Entropy-driven phase stability and slow diffusion kinetics in an Al0.5CoCrCuFeNi high entropy alloy

ARTICLEOPENReceived8Apr2015|Accepted25Aug2015|Published29Sep2015Entropy-stabilized oxidesChristina M.Rost1,Edward Sachet1,Trent Borman1,Ali Moballegh1,Elizabeth C.Dickey1,Dong Hou1,Jacob L.Jones1,Stefano Curtarolo2&Jon-Paul Maria1Configurational disorder can be compositionally engineered into mixed oxide by populating asingle sublattice with many distinct cations.The formulations promote novel and entropy-stabilized forms of crystalline matter where metal cations are incorporated in new ways.Here,through rigorous experiments,a simple thermodynamic model,and afive-componentoxide formulation,we demonstrate beyond reasonable doubt that entropy predominatesthe thermodynamic landscape,and drives a reversible solid-state transformation betweena multiphase and single-phase state.In the latter,cation distributions are proven tobe random and homogeneous.Thefindings validate the hypothesis that deliberateconfigurational disorder provides an orthogonal strategy to imagine and discover new phasesof crystalline matter and untapped opportunities for property engineering.1Department of Materials Science and Engineering,North Carolina State University,Raleigh,North Carolina27695,USA.2Department of Mechanical Engineering and Materials Science,Center for Materials Genomics,Duke University,Durham,North Carolina27708,USA.Correspondence and requests for materials should be addressed to J.-P.M.(email:jpmaria@)or to S.C.(email:stefano@).A grand challenge facing materials science is the continuoushunt for advanced materials with properties that satisfythe demands of rapidly evolving technology needs.The materials research community has been addressing this problem since the early1900s when Goldschmidt reported the‘the method of chemical substitution’1that combined a tabulation of cationic and anionic radii with geometric principles of ion packing and ion radius ratios.Despite its simplicity,this model enabled a surprising capability to predict stable phases and structures.As early as1926many of the technologically important materials that remain subjects of contemporary research were identified (though their properties were not known);BaTiO3,AlN,GaP, ZnO and GaAs are among that list.These methods are based on overarching natural tendencies for binary,ternary and quaternary structures to minimize polyhedral distortions,maximize spacefilling and adopt polyhedral linkages that preserve electroneutrality1–3.The structure-field maps compiled by Muller and Roy catalogue the crystallographic diversity in the context of these largely geometry-based predictions4.There are,however,limitations to the predictive power,particularly when factors like partial covalency and heterodesmic bonding are considered.To further expand the library of advanced materials and property opportunities,our community explores possibilities based on mechanical strain5,artificial layering6,external fields7,combinatorial screening8,interface engineering9,10and structuring at the nanoscale6,11.In many of these efforts, computation and experiment are important companions.Most recently,high-throughput methods emerged as a power-ful engine to assess huge sections of composition space12–17and identified rapidly new Heusler alloys,extensive ion substitution schemes18,19,new18-electron ABX compounds20and new ferroic semiconductors21.While these methods offer tremendous predictive power and an assessment of composition space intractable to experiment, they often utilize density functional theory calculations conducted at0K.Consequently,the predicted stabilities are based on enthalpies of formation.As such,there remains a potential section of discovery space at elevated temperatures where entropy predominates the free-energy landscape.This landscape was explored recently by incorporating deliberatelyfive or more elemental species into a single lattice with random occupancy.In such crystals,entropic contributions to the free energy,rather than the cohesive energy, promote thermodynamic stability atfinite temperatures.The approach is being explored within the high-entropy-alloy family of materials(HEAs)22,in which extremely attractive properties continue to be found23,24.In HEAs,however,discussion remains regarding the true role of configurational entropy25–28, as samples often contain second phases,and there are uncertainties regarding short-range order.In response to these open discussions,HEAs have been referred to recently as multiple-principle-element alloys29.It is compelling to consider similar phenomena in non-metallic systems,particularly considering existing information from entropy studies in mixed oxides.In1967Navrotsky and Kleppa showed how configurational entropy regulates the normal-to-inverse transformation in spinels,where cations transition between ordered and disordered site occupancy among the available sublattices30,31.These fundamental thermodynamic studies lead one to hypothesize that in principle,sufficient temperature would promote an additional transition to a structure containing only one sublattice with random cation occupancy.From experiment we know that before such transitions,normal materials melt,however,it is conceivable that synthetic formulations exist,which exhibit them.Inspired by research activities in the metal alloy communities and fundamental principles of thermodynamics we extend the entropy concept tofive-component oxides.With unambiguous experiments we demonstrate the existence of a new class of mixed oxides that not only contains high configurational entropy but also is indeed truly entropy stabilized.In addition,we present a hypothesis suggesting that entropy