A simple method
A simple method for solving unidirectional methane
A simple method for solving unidirectional methane gas flow in coal seam based on similarity solutionZhou Yan a,⇑,Meng Qian b ,Lin Baiquan a ,Qin Jilong a ,Zhou Guiping aa Key Laboratory of Gas and Fire Control for Coal Mines (China University of Mining &Technology),Ministry of Education,Xuzhou 221116,China bSchool of Computer Science and Technology,Jiangsu Normal University,Xuzhou 221116,Chinaa r t i c l e i n f o Article history:Received 12February 2016Received in revised form 22May 2017Accepted 16June 2017Available online 16December 2017Keywords:Coalbed methane MigrationUnidirectional flow Similarity solution Simplified solving Numerical methoda b s t r a c tThe equation used to model the unidirectional flow of methane gas in coal seams is usually formulated as a nonlinear partial differential equation,which needs to be solved numerically with a computer program.Nevertheless,for people without access to the computer program,the conventional numerical method may be inconvenient.Thus,the objective here is to seek some method simpler than the conventional one for solving the flow problem.A commonly used model of the unidirectional methane gas flow is con-sidered,where the methane adsorption is described by the Langmuir isotherm and the free gas is treated as real gas.By introducing the similarity solution,a simple method for solving the flow model is pro-posed,which can be done on a hand calculator.It is shown by two examples that the gas pressure profile obtained by the proposed method agrees well with the direct numerical solution of the flow model.Ó2017Published by Elsevier B.V.on behalf of China University of Mining &Technology.This is an openaccess article under the CC BY-NC-ND license (/licenses/by-nc-nd/4.0/).1.IntroductionAs coal is porous in nature,significant amounts of methane can be retained in coal bed,and coalbed methane (CBM)is both a potentially valuable energy resource and a hazard in active coal mines [1–3].Understanding the methane gas migration in coal seams is essential for both CBM recovering and coal mine gas con-trol.But,the CBM flow equation is usually formulated as a nonlin-ear partial differential equation (PDE),which can hardly be solved by purely analytical techniques [4,5].The unidirectional flow is one of the three basic patterns of methane gas migration in coal seams,while the other two are radial flow and spherical flow [6].The unidirectional flow of methane gas is a kind of one-dimensional transient flow.It refers to the situation where the methane gas migrates towards a coal face,of which the height is equal to the thickness of the coal seam,as shown in Fig.1.For one-dimensional transient gas flow (without adsorption and desorption)in porous media,a traveling wave solution has been present by Hayek [7].Because the CBM flow is usually accompa-nied by methane desorption [8,9],and the coal methane content is nonlinearly dependent on the pore gas pressure [10,11],the problem of CBM flow is more complex,and we have to solve it numerically using a computer program.As is well known,there are many parameters controlling the methane gas flow in coal seams,such as gas pressure,coal seam permeability,adsorption coefficients,etc.While trying to investi-gate the effects of these parameters on the flow process,one needs to solve the flow model many times for different values of the parameters,and the computational cost rises rapidly as the param-eter number increases.Moreover,and importantly,the conven-tional numerical analysis may be inconvenient for those,such as field engineers,field technicians,and so on,who might not have access to the computer program.Thus,the objective of this study is to seek a method for solving the flow model,which is simpler than the conventional numerical analysis,and is accurate enough,and can be done even without a computer.Of course,such a method can also be easily programmed to run efficiently on a computer.2.Basic equationWhile the methane adsorption is described by the Langmuir isotherm [12–14],and the free gas is treated as real gas [4,15],a commonly used model of the unidirectional methane gas flow can be written as [10,16]:https:///10.1016/j.ijmst.2017.12.0062095-2686/Ó2017Published by Elsevier B.V.on behalf of China University of Mining &Technology.This is an open access article under the CC BY-NC-ND license (/licenses/by-nc-nd/4.0/).⇑Corresponding author.E-mail address:zhouyan@ (Y.Zhou).International Journal of Mining Science and Technology 28(2018)331–334Contents lists available at ScienceDirectInternational Journal of Mining Science and Technologyjournal homepage:www.else v i e r.c o m /l o c a t e /i j m st@P @t ¼2M ffiffiffiP p 1þb ffiffiffiP p 21þU ð1þb ffiffiffiP p Þ2=p n Á@2P @x2ð1Þwhere P is the square of the coal seam gas pressure,MPa 2,and P =P (x ,t )=p 2(x ,t );p is the pore gas pressure,MPa;x is the spatial coor-dinate,m;t is the time coordinate,s;M ¼k =ðab Þ,m 2/(MPa s);k is the permeability coefficient of the coal seam,m 2/(MPa 2s);a is the maximum adsorbed gas content,m 3/m 3;b is the equilibrium con-stant,MPa À1;U ¼/=ðab Þ,MPa;/is the porosity;p n is the normal gas pressure,here taking p n %0.1MPa.If the free gas is ignored,Eq.(1)reduces to:@P@t ¼2M ffiffiffiP p 1þb ffiffiffiP p 2@2P @x 2ð2ÞFor both Eqs.(1)and (2),the initial and boundary conditions are as follows:P ðx ;0Þ¼P 0¼p 20P ð0;t Þ¼P 1¼p 2n P ð1;t Þ¼P 0¼p 208><>:ð3Þwhere P 0is the square of the original gas pressure in the coal seam,MPa 2;p 0is the original gas pressure,MPa;P 1is the square of the gaspressure at the coal face,and here we assume P 1=p 2n =0.01MPa 2.Obviously,Eqs.(1)and (2)with their initial and boundary con-ditions in Eq.(3)form two initial and boundary value problems (IBVP)of nonlinear PDE,which need to be solved numerically by using a computer program.3.A simple method for solving the flow model 3.1.Similarity transformationsBy introducing suitable similarity transformations,some PDEs can be reduced into ordinary differential equations (ODE)and the solutions of the ODEs are called the similarity solutions of the PDEs [17–21].If the similarity solutions are known in advance,the solu-tions of the original PDEs can be easily obtained.It is not too difficult to prove that both Eqs.(1)and (2)can be transformed into ODEs by introducing a similarity variable like x =ffiffit p .In order to reduce the number of the model parameters,and to make the initial and boundary conditions simpler,we define two similarity variables as follows:g ¼P =P 0n ¼xffiffiffiffiffiffiffiffiffiffiffiab4k P 1=20tr 8<:ð4Þwhere g and n are similarity variables,dimensionless.Substituting the similarity variables into Eqs.(1)–(3)separately leads toÀn g 0¼ffiffiffig p 1þr ffiffiffig p ÀÁ21þ10U 1þr ffiffiffigp ÀÁ2g00ð5ÞÀn g 0¼ffiffiffig p 1þr ffiffiffig p 2g00ð6Þandg ð0Þ¼g 0g ð1Þ¼1&ð7Þwhere g 0¼d g d n ,g 00¼d 2gd n 2,r ¼b ffiffiffiffiffiP 0p ¼bp 0,and g 0¼P 1=P 02(0,1).So,the original two IBVPs have been transformed into two boundary value problems (BVP).Eqs.(5)and (6)are the so called similarity equations of Eqs.(1)and (2),separately.Obviously,the similarity equation is easier to be solved than its original equation.Moreover,it is worth mentioning that there are only two model parameters,i.e.,r and g 0,left in Eq.(6)and its boundary condi-tions.That means the solving of Eq.(6)only needs to be repeated for every (r ,g 0).So,it will be not too difficult to tabulate or graph the solutions of Eq.(6)in advance for further use to solve Eq.(2).However,there are three model parameters,i.e.,U ,r and g 0,left in Eq.(5)and its boundary conditions.So it will be difficult to tabulate or graph the solutions of Eq.(5)systematically in advance.3.2.Proposed methodsBecause the free gas is usually less than the adsorbed gas,Eq.(2)can be regarded as a rough approximation to Eq.(1),and Eq.(6)a rough approximation to Eq.(5).As the basis of following consider-ation,Eq.(6)is solved using the shooting method [22],and its numerical solution sets for a range of values of r and g 0are obtained as shown in Fig.2.Here,only the solution sets for the cases of r =0.56,1.8and 5.8are present because of the space restrictions.Without loss of generality,suppose we are looking for the solu-tion of Eq.(5)at n =n k ,with r and g 0known.Here,n k is a certain value of n ,which corresponds to some certain point of the space-time coordinate of (x ,t ).The basic ideas of the proposed method are as follows.Firstly,we get the solution of Eq.(6)corresponding to the known r and g 0at n =n k from the solution sets as shown in Fig.2,and denote this solution as g f,k .Secondly,we setB ¼1þ10U 1þr ffiffiffiffiffiffiffig f ;kp2ð8ÞThirdly,we rewrite Eq.(5)approximately asÀn d ^g d n ¼1Bffiffiffi^gq 1þr ffiffiffi^g q 2d 2^g d n 2ð9Þwhere ^gis an approximation of g .Fourthly,we set^n ¼ffiffiffiB p nð10Þand substitute it into Eq.(9),and getÀ^n ^g 0¼ffiffiffi^g q 1þr ffiffiffi^g q 2^g 00ð11Þwhere ^g 0¼d ^g d ^n and ^g 00¼d 2^g d ^n2.The boundary conditions for Eq.(11)is^gð0Þ¼g 0^gð1Þ¼1&ð12ÞObviously,Eq.(11)is identical in form to Eq.(6),and the bound-ary conditions in Eq.(12)are also identical to that in Eq.(7).So the solution of Eq.(11)can also be determined from the solution sets of Eq.(6)as shown in Fig.2.We can take the solution of Eq.