Description of the spin structure function g_1 at arbitrary $x$ and arbitrary Q^2

Home Search Collections Journals About Contact us My IOPscienceMagnetic and magnetothermal properties and the magnetic phase diagram of high purity single crystalline terbium along the easy magnetization directionThis content has been downloaded from IOPscience. Please scroll down to see the full text.2014 J. Phys.: Condens. Matter 26 066001(/0953-8984/26/6/066001)View the table of contents for this issue, or go to the journal homepage for moreDownload details:IP Address: 61.161.168.25This content was downloaded on 21/04/2015 at 06:22Please note that terms and conditions apply.Journal of Physics:Condensed Matter J.Phys.:Condens.Matter26(2014)066001(7pp)doi:10.1088/0953-8984/26/6/066001Magnetic and magnetothermal properties and the magnetic phase diagram of high purity single crystalline terbium along the easy magnetization directionV I Zverev1,2,A M Tishin1,2,A S Chernyshov3,Ya Mudryk4,K A Gschneidner Jr4,5and V K Pecharsky4,51Faculty of Physics,M V Lomonosov Moscow State University,119991,Moscow,Russia2Advanced Magnetic Technologies and Consulting LLC,142190,Troitsk,Russia3Western Digital,Advanced Media Development1710Automation Pkwy,San Jose,CA95131,USA4The Ames Laboratory,US Department of Energy,Iowa State University,Ames,IA50011-3020,USA5Department of Materials Science and Engineering,Iowa State University,Ames,IA50011-2300,USAE-mail:vi.zverev@physics.msu.ruReceived14September2013,revised20November2013Accepted for publication9December2013Published21January2014AbstractThe magnetic and magnetothermal properties of a high purity terbium single crystal have beenre-investigated from1.5to350K in magneticfields ranging from0to75kOe usingmagnetization,ac magnetic susceptibility and heat capacity measurements.The magneticphase diagram has been refined by establishing a region of the fan-like phase broader thanreported in the past,by locating a tricritical point at226K,and by a more accurate definitionof the criticalfields and temperatures associated with the magnetic phases observed in Tb.Keywords:magnetic materials,rare-earth metals,single crystalline terbium,phase diagram,magnetic transitions(Somefigures may appear in colour only in the online journal)1.IntroductionThe rare-earth metal Tb has the second largest spin moment among lanthanide metals and its total magnetic moment, 9µB,is next to Dy and Ho.Tb crystallizes in the hexago-nal close packed(hcp)structure[1].Magnetization data of polycrystalline terbium over the temperature range from4to 375K in magneticfields ranging from50Oe to18kOe were first reported by Thoburn et al[2].Measurements in weak magneticfields from50to800Oe indicated a paramagnetic (PM)–antiferromagnetic(AFM)order–disorder transition at ∼230K.It was also suggested that terbium is a weak anti-ferromagnet(of an unknown type)between∼218and230K. The AFM state vanishes in magneticfields exceeding200Oe, being replaced by the ferromagnetic(FM)state.Below218K, Tb was reported to be a ferromagnet.A few years later,mag-netization measurements along all crystallographic directions were repeated on single crystalline Tb by Hegland et al[3]. The results generally agreed with those of the polycrystalline sample,with the exception of the Curie and N´e el temperatures, that were reported as221K and229K,respectively.The magnetic structure of terbium was investigated by neutron scattering[4].Koehler et al reported that in the narrow AFM region the magnetic structure of Tb is helical or spiral.The interlayer turn angle varies from20.5◦per layer at the N´e el point(229K)to18.5◦per layer at the AFM–FM transition(218K).In the ferromagnetic state the moments (∼9.0µB per Tb atom)were reported to be in the basal plane. Similar to dysprosium[5],the AFM–FM transition in terbium is a magnetostructural transformation(MST)observed in the vicinity of the Curie point in both zero and non-zero external magneticfields.According to x-ray diffraction measurementsby Darnell[6],the crystallographic symmetry is reduced from hexagonal to orthorhombic at218K.Dietrich et al[7]have reported that the transition between the FM and spiral(helical)structure is of thefirst order;they also determined the N´e el temperature to be∼226K and have shown that in the close vicinity of this temperature the turn angle per layer for the helix varies from20.7◦at226K to 16.5◦at216K,which is in good agreement with previous data[4].In addition to the well known magnetic phases observed in Tb by various experimental techniques,the question of whether the fan phase exists is still under debate.The the-oretical description of the fan structure is given in[1]as a structure in which the moments make an angleθwith thefield direction.The opening angle of the fan thus goes continuously to zero at the second-order transition to the ferromagnetic phase.In the antiferromagnetic phase,the application of low magneticfields in the basal plane of the helical structure should cause a distortion of the helix.According to Nagamiya and Kitano[8],the moments antiparallel to thefield rotate when a criticalfield is exceeded,forming a fan state.The suggestion that the fan phase is possible in Tb was made after a transition from the fan phase to the ferromagnetic state was first indicated by the minimum in thefield dependence of the elastic modulus constant c33in Dy[9].Later,the existence of this phase in Dy was supported by other experimental methods[10,11].Analogous to Dy,the anomaly of elastic modulus(the minimum of c33infields higher than3.5kOe in the temperature range214–218K)measured by Jiles et al[12] has been considered a signature of the fan structure in Tb. However,the authors also note that,instead of a fan,a distorted helical structure in which large ferromagnetic regions had grown from domain walls aligned parallel to thefield direction is also possible.Because of rather contradictory evidence, the fan phase was not included on the phase diagram of Tb in[12].The elastic modulus of terbium has been re-investigated as a function of temperature between200and230K as a function of magneticfield applied along the easy magnetiza-tion direction[13].Based on the observed anomalies in the elastic constants,a magnetic phase diagram was constructed with the Curie temperature at219.5K and the N´e el tem-perature at∼230K.Since the values of the criticalfields reported by the authors differed by as much as a factor of two from those of previously published results,it was concluded that sample purity is of crucial importance in studying the intrinsic behavior of the antiferromagnetic phase of terbium.The existence of the fan phase in dysprosium and re-lated rare-earth metals was shown theoretically by Bagguley et al[14].The authors consider the fan as the evolution of a spiral structure with increasing external magneticfield,but at the same time there may be multiple factors(including sample purity,that leads to different domain wall configurations) which can influence the behavior of the transition from the FM or helical state,and this is why the existence or the absence of the fan phase should be determined in each case. To the best of our knowledge,this phase has only been observed experimentally by measuring the elastic and acoustic properties in magneticfields[15](at the same time,the critical field values determined in the paper have not been corrected for demagnetization);none of the other techniques employed have revealed the fan phase in Tb.For example,measurements of the magnetocaloric effect(MCE)of a Tb single crystal in weak magneticfields<0.1T in the temperature interval220–230K indicated the existence of a tricritical point at228.5K,and even allowed the authors[16]to construct the magnetic phase diagram in the basal plane,but it was impossible to determine the boundaries of the fan phase from MCE measurements. Thus,the only phase diagram of Tb which includes the fan phase was proposed by Kataev et al[17].Combining the data from elastic,magnetic and magnetocaloric measurements,the authors constructed the phase diagram,which mainly repeats the previous ones and also includes the region of the fan phase in the222–228K interval from100to300Oe.Outside this region the fan phase is suppressed.Jennings et al[18]measured the heat capacity of terbium in the temperature range from15to350K.A lambda-type anomaly was observed at227.7K.There was also another anomaly near220K.The magnetic contribution to the heat capacity,C M,was estimated and agreed well with the known magnetization and electrical resistivity data[19].In the past,the magnetic and thermal properties of single crystal Tb were studied using different quality samples,in most cases on samples of unknown and,often,low purity.There is surprisingly little(e.g.in comparison with other rare-earth metals Ho and Dy)information about the magnetic phases existing in Tb,especially about the fan phase.In addition, there also has been a large spread of reported values of the criticalfields and temperatures,which is probably associated with the different experimental techniques used and differ-ent purities of the samples.A thorough investigation of the magnetic and thermal properties of high purity single crystals of Tb is of fundamental importance,because magnetic phase transitions may be strongly affected if the total concentration of impurities exceeds a few hundred ppm by weight[20](we note that concentrations of interstitial impurities are high, but generally their levels are not quoted in commercially available lanthanides).In this paper we report measurements carried out using high purity Tb crystals with the magnetic field applied parallel to the b(in-plane)direction using dc-magnetization,ac magnetic susceptibility,and heat capacity measurements as a function of temperature and applied mag-neticfield.The terbium magnetic phase diagram generated from this investigation is compared with previously known data[21–23].2.Experimental detailsThe single crystals of Tb were prepared by the Materials Preparation Center at the Ames Laboratory6.The major impurities in the polycrystalline metal used to grow the single crystal using a strain-anneal process[24]were as 6Materials Preparation Center,Ames Laboratory of US Department of Energy,Ames,IA,().follows(in ppm at.):O,1900;C,1100;N,180;F,40; Cl,33;Fe,20;Al,5;Cr, 4.4;Cu, 2.3;Si,2;thus the starting material was99.67at.%(99.993wt%)pure.The material has a residual resistivity ratio of160.Crystallographic directions were determined using the back reflection Laue technique.The combined accuracy of the alignment of the crystallographic axes with the direction of the magnetic-field vector was±5◦.The sample for the dc-magnetization and ac magnetic susceptibility measurements was cut in the shape of a parallelepiped,0.96×2.85×0.56mm3(mass9.8mg), by using the spark-eroding technique from a large grain.The longest axis of the parallelepiped was aligned parallel to the b crystallographic axis([110]crystallographic direction)of Tb.The sample for the heat capacity measurements,also cut from a large grain of the same specimen,was aflat cylinder, 3mm high,and10mm in diameter.The b crystallographic axis was perpendicular to the plane of the sample.All isothermal magnetization measurements have been corrected for demagnetization[25].The value of the de-magnetization factor was0.10.The dc-magnetization data (isothermal magnetic-field dependences and isofield temper-ature dependences)and the ac magnetic susceptibility were measured using a Quantum Design MPMS-XL7magnetome-ter.Magnetic measurements were made in external magnetic fields varying from0to70kOe and over the temperature interval from5to300K.The rms(root mean square)amplitude of the ac magneticfield was2.5Oe,and the ac magneticfield working frequency was125Hz.The accuracy of the magnetic measurements is better than1%.The heat capacity in constant magneticfields ranging from0to75kOe was measured between1.5and350K in a semiadiabatic heat pulse calorimeter,which has been described elsewhere[26].The accuracy of the heat capacity data was better than∼0.6%in the temperature interval from 20to350K and better than∼1%in the temperature range 4–20K.3.Magnetic propertiesThe isothermal dependences of the magnetization of the Tb single crystal measured from5to212K with the magnetic field applied parallel to the b axis are shown infigure1.The experimental results are in good agreement with the previous data[2,3].The magnetization is nearly saturated at 6kOe.The saturation value of∼9.02µB(∼315emu g−1) at5K is in good agreement with previous experimental data[3]and the theoretical g J=9µB[1].In the given temperature interval,Tb is reported to be a simple ferromagnet and no metamagnetic features indicatingfield-induced phase transitions are expected or seen,even atfields much lower than the saturationfields.Above212K but below221K(figure2(a)),Tb exhibits no magnetic-field-induced transitions.Further,no anomalies are seen in the isofield magnetic measurements of heat capacity(see below)and magnetic susceptibility(not shown)at temperatures below221K,Figure1.Isothermal magnetization of Tb measured between5and 212K with the magnetic-field vector parallel to the b axis in magneticfields from0to40kOe.which leads to the conclusion that there are nofield-induced transitions in Tb below221K,and it behaves as a typical ferromagnetic material.It is common for rare-earth metals with helical ordering that the magnetizationfirst nearly linearly increases with the magneticfield,and when thefield exceeds some critical value an abrupt change in the magnetization is observed, after which it relatively quickly saturates below the N´e el temperature.Thus,in Tb weak metamagnetic-like features in the magnetization corresponding to a magnetic-field-induced AFM–FM transformation are observed above221K.Only the lowfield parts of the magnetization curves are shown infigure2(b)for clarity,since metamagnetic features are not noticeable at higherfields.In contrast with previous investigations,we collected M(H)data including lowfields, which was not done in the past due to large demagnetizing fields.Oosthuizen et al[27]constructed the magnetic phase diagram based on M(H)and M(T)measurements.The values of the criticalfields have been estimated from intersections of extrapolated linear parts of the magnetization curves,since the authors did not have reliable data in the lowfield region.As a result,the phase diagram represents only three phases,with the helix AFM phase between221and228K and in thefield interval limited to150Oe.At the same time,the errors in determination of the criticalfields were as large as one-third of the values themselves due to the interpolation procedure. By minimizing the demagnetization factor(i.e.having an elongated sample)we were able to measure magnetization values in the lowfield region.This may be not crucial for temperatures below220K,but becomes quite important at higher temperatures.Our results show that the helix AFM phase exists from221to228K and from∼10to∼150Oe.The criticalfield associated with the FM to helix AFM transition first increases from∼10Oe at221K to∼150Oe(the maximum value at226K)and then decreases to zero at the N´e el point,228K(seefigure3),where the AFM phase is completely suppressed.Figure 2.