Martensitic transition and magnetoresistance in a Cu-Al-Mn shape memory alloy. Influence of

合集下载

Cu掺杂对TiNi合金马氏体相变路径影响的第一性原理研究

Cu掺杂对TiNi合金马氏体相变路径影响的第一性原理研究严顺涛;姜振益【期刊名称】《物理学报》【年(卷),期】2017(66)13【摘要】不同浓度的Cu元素掺杂会极大地影响TiNi二元合金的物理性质和相变行为.为了解释其中的物理机制,本文通过第一性原理计算,对TiNi和Ti50Ni25Cu25的相变机制和相稳定性进行了计算和讨论.通过计算Cu掺杂前后立方相到正交相、再到单斜相过程中的相变路径和相变势垒,解释了Cu掺杂对二元合金TiNi相变过程的影响.计算结果表明:TiNi合金的正交相和单斜相之间存在一个大小为1.6 meV的相变势垒;而对于Ti50Ni25Cu25,这两个相之间的相变势垒大小至少为10.3 meV,如此大的一个相变势垒意味着Ti50Ni25Cu25合金的正交相很难跨过势垒相变到单斜相.%As is well known, copper is such an unbelievable element that it can affect the phase transition behaviors of binary TiNi alloy when it displaces Ni element up to near upon 25%. The martensitic transition behaviors of TiNi1?xCux alloys appear from high-temperature cubic B2 phase to intermediate B19 structure with orthorhombic system and then finally to low-temperature B19′ phase with monoclinic system with x 610%on cooling, so called two-stage martensitic phase transformation. Whereas, it directly transforms into orthorhombic B19 phase with x>20%on cooling, so called one-stage martensitic phase transformation. The orthorhombic B19 phase becomes final low-temperature phase while monoclinic phase will be unstable on cooling.The electronic structures and the formation energies of various point defects, Mulliken bond orders, etc. are studied for TiNi1?xCux alloys, however, the phase transition pathway at an atomic level has not been described at all, and further, the difference in transition pathway between TiNi and Ti1Ni1?xCux has not been understood so far. In this work, we optimize the crystal structures of TiNi and Ti50Ni25Cu25 alloys with initial geometry from experimental data. In order to choose the proper positions of Cu atom, we calculate the total energy of each doping system and find the most stable configuration. To study the transformation mechanism of TiNi, we calculate the phonon-dispersion spectra of each phase with both frozen-phonon method and linear response method, and then find the atomic vibrations with the imaginary frequency. Finally, with the help of this atomic vibration direction with negative frequency, we find the intermediate structures by the linear interpolation method and calculate their total energies. The phase transformation of TiNi from cubic to orthorhombic phase is driven by the phonon softening at the M point (0.5, 0.5, 0) of Brillouin zone. For orthorhombic and monoclinic phase, TiNi has real phonon frequencies for all k points and modes. A barrier of 1.6 meV is calculated between orthorhombic and monoclinic phase while no barrier is found between cubic and orthorhombic phase of TiNi, so it is easy to transform from cubic to orthorhombic and then to monoclinic phase. There exists a potential energy barrier of 10.3 meV at least between orthorhombic and monoclinic phase for Ti50Ni25Cu25, which is too high for its transition to overcome the maximum value of potential energywhich corresponds to γ = 93.4?. The difference in transition pathway between TiNi and Ti50Ni25Cu25 accords well with the experimental measurement, so that the copper concentration with 25% in binary TiNi alloy will offer a new transition path from cubic to orthorhombic phase.【总页数】7页(P57-63)【作者】严顺涛;姜振益【作者单位】西北大学现代物理研究所, 陕西省理论物理前沿重点实验室, 西安710069;西北大学现代物理研究所, 陕西省理论物理前沿重点实验室, 西安 710069【正文语种】中文【相关文献】1.Cu掺杂6000系铝合金中β″相的第一性原理研究 [J], 温柏杨;贾志宏;吴小志;刘庆2.内在缺陷与Cu掺杂共存对ZnO电磁光学性质\r影响的第一性原理研究 [J], 张梅玲;陈玉红;张材荣;李公平3.Cu掺杂对TiO2性质影响的第一性原理研究 [J], He Chengdong;Zhang Yulin4.Zn掺杂对Heusler型磁性形状记忆合金Ni_(2)FeGa_(1-x)Zn_(x)(x=0-1)电子结构、磁性与马氏体相变影响的第一性原理研究 [J], 孙凯晨;刘爽;高瑞瑞;时翔宇;刘何燕;罗鸿志5.Al-Cu合金中Sc掺杂θ′/Al界面稳定性和电子结构的第一性原理研究 [J], 张冬兰;汪炯;孔毅;邹有;杜勇因版权原因，仅展示原文概要，查看原文内容请购买。

《2024年铁磁-反铁磁体系中交换偏置的角度依赖关系及其阶跃现象》范文

《铁磁-反铁磁体系中交换偏置的角度依赖关系及其阶跃现象》篇一铁磁-反铁磁体系中交换偏置的角度依赖关系及其阶跃现象一、引言在当代物理学中，铁磁（FM）和反铁磁（AFM）材料之间的相互作用是理解诸多物理现象的基础之一。