(11)Fig.1.Unidirectional methane gas flow in coal seam.332Y.Zhou et al./International Journal of Mining Science and Technology 28(2018)331–334as an approximate solution of Eq.(5).With this approximate solu-tion,the solution of Eq.(1)can be obtained easily based on the def-inition of the similarity variables g and n .4.Examples4.1.A real field case exampleThe 3#coal seam in Jincheng coal field of China,of which parameters are given in Table 1,is chosen to show how to estimate the gas pressure profile by using the proposed method.This exam-ple is typical in that the free gas content is considerably high (the gas pressure is quite high and the porosity relatively large).Since r =bp 0%0.56and g 0=P 1/P 0=0.0025,the solution of Eq.(6)for this case happens to be the first curve from the bottom in Fig.2a.Obviously,for other values of r or g 0,the solution can be obtained by interpolation.Several data points in the solution of Eq.(6)for this example are listed in Table 2(the column labeled as g f ).Substituting the values of g f into the definition formula of g as shown in Eq.(4),we get the corresponding values of gas pres-sure as shown in the column labeled as p f in Table 2,which are indeed the gas pressure values we can obtain by ignoring the free gas.In other words,for the cases where the free gas can be ignored,the gas pressure profile can be determined directly from the simi-larity solutions as shown in Fig.2,and there is no more need to solve the differential equation Eq.(6)or Eq.(2).Next,we will take the following steps to finish the solving.Step 1:Using Eq.(8),we get the values of B ,as shown in the 4th column of Table 2.Step 2:Using Eq.(10),we get the values of ^n corresponding to different values of n ,as shown in the 5th column of Table 2.Step 3:According to the values of r and g 0,we determine the solution of Eq.(11)from Fig.2.Obviously,the solution is still the first curve from the bottom in Fig.2a.From this curve,wecan estimate the values of ^g at different values of ^n ,as shown in the column labeled as ^g in Table 2.Step 4:Based on the definition of g ,we get the values of gaspressure,as shown in the column labeled as ^pin Table 2,and here,^pis the approximation of p .Obviously,the calculations required for the above steps arequite simple,since only algebraic manipulations are involved.Even for someone who does not have a computer,he can still do the cal-culations on a hand calculator.In order to check the accuracy of the proposed method,we pre-sent the direct numerical solutions of Eq.(5)at different values of n in Table 2,as shown in the column labeled as g d .The correspond-ing values of gas pressure are listed in the column labeled as p d .From the data in Table 2,it can be found that the gas pressure profile obtained by the proposed method agrees well with the direct numerical solutions,and is much better than that obtained by ignoring the free gas.This can be seen more clearly in Fig.3.4.2.A fictitious extreme exampleIn order to further test the accuracy of the proposed method,we introduce a fictitious case example where the free gas content is extremely high.The parameters of this extreme case are shown in Table 3.From these parameters,we can calculate that the orig-inal free gas content is 8.0m 3/m 3,while the original adsorbed gas content about 5.4m 3/m 3.The results of the direct numerical solution,the method of ignoring free gas,and the proposed method are presented in Fig.4,respectively.Fig.2.Numerical solution sets of Eq.(6).Table 1Parameters of the real field case [23].p 0(MPa)a (m 3m À3)b (MPa À1)k (m 2MPa À2s À1)/2.041.50.2790.003840.173Table 2Calculating the gas pressure profile of the real field case.n g fp f (MPa)B ^n ^g ^p (MPa)g dp d (MPa)00.00250.100 1.15800.00250.1000.00250.1000.0200.0160.250 1.1710.0210.0170.2580.0180.2650.0900.0630.500 1.1940.0980.0680.5220.0710.5320.2050.1370.740 1.2170.2260.1500.7750.1550.7870.3890.250 1.00 1.2440.4340.276 1.050.282 1.061.020.563 1.50 1.300 1.160.618 1.570.622 1.582.370.9031.901.3492.760.9421.940.9421.94Fig.3.Results of different methods in the real field case.Y.Zhou et al./International Journal of Mining Science and Technology 28(2018)331–334333As seen in Fig.4,the gas pressure profile obtained by the pro-posed method still agrees fairly well with the direct numerical solutions,even for this extreme case.5.Conclusions(1)The model of unidirectional methane gasflow in coal seam isusually formulated as a nonlinear partial differential equa-tion,which needs to be solved numerically with a computer program.Nevertheless,for people without access to the computer program,the conventional numerical analysis may be inconvenient.(2)A commonly used model is considered where the methaneadsorption is described by the Langmuir isotherm and the free gas is treated as real gas.By introducing the similarity transformations,the model is reduced into an ordinary equation,of which the solutions are the similarity solutions of the original model.(3)For the case where the free gas is ignored,there are only twomodel parameters left in the similarity model.Based on the similarity solution sets tabulated or graphed in advance for such case,a method is proposed to solve the commonly used model.(4)Since only algebraic manipulations are involved,the pro-posed method is simple and can be done on a hand calculator.(5)Two examples are introduced to test the accuracy of the pro-posed method.One is a realfield case example,and another is afictitious extreme example.It is shown that the gas pres-sure profile obtained by the proposed method agrees well with the direct numerical solution.AcknowledgmentsFinancial support for this work,provided by the Priority Academic Program Development of Jiangsu Higher Education Institutions(PAPD),is gratefully acknowledged.References[1]Pillalamarry M,Harpalani S,Liu S.Gas diffusion behavior of coal and its impacton production from coalbed methane reservoirs.Int J Coal Geol2011;86(4):342–8.[2]Zhou LH,Pritchard C,Zheng Y.CFD modeling of methane distribution at acontinuous miner face with various curtain setback distances.Int J Min Sci Technol2015;25(4):635–40.[3]Lin HF,Huang M,Li SG,Zhang C,Cheng L.Numerical simulation of influence ofLangmuir adsorption constant on gas drainage radius of drilling in coal seam.Int J Min Sci Technol2016;26(3):377–82.[4]Wang JG,Kabir A,Liu JS,Chen Z.Effects of non-Darcyflow on the performanceof coal seam gas wells.Int J Coal Geol2012;93(1):62–74.[5]Hooman K,Tamayol A,Dahari M,Safaei MR,Togun H,Sadri R.A theoreticalmodel to predict gas permeability for slipflow through a porous medium.Appl Therm Eng2014;70(1):71–6.[6]Zhou SN.Application 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[10]Zhou SN,Lin BQ.The theory of gasflow and storage in coalseams.Beijing:China Coal Industry Publishing House;1999.[11]Mazzotti M,Pini R,Storti G.Enhanced coalbed methane recovery.J SupercritFluids2009;47:619–27.[12]Ziarani AS,Aguilera R,Clarkson CR.Investigating the effect of sorption time oncoalbed methane recovery through numerical simulation.Fuel2011;90(7):2428–44.[13]Clarkson CR.Production data analysis of unconventional gas wells:workflow.Int J Coal Geol2013;109–110:147–57.[14]Xue S,Wang YC,Xie J,Wang G.A coupled approach to simulate initiation ofoutbursts of coal and gas–model development.Int J Coal Geol2011;86(2–3):222–30.[15]Alexeev AD,Feldman EP,Vasilenko TA.Methane desorption from a coal-bed.Fuel2007;86(16):2574–80.[16]Xu T,Tang CA,Yang TH,Zhu WC,Liu J.Numerical investigation of coal and gasoutbursts in underground collieries.Int J Rock Mech Min Sci2006;43(6):905–19.[17]Iqbal M,Mustafa MT,Siddiqui AA.A method for generating approximatesimilarity solutions of nonlinear partial differential equations.Abstract Appl Anal2014;5:1–6.[18]Zhao GC,Du X,Song LP,Kong JR.Similarity solutions and approximationsolutions of velocity and temperature in laminar boundary layer of subsonic and supersonic wedgeflows.J Aerosp Power2014;29(12):2785–94.[19]Kolomenskiy D,Moffatt HK.Similarity solutions for unsteady stagnation pointflow.J Fluid Mech2012;711:394–410.[20]Ancey C,Cochard S,Rentschler M,Wiederseiner S.Existence and features ofsimilarity solutions for non-Boussinesq gravity currents.Physica D2007;226(1):32–54.[21]Mortensen J,Olsen S,Parlange JY,Telyakovskiy AS.Approximate similaritysolution to a nonlinear diffusion equation with spherical symmetry.Int J Numer Anal Model2012;9(1):105–14.[22]Gerald CF,Wheatley PO.Applied numerical analysis.Boston:Addison-Welsley;2004.[23]Ma DM,Zhang SA,Wang PG,Lin Y,Wang C.Mechanism of coalbed methanedesorption at different temperatures.Coal Geol Expl2011;39(1):20–3.Table3Parameters of thefictitious extreme example.p0(MPa)a(m3mÀ3)b(MPaÀ1)k(m2MPaÀ2sÀ1)/4.0150.13950.003840.2Fig.4.Results of different methods in thefictitious extreme example.334Y.Zhou et al./International Journal of Mining Science and Technology28(2018)331–334。
一种方法还是一个方法英文
