• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Effect of interface anisotropy on tilted growth of eutectics:A phase field study

    2022-10-26 09:53:26MeiRongJiang姜美榮JunJieLi李俊杰ZhiJunWang王志軍andJinChengWang王錦程
    Chinese Physics B 2022年10期
    關(guān)鍵詞:王志軍李俊

    Mei-Rong Jiang(姜美榮), Jun-Jie Li(李俊杰), Zhi-Jun Wang(王志軍), and Jin-Cheng Wang(王錦程)

    State Key Laboratory of Solidification Processing,Northwestern Polytechnical University,Xi’an 710072,China

    Keywords: tilted eutectics,interfacial energy anisotropy,multi-phase field model

    1. Introduction

    Tilted eutectic,[1–8]in which the growth orientation of eutectics deviates from the direction of the imposed temperature gradient (G) during directional solidification, is a common microstructure for eutectic alloys. As is well known,the mechanical properties of eutectic materials are closely related to its growth orientation. Thus, deep understanding the tilted growth of eutectic is very important for the better control of microstructure and improvement of properties.

    Like the tilted growth of dendritic arrays,[9–14]the growth of eutectic is governed by the temperature field, concentration field, and preferred crystal orientation of solidified phase. However, owing to the characteristics of the cooperative growth, the mixed solute diffusion near the front of solid–liquid interfaces, and the force balance at triple points,the tilted growth of eutectic is much more complex than that of dendrite arrays. In particular, typical eutectic patterns are composed of two solid phases with different preferred crystal orientations, which makes the tilted growth of eutectic more flexible and thus more complex in turn.

    Up to now,many efforts have been made to elucidate the formation of tilted eutectics.Several experimental and theoretical studies[3,4,6,15–21]suggested that the tilted growth of eutectic lamellae is dependent on the solidification dynamic behavior. It was well demonstrated that the solidification dynamic behavior often relies on initial conditions,[22,23]in which the initial lamellae spacingλ0is an important factor that influences the dynamics behavior. Whenλ0>aλm, whereais a constant related to the solidification conditions andλmis the minimum undercooling spacing,[24]a homogeneous tilt bifurcation (a tilted periodic state) was observed.[6]And a paritybreaking transition from the symmetric state to a tilted state has also been observed for the liquid–solid interface front profile during the tilted growth of eutectics.[19]Although these reports presented some explanations on the formation of tilted eutectics,the effect of the anisotropic interface energy on tilted growth of eutectics was not taken into account.

    With the development of eutectic solidification theory and research methods, the importance of interfacial energy anisotropy on tilted eutectics is well recognized.[7,25–34]From thein-situdirectional solidification experiments of transparent alloys, Caroliet al.[25]found that the tilted growth of lamellae and symmetry reflection of the solid–liquid interface front profile are broken,induced by interfacial energy anisotropies.Having made further theoretical analysis,they concluded that the anisotropy of solid–solid interface energy attempts to tilt lamellae into the orientation with the lowestα/βinterface energy,while the anisotropy of solid–liquid interface energy may modify the pinning angle forαphase andβphase at triple points. Thus,it can be assumed that the contribution of solid–solid interface energy anisotropy to eutectic growth is comparable to that of solid–liquid interface energy anisotropy. Akamatsuet al.[7]observed that the shape of solid–liquid interface in anisotropy-driven traveling lamellae patterns can be maintained to be approximately mirrorsymmetric by a modified directional solidification methodology called rotating directional solidification. To simplify the analysis, they further assumed that the shape of the solid–liquid interface is exactly symmetric; in other words, they omitted the effect of solid–liquid interface energy anisotropy on the formation of eutectics and concluded that the solid–solid interface anisotropy plays an important role in the forming of tilted eutectics.Based on Akamatsuet al.’s experimental results,Ghoshet al.[35–37]investigated the effect of solid–solid interface energy anisotropy on tilted growth of eutectics by using a multi-phase field model,and found that the anisotropy of solid–solid interphase energy can significantly affect the growth direction of eutectics. Tuet al.[38,39]further investigated the effect of solid–solid interphase energy anisotropy on lamellar eutectic morphology.They found that whenλ0is slightly larger thanλm,the lamellar morphology is mainly affected by the anisotropic interface energy of two solid phases, which results in the formation of a stable tilted lamellar pattern. However, whenλ0is significantly larger thanλm, the morphology is controlled by the variation ofλ0,resulting in the formation of an unstable mixed oscillation pattern.

    In summary, the investigations mentioned above[7,25–39]have demonstrated that the anisotropic interface energy plays a vital role in the forming of tilted eutectics. However, the effect of the solid–liquid interface energy anisotropy on the tilted growth of eutectics is often ignored. As mentioned earlier by Caroliet al.,[25]the effect of solid–liquid interface energy anisotropy on the pinning angle forαphase andβphase at triple points during eutectic solidification have been confirmed. As is well known,a small variation of the pinning angle can significantly influence the local force balance at triple points,which will sharply influence microstructure evolution.Thus, further investigations of the effect of solid–liquid interface energy anisotropy on the formation of tilted eutectics are urgently needed. And the mutual interaction between the anisotropic solid–solid interface energy and the solid–liquid interfaces energy is also a challenge.

    The phase field method,as a popular mesoscale numerical method,has been demonstrated as a powerful method in investigating microstructure evolution. Especially, the multiphase field model has been employed widely to study the eutectic solidification.[40–43]In this study,a multiphase field model was employed to investigate the effect and mechanism of solid–liquid interface energy anisotropy on tilted eutectics. Moreover,the interactions between solid–solid and solid–liquid interface energy anisotropy during the formation of tilted eutectics are also explored.

