field, in which high concentration of O3 can be quickly activated by hyperaccumulated OH− ions along with assistance of energy released by MNBs collapse, ultimately boosting •OOH generation significantly. In addition, •OOH/•O2- performed as critical intermediates for the formation of •OH in O3/MNBs process. O3/MNBs system demonstrated favorable and steady performance during long-term advanced treatment of industrial wastewater (∼7 m3/h) with significantly lower ΔO3/ΔCOD (1.41) than O3/MaBs system (2.69). The pilot-scale demonstration of O3/MNBs efficiently degraded all four categories of organic contaminants according to EEM fluorescence spectra. The study demonstrated an environmentally-benign technology for effective treatment of industrial wastewater.

A coarse‐grained molecular dynamics study on the mechanical behavior of carbon nanotubes reinforced vulcanized natural rubber composites

AbstractIn the present study, coarse‐grained (CG) molecular models of carbon nanotubes (CNTs) strengthened vulcanized natural rubber (VNR) composites are constructed to systematically investigate the effects of length, inter‐tube cross‐linking, and polymer‐grafting of CNTs on the stress–strain behavior of VNR composites under uniaxial tension. The interfacial CG force field between CNTs and VNR is derived via the energy matching approach. The results demonstrate that increasing the length of CNTs is able to effectively enhance the mechanical performance of VNR composites, and the reinforcing efficiency increases gradually and tends to stabilize with increasing CNT length. Moreover, the cross‐linking and polymer‐grafting of CNTs are also effective approaches to significantly enhance the mechanical performance of VNR composites. The enhancement mechanism of CNTs is interpreted from the perspective of CNT networks, VNR networks, CNT‐VNR interface networks, and the interfacial load‐transfer behavior. Specifically, the dispersion of CNTs, the orientation of CNTs and VNR molecular chains, and the wrapping and interlocking behaviors between CNTs and the VNR matrix reveal a detailed structure‐mechanics relationship of CNTs‐reinforced VNR composites at the molecular level. These findings present theoretical instruction for the structural design of high‐performance rubber composites.Highlights A coarse‐grained model of carbon nanotube‐natural rubber composites is built. The composite network structures are quantitatively characterized. The length, cross‐linking, and grafting effects of carbon nanotubes are studied. The reinforcement mechanisms of carbon nanotubes are revealed.

Surface Modification in CsPb0.5Sn0.5I2Br Inorganic Perovskite Solar Cells: Effects of Bifunctional Dipolar Molecules on Photovoltaic Performance.

Inorganic tin-lead binary perovskites have piqued the interest of researchers as effective absorbers for thermally stable solar cells. However, the nonradiative recombination originating from the surface undercoordinated Sn2+ cations and the energetic offsets between different layers cause an excessive energy loss and deteriorate the perovskite device's performance. In this study, we investigated two thioamide derivatives that differ only in the polar part connected to their common benzene ring, namely, benzenecarbothioamide and 4-fluorophenylcarbothioamide (F-TBA). These two molecules were implemented as modifiers onto the inorganic tin-lead perovskite (CsPb0.5Sn0.5I2Br) surface in the perovskite solar cells. Modifiers that carry C═S and NH2 functional groups, equipped with lone electron pairs, can autonomously associate with surface Sn2+ through coordination and electrostatic attraction mechanisms. This interaction serves effectively to passivate the surface. In addition, due to the permanent dipole moment of the intermediate layer, an interfacial dipole field appears at the PCBM/CsPb0.5Sn0.5I2Br interface, reducing the electron extraction potential barrier. Consequently, the planar solar cell with an ITO/PEDOT:PSS/CsPb0.5Sn0.5I2Br/PCBM/BCP/Ag layered structure featuring an F-TBA surface post-treatment demonstrated a noteworthy power conversion efficiency of 14.01%. Simultaneously, after being stored for 1000 h in an inert atmosphere glovebox, the non-encapsulated CsPb0.5Sn0.5I2Br solar cells managed to preserve 94% of their original efficiency.

Immiscible displacement flows in axially rotating pipes

We experimentally study buoyant immiscible displacement flows in an axially rotating pipe, with varying flow parameters, such as the mean imposed flow velocity, density difference, pipe rotation speed, and pipe inclination angle. Via employing image processing and ultrasound Doppler velocimetry techniques, we analyze key flow features, including displacement regimes, interfacial instabilities, interfacial front velocities, and velocity and concentration fields. We find that immiscible displacement flows are distinguished by the emergence of one or two heavy fluid fronts, particularly depending on the rotation speed. Furthermore, our dimensional analysis reveals that the displacement flow is governed by four dimensionless parameters, including the Reynolds, densimetric Froude (or Archimedes), and Rossby numbers, as well as the pipe inclination angle. Using these dimensionless groups, we succeed in categorizing the main flow regimes as efficient and inefficient displacements. Moreover, we classify the interfacial regimes as stable, intermittently unstable, kinks, and separating interfacial patterns. Our analysis shows that the interfacial instabilities observed are indeed characterized by the Kelvin–Helmholtz instability. Our analysis of the velocity fields suggests remarkable differences between displacements in stationary and rotating pipes, especially in terms of the absence and presence of a countercurrent flow, respectively. Finally, our assessment of concentration fields using a Fourier transform approach provides a preliminary fundamental understanding of the characteristics of concentration waves and their corresponding amplitudes.