一种方法还是一个方法英文IntroductionIn the pursuit of solving complex problems or accomplishing goals, individuals and organizations often rely on methods or approaches. These systematic processes are designed to provide structure, guidance, and clarity to achieve desired outcomes. In this article, we will explore the concept of methods, their significance, and how they contribute to success. We will also delve into the differences between a method and an approach, and when to use each one.Understanding MethodsMethods are systematic procedures or processes used to achieve specific objectives. They provide steps, guidelines, and tools to help individuals or groups navigate challenging tasks. Methods are often developed based on research, best practices, and prior experiences. They offer a well-defined path, allowing for consistent and reliable outcomes. For example, in project management, the waterfall method provides astep-by-step approach, ensuring that each phase is completed before moving on to the next.The Significance of MethodsMethods play a crucial role in various fields and industries, offering several advantages:1. Efficiency: Methods help streamline and optimize processes, reducingwaste, errors, and redundancies. By eliminating unnecessary steps and focusing on essential tasks, efficiency and productivity are enhanced. 2. Consistency: Methods provide a standardized approach, ensuring consistent results even when different individuals are involved. This fosters reliability and quality across projects and endeavors.3. Learning from Experience: Methods are often built upon past successes and failures. They incorporate lessons learned, making them a valuable repository of knowledge. Individuals or organizations can leverage this expertise to ensure better outcomes.4. Risk Mitigation: Methods often include risk assessment and mitigation strategies. By following a proven method, potential risks are identified early on, allowing preemptive actions to reduce their impact. Understanding ApproachesWhile methods provide a structured and systematic way of tackling problems, approaches are broader and more flexible in nature. Approaches refer to the overall strategy or mindset employed to address a challenge. Unlike methods, they are not necessarily bound by specific steps or guidelines. Approaches are adaptive and can be customized to suit the unique needs of a situation. For instance, a collaborative approach focuses on teamwork and open communication, allowing for creative problem-solving.When to Use a Method or an ApproachDetermining whether to use a method or an approach depends on several factors:1. Task Complexity: Methods are well-suited for complex and intricate tasks that require a precise sequence of steps and guidelines. When dealing with straightforward or less structured challenges, approaches offer more flexibility.2. Goal Clarity: If the desired outcome is clearly defined, a method ensures the path to success is explicitly laid out. However, when goals are vague or evolve over time, an approach may be preferable, as it allows for adaptability.3. Real-World Constraints: Limited resources, time constraints, or uncertain variables may require an adaptive approach. Methods, on the other hand, provide structure and guidance, which can be beneficial when dealing with such constraints.It is important to note that methods and approaches are not mutually exclusive but rather complementary. Depending on the situation, a combination of both can lead to the most effective and efficient results. ConclusionMethods and approaches are valuable tools in problem-solving and goal achievement. Methods provide structure, consistency, efficiency, and risk mitigation, while approaches offer adaptability and flexibility. Choosingbetween a method or an approach depends on the task complexity, goal clarity, and real-world constraints. The key lies in understanding the unique requirements of each situation and selecting the most suitable approach to maximize success. By leveraging methods and approaches effectively, individuals and organizations can navigate challenges and achieve desired outcomes with confidence.。
A simple method to synthesize Ba0.6Sr0.4TiO3 nano-powders through
Short communicationA simple method to synthesize Ba 0.6Sr 0.4TiO 3nano-powders through high-energy ball-millingCheng Liu a ,Peng Liu a ,⁎,Xiao-gang Lu b ,Chang-jie Gao b ,Gang-qiang Zhu a ,Xiao-ming Chen aa College of Physics and Information Technology,Shaanxi Normal University,Xi'an,710062,PR China bInstitute 206of China Ordnance Industries Group Corporation,Xi'an,710100,PR Chinaa b s t r a c ta r t i c l e i n f o Article history:Received 22January 2011Received in revised form 13May 2011Accepted 14May 2011Available online 26May 2011Keywords:BSTPowder preparation Thermal analysis MicrostructureIn this study,we fabricated Ba 0.6Sr 0.4TiO 3(BST)powders via a high-energy ball-milling (HEBM)method.The processing parameters were optimized to obtain an optimum synthesis condition.BST nano-powders (with a mean grain size of 475nm)were derived from the precursor milled at 400/800rpm for 5h and calcined at 1000°C for 2h.This synthesis temperature was much lower than that required by traditional solid state reaction.It was suggested that HEBM is a simple and practical route to synthesize BST nano-powders.©2011Elsevier B.V.All rights reserved.1.IntroductionBST (Ba x Sr 1−x TiO 3,0b x b 1)ferroelectric material is an attractive candidate in phase shifters,filters,varactors and delay lines due to its high dielectric nonlinearity and low dielectric loss [1,2].Recently,with the development of wireless portable communication systems and the miniaturization of electronic devices,new applications in microwave frequency range demand materials that can be co-fired with silver (or copper)electrode so as to achieve low-temperature co-fired ceramics (LTCC)[3–5].However,the sintering temperatures of BST ceramics prepared by traditional solid state reaction are 1350~1400°C [6],thus blocking its applications in LTCC.To have a low sintering temperature,BST powders should be synthesized at a low temperature.Chemical methods are always adopted for preparing BST nano-powders at a relatively low temperature [7–11],but such processes are complicated for industrialization.High-energy ball milling (HEBM),as a mechanochemical way,has been used to synthesize nano-crystalline ferroelectrics and other alloys [12–14].Compared with traditional solid-state reaction technique,HEBM can lower the calcination temperature [15–17].Nevertheless,the application of HEBM on the synthesis of BST nano-powders has been rarely reported.In this paper,we fabricated Ba 0.6Sr 0.4TiO 3(BST)nano-powders via a HEBM route,whose synthesis temperature was dramatically decreased.Phase formation and microstructure of the BST nano-powders were also investigated.2.ExperimentalCommercially available BaCO 3(99.92%),SrCO 3(99.61%)and TiO 2(99.99%)powders were used as the starting materials.The raw materials with the nominal composition of Ba 0.6Sr 0.4TiO 3were milled in air with different milling parameters (milling speed:300/600,400/600and 400/800rpm respectively;and milling time:5and 10h respectively for each speed).All experiments were carried out by using a Fritsch Vario-Planetary Mill (pulverisette P4™).A tungsten carbide vial with a diameter of 80mm and 25tungsten carbide balls with a diameter of 10mm were used as a milling medium.Then the milled powders were calcined at different temperatures (850,900,950and 1000°C)for 2h.Particle size distribution was analyzed by using a laser particle size analyzer (Model BI-90Plus,BrookHaven,USA).Phase structure of the uncalcined BST powders was investigated by using a thermal gravimetric and differential thermal analyzer (TG/DTA;SDT Q600V8.0Build 95,USA)at a heating rate of 10°C/min in air from room temperature to 1100°C.The calcined BST powders were subsequently examined by an X-ray diffractiometer (XRD,Model D/MAX-2550X,Rigaku,Japan)at a scanning rate of 10°/min in the range of 10°≤2θ≤90°,using Cu K αradiation (λ=1.5406Å)at 40kV and 50mA.Morphology of the calcined powders was observed by using a scanning electron microscopy (SEM,Model QUANTA 200,FEI,Netherlands).3.Results and discussionFig.1(a –f)shows lognormal distributions of particle sizes of the powders milled at different conditions.Fig.1(g)exhibits the corre-sponding mean particle diameters.After milling for 5h,the meanPowder Technology 212(2011)299–302⁎Corresponding author.Tel.:+862985303732.E-mail address:liupeng@ (P.Liu).0032-5910/$–see front matter ©2011Elsevier B.V.All rights reserved.doi:10.1016/j.powtec.2011.05.010Contents lists available at ScienceDirectPowder Technologyj o u r n a l h o me p a g e :w w w.e l sev i e r.c o m /l oc a t e /pow t e cparticle size is 1433,616and 480nm for the milling speed of 300/600,400/600and 400/800rpm,respectively.After extending the milling time to 10h,the particle size continues to decline,reaching to an average diameter of 582,330and 240nm,respectively.These results con firm that HEBM method can reduce the particle size to nanometer effectively.Fig.2shows TG/DTA curves of the BST powders milled at 400/800rpm for 10h.One endothermic peak (A)and four exothermic peaks (B,C,D and E)are observed.The endothermic peak A at 105°C is attributed to the weight loss of water.The exothermic peak B at about 600°C,supported by a second fall of weight,is due to the decomposition of SrCO 3and BaCO 3and the formation of BST phase.Then the weight loss curve continues to decline till about 950°C,along with exothermic peaks C and D at 850and 900°C,respectively.The exothermic peak E emerges at about 1015°C.These exothermic peaks correspond to different phase formation,which will be discussed in detail in