当铁磁材料与反铁磁材料形成交联系统时，一种重要的现象就是交换偏置（Exchange Bias），其显著影响着系统的磁性性质和自旋电子学器件的应用。

在众多研究之中，探讨交换偏置的角度依赖关系及其出现的阶跃现象对深化我们对这些系统的理解具有至关重要的意义。

二、交换偏置的基本概念交换偏置是一种由铁磁与反铁磁层间的耦合产生的特殊效应。

这种效应通常发生在反铁磁层的极化方向固定在某个特定方向后，与之邻近的铁磁层产生一个非零的偏置场。

该偏置场的存在导致铁磁层的矫顽力增加，并且可能在室温下表现出显著的非共线行为。

三、角度依赖关系角度依赖关系是指在不同角度下测量铁磁层和反铁磁层间的交换偏置时所观察到的变化。

当磁场与反铁磁层的极化方向之间的角度变化时，交换偏置的大小和方向都会发生变化。

这种变化反映了系统内部自旋排列的复杂性以及不同材料间相互作用的复杂性。

四、阶跃现象在研究过程中，我们观察到在特定的角度下，交换偏置会出现明显的阶跃现象。

这种阶跃现象可能是由于在特定角度下，系统内部的自旋排列突然发生改变，导致交换偏置的突然变化。

这种阶跃现象对于理解自旋电子学器件中的磁化翻转机制以及优化器件性能具有重要意义。

五、实验与理论分析为了研究角度依赖关系及其阶跃现象，我们设计了一系列实验并进行了理论分析。

通过改变磁场与反铁磁层极化方向之间的角度，我们观察到交换偏置的变化趋势，并发现阶跃现象的存在。

通过理论分析，我们发现这种阶跃现象与系统内部的自旋排列和材料间的相互作用密切相关。

六、结论通过对铁磁/反铁磁体系中交换偏置的角度依赖关系及其阶跃现象的研究，我们加深了对这些系统的理解。

我们发现，交换偏置的角度依赖关系反映了系统内部自旋排列的复杂性以及不同材料间相互作用的复杂性。

Origins of the magnetomechanical effect

*Corresponding author.E-mail addresses:daniel.bulte@utoronto.ca(D.P.Bulte),ngman@.au(ngman).0304-8853/02/$-see front matter r2002Elsevier Science B.V.All rights reserved. P II:S0304-8853(02)00588-7applied simultaneously both in the direction of magnetisation,and perpendicular to it,while ﬁelds of up to 5kA/m were cycled at 0.05Hz to produce ‘‘near saturation loops’’.Groups of these loops were then superimposed onto a single set of axes to allow easy comparison of their features.The stresses are applied by means of a system of levers and are measured by strain gauges glued to both sides of the steel in the x -and y -axis,four gauges in all.The levers are adjusted so that both x gauges read the same to within three microstrain,and similarly for the y gauges.In this way the stresses are known to an error of not more that 1MPa in each axis.The gauges on opposite faces are essential to conﬁrm that no bending of the cruciform occurs.A ﬁnite element model of the cruciform showed that the stress pattern is uni-form to within 5%inside a circle 30mm in diameter.The gauges,Hall plate and ﬂux coil are all inside this area.There is also some distortion in the strain adjacent to the holes for the ﬂux coil,but 95%of the steel enclosed by the coil sees the same strain pattern as if the holes were absent [2].The hysteresis loops were checked with those from a permeameter for an unstressed specimen of the identical steel and the difference was less than 2%over a range of ﬂux density from 0to 1.4T.Data were also collected from three samples ofalloy steel using a completely different set of equipment.Thus,we are conﬁdent that effects reported here are genuine.2.The DataFig.1shows initial curves obtained using the method described in Ref.[3]from a mild steel cruciform in the stress rig using the twin U-cores with no applied stress,and a rectangular-bar-shaped specimen cut from the same plate,in a standard permeameter.The ﬂux densities are slightly different,however,the general shapes of the curves are very similar.It was therefore considered that the loops and curves may be compared with others obtained using similar equipment and conditions.Fig.2is the most important set of results presented here.It shows a superposition of seven curves,all with zero applied stress in the y -direction (perpendicular to the applied ﬁeld),and a range of stresses in the x -direction (parallel to the ﬁeld).The dominant feature of this graph is the two coincident points which are common to all curves in the second and fourth quadrants.In order to further investigate the nature of these coincident points,a series ofstressedparison of initial curves obtained from bar and cruciform specimens.D.P.Bulte,ngman /Journal of Magnetism and Magnetic Materials 251(2002)229–243230hysteresis loops were obtained with lower max-imum applied ﬁelds.These curves are presented in Fig.3,and as can be seen,the coincident points occur at approximately the same applied magnetic ﬁeld strength (B 200A =m),but at a lower ﬂux density.Fig.4shows a major hysteresis loop obtained from the mild steel cruciform in the stress rig using the twin U-cores with À120MPa (compression)in the x -direction (parallel to the applied ﬁeld),and 120MPa (tension)in the y -direction (perpendicu-lar to the ﬁeld).As can be seen in this graph the gradual ‘‘S’’-shaped curve which usually forms one side of the hysteresis loop has developed more of a discontinuity of slope in the second quadrant (and fourth quadrant on the other side).It may also be noted that this ‘‘kink’’in the loop occurs at approximately the same ﬁeld as thecoincidentFig.2.Superimposition of hysteresis loops of mild steel under a range of stresses parallel to the direction ofmagnetisation.Fig.3.Hysteresis loops of stressed mild steel with maximum ﬁeld values considerably less than the saturation ﬁeld.D.P.Bulte,ngman /Journal of Magnetism and Magnetic Materials 251(2002)229–243231point mentioned previously.Upon re-examining Fig.2,it can be seen that,at low applied stresses,the curvature of the upper portion of the loop between the maximum and the coincident point tends to be convex up,and between the coincident point and the negative maximum,convex down.This allows for a smooth transition at the coincident point.With the application of appro-priate stresses these curvatures decrease,and as the three points do not lie on a straight line,the discontinuity in slope becomes apparent.As these two features are the most startling and interesting of the results,their validation was deemed to be vital.Two experiments were designed to attempt to repeat the effects using completely different and independent equipment and materials.In this way,if the coincident points and kink were due to the cruciform,the stress rig,the twin U-cores,or the computer/software,and not a true feature of the material,the effects would not be present.3.VeriﬁcationThe ﬁrst experiment designed employed a cylindrical rod specimen of mild steel with a diameter of 20mm and a length of 410mm.A ﬂux sensing coil of 50turns was wrapped around the rod.The rod was placed in a universal testing machine which would apply the (uniaxial)stressesand would also serve to provide a closed magnetic circuit (even though the machine provided a fairly low magnetic permeability path,it is signiﬁcantly better than air).The magnetising ﬁeld was applied using a permeameter coil with 550turns and an inner diameter of 75mm.The ﬁeld was measured using a Linear Hall Effect IC.The ﬂux sensing coil was connected to an HP8875A differential ampliﬁer,which was in turn connected to an analog integrator,the output of which was connected to a Hewlett-Packard 7035B X–Y Recorder (plotter).The Hall probe was also ampliﬁed by an HP8875A and connected to the X–Y plotter.Hysteresis loops were taken at four different applied stresses,both compressive and tensile in nature.These plots were then scanned and super-imposed graphically.The result of this hybrid is shown in Fig.5.The errors inherent in this method are unfortunately much greater than obtained using the rig and software.The graphs were superimposed by hand and placed where they looked ‘‘as central as possible’’.However,the coincident point is still strongly indicated by the data.The second experiment employed the same system as used before,but using a nickel specimen instead of mild steel.A length of nickel wire with a diameter of 1.5mm was selected based on avail-ability.The wire was cut to 430mm in length,and had 4000turns of ﬁne copper wire woundcloselyFig.4.Hysteresis loop of mild steel with À120MPa along the axis of magnetisation and 120MPa perpendicular to the axis.D.P.Bulte,ngman /Journal of Magnetism and Magnetic Materials 251(2002)229–243232around it as a ﬂux-sensing coil.It was then placed in the permeameter.A Hall probe was located against the wire.To apply tension,the end of the wire was connected to a cable which ran over a pulley,allowing weights to be suspended from it.Hyster-esis loops were taken with tensions of 2.5,12.5,20,and 30MPa.The loops obtained