    2. Methods

    2.1. Phase field model

    In binary eutectic solidification,two solid phases(αandβ) are simultaneously formed from the melt (L). Thus, the multi-phase field model proposed by Kimet al.[40,44]was employed to study the tilted growth of eutectics in this study.Three order parametersφi(i=1,2,3)were introduced to distinguish different phases during eutectic solidification:φ1=1,φ2=0,φ3=0 represents the liquid phase,φ1=0,φ2=1,φ3=0 andφ1=0,φ2=0,φ3=1 denote the bulk phase ofαandβ,respectively. And 0<φi(i=1,2,3)<1 indicates the interface.

    A general free energy function description in this multiphase field model of a eutectic system includes the interfacial free energyfPand thermodynamic potentialfT,which can be written as

    whereξis the Lagrange multiplier for the restriction condition conserving the sum of phase fields at random point in the system. According to the variational principle, the governing equation of the phase-field variable can be described as

    whereT0is the initial solidification temperature,Gis the temperature gradient,andVis the pulling velocity.

    2.2. Interfacial energy anisotropy

    A two-fold symmetric interfacial energy anisotropy function[35–37]was used to characterize the effect of interfacial energy anisotropy on the formation of tilted eutectics. It can be expressed as

    whereγdenotes the interface energy;γ0the average interface energy;δthe anisotropy strength:δis set to be 0.005 when interface energy is anisotropic,and 0.0 when interface energy is isotropic;θRis the rotation angle,which is defined as the angle between the preferred crystal axis and the direction ofG;θis the angle between the interface normal direction and thexaxis as shown in Fig. 1(a). Figure 1(b) shows the schematic definitions of simulation parameters used in the prensent study,where theyaxis is parallel to theG. The tilt angle(θt)is the angle between the direction of the lamellae growth and that of theGdirection. Here, the direction, from the center position of the bulk phase (αorβ) at the beginning of solidification to that at the ending of solidification,is defined as the eutectic growth direction. Thus,θtcan be easily measured as shown in Fig.2(a). The other parameters in Fig.1(b)will be described in Section 3.

    Fig.1. (a)Definition of θ and θR,(b)definitions of θt,(c)initial eutectic patterns and boundary conditions.

    2.3. Parameters

    In this study,we took a binary eutectic alloy with a symmetric phase diagram[36]for example,and all parameters used in this simulation are listed in Table 1.

    Table 1. Parameters used in this simulation.

    All simulations were performed in a domain of 800dx×100dxwith a regular grid. The initial eutectic patterns were set to be a periodic lamellae with a size of 10dx×100dxat the bottom of the simulation cell and paralleled to theG. Periodic boundary conditions were imposed in thex-axis direction,indicating an infinite periodic cycle of lamellae along thexaxis,while adiabatic boundary conditions were used in theydirection to ensure the solute conservation in this direction[40]as shown in Fig.1(c).

    3. Results and discussion

    3.1. Effect of interface energy anisotropy on tilted growth of eutectics

    Figure 3 shows the evolution of eutectic morphologies under different interface energy conditions andθR=45°. The triple-point trajectories and the local force balance at the triple points, are also presented. From this figure, one can see that the lamellar growth direction aligns with the direction ofGwhen interface energy is isotropic. The pinning angle forαphase andβphase at the triple points are the same,i.e.,θα(61°)=θβ(61°). Here,the pinning angle is defined as the angle between the tangent of the solid–liquid interface and thexaxis at triple points. It can be determined from two steps:firstly calculating the value ofφy/φx;and then determining the pinning angle from the arctan functionθα=arctan(φαy/φαx),and the results are shown in Fig.2(b). The same pinning angles at triple points indicate that the solid–liquid interface ofL/αandL/βare symmetrical. Component force ofL/αinterfacial tension (σLα) andL/βinterfacial tension (σLβ) in thex-axis direction are equal, resulting in that the minimum interfacial tension of solid–solid interface is parallel to the direction ofG(yaxis). As is well known,during eutectic solidification, the lamellar growth direction always coincides with the direction of the minimum solid–solid interfacial tension.Therefore, the direction of eutectics growth aligns with that ofG, that is, non-tilted growth of lamellae occurs as shown in Fig. 3(a). However, when interface energy is anisotropic,the lamellar growth direction deviates from the direction ofGclearly. This indicates that the interface energy anisotropy has a significant effect on the lamellar growth direction.Generally,during eutectic solidification,when there exists anisotropic interface energy,the growth rates for different crystal planes are not the same,and the plane with a small interface energy will grow slow. The plane that grows fast will disappear,while the plane that grows slow is preserved in the crystal growth process. The difference in growth rate between different planes will induce the misalignment between the direction of minimum solid–solid interfacial tension and that ofG. Consequently,the tilted growth of lamellae is observed as shown in Figs.3(b)–3(d).And the force balance at triple points is shown at the bottom of Fig.3,where the dashed vectors represent the isotropic force vectors, the solid vectors are the anisotropic ones,andθα1,θβ1denote the deviation between the isotropic force vectors and the anisotropic ones. WhenL/αinterface energy is anisotropic, the force vector in the case of with anisotropy (the red solid arrow at the bottom of Fig. 3(b)) is different from that of without anisotropy (the red dashed arrow at the bottom of Fig. 3(b)). This variation of force vectorσL/αwill induce variations of other vectors(σL/β,σα/β)at triple points to maintain the force balance, resulting in the direction misalignment between the minimum solid–solid interfacial tension andGas shown at the bottom of Fig. 3(b).Similar processes are also observed whenL/βorβ/αinterface energy is anisotropic as shown by the force balance at bottom of Figs. 3(c) and 3(d), respectively. Moreover, it is found that the pinning angles forαphase andβphase at the triple points obviously are not the same even whenθtis small.This reveals that the symmetry of solid–liquid interface front profile is broken spontaneously when eutectic lamellae grows obliquely. However,noticeable discrepancies appear inθtunder different interfacial energy anisotropy conditions. From Figs.3(b)and 3(c),it can be seen clearly thatθt(1.4°)caused byL/αinterface energy anisotropy is smaller than that(6.4°)caused byL/βinterface energy anisotropy. This is because of different concentration distributions at the front ofL/αandL/β,which induces different driving forces in the cases ofαandβ. From Figs. 3(c) and 3(d), it can be observed thatθt(1.1°) caused byα/βinterface energy anisotropy is smaller than that (6.4°) caused byL/βinterface energy anisotropy.The reason for this phenomenon is that the direction deviation between the preferred orientation ofβand the direction ofGinduces the anisotropy of theL/βinterface energy, whereas the difference in the relative crystal orientation betweenαdirection andβdirection induces the anisotropy of theα/βinterface energy.

