鎂合金專業(yè)英語作業(yè).doc

Hot deformation behavior of Mg3Gd1Zn (GZ31) magnesium alloy was studied by hot compression tests over the temperature range of 300500 C under strain rates of 0.00010.1 s-1. This material exhibited typical broad single-peak dynamic recrystallization behavior followed by a gradual drop towards the steady state stress.The constitutive behavior of the tested alloy was studied by the power,exponential,and hyperbolic sine laws.The stress multiplier and the hyperbolic sine exponent were calculated as 0.024 MPa-1 and 3.42,respectively.The deformation activation energy was found to be about 173.2 kJ/mol,which is higher than the lattice self-diffusion activation energy of magnesium (135 kJ/mol).The latter can be ascribed to the presence of gadolinium, which shows the importance of rare earth elements in increasing the deformation resistance at high temperatures.在300500溫度范圍內(nèi)，0.00010.1 s-1的應(yīng)變速率下進(jìn)行熱壓縮試驗(yàn)研究Mg3Gd1Zn (GZ31)鎂合金的熱變形行為。該材料具有典型的寬單峰動(dòng)態(tài)再結(jié)晶行為其次是對(duì)穩(wěn)定狀態(tài)的壓力逐漸下降。用動(dòng)力，指數(shù)，雙曲正弦定律研究了被測(cè)合金的本構(gòu)行為。應(yīng)力乘子為0.024 MPa-1，雙曲正弦指數(shù)為3.42。變形激活能為173.2kJ/mol，高于鎂的晶格自擴(kuò)散激活能（135kJ/mol）。后者可以歸因于釓的存在，說明了稀土元素在增加高溫下變形抗力中的重要性。Due to their excellent combination of properties,magnesium alloys have attracted a considerable attention from automobile,aviation,electronic and communication industries 1. Currently,some of the best heat-resistant magnesium alloys,with good mechanical properties, at both ambient and elevated temperature,are those based on MgREZn system 2,3.The addition of gadolinium (Gd) can remarkably improve the heat resistance and high strength of magnesium alloys due to solution hardening and precipitation strengthening 4.由于其優(yōu)異的綜合性能，鎂合金已經(jīng)在汽車，航空，電子和通信行業(yè)引起相當(dāng)?shù)闹匾暋Ｄ壳?，一部分最?yōu)異的在環(huán)境溫度和更高的的溫度下具有良好機(jī)械性能的耐熱鎂合金，是基于MGREZn系統(tǒng)的。由于固溶強(qiáng)化和析出強(qiáng)化，釓（Gd）的加入能顯著提高鎂合金的耐熱性和強(qiáng)度。The activation of additional slip systems of the hexagonal closed packed (hcp) crystal structure at elevated temperatures normally increases the workability of Mg alloys, and hence, hot deformation processing can be considered as a viable route for shaping of these alloys 5,6.Moreover,hot working can significantly alter the as-cast microstructures by dynamic recrystallization (DRX) during deformation and static restoration processes between deformation passes,which in turn enhance the final properties of the material7,8.密排六方結(jié)構(gòu)的額外滑移系統(tǒng)在升高溫度下的激活通常會(huì)提高鎂合金的工藝性能，因此熱變形處理被看做是一種可行的鎂合金塑形方式。此外，熱處理可以在變形和靜態(tài)恢復(fù)之間的過渡過程中通過動(dòng)態(tài)再結(jié)晶顯著改變鑄態(tài)組織，從而提高材料的最終性能。Among the magnesium alloys containing rare earth elements,the Mg alloyed with Gd and Y is the most common system 921but the MgGdZn alloys are relatively new 22,23,and their hot deformation behaviors have not been investigated in detail. Hence,for future applications of MgGdZn alloys with high strength, high creep and corrosion resistance, a thorough knowledge of the structureproperty correlation is essential.In the current work, the hot deformation behavior of Mg3Gd1Zn (GZ31)magnesium alloy as a famous wrought alloy in this system is studied during hot compression test.