were perfect diamonds,i.e.four straight lines with sharp discontinuities in slope (see Fig.6).From this it was deduced that the nickel had been plastically strained during the wire-forming process.In order to remove the internal stresses and dislocations,the wire was annealed [4]in a kiln at ð1050710Þ1for 4h,then allowed to cool over 12h.The wire was then once again placed in the permeameter and loops were obtained at the indicated tensions.These graphs are presented in Fig.7.It is immediately clear that the features of these graphs are different from those seen in the mild steel data.In order to obtain more detail about the features of the curves a second series of hysteresis loops were acquired with a greater maximum applied ﬁeld.These loops are shown in Fig.8.In contrast with the mild steel graphs the coincident points appear to be at the coercive ﬁeld in both Figs.7,and 8.The prominent kinks for tension in Fig.8are in the ﬁrst and third quadrants,and are not at the same ﬁelds as the coincident points,and thus occur at different ﬂux densities for each applied tension.The kinks do appear to be occurring at the same applied ﬁeld strength for each curve,however,more data are required to substantiate this.In summary,the secondary investigations have conﬁrmed the existence of the coincident points in mild steel and nickel,as well as the distinct change in slope (kink)caused by high stresses of an appropriate nature (compression in steel and tension in nickel).4.AnalysisThe hysteresis data obtained from the mild steel cruciform may be analysed in a number of different ways.The ways chosen were:(i)examin-ing individual hysteresis loops at speciﬁcstressFig.5.Superimpostion of hysteresis loops of mild steel rod with different applied uniaxial stresses taken using alternative equipment.The stresses applied were À150;À100;0,and +50MPa.patterns,and (ii)examining groups of hysteresis loops at different stress patterns superimposed onto one set of axes.The ﬁrst method is useful for seeing the shape of the loop,and identifying features and characteristics of the hysteresis loop at a particular biaxal strain.The second method is useful for identifying changes which occur in loop shapes at different strains,and for showing points where the ﬂux density differs at particular strains,and where the loops intersect each other.TheFig.7.Superimpostion of hysteresis loops of annealed nickel wire with different applied uniaxial tensions at lowﬁelds.Fig.8.Superimpostion of hysteresis loops of annealed nickel wire with different applied uniaxial tensions at higher ﬁelds.D.P.Bulte,ngman /Journal of Magnetism and Magnetic Materials 251(2002)229–243234hysteresis loops obtained during this research have been considered in both of these ways,and the implications of the subsequent speculations docu-mented.4.1.Considering the graphsSuperimposition of the B vs.H hysteresis loops of steel under biaxial stress clearly shows two important new features.Theﬁrst is the two coincident points(Fig.2)where all of the curves intersect.The second is the noticeable kink(Fig.4) in curves with compression in the direction of magnetisation,which occurs at this intersection.It would appear that at the particular appliedﬁeld (hereafter referred to as the critical rotationﬁeld, H n[5])at which the coincident point and kink occur,the magnetisation of the sample is essen-tially independent of the applied(biaxial)stress. It would seem that the mechanism that connects stress and magnetism is either not present,or rendered inactive by the application of this critical rotationﬁeld.The implications of this phenomen-on,regarding the mechanism by which applied stress and magnetic properties are interrelated,are of fundamental importance.It is important to note that the coincident points are not seen unless the steel is magnetised to several hundred Ampere per metre;the critical rotationﬁeld(which is approximately7200A=m for mild steel)must be exceeded by approximately twice this value before the effect is discernable. Hysteresis loops which have maximum applied ﬁelds of much less than the saturationﬁeld,but are still sufﬁciently greater than the critical rotation ﬁeld,will show the coincident point at the same ﬁeld strength,but at a lowerﬂux density(Fig.3). In the nickel wire,however,the effects are markedly different.In the data obtained before the specimen was annealed,the kink is very promi-nent;the discontinuity in the slope being quite dramatic(see Fig.6).However,in all of the nickel data,the coincident point is clearly not at the kink point,rather it appears to be at the coerciveﬁeld (Fig.7).It must be noted as well that due to the negative magnetostriction of nickel,the effect of stress is in some ways reversed from that seen in iron and steel.Tension parallel to theﬁeld tends to reduce theﬂux density,producing the more lentil/ diamond-shaped loops seen for compression in iron and pression parallel to theﬁeld could not be investigated due to the sample of nickel used being very thin.5.The magnetisation processIn order to explain the coincident point and kink found on hysteresis curves of materials under stress,it is necessary to consider the accepted theory which explains magnetisation processes[6]. Consider a small,relatively perfect crystal of ferromagnetic material in an ideally demagnetised state.The domains will be aligned with easy directions in the crystal.If an external magnetic ﬁeld is applied to this crystal,the domain walls will move so that the domains with directions closer to that of the appliedﬁeld will grow at the expense of the others.This appliedﬁeld must exceed a certain critical value for irreversible wall motion to occur [5].Beneath this value,the walls will move slightly, or bulge,but would return to their original location where theﬁeld to be removed(the true Raleigh region).In a real sample of ferromagnetic material, however,the situation is complicated by the fact that the overall structure is not a regular crystal lattice,rather it is made up of small regions,or grains,within which the structure of the crystal lattice is relatively perfect.Domain walls can only move across a region of relatively regular crystal structure(in the materials considered in the scope of this article),in which lattice imperfections cause small Barkhausen jumps or Barkhausen noise,and domain wall‘‘snapping’’[7,8].At a boundary between grains,the wall will presumably be absorbed by the boundary.In order for grain saturation to be reached, another effect must also play a part:the irrever-sible rotation of domain magnetisation or large Barkhausen jumps[9].A point is reached during the application of an increasingﬁeld when theﬁeld is strong enough to spontaneously snap the atomic moments from one easy axis to another.Conse-quently,instead of a wall moving gradually across a domain,whole domains in iron and steel willD.P.Bulte,ngman/Journal of Magnetism and Magnetic Materials251(2002)229–243235change direction by901or1801;with effectively simultaneous movement of all of the spins.At even higherﬁelds,the increase in magnetisa-tion will be due to the process of reversible rotation of the magnetic moments away from easy directions towards the direction of the applied ﬁeld.Once a sufﬁcientﬁeld strength has been reached to rotate the spin from the easy to the hard direction(ignoring precession effects),tech-nical saturation has been reached as all spins are now experiencing sufﬁcientﬁeld to rotate them to the appliedﬁeld direction[10].6.External stress and non-easy moments Magnetism can be conceptualised on a number of different levels;macroscopic,domain,atomic, and subatomic,although these are all somewhat arbitrary.Explanations of magnetic effects have traditionally concentrated on producing theories based on only one of these approaches.Magneto-mechanics is an area in