    Fig. 3. Lamellar patterns, interface trajectories, and local force balance at triple points under different interfacial energy conditions, where a indicates preferred crystal orientation and v is growth rate of lamellae, showing (a) isotropic interface energy, (b) L/α interface energy anisotropy,(c)L/β interface energy anisotropy,and(d)α/β interphase energy anisotropy.

    Figure 4 shows the curve ofθtversus θRunder different conditions of interfacial energy anisotropies. It is obvious that the whole trend of variation ofθtwithθRis almost the same when the interface energy is anisotropic,i.e. θtincreases initially and then decreases with the increase ofθR.However,obvious difference in variation trend between different anisotropic interface energy are also observed. When the solid–liquid(L/α,orL/β,orL/αandL/β)interface energy is anisotropic andθRis small,a very smallθtis observed. The preferred lamellae orientation deviates slightly from the direction ofG,resulting in small variations of the pinning angle for bothαphase andβphase at triple points. These small variations of the pining angle further result in a small deviation of the direction of minimum solid–solid interfacial tension from the direction ofG.On the contrary,a largeθtis observed whenα/βinterface energy is anisotropic andθRis small. In this case,the relative difference in crystal orientation between two solid phases is small.However,the preferred orientation direction ofα(aα)andβ(aβ)are the same,i.e.,all the preferred orientations are leftward as shown in Fig.5(a),indicating thataαandaβcan promote the tilted growth of lamellae.With the increase ofθR,θtincreases gradually,whether there exists interface energy anisotropy of solid–liquid or that of solid–solid,but the trend of its increase with solid–liquid interface energy anisotropy is obviously slower than with solid–solid interface energy anisotropy. WhenθRis large and solid–liquid interface energy is anisotropic, a largeθtis found. The preferred orientation of lamellae greatly deviates from the direction ofG, resulting in large variations of pinning angle forαphase andβphase at triple points,thus inducing a largeθtby maintaining the local force balance. In contrast, a smallθtis observed when solid–solid interface energy is anisotropic andθRis large. The relative difference in crystal orientation betweenαandβis very large. If the preferred orientation ofα(aα)remains unchanged, the direction ofaβchanges from left to right,and the preferred orientation ofaαandaβare opposite as shown in Fig. 5(b). Owing to the coupled growth of the two eutectic phases during solidification,the growth direction of eutectics tends to be parallel to the direction ofG. Similarly, whenθRis very large,θtis very small or even nearly 0°, with a solid–solid interface energy anisotropic. Whereas,when the solid–liquid interface energy is anisotropic andθRis very large,the preferred orientation of lamellae trends to be perpendicular to the direction ofG. Theoretically,θtshould be very large, but largeθtmust match largeθα1andθβ1to keep the force balance at triple points. It is a common fact that large angle variation needs larger energy than small one at triple point. If theθtis very large, the stable state cannot be obtained easily during solidification. Thus,θtwill decrease withθRincreasing further after achieving the maximum tilt angle.

    Fig. 4. (a) Curves of θR versus θt with different solid–liquid (L/α, L/β,or L/α and L/β)interface energy anisotropy(aniso), and(b)curves of θR versus θt with solid–liquid(L/α and L/β)interface energy anisotropy and α/β interface energy anisotropy.

    Fig.5. Phase-field patterns and schematics of crystal orientation of two-solid phases with different rotation angles: (a)θR=10° and(b)θR=60°.

    3.2. Tilted growth with both anisotropies of solid–liquid and solid–solid interface energy

    Figure 6 shows the eutectic patterns against rotation angle when bothL/α,L/β, andα/βinterface energies are anisotropic. It can be found that asθRincreases, the growth direction of eutectic lamellae gradually deviates from the direction ofG,i.e.,θtincreases gradually. However, with the further increase ofθR, the growth of lamellae changes from tilted to non-tilted growth. In addition, whenθR=20°, the solid–solid interphase is rough,i.e., a small disturbance appears. Through the stable growth rate of lamellae and concentration distribution at the front of the solid–liquid interface,it is demonstrated that this disturbance of the solid–solid interphase is not induced by the instable growth of eutectic. Thus,a conclusion can be obtained that anisotropic interface energy may induce a non-smooth solid–solid interface. This may result from a small adjustment of interlamellar spacing caused by the anisotropic force balance at triple point.

    Figure 7 shows the comparison between the simulated and the measured curves ofθRversus θt. It can be seen that whenL/α,L/β, andα/βinterface energies are anisotropic,theθRcorresponding to theθtmaxfrom phase feild simulations is approximately 30°,which accord well with the experimentalresults byAkamatsuetal.[7]However,theθRcorresponding totheθtmaxis20°when onlyα/βinterface energy is anisotropic, whereas it is 60°when bothL/αandL/βinterface energies are anisotropic.This reveals that the solid–liquid(L/α,L/β)and solid–solid(α/β)play vital roles in the forming of tilted eutectics. Moreover, whenL/α,L/β, andα/βinterface energies are anisotropic andθRis larger than 60°,θtis small, which is the same as the case ofα/βinterface energy anisotropy, indicating that the solid–solid interfacial energy anisotropy plays an important role in the tilted growth of lamellae,while the anisotropy of solid–liquid interface energy plays a less important role. However, the latter anisotropies can still influence theθRcorresponding to theθtmaxby affecting the local force balance at triple point.WhenL/α,L/β,andα/βare anisotropic andθRis small (less than 30°), a largeθtappears. This is also similar to the case ofα/βinterface energy anisotropy, suggesting that the tilted growth of lamellae is mainly controlled by the anisotropy ofα/βinterface energy. However, whenθRis approximately 40°, andL/α,L/β, andα/βinterface energies are anisotropic,θtcan be regarded as the superposition of contributions from the solid–liquid solid–solid interface energy anisotropy and the solid–solid interface energy anisotropy. This indicates that the tilted growth of lamellae is affected not only by solid–solid interface energy anisotropy, but also by solid–liquid interface energy anisotropy.