the following XRD analysis.Fig.3shows XRD patterns of the powders calcined at different temperature for 2h after different milling processes.In Fig.3(a1),BST phase is detected,but small amount of BaCO 3,TiO 2(rutile structure),Ti 3O 5,Sr 2WO 5and Ba 3WO 6are also found.Similar results are observed in Fig.3(b1).In Fig.3(c1),BaCO 3and Ti 3O 5phases disappear but Ba 2TiO 4phase emerges with the milling time increased to 10h.These phases are also detected in the powders calcined at 900°C [see Fig.3(a2)and (b2)].The formation of Ba 2TiO 4in the mixture can be described in the following equation [18,19].2BaCO 3+TiO 2=Ba 2TiO 4+2CO 2ð1ÞThe decomposition of BaCO 3and Ti 3O 5and the formation of Ba 2TiO 4at about 850°C could be responsible for the exothermic peak C (Fig.2).In the sample milled at 400/800rpm for 10h and calcined at 900°C,as shown in Fig.3(c2),Sr 2WO 5and Ba 2TiO 4disappear,which could be related to the exothermic peak D (Fig.2).However,after being calcined at 950°C,all the powders are composed of BST,Ba 3WO 6,TiO 2and BaWO 4[Fig.3(a3),(b3)and (c3)].Ba 3WO 6and TiO 2peaks decrease dramatically with increasing the milling speed (400/800rpm)and time (10h),and vanish after being calcined at 1000°C in the samples milled at 300/600and 400/800rpm for 5h,as showed in Fig.3(a4)and (b4).The presence of slight amount of tungstates,such as Sr 2WO 5and Ba 3WO 6phases in the samples calcined at lower synthesis temperatures (850and 900°C)and BaWO 4at higher temperatures (950and 1000°C),should be attributed to the contamination of tungsten carbide (WC)due to the long milling time duration.The synthesis temperature 1000°C is lower than that of the BST powders (1250°C)prepared by traditional solid-state process [20].This is associated with the particle re finement,similar to the mechanism of chemical methods [7–11].After milling for 10h,the amount of BaWO 4increases and another unknown phase emerges [Fig.3(c4)].The emergence of the unknown phase is probably responsible for the exothermic peak E at about 1015°C (Fig.2).Fig.4shows SEM images of the powders calcined at 1000°C after being milled at 300/600for 5h,400/800rpm for 5h and 400/800rpm for 10h,respectively.The mean grain size of the calcined BST powders milled at 300/600rpm for 5h is 1612nm.For the sample milled at 400/800rpm,as shown in Fig.4(b),the mean grain size is reduced to 475nm.Then the grain size is further reduced to about 290nm in the sample milled for 10h.The slight particle agglomeration can be associated with the higher speci fic surface energy of the nano-sized particles [17].With the XRD and SEM results,we suggest that milling at 400/800rpm for 5h and calcining at 1000°C are optimum conditions to synthesize BST nano-powders.As BaWO 4is a promising microwave dielectric material [21],and BST is often modi fied by different microwave dielectrics,such as MgO,MgTiO 3,MgAl 2O 4,Mg 2SiO 4et al.[22–26],to achieve improved microwave tunable properties,the presence of BaWO 4could be an additional bene fit for BST ceramics.Dielectric properties of BST ceramics derived from the nano-powders will be reported separately.4.ConclusionsBa 0.6Sr 0.4TiO 3(BST)nano-powders with minor amount of second-ary phases can be derived from the precursors treated by HEBMatFig.1.Lognormal distribution of particle sizes (a –f)and variation of mean diameters (g)of the powders obtained by different millingprocesses.Fig.2.TG/DTA curves of the powders milled at 400/800rpm for 10h.300 C.Liu et al./Powder Technology 212(2011)299–302relatively low temperature.Well-crystallized BST nano-powders with a mean grain size of 475nm were gained for the sample milled at 400/800rpm for 5h and calcined at 1000°C for 2h.AcknowledgmentsThis work was supported by the National Natural Science Foundation of China (grant no.50872078,51072110and 11004127);the Fundamental Research Funds for the Central Universities (program no.2010ZYGX018and GK200901018).References[1]S.S.Gevorgian,E.L.Kollgerg,Do we really need ferroelectrics in paraelectric phaseonly in electrically controlled microwave devices?IEEE Trans.Microwave Theory Tech.49(2001)2117–2124.[2]L.C.Sengupta,S.Sengupta,Novel ferroelectric materials for phased arrayantennas,IEEE Trans.Ultrason Ferroelectr.Freq.Control 44(1997)792–797.[3] C.C.Cheng,T.E.Hsieh,I.N.Lin,Microwave dielectric properties of glass –ceramiccomposites for low temperature co-firable ceramics,J.Eur.Ceram.Soc.23(2003)2553–2558.[4]H.Jantunen,T.Kangasvieri,J.Vahakangas,S.Leppavuori,Design aspects of microwavecomponents with LTCC technique,J.Eur.Ceram.Soc.23(2003)2541–2548.[5]M.Valant, D.Suvorov,Low-temperature sintering of (Ba 0.6Sr 0.4)TiO 3,J.Am.Ceram.Soc.87(2004)1222–1226.[6]J.H.Jeon,Y.D.Hahn,H.D.Kim,Microstructure and dielectric properties of barium –strontium titanate with a functionally graded structure,J.Eur.Ceram.Soc.21(2001)1653–1656.[7] C.L.Mao,G.S.Wang,X.L.Dong,et al.,Low temperature synthesis of Ba 0.70Sr 0.30TiO 3powders by the molten-salt method,Mater.Chem.Phys.106(2007)164–167.[8]Y.B.Khollam,H.S.Potdar,S.B.Deshpande,A.B.Gaikwad,Synthesis of star shapedBa 1−x Sr x TiO 3(BST)powders,Mater.Chem.Phys.97(2006)295–300.[9]T.Hu,H.Jantunen,A.Uusimaki,S.Leppavuori,Ba 0.7Sr 0.3TiO 3powders with B 2O 3additive prepared by the sol –gel method for use as microwave material,Mater.Sci.Semiconduct.Process 5(2002)215–221.[10]X.H.Zuo,X.Y.Deng,Y.Chen,et al.,A novel method for preparation of bariumstrontium titanate nanopowders,Mater.Lett.64(2010)1150–1153.[11]X.F.Zhang,Q.Xu,Y.H.Huang,et al.,Low-temperature synthesis of super finebarium strontium titanate powder by the citrate method,Ceram.Int.36(2010)1405–1409.[12] D.J.Fatemi,V.G.Harris,V.M.Browning,J.P.Kirkland,Processing and cationredistribution of MnZn ferrites via high-energy ball milling,J.Appl.Phys.83(1998)6867–6869.[13]S.K.S.Parashar,R.N.P.Choudhary,Ferroelectric phase transition in Pb 0.92Gd 0.08(Zr 0.53Ti 0.47)0.98O 3nanoceramic synthesized by high-energy ball milling,J.Appl.Phys.94(2003)6091–6096.[14]S.K.Manik,S.K.Pradhan,Preparation of nanocrystalline microwave dielectricZn 2TiO 4and ZnTiO 3mixture and X-ray microstructure characterization by Rietveld method,Physica E 33(2006)69–76.[15]L.B.Kong,T.S.Zhang,et al.,Progress in synthesis of ferroelectric ceramic materialsvia high-energy mechanochemical technique,Prog.Mater.Sci.53(2008)207–322.[16] C.C.Koch,The synthesis and structure of nanocrystalline materialsproduced by mechanical attrition:a review,Nanostruct.Mater.2(1993)109–129.[17]Z.F.Fu,P.Liu,X.M.Chen,et al.,Low-temperature synthesis of Mg 4Nb 2O 9nanopowders by high-energy ball-milling method,J.Alloys Compd.493(2010)441–444.[18]L.B.Kong,J.Ma,H.Huang,et al.,Barium titanate derived from mechanochemicallyactivated powders,J.Alloys Compd.337(2002)226–230.[19]V.Berbenni, A.Marini,G.Bruni,Effect of mechanical milling on solid stateformation of BaTiO 3from BaCO 3–TiO 2(rutile)mixtures,Thermochim.Acta 374(2001)151–158.[20]P.Liu,J.L.Ma,L.Meng,et al.,Preparation and dielectric properties of BST –Mg 2TiO 4composite ceramics,Mater.Chem.Phys.114(2009)624–628.Fig.3.XRD patterns of the calcined powders obtained by different coupled processes (Group a –c for different milling speed and time:300/600rpm for 5h,400/800rpm for 5h and 400/800rpm for 10h ,respectively;Group 1–4for different calcinations temperature:850,900,950and 1000°C ,respectively).Fig.4.SEM images of the powders calcined at 1000°C from the mixtures milled at (a)300/600rpm for 5h,(b)400/800rpm for 5h and (c)400/800rpm for 10h.301C.Liu et al./Powder Technology 212(2011)299–302[21]S.Nishigaki,S.Yano,Kato Hiroshi,T.Hirai,T.Nonomura,BaO–TiO2–WO3microwaveceramics and crystalline BaWO4,J.Am.Ceram.Soc.71(1988)C11–C17.[22]L.C.Sengupta,S.Sengupta,Breakthrough advances in low loss tunable dielectricmaterials,Mater.Res.Innovations2(1999)278–282.[23]X.F.Liang,Z.Y.Meng,W.B.Wu,Effect of acceptor and donor dopants on thedielectric and tunable properties of barium strontium titanate,J.Am.Ceram.Soc.87(2004)2218–2222.[24]L.C.Sengupta.Ceramic Ferroelectric Composite Material BSTO-ZrO2,US Patent5486491,Jan23,1996.[25]T.N.Lin,J.P.Chu,S.F.Wang,Structures and properties of Ba0.3Sr0.7TiO3:MgTiO3ceramic composites,Mater.Lett.59(2005)2786–2789.[26]L.C.Sengupta.Ceramic Ferroelectric Composite Material-BSTO-Magnesium BasedCompound,US Patent5635434,June3,1997.302 C.Liu et al./Powder Technology212(2011)299–302。
简易计算百分之五十终点方法(A simple method of estimating fifty percent endpoints)
494
L. J . REED AND H. MUENCH
dilutions. By inclining to equalize chance variations, the method tends to define the point more nearly than would be possible if it were simply interpolated between the two bracketing results. For purposes of illustration the results of a hypothetical titration of a protective serum are given in table 1. Six mice are tested at each
TABLE 2 Abridged tabulation of the results of table 1 Total Dilution a 1 :8 16 32 64 128 Alive b 6 4 2 2 0 Dead c 0 2 4 4 6 Alive d 14 8 4 2 0 Dead e 0 2 6 10 16
THE AMERICAN
JOURNAL OF HYGIENE
VOL. 27 MAY, 1938 No. 3 A SIMPLE METHOD OF ESTIMATING FIFTY PER CENT ENDPOINTS l ' 2
BY
L. J. REED AND H. MUENCH (Received for publication October 26th, 1937)
TABLE 1
Titration of a hypothetical protective serum
036朱楠_A Simple Method to Evaluate Substrate Layout for Power Modules