含稀土元素的鎂合金中，釓鎂合金和釔鎂合金是最常見的，但是MgGdZn合金卻相對(duì)較新，其熱變形行為并沒有被詳細(xì)研究。因此，為了高強(qiáng)度，高抗蠕變和高耐腐蝕性的MgGdZn合金的未來應(yīng)用，對(duì)其結(jié)構(gòu)與性能相關(guān)性進(jìn)行深入了解是必不可少的。在當(dāng)前的工作中，研究了此合金系統(tǒng)中著名的鍛造合金Mg3Gd1Zn (GZ31)鎂合金在熱壓縮實(shí)驗(yàn)過程中的熱變形行為。2.Experimental and procedures2.1.Material and processing The Mg3Gd1Zn alloy was prepared from high purity Mg, Zn, and an Mg30Gd master alloy,which were melted in an electric furnace under a covering flux.The details of melting,alloying,and casting processes have been described elsewhere for a similar alloy 24 and will not be explained here.The homogenization treatment was performed at 500 C for 10h.The homogenized slab was then hot rolled with a light reduction of 10% at 480 C.The rolled slab was annealed at 400 C for 1 h and quenched in water.Hot compression test specimens with height of 8 mm and diameter of 5 mm with compression axis parallel to the transverse direction of rolling were prepared by machining.2. 實(shí)驗(yàn)步驟2.1.材料與加工 Mg3Gd1Zn合金是通過高純度鎂和在電爐內(nèi)覆蓋層下熔融的Mg30Gd中間合金制備。融化，合金化和鑄造工藝的細(xì)節(jié)已經(jīng)在另一種類似合金那里描述過了，這里不再解釋。均質(zhì)化處理是在500度下進(jìn)行10小時(shí)。然后將均質(zhì)板在480度下進(jìn)行10%小壓下量的熱軋。卷板在400度下退火一小時(shí)并且在水中淬火。最后用機(jī)械加工的方法制備用于熱壓縮實(shí)驗(yàn)的高8毫米，直徑5毫米的試樣，壓縮軸方向與軋制方向的橫向平行。2.2.Hot compression testCompression tests were carried out at temperatures of 300500 C under strain rates of 0.00010.1 s-1 using an MTS universal testing machine.Mica sheets were used as the lubricant at the interface between the anvil and the sample. Specimens were heated at a rate of 1.5 C/s to the desired deformation temperature and held for 15 min to eliminate thermal gradients.The specimens were then water-quenched immediately after compression to preserve the deformed microstructure.The microstructural observations were carried out on the longitudinal sections after etching in a solution containing 100 ml ethanol,2.5 g picric acid, 25 ml acetic acid and 25 ml water.2.2.熱壓縮實(shí)驗(yàn)壓縮實(shí)驗(yàn)使用MTS萬能試驗(yàn)機(jī)在300-500度和0.0001-0.1每秒的變形速率下進(jìn)行。云母片被用做鐵氈和樣品之間界面的潤(rùn)滑劑。樣品以1.5度每秒的速度加熱到要求的變形溫度，并且保持15分鐘以消除熱梯度。在壓縮后立即進(jìn)行水淬以保存變形組織。在100毫升乙醇，2.5克苦味酸，25毫升乙酸和25毫升水的混合溶液中侵蝕以后，對(duì)縱截面進(jìn)行微觀組織觀察。3.Results and discussion3.1.Hot flow behavior The true stressstrain curves obtained at different deformation temperatures and different strain rates are shown in Fig.1a.In many cases such as 400 C/0.01 s-1,the material exhibited typical broad single peak dynamic recrystallization behavior,followed by a gradual fall toward the steady-state stress 8.However,for some deformation conditions,the imposed strain is insufficient for the completion of DRX and the steady-state condition is not attained.Fig.1 b and c reveal that the lower temperatures and higher strain rates will increase the flow stress of the GZ31 magnesium alloy,which is consistent with the general behavior of materials in hot working.The drop in flow stress with deformation temperature may be attributed to the increase in the rate of restoration processes and decrease in the strain hardening rate.In the same way,the increase in the flow stress with strain rate can be ascribed to the decrease in the rate of restoration processes and increase in strain hardening rate 25.However,in some samples such as 350 C/0.01 s-1,an unexpected steep loss in flow stress occurred due to the intense deformation twinning and shearing as can be seen in Fig.2b.As a result of this strange behavior,the flow stress of this sample falls under that of 400 C/0.01 s-1 by continued straining.3. 