which all levels are affected,and thus a theory needs to consider responses to models at each level of complexity,and ideally evolve smoothly from one to the next. For this reason the following hypotheses are explained in terms of domains,crystals,and quantum mechanics,so that the features of the model can be understood from each of these view points.6.1.Domain wallsWhen a mechanical stress is applied to a sample, its magnetic behaviour can change dramatically. In iron and steel,compression in theﬁeld direction makes magnetisation harder,whilst tension initi-ally makes it easier[11–13].These effects will now be explained primarily in terms of the structure of domain walls,rather than their movement,as previous explanations have done[14].Domains form within a region of coherent crystal lattice and orient themselves in directions of easy magnetisation[15,16].In a901wall,none of the spins within the wall will lie in easy directions.In a1801wall,the centre of the wall will lie in an easy direction but the rest of the wall spins will all be in non-easy directions(Fig.9 (from[17])).The spins in a wall are in away Fig.9.Schematic of spin rotations in a1801domain wall(from Ref.[17]).D.P.Bulte,ngman/Journal of Magnetism and Magnetic Materials251(2002)229–243236analogous to the reversible rotations of moments within a domain that are induced by large applied ﬁelds against the opposing anisotropy forces. Applied stresses distort the crystal lattice. Consequently,for a cubic lattice the/100S; /010S;and/001S directions will no longer be perpendicular.Depending on the orientation of the lattice with regards to the applied stress,the angles between the easy directions will increase or decrease,and the relative separations of the atoms will also change.Any non-easy-aligned spins will be affected by these lattice distortions.In this way, the energy associated with the position of a non-easy-aligned spin is determined by its magnetic anisotropy,which is dependent on the relative angles the moment forms with respect to the three crystallographic directions,and which is also critically interdependent on the exchange energy (see Section7).When the axes and the atoms move relative to each other,the changes in anisotropy energy and exchange energy modify the energy required to keep the moments pointing in any given direction.This is of fundamental importance to the magnetomechanical effect.As domain walls are effectively groups of non-easy-aligned moments,they will be affected by applied external stresses.Wall motion will occur for901walls as the effective‘‘pressure’’on the wall caused by the applied stress will be in one direction only.The pressure on1801walls will be on both sides of the wall but in opposite directions,and so the thickness of the wall will change slightly,but its position will not alter.In the demagnetised state,this process alone will not cause magnetisa-tion,as the net magnetisation will remain zero.In iron and steel when the specimen has a non-zero net magnetisation,the stress will affect the magnetisation as it will reduce(via compression), or increase(via tension)the size of favourably oriented domains via the movement of901walls.6.2.Hysteresis loopsThe behaviour of the material is different again once it has been magnetised and is on the hysteresis loop[18].As the magnetisation of the material moves along the major hysteresis loop from the tip of the loop in theﬁrst quadrant to the negative coincident point in the second quadrant, the appliedﬁeld isﬁrst reduced to zero,leaving some non-zero,positive internalﬁeld(the rema-nence).This internalﬁeld is sufﬁcient to maintain some reversible rotation of magnetic moments.As a negativeﬁeld of increasing magnitude is applied, the point is reached where the netﬁeld experienced by the magnetic moments is insufﬁcient to main-tain reversible rotation.The net magnetisation of the material is still positive,as it is the sum of the internal and appliedﬁelds,however,no magnetic moments are experiencing sufﬁcientﬁeld strength to overcome the net anisotropy(crystal,stress, etc.)and thus are aligned in the easy directions which are closest to the direction of the original ﬁeld.Thus,no domain walls will exist within the grains.At this point,there are no non-easy aligned spins,and so the magnetisation is independent of the applied stress,and dependent only on the history,temperature,and appliedﬁeld.Conse-quently,all hysteresis curves of that sample with the same history,temperature,andﬁeld strength will coincide at that point no matter which stresses are applied to the sample.Measurement shows that the coincident points also occur on loops which have lower maximum appliedﬁeld values,however,these points will be at successively lowerﬂux density values.At these points,1801domain walls will presumably be present within the material,thus lowering the globalﬂux density,however,the magnetisation of the material will still be independent of the applied stress as1801walls are not affected by stress.Atﬁelds greater than the critical rotationﬁeld, the sample will once again be affected by stress as reversible rotations will begin taking spins away from the easy directions.The greater the number of easy directions which are closely aligned to the ﬁeld,the more dramatic this change will be.In a sample with all easy directions aligned with the ﬁeld,a hysteresis loop of the form shown in Fig.10a would be expected[19].This shows no reversible rotations occurring,and ideally no901 wall motion;the magnetisation process is carried out purely by1801irreversible domain rotation.If, however,only hard directions were aligned with theﬁeld,a loop of the form shown in Fig.10b would result.This corresponds to an arrangementD.P.Bulte,ngman/Journal of Magnetism and Magnetic Materials251(2002)229–243237where all magnetisation is due to reversible rotation;from positive saturation to ÀH n ;the moments are rotating back to an easy direction.From ÀH n to negative saturation,the rotation is from the easy direction to the hard direction,but through a greater angle.An important question is:Why does the slope of the loop change at this point,particularly in the x -direction compression loops?This may be ex-plained by the angles involved.Consider a simple non-stressed crystal unit (Fig.11)with a magnetic moment directed along the [111]direction due to an applied ﬁeld in that direction.In Fig.12this would result in the magnetic moment of the central ion (for a body-centred cubic like iron)pointing at position 1.Removal of this ﬁeld and application of a critical rotation ﬁeld in the opposite direction will rotate the moment to the [100]direction (position 2).This is the closest ‘‘easy direction’’to its starting orientation,and thus the lowest energy path.Increasing the magnitude of the ﬁeld to saturation levels will rotate the moment to position 3.Removal of this ﬁeld and application of a critical rotation ﬁeld in the original direction will turn the moment to position 4,being the closest easyaxis.Fig.11.The ð1%10Þplane in a cubic crystal[17].Fig.12.Schematic of the {110}plane in a body-centred cubiccrystal,and the rotation of a magnetic moment around a major hysteresis loop.D.P.Bulte,ngman /Journal of Magnetism and Magnetic Materials 251(2002)229–243238Within a single cycle of appliedﬁeld,from positive to negative to positive again,any parti-cular magnetic moment will rotate in one plane only,describing aﬂat circle.This is the lowest energy path which the moment can take.The anisotropy energy associated with the[111] direction is the same as that associated with the ½111 direction,yet the angle through which the moment must rotate from the[100]direction to the½111 direction is much greater(125:31)as opposed to the angle between the[111]and the [100]directions(54:71).This means that a given change inﬁeld strength in the