A Simple Method to Evaluate Substrate Layout for Power Modules Nan Zhu, Min Chen, Dehong XuDepartment of Electrical Engineering, Zhejiang University, Hangzhou, ChinaE-mail: zhunan_zju@AbstractThis paper aims to provide a simple and convenient method to evaluate substrate layout design for power modules. By identifying the critical commutation paths and defining an indicator of commutation loop inductance, the stray inductances of a substrate layout can be easily evaluated without the time consuming finite element analysis (FEA). A case study of the layout design of a half-bridge IGBT module is carried out. Several different substrate layout designs are evaluated by this method. Stray inductances calculated by FEA tool confirm the effectiveness of the proposed evaluation method. IGBT modules adopting the best layout design are fabricated. And tests have been done upon the fabricated IGBT module sample to verify its low stray inductances.1IntroductionOne of the major concerns of designing the package lay-out of a power module is the parasitic inductances within the module. When the power switch is turning off, the en-ergy stored in these inductances will cause voltage spikes and ringing with the parasitic capacitances of the device. Thus, a poorly designed layout might result in severe turn-off overvoltage and electromagnetic interference (EMI) problems that will strongly affect the safe opera-tion of the module. With the recent rapid improvements of power semiconductor technologies, power switches can switch faster and faster, which makes such problem even more critical.In a conventional wire-bond power module, the stray in-ductances are mainly introduced by power terminals, cop-per trace on the upper side of DBC and chip wire bonds [1]. Poorly designed layout might result in severe turn-off overvoltage that will strongly affect the safe operation of the module. A lot of efforts have been made to optimize the layout design of power modules that can minimize the parasitic inductances [2-4].For power terminals, it is preferred to adopt laminated bus bar structure which will largely reduce the stray induct-ances of power terminals [5, 6]. Therefore, DBC metalli-zation and bonding wires play more and more important roles in power module stray inductances. The substrate layout and chip locations should be carefully designed to minimize stray inductances of the substrate.This paper aims to provide a simple and convenient method to evaluate stray inductances of substrate metalli-zation instead of the time consuming finite element analy-sis (FEA). Using this method, the fitness of a substrate layout design can be instantly judged. A case study of the layout design of a half-bridge IGBT module is carried out. Several layout design examples are evaluated by such method. Stray inductances calculated by FEA tool con-firm the effectiveness of this method. IGBT modules adopting the best layout design are fabricated. And tests have been done upon the fabricated IGBT module sample to verify its low stray inductances.2Substrate layout evaluation meth-odAs the substrate layout of a power module often adopts complex design, time consuming finite element analysis (FEA) is needed when calculating the stray inductances of the substrate. In the designing phase of a power module, the designer may try numerous different layout designs and calculate their stray inductances to make the best choice among them. However, if FEA is required in each calculation, the designing phase will be very time con-suming. The proposed substrate layout evaluation method provides a convenient alternative for evaluating the stray inductances, which will effectively shorten the long de-sign cycles for power modules.Another problem of substrate layout design for power modules is that the design principles are not so clear. For a commutation loop, the loop inductance is determined by both the loop area and loop length, however which ele-ment plays a more important role is unclear. Moreover, the commutation paths on the substrate are open loops, thus the situation is different with that of closed loops.In this section, the proposed substrate layout evaluation method will be described in detail. Taking the open loop characteristic of substrate commutation paths into consid-eration, the concept of partial inductance is adopted. An indicator of commutation loop inductance is derived. Anda set of substrate layout design principles is given.2.1Identification of the critical commuta-tion pathsFirst, the conducting paths on the substrate of a power module before and after current commutation must be identified.Parts of the current conducting paths may be the same be-fore and after current commutation. These parts do not have high frequency AC currents flowing through, thus are irrelevant to stray inductances. On the other hand, the parts that do not overlap are the critical commutation paths, because currents flowing through these paths con-tain high frequency AC components which will induce voltages on their stray inductances.For the sake of simplicity, all the conducting paths are considered as homogeneous conductors with the same cross-sectional area which is very small compared to the lengths of the conductors.2.2 Concepts of partial inductanceThe critical commutation paths are incomplete loops. The calculation of their inductances is different with closed loop conductors. By adopting the concepts of partial in-ductance introduced in [7] and [8], the inductance of an open loop can be evaluated.2.2.1 Definition of partial inductanceFor a closed conductor loop, the area of flux induced by the current carried by the conductor is bounded by the loop. Thus, it seems no flux is associated with an open loop. However, according to the definition of partial in-ductance given in [7] and [8], the flux area associated with a segment of conductor is bounded by the conductor segment and infinity. As depicted in Figure 1, given two straight conductor segments i and j , the flux area associat-ed with partial inductance L ij is shown as the shaded area [7].jb jc jFigure 1 Flux area associated with two conductor seg-mentsTherefore, by adopting Stokes’ theorem, the partial in-ductance L ij can be defined as [7]14i j i j i jc c ij i j b b i j ij a ad d L da da a a r μπ⋅=⎰⎰⎰⎰i j l l (1)where a i and a j are the cross-sectional areas of the two conductor segments, l i and l j are the vectors assigned in the directions of current flow, r ij is the distance between the two conductor segments.2.2.2 Definition of open loop inductanceOpen loop inductance is the partial inductance of an in-complete loop, which is always the case for the commuta-tion paths on the substrate of a power module.By defining a reasonable closing path, the incomplete loop will become a closed loop of which the self induct-ance can be easily calculated with empirical equations. Then, the open loop inductance is the closed loop induct-ance with the partial inductance of the closing path re-moved [7].2.3 Proposed indicator for stray inductanceevaluationIn this section, an indicator will be derived for evaluating the stray inductances of the commutation loops on the substrate of a power module.Again, for the sake of simplicity, filament approximation is applied to all the conducting paths. Thus, the problem is simplified to finding the relation between the inductance of an open loop and its geometrical dimensions.2.3.1 Partial inductance of some basic geometriesPartial self-inductance is defined by Eq. (1) where i and j denote the same conductor. However, the integrand of Eq. (1) becomes singular for the integration is over the samevolume. By using numerical integration, approximationscan be made to evaluate the inductances of the loops with certain geometries. The basic geometriesare rectangular loops and straight line segments.The self-inductance of a single turn rectangular loop with round cross section is given in [9] as()032ln ln ln ln 10L w h h h w w h w d d μπ-⎛⎫⎡=-++⎢⎣⎤⎛⎫⎛⎫+++⨯ ⎪ ⎪⎥⎝⎭⎝⎭⎦ (2)where w (mm) and h (mm) are the width and height of the rectangular loop respectively, d (mm) is the diameter of the cross section (d <<w,h ), μ0 is vacuum permeability, and L (H) is the loop inductance.The partial self inductance of a single straight conductor is given in [9] as302ln 1102l l L d μπ-⎛⎫=-⋅ ⎪⎝⎭ (3)where l (mm) is the length of the conductor, and d (mm) is the diameter of the cross section (d <<l ).Derived from Eq. (2), given the assumption that d <<w,h , the following approximation of the self-inductance of a rectangular loop holds:()()()230320ln mm 1010ln mm 2L w h w h C S μπμπ--≈+⋅⋅⋅=⋅⋅⋅ (4)where C =2·(w+h ) is the perimeter of the loop, and S =w·h is the area of the loop. Thus, the inductance of a rectangu-lar loop is linearly proportional to C ·ln S .For closed loops in other geometries, positive correlation between loop inductance and C ·ln S still holds.As for the straight line conductor, derived from Eq. (3), given the assumption that d <<l , the following approxima-tion of the self-inductance of a single straight conductor holds: ()3010ln 2mm 12L l l μπ-≈⋅⋅⋅-⎡⎤⎣⎦ (5)2.3.2 The choice of the closing pathFor an open loop conductor, the choice of the closing path seems arbitrary. However, to minimize the influence of the closing path on the total inductance of the open loop and to simplify the calculation of the partial inductance of the closing path, the shortest closing path is chosen, that is the straight line connecting the terminals of the path. Here, the partial mutual inductances associated with the closing path are neglected, only the partial self-inductance of the closing conductor is taken into consideration.Then, by removing the partial self-inductance of the clos-ing path from the inductance of the closed loop, the in-ductance of the open loop is obtained.2.3.3 The proposed indicatorFrom Eq. (4) and (5), an indicator of commutation loop inductance can be defined as:()()2ln mm ln 2mm 1C S l l λ=⋅-⋅-⎡⎤⎣⎦ (6)For a commutation loop, a positive correlation exists be-tween the stray inductance and the indicator λ. A large λ value will result in large stray inductance. Thus, one of the main purposes of substrate layout design for power modules is to minimize the λ values of the commutation loops.2.4 Substrate layout design principlesAccording to the indicator of commutation loop induct-ance derived in the previous section, some advices for the substrate layout design for power modules can be given as the following set of substrate layout design principles:1) Carefully place the chips and power terminals to min-imize the areas of all the possible commutation loops. 