(a)Isothermal magnetization of Tb measured between 215and 220K with the magnetic-field vector parallel to the b axis inmagnetic fields from 0to 20kOe.(b)Isothermal magnetization of Tb measured between 221and 225K with the magnetic-field vector parallel to the b axis in magnetic fields from 0to 1kOe.The data have been corrected fordemagnetization.Figure 3.Isothermal magnetization of Tb measured between 226and 250K with the magnetic-field vector parallel to the b axis in magnetic fields from 0to 2.5kOe.A step-like increase in the magnetization is clearly ob-served at 227K,but at 228K,which is the N´e el temperature,it is reduced to a change of slope of the M (H )function.At 229K and higher temperatures there are no metamagnetic fea-tures in magnetization curves,as Tb adopts the paramagnetic state,and at temperatures higher than 244K the behavior of the magnetization becomes nearly linear.The M (H )curves measured just above the N´e el temperature (229–239K)are not straight lines in the low field region,which is associated with a continuous character of the second-order AFM–PM transition,and with spin fluctuations that persist well above the magnetic ordering temperature.Thus the analysis of the M (H )curves indicates that Tb is ferromagnetic up to 221K,that from 221to 228K in fields of 0–150Oe helical AFM structure is observed,and that above 228K it is paramagnetic.Unlike the case in some of the previous studies,there is no evidence of a fan structure in our isothermal magnetic measurements.Greenough et al [28]argued that limited appearance of a linear region near the knee of the magnetization curves at T C <T <222.8K indicates the existence of fan structure which is restricted by a narrow temperature interval just above the Curie temperature.Sincethe samples used in [28]were spherical in shape,internal field was strongly affected by demagnetization,and M (H )data in the fields below 200Oe were not presented.Further,the linear regions in the magnetization curves observed above the Curie temperature may have been associated with experimental errors because they did not account for the demagnetization factor.We also note that the residual resistivity ratio for the sample used in [28]was 120,indicating a high purity of the material.Thus,one can reasonably conclude that it is difficult,and even may be impossible,to prove the existence of the fan phase in Tb using only magnetic measurements.The temperature dependence of the magnetization along the b axis measured at 50and 100Oe is shown in figures 4(a)and (b).Peaks observed at 220and 228K at 50Oe (inset,fig-ure 4(a))and at the same temperatures at 100Oe correspond to the first-order FM–AFM and second-order AFM–PM mag-netic phase transitions,respectively.The M (T )data are in good agreement with the previously published results [3].The AFM–PM transition shifts towards lower temperatures with increasing magnetic field,as is typical for antiferromag-nets.For the 100Oe data at temperatures below 221K,the magnetization behavior of the zero-field-cooled (ZFC)sample (measurements on heating)is significantly different from the same measured during cooling in field (FC)(see figure 4(b)).Once the material forms domains below the ordering tempera-ture,magnetic field higher than coercive field is required to align them.When the sample is cooled in low field from room temperature the domains align easily just below the Curie temperature (low coercive field),and when the sample is heated after being cooled in zero field the domains may become ‘pinned’(high coercive field),resisting the alignment until warmed up.In figure 4(b)one can see that the coercive field is higher than 100Oe up to the Curie temperature,where the ferromagnetic ordering is beginning to be replaced by the intermediate phase.There is a small temperature hysteresis for the Curie temperature (the first peak in the M (T )dependence),which confirms the first-order character of the AFM–FMFigure4.(a)Isofield magnetization of Tb measured during zero-field-cooled heating from5to250K with the50and100Oe magneticfield parallel to the b axis.The inset shows the expanded view of the region between200and250K.(b)Isofield magnetization with the100Oemagneticfield from5to280K measured during zero-field-cooled heating andfield-heatedcooling.Figure5.Isofield magnetization of Tb measured duringzero-field-cooled heating from150to260K with the500and 1000Oe magneticfields parallel to the b axis.The inset showsisofield magnetization of Tb measured during zero-field-cooled heating andfield-heated cooling from5to280K with the1000Oe magneticfield parallel to the b axis.transition.At the same time,no hysteresis is observed for the second-order AFM–PM transition.Two anomalies are still present in the M(T)dependences at500and1000Oe(figure5).Distinct peaks corresponding to the Curie and the N´e el temperatures are no longer observed(compared with the low field measurements infigure4).There are however two cusps (marked with arrows)on the M(T)dependences,which can be associated with the phase transition locations.Moreover, the locations of the cusps depend on the magneticfield.The N´e el temperature continues to shift to lower temperature but the Curie temperature shifts in the opposite direction with increasing magneticfield.As expected,the difference between ZFC and FC data is significantly reduced compared with 100Oe.Figure6shows the M(T)behavior at3.5and5kOe.The maxima at the transition points disappear and the magnetization exhibits a monotonic decrease withincreasing Figure6.Isofield magnetization of Tb measured duringzero-field-cooled heating from180to280K with3.5and5kOe magneticfields parallel to the b axis.The inset shows the behavior of the d M/d T dependences in the same temperature range.temperature.As follows from the d M/d T behavior(figure6, inset),a single minimum is observed at everyfield,in good agreement with the heat capacity data(see below).It is notice-able that the transition temperature(taken as the minimum of d M/d T)shifts towards higher temperatures with increasing magneticfield.d M/d T shows an asymmetric minimum at 3.5kOe,but a nearly symmetric one at5kOe,which can be related to the disappearance of the AFM phase.As will be shown below(see the heat capacity data),the criticalfield value required to suppress the AFM ordering is5kOe.The temperature dependences of the real and imaginary compo-nents of ac magnetic susceptibility measured along the b axis from5to300K do not reveal additional phase transitions in Tb,and therefore they are not shown here for conciseness.4.Magnetothermal propertiesThe temperature dependences of the heat capacity with the magneticfield applied along the easy magnetization b axis ofFigure7.Temperature dependence of the heat capacity of Tb in several magneticfields between0and75kOe applied along theb axis from1.5to350K.The inset shows temperature dependences of the heat capacity of Tb in low magneticfields between0and5kOe applied along the b axis from200to250K.Tb measured in the temperature interval from1.5to350K are shown infigure7.Two peaks corresponding to the Curie and the N´e el temperatures are observed at∼222and229K,respectively, in zero magneticfield.The peak positions agree well with the results reported in the literature[18,19].The sharp peak at222K corresponding to the Curie temperature represents a minor anomaly compared with the broadλ-type maximum peaking at229K,corresponding to the N´e el temperature.This behavior is consistent with the different natures of the two transitions:first order at the Curie temperature,and second order at the N´e el temperature.The magnitude of the sharp peak at the Curie temperature is indicative of a small entropy change involved in this phase transition,and therefore it may be characterized as a weaklyfirst-order phase transformation. In low magneticfields(less than5kOe)the C(T)curves exhibit two maxima(see the inset),but at5kOe the222Kmaximum disappears,indicating that the AFM–FM transitionis suppressed by5kOe magneticfield.In high magneticfields,theλ-shape peak at229K becomes a broad maximum thatcorresponds to a single FM–PM transition.Upon increasingthe magneticfield,this broad maximum shifts slowly towardshigh temperatures,in agreement with the M(T)data.5.DiscussionExperimental data presented above generally agree with theprevious results[13,15,17,23].The H–T phase diagramwith the magneticfield applied along the easy magnetization(b crystallographic)direction constructed based on our data isshown infigures8(a)and(b).The helix AFM phase exists from∼222to228K in mag-neticfields lower than∼160Oe.The overestimated criticalfield values of300–800Oe reported in the past are mostlikely the result of higher levels of impurities in the samples,which played the role of pinning sites,thus preventing thetransformation of the helix AFM phase by increasing magneticfield.The H crit(T)dependence is a slightly asymmetrical bell-like function with the apparent maximum at226K.The criticalfield is zero at both the Curie and N´e el tem-peratures,which indicates that the helical ordering is easilysuppressed by even the smallest magneticfields at thesepoints.With increasingfield,a broad region of an intermediatephase is observed in the same temperature interval(i.e.be-tween∼221and228K)infields up to5kOe.Accordingto the theoretical investigations[8]and elastic modulus[12]measurements made previously,we believe that this interme-diate phase has a fan structure.Magnetic and magnetothermalproperties measured in the present work do not contain anypeculiar features which could be directly associated with thefan-like phase existence.However,the locations of the phaseboundaries determined from the anomalies of the measuredproperties allowed us to determine the approximate regionofFigure8.(a)The magnetic phase diagram of Tb in intermediate magneticfields with the magnetic-field vector parallel to the easy magnetization direction(b axis)of the crystal at218to234K,and0to6kOe.(b)The magnetic phase diagram of Tb in low magneticfields with the magnetic-field vector parallel to the easy magnetization direction(b axis)of the crystal from of218to234K,and0to600Oe.this phase existence.The fan phase is located between the ferromagnetic and paramagnetic states,i.e.in the temperature range∼221–229K with the highfield limit of5kOe.In the lowfield region(as described above),it is replaced by the helix AFM structure.The fan structure disappears at∼227.3K and ∼5kOe.The main feature of the phase diagram presented here is the relatively broad region of the fan phase.In the previous studies,only one phase diagram containing the fan phase has been reported[17];other reports did not include this phase in the diagrams.However,the question of whether this is a fan-like structure or a different distortion of a helix remains open.In the magneticfields exceeding5kOe,where only two phases(PM and FM)remain,the phase transition boundaries in Tb are rather difficult to determine from the heat capacity data,since the curves exhibit broad maxima.Since it is a second-order phase transition,the location of the PM–FM boundary should remain nearly constant infields exceeding ∼5kOe.In the temperature range between the Curie temperatureand the temperature where the fan phase vanishes,d H critd T >0and the curve represents the phase boundary of afirst-order FM–fan transition.From the other side,in the region whered H crit d T <0,the curve H crit(T)is the phase boundary of thesecond-order fan–PM transition.The point where the phase boundary of thefirst order turns into the phase boundary of the second order is located at227K and∼5kOe.Thus according to Landau theory this point is the tricritical one,reflecting coexistence of FM,PM and fan phases.6.ConclusionDetailed heat capacity,magnetization and ac-susceptibility measurements of single crystal terbium in applied magnetic fields up to75kOe along b and a axes have been carried out from4.2to350K.This information,together with the known ferromagnetic state below221K and the PM state above229K, has allowed us to construct a magnetic phase diagram with the magneticfield applied in the basal plane(along the easy magnetization b direction)of single crystal Tb.The helical antiferromagnetic structure exists from221to228K.The maximum criticalfield of the helical ordering is∼160Oe, correcting the overestimated values of300–800Oe reported earlier.A magnetic phase,which we believe is of the fan type, has been located between221and228K in magneticfields lower than5kOe.This criticalfield is about ten times higher when compared with theoretical predictions and previous experiments,which may be related to the higher purity of our crystals.Even though the presence of the fan-like phase has not been strictly confirmed,the thermodynamic conditions for its likely presence have been established,being compatible with previous elastic and magnetic experiments.However,neutron scattering experiments are required tofirmly establish the fan structure.Hence,the phase relationships presented here are more representative of the intrinsic behaviors of Tb.A tricritical point is located at227K and∼5kOe.AcknowledgmentsWork at the Ames Laboratory is supported by the Office of Basic Energy Sciences,Materials Sciences and Engineering Division of the Office of Science of the US Department of Energy,under contract No DE-AC02-07CH11358with Iowa State University(YaM,VKP and KAG).AMT and VIZ acknowledge support by the AMT&C Group,UK. 