    Fig.6. Variation of lamellar patterns with rotation angle with interface energy being anisotropic for all interfaces(L/α,L/β,and α/β).

    Fig. 7. Comparison between simulated and measured curves of tilt angle(θt)versus rotation angle(θR)for different interface energy anisotropies.

    As is well known, the distributions of solute concentration near the front of solid–liquid interface greatly influence the microstructural evolution during solidification. To further explore the effect of anisotropic interface energy on the formation of tilted eutectic, the solute concentration distribution at the front of the solid–liquid interfaces are investigated. Studies[7,25]have shown that the concurrent or competitive contributions of the anisotropies of solid–liquid interface energy and solid–solid one on the formation of eutectic patterns may exist. This implies that the local force balance at triple point is highly complex when interface energy is anisotropic. However, the force balance at the triple point must be maintained during the eutectic solidification,i.e.the following equations need to be satisfied:

    When interface energy is isotropic (|σLα|=|σLβ|), the pinning angle ofα(θα)equals that ofβ(θβ)at triple points.According to Eq.(6),it can be obtained easily thatθtequals 0°,indicating that the component forcesσLαandσLβin thexdirection can be canceled out.And non-tilted growth of lamellae is observed. However, when interface energy is anisotropic,the pinning angleθα/=θβat triple point, indicating thatθtmust not be equal to 0°, and the component forcesσLαandσLβin thexdirection are not canceled out. Thus, there must be a force in thex-axis direction that drives the evolution of eutectic patterns, resulting in the tilted growth of lamellae.When eutectic patterns grow obliquely, the growth rate can be expressed asv=vn/cosθt, and the interlamellar spacingλ=λt/sinθt, wherevnis the normal growth rate of lamellae,andλtis the tangential interlamellar spacing as shown in Fig.1(b). Therefore,if the interface energy is anisotropic,the solution of the solute diffusion equation at the front of the interface is as follows:

    wherec∞is the actual composition far from the solid–liquid interface during eutectic solidification andλiis the half-width of theiphase.According to Eq.(7),the solute distributions at the front of the solid–liquid interface for the tilted(anisotropic interface energy)and non-tilted growth of lamellae(isotropic interface energy)are shown in Fig.8(a). It can be observed that the concentration gradients at the front of the interface with interfacial energy anisotropy are higher than without interfacial energy anisotropy. This indicates that the concentration disturbance near the solid–liquid interface with anisotropic interface energy is larger than without anisotropic interface energy. It should also be noted that no solution can be obtained from Eq. (7) if the tilt angle of lamellar is 0°and interface energy is anisotropic. However,in this case,the solution still exists, which is because only very small variation of pinning angle at triple point occurs to keep the force balance. The small variation will further induce different solute-diffusion rates on both sides of triple point,leading to a large concentration disturbance near the solid–liquid interface. Although this concentration disturbance is not enough to induce the tilted growth of eutectics,it can result in a larger concentration gradient at the front of the solid–liquid interface than the counterpart of isotropic interface energy. Thus, the same conclusion still holds true even when the tilt angle of lamellar is 0°and interface energy is anisotropic. Figures 8(b) and 8(c) show the solute concentration distributions near the solid–liquid interfaces obtained by phase-field simulations with and without anisotropic interface energy,respectively. The differences between the maximum solute concentrations ofα(cminα)at the front of the solid–liquid interface and the equilibrium concentrations in the liquid (ceqL) with and without anisotropic interface energy are shown in the lower right of Fig. 8. The differences between the minimum solute concentrations ofβ(cminβ)at the front of the solid–liquid interface andceqLwith and without anisotropic interface energy are also shown in the lower right of Fig.8. It can be clearly seen that the concentration gradient from phase-field simulation near the solid–liquid interface with isotropic interface energy is lower than with anisotropic one. This result is in good agreement with the theoretical solution of the solute diffusion equation, demonstrating the reliability of our phase field results. Moreover,when the interface energy is isotropic, the solute concentration distribution at the front of the solid–liquid interface is almost symmetrical along theyaxis. However, when the interface energy is anisotropic, it is almost symmetrical along the inclined growth axis. This symmetrical concentration distribution along the inclined growth axis is because different pinning angles at triple point will result in different solute diffusion rates on both sides of triple point. In addition, owing to theGandVexisting along theydirection,the symmetrical axis of solute concentration distribution near the solid–liquid interface that tends to be parallel to the direction ofGmay be observed as shown at point A of Fig. 8(c). Theoretically,this solute distribution near point A of Fig.8(c)cannot maintain stable tilted growth of lamellae. However,if the strength of interface energy anisotropy is sufficiently high, the effect ofGon solute concentration distribution is lower than that of anisotropic interface energy. The effect of concentration distribution near point A of Fig. 8(c) on the tilted growth of the lamellae can be ignored. Consequently, the stable tilted growth of lamellae can be obtained.

    Fig. 8. Concentration distributions near the interfaces: (a) theoretical prediction results with isotropic and anisotropic interface energies,respectively,(b)phase-field simulation results with isotropic interface energy,and(c)phase-field simulation results with L/α,L/β,and α/β interface energy anisotropies.