Ferromagnetism emerged from non-ferromagnetic atomic crystals

The recently emerged ferromagnetic two-dimensional (2D) materials provide unique platforms for compact spintronic devices down to the atomic-thin regime; however, the prospect is hindered by the limited number of ferromagnetic 2D materials discovered with limited choices of magnetic properties. If 2D antiferromagnetism could be converted to 2D ferromagnetism, the range of 2D magnets and their potential applications would be significantly broadened. Here, we discovered emergent ferromagnetism by interfacing non-magnetic WS2 layers with the antiferromagnetic FePS3. The WS2 exhibits an order of magnitude enhanced Zeeman effect with a saturated interfacial exchange field ~38 Tesla. Given the pristine FePS3 is an intralayer antiferromagnet, the prominent interfacial exchange field suggests the formation of ferromagnetic FePS3 at interface. Furthermore, the enhanced Zeeman effect in WS2 is found to exhibit a strong WS2-thickness dependence, highlighting the layer-tailorable interfacial exchange coupling in WS2-FePS3 heterostructures, which is potentially attributed to the thickness-dependent interfacial hybridization.

Optical Switching of Hole Transfer in Double Perovskite/Graphene Heterostructure.

Synergically combining their respective ultrahigh charge mobility and strong light absorption, graphene (Gr)/semiconductor heterostructures are promising building blocks for efficient optoelectronics, particularly photodetectors. Charge transfer (CT) across the heterostructure interface crucially determines device efficiency and functionality. Here we report that hole transfer processes dominate the ultrafast CT across strongly coupled double perovskite Cs2 AgBiBr6 /graphene (DP/Gr) heterostructures following optical excitation. While holes are the primary charges flowing across interfaces, their transfer direction, as well as efficiency, show a remarkable dependence on the excitation wavelength. For excitation with photon energies below the bandgap of DPs, the photoexcited hot holes in graphene can compete with the thermalization process and inject into in-gap defect states in DPs. In contrast, above-bandgap excitation of DP reverse the hole transfer direction, leading to hole transfer from the valence band of DPs to Gr. We further provide experimental evidence that increasing the excitation photon energy enhances CT efficiency for both below- and above-bandgap photoexcitation regimes, unveiling the positive role of excess energy in enhancing interfacial CT. The possibility of switching the hole transfer direction and, thus, the interfacial photogating field by tuning the excitation wavelength, provides a novel way to control the interfacial charge flow across a DP/Gr heterojunction. This article is protected by copyright. All rights reserved.

Role of interfacial electric field on thermal conductivity of In x Al1−x N/GaN superlattice (x = 0.17)

Abstract In this paper, we report the role of the interfacial polarization electrical field in thermal conductivity of In x Al1−x N/GaN superlattice. Thermal conductivity reduction is one recent effort to improve thermoelectric device efficiency because a small reduction in thermal conductivity can enhance the figure of merit significantly. Quantum size effect and thermal boundary resistance are responsible for this reduction. The theoretical results demonstrate that the interfacial polarization electric field modifies acoustic phonon properties through elastic moduli and phonon group velocity as a result of the inverse piezoelectric effect. This enhances phonon scattering and thermal boundary resistance. Consequently, the thermal conductivity of the superlattice is reduced. Room temperature thermal conductivity is found to be 2.94 (3.35) W m−1 K−1 for In x Al1−x N/GaN superlattice (x = 0.17) in the presence (absence) of an electric field.

Energy-Resolved Femtosecond Hot Electron Dynamics in Single Plasmonic Nanoparticles.

Efficient excitation and harvesting of hot carriers from nanoscale metals is central to many emerging photochemical, photovoltaic, and ultrafast optoelectronic applications. Nevertheless, direct experimental evidence of the energy-dependent femtosecond dynamics in ubiquitous tens-of-nanometer gold structures remains elusive, despite the potentially rich interplay between interfacial and internal plasmonic fields, excitation distributions, and scattering processes. To explore the effects of nanoscale structure on these dynamics, we employ simultaneous time-, angle-, and energy-resolved photoemission spectroscopy of single plasmonic nanoparticles. Photoelectron velocity and electric field distributions reveal bulk-like ballistic hot electron transport in different geometries, lacking any signatures of surface effects. Energy-resolved dynamics are measured in the 1-2 eV range and extrapolated to lower energies via Boltzmann theory, providing a detailed view of hot electron lifetimes within nanoscale gold. We find that particles with relevant dimensions as small as 10 nm serve as exemplary platforms for studying intrinsic metal dynamics.