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东师范英语语言学16秋在线作业1答案----------------------------------单选题----------------------------------1. _____ refers to the fact that a speaker changes from one language to the other in different situations or when talking about different topics.A. BilingualismB. Code-mixingC. Code-switchingD. Pidgin正确答案：C2. ____________is a process that creates new words by dropping a real or supposed suffix. Edit was originally backformed from editor, and peddle from peddler.A. InformationB. backformulaC. backformationD. backformative正确答案：C3. impossible （为下列单词选择相对应的构词法）A. DerivationB. ConversionC. BackformationD. Blending正确答案：A4. The language used to talk about language is called .A. special languageB. local languageC. metalanguageD. human language正确答案：C5. ______ is a term widely used to refer to varieties according to use in sociolinguistics.A. RegisterB. DialectC. TenorD. Variety正确答案：A6. （Watt ）is the measurement unit of electricity. （为括号部分的单词选择相对应的构词法）A. CoinageB. Sound ReduplicationC. ClippingD. Eponym正确答案：D7. Traditionally, free morphemes were called _________.A. affixesB. prefixC. suffixD. root正确答案：D8. This （vet ）is famous in the town. （为括号部分的单词选择相对应的构词法）A. Sound ReduplicationB. CoinageC. EponymD. Clipping正确答案：D9. The language, used to talk about language, is called__________.A. metalanguageB. artificial languageC. natural languageD. language正确答案：A10. are words that originate from proper names of individuals or places. Sandwich is a common noun originating from the fourth Earl of Sandwich, who put his food between two slices of bread so that he could eat while gambling.A. OriginatorsB. EponymsC. AbbreviationsD. Compoundings正确答案：B11. In Modern linguistics __________ language is regarded as premier.A. writtenB. spokenC. standardD. formal正确答案：B12. ____ is defined as the study of the internal structure and the formation of words.A. MorphologyB. SyntaxC. LexiconD. Morpheme正确答案：A13. ______ is a minimal pair.A. moon/noonB. foot/foodC. she/sheetD. sea/sea正确答案：A14. ____ holds that language is a product of evolutionary development of the human species.A. The Yo-he-ho theoryB. The Pooh-pooh theoryC. The evolution theoryD. The Bow-wow theory正确答案：C15. _____ is related to how we communicate, through speech or writing.A. FieldB. RegisterC. ModeD. Tenor正确答案：C16. It is the ____ function of language, in a sense, that brings the world into our mind.A. IdeationalB. InterpersonalC. LogicalD. Textual正确答案：A17. refers to a specific-general semantic relationship between lexical items. Dog and cat are subordinates of livestock.A. MeronymyB. HyponymyC. PolysemyD. Antonymy正确答案：B18. refers to the process through which people use language to classify the world around and inside them.A. ApproachB. CategorizationC. PrototypeD. Cognition正确答案：B19. ______ refers to the fact that a speaker changes from one language to the other when talking about different topics or in different situations.A. BilingualismB. Code-mixingC. Code-switchingD. Pidgin正确答案：C20. The smallest distinctive linguistic unit that can contrast words in meaningand in form is called a ________.A. phonemeB. phoneC. morphemeD. morph正确答案：A----------------------------------判断题----------------------------------1. The idea that people cooperate with each other in conversing is generalized by Grice (1975) as the politenessprinciple.A. 错误B. 正确正确答案：A2. Language contains two subsystems, one of sounds and the other of meanings.A. 错误B. 正确正确答案：B3. Sodium Chloride and salt, which denote the same substance, differ in Mode of communication.A. 错误B. 正确正确答案：A4. The voiceless bilabial stop in pin and the one in spin are in complementary distribution.A. 错误B. 正确正确答案：B5. 24. Tenor is a term widely used in sociolinguistics to refer to varieties according to use.A. 错误B. 正确正确答案：A6. Rhetorically, homonyms are often used as puns.A. 错误B. 正确正确答案：B7. Insertion sequences are a fundamental unit of conversational structure.B. 正确正确答案：A8. The ideational function is realized by the transitivity system of language.A. 错误B. 正确正确答案：B9. Intonation is the variation of pitch to distinguish utterance meaning.A. 错误B. 正确正确答案：B10. Tone belongs to suprasegmental features.A. 错误B. 正确正确答案：B11. he idea that the learners have a sense of achievement as long as they learn if of vital importance. This kind of motivation may be termed integrative motivation.A. 错误B. 正确正确答案：A12. The focus of traditional linguistics is on diachronic study of language, rather than on synchronic study of language.A. 错误B. 正确正确答案：B13. Semantics is the only discipline that studies meaning.A. 错误正确答案：A14. Krashen’s Monitor Theory belongs to nativist theories.A. 错误B. 正确正确答案：B15. Euphemism refers to a prohibition on the use of, mention of, or association with particular objects, action, or persons.A. 错误B. 正确正确答案：A16. Abbreviation is a process that puts an existing word of one class into another class.A. 错误B. 正确正确答案：A17. English is a typical tone language.A. 错误B. 正确正确答案：A18. In telegraphic stage, children use single words to represent various meanings.A. 错误B. 正确正确答案：A19. Eponyms are words that originate from proper names of individuals or places.A. 错误B. 正确正确答案：B20. Sandwich is a common noun originating from the fourth Earl of Sandwich, who put his food between two slices of bread so that he could eat while gambling.A. 错误B. 正确正确答案：B。

a r X i v :h e p -p h /9711228v 1 4 N o v 1997hep-ph/9711228October 1997O (α)QED Corrections to Polarized Elastic µe and Deep Inelastic lN ScatteringDima Bardin a,b,c ,Johannes Bl¨u mlein a ,Penka Christova a,d ,and Lida Kalinovskaya a,caDESY–Zeuthen,Platanenallee 6,D–15735Zeuthen,GermanybINFN,Sezione di Torino,Torino,ItalycJINR,ul.Joliot-Curie 6,RU–141980Dubna,RussiadBishop Konstantin Preslavsky University of Shoumen,9700Shoumen,BulgariaAbstractTwo computer codes relevant for the description of deep inelastic scattering offpolarized targets are discussed.The code µe la deals with radiative corrections to elastic µe scattering,one method applied for muon beam polarimetry.The code HECTOR allows to calculate both the radiative corrections for unpolarized and polarized deep inelastic scattering,including higher order QED corrections.1IntroductionThe exact knowledge of QED,QCD,and electroweak (EW)radiative corrections (RC)to the deep inelastic scattering (DIS)processes is necessary for a precise determination of the nucleon structure functions.The present and forthcoming high statistics measurements of polarized structure functions in the SLAC experiments,by HERMES,and later by COMPASS require the knowledge of the RC to the DIS polarized cross-sections at the percent level.Several codes based on different approaches for the calculation of the RC to DIS experiments,mainly for non-polarized DIS,were developped and thoroughly compared in the past,cf.[1].Later on the radiative corrections for a vast amount of experimentally relevant sets of kinematic variables were calculated [2],including also semi-inclusive situations as the RC’s in the case of tagged photons [3].Furthermore the radiative corrections to elastic µ-e scattering,a process to monitor (polarized)muon beams,were calculated [4].The corresponding codes are :•HECTOR 1.00,(1994-1995)[5],by the Dubna-Zeuthen Group.It calculates QED,QCD and EW corrections for variety of measuremets for unpolarized DIS.•µe la 1.00,(March 1996)[4],calculates O (α)QED correction for polarized µe elastic scattering.•HECTOR1.11,(1996)extends HECTOR1.00including the radiative corrections for polarized DIS[6],and for DIS with tagged photons[3].The beta-version of the code is available from http://www.ifh.de/.2The Programµe laMuon beams may be monitored using the processes ofµdecay andµe scattering in case of atomic targets.Both processes were used by the SMC experiment.Similar techniques will be used by the COMPASS experiment.For the cross section measurement the radiative corrections to these processes have to be known at high precision.For this purpose a renewed calculation of the radiative corrections toσ(µe→µe)was performed[4].The differential cross-section of polarized elasticµe scattering in the Born approximation reads,cf.[7],dσBORNm e Eµ (Y−y)2(1−P e Pµ) ,(1)where y=yµ=1−E′µ/Eµ=E′e/Eµ=y e,Y=(1+mµ/2/Eµ)−1=y max,mµ,m e–muon and electron masses,Eµ,E′µ,E′e the energies of the incoming and outgoing muon,and outgoing electron respectively,in the laboratory frame.Pµand P e denote the longitudinal polarizations of muon beam and electron target.At Born level yµand y e agree.However,both quantities are different under inclusion of radiative corrections due to bremsstrahlung.The correction factors may be rather different depending on which variables(yµor y e)are used.In the SMC analysis the yµ-distribution was used to measure the electron spin-flip asymmetry A expµe.Since previous calculations,[8,9],referred to y e,and only ref.[9]took polarizations into account,a new calculation was performed,including the complete O(α)QED correction for the yµ-distribution,longitudinal polarizations for both leptons,theµ-mass effects,and neglecting m e wherever possible.Furthermore the present calculation allows for cuts on the electron re-coil energy(35GeV),the energy balance(40GeV),and angular cuts for both outgoing leptons (1mrad).The default values are given in parentheses.Up to order O(α3),14Feynman graphs contribute to the cross-section forµ-e scattering, which may be subdivided into12=2×6pieces,which are separately gauge invariantdσQEDdyµ.(2) One may express(2)also asdσQEDdyµ+P e Pµdσpol kk=1−Born cross-section,k=b;2−RC for the muonic current:vertex+bremsstrahlung,k=µµ;3−amm contribution from muonic current,k=amm;4−RC for the electronic current:vertex+bremsstrahlung,k=ee;5−µe interference:two-photon exchange+muon-electron bremsstrahlung interference,k=µe;6−vacuum polarization correction,runningα,k=vp.The FORTRAN code for the scattering cross section(2)µe la was used in a recent analysis of the SMC collaboration.The RC,δA yµ,to the asymmetry A QEDµeshown infigures1and2is defined asδA yµ=A QEDµedσunpol.(4)The results may be summarized as follows.The O(α)QED RC to polarized elasticµe scattering were calculated for thefirst time using the variable yµ.A rather general FORTRAN codeµe la for this process was created allowing for the inclusion of kinematic cuts.Since under the conditions of the SMC experiment the corrections turn out to be small our calculation justifies their neglection. 3Program HECTOR3.1Different approaches to RC for DISThe radiative corrections to deep inelastic scattering are treated using two basic approaches. One possibility consists in generating events on the basis of matrix elements including the RC’s. This approach is suited for detector simulations,but requests a very hughe number of events to obtain the corrections at a high precision.Alternatively,semi-analytic codes allow a fast and very precise evaluation,even including a series of basic cuts andflexible adjustment to specific phase space requirements,which may be caused by the way kinematic variables are experimentally measured,cf.[2,5].Recently,a third approach,the so-called deterministic approach,was followed,cf.[10].It treats the RC’s completely exclusively combining features of fast computing with the possibility to apply any cuts.Some elements of this approach were used inµe la and in the branch of HECTOR1.11,in which DIS with tagged photons is calculated.Concerning the theoretical treatment three approaches are in use to calculate the radiative corrections:1)the model-independent approach(MI);2)the leading-log approximation(LLA); and3)an approach based on the quark-parton model(QPM)in evaluating the radiative correc-tions to the scattering cross-section.In the model-independent approach the QED corrections are only evaluated for the leptonic tensor.Strictly it applies only for neutral current processes.The hadronic tensor can be dealt with in its most general form on the Lorentz-level.Both lepton-hadron corrections as well as pure hadronic corrections are neglected.This is justified in a series of cases in which these corrections turn out to be very small.The leading logarithmic approximation is one of the semi-analytic treatments in which the different collinear singularities of O((αln(Q2/m2l))n)are evaluated and other corrections are neglected.The QPM-approach deals with the full set of diagrams on the quark level.Within this method,any corrections(lepton-hadron interference, EW)can be included.However,it has limited precision too,now due to use of QPM-model itself. Details on the realization of these approaches within the code HECTOR are given in ref.