結(jié)果與討論3.1.熱流動(dòng)性不同變形溫度和變形速率下獲得的實(shí)際應(yīng)力應(yīng)變曲線如Fig.1a圖所示。在很多情況下，例如溫度400度，變形速率0.01每秒，材料表現(xiàn)出典型的寬單峰的動(dòng)態(tài)再結(jié)晶行為，其次是對(duì)穩(wěn)態(tài)應(yīng)力的逐漸下降。不過，在某些變形條件下，施加壓力不足以完成動(dòng)態(tài)再結(jié)晶，且達(dá)不到穩(wěn)態(tài)條件。圖Fig.1 b和c顯示較低的溫度和高應(yīng)變速率將增加GZ31鎂合金的流動(dòng)應(yīng)力，這與材料熱加工的通常表現(xiàn)一致。流動(dòng)應(yīng)力隨變形溫度的下降而下降可以歸因于恢復(fù)過程速率的上升和應(yīng)變硬化速率的下降。同樣的，流動(dòng)應(yīng)力隨變形速率的上升可以歸因于恢復(fù)過程速率的下降和應(yīng)變硬化速率的上升。不過在某些樣品如300度，0.01每秒下，由于強(qiáng)烈的孿生和剪切變形，流動(dòng)應(yīng)力發(fā)生了意想不到的大幅度降低，正如圖Fig.2b中所示。由于這種特殊的現(xiàn)象，這種試樣的流動(dòng)應(yīng)力在持續(xù)變形下跌落到了400度，0.01每秒的試樣之下。3.2.Microstructure evolution Some representative micrographs of the GZ31 alloy after casting are shown in Fig.3. The as-cast microstructure of Fig.3a shows the typical dendritic microstructure and Fig.3b reveals that the as-cast microstructure includes coarse grains with eutectic -Mg5Gd phase between dendrite arms 26.Most of the phase exists as network structure,while some particles are distributed inside grains.The presence of the phase was subsequently verified by XRD patterns as shown in Fig.4.After homogenization at 500 C for 10 h,the dendritic structure disappears as shown in Fig.5 and the average linear intercept length was determined as 300 m.The homogenized plate was hot rolled and then annealed followed by water quenching. The resulting microstructure is shown in Fig.6,showing equiaxed grains with considerable amount of mechanical twins.This is the initial microstructure form which the samples for hot compression were machined.3.2.組織演變GZ31合金鑄造后一些代表性的顯微照片如圖Fig.3所示。Fig.3a中的鑄態(tài)組織顯示了典型的樹枝狀結(jié)構(gòu)，F(xiàn)ig.3b顯示，鑄態(tài)組織包含了枝間是-Mg5Gd共晶相的粗晶粒。大部分的相以網(wǎng)狀結(jié)構(gòu)存在，而一些顆粒散布在晶粒內(nèi)。如圖Fig.4所示，相的存在隨后通過XRD圖譜被驗(yàn)證。在500度下均質(zhì)化處理10小時(shí)后，樹枝狀結(jié)構(gòu)消失，如表Fig.5所示，平均線性截距長(zhǎng)度被確定為300微米。均質(zhì)鋼板熱軋之后進(jìn)行退火然后水淬，由此產(chǎn)生的微觀結(jié)構(gòu)展示在圖Fig.6，顯示了有相當(dāng)數(shù)量機(jī)械孿晶的等軸晶粒。這是熱壓縮變形試樣經(jīng)機(jī)械加工后的初始組織形式。 Some representative micrographs of the GZ31 alloy after hot deformation are shown in Fig.7.It is apparent that the necklace DRX (Figs.7 and 2a)is responsible for significant grain refinement(Fig.7b).This grain refinement ability can be ascribed to the fact that in single peak DRX,nucleation occurs essentially along existing grain boundaries and the growth of each grain is stopped by the concurrent deformation as a result of increasing the dislocation density of the new grains and reducing the driving force for their further growth 27.The DRX process continues until the completion of the first layer of necklace to cover the entire grain boundary.Afterwards,the subsequent layers form at the recrystallization front between the recrystallized and unrecrystallized portions to continue the recrystallization process.GZ31合金經(jīng)過熱變形后的一些有代表性的顯微照片顯示在圖Fig.7。