2) For substrate layout designs with similar commutation loop areas, the one with shorter commutation path length is preferred.3) Evaluate the stray inductances of all the layout design candidates with the proposed indicator λ. The layout design with the smallest λ values can be considered optimal in the perspective of minimizing the stray in-ductances of the commutation loops.3Substrate layout design: a case studyIn this section, a case study of the substrate layout designof a half-bridge IGBT module with the ratings of 1200V/100A is given.Different layout design examples are evaluated by the previously presented evaluation method. Stray inductanc-es calculated by FEA tool confirm that the proposed indi-cator can serve as an effective criterion for substrate lay-out evaluation. And a sample module adopting the best design is fabricated.Experimental tests have been done on the fabricated sam-ple module to extract the critical stray inductances.3.1 Substrate layout design examplesIn this section, three different substrate layout designs for the 1200V/100A half-bridge IGBT module are studied. Two of them are obtained from commercial products, and the other one is a customized layout design for the power section of an IPM with the same ratings.Figure 2(a) shows the equivalent circuit of a half-bridge IGBT module including all the inductive parasitics, where L lead1, L lead2, L lead3 are stray inductances of the positive, negative and output terminals respectively, and L C1, L E1, L a1, L k1, L C2, L E2, L a2, L k2, L trace are the stray inductances on the substrate including wire bonds and DBC copper traces. Figure 2(b) shows the substrate layout of a com-mercial half-bridge module. Under inductive loads, the commutating devices are upper arm IGBT T 1 and lower arm diode D 2, or upper arm diode D 1 and lower arm IGBT T 2. When load current i load is flowing out of the output terminal, current commutates between the upper arm IGBT T 1 and lower arm diode D 2. The conducting paths before and after commutation are shown in both figures by line with arrows in different colors. The parts that do not overlap are the critical commutation paths which are highlighted in Figure 2(b) with white dashed lines.-T T L L L(a) (b)Figure 2 (a) Equivalent circuit of the half-bridge IGBT module; (b) Substrate layout of a commercial productAs listed in Table 1, substrate layout design #1 and #2 are the layouts of the commercial products, and #3 is one of the substrate layout designs for the power section of aD 1T 1T 2D 2+-outCommutating devices: T 1, D 2Commutating devices: T 2, D 1+out-D 1T 1D 2T 2Commutating devices: T 1, D 2Commutating devices: T 2, D 1=55mm 2 =129mm =16.76mm S =55mm 2 C =129mm l =16.76mm D 1T 2T 1D 2out+-Commutating devices: T 1, D 2Commutating devices: T 2, D 1=222.3mm 2 =59.55mm =8mm S =240.1mm 2 C =60.56mm l =8mm +-outABC D(a)PCBout+-Power section(b)TFigure 3 Designed IPM module structure: (a) Layout of power section of the IPM; (b) Structure of the overall IPM; (c) Detailed substrate layout diagram; (d) Equiva-lent circuit of the module Table 2 Stray inductances of the adopted module layout extracted by Ansoft Q3D3.2 Power module dynamic testsSample modules adopting layout design #3 are fabricated. The photograph of the fabricated module is shown in Figure 4. The materials and dimensions of the module are listed in Table 3.Figure 4 Photograph of the fabricated sample moduleTable 3 Dimensions and materials of the moduleTo experimentally measure the stray inductances of the module, dynamic tests are done on the fabricated sample module. The circuit diagram of the test system is shown in Figure 5. Chopper circuit and single pulse test method are adopted. During the test, upper arm IGBT T 1 is kept off, and a single pulse drive signal is put on the lower IGBT T 2. The test equipments used in the tests are listed in Table 4. The bandwidths of the test equipments, espe-cially the current probe, are critical in the tests of dynamic characteristics. Here a coaxial shunt which has a suffi-cient bandwidth of up to 400MHz is used as the current probe.The current and voltage waveforms of IGBT T 2 during a turn-off transient as well as the voltages of the partial in-ductances are measured. As shown in Figure 5, v CE is the voltage of the lower arm IGBT T 2, i c is the current of IGBT T 2 tested with the coaxial shunt, v L1 is the voltage induced on the inductance L lead2+L E2, v L2 is the voltage induced on the inductance L lead1+L k1. The test points of v CE are auxiliary terminal E and auxiliary terminal C; those of v L1 are negative power terminal and auxiliary terminal E; and those of v L2 are auxiliary terminal K and positive power terminal. The test points are shown in Figure 3(c) and Figure 4. The obtained waveforms and test conditions are shown in Figure 6.-VFigure 5 Circuit diagram of test systemTable 4 Test equipments for dynamic testsI c : 20A/divV CE :200V/div V GE =+15V/-8V V dc =600V R g =6.8ΩT j =25℃Turn-off0200ns/div V L1:10V/div(a)V GE =+15V/-8V V dc =600V R g =6.8ΩT j =25℃0V L2:10V/div(b)Figure 6 Current and voltage waveforms during an IGBT turn-off transient and waveforms of (a) v L1 and (b) v L2From the maximum voltages of v L1 and v L2 as well as cur-rent changing rate obtained from the waveforms, the in-ductances of L lead1+L k1 and L lead2+L E2 can be deduced, as listed in Table 5.If the inductance of L a1 is neglected, the overall induct-ance of the commutation path when T 2 and D 1 are com-mutating is 30.9nH, which matches well with the simula-tion result. Therefore, it is confirmed that the adopted module structure has low stray inductances.Table 5 Stray inductances derived from test results4 ConclusionTo provide a simple and convenient method for the evalu-ation of the stray inductances of the substrate layout in a power module, the relation between the stray inductances and the geometrical dimensions of the commutation loops is studied. By adopting the proposed evaluation method instead of the time consuming FEA analysis, the lengthy design cycles for power modules can be largely shortened. A case study of the substrate layout design for a half-bridge IGBT module is carried out to verify the validity of the proposed method. The simulation and experimental test results confirm that the proposed method can serve as a useful guide for substrate layout design.5 References[1] K. Xing, F. C. Lee and D. Boroyevich, "Extractionof parasitics within wire-bond IGBT modules," in Applied Power Electronics Conference and Exposi-tion, 1998. APEC '98. Conference Proceedings 1998., Thirteenth Annual, 1998, pp. 497-503 vol.1. [2] N. Puqi, W. Fei and K. D. T. Ngo, "Automatic Lay-out Design for Power Module," Power Electronics, IEEE Transactions on, vol. 28, pp. 481-487, 2013. [3] L. Shengnan, L. M. Tolbert, F. Wang, and Z. P.Fang, "P-cell and N-cell based IGBT module: Lay-out design, parasitic extraction, and experimental verification," in Applied Power Electronics Confer-ence and Exposition (APEC), 2011 Twenty-Sixth Annual IEEE, 2011, pp. 372-378.[4] L. Shengnan, L. M. Tolbert, F. Wang, and Z. P.Fang, "Reduction of stray inductance in power elec-tronic modules using basic switching cells," in Ener-gy Conversion Congress and Exposition (ECCE), 2010 IEEE, 2010, pp. 2686-2691.[5] M. C. Caponet, F. Profumo, R. W. De Doncker, andA. Tenconi, "Low stray inductance bus bar design and construction for good EMC performance in power electronic circuits," Power Electronics, IEEE Transactions on, vol. 17, pp. 225-231, 2002.[6] F. Zare and G. F. Ledwich, "Reduced layer planarbusbar for voltage source inverters," Power Elec-tronics, IEEE Transactions on, vol. 17, pp. 508-516, 2002.[7] A. E. Ruehli, "Inductance Calculations in a ComplexIntegrated Circuit Environment," IBM Journal of Research and Development, vol. 16, pp. 470-481, 1972.[8] R. Wu, K. Chien-nan and K. C. Kwei, "Inductanceand resistance computations for three-dimensional multiconductor interconnection structures," Micro-wave Theory and Techniques, IEEE Transactions on, vol. 40, pp. 263-271, 1992.[9] M. K. Mills, "Self inductance formulas for multi-turn rectangular loops used with vehicle detectors," in Vehicular Technology Conference, 1983. 33rd IEEE, 1983, pp. 65-73.。