hard direction will result in a percentage change in angle equivalent to the percentage change in the opposite direction. However,the magnitude of the change in angle will be greater in the[100]to½111 transition due to the larger total change.As the change inﬂux density is purely a function of the change in angle of the magnetic moment,an increase(negative)in the magnitude of the appliedﬁeld in the[100]to ½111 region will result in a greater change in B than would result in the[111]to[100]region. Thus,the slope of the curve is steeper in this region of the curve.The proportions of the changes in ﬂux to angles would only be equivalent in an ideal crystal at appropriateﬁelds.The Stoner–Wohlfarth model uses an ideal crystal with901between the easy and hard axes and thus does not show these effects.The hysteresis loops produced by this model are symmetrical and are linear for the hard direction. Such a model,though useful in many respects, does not give a very accurate representation of iron or nickel,as the assumptions made regarding the properties of the crytals and domains are inaccurate.In real samples there is a distribution of lattice directions as each grain has its own orientation with relation to appliedﬁelds or stresses.This results in the more familiar curved hysteresis loops.Externally applied stresses will cause an iron or steel sample to behave as if it has either more(tension)or fewer(compression)easy axes aligned with the appliedﬁeld.As the anisotropy energy of each particular direction changes,the ﬁeld required to force the magnetic moments towards that direction also changes.Thus,the number of magnetic moments which are experien-cing sufﬁcientﬁeld to become aligned with theappliedﬁeld is dependent on the stress.At someﬁelds,901and1801wall motion will occursimultaneously with reversible rotation in differentgrains depending on their orientation.Inclusions,dislocations and different internal stresses will allcombine to smooth out the curves under mostconditions.During an initial magnetisation,there are manydomains and walls in the material,and the closuredomains are some of the last to be removed.Thus,all walls may not have been swept from thematerial(particularly if compressed)when thecritical rotationﬁeld is reached.There may also bea region on the initial curve where both rotationand wall motion processes are active.For thesereasons the coincident point does not appear onthe initial curve.6.3.NickelIn nickel the processes involved are similar,butimportant differences produce results which aremarkedly different from iron and steel.Nickel has /111S easy directions,which means that it can have711;1091;and1801domain walls.The wallswhich are affected by stress are the711and1091walls.If,for example,the appliedﬁeld wereparallel to the[100]direction(hard),when theﬁeld was reduced and brought to the kink point,all moments would be in easy directions.However,the easy directions closest to theﬁeld direction are[111],½1%11 ;½11%1 ;and½111 ;therefore the sample will contain only711and1091walls,andstill be very dependent on any applied stresses.When theﬁeld reaches the negative coerciveﬁeld,an amount of1801rotation has occurred dueto wall motion so that the number of moments inthe½111 ;½1%11 ;½11%1 ;and½111 directions is equal to the number in the½%111 ;½111 ;½%11%1 ;and ½111 directions.This will ideally result in all of the walls being1801walls,and therefore,the magnetic properties of the material will be independent of any applied stresses.If,however,the appliedﬁeld was parallel to the½111 direction,a loop of the shape shown in Fig.10a would result,as magne-tisation would only be a result of1801rotations.The fact that the response of nickel is opposite to that of iron and steel is partially due to the fact that the easy and hard directions are reversed. Therefore,stresses which result in alterations to the crystal lattice structure which favour either the /111S directions or the/100S directions will naturally have opposing effects on the materials.7.Spins and lattice mechanismsAn externally applied stress does more than apply an effective pressure on domain walls;it also alters the relative positions of atoms within the lattice.The interactions between nearest neigh-bours in a metallic crystal,like iron,are very complex.The fundamental relationships are the spin–spin,spin–orbit,spin–lattice,and orbit–lat-tice interactions[17].The key relationship which forms the basis of ferromagnetism is the spin–spin interaction,which depends on the exchange energy (or exchange force).The exchange energy is most commonly presented in a form similar toE ex¼À2J ex S iÁS j¼À2J ex S i S j cos f;ð1Þwhere J ex is the exchange integral[17].This is essentially the Heisenberg model of ferromagnet-ism[17],which can be determined via the Heitler–London approximation[20].The analysis of atoms heavier than hydrogen is currently beyond modern physics,so problems are generally simpliﬁed to smaller hydrogen-like sys-tems,and therefore,such systems will be consid-ered in the remainder of this section.The spin of a two-electron system is dependent on the singlet–triplet energy splitting.When the two nuclei are far apart,the ground state describes two independent atoms and is therefore fourfold degenerate.When the atoms are closer together,there is a splitting of the fourfold degeneracy due to interactions be-tween the atoms[21].However,this splitting is small compared with the other excitation energies of the two electron system,and analysis is often simpliﬁed by ignoring the higher states,thus representing the molecule as a simple four-state system.Within this system an operator is deﬁned, known as the Spin Hamiltonian(Eq.(2)),whose eigenvalues are the same as those of the original Hamiltonian within the four-state manifold,and whose eigenfunctions give the spin of the corre-sponding states.H spin¼ÀXJ S1ÁS2:ð2ÞIt is important to note that the coupling in the Spin Hamiltonian depends only on the relative orientation of the two spins but not on their directions with respect to the locations,or separa-tion of the atomic nuclei.This is a consequence of the spin independence of the original Hamiltonian, and holds without any assumption about its spatial symmetry.Terms that break rotational symmetry in spin space,such as dipolar interac-tions or spin–orbit coupling,must be included in the original Hamiltonian in order to produce a Spin Hamiltonian with anisotropic coupling.It must also be noted that,for only products of pairs of spin operators to appear in Eq.(2),it is necessary for all magnetic ions to be far enough apart that the overlap of their electronic wave functions is very small.A consequence of these considerations is that the exchange energy,which determines the strength of the spin–spin interaction,is actually dependent on both the relative separation,and relative orientation of the atomic nuclei about which the electrons are orbiting.Therefore,the spin–orbit coupling,which determines the magne-tocrystalline anisotropy is also dependent on these variables.Consequently,externally applied stres-ses may also alter the energies determining the number,and locations,of domain walls,as well as the anisotropy energies for given crystallographic directions.Stress-induced anisotropy which favours one easy direction above another is,in part,caused by an asymmetry of the overlap of electron distribu-tions on neighbouring ions[22].Due to spin–orbit interactions,the charge distribution of an ion is spheroidal,not spherical.This asymmetry is linked to the direction of the spin,so that the rotation of the spin directions relative to the crystal axes changes the exchange energy and also the electro-static interaction energy of the charge distributions on pairs of atoms.Both effects give rise to an anisotropy energy.In Fig.13a the relative values。