很明顯，這些再結(jié)晶結(jié)構(gòu)（圖Figs.7和2a）是負(fù)責(zé)顯著細(xì)化晶粒的（圖Fig.7b）。這種細(xì)化晶粒的能力可以歸因于以下事實(shí)：?jiǎn)畏宓膭?dòng)態(tài)再結(jié)晶中，成核的發(fā)生基本沿著現(xiàn)有的晶界，并且并行變形會(huì)阻止每個(gè)晶粒的生長(zhǎng)，因?yàn)椋ㄟ@）增大了新晶粒的位錯(cuò)密度并且減小了（晶粒）進(jìn)一步生長(zhǎng)的驅(qū)動(dòng)力。動(dòng)態(tài)再結(jié)晶過程繼續(xù)下去，直到（ ）再結(jié)晶第一層覆蓋整個(gè)晶界。隨后，后續(xù)層在再結(jié)晶區(qū)和非結(jié)晶區(qū)之間的再結(jié)晶區(qū)前沿形成，繼續(xù)進(jìn)行再結(jié)晶過程。3.3.Grain refinement Since DRX involves repeated nucleation but limited growth of new grains,the mean DRX grain size varies slightly as recrystallization proceeds.However,in a partially recrystallized structure,deformed grains contribute to the measurement of grain size.As a result,the average grain size ( D) continuously decreases until the probable completion of DRX 25.But in this investigation,there were partially recrystallized samples that deformed less than true strain of 0.6 at 400 C with strain rate of 0.01 s-1 and they do not show their final DRX microstructure.Therefore,for grain size analysis, only those cases in which steady state were reached before quenching were used.Hence,the average grain size( D ) was equal to fully dynamically recrystallized grain size ( Ds)25.Fig.8 shows the variation of the average grain size ( D ) versus Z.As can be seen in this figure,the DRX grain size significantly decreases as Z increases.The increase in grain size with rising temperature and declining strain rate could be attributed to decline in dislocation density and increase in the mobility of grain boundaries and hence the growth rate 25.The smallest grain size obtained in the present study is about 10m when the strain rate is 0.001 s-1 and the deformation temperature is 400 C.The data in Fig.8 can be fitted to the following power relationship：where Ds and rp are expressed in m and MPa,respectively.3.3.晶粒細(xì)化因?yàn)閯?dòng)態(tài)再結(jié)晶包含重復(fù)的形核過程并且新晶粒的生長(zhǎng)受到抑制，所以再結(jié)晶過程中再結(jié)晶晶粒的平均尺寸略有不同。然而，在部分再結(jié)晶結(jié)構(gòu)，變形的晶粒有助于晶粒尺寸的測(cè)量。因此，晶粒平均尺寸不斷地減小直到動(dòng)態(tài)再結(jié)晶完成。但在本次研究中，有部分再結(jié)晶的樣品在400度，應(yīng)變速率0.01每秒下的變形比真應(yīng)變小0.6，并且不顯示最后的動(dòng)態(tài)再結(jié)晶組織。所以，粒度分析只在材料淬火前就達(dá)到穩(wěn)定狀態(tài)的情況下使用。因此平均晶粒尺寸（D）等于完全動(dòng)態(tài)再結(jié)晶的晶粒尺寸（DS）。圖Fig.8顯示了平均晶粒尺寸對(duì)Z的變化。如在此圖中可以看到隨著Z的增大，再結(jié)晶晶粒尺寸明顯減小。晶粒尺寸隨著溫度的升高和應(yīng)變速率的下降而增加，可以歸因于位錯(cuò)密度的下降，上升的晶界遷移率和增長(zhǎng)速率。本研究中最小的晶粒尺寸出現(xiàn)在應(yīng)變速率為0.001每秒和變形溫度為400度的情況下，大約為10微米。Fig.8的數(shù)據(jù)適用于以下的動(dòng)力關(guān)系Ds和Rp分別以微米和兆帕表示。3.4.Constitutive analyses Sellars and Tegart,using hyperbolic function proposed by Garofalo,showed that hot deformation can be considered as athermally-activated process which can be described by strain rate equations similar to those employed in creep studies.The ZenerHollomon parameter ( Z ),which is the temperature compensated strain rate,can be associated with the flow stress in different ways,as shown in Eq.