特别简单的方法作文英语
特别简单的方法作文英语Title: The Easiest Way to Write an English Composition。
Writing an English composition can seem like a daunting task, especially when faced with a blank page and amultitude of ideas swirling in your mind. However, fear not! There is indeed a remarkably simple method to approach this endeavor. In this essay, I will outline a step-by-stepguide to effortlessly compose an English composition.First and foremost, it's essential to choose a topicthat interests you. Selecting a subject that you are passionate about will not only make the writing processmore enjoyable but will also result in a more engaging and authentic composition. Whether it's a personal experience,a current event, or a topic from your studies, ensure thatit resonates with you on some level.Once you've decided on a topic, it's time to brainstorm ideas. Take a few minutes to jot down any thoughts,anecdotes, or arguments related to your chosen subject. Don't worry about organizing them at this stage; the goalis simply to get your ideas flowing freely.Next, create an outline. This step is crucial for organizing your thoughts and structuring your composition effectively. Divide your essay into sections –introduction, body paragraphs, and conclusion – andoutline the main points you intend to cover in each. This will provide you with a roadmap to follow as you write, preventing you from feeling lost or overwhelmed.With your outline in hand, begin writing your introduction. Start with a hook – a compelling opening sentence that grabs the reader's attention and sets the tone for the rest of the essay. Then, provide some background information on your topic and end with a thesis statement – a concise summary of the main point or argument you will be making in your composition.Once your introduction is complete, move on to the body paragraphs. Each paragraph should focus on a single mainidea and provide supporting evidence or examples to bolster your argument. Remember to use transition words and phrases to ensure a smooth flow between paragraphs and ideas.As you write, don't worry too much about perfection. The key at this stage is to get your ideas down on paper; you can always revise and edit later. Keep your language clear and concise, and avoid unnecessary jargon or complex sentences that may confuse your reader.Finally, conclude your composition by summarizing your main points and reiterating your thesis statement. Leave the reader with a thought-provoking final thought or question that encourages further reflection on the topic.In conclusion, writing an English composition doesn't have to be a daunting task. By following the simple steps outlined above – choosing a topic, brainstorming ideas, creating an outline, writing your introduction and body paragraphs, and concluding your essay – you caneffortlessly compose a well-structured and engagingcomposition. So go ahead, pick up your pen (or keyboard) and start writing!。
怎样简单的方法作文英语
怎样简单的方法作文英语Writing an English essay can seem daunting, but with the right approach, it can be simplified. Here are some simple methods to help you write a compelling English essay without revealing your prompt:1. Understand the Prompt: Before you begin writing, make sure you fully understand the essay prompt. Identify the main topic or question you're supposed to address.2. Create an Outline: Organize your thoughts by creating a basic outline. Divide your essay into introduction, body paragraphs, and conclusion. Jot down key points or arguments you want to make in each section.3. Introduction: Start your essay with an attention-grabbing opening sentence that introduces the topic. Provide some background information and clearly state your thesis statement, which outlines the main argument or purpose of your essay.4. Body Paragraphs: Each body paragraph should focus ona single idea or argument that supports your thesis. Start each paragraph with a topic sentence that introduces the main point, followed by supporting evidence or examples. Remember to use transitions to connect your ideas smoothly.5. Supporting Evidence: Use evidence from credible sources to support your arguments. This could include quotations, statistics, or examples from literature, history, or personal experience. Make sure to properly cite your sources according to the required citation style.6. Analysis and Interpretation: Don't just summarize the evidence; analyze it and explain how it supports your thesis. Offer your own interpretation or insights, demonstrating critical thinking and understanding of the topic.7. Counterarguments: Acknowledge and address potential counterarguments to your thesis. Anticipating and refuting opposing viewpoints strengthens your argument anddemonstrates intellectual honesty.8. Conclusion: Summarize the main points of your essay and restate your thesis in different words. Leave the reader with a thought-provoking closing statement or a call to action related to your topic.9. Proofread and Revise: Once you've finished writing, take time to proofread your essay for grammar, punctuation, and spelling errors. Also, review the content to ensure clarity, coherence, and consistency of your arguments. Make any necessary revisions to improve the overall quality of your essay.10. Seek Feedback: If possible, have someone else read your essay and provide feedback. Fresh eyes can catch mistakes or offer suggestions for improvement that you might have missed.By following these simple steps, you can write a well-structured and persuasive English essay without revealing your prompt. Remember to stay focused, provide strongevidence to support your arguments, and express your ideas clearly and concisely.。
训练简单的方法英文
训练简单的方法英文Training is an important process that helps individuals acquire new skills and knowledge. Whether it is for personal growth or professional development, finding simple methods for training can make the learning journey more effective and enjoyable. In this article, we will explore some practical techniques that can be easily incorporated into any training routine.1. Set Clear ObjectivesBefore starting any training program, it is crucial to set clear objectives. Knowing what you want to achieve will provide a sense of direction and motivation throughout the training process. Clear objectives help you stay focused and determine whether the training is successful or needs adjustments.When setting objectives, it is beneficial to make them specific, measurable, attainable, relevant, and time-bound (SMART). For example, a SMART objective for improving public speaking skills could be, "To be able to confidently deliver a 5-minute presentation without notes in front of 20 people within six months." Having a concrete objective enhances the effectiveness of the training and ensures measurable progress.2. Break Down Complex SkillsComplex skills can often feel overwhelming, but breaking them down into smaller parts makes them more manageable. Instead of attemptingto learn everything at once, focus on breaking down the skill into smaller, bite-sized tasks. By mastering each task individually, you will gradually build up your overall proficiency.For example, if you want to learn to play the piano, start by learning basic scales and chords before moving on to more complex pieces. Similarly, if you aim to master a new software program, begin with the fundamental features before delving into the advanced functionalities. Breaking down complex skills allows for a gradual learning curve, boosts confidence, and increases overall understanding.3. Practice RegularlyConsistency is key when it comes to training. Regular practice helps reinforce newly acquired skills and ensures steady progress. Whether it is dedicating a specific time slot each day or practicing a few times a week, establishing a routine is essential.Consider incorporating short study or practice sessions into your daily schedule. Consistency, even if it is for a short period, is more beneficial than sporadic, longer sessions. By making training a regular part of your routine, you will develop discipline and create a habit that leads to long-lasting results.4. Seek Feedback and Evaluate ProgressFeedback plays a crucial role in the training process. Actively seek feedback from trainers, mentors, or peers to identify areas forimprovement and validate your progress. Constructive feedback helps in addressing weaknesses and honing skills effectively.In addition to seeking external feedback, it is also essential to evaluate your own progress. Set benchmarks along the way to measure your development and assess whether you are meeting your objectives. Regularly reviewing your progress allows for adjustments and modifications in the training process, if necessary.5. Utilize Resources and TechnologyTraining can be significantly enhanced by utilizing various resources and technology. Books, online courses, tutorials, and podcasts offer a wealth of information and expertise. Take advantage of these resources to deepen your knowledge and gain insights from experts in your field. Moreover, technology can be a valuable tool for training. Interactive learning platforms, video tutorials, and virtual reality simulations provide engaging and immersive learning experiences. Embracing technology allows for more interactive and dynamic training sessions, leading to better retention and application of knowledge.6. Collaborate and Share KnowledgeLearning is not limited to individual efforts. Collaborating with others who are also seeking to learn or have expertise in the field can enhance the training experience. Engage in study groups, discussion forums, or workshops to exchange ideas and perspectives.Sharing knowledge with others not only solidifies your understanding of the subject matter but also provides an opportunity to learn from different viewpoints. Additionally, teaching others allows for a deeper grasp of the material and reinforces your own learning.ConclusionTraining should not be a daunting task. By implementing these simple methods, you can make your training journey more effective and enjoyable. Set clear objectives, break down complex skills, practice regularly, seek feedback and evaluate progress, utilize resources and technology, and collaborate with others. Embrace these techniques, and you will find yourself well on the path to mastering new skills and achieving your training goals.。