    It should also be noted that beside the interface energy anisotropy,the initial conditions,such as initial lamellar spacing,is also an important factor on the tilted growth of eutectics.In this study,however,we restrict ourselves to a range of regular lamellar eutectic formed by the initial lamellar spacing to investigate the effect of interfacial energy anisotropy on tilted growth of eutectic. As to the case of irregular eutectic structures,i.e.,the initial lamellar spacing is beyond this range,so,further studies are needed.interface energy, which is in good agreement with the theoretical analysis of the solute diffusion equation. Our findings not only elucidate the formation mechanism of tilted eutectics but also provide theoretical guidance for controlling the microstructure evolution.

    4. Conclusions

    Based on the multi-phase field model,the effect of solid–liquid or solid–solid energy anisotropy on the tilted growth of lamellae during eutectic solidification is investigated. And the mutual interactions between solid–liquid and solid–solid interface energy anisotropies are explored. The results show that both the solid–liquid and solid–solid interface energy anisotropies can induce the tilted growth of lamellae. When the anisotropy of solid–solid interface energy and solid–liquid interface energy are considered,the phase-field simulation results are in good agreement with the experimental results,indicating that the anisotropies of solid–solid and solid–liquid interface energies play important roles in tilted growth of eutectic. However,whenθRis small(less than 30°)or large(higher than 60°),the tilted growth of eutectic patterns is mainly controlled by the solid–solid interface energy anisotropy;whereas ifθRis between 30°and 60°, and the tilted growth is jointly affected by both solid–liquid interface energy anisotropy and solid–solid interface energy anisotropy. In addition, the results also demonstrate that the solute concentration gradient with anisotropic interface energy is higher than with isotropic

    Acknowledgements

    The authors thank the High-Performance Computing Center of Northwestern Polytechnical University, China, for the computer time and facilities.

    Project supported by the National Natural Science Foundation of China(Grant Nos.51871183 and 51571165).