(2).These are the power law at relatively low stresses,exponential law at high stresses,and hyperbolic sine law for a wide range of deformation conditions 28,29where Q is the deformation activation energy,_e is the strain rate, T is the absolute temperature,R is the universal gas constant,and A0,A00,A,n0,n,b and a(b/n0) are material constants.The stress multiplier is an adjustable constant which brings ar into the correct range that gives linear and parallel lines in ln_e versus ln sinh（） plots 5.Based on Eq.(2),the expressions of n0=【ln_e=lnrp】T,b=【ln_e=rp】T,and n=【ln_e=lnfsinhep 】T can be derived and the values of n0,b,and n can be calculated30.The required plots are shown in Fig.9.Subsequently,the value of a=b/n0=0.024 can be calculated from these results. The following expression can also be derived from the hyperbolic sine law of Eq.(2) 5,30:3.4.本構(gòu)分析塞拉斯和特加特利用加羅法洛提出的雙曲函數(shù)，表明熱變形可以當(dāng)做一個(gè)熱激活過程，用應(yīng)變率方程來研究，這一方程類似于在蠕變研究中所用的方程。齊納變形常數(shù)（Z），即溫度補(bǔ)償應(yīng)變速率，可以用不同方式與流動(dòng)應(yīng)力聯(lián)系起來，如公式 Eq.(2)。這些是冪定律在較低的應(yīng)力，指數(shù)定律在高應(yīng)力和雙曲正弦定律在廣泛的變形條件下。其中Q是變形激活能，_e是應(yīng)變率，T是絕對(duì)溫度，R是通用氣體常數(shù)，和A0，A00，一，N0，N，B和（BN0）是材料常數(shù)。應(yīng)力乘數(shù) 是一個(gè)可變常數(shù)，可以使rou到正確的范圍，以在以下公式中給出直線和平行線?；诜匠蘀q.2，以下幾個(gè)公式可以被推導(dǎo)，n，和n可以被計(jì)算出來。所需圖如 Fig.9所示。隨后=/N=0.024的值可以從這些結(jié)果中計(jì)算出來。下面的表達(dá)式也可由圖Eq.（2）的雙曲正弦定律推導(dǎo)出來。 It follows from these expression that the slope of the plots of ln_e and 1/T against lnsinhea rp） can be used for obtaining the value of Q .The required plot is shown in Fig.10 and the value of Q was determined as 173.2 kJ/mol which is higher than the lattice self-diffusion activation energy of magnesium (135 kJ/mol)5 or the grain boundary diffusion activation energy (92 kJ/mol)9.This can be ascribed to the presence of gadolinium，showing the importance of rare earth elements on increasing the deformation resistance at high temperatures 31,32.For instance,as shown in Fig.1b,the level of flow stress of the GZ31 alloy at the temperature 500 C and strain rate of 0.01s-1 is significantly higher than that of the AZ31 alloy,which is one of the most commercially important Mg alloys 5,33. The value of 173.2 kJ/mol was used to calculate theZparameter.According to Eq.(2), plots of LnZversus lnfsinhe arpTHg,rp and lnrp may be used to find the relationship between Z and rp25.The corresponding curves are shown in Fig.11.The resultant equations with new regression constants are shown in Eq.(4):從這些A式對(duì)B式斜率的表達(dá)式，可以獲得Q的值。如Fig.10圖所示，Q的值被確定為173.2 kJ/mol，高于鎂的晶格自擴(kuò)散激活能（135 kJ/mol）或晶界擴(kuò)散激活能（92 kJ/mol）。這可以歸因于釓元素的存在，顯示了稀土元素在高溫下提高變形阻力中的重要性。例如，在圖Fig.1b，GZ31合金在500度，0.01每秒的形變速率下的流動(dòng)應(yīng)力水平顯著高于AZ31合金，而后者是商業(yè)上最重要的一種鎂合金。173.2 kJ/mol這個(gè)值被用來計(jì)算Z的值。如式Eq.2，式A對(duì)式B和式C可以用來找到Z與rp之間的關(guān)系。相應(yīng)的曲線如圖Fig.11所示。新的回歸常數(shù)所得的方程如（4）式所示。In Fig.11a,the excluded point corresponds to the deformation temperature of 300 C under strain rate of 0.01 s-1.The point does not follow the trend due to inability of the power law at high stresses.The excluded points in Fig.11b correspond to deformation temperature of 500 C under strain rates of 0.01,0.001,and 0.0001s-1.Again,these points do not follow the general trend due to inability of the exponential law at low stresses.However,the hyperbolic sine law 5,as shown in Fig.11c,can give the appropriate constitutive equation for a wide range of deformation conditions.A comparison between the calculated and measured values of flow stress by the hyperbolic sine relation of Eq.