Non-linear effective field theory simulators in two-fluid interfaces

Analogue gravity offers an approach for testing the universality and robustness of quantum field theories in curved spacetimes and validating them using down-to-earth, laboratory-based experiments. Fluid interfaces are a promising framework for creating these gravity simulators and have successfully replicated phenomena such as Hawking radiation and black hole superradiance. Recent work has shown that hydrodynamical instabilities on the interface between two fluids can capture features of the post-inflationary thermalisation of the Early Universe. In this study, we extend fluid dynamics methods to develop an effective field theory for the interface between two fluids, demonstrating the equivalence between the governing equations and a relativistic scalar field in an analogue spacetime. We also show that the interfacial height field serves as the analogue relativistic field even in a nonlinear, interacting field theory. We propose that these mathematical equivalences can be extrapolated to probe regimes where calculations are challenging or impractical. Our work provides a new framework for simulating far-from-equilibrium cosmological and gravitational scenarios in the laboratory.

Dual Optimization of Back Electrode Interface and Bulk via the Synergistic Passivation Effect of Niobium Pentoxide Enables Efficient Kesterite Solar Cells

As compared to the predecessor Cu(In,Ga)Se2 device, the current efficiency of kesterite Cu2ZnSn(S,Se)4 (CZTSSe) solar cells is still much lower mainly due to the known carriers recombination issue within interface and absorber bulk. In contrast to the majority of researches concerning recombination issues that focus on either single absorber bulk or interface passivation strategy, this study is pioneering in constructing synergistic passivation effects (SPE) to address the bulk and interface recombination issue simultaneously. By introducing a novel niobium pentoxide passivation layer into the back electrode interface (BEI), it is identified that SPE can be constructed due to Nb (& O) diffusion from Nb2O5 layer to absorber bulk and BEI during high‐temperature selenization. The chemical passivation effect is fulfilled via the intrinsic high resistance characteristic of Nb2O5 layer, and also through the NbOx passivation aiming to absorber bulk benefited from Nb (& O) diffusion. Meanwhile, the occupations of Nb (& O) on the Mo (& Se) sites induce a conduction type inversion in MoSe2 interfacial layer and create a preferable interface p+‐Mo(Se,O)2:Nb/CZTSSe, achieving an interfacial field passivation effect. Ultimately, the promoted absorber quality and improved charge carrier transportation from SPE contribute to the boost of device performance beyond 10% efficiency.

Tuning the Interfacial Electrical Field of Bipolar Membranes with Temperature and Electrolyte Concentration for Enhanced Water Dissociation

A coupled experimental and numerical study was performed for a fundamental understanding of the impact of operating conditions, i.e., temperature and electrolyte concentration, as well as interfacial abruptness, on the bipolar membrane (BPM) performance. A comprehensive multiphysics-based model was developed to optimize the operation condition and interfacial properties of BPM, and the model was used to guide the design and engineering of high-performing BPMs. The origin of the enhanced BPM performance at a high temperature was identified, which was attributed to the intrinsic reaction rate enhancement as well as the increase in electrolyte ionic conductivity. The experimentally demonstrated current density–voltage characteristics of BPMs clearly exhibited three distinctive regions of operation: ion-crossover region, water dissociation region, and water-limiting region, which agreed well with the multiphysics simulation results. In addition, the model revealed that a sharper interfacial abruptness led to improved BPM performance due to the enhanced interfacial electric field at the water dissociation region. The decrease of the electrolyte concentration, which increased the dielectric constant of the electrolyte, enhanced the interfacial electric field, leading to improved electrochemical performances. The present study offers an in-depth perspective to understand the species transport as well as water dissociation mechanism under various operation conditions and membrane designs, providing the optimal operation conditions and membrane designs for maximizing the BPM performance at high current densities.

Phase field modelling combined with optimization algorithm for maximizing the resistance in two-phase composites

Recently, the phase field modelling is widely used to model and simulate material damage. In present work, we present a framework of the topology optimization combined with the phase-field modelling with/ without interfacial damage for optimizing the damage resistance of the inclusion-matrix composites. The first phase field method with the interfacial damage described by the phase field variable d(x) and an interfacial phase field variable β(x), thus the crack occurs in the interaction between the bulk fracture and the interfacial one; the second phase field method without the interfacial damage describes the crack by using only a damage variable d(x), thus the crack initiates at the points where stress concentration occurs (damage only occurring in the phases). Extended bi-directional evolutionary structural optimization algorithm (BESO) is used to optimize the inclusion distribution in order to reduce its volume while keeping the fracture resistance value of the initial design unchanged. Moreover, the strain tensor orthogonal decompositions are implemented into the phase field methods to improve the inaccuracy in the mechanical behavior of the materials. We compare the inclusion optimal distribution, the crack propagation and the fracture resistance between the proposed models through several numerical examples.