[5,11].3.2O (α)QED Corrections for Polarized Deep Inelastic ScatteringTo introduce basic notation,we show the Born diagramr rr r j r r r r l ∓( k 1,m )l ∓( k 2,m )X ( p ′,M h )p ( p ,M )γ,Z ¨¨¨¨B ¨¨¨¨£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡£¢ ¡z r r r r r r r r r r r r r rr ¨¨¨¨B ¨¨¨¨r r r r j r r r r and the Born cross-section,which is presented as the product of the leptonic and hadronic tensordσBorn =2πα2p.k 1,x =Q 2q 2F 1(x,Q 2)+p µ p ν2p.qF 3(x,Q 2)+ie µνλσq λs σ(p.q )2G 2(x,Q 2)+p µ s ν+ s µ p νp.q1(p.q )2G 4(x,Q 2)+−g µν+q µq νp.qG 5(x,Q 2),(8)wherep µ=p µ−p.qq 2q µ,and s is the four vector of nucleon polarization,which is given by s =λp M (0, n )in the nucleonrest frame.The combined structure functions in eq.(8)F1,2(x,Q2)=Q2e Fγγ1,2(x,Q2)+2|Q e|(v l−p eλl a l)χ(Q2)FγZ1,2(x,Q2)+ v2l+a2l−2p eλl v l a l χ2(Q2)F ZZ1,2(x,Q2),F3(x,Q2)=2|Q e|(p e a l−λl v l)χ(Q2)FγZ3(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)F ZZ3(x,Q2),G1,2(x,Q2)=−Q2eλl gγγ1,2(x,Q2)+2|Q e|(p e a l−λl v l)χ(Q2)gγZ1,2(x,Q2),+ 2p e v l a l−λl v2l+a2l χ2(Q2)g ZZ1,2(x,Q2),G3,4,5(x,Q2)=2|Q e|(v l−p eλl a l)χ(Q2)gγZ3,4,5(x,Q2),+ v2l+a2l−2p eλl v l a l χ2(Q2)g ZZ3,4,5(x,Q2),(9) are expressed via the hadronic structure functions,the Z-boson-lepton couplings v l,a l,and the ratio of the propagators for the photon and Z-bosonχ(Q2)=Gµ2M2ZQ2+M2Z.(10)Furthermore we use the parameter p e for which p e=1for a scattered lepton and p e=−1for a scattered antilepton.The hadronic structure functions can be expressed in terms of parton densities accounting for the twist-2contributions only,see[12].Here,a series of relations between the different structure functions are used in leading order QCD.The DIS cross-section on the Born-leveld2σBorndxdy +d2σpol Borndxdy =2πα2S ,S U3(y,Q2)=x 1−(1−y)2 ,(13) and the polarized partdσpol BornQ4λp N f p S5i=1S p gi(x,y)G i(x,Q2).(14)Here,S p gi(x,y)are functions,similar to(13),and may be found in[6].Furthermore we used the abbrevationsf L=1, n L=λp N k 12πSy 1−y−M2xy2π1−yThe O(α)DIS cross-section readsd2σQED,1πδVRd2σBorndx l dy l=d2σunpolQED,1dx l dy l.(16)All partial cross-sections have a form similar to the Born cross-section and are expressed in terms of kinematic functions and combinations of structure functions.In the O(α)approximation the measured cross-section,σrad,is define asd2σraddx l dy l +d2σQED,1dx l dy l+d2σpol radd2σBorn−1.(18)The radiative corrections calculated for leptonic variables grow towards high y and smaller values of x.Thefigures compare the results obtained in LLA,accounting for initial(i)andfinal state (f)radiation,as well as the Compton contribution(c2)with the result of the complete calculation of the leptonic corrections.In most of the phase space the LLA correction provides an excellent description,except of extreme kinematic ranges.A comparison of the radiative corrections for polarized deep inelastic scattering between the codes HECTOR and POLRAD[17]was carried out.It had to be performed under simplified conditions due to the restrictions of POLRAD.Corresponding results may be found in[11,13,14].3.3ConclusionsFor the evaluation of the QED radiative corrections to deep inelastic scattering of polarized targets two codes HECTOR and POLRAD exist.The code HECTOR allows a completely general study of the radiative corrections in the model independent approach in O(α)for neutral current reac-tions including Z-boson exchange.Furthermore,the LLA corrections are available in1st and2nd order,including soft-photon resummation and for charged current reactions.POLRAD contains a branch which may be used for some semi-inclusive DIS processes.The initial state radia-tive corrections(to2nd order in LLA+soft photon exponentiation)to these(and many more processes)can be calculated in detail with the code HECTOR,if the corresponding user-supplied routine USRBRN is used together with this package.This applies both for neutral and charged current processes as well as a large variety of different measurements of kinematic variables. Aside the leptonic corrections,which were studied in detail already,further investigations may concern QED corrections to the hadronic tensor as well as the interference terms. References[1]Proceedings of the Workshop on Physics at HERA,1991Hamburg(DESY,Hamburg,1992),W.Buchm¨u ller and G.Ingelman(eds.).[2]J.Bl¨u mlein,Z.Phys.C65(1995)293.[3]D.Bardin,L.Kalinovskaya and T.Riemann,DESY96–213,Z.Phys.C in print.[4]D.Bardin and L.Kalinovskaya,µe la,version1.00,March1996.The source code is availablefrom http://www.ifh.de/~bardin.[5]A.Arbuzov,D.Bardin,J.Bl¨u mlein,L.Kalinovskaya and T.Riemann,Comput.Phys.Commun.94(1996)128,hep-ph/9510410[6]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,DESY96–189,hep-ph/9612435,Nucl.Phys.B in print.[7]SMC collaboration,D.Adams et al.,Phys.Lett.B396(1997)338;Phys.Rev.D56(1997)5330,and references therein.[8]A.I.Nikischov,Sov.J.Exp.Theor.Phys.Lett.9(1960)757;P.van Nieuwenhuizen,Nucl.Phys.B28(1971)429;D.Bardin and N.Shumeiko,Nucl.Phys.B127(1977)242.[9]T.V.Kukhto,N.M.Shumeiko and S.I.Timoshin,J.Phys.G13(1987)725.[10]G.Passarino,mun.97(1996)261.[11]D.Bardin,J.Bl¨u mlein,P.Christova,L.Kalinovskaya,and T.Riemann,Acta Phys.PolonicaB28(1997)511.[12]J.Bl¨u mlein and N.Kochelev,Phys.Lett.B381(1996)296;Nucl.Phys.B498(1997)285.[13]D.Bardin,J.Bl¨u mlein,P.Christova and L.Kalinovskaya,Preprint DESY96–198,hep-ph/9609399,in:Proceedings of the Workshop‘Future Physics at HERA’,G.Ingelman,A.De Roeck,R.Klanner(eds.),Vol.1,p.13;hep-ph/9609399.[14]D.Bardin,Contribution to the Proceedings of the International Conference on High EnergyPhysics,Warsaw,August1996.[15]M.Gl¨u ck,E.Reya,M.Stratmann and W.Vogelsang,Phys.Rev.D53(1996)4775.[16]S.Wandzura and F.Wilczek,Phys.Lett.B72(1977)195.[17]I.Akushevich,A.Il’ichev,N.Shumeiko,A.Soroko and A.Tolkachev,hep-ph/9706516.-20-18-16-14-12-10-8-6-4-200.10.20.30.40.50.60.70.80.91elaFigure 1:The QED radiative corrections to asymmetry without experimental cuts.-1-0.8-0.6-0.4-0.200.20.40.60.810.10.20.30.40.50.60.70.80.91elaFigure 2:The QED radiative corrections to asymmetry with experimental cuts.-50-40-30-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 3:A comparison of complete and LLA RC’s in the kinematic regime of HERMES for neutral current longitudinally polarized DIS in leptonic variables.The polarized parton densities [15]are used.The structure function g 2is calculated using the Wandzura–Wilczek relation.c 2stands for the Compton contribution,see [6]for details.-20-100102030405000.10.20.30.40.50.60.70.80.91HectorFigure 4:The same as in fig.3,but for energies in the range of the SMC-experiment.-20-10010203040500.10.20.30.40.50.60.70.80.91HectorFigure 5:The same as in fig.4for x =10−3.-200-150-100-5005010015020000.10.20.30.40.50.60.70.80.91HectorFigure 6:A comparison of complete and LLA RC’s at HERA collider kinematic regime for neutral current deep inelastic scattering offa longitudinally polarized target measuring the kinematic variables at the leptonic vertex.。

Thank you very much for your email on 9 Mar 2009 with which you sent us the reviewer’s report on our paper with the reference number L09-01810. We also wish to take this opportunity to thank the reviewer for his constructive comments and valuable recommendations. We have carefully revised the manuscript according to reviewer’s suggestion.Our responses to several comments are listed below:Comment 1: Authors discussed their results in the frame of the surface phase separation (PS) scenario. Unfortunately, I am not sure that authors presented enough data to prove this scenario. Authors explain the presence of exchange bias (EB) effect as result of the coexistence of AFM and FM phases. Indeed, the most of observation of the EB effect were studied on AFM/FM interface.. But recent studies have shown that in addition to FM/AFM systems, the EB effect was also observed in samples involving a ferrimagnet (FI) or a spin-glass phase (FI/AFM, FM/FI, FI/SG, AFM/SG), see recent review of Nogues et al. Physics Reports 422 (2005) 65 (2005) (page 77). The surface phase may behave as SG phase, see again review of Nogues.Reply: Indeed, the phase separation (PS) scenario in original manuscript is ill-considered. We have noted that a clear bifurcation of ZFC and FC magnetization curves in Fig. 3, which is an indication of a glassy behavior at low temperature (Ref. 1). In addition, the observed hysteresis curve at 3 K did not show the saturation in fields up to 5 KOe like other conventional SG systems, and they reveal weak ferromagnetism may be due to spin freezing, where the SG-like surface layers may act as the weak “FM” on AFM nanoribbons. The SG-like order probably arises as a result of the higher surface-to-volume ratio afforded by the nanoribbon geometry, i.e., surface effects, which can result in uncompensated spin and a suppression of the long-range AFM order observed in the bulk. These results suggest that the surface phase in the SrMn3O6-δnanoribbons could behave as SG phase induced by surface effect of nanoribbons. Therefore, we reinterpret the presence of exchange bias effect as result of the coexistence of AFM and SG-like phase in the revised manuscript.In the revised manuscript, Page 4, Line 15, we replace “Furthermore, it is very relevant to note that .…a suppression of the long-range AFM order observed in the bulk.” with “Recently, studies have shown that the antiferromagnetism in bulk manganites is suppressed in both nanowires and nanoparticles, accompanied with an appearance of weak ferromagnetism.6,19 A core-shell phenomenological model was proposed, where the relaxation of superexchange interaction on the surface of nanowires or nanoparticles allows the formation of a FM or SG shell, resulting in natural AFM/FM or FM/SG interface.17,20 Considering the SG-like characteristic of magnetization curves in Fig. 3, which is further indicated by the unsaturated M-H curve at 3 K in fields up to 5 KOe like other conventional SG systems in Fig. 4, a similar description for the magnetic structure of the SrMn3O6-δnanoribbons could be suggested, that is, an AFM core and a SG-like shell, where the SG-like surface layers may act as the weak “FM” on AFM nanoribbons.15 The SG-like order probably arises as a result of the higher surface-to-volume ratio afforded by the nanoribbon geometry, i.e., surface effects, which can result in uncompensated spin and a suppression of the long-range AFM order observed in the bulk.”Page 5, Line 10, we insert “It is also observed in the hysteresis curve, which did not show the saturation in fields up to 5 KOe like other conventional SG systems.16 The observed M-H curve at 3 K reveals weak ferromagnetism may be due to spin freezing.”Reference No. 16 is added in the revised manuscript.Comment 2: Page 4, lines 5-7 from the top: “It can be seen that the M(T) curves display a weak AFM transition at T N (~ 46 K), which is typical of the AFM ordering in bulk SrMn3O6-δ reported previously (Ref. 10).” In contrast with results of Ref. 10 where the Neel temperature for the bulk was determined form ac susceptibility, from results presented in Fig. 3 it is impossible to determine the Neel temperature. The deviation of 1/M from CW law may not correspond T N, and it may differ significantly from T N of the bulk.Reply: Yes, from the M(T) curves and the deviation of 1/M from CW law in Fig. 3 it is impossible to determine the Neel temperature.In the revised manuscript, Page 4, Line 5, we delete the sentence “It can be seen that the M(T) curves display a weak AFM transition at T N (~ 46 K), which is typical of the AFM ordering in bulk SrMn3O6-δ reported previously (Ref. 10).” and insert the sentence “The ZFC magnetization curve exhibit a sharp peak at T m (~26 K) accompanied by a clear bifurcation of ZFC and FC magnetization curves, which is an indication of a glassy behavior at low temperature.9,16 ”Comment 3: Page 4, lines 13-14 from the top. “The formation of ferromagnetism at low temperature is further confirmed by the open hysteresis curves at 3 K shown in Fig. 4.” Unfortunately, I don't see any indication of spontaneous magnetization characteristic of FM phase.Reply: Considering the SG-like characteristic, the observed M-H curve at 3 K reveals weak ferromagnetism in the present nonoribbons may be due to spin freezing. Therefore, in our revised manuscript, the sentence “The formation of ferromagnetism at low temperature is further confirmed by the open hysteresis curves at 3 K shown in Fig. 4.” is deleted.Comment 4: Page 6, lines 2-3 from the top: “Results indicate that the exchange bias in the SrMn3O6-δnanoribbons increase with the increasing cooling field.” I believe that the results presented are not enough for such statement. Authors present the results of measurements for 0.5 kOe and 2 kOe only and they don't know the behavior of the exchange bias parameters in magnetic fields between 0.5 and 2 kOe and in H > 2 kOe.Reply: We measured the hysteresis loop at 3 K after the FC in magnetic field of 5 KOe, and show the additional result of measurement for H cool = 5 KOe in FIG. 4 in the revised manuscript. It can be seen that the exchange bias field H E increase with the increasing cooling field.Other modifications include:1.[Abstract, Page 1, Line 8] Replace “In contrast with the antiferromagnetic … may induce aninterfacial exchange anisotropy.” with “In contrast with the antiferromagnetic bulk material, magnetization measurements reveal weak ferromagnetism at low temperature in thesenanoribbons. Most interestingly, a notable exchange-bias effect is observed in the SrMn3O6-δnanoribbons, and the exchange bias is strongly dependent on the cooling field. These results suggest that the phase inhomogeneity in one-dimensional nanostructural manganite may induce exchange anisotropy.”2.[Page 2, Line 3 from bottom] Replace “Recently, exchange bias phenomenon has … and AFMmatrix was proposed.” with “But recent studies have shown that in addition to FM/AFM systems, exchange bias phenomenon was also observed in samples involving a ferrimagnet (FI) or a spin-glass phase ( FI/AFM, FM/SG, SG/AFM ).15 ”We hope that our revised version will be satisfactory for publication in APL. Great thanks to you and the referee for the time and effort you expend on this paper.Ref. 1 S. Karmakar, S. Taran, E. Bose, and B. K. Chaudhuri, Phys. Rev. B 77, 144409 (2008).。