用很简单的方法作文英语
Writing an essay in English can seem daunting, but it doesnt have to be. Heres a simple method to help you compose an essay effectively:1. Understand the Topic: Before you start writing, make sure you understand the prompt or question. If its a topic, think about what you know about it and what you need to find out.2. Brainstorm Ideas: Write down all the ideas that come to your mind about the topic. Dont worry about organization at this stage just let your thoughts flow.3. Create an Outline: Organize your brainstormed ideas into a logical order. An outline typically includes an introduction, body paragraphs, and a conclusion.4. Introduction: Start your essay with a catchy opening sentence that grabs the readers attention. Introduce the topic and provide a brief overview of what you will discuss.5. Body Paragraphs: Each paragraph should focus on one main idea that supports your thesis statement. Start with a topic sentence, provide evidence or examples, and explain how this supports your argument.6. Evidence and Examples: Use specific examples, facts, quotes, or statistics to back up your claims. This will make your essay more convincing and interesting to read.7. Transitions: Use transitional words and phrases to connect your ideas smoothly. This helps the reader follow your argument without feeling jolted from one point to another.8. Conclusion: Summarize your main points and restate your thesis in a new way. End with a strong closing statement that leaves a lasting impression on the reader.9. Revise and Edit: After writing your first draft, take some time to review and revise your work. Check for clarity, coherence, grammar, and spelling.10. Proofread: Finally, proofread your essay to catch any remaining errors. Its often helpful to read your essay out loud or ask someone else to read it for a fresh perspective.Remember, writing is a process, and practice makes perfect. Dont be afraid to experiment with different styles and structures until you find what works best for you. And most importantly, enjoy the process of expressing your thoughts and ideas in English.。
英语method的中文是什么意思
英语method的中文是什么意思英语method的中文是什么意思method的用法是很简单的，但还是要了解清楚它的中文意思。
下文是店铺为大家准备了英文单词method的几种中文意思，希望能对大家有所帮助!method的中文意思英 [ˈmeθəd] 美 [ˈmɛθəd]第三人称复数：methods名词方法; 条理相关例句名词1. A new training method was introduced.引进了一种新的训练方法。
2. His book is totally without method.他写的那本书毫无条理。
3. Our teacher is showing us a new method of writing.老师告诉我们一种书写的新方法。
4. If you had used more method, you wouldn't have wasted so much time.要是你安排得更有条理些，就不会浪费那么多时间了。
method的单语例句1. But it is the new " little telescope that could " method that has researchers buzzing.2. China will change its method of cadre selection from appointment to open competition, according to a provisional regulation released Wednesday.3. Apple earlier blamed the reception problem on a wrong method to calculate signal strength, and promised to fix the glitch with software updates.4. The top statistics official's pledge to steadily reform the method of calculating the country's house sale prices in 2011 is welcome.5. Sources said the tax authorities propose to adjust the method for calculating the resource tax to reflect the price of the products.6. The administration announced in February that 10 municipalities and provinces had started experimental work to carry out the calculating method.7. The parties may agree on the method of an overall calculation and one time payment, or of an overall calculation and payment by installment.8. The NBS will release the country's property price index on Friday, the first time it will incorporate a revised method of calculation.method的双语例句1. Radiant and platen superheater`s new method are more agree with the practice law.辐射式过热器和屏式过热器的计算新方法更符合实际运行规律。
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H. FOLLand M. WILKENS : Analysis of Dislocation Loops
phys. stat. sol. (a) 31, 519 (1975) Subject classification: 10
519
Institut fur Ph,llforschung, Stuttgart
Es wird eine neue Methode vorgeschlagen, um anhand des sogenannten “inside-outside” Kontrastes von Versetzungsringen deren Natur (Leerstellen- bzw. Zwischengitteratom-Typ) zu bestimmen. Es ergibt sich eine einfache und einheitliche Verfahrensvorschrift, die in gleicher Weise auf Versetzungsringe mit und ohne Scherkomponente angewandt werden kann, unabhitngig von der Ringorientierung in der Durchstrahlungsprobe. Insbesondere bedingt diese Vorschrift keine Aufteilnng der Ringorientierungen in ,,sichere“ und ,,nnsichere“ Orientierungen, wie dies bei Anwendung der Methode von Maher und Eyre erforderlich ist.
1. Introduction
The analysis of the type of a dislocation loop, vacancy or interstitial, is a common task in transmission electron microscopy of crystalline specimens. If the loops are large enough in order t o give rise to a well-resolved loop image or a t least t o a “double-arc” contrast figure the analysis is best performed by application of the so-called “inside-outside” contrast method (I-0-method) first introduced by Groves and Kelly [l] and used with minor variations by Mazey et al. [ 2 ] and Edmondson and Williamson [3]. This method is based on the fact that under kinematical diffraction conditions the image contrast of a dislocation loop lies either inside or outside the true loop position as projected onto the image plane, depending upon (i) the type of the loop, (ii) its orientation with respect to the electron beam and the operating diffraction vector 9 , and (iii) the sign of the excitation error s. The application of the I-0-method, for instance in the form as described by Hirsch et al. [ 4 ] ,is straightforward in the case of pure edge loops (Burgers vector b perpendicular to the loop plane). A rigid application of this procedure to nonedge loops (loops with b non-perpendicular to the loop plane, sometimes called “loops with shear components”) may lead t o incorrect results. This was first pointed out by Maher and Eyre [5]. I n order to avoid these difficulties Maher and Eyre and, in a slightly different form, Kelly and Blake [6] have worked out
520
H. FOLLand M. WILKENS
somewhat more coniplicated variants of the I-0-method which should yield correct results also in the case of non-edge loops. An essential point of both these variants of the I-0-method is the use of the so-called FS/RH-rule (“finishstartlright-hand”) [?, 41 which is applied in order to define the Burgers vector of the loop. I n the present paper we will show that the I-0-method can be cast into a form which is equally suitable for edge and non-edge loops and which is, to our understanding, more easily applied in practical cases than those of [5, 61. The essential step in our approach is the replacement of the FS/RH-rule by another definition of the Burgers vector of a dislocation loop which was introduced by Kroner [8] and Kroupa [9]. 2. Definitions The crystallographic nature of a dislocation loop is fully characterized by the normal, n , of the loop plane and the Burgers vector, b , of the loop dislocation. In this section we introduce definitions of n and b which will be used later. 1. For a given vector, say v, we distinguish between the “axis” and the “direction” of v. The difference between these two notions is recognized easily, if one considers that two vectors of opposite directions, i.e., v and -v, have a common axis. 2. We define as the loop normal n that unit vector perpendicular to the loop plane which points upwards in the electron microscope, i.e., towards the electron s0urce.l) 3. We may define a positive and a negative surface of the loop area, with the positive surface showing upwards, cf. Fig. 1. Thus n points from the negative to the positive surface. Now the positive direction of the Burgers vector b of the loop is defined as follows: The loop is formed by shifting the negative surface against the positive surface by a displacement b (of course, a t the same time matter has to be removed or added, depending on (n. b ) ) .Prom this definition it follows2): (n . b ) 0 =+ loop of vacancy type , (n b ) 0 jloop of interstitial type .