stabilization is particularly effective in a compound with ionic character.ResultsChoosing an appropriate experimental candidate.The candi-date system is an equimolar mixture of MgO,CoO,NiO,CuO and ZnO,(which we label as‘E1’)so chosen to provide the appropriate diversity in structures,coordination and cationic radii to test directly the entropic ansatz.The rationale for selection is as fol-lows:the ensemble of binary oxides should not exhibit uniform crystal structure,electronegativity or cation coordination,and there should exist pairs,for example,MgO–ZnO and CuO–NiO, that do not exhibit extensive solubility.Furthermore,the entire collection should be isovalent such that relative cation ratios can be varied continuously with electroneutrality preserved at the net cation to anion ration of unity.Tabulated reference data for each component,including structure and ionic radius,can be found in Supplementary Table1.Testing reversibility.In thefirst experiment,ceramic pellets of E1are equilibrated in an air furnace and quenched to room temperature.The temperature spanned a range from700to 1,100°C,in50-°C increments.X-ray diffraction patterns showing the phase evolution are depicted in Fig.1.After700°C,two prominent phases are observed,rocksalt and tenorite.The tenorite phase fraction reduces with increasing equilibration temperature.Full conversion to single-phase rocksalt occurs between850and900°C,after which there are no additional peaks,the background is low andflat,and peak widths are narrow in two-theta(2y)space.Reversibility is a requirement of entropy-driven transitions. Consequently,low-temperature equilibration should transform homogeneous1,000°C-equilibrated E1back to its multiphase state(and vice versa on heating).Figure1also shows a sequence of X-ray diffraction patterns for such a thermal excursion;initial equilibration at1,000°C,a second anneal at750°C,andfinally a return to1,000°C.The transformation from single phase,to multiphase,to single phase is evident by the X-ray patterns and demonstrates an enantiotropic(that is,reversible with tempera-ture32)phase transition.Testing entropy though composition variation.A composition experiment is conducted to further characterize this phase tran-sition to the random solid solution state.If the driving force is entropy,altering the relative cation ratios will influence the transition temperature.Any deviation from equimolarity will reduce the number of possible configurations O(S c¼k B log(O)), thus increasing the transition temperature.Because S c(x i)is logarithmically linked to mole fraction via B x i log(x i),the com-positional dependence is substantial.This dependency underpins our gedankenexperiment where the role of entropy can be tested by measuring the dependency of transition temperature as a function of the total number of components present,and of the composition of a single component about the equimolar formulation.The calculated entropy trends for an ideal mixture are illustrated in Fig.2b,which plots configurational entropy for a set of mixtures having N species where the composition of an individual species is changed and the others(NÀ1)are keptequimolar.Two dependencies become apparent:the entropy increases as new species are added and the maximum entropy is achieved when all the species have the same fraction.Both dependencies assume ideal random mixing.Two series of composition-varying experiments investigate the existence of these trends in formulation E1.The first experiment monitors phase evolution in five compounds,each related to the parent E1by the extraction of a single component.The sets are equilibrated at 875°C (the threshold temperature for complete solubility)for 12h.The diffraction patterns in Fig.2a show that removing any component oxide results in material with multiple phases.A four-species set equilibrated under these conditions never yields a single-phase material.The second experiment uses five individual phase diagrams to explore the configurational entropy versus composition trend.In each,the composition of a single component is varied by ±2,±6and ±10%increments about the equimolar composition while the others are kept even.Since any departure from equimolarity reduces the configurational entropy,it should increase transition temperatures to single phase,if thattransitionI n t e n s i t y2030405060702 (°)801.81,100N =5No ZnONo MgON =4No CuON =3No NiONo CoON =21,0501,000950T e m p e r a t u r e (°C )T e m p e r a t u r e (°C )T e m p e r a t u r e (°C )T e m p e r a t u r e (°C )T e m p e r a t u r e (°C )S /k B9008501,1001,0501,0009509008501,1001,0501,0009509008501,1001,0501,0009509008501,1001,0501,0009509008500.0X NX NiOX CuOX ZnOX MgoX CoO0.5 1.00.10.20.30.10.20.30.10.20.30.10.20.30.10.20.31.62223112202001111.41.21.00.80.60.40.20.0J14**********Figure 2|Compositional analysis.(a )X-ray diffraction analysis for a composition series where individual components are removed from the parent composition E1and heat treated to the conditions that would otherwise produce full solid solution.Asterisks identify peaks from rocksalt while carrots identify peaks from other crystal structures.