Chapter 2Speech Sounds2.1 Phonetics and PhonologyWe can analyze speech sounds from various perspectives and the two major areas of study are phonetics and phonology•Phonetics studies how speech sounds are produced, transmitted, and perceived. •Phonology is the study of the sound patterns and sound systems of languages.Major branches of phonetics：1. Acoustic phonetics (发音语音学): the study of the physical properties of the speech sounds.2. Auditory phonetics (声学语音学): the study of the way listeners perceive these speech sounds.3. Articulatory phonetics (听觉语音学): the study of how the vocal tract produces the sounds of language.•Phonology is the study of the sound patterns and sound systems of languages.–It aims to ‗discover the principles that govern the way sounds are organized in languages, and to explain the variations that occur‘.–In phonology we normally begin by analyzing an individual language, say English, in order to determine its phonological structure, i.e. which sound units are used and how they are put together.–Then we compare the properties of sound systems in different languages in order to make hypotheses about the rules that underlie the use of sounds in them,–and ultimately we aim to discover the rules that underlie the sound patterns of all languages. Differences Between Phonology and Phonetics2.2 Speech organsPositions of vocal folder( 声带)•V oiceless: [p, s, t] 声带分开，气流无阻碍•V oiced: [b, z, d] 声带相连，气流受阻•Glottal stop(喉塞音): [?] 声带紧闭，无气流通过•Nasals: [m, n, ŋ] 双唇紧闭，鼻腔发音2.3 Segments, divergences and phonetic transcription•Segment音段：there are 4 sound segments in pronouncing “above” (a-b-o-v)•Divergence偏差：ghoti → enough [f] →women [i] →[f i∫] fishnation [∫]→•phonetic transcription音标The IPA→International Phonetic AssociationInternational Phonetic Alphabet•In 1886, the Phonetic Te achers‘ Association was inaugurated by a small group of language teachers in France who had found the practice of phonetics useful in their teaching and wished to popularize their methods. It was changed to its present title of the International Phonetic Association (IPA) in 1897. The first version of the International Phonetic Alphabet (the IPA chart) was published in August 1888.2.4 Consonants and vowels•Consonants The sounds in the production of which there is an obstruction of the air-stream at some point of the vocal tract.•Vowel The sounds in the production of which no vocal organs come very close together and the air-stream passes through the vocal tract without obstruction.In what ways consonants differ from vowels?•Air-stream in Articulation--consonants: the flow of air comes out with some obstructions.--vowels: the flow of air comes out freely2) Function:--consonants are used to separate the vowels.--vowels are used to help the speech organs to get from one consonant position to the next.Categories of consonants:(according to manner of articulation & place of articulation)According to manner of articulation•Stop/plosive 爆破音Oral stop 口腔爆破[ b, p, t, d, k, g]Nasal stop 鼻腔爆破[ m, n, ŋ]•Fricative 摩擦音[ f, v, θ, ð, s, z ʃ, ʒ, h]•(median) Approximant 无摩擦延续音[w, ɹ, j]•Lateral (Approximant)舌边音[ l ]•Affricate (stop + fricative) 塞擦音[ tʃ, dʒ]•others: trill颤音tap一次性接触音flap闪音[r]According to places of articulation•Bilabial 双唇音[b, p, m]•Labiodental 唇齿音[f, v]•Dental 齿音[θ, ð ]•Alveolar 齿龈音[ t, d, n, s, z, ɹ, l ]•Postalveolar / palatal-alveolar颚齿龈音[ ʃ, ʒ]•Retroflex 卷舌音[ r ]•Palatal舌面中音[ j ]•Velar 软颚音[ k, g, ŋ]•Uvular 小舌音（法语中）•Pharyngeal 咽头音（阿拉伯语中）•Glottal 喉音[ h ]Table of English ConsonantsDescription of English consonants•The consonants of English can be described in the following manner:[p] voiceless bilabial stop[b] voiced bilabial stop[s] voiceless alveolar fricative[z] voiced alveolar fricativeV owels•English vowels P52V owel glides•Pure/ monophthong vowels [a] [i]•V owel glidesDiphthongs [ai] [ei]Triphthong [aie] [aue]Description of English vowels•The description of English vowels needs to fulfill four basic requirements:–the height of tongue raising (high, mid, low);–the position of the highest part of the tongue (front, central, back);–the length or tenseness of the vowel (tense vs. lax or long vs. short), and–lip-rounding (rounded vs. unrounded).•We can now describe the English vowels in this way:–[♓] high front tense unrounded vowel–[✞] high back lax rounded vowel–[ ] mid central lax unrounded vowel–[✈] low back lax rounded vowelEnglish vowels2.5 Coarticulation and Phonetic Transcription•2.5.1 Coarticulation•Sounds continually show the influence of their neighbors. For example, map, lamb. When such simultaneous or overlapping articulations are involved, we call the process coarticulation.–If the sound becomes more like the following sound, as in the case of lamb, it is known as anticipatory coarticulation.–If the sound shows the influence of the preceding sound, it is perseverative coarticulation, as is the case of map.2.5.2 Narrow and Broad Phonetic Transcription•◆Broad transcription: omit some details, not necessarily phonological, used in most dictionaries and language textbooks, often in square brackets [ ]◆Narrow transcription: phonological in character, differentiate speech sounds in more detail with the help of the diacritics, enclosed in slant brackets / /•[p] is aspirated in peak and unaspirated in speak.–This aspirated voiceless bilabial stop is thus indicated by the diacritic h, as [p h], whereas the unaspirated counterpart is transcribed as [p].2.6 Phonological AnalysisDefinition of Phonology•Yule‘s book, P54―Phonology is essentially the description of the systems and patterns of speech sounds in a language.‖ It studies speech as a purposeful human activity; it views speech as a sys tematically organized activity, intended– under normal circumstances—to convey meaning.Some Key Concepts of PhonologyPhone and Phoneme•A phone is a phonetic unit or segment. It does not necessarily distinguish meaning; some do, some don’t. e.g. [tin] → [t] [i] [n]•A phoneme can be defined as a minimal unit of sound capable of distinguishing words of different meanings. E.g. [tin] [din] → /t/ /d/–In English, the distinction between aspirated [p h] and unaspirated [p] is not phonemic.–In Chinese, however, the distinction between /p/ and /p h/ is phonemic.Differences Between Phone & Phoneme2.6.1 Phonemes and Allophones•Minimal Pairs•§Minimal pairs: When two words such as ―pat‖ and ―bat‖ are identical in form except for a contrast in one phoneme, occurring in the same position, the two words are described as a minimal pair.Allophones•Allophone: the phonetic variants of a phoneme, or, a set of different forms of a phoneme. e.g. the 2 allophones of the same phoneme /p/ are [pʰ] as in pin and [p] in spin.Complementary distribution•In this case the allophones are said to be in complementary distribution because they never occur in the same context:–[p] occurs after [s] while [p h] occurs in other places./p/ [p] / [s] _____[p h] elsewhere•This phenomenon of variation in the pronunciation of phonemes in different positions is called allophony or allophonic variation.•Phonetic similarity: the allophones of a phoneme must bear some phonetic resemblance•Free Variants and Free Variation (P59)Apart from complementary distribution, a phoneme may sometimes have free variants. For example, cup→[kʰɅpʰ] or [kʰɅpɅ] (the diacritic ― Ʌ‖ indicates no audible release in IPA symbols) The difference may be caused by dialect, habit or individual preference, instead of by any diatribution rule, such phenomenon is called free variation.2.6.2 Phonological processesAssimilationDefinition ---When two phonemes occur in sequence and some aspect of one phoneme is taken or ―copied‖ by the other, the process is known as assimilation, which is also often used synonymously with coarticulation.Types ---•Regressive assimilation /anticipatory coarticulation ( a following sound influences a preceding sound, e.g lamb);•Progressive assimilation /perseverative coarticulation (a preceding sound influences a following sound ,e.g ?to meet you )•Note: assimilation is also happened between words,e.g. sun glass /ŋ/, you can keep them. /ŋ/2.6.3 phonological rules•Nasalization rule (鼻音化):[-nasal] → [+nasal] / ____ [+nasal]→stands for “becomes”/ refers to “in the environment of ”___ “ focus bar” refers to “ the location of the change”/æ/→[æ̃] /____+nasal,+ consonant.e.g. lamb → [læ̃m b] can → [cãn]•Dentalization rule（齿音化）:[-dental] → [+dental] / ____ [+dental]e.g. tent [tɛnt] tenth [tɛṋθ]/n/ is dentalized before a dental fractive /θ/•Velarization rule（颚音化）:[-velar] → [+velar] / ____ [+velar]e.g. since [siṋθ] sink [siŋk]the alveolar nasal /n/ becomes the velar nasal /ŋ/ before the velar stop /k/. (They are all instances of assimilation.)Aspiration rule•V oiceless stop →aspirated/ word initially and initially in stressed syllable•V oiceless stop →unaspireted /#s __ (#:word boundary)voiceless stops are aspirated when they are the initial of a stressed syllable; and are unaspirated after /s/.e. g. “pin” for the first case, and “spin” for the latter one.Lengthening rule•V →V___C# voiced•(V owels are lengthened preceding voiced consonant)Flapping rule•Alveolar stop →voiced flap/V__V unstressed•(/t/,/d/ become [D] between two vowels, the second of which is unstressed)G lottalization rule•Stop voiceless →[?]/__σor /__nasal (σ:syllable boundary)•(/p/, /t/, /k/, especially /t/. Are glottalized when syllable-final or before nasals).Deletion rule•§Under certain circumstances some sounds disappear. Some preceding fricatives and affricates will be influenced by the following sound, which is a devoicing process, namely, the voiced sound will become voiceless.•[+voiced] →[+voiceless]/__ [+voiceless]•(f, v, s, and others)•( love to →[ lΛvtə] [lΛftə] ;•(For more examples please refer to P 61)The English pluralsEnglish Past Tense form•The regular past tense form in English is pronounced as [t] when the word ends with a voiceless consonant, [d] when it ends with a voiced sound, and [ɪd] when it ends with [t] or [d]. e.g. •stopped, walked, coughed, kissed, leashed, reached•stabbed, wagged, achieved, buzzed, soothed, bridged•steamed, stunned, pulled•played, flowed, studied•wanted, located, decided, guided2.7 Distinctive FeaturesThe idea of Distinctive Features was first developed by Roman Jacobson (1896-1982) in the 1940s as a means of working out a set of phonological contrasts or oppositions to capture particular aspects of language sounds. Since then several versions have been suggested.Definition: A particular characteristic which distinguishes one distinctive sound of a language (phoneme) from another or one group of sounds from another group.•[+voiced]& [+nasal] are distinctive features.•Some of the major distinctions include [consonantal], [nasal] and [voiced].–The feature [consonantal] can distinguish between consonants and vowels, so all consonants are [+consonantal] and all vowels [–consonantal].–[nasal] and [voiced] of course distinguish nasal (including nasalized) sounds and voiced sounds respectively•These are known as binary features because we can group them into two categories: one with this feature and the other without.–Binary features have two values or specificati ons denoted by ‗ + ‘ and ‗–‘ so voiced obstruents are marked [+voiced] and voiceless obstruents are marked [–voiced].•The place features are not binary features – they are divided up into four values:–[PLACE: Labial]–[PLACE: Coronal]–[PLACE: Dorsal]–[PLACE: Radical]•They are often written in shorthand forms. P672.8 Syllables•Suprasegmentals•Suprasegmental features are those aspects of speech that involve more than single sound segments.•The principal suprasegmentals are:2.8.1 the Syllable Structure•Syllable•Words can be cut up into units called syllables. A unit in speech which is often longer than one sound and smaller than a whole word.•Onset: the beginning sounds of the syllable; the ones preceding the nucleus. These are always consonants in English.•Rhyme( or rime): the rest of the syllable, after the onset. The rhyme can also be divided up: rhyme=nucleus + coda•Nucleus: the core or essential part of a syllable.•Coda: the final sounds of a syllable; the ones following the nucleus. These are consonants in English2.8.2 The syllable structureσO(nset) R(hyme)N(ucleus ) Co(da)k r æ k t •Monosyllabic word: a word with one syllable, like cat and dog,•Polysyllabic word: a word with more than one syllable, like transplant or festival•Open syllable: bar, tie•Closed syllable: bard, tied•Maximal Onset Principle (MOP)–When there is a choice as to where to place a consonant, it is put into the onset rather than the coda. /k∧ntri/2.9 Stress•Stress refers to the degree of force used in producing a syllable. In transcription, a raised vertical line [│] is often used just before the syllable it relates to.–A basic distinction is made between stressed and unstressed syllables, the former being more prominent than the latter.–Types: primary ~; secondary ~Changing English Stress PatternBecoming norm •inTEGral •coMMUNal •forMIDable •conTROVersyVerb •conVICT •inSULT •proDUCE •reBEL•BLACKboard•BLACKbird。