Controlled Excitation and Saturation of Magnetisat

专利名称：Controlled Excitation and Saturation ofMagnetisation Transfer Systems发明人：Rui Pedro Azeredo Gomes Teixeira,JosephVilmos Hajnal,Shaihan Jalal Malik,Daniel JohnWest申请号：US16500515申请日：20180406公开号：US20200057128A1公开日：20200220专利内容由知识产权出版社提供专利附图：摘要：The present invention relate to a system and associate method of MRI and MRspectroscopy which provide stable measurements of the relaxation times, T1 and T2, by using tailored multi-band RF pulses that direct control of the saturation conditions in the background pool of macro-molecular protons, and hence provide a flexible means to induce constant Magnetisation Transfer (MT) effects. In doing this, equal saturation of the background pool is obtained for all measurements independent of the parameters that may be changed, for example, the rotation rate used to obtain a desired flip angle, that is, the degree of change in the magnetisation of the free pool of protons.申请人：King's College London地址：London GB国籍：GB更多信息请下载全文后查看。

强锚定扭曲向列相液晶的一种弗雷德里克兹转变

强锚定扭曲向列相液晶的一种弗雷德里克兹转变
弗雷德里克兹转变是一种强锚定扭曲向列相液晶的特殊类型。

它是一种线性结构和液晶相，液晶组成中的分子以高度极化的有序排列组成。

它是由美国物理学家爱德华·弗雷德里克兹在20世纪60年代的研究中发现的，也被称为“弗雷德里克兹假设”或“弗雷德里克兹相”。

强锚定扭曲向列液晶的特征在于它的液晶分子经过特殊的构造处理，可以在特定温度和压强下特定的溶液中形成稳定的相变。

这种方式的弗雷德里克兹转变可以看作是强锚定双晶液晶和分子液晶形成一个合成液晶，其作用是将双晶液晶和分子液晶完美地结合在一起。

在发现弗雷德里克兹转变的早期，研究者们在实验上发现，在合成的弗雷德里克兹分子中，其结构具有可调节性和极化性，它们在特定环境条件下可以形成自组织形态。

实验表明，自组织态变可以通过给定磁场来实现，因此被称为弗雷德里克兹转变。

弗雷德里克兹转变具有重要的应用价值，它可以用于构建和控制新型材料。

特别是在隔离弱磁性材料的有机液晶晶体结构时，它也被广泛用于研究和制备多层结构有机液晶晶体。

此外，由于弗雷德里克兹相的极化性和可调节性，它也被用于开发一种新型的超灵敏传感器和复合结构，可以用于探测环境参数、空间折叠以及机器学习等应用。

Magnetism and magnetic properties of materials

Magnetism and magnetic properties ofmaterials介绍磁性及其磁性能是材料科学中很重要的一块，磁性是指物质受到磁场作用时表现出来的各种现象，如吸引或排斥等。