(4) is shown in Fig.12.It can be seen that the calculated and the measured values are in a good agreement,which shows that the predictions of the proposed constitutive equation are satisfactory.在表Fig.11a中，排除的點(diǎn)對(duì)應(yīng)變形溫度300度，應(yīng)變速率0.01每秒。并不遵循在高應(yīng)力下冪定律無力的趨勢(shì)。Fig.11b中的排除點(diǎn)對(duì)應(yīng)變形溫度500度，應(yīng)變速率0,01，0.001和0.0001每秒。再次的，這些點(diǎn)不遵循低應(yīng)力下指數(shù)定律無力的趨勢(shì)。不過，雙曲正弦定律可以給出大范圍變形條件下的適當(dāng)?shù)谋緲?gòu)方程，如Fig.11c所示。Eq.(4)中雙曲正弦關(guān)系下流動(dòng)應(yīng)力的計(jì)算值和實(shí)測(cè)值的比較如Fig.12圖所示?？梢钥闯?，計(jì)算值與實(shí)測(cè)值吻合較好，表明所提出的本構(gòu)方程預(yù)測(cè)是符合要求的。4.Conclusions (1)The flow curves of GZ31 alloy showed typical broad single peak dynamic recrystallization behavior followed by a gradual fall towards the steady state stress. (2)The deformation activation energy was determined as 173.2 kJ/mol,which is higher than the lattice self-diffusion activation energy of 135 kJ/mol for magnesium.The latter can be ascribed to the presence of gadolinium and shows the importance of this element in increasing the deformation resistance at high temperatures.This was proved by comparing the flow stress of GZ31 alloy with AZ31 alloy. (3)The power and the exponential laws were found to be unsuitable for description of the flow stress of GZ31 alloy at high and low stresses,respectively.However,the hyperbolic sine law was able to represent the constitutive behavior in a wide range of Z parameter. (4)The stress multiplier and the hyperbolic sine exponent were calculated as 0.024 MPa-1 and 3.42,respectively.Therefore,the following constitutive equation,which can be used to express the hot flow behavior of this material, was proposed and verified: (5)Significant grain refinement occurred as a result of necklace DRX mechanism.The average dynamically recrystallized grain size decreased with increasing strain rate and decreasing deformation temperature.It was related to ZenerHollomon parameter and by power equations with exponents of 0.28 4. 結(jié)論（1） GZ31合金的流動(dòng)曲線呈典型寬單峰動(dòng)態(tài)再結(jié)晶表現(xiàn)，隨后對(duì)穩(wěn)態(tài)應(yīng)力逐漸下降。（2） 變形激活能被確定為173.2 kJ/mol，高于鎂的晶格自擴(kuò)散激活能135 kJ / mol。后者可以歸因于釓的存在，并且顯示了這種元素在高溫下增加變形抗力的重要性。這一點(diǎn)可以通過比較GZ31合金和AZ31合金的流動(dòng)應(yīng)力來證實(shí)。（3） 動(dòng)力和指數(shù)定律被發(fā)現(xiàn)不適合用來描述GZ31合金分別在高低壓力下的流動(dòng)應(yīng)力。然而，雙曲正弦規(guī)律能在大范圍的Z值內(nèi)表示該合金的本構(gòu)行為。（4） 壓力乘數(shù)和雙曲正弦指數(shù)分別算出為0.024 MPa-1和3.42,。因此，下面的本構(gòu)方程可以用來表示該材料的高溫流變行為，且已被提出并驗(yàn)證。（5） 顯著的晶粒細(xì)化是（ ）動(dòng)態(tài)再結(jié)晶機(jī)制的結(jié)果。應(yīng)變速率升高，變形溫度下降時(shí)平均動(dòng)態(tài)再結(jié)晶晶粒尺寸減小。這與齊納變形指數(shù)和指數(shù)為0.28的功率方程有關(guān)。References（工具書類）（6） 1H.E.Friedrich, B.L.Mordike,Magnesium TechnologyMetallurgy, Design Data Applications, Springer-Verlag, Berlin, Heidelberg, Germany,2006.（7） 2Z.Yang, J.P.Li, J.X. 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