Fuji Switching Power Supply Control IC Green mode Quasi-resonant ICFA5571/71A/72/73/74/5570/5671Application NoteJanuary 2010Fuji Electric Systems Co., Ltd.Contents1.Description・・・・・・・・・・・・・・・・・ 42.Features・・・・・・・・・・・・・・・・・ 43.Outline drawing・・・・・・・・・・・・・・・・・ 44.Block diagram・・・・・・・・・・・・・・・・・ 5-65.Functional description of pins・・・・・・・・・・・・・・・・・ 66.Rating and Characteristics ・・・・・・・・・・・・・・・・・ 7-107. Characteristic curve ・・・・・・・・・・・・・・・・・ 11-158. Basic operation ・・・・・・・・・・・・・・・・・ 169. Description of the function ・・・・・・・・・・・・・・・・・ 17-2310. Method for using each pin ・・・・・・・・・・・・・・・・・ 24-2811. Advice for designing ・・・・・・・・・・・・・・・・・ 29-3212.Precautions for us ・・・・・・・・・・・・・・・・・ 33-3513. Example of application circuit・・・・・・・・・・・・・・・・・ 36Caution)・The contents of this note will subject to change without notice due to improvement.・The application examples or the components constants in this note are shown to help your design, and variation of components and service conditions are not taken into account. In using these components, a design with due consideration for these conditions shall be conducted.1. OverviewFA5571/71A/72/73/74/70/5671 is a quasi-resonant type switching power supply control IC with excellent stand-by characteristics. Though it is a small package with 8 pins, it has a lot of functions and enables to decrease external parts. Therefore it is possible to realize a small footprint and a high cost-performance power supply.2. Features・A quasi-resonant type switching power supply.・A power supply with excellent standby characteristics. ・Low power consumption with a built-in startup circuit. ・Low current consumption, in operation: 1.35mA・Built-in maximum frequency limitation function: 120kHz(FA5571/72/73/74/70), 170kHz(FA5571A/5671)・Operation at light load (FA5571/71A/72/70/5671: built-in burst function, FA5573/74: built-in frequency reductionfunction)・Built-in drive circuit possible to connect to a power MOSFET directly. Output current: 0.5A (sink) 0.25A (source) ・Built-in overload protection function (FA5571/71A/73/70/5671: auto restart, FA5572/74: timer latch) ・Built-in latch protection function with the secondary over-voltage detection. ・Built-in transformer short circuit protection function. ・Built-in low voltage malfunction protection circuit. ・Package: SOP-8Function list by types3. Outline drawingsType Overload protectionLight load operationMaximum blanking frequencyZCD pin timer latch Delay time T LAT1IS pin latch shutdown thresholdVCC pin OVP thresholdIS pin OCP thresholdFA5571 120kHz(TYP)2.3us(TYP) 2.0V(TYP) nonfunctional 1.0V(TYP)FA5571A Auto restart Burst170kHz(TYP) 4.5us(TYP) 2.0V(TYP) nonfunctional 1.0V(TYP)FA5570 120kHz(TYP)nonfunctional nonfunctional nonfunctional1.0V(TYP)FA5671 Auto restart Burst170kHz(TYP)nonfunctionalnonfunctional 28V(TYP) 0.5V(TYP)FA5572 Timer latch Burst120kHz(TYP) 2.3us(TYP) 2.0V(TYP) nonfunctional 1.0V(TYP)FA5573 Auto restart Frequency reduction 120kHz(TYP) 2.3us(TYP) 2.0V(TYP) nonfunctional 1.0V(TYP)FA5574Timer latchFrequency reduction120kHz(TYP)2.3us(TYP) 2.0V(TYP) nonfunctional1.0V(TYP)SOP-84. Block diagramFA5571/71A/70/5671FBISFA5572ISFA5573ISFA5574IS5. Functional description of pinsPin numberPin name Pin function1ZCDZero current detection input2 FB Feed-back input3 IS Current sense input4 GND Ground5 OUT Output6 VCC Power supply7 NC 8VHHigh voltage input6. Rating and characteristics* “+” shows sink and “–“ shows source in current prescription.(1) Absolute maximum ratingItem Symbol Rating UnitPower supply voltage V CC 30VI OH -0.25 A OUT pin output peak current I OL +0.5 A OUT pin voltage V OUT -0.3 to VCC+0.3 V FB, IS pin input voltage V LT-0.3 to 5.0V I SOZCD -2.0 ZCD pin current I SIZCD +3.0 mA VH pin input voltage V VH -0.3 to 500V Total loss (Ta<25℃)Pd 400 (SOP-8) mWMaximum junction temperature Tj 125 ℃ Storage temperature Tstg‐40 to +150℃* Allowable loss reduction characteristics-302585 125400mW(SOP)Ambient temperature Ta [℃]A l l o w a b l e l o s s(2) Recommended operating conditionItem Symbol MIN TYP MAX UnitPower supply voltage(FA5571/ 71A/72/73/70)11 15 28 V Power supply voltage(FA5671) V CC11 15 26 VVH pin input voltage V VH 80 - 450 V VCC pin capacity C VCC 10 47 220 µFOperating ambient temperature Ta-40-85℃(3) Electric characteristics (Unless otherwise specified : Vcc=15V, Tj=25℃)Current sensing part (IS pin)Item Symbol Condition MIN TYP MAX UnitInput bias current I IS V IS =0V -60 -50 -40 µA V FB =3V, FA5571/71A/72/73/74/70 0.9 1.0 1.1 V Maximum input threshold voltage V thIS V FB =3V, FA5671 0.45 0.5 0.55 V Voltage gain AV IS ⊿V FB /⊿V IS 1.75 2.0 2.25 V/VMinimum ON width Tonmin FB=3V, IS=1.5V 260380500nsOutput delay time *1 T pdISIS input: 0V to 1.5V (Pulse signal)100 175 320 ns Latch shutdown threshold voltageVthISat1.82.0 2.2 VFeedback part (FB pin)Item Symbol Condition MIN TYP MAX UnitPulse shutdown FB pin voltage V THFB0Duty cycle=0%340400460mVFB pin input resistanceR FBFA5571/71A/72/70/5671 V FB =1V to 2V14.4 18.0 21.6 k ΩFA5573/74 V FB =1V to 2V 17.6 22.0 26.4k ΩFB pin currentI FB0 V FB =0V -240 -200 -160 µAFB pin threshold voltagefor light load modeV FBM FA5573/740.951.151.35VMinimum oscillation frequencyF min FA5573/74 V FB =0.5V 0.15 0.3 0.4 kHzZero current detection part (ZCD pin)Item Symbol Condition MIN TYP MAX Unit V THZCD1 V ZCD decreasing 40 60 100 mV Input threshold voltage V THZCD2V ZCD increasing 150 250 340 mVHysteresis width V HYZCD 110190240mVV IHI ZCD =+3mA (High state) 8.2 9.2 10.2 V Input clamp voltageV ILI ZCD =-2mA (Low state)-0.93 -0.8 - V ZCD delay time *1 T ZCD -155300nsFA5571/72/73/74/70 108 120 140 kHz Maximum blankingfrequencyF max FA5571A/5671 155 170 185 kHz Timeout period from the last ZCD trigger *1 T OUT 10 14 18 µs ZCD pin internal resistanceRzcd22.53037.5k ΩOver-voltage protection part (ZCD pin)Item SymbolConditionMINTYPMAXUnit ZCD pin over-voltagethreshold levelV OVP 6.4 7.2 8.0 V VCC pin over-voltagethreshold levelV OVP1FA5671 26 28 30 VDelay from turn-off FA5571/72/73/74 1.8 2.3 2.8 µsTimer latch delay time *1 T LAT1Delay from turn-offFA5571A3.54.55.5 µsT LAT2Delay from exceedingthe Vovp voltage40 57 75 µsOverload protection part (FB pin)Item SymbolConditionMINTYPMAXUnitV OLP1VFBincreasing 3.3 3.5 3.8 V FB pin overload detectionthreshold level *1 VOLP2VFBdecreasing 3.0 3.3 3.6 VOLP delay time T OLP FA5571/71A/73/70/5671: Switching continuingtime after detectingoverload.FA5572/74: Timer latch delay timeafter detecting overload.133 190 247 msOLP output shutdown time *1 T OFFSwitchingshutdowntime afterT OLP periodFA5571/71A/73/70/5671930 1330 1730 msSoft start partItem SymbolConditionMINTYPMAXUnit Soft start time *1 T SFT 1.6 2.6 3.6 msOutput part (OUT pin)Item SymbolConditionMINTYPMAXUnitL output voltage V OL I OL=100mAVCC=15V0.5 1.0 2.0 VH output voltage V OH I OH=-100mAV CC=15V12 13.2 14.5 VRise time *1 tr CL=1nF, Tj=25°C 20 40 100 ns Fall time *1 tf CL=1nF, Tj=25°C 15 30 70 nsHigh voltage input part (VH pin)Item SymbolConditionMINTYPMAXUnitI VHrun V VH=400V,V CC>V STOFF10 30 60 µAI VH1V CC=6.5V, V VH=100VTj=25°C4.0 6.8 9.6 mAVH pin input currentI VH0V CC=0V, V VH=100VTj=25°C0.8 1.6 2.5 mAI pre1V CC=8V, V VH=100VTj=25°C-9 -6.4 -3.7 mAVCC pin charging currentI pre2V CC=16V, V VH=100VTj=25°C-8 -4.8 -3 mALow voltage malfunction protection circuit (UVLO) part (VCC pin)Item SymbolConditionMINTYPMAXUnit ON threshold voltage V CCON UVLO 16 18 20 VOFF threshold voltage V CCOFF UVLO 7 8 9 VHysteresis width V HYS18 10 12 VStartup current shutdown voltage V STOFF Vccincreasing 9.5 10.5 12 VStartup current reset voltage V STRST1 Vccdecreasing 8 9 10 VHysteresis width (startupcurrent)V HYS20.5 1.5 2.0 VCurrent consumption (VCC pin)Item SymbolConditionMINTYPMAXUnitI CCOP1VFB=2.5V、VIS＝1.5V、VZCD=0V、OUT=no_load0.9 1.35 2.0 mAPower supply current inoperationI CCOP2Duty cycle=0%,VFB=0V0.9 1.33 1.9 mAPower supply current at latch I CClatFB=openVCC=11V350 500 650 µA*1 : Regarding to these items, 100% test is not carried out. A specified value is a design guarantee. The column showing ‘-‘ has no specified value.7. Characteristic curve・Unless otherwise specified : Ta=25℃, VCC=15V(*FA5571) ・“+” shows sink and “–“ shows source in current prescription.・Data listed here shows the typical characteristics of an IC and does not guarantee the characteristics.8. Basic operationThe basic operation of the power supply using IC is not switchingoperation with fixed frequency using an oscillator but switching with self-excited oscillation. This is shown in Fig.1 Schematic circuit diagram and Fig.2 Waveform in the basic operation.t1 to t2Q1 turns ON and then Q1 drain current Id (primary current of T1) begins to rise from zero. Q1 current is converted into the voltage by Rs and is input into IS pin.t2When the current of Q1 get to the reference voltage of the current comparator that is fixed by the voltage of FB pin, a reset signal is input into RS flip-flop and Q1 turns OFF.t2 to t3When Q1 turns OFF, then the coil voltage of the transformer turns over and the current I F is provided from the transformer into the secondary side through D1.t3 to t4When the current from the transformer into the secondary side stops and the current of D1 gets to zero, the voltage of Q1 turns down rapidly due to the resonance of the transformer inductance and the capacitor Cd. At the same time the transformer auxiliary coil voltage Vsub also drops rapidly.ZCD pin receives this auxiliary coil voltage but then it has a little delay time because of CR circuit composed with R ZCD and C ZCD on the way. t4If ZCD pin voltage turns down lower than the threshold voltage(60mV(typ.)) of Valley detection, a set signal is input into R-S flip-flop and Q1 turns ON again. If the delay time of CR circuit placed between the auxiliary coil and ZCD pin is adjusted properly, Q1 voltage can be turned on at the bottom. This operation makes the switching loss of TURN ON to the minimum.(Return to t1)Subsequently repeat from t1 to t4 and continue switching.OUTQ1VdsQ1IdD1I FVsubZCD PinCurrentcomparatorout put(reset)1 shotout put(Valleysignal、set)Fig.2 Waveform in basic operation9. Description of the function(1) Steady- state operation and burst operation at light load (FA5571/72/70)FA5571A/5671 Maximum blanking frequency：170kHzSteady- state operationMax fswValleySignalOUTpulseFig.3 Steady-state operation timing chartAt each switching cycle, TURN ON is carried out at the first Valley signal that exceeds the time corresponding to the maximum frequency limit of 120kHz (170kHz : 5571A/5671), counting from the previous TURN ON.Fig.4 Burst operation at light loadWhen FB pin voltage drops lower than the pulse shutdown threshold voltage, switching is shut down. On the contrary when FB pin voltage rises higher than the pulse shutdown threshold voltage, switching is started again. FB pin voltage overshoots and undershoots centering around the pulse shutdown threshold voltage for mode change. Continuous pulse is output during the overshoot period and long period burst frequency is obtained during the undershoot period.FB pin VoltageOUT pinSwitching pulsePulse stop voltage VTHFB00.4 V (typ.)PofswMin ：(ex ）0.3ｋＨｚ　→Fig. 5 Oscillation frequency (f sw) vs output power characteristics (Po)VdsMax fswValley signalOUT pulseFig.6 Steady-state operation timing chartIn the normal operation, each switching cycle is turned on at the first valley signal beyond the time corresponding to the maximum frequency limitation of 120 kHz after the previous turn-on. Moreover, in the light load operation, the maximum frequency limitation is decreased. The frequency lowers approximately to 0.3 kHz at minimum.Start upcircuitSwitchingFig.7 Startup and shutdown (the auxiliary coil voltage is higher than 9 V) Array Vcc10.5VStart upcircuitSwitchingFig.8 Startup and shutdown (the auxiliary coil voltage is lower than 9 V)If the auxiliary coil voltage is higher than 9V, the startup circuit operates only at the startup and since then operates being provided with the auxiliary coil voltage as a power supply.While the auxiliary coil voltage is lower than 9V, the startup circuit continues to keep Vcc between 9V and 10.5V by ON-OFF.(4) Operation at overload■FA5571/71A/73/70/5671 (Auto restart type)VccStart up Circuit On/Off signal10.5V 9V 8VTimer outputSwitchingFB pin Timer operation18VFig.9 Operation at overload (FA5571/71A/73/70/5671)If the overload condition continues longer than 190ms, switching is forced to shut down using an internal timer. The startup circuit is possible to operate within 1520ms after the beginning of the overload condition.If the overload condition continues, switching is done for 190ms and after then Vcc is provided with the startup circuit for 1330ms and the operation shutdown condition is maintained.When 1520ms passes after the beginning of the overload condition, a startup circuit stops its operation and Vcc begins to decrease. When Vcc gets down to 8.0V, the IC is once reset and restarted. Since then startup and shutdown are repeated if the overload condition continues. If the load returns to normal, the IC returns to the normal operation.■FA5572/74(latch type)Fig.10 Operation at overload (FA5572/74)If the overload condition continues longer than 190ms, switching is forced to shut down using an internal timer, and changes to latch mode to maintain this condition. During the condition when switching is shut down due to an overload latch, Vcc is provided with the startup circuit and the operation shutdown condition is maintained.To reset the overload latch, shut down the supply of Vcc from the startup circuit by stopping the input voltage and reduces Vcc lower than 8.0V, the OFF-threshold voltage.Even then, the output voltage must rise up to the setting value at the startup within 190ms settled with a timer.