而磁性能是指物质在磁场中的一系列特性表现。

磁性不仅影响着我们生活中常用的许多物品，如电视、电脑、磁性材料，而且还对应用在电磁设备、航空航天、生物医学等方面具有重要的应用价值。

磁性基础知识磁性是由原子和分子的磁性质决定的。

原子既具有电子轨道运动所形成的轨道磁矩，又具有自旋运动所形成的自旋磁矩。

物质的磁性取决于自旋磁矩、轨道磁矩的合成，并受到分子结构、晶格结构、温度等因素的影响。

然而，对于许多材料而言，这种合成是非常微弱的，因此物质磁化的来源主要是出现了局域磁时原子间作用的形成及相互偏转。

物质磁化度的计量单位是磁通量密度，即每个单位面积上磁通量的总数。

如果表面积为A, 磁通量为Φ，磁化密度J可以用下式表示：J = Φ/A磁性种类物质的磁性取决于其内部的微观结构，不同结构具有不同的磁性。

根据物质的磁特性，可分为顺磁性、铁磁性、反磁性及亚铁磁性。

顺磁性是指物质受磁场作用后，始终在磁场的方向上产生一个磁矩，而它的方向又是与磁场方向相同的微弱磁性。

顺磁性是由于原子或离子中的未成对电子对磁场的响应所引起的，其性能与温度成正比，并随着温度升高而减小。

反磁性是指物质受磁场作用后，使之形成的磁场方向相反，而且是以极微弱的程度出现。

这种类型的磁性主要是由于原子自旋磁矩和轨道磁矩的相互抵消所引起的。

亚铁磁性是介于顺磁性和铁磁性之间的一种磁性，通常将它称为温和的顺磁性或极弱的铁磁性。

其过渡相变点温度通常在零下20至100度之间正好还接近室温，而且其磁滞回线比较宽，在低温时磁性比较强，而温度升高时磁性明显减弱。

铁磁性是指物质受到磁场作用后，产生与磁场一致方向的强磁性。

铁性铁磁性是由于各个原子磁矩以相同方向排列而形成的。

铁磁性材料在常温下可能具有永久磁性，常见的亲铁磁材料有铁、钴、镍等。

ABX3型钙钛矿化合物的带隙调控及磁、光性质的第一性原理研究

博士学位论文D O C T O R A L D I S SE R T A T I O N ABX 3型钙钛矿化合物的带隙调控及磁、光性质的第一性原理研究分类号： O 469密级：公开学校代码：10697 学号：201510099学科名称：凝聚态物理作者：黄海铭指导老师：姜振益教授西北大学学位评定委员会二〇一八年六月First Principles Study of Band Gap Regulation, Magnetic and Optical Properties of ABX3 Perovskite CompoundsA dissertation submitted toNorthwest Universityin partial fulfillment of the requirementsfor the degree of Doctor of Philosophyin PhysicsByHuang Hai-MingSupervisor: Jiang Zhen-Yi ProfessorJune 2018摘要摘要随着社会的高速发展, 人类对能源的需求也日益增长, 传统化石能源的有限性和大量消耗所引起的环境污染及气候变暖等问题, 引发了人们对可持续能源的迫切需求。

2009年，基于甲胺碘铅MAPbI3（MA=CH3NH3+）制备出的钙钛矿太阳能电池引起了研究人员对ABX3型钙钛矿材料的研究热情。

然而，甲胺碘铅中铅元素的毒性和其光响应范围不够宽是制约这类太阳能电池进一步发展的两个关键因素。

为了实现以上两个关键问题的解决。

本文采用基于密度泛函理论的第一性原理计算方法，在研究MAPbI3结构的基础上，通过替位掺杂来寻找无铅型钙钛矿太阳能电池材料，并同时实现对MAPbI3带隙的调控。

本文研究所获得的创造性成果主要有：第一，拉伸应变和压缩应变能够调控MAPbI3的带隙。

对MAPbI3施加拉伸应变，能够增大MAPbI3的带隙，而施加压缩应变后，MAPbI3的带隙将减小。

高三物理科学与自然现象英语阅读理解20题

高三物理科学与自然现象英语阅读理解20题1<背景文章>Refraction of light is a fascinating phenomenon that occurs when light passes from one medium to another. The change in the speed of light as it enters a different medium causes the light to bend. This bending of light is known as refraction.The principle of refraction can be explained by Snell's law. According to Snell's law, the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the refractive indices of the two media. In simple terms, when light travels from a medium with a lower refractive index to a medium with a higher refractive index, it bends towards the normal. Conversely, when light travels from a medium with a higher refractive index to a medium with a lower refractive index, it bends away from the normal.Refraction of light has many applications in our daily lives. One of the most common applications is in lenses. Lenses use the principle of refraction to focus light. For example, in a camera, the lens focuses light onto the film or digital sensor to create an image. In eyeglasses, lenses are used to correct vision problems by bending light in a way that allows the eye to focus properly. Another application of refraction is in rainbows.Rainbows are formed when sunlight is refracted and reflected by raindrops. The different colors of the rainbow are due to the different wavelengths of light being refracted at different angles.1. What causes light to bend when it passes from one medium to another?A. The change in the color of light.B. The change in the intensity of light.C. The change in the speed of light.D. The change in the direction of light.答案：C。

Novel type of phase transition in a system of self-driven particles

Abstract
A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation (η) added. We present numerical evidence that this model results in a kinetic phase transition from no tran |va| = 0) to ﬁnite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous since |va| is found to scale as (ηc − η)β with β ≃ 0.45.
——————–
One of the most interesting aspects of many particle systems is that they exhibit a complex cooperative behavior during phase transition [1]. This remarkable feature of equilibrium systems has been studied in great detail for the last couple of decades leading to a deeper understanding of processes which may take place in an assembly

二维伊辛模型磁化强度曲线

二维伊辛模型磁化强度曲线【原创版】目录1.二维伊辛模型的概述2.磁化强度曲线的定义和意义3.二维伊辛模型磁化强度曲线的特点4.二维伊辛模型磁化强度曲线的应用正文一、二维伊辛模型的概述二维伊辛模型（Ising Model）是一种描述磁性材料中磁化强度与温度关系的数学模型，该模型由英国物理学家威廉·伊辛（William L.Ising）在 1920 年提出。