    猜你喜歡
    王志軍李俊
    國畫:慕思春雨
    TSCL-SQL:Two-Stage Curriculum Learning Framework for Text-to-SQL
    Design method of reusable reciprocal invisibility and phantom device
    王志軍 油畫作品
    李俊杰作品
    大眾文藝(2021年5期)2021-04-12 09:31:08
    李俊儒論
    中華詩詞(2020年11期)2020-07-22 06:31:16
    李俊彥
    A Brief Analysis On How To Improve Students’ Participation Enthusiasm In Classroom
    李俊邑
    對腎病患者的臨終關(guān)懷(短篇小說)
    国产成人91sexporn| 欧美极品一区二区三区四区| 在线播放无遮挡| 国产精品一区二区性色av| avwww免费| 超碰av人人做人人爽久久| 人妻少妇偷人精品九色| 成人综合一区亚洲| 午夜福利在线观看免费完整高清在 | 免费大片18禁| 久久99热6这里只有精品| 国内精品久久久久精免费| 大香蕉久久网| 日韩精品有码人妻一区| 亚洲欧美日韩卡通动漫| 人妻久久中文字幕网| 欧美高清成人免费视频www| 色哟哟哟哟哟哟| 高清日韩中文字幕在线| 午夜免费激情av| 免费黄网站久久成人精品| 久久久久久久久久成人| 亚洲真实伦在线观看| 亚洲国产欧美人成| 非洲黑人性xxxx精品又粗又长| 久久久久久久亚洲中文字幕| 久久精品91蜜桃| 久久久久久久久大av| 69av精品久久久久久| 99热6这里只有精品| 美女被艹到高潮喷水动态| av.在线天堂| 久久99热这里只有精品18| 岛国在线免费视频观看| 中文字幕免费在线视频6| 成人永久免费在线观看视频| 深夜a级毛片| 18禁在线播放成人免费| 亚洲精品456在线播放app| av在线亚洲专区| 此物有八面人人有两片| 中国国产av一级| 51国产日韩欧美| 大又大粗又爽又黄少妇毛片口| 成人亚洲欧美一区二区av| 丰满的人妻完整版| 好男人视频免费观看在线| 国产91av在线免费观看| 免费av不卡在线播放| 日韩中字成人| 91久久精品国产一区二区成人| 免费看日本二区| 国产伦一二天堂av在线观看| 日韩精品有码人妻一区| 一个人观看的视频www高清免费观看| 成人二区视频| av在线亚洲专区| 国产三级在线视频| 一级二级三级毛片免费看| 少妇熟女欧美另类| 亚洲无线观看免费| 亚洲精品成人久久久久久| 日本av手机在线免费观看| 干丝袜人妻中文字幕| 国产精品不卡视频一区二区| 成人三级黄色视频| 天美传媒精品一区二区| 中出人妻视频一区二区| 人人妻人人澡人人爽人人夜夜 | 天天一区二区日本电影三级| 亚洲美女视频黄频| 嫩草影院入口| 国产色爽女视频免费观看| av福利片在线观看| 日韩欧美精品v在线| 国产精品国产三级国产av玫瑰| 亚洲国产欧美在线一区| 国产高清视频在线观看网站| 亚洲欧洲日产国产| 免费大片18禁| 六月丁香七月| 亚洲国产精品成人久久小说 | 亚洲人成网站在线播放欧美日韩| 99久久久亚洲精品蜜臀av| 欧美又色又爽又黄视频| 日本色播在线视频| 精品一区二区免费观看| 噜噜噜噜噜久久久久久91| 能在线免费观看的黄片| 色5月婷婷丁香| 亚洲自拍偷在线| 天美传媒精品一区二区| 内地一区二区视频在线| 成年女人看的毛片在线观看| 丰满乱子伦码专区| 久久草成人影院| 成人高潮视频无遮挡免费网站| 26uuu在线亚洲综合色| 卡戴珊不雅视频在线播放| 直男gayav资源| 成人亚洲欧美一区二区av| 日韩欧美三级三区| a级毛片a级免费在线| 麻豆乱淫一区二区| 岛国毛片在线播放| 美女国产视频在线观看| av女优亚洲男人天堂| 免费一级毛片在线播放高清视频| 欧美+亚洲+日韩+国产| 青春草亚洲视频在线观看| 婷婷色av中文字幕| 特级一级黄色大片| eeuss影院久久| 毛片一级片免费看久久久久| av黄色大香蕉| 精品人妻偷拍中文字幕| 国产黄片视频在线免费观看| 级片在线观看| 日韩一本色道免费dvd| or卡值多少钱| 国产精品蜜桃在线观看 | 深爱激情五月婷婷| 亚洲美女搞黄在线观看| 少妇高潮的动态图| 床上黄色一级片| 久久精品夜色国产| 国产精品一区二区三区四区免费观看| 我的女老师完整版在线观看| 在线免费观看不下载黄p国产| 日韩成人伦理影院| 99久久精品热视频| 久久久色成人| 国产精品99久久久久久久久| 国产蜜桃级精品一区二区三区| 国产亚洲精品久久久com| 啦啦啦韩国在线观看视频| 亚洲精品自拍成人| 色播亚洲综合网| 最近最新中文字幕大全电影3| 成人毛片60女人毛片免费| 中国国产av一级| 午夜福利成人在线免费观看| 女同久久另类99精品国产91| 一级毛片电影观看 | 99热这里只有精品一区| 精品一区二区三区人妻视频| 少妇裸体淫交视频免费看高清| 中文字幕免费在线视频6| 全区人妻精品视频| 超碰av人人做人人爽久久| 亚洲精品乱码久久久v下载方式| 插逼视频在线观看| 黄色视频,在线免费观看| 成人亚洲精品av一区二区| 老熟妇乱子伦视频在线观看| 哪里可以看免费的av片| 人妻久久中文字幕网| 亚洲电影在线观看av| 成年女人永久免费观看视频| 精品久久久久久成人av| 日韩av不卡免费在线播放| 综合色丁香网| 亚洲在线自拍视频| 国产 一区精品| 欧美成人一区二区免费高清观看| 国产精品不卡视频一区二区| 在线免费观看的www视频| 人妻少妇偷人精品九色| 婷婷精品国产亚洲av| 精品午夜福利在线看| 热99re8久久精品国产| 国产伦在线观看视频一区| www.