(5) OthersBy pulling-up ZCD pin voltage higher than 7.2V from the outside, shutdown can be carried out. This condition is maintained until the input voltage is shut down and Vcc drops to the OFF threshold voltage of UVLO.Automatic reset with overload protectionIf Vcc is provided by other power supply, latch-stop is carried out.10. Direction for use of pins(1) No.1 pin (ZCD)Function(ⅰ) Detection of timing to make a MOSFET turn ON.(ⅱ) Latch protection with an external signal.(ⅲ) Latch protection for over-voltage on the secondary side.Usage(ⅰ) Detection of turn-on timing・ConnectionThis pin is connected to a transformer auxiliary winding through CR circuit with RZCD and CZCD. (Fig.11)Be careful about polarity of anauxiliary winding.・OperationWhen ZCD pin voltage drops lower than 60mV, MOSFET is turned on.The auxiliary winding voltage swings + and – direction widely along with switching. A clamp circuit is equipped to protect IC from this voltage. If the auxiliary winding voltage is plus, it passes a current shown in Fig. 12 and if minus, shown in Fig.13. And then it clamps ZCD pin voltage.・ComplementSince the threshold voltage of latch protection by an external signal is 6.4V (min.) as described in function (ⅱ), the resistor RZCD must be adjusted for ZCD pin voltage not to exceed 6.4V in ordinary operation. At the same time the resistor RZCD must be adjusted for ZCD pin current not to exceed the absolute maximum rating.The MOSFET voltage oscillates just before TURN ON due to the resonance effect between transformer inductance and resonant capacitor Cd. CZCD is adjusted for MOSFET to turn on at the bottom of this resonance (Fig.14). Generally RZCD is several 10kΩ and CZCD is several 10pF. However CZCD is unnecessary if good timing is obtained.(ⅱ) Latch protection with an external signal▪ ConnectionPull up ZCD pin by an external signal.A connection example in case of over-voltage on the primary side is shown in Fig.15. (Constants are examples. Check the behavior in actual circuit.)▪ OperationIf ZCD pin voltage exceeds 7.2V (typ.) and this condition continues longer than 57µs(typ.), latch protection is carried out.Once latch protection is carried out, the output pulse of the IC is shut down and this condition is maintained.Reset is done by decreasing Vcc lower than UVLO off-Fig.11 ZCD pin circuitFig.12 Clamping circuit (auxiliary coil voltage is plus)Fig.13 Clamping circuit (auxiliary coil voltage is minus) VdsFig.14 Vds waveformdo not guarantee the operation.(ⅲ) Latch protection for over-voltage on the secondary side ▪Connection (FA5571/71A/72/73/74) Same as (ⅰ) Detection of turn-on timing.▪ OperationIf the secondary output voltage (Vo) gets to theover-voltage, the auxiliary coil voltage and ZCD pin voltage also rise.When ZCD pin voltage exceeds 7.2V (typ.) and 2.3 uS (typ.) (71A：4.5us) passes after FET turns off, the latch operation is carried out being fitted with the upper condition and output switching is shut down. (Fig.16)In the latch operation, Vcc voltage is maintained by the start-up circuit and the latch operation is maintained.(2) No.2 pin (FB pin)Function(ⅰ) Input of a feed-back signal from secondaryerror-amplifier.(ⅱ) Detection of an overload condition.Usage(ⅰ) Input of a feedback signal・ConnectionThis pin is connected with the receiver unit of a photo coupler. Concurrently it is connected a capacitor in parallel with the photo coupler to protect noise. (Fig. 17)・OperationThis pin is biased by an IC internal power supply through a diode and a resistor.The FB pin voltage is level-shifted and is input into a current comparator and finally gives the threshold voltage for MOSFET current signal that is detected on IS pin.(ⅱ) Detection of overload・ConnectionSame as (ⅰ) Input of the feed back signal.・OperationIf the output voltage of a power supply drops lower than the set value in an overload condition, FB pin voltage rises and scales out. This state is detected and judged as an overload condition. The threshold voltage to detect an overload is 3.5V (typ).・ComplementFA5571/71A/73/70/5671 operates intermittently in an overload condition and auto restart if the overload condition is removed. Refer to pages 20 for detail operation.FA5572/74 stops switching in an overload condition and goes into latch mode to maintain this condition. Refer to page 21 for detail operation.Vozcdpin0V0VFig.16 ZCD pin waveform for over-voltage on thesecondary sideFig.17 FB pin circuit(3) No.3 pin (IS pin)Function(ⅰ) Detection of MOSFET current(ⅱ) Difficulty for a burst operation at light load(FA5571/71A/72/70/5671) (ⅲ) fsw reduction adjustment (FA5573/74)(ⅳ) Detection of transformer short circuit protectionUsage(ⅰ) Current detection・ConnectionConnect a current detecting resistor Rs between a source pin of MOSFET and GNC. Input The current signal that arises in the MOSFET is input to this resistor (Fig.18).・OperationA MOSFET current signal that is input into IS pin is inputinto a current comparator. When it gets to the threshold voltage that is designated by FB pin, it turns off MOSFET.The maximum threshold voltage is 1V (typ.). MOSFET current is restricted by the current that corresponds to this voltage (1V) even in a transient condition at the startup or in an abnormal condition at overload(ⅱ) Burst operation adjustment (for FA5571/71A/72/70/5671) ・ConnectionA resistor RIS is inserted additionally between the currentdetecting resistor Rs and IS pin (Fig. 19).・OperationA 50μA current supply is included in IS pin of FA5571/71A/72/70/5671, and electric current is sent out from IS pin. The voltage that is equal to the multiplication of the currentvalue and the resistor value is effective to restrain burstoperation.・ComplimentFor example, when getting into burst operation in case of a heavy load, the output ripple becomes bigger. If this is aproblem, this pin should be used. However the moredifficult it becomes to get into burst operation, the moreelectric power consumption in waiting increases.(ⅲ) fsw reduction adjustment▪ ConnectionSame as (ⅱ) Burst operation adjustment▪ OperationFA5573/74 has 50μA internal current source inside IS pin and electric current flows out from IS pin. With the effect of the voltage resulting from the multiplication of this currentvalue and the resistor Ris value, the frequency at light load has difficulty to lower.▪ ComplimentFor example, if switching frequency gets down to the audible frequency in waiting state and this is the problem, this method is used. increases the more power consumption in waiting increases.Fig.18 IS pin circuitFig.19 IS pin filter(ⅳ) Detection of transformer short circuit protection▪ ConnectionSame as (ⅱ) Burst operation adjustment.▪ OperationIf IS pin voltage exceeds 2.0V (typ.) due to the transformer short circuit and so on, FA5571/71A/72/73/74 causes latch stop.(4) No.4 pin (GND pin)FunctionThis is the standard voltage for each IC.(5) No.5 pin (OUT pin)FunctionDriving of MOSFET.Usage・ConnectionThis pin is connected to MOSFET gate pin through a resistor (Fig.20, Fig.21, & Fig.22).・OperationDuring the period MOSFET is ON, this pin is kept in high position and almost the same voltage as Vcc is output.During the period MOSFET is OFF, this pin is kept in lowposition and nearly zero voltage is output.・ComplimentA gate resistor is connected to restrict current of OUT pinand to protect oscillation of gate pin voltage.Output current rating of IC is 0.25A for source and 0.5A for sink.(6) No.6 pin (VCC pin)Function(ⅰ) Provide power supply for IC(ⅱ) Detect over-voltage in primary side and activate latch protection. (FA5671)Usage(ⅰ) Provide power supply for IC▪ ConnectionGenerally the auxiliary coil voltage of a transformer isrectified and smoothed and is connected to this pin.(Fig. 23)In addition the auxiliary coil that is connected to ZCD pin can also be used for this pin.▪ OperationThe voltage provided by the auxiliary coil should be set 11V to 28V(11V to 26V : FA5671) in normal operation.It is possible to drive an IC with the current provided by the startup circuit without using an auxiliary coil, but standbypower increases and heat dissipation of the IC alsoincreases. Therefore it is better to provide Vcc from an And also attention should be paid in selecting a MOSFET to drive because there is limitation of the current to be provided when it is driven only by the startup circuit.Fig.20 OUT pin circuit (1)Fig.21 OUT pin circuit (2)Fig.22 OUT pin circuit (3)Fig.23 VCC circuit(ⅱ) Protection of over voltage (FA5671)・ConnectionSame as the connection described in (ⅰ)Provision of power supply for IC.・OperationIf Vcc exceeds 28V (typ.) and maintains morethan 57µs (typ.), protection of over voltage isactivated and IC is latched.・ComplimentFor example, if the output voltage risesabnormally due to the error of a feedbackcircuit, also Vcc rises abnormally. When Vccexceeds 28V, latch protection is activated.Therefore that operates as over voltageprotection of primary side detection.(7) No.7 pin (N.C.)As this pin is next to a high voltage pin, this pin is not yet connected to IC inside.(8) No.8 pin (VH pin)FunctionProvides startup current.Usage・ConnectionThis pin is connected to a high voltage line. If this isconnected after the current is rectified, this should beconnected through a resistor of several kΩ (Fig.24). Onthe other hand, if connected before the current is rectified, this should be connected to a high voltage line through aresistor of several kΩand a diode (Fig.25, Fig.26).・OperationIf VH pin is connected to high voltage, current flows outfrom Vcc pin through the startup circuit in the IC. Thiscurrent charges the capacitor between Vcc and GND, and Vcc voltage rises. When Vcc exceeds 18V (typ), IC isactivated and begins to operate.If Vcc is provided by an auxiliary winding, a startup circuit goes into shutdown state. On the other hand, if no power is supplied from the auxiliary winding, IC operates normally with a current provided by the startup circuit.・ComplimentIf Vcc is provided not by an auxiliary winding but only by a startup circuit, standby power requirement becomes larger and heat dissipation increases. Therefore it is better to provide Vcc by an auxiliary winding for low standby power dissipation requirement.In addition, much attention is required in selecting MOSFET to drive, because there is a limit to the current to be provided when IC is driven only by a startup circuit.Fig.24 VH pin circuit (1)Fig.25 VH pin circuit (2)Fig.26 VH pin circuit (3)11. Advice for designing(1) Compensation for overload current detectionIf the output of the power supply gets to the overload condition, the current to the MOSFET is limited by the maximum input threshold voltage of IS pin and the output voltage of the power supply drops down. If this conditioncontinues, the current is shut down in the latch mode with overload protection function. (For the details of overload protection function, refer “9-(4) operation at overload”.)At this time, the output current shut down in the latch mode varies according to the input voltage. In some case of shutdown in the latch mode, the higher the input voltage is, the bigger the output current becomes.If this behavior is a problem, a resistor Ris should be connected between a current detection resistor Rs and IS pin and additionally a resistor R1 should be added for compensation. A resistor R1 is approximately several100kΩ to several MegΩ depending on Ris.Be careful that even if the input voltage is low with compensation, the output current of a power supply that is shut down in the latch mode is reduced a little.(2) Input power improvement at light load (FA5573/74)FA5573/74 has a function in it that reduces the power loss by reducing oscillating frequency at light load.But if reduction of the switching frequency is insufficient depending on a circuit being used, the power loss reduction at light load may be insufficient.In such a case, a resistor R2 should be connected between an auxiliary coil and IS pin as shown in Fig.28. If Ris is 1kΩ, R2 is approximately several 100 kΩ to 1MegΩ. If R2 value is made smaller, the switching frequency can be decreased more at light load.But during the MOSFET is ON, the minus voltage may be impressed to IS pin by R2 for a length of time. This minus voltage should not be lower than the absolute maximum rating, –0.3V.In addition, if the switching frequency at light load is set too low, some noise in the transformer may be caused.Fig.27 Compensation for overload protectionFig.28 Compensation for input power improvement atlight load。