二维伊辛模型是伊辛模型在二维空间上的推广，相较于一维伊辛模型，二维伊辛模型能更准确地描述磁性材料在二维空间中的磁化行为。

二、磁化强度曲线的定义和意义磁化强度曲线（Magnetization Curve）是描述磁性材料在外加磁场作用下磁化强度与磁场强度之间关系的曲线。

磁化强度是指单位体积内磁偶极矩的矢量和，用符号 M 表示。

磁化强度曲线是磁性材料在磁场中磁化行为的重要表现形式，对于研究磁性材料的磁性能有着重要的意义。

三、二维伊辛模型磁化强度曲线的特点二维伊辛模型磁化强度曲线具有以下特点：1.在零磁场下，磁化强度为零。

当外加磁场强度逐渐增大时，磁化强度逐渐增大。

2.当磁场强度达到一定值时，磁化强度达到饱和状态，此时磁化强度不再随磁场强度的增大而增大。

3.二维伊辛模型磁化强度曲线在磁场强度为零和饱和状态时，分别对应着顺磁性和铁磁性。

4.在曲线的饱和磁场强度附近，磁化强度曲线的斜率会发生剧变，这一现象称为磁化强度的“膝点”（Knee Point）。

四、二维伊辛模型磁化强度曲线的应用二维伊辛模型磁化强度曲线在磁性材料的研究中有着广泛的应用，例如：1.分析磁性材料的磁性能，如磁化强度、饱和磁场强度、矫顽力等参数。

2.研究磁性材料的磁化过程，了解磁性材料在外加磁场作用下的磁化行为。

3.指导磁性材料的设计和应用，如磁性材料的磁场调控、磁性材料的磁性能优化等。

1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。

PACS numbers: PACS numbers: 81.30.Kf, 75.80.+q, 64.75.+g
I.
INTRODUCTION
The shape-memory eﬀect [1] is characteristic of certain alloys (the so-called shape-memory alloys), which exhibit a martensitic transition (MT) from an ordered bcc -phase (β -phase) towards a close-packed low-temperature phase (M -phase). This eﬀect is related to unique thermomechanical properties such as the ability to recover from large permanent deformations produced in the M -phase by the reverse transition when temperature is increased. During the nineties a great deal of interest has been devoted to the study and development of magnetic shapememory materials. This interest is mostly due to the possibility of a magnetic control of the shape-memory eﬀect, which has been made evident in the ferromagnetic NiMn-Ga alloy close to the Heusler composition Ni2 MnGa [2]. Furthermore, these materials have been shown to exhibit unexpected pretransitional behaviour [3]. The present paper deals with the study of the CuAl-Mn alloy. This Hume-Rothery material [4] shares a number of features with the Ni-Mn-Ga alloy system. It displays the same high-temperature crystallographic structure, a martensitic transformation with associated shape-memory eﬀect and interesting magnetic properties. For Cu-Al-Mn, however, the martensitic transition occurs in a composition region far from the Heusler stoichiometry. For this composition range, the β -phase is only stable at high temperatures, but can be retained at low-temperature by means of suitable cooling. During this cooling the system develops an ordered L21 structure
Martensitic transition and magnetoresistance in a Cu-Al-Mn shape memory alloy. Inﬂuence of ageing.
Jordi Marcos, Antoni Planes and Llu´ ıs Ma˜ nosa
Departament d’Estructura i Constituents de la Mat` eria, Facultat de F´ ısica, Universitat de Barcelona. Diagonal, 647, E-08028 Barcelona, Catalonia
(F m3m, Heusler symmetry) in two successive disorderorder transitions: A2 (Im3m) → B 2 (P m3m) at Tc1 and B 2 → L21 at Tc2 [5]. Upon further cooling it undergoes a martensitic transition at a temperature which is strongly composition dependent. This transition has a diﬀusionless nature which ensures that the atomic distribution of the L21 phase is inherited by the M -phase. It is worth noting that this feature is common to all Cu-based shapememory materials [6]. Magnetic properties arise from localized magnetic moments at Mn-atoms as occurs in the Ni-Mn-Ga system [7]. These magnetic moments are coupled through an oscillating eﬀective interaction (RKKY interaction). ALCHEMI (Atom Location by Channelling Enhanced Microanalysis) experiments [8] have shown that Mn atoms are located preferentially in one of the four distinguishable f cc sublattices of the L21 structure (the 4b sites in Wyckoﬀ notation). For this conﬁguration, ferromagnetic coupling is dominant and close to the Cu2 AlMn composition the system is ferromagnetic. However, for nonstoichiometric alloys the 4b sites are not fully occupied by Mn-atoms and this results in magnetic disorder, which gives rise to diﬀerent magnetic behaviour depending on the temperature range [9, 10]. Magnetic clustering has been suggested to be at the origin of the magnetoresistive properties recently reported in Cu-Al-Mn melt-spun ribbons [11, 12]. An interesting feature is the fact that a phase separation between Cu3 Al-rich and Cu2 AlMnrich phases may occur below the L21 ordering line. It is therefore expected that the magnetic and structural

arXiv:cond-mat/0207254v1 [cond-mat.mtrl-sci] 10 Jul 2002
Am´ ılcar Labarta and Bart Jan Hattink
Departament de F´ ısica Fonamental, Facultat de F´ ısica, Universitat de Barcelona. Diagonal, 647, E-08028 Barcelona, Catalonia (Dated: February 1, 2008) We have studied the eﬀect of ageing within the miscibility gap on the electric, magnetic and thermodynamic properties of a non-stoichiometric Heusler Cu-Al-Mn shape-memory alloy, which undergoes a martensitic transition from a bcc-based (β -phase) towards a close-packed structure (M phase). Negative magnetoresistance which shows an almost linear dependence on the square of magnetization with diﬀerent slopes in the M - and β -phases, was observed. This magnetoresistive eﬀect has been associated with the existence of Mn-rich clusters with the Cu2 AlMn-structure. The eﬀect of an applied magnetic ﬁeld on the martensitic transition has also been studied. The entropy change between the β - and M -phases shows negligible dependence on the magnetic ﬁeld but it decreases signiﬁcantly with annealing time within the miscibility gap. Such a decrease is due to the increasing amount of Cu2 MnAl-rich domains that do not transform martensitically.