色视频.com| 亚洲成人久久爱视频| 国产午夜精品论理片| 久久精品久久久久久噜噜老黄 | 真实男女啪啪啪动态图| 2022亚洲国产成人精品| 国模一区二区三区四区视频| 国产伦一二天堂av在线观看| 天堂√8在线中文| 国产精品一二三区在线看| 欧美不卡视频在线免费观看| 九九热线精品视视频播放| 欧美成人免费av一区二区三区| 国产熟女欧美一区二区| 综合色丁香网| 成人欧美大片| 久久精品国产亚洲av香蕉五月| 午夜爱爱视频在线播放| 婷婷精品国产亚洲av| 亚洲欧洲日产国产| 又爽又黄a免费视频| 大型黄色视频在线免费观看| 午夜福利在线观看吧| 精品久久久久久久人妻蜜臀av| 国产 一区精品| 插阴视频在线观看视频| 国产免费男女视频| 床上黄色一级片| 人妻久久中文字幕网| 12—13女人毛片做爰片一| av在线天堂中文字幕| 亚洲不卡免费看| 一进一出抽搐gif免费好疼| 一夜夜www| 国产大屁股一区二区在线视频| 日韩av不卡免费在线播放| 欧美成人a在线观看| 亚洲av中文字字幕乱码综合| 爱豆传媒免费全集在线观看| 精品日产1卡2卡| 国产高潮美女av| 亚洲欧美日韩卡通动漫| 亚洲成av人片在线播放无| 久久久成人免费电影| 国产精华一区二区三区| 乱码一卡2卡4卡精品| 成人高潮视频无遮挡免费网站| 只有这里有精品99| 国产视频首页在线观看| 亚洲最大成人手机在线| 国产精品永久免费网站| 老熟妇乱子伦视频在线观看| 国产一区二区在线观看日韩| 亚洲欧美日韩卡通动漫| 老司机福利观看| av天堂中文字幕网| 国产精品一及| 亚州av有码| 美女黄网站色视频| 91久久精品国产一区二区成人| 国产精品久久久久久久久免| 日日摸夜夜添夜夜添av毛片| 日韩精品青青久久久久久| 欧美性猛交黑人性爽| 亚洲欧美日韩高清专用| 99精品在免费线老司机午夜| 国内少妇人妻偷人精品xxx网站| 有码 亚洲区| 99热全是精品| 久久精品国产亚洲av涩爱 | 一本久久精品| 欧美极品一区二区三区四区| 人人妻人人澡人人爽人人夜夜 | 成人综合一区亚洲| 日韩欧美精品v在线| 99riav亚洲国产免费| 成人一区二区视频在线观看| 国内精品美女久久久久久| 免费不卡的大黄色大毛片视频在线观看 | 精品少妇黑人巨大在线播放 | 男人的好看免费观看在线视频| 91狼人影院| 草草在线视频免费看| 亚洲成a人片在线一区二区| 欧美日韩一区二区视频在线观看视频在线 | 国产亚洲欧美98| 国产成人精品久久久久久| 精品免费久久久久久久清纯| 亚洲在线观看片| 国内少妇人妻偷人精品xxx网站| 国国产精品蜜臀av免费| av女优亚洲男人天堂| 中国美白少妇内射xxxbb| 婷婷六月久久综合丁香| 好男人视频免费观看在线| 老师上课跳d突然被开到最大视频| 国产免费男女视频| av免费观看日本| 欧美xxxx黑人xx丫x性爽| 直男gayav资源| 国产午夜福利久久久久久| 国产高清视频在线观看网站| 美女 人体艺术 gogo| 国产成人一区二区在线| 亚洲欧美精品专区久久| 观看美女的网站| 中出人妻视频一区二区| 亚洲经典国产精华液单| 高清日韩中文字幕在线| 国内精品宾馆在线| 国产成人精品一,二区 | 国产老妇伦熟女老妇高清| 可以在线观看毛片的网站| 男女做爰动态图高潮gif福利片| 国产日本99.免费观看| av在线蜜桃| 能在线免费看毛片的网站| 搞女人的毛片| 一级二级三级毛片免费看| 欧美潮喷喷水| 国产黄a三级三级三级人| 亚洲不卡免费看| 少妇人妻一区二区三区视频| 久久精品久久久久久久性| 国产乱人视频| 最近手机中文字幕大全| av天堂中文字幕网| 亚洲高清免费不卡视频| 亚洲av二区三区四区| 搡老妇女老女人老熟妇| 色5月婷婷丁香| 久久久久久国产a免费观看| 亚洲在线自拍视频| 亚洲国产欧美在线一区| 天堂网av新在线| 久久精品国产亚洲av香蕉五月| 久久草成人影院| 蜜臀久久99精品久久宅男| 国产老妇伦熟女老妇高清| 国产熟女欧美一区二区| 激情 狠狠 欧美| 精品99又大又爽又粗少妇毛片| 国产黄片美女视频| 国产精品av视频在线免费观看| 69av精品久久久久久| 婷婷色av中文字幕| 人妻制服诱惑在线中文字幕| 精品一区二区免费观看| 夜夜夜夜夜久久久久| 成人亚洲欧美一区二区av| 久久精品国产清高在天天线| 亚洲国产精品成人久久小说 | 国产男人的电影天堂91| 麻豆av噜噜一区二区三区| 久久久久国产网址| www.色视频.com| 高清毛片免费观看视频网站| av专区在线播放| 婷婷色综合大香蕉| 夜夜爽天天搞| 精品国内亚洲2022精品成人| 菩萨蛮人人尽说江南好唐韦庄 | 久久精品夜色国产| 在线天堂最新版资源| 亚洲最大成人av| 日韩一区二区视频免费看| 国产精品一区二区三区四区久久| 精品久久久久久久久久免费视频| 亚洲一级一片aⅴ在线观看| 99久久成人亚洲精品观看| 精品国产三级普通话版| 亚洲第一电影网av| 日韩欧美一区二区三区在线观看| 亚洲天堂国产精品一区在线| 国产精品免费一区二区三区在线| 久久久久久久亚洲中文字幕| 又粗又硬又长又爽又黄的视频 | 草草在线视频免费看| 午夜精品国产一区二区电影 | 在线观看一区二区三区| 久久久久久九九精品二区国产| 激情 狠狠 欧美| 国产91av在线免费观看| 亚洲成人av在线免费| 亚洲欧洲日产国产| 亚洲一区高清亚洲精品| 小说图片视频综合网站| 国产亚洲91精品色在线| 中文字幕精品亚洲无线码一区| 日本黄色视频三级网站网址| 国产成人a∨麻豆精品| 国产精品人妻久久久久久| 亚洲激情五月婷婷啪啪| 91在线精品国自产拍蜜月| 内地一区二区视频在线| 边亲边吃奶的免费视频| 国产精品女同一区二区软件| 三级毛片av免费| 色综合色国产| 国产精品免费一区二区三区在线| 中文字幕精品亚洲无线码一区| 黄色一级大片看看| 哪里可以看免费的av片| 干丝袜人妻中文字幕| 日本-黄色视频高清免费观看| 欧美性猛交╳xxx乱大交人| a级一级毛片免费在线观看| 国产一区二区在线av高清观看| 欧美最黄视频在线播放免费| 综合色av麻豆| 亚洲在久久综合| 91在线精品国自产拍蜜月| 人妻制服诱惑在线中文字幕| 欧美成人a在线观看| 人人妻人人澡人人爽人人夜夜 | 免费观看人在逋| 国产免费男女视频| 色播亚洲综合网| 黄色日韩在线| 美女cb高潮喷水在线观看| 亚洲第一区二区三区不卡| 日韩亚洲欧美综合| 男人舔奶头视频| 欧美xxxx性猛交bbbb| 日韩精品青青久久久久久| 久久精品国产亚洲网站| 国产 一区精品| 人妻久久中文字幕网| 热99在线观看视频| 