卷积神经网络机器学习相关外文翻译中英文2020英文Prediction of composite microstructure stress-strain curves usingconvolutional neural networksCharles Yang，Youngsoo Kim，Seunghwa Ryu，Grace GuAbstractStress-strain curves are an important representation of a material's mechanical properties, from which important properties such as elastic modulus, strength, and toughness, are defined. However, generating stress-strain curves from numerical methods such as finite element method (FEM) is computationally intensive, especially when considering the entire failure path for a material. As a result, it is difficult to perform high throughput computational design of materials with large design spaces, especially when considering mechanical responses beyond the elastic limit. In this work, a combination of principal component analysis (PCA) and convolutional neural networks (CNN) are used to predict the entire stress-strain behavior of binary composites evaluated over the entire failure path, motivated by the significantly faster inference speed of empirical models. We show that PCA transforms the stress-strain curves into an effective latent space by visualizing the eigenbasis of PCA. Despite having a dataset of only 10-27% of possible microstructure configurations, the mean absolute error of the prediction is <10% of therange of values in the dataset, when measuring model performance based on derived material descriptors, such as modulus, strength, and toughness. Our study demonstrates the potential to use machine learning to accelerate material design, characterization, and optimization.Keywords：Machine learning，Convolutional neural networks，Mechanical properties，Microstructure，Computational mechanics IntroductionUnderstanding the relationship between structure and property for materials is a seminal problem in material science, with significant applications for designing next-generation materials. A primary motivating example is designing composite microstructures for load-bearing applications, as composites offer advantageously high specific strength and specific toughness. Recent advancements in additive manufacturing have facilitated the fabrication of complex composite structures, and as a result, a variety of complex designs have been fabricated and tested via 3D-printing methods. While more advanced manufacturing techniques are opening up unprecedented opportunities for advanced materials and novel functionalities, identifying microstructures with desirable properties is a difficult optimization problem.One method of identifying optimal composite designs is by constructing analytical theories. For conventional particulate/fiber-reinforced composites, a variety of homogenizationtheories have been developed to predict the mechanical properties of composites as a function of volume fraction, aspect ratio, and orientation distribution of reinforcements. Because many natural composites, synthesized via self-assembly processes, have relatively periodic and regular structures, their mechanical properties can be predicted if the load transfer mechanism of a representative unit cell and the role of the self-similar hierarchical structure are understood. However, the applicability of analytical theories is limited in quantitatively predicting composite properties beyond the elastic limit in the presence of defects, because such theories rely on the concept of representative volume element (RVE), a statistical representation of material properties, whereas the strength and failure is determined by the weakest defect in the entire sample domain. Numerical modeling based on finite element methods (FEM) can complement analytical methods for predicting inelastic properties such as strength and toughness modulus (referred to as toughness, hereafter) which can only be obtained from full stress-strain curves.However, numerical schemes capable of modeling the initiation and propagation of the curvilinear cracks, such as the crack phase field model, are computationally expensive and time-consuming because a very fine mesh is required to accommodate highly concentrated stress field near crack tip and the rapid variation of damage parameter near diffusive cracksurface. Meanwhile, analytical models require significant human effort and domain expertise and fail to generalize to similar domain problems.In order to identify high-performing composites in the midst of large design spaces within realistic time-frames, we need models that can rapidly describe the mechanical properties of complex systems and be generalized easily to analogous systems. Machine learning offers the benefit of extremely fast inference times and requires only training data to learn relationships between inputs and outputs e.g., composite microstructures and their mechanical properties. Machine learning has already been applied to speed up the optimization of several different physical systems, including graphene kirigami cuts, fine-tuning spin qubit parameters, and probe microscopy tuning. Such models do not require significant human intervention or knowledge, learn relationships efficiently relative to the input design space, and can be generalized to different systems.In this paper, we utilize a combination of principal component analysis (PCA) and convolutional neural networks (CNN) to predict the entire stress-strain c urve of composite failures beyond the elastic limit. Stress-strain curves are chosen as the model's target because t hey are difficult to predict given their high dimensionality. In addition, stress-strain curves are used to derive important material descriptors such as modulus, strength, and toughness. In this sense, predicting stress-straincurves is a more general description of composites properties than any combination of scaler material descriptors. A dataset of 100,000 different composite microstructures and their corresponding stress-strain curves are used to train and evaluate model performance. Due to the high dimensionality of the stress-strain dataset, several dimensionality reduction methods are used, including PCA, featuring a blend of domain understanding and traditional machine learning, to simplify the problem without loss of generality for the model.We will first describe our modeling methodology and the parameters of our finite-element method (FEM) used to generate data. Visualizations of the learned PCA latent space are then presented, a long with model performance results.CNN implementation and trainingA convolutional neural network was trained to predict this lower dimensional representation of the stress vector. The input to the CNN was a binary matrix representing the composite design, with 0's corresponding to soft blocks and 1's corresponding to stiff blocks. PCA was implemented with the open-source Python package scikit-learn, using the default hyperparameters. CNN was implemented using Keras with a TensorFlow backend. The batch size for all experiments was set to 16 and the number of epochs to 30; the Adam optimizer was used to update the CNN weights during backpropagation.A train/test split ratio of 95:5 is used –we justify using a smaller ratio than the standard 80:20 because of a relatively large dataset. With a ratio of 95:5 and a dataset with 100,000 instances, the test set size still has enough data points, roughly several thousands, for its results to generalize. Each column of the target PCA-representation was normalized to have a mean of 0 and a standard deviation of 1 to prevent instable training.Finite element method data generationFEM was used to generate training data for the CNN model. Although initially obtained training data is compute-intensive, it takes much less time to train the CNN model and even less time to make high-throughput inferences over thousands of new, randomly generated composites. The crack phase field solver was based on the hybrid formulation for the quasi-static fracture of elastic solids and implementedin the commercial FEM software ABAQUS with a user-element subroutine (UEL).Visualizing PCAIn order to better understand the role PCA plays in effectively capturing the information contained in stress-strain curves, the principal component representation of stress-strain curves is plotted in 3 dimensions. Specifically, we take the first three principal components, which have a cumulative explained variance ~85%, and plot stress-strain curves in that basis and provide several different angles from which toview the 3D plot. Each point represents a stress-strain curve in the PCA latent space and is colored based on the associated modulus value. it seems that the PCA is able to spread out the curves in the latent space based on modulus values, which suggests that this is a useful latent space for CNN to make predictions in.CNN model design and performanceOur CNN was a fully convolutional neural network i.e. the only dense layer was the output layer. All convolution layers used 16 filters with a stride of 1, with a LeakyReLU activation followed by BatchNormalization. The first 3 Conv blocks did not have 2D MaxPooling, followed by 9 conv blocks which did have a 2D MaxPooling layer, placed after the BatchNormalization layer. A GlobalAveragePooling was used to reduce the dimensionality of the output tensor from the sequential convolution blocks and the final output layer was a Dense layer with 15 nodes, where each node corresponded to a principal component. In total, our model had 26,319 trainable weights.Our architecture was motivated by the recent development and convergence onto fully-convolutional architectures for traditional computer vision applications, where convolutions are empirically observed to be more efficient and stable for learning as opposed to dense layers. In addition, in our previous work, we had shown that CNN's werea capable architecture for learning to predict mechanical properties of 2Dcomposites [30]. The convolution operation is an intuitively good fit forpredicting crack propagation because it is a local operation, allowing it toimplicitly featurize and learn the local spatial effects of crack propagation.After applying PCA transformation to reduce the dimensionality ofthe target variable, CNN is used to predict the PCA representation of thestress-strain curve of a given binary composite design. After training theCNN on a training set, its ability to generalize to composite designs it hasnot seen is evaluated by comparing its predictions on an unseen test set.However, a natural question that emerges i s how to evaluate a model's performance at predicting stress-strain curves in a real-world engineeringcontext. While simple scaler metrics such as mean squared error (MSE)and mean absolute error (MAE) generalize easily to vector targets, it isnot clear how to interpret these aggregate summaries of performance. It isdifficult to use such metrics to ask questions such as “Is this modeand “On average, how poorly will aenough to use in the real world”　given prediction be incorrect relative to some given specification”. Although being able to predict stress-strain curves is an importantapplication of FEM and a highly desirable property for any machinelearning model to learn, it does not easily lend itself to interpretation. Specifically, there is no simple quantitative way to define whether two-world units.stress-s train curves are “close” or “similar” with real Given that stress-strain curves are oftentimes intermediary representations of a composite property that are used to derive more meaningful descriptors such as modulus, strength, and toughness, we decided to evaluate the model in an analogous fashion. The CNN prediction in the PCA latent space representation is transformed back to a stress-strain curve using PCA, and used to derive the predicted modulus, strength, and toughness of the composite. The predicted material descriptors are then compared with the actual material descriptors. In this way, MSE and MAE now have clearly interpretable units and meanings. The average performance of the model with respect to the error between the actual and predicted material descriptor values derived from stress-strain curves are presented in Table. The MAE for material descriptors provides an easily interpretable metric of model performance and can easily be used in any design specification to provide confidence estimates of a model prediction. When comparing the mean absolute error (MAE) to the range of values taken on by the distribution of material descriptors, we can see that the MAE is relatively small compared to the range. The MAE compared to the range is <10% for all material descriptors. Relatively tight confidence intervals on the error indicate that this model architecture is stable, the model performance is not heavily dependent on initialization, and that our results are robust to differenttrain-test splits of the data.Future workFuture work includes combining empirical models with optimization algorithms, such as gradient-based methods, to identify composite designs that yield complementary mechanical properties. The ability of a trained empirical model to make high-throughput predictions over designs it has never seen before allows for large parameter space optimization that would be computationally infeasible for FEM. In addition, we plan to explore different visualizations of empirical models-box” of such models. Applying machine in an effort to “open up the blacklearning to finite-element methods is a rapidly growing field with the potential to discover novel next-generation materials tailored for a variety of applications. We also note that the proposed method can be readily applied to predict other physical properties represented in a similar vectorized format, such as electron/phonon density of states, and sound/light absorption spectrum.ConclusionIn conclusion, we applied PCA and CNN to rapidly and accurately predict the stress-strain curves of composites beyond the elastic limit. In doing so, several novel methodological approaches were developed, including using the derived material descriptors from the stress-strain curves as interpretable metrics for model performance and dimensionalityreduction techniques to stress-strain curves. This method has the potential to enable composite design with respect to mechanical response beyond the elastic limit, which was previously computationally infeasible, and can generalize easily to related problems outside of microstructural design for enhancing mechanical properties.中文基于卷积神经网络的复合材料微结构应力-应变曲线预测查尔斯，吉姆，瑞恩，格瑞斯摘要应力-应变曲线是材料机械性能的重要代表，从中可以定义重要的性能，例如弹性模量，强度和韧性。