国产在线精品亚洲第一网站| 国产一区二区亚洲精品在线观看| 欧美日本视频| 狠狠狠狠99中文字幕| 成年版毛片免费区| 亚洲精品久久国产高清桃花| 国产极品精品免费视频能看的| 亚洲av免费高清在线观看| 亚洲欧美精品自产自拍| 国产真实乱freesex| 欧美+亚洲+日韩+国产| 国产精品一二三区在线看| 日本色播在线视频| 精品久久久久久久久久久久久| 日韩欧美三级三区| 看片在线看免费视频| 国产一区二区三区在线臀色熟女| 内射极品少妇av片p| 69人妻影院| 国产毛片a区久久久久| 亚洲婷婷狠狠爱综合网| 成人特级黄色片久久久久久久| 国产精品嫩草影院av在线观看| 午夜福利高清视频| 成年免费大片在线观看| 亚洲美女视频黄频| 日韩视频在线欧美| 黄色视频,在线免费观看| 日本熟妇午夜| 99riav亚洲国产免费| 国内精品美女久久久久久| 日韩 亚洲 欧美在线| 国产精品福利在线免费观看| 高清毛片免费看| 亚洲一级一片aⅴ在线观看| 青春草视频在线免费观看| 男女边吃奶边做爰视频| 搞女人的毛片| 能在线免费看毛片的网站| 身体一侧抽搐| 国产精品一二三区在线看| 少妇被粗大猛烈的视频| 一本精品99久久精品77| 有码 亚洲区| 国产午夜精品论理片| 日韩av在线大香蕉| 日本黄大片高清| 精品无人区乱码1区二区| 欧美日本亚洲视频在线播放| 内地一区二区视频在线| 国产精品一区二区三区四区久久| 在线播放无遮挡| 99国产精品一区二区蜜桃av| 午夜福利在线观看免费完整高清在 | 成人高潮视频无遮挡免费网站| 欧美xxxx黑人xx丫x性爽| av在线蜜桃| 国产日本99.免费观看| 看非洲黑人一级黄片| 亚洲第一电影网av| 精品久久国产蜜桃| 日韩国内少妇激情av| 欧美成人一区二区免费高清观看| 边亲边吃奶的免费视频| 久久精品国产99精品国产亚洲性色| 久久这里只有精品中国| 99精品在免费线老司机午夜| 一个人免费在线观看电影| 波野结衣二区三区在线| 1024手机看黄色片| 日韩欧美精品v在线| 女人十人毛片免费观看3o分钟| 婷婷亚洲欧美| 亚洲av免费高清在线观看| 日日啪夜夜撸| 人妻久久中文字幕网| 国产精品国产三级国产av玫瑰| 看片在线看免费视频| 搡老妇女老女人老熟妇| 你懂的网址亚洲精品在线观看 | 国产激情偷乱视频一区二区| 亚洲内射少妇av| 亚洲欧美日韩高清在线视频| 三级国产精品欧美在线观看| 亚洲欧美成人综合另类久久久 | 免费观看的影片在线观看| 婷婷精品国产亚洲av| 两个人视频免费观看高清| 亚洲成av人片在线播放无| 欧美性猛交黑人性爽| 联通29元200g的流量卡| 日韩欧美三级三区| 最近最新中文字幕大全电影3| 久久久成人免费电影| 日本一本二区三区精品| 亚州av有码| 男女那种视频在线观看| 日韩欧美三级三区| 久久久a久久爽久久v久久| 久久久久久伊人网av| 日本在线视频免费播放| 男人舔女人下体高潮全视频| 欧美极品一区二区三区四区| 3wmmmm亚洲av在线观看| 老司机福利观看| 成人国产麻豆网| 亚洲美女搞黄在线观看| 久久99热这里只有精品18| 久久精品国产鲁丝片午夜精品| 一区福利在线观看| 欧美另类亚洲清纯唯美| 男女下面进入的视频免费午夜| 国产成人精品一,二区 | 久久精品91蜜桃| 夜夜夜夜夜久久久久| 99热网站在线观看| 波多野结衣巨乳人妻| 久久韩国三级中文字幕| 日韩欧美 国产精品| 晚上一个人看的免费电影| 亚洲自偷自拍三级| 国产探花极品一区二区| 日韩亚洲欧美综合| 精品久久久久久久久亚洲| 国内精品久久久久精免费| 日韩成人av中文字幕在线观看| 欧美日韩一区二区视频在线观看视频在线 | 精品国内亚洲2022精品成人| 狠狠狠狠99中文字幕| 色哟哟哟哟哟哟| 91精品国产九色| 欧美bdsm另类| 日本在线视频免费播放| 日日撸夜夜添| 亚洲四区av| 日本三级黄在线观看| 亚洲欧美成人综合另类久久久 | 麻豆精品久久久久久蜜桃| 日韩av不卡免费在线播放| 久久人人爽人人片av| 国产极品天堂在线| 免费在线观看成人毛片| 欧美又色又爽又黄视频| 成人鲁丝片一二三区免费| 哪个播放器可以免费观看大片| 国产v大片淫在线免费观看| 亚洲成人中文字幕在线播放| 亚洲久久久久久中文字幕| 日韩欧美一区二区三区在线观看| 国产亚洲av片在线观看秒播厂 | 国产精品永久免费网站| 国产精品免费一区二区三区在线| 久久久精品大字幕| 男女边吃奶边做爰视频| 久久久久免费精品人妻一区二区| 在线观看美女被高潮喷水网站| 岛国毛片在线播放| 中国美女看黄片| 国产一级毛片七仙女欲春2| 人妻少妇偷人精品九色| 男女做爰动态图高潮gif福利片| 中文字幕av在线有码专区| 好男人视频免费观看在线| 99国产极品粉嫩在线观看| 国产 一区 欧美 日韩| 成人漫画全彩无遮挡| 国产午夜福利久久久久久| 国产精品蜜桃在线观看 | 国产大屁股一区二区在线视频| 深爱激情五月婷婷| 色哟哟哟哟哟哟| 国产91av在线免费观看| 国产精品爽爽va在线观看网站| 在线观看66精品国产| 美女高潮的动态| 天堂√8在线中文| 国产白丝娇喘喷水9色精品| 日韩 亚洲 欧美在线| av福利片在线观看| 啦啦啦啦在线视频资源| 国产国拍精品亚洲av在线观看| 国产精品国产高清国产av| 三级毛片av免费| 国产精品免费一区二区三区在线| 一个人看视频在线观看www免费| 男人和女人高潮做爰伦理| 精品久久久久久久久亚洲| 波多野结衣巨乳人妻| 午夜免费激情av| 五月伊人婷婷丁香| 赤兔流量卡办理| 一本久久中文字幕| 18禁黄网站禁片免费观看直播| 天堂av国产一区二区熟女人妻| 欧美成人一区二区免费高清观看| 亚洲成人精品中文字幕电影| 成人美女网站在线观看视频| 99久久无色码亚洲精品果冻| 欧美又色又爽又黄视频| 亚洲av成人精品一区久久| 卡戴珊不雅视频在线播放| 只有这里有精品99| 大又大粗又爽又黄少妇毛片口| 六月丁香七月| 亚洲成人精品中文字幕电影| 成人欧美大片| 国产成人影院久久av| 免费观看a级毛片全部| 赤兔流量卡办理| 久久九九热精品免费| 热99在线观看视频| 成人永久免费在线观看视频| 国产精品一区www在线观看| 99久久中文字幕三级久久日本|