(b )Calculated configurational entropy in an N -component solid solutions as a function of mol%of the N th component,and (c –g )partial phase diagrams showing the transition temperature to single phase as a function of composition (solvus )in the vicinity of the equimolar composition where maximum configurational entropy is expected.Error bars account for uncertainty between temperature intervals.Each phase diagram varies systematically the concentration of one element.L o g i n t e n s i t y750 °C750 °C800 °C850 °C900 °C1,000 °C2001111,000 °C 2 (°)T (200)T (002)T (110)T (200)T (002)T (110)Figure 1|X-ray diffraction patterns for entropy-stabilized oxide formulation E1.E1consists of an equimolar mixture of MgO,NiO,ZnO,CuO and CoO.The patterns were collected from a single pellet.The pellet was equilibrated for 2h at each temperature in air,then air quenched to room temperature by direct extraction from the furnace.X-ray intensity is plotted on a logarthimic scale and arrows indicate peaks associated with non-rocksalt phases,peaks indexed with (T)and with (RS)correspond to tenorite and rocksalt phases,respectively.The two X-ray patterns for 1,000°C annealed samples are offset in 2y for clarity.is in fact entropy driven.The specific formulations used are given in Supplementary Table 2.Figure 2c–g are phase diagrams of composition versus transformation temperature for the five sample sets that varied mole fraction of a single component.The diagrams were produced by equilibrating and quenching individual samples in 25°C intervals between 825and 1,125°C to obtain the T trans -composition solvus .In all cases equimolarity always leads to the lowest transformation temperatures.This is in agreement with entropic promotion,and consistent with the ideal model shown in Fig.2b.One set of raw X-ray patterns used to identify T trans for 10%MgO is given as an example in Supplementary Fig.1.Testing endothermicity .Reversibility and compositionally dependent solvus lines indicate an entropy-driven process.As such,the excursion from polyphase to single phase should be endothermic.An entropy-driven solid–solid transformation is similar to melting,thus requires heat from an external source 33.To test this possibility,the phase transformation in formulation E1can be co-analysed with differential scanning calorimetry and in situ temperature-dependent X-ray diffraction using identical heating rates.The data for both measurements are shown in Fig.3.Figure 3a is a map of diffracted intensity versus diffraction angle (abscissa)as a function of temperature.It covers B 4°of 2y space centred about the 111reflection for E1.At a temperature interval between 825and 875°C,there is a distinct transition to single-phase rocksalt structure—all diffraction events in that range collapse into an intense o 1114rocksalt peak.Figure 3b contains the companion calorimetric result where one finds a pronounced endotherm in the identical temperature window.The endothermic response only occurs when the system adds heat to the sample,uniquely consistent with an entropy-driven transformation 33.We note the small mass loss (B 1.5%)at the endothermic transition.This mass loss results from the conversion of some spinel (an intermediate phase seen by X-ray diffraction)to rocksalt,which requires reduction of 3þto 2þcations and release of oxygen to maintain stoichiometry.To address concerns regarding CuO reduction,Supplementary Fig.2shows a differential scanning calorimetry and thermal gravimetric analysis curve for pure CuO collected under the same conditions.There is no oxygen loss in the vicinity of 875°C.Testing homogeneity .All experimental results shown so far support the entropic stabilization hypothesis.However,all assume that homogeneous cation mixing occurs above the tran-sition temperature.It is conceivable that local composition fluc-tuations produce coherent clustering or phase separation events that are difficult to discern by diffraction using a laboratory sealed tube diffractometer.The solvus lines of Fig.2c–g support random mixing,as the most stable composition is equimolar (a condition only expected for ideal/regular solutions),but it is appropriate to ensure self-consistency with direct measurements.To characterize the cation distributions,extended X-ray absorption fine structure (EXAFS)and scanning transmission electron microscopy with energy dispersive X-ray spectroscopy (STEM EDS)is used to analyse structure and chemistry on the local scale.EXAFS data were collected for Zn,Ni,Cu and Co at the Advanced Photon Source 12-BM-B 34,35.The fitted data are shown in Fig.4,the raw data are given in Supplementary Fig.3.The fitted data for each element provide two conclusions:the cation-to-anion first-near-neighbour distances are identical (within experimental error of ±0.01Å)and the local structures for each element to approximately seven near-neighbour distances are similar.Both observations are only consistent with a random cation distribution.As a corroborating measure of local homogeneity,chemical analysis was conducted using a probe-corrected FEI Titan STEM with EDS detection.Thin film samples of E1,prepared by pulsed laser deposition,are the most suitable samples to make the assessment.Details of preparation are given in the methods,and X-ray and electron diffraction analysis for the film are provided in Supplementary Figs 4and 5.The sample was thinned by mechanical polishing and ion milling.Figure 5shows a collection of images including Fig.5a,the high-angle annular dark-field signal (HAADF).In Fig.5b–f,the EDS signals for the K a emission energies of Mg,Co,Ni,Cu and Zn are shown (additional lower magnification images are included in Supplementary Fig.6).All magnifications reveal chemically and structurally homogeneous material.1,100R 111R 111Mass change (%)510151,000900800700600500400300200DSC –30–20Endo DSC (mW) Exo35.536.537.52θ (°)–10010Mass100T e m p e r a t u r e (°C )T e m p e r a t u r e (°C )Figure 3|Demonstrating endothermicity.(a )In situ X-ray diffraction intensity map as a function of 2y and temperature;and (b )differential scanning calorimetry trace for formulation ‘E1’.Note that the conversion to single phase is accompanied by an endotherm.Both experiments were conducted at a heating rate of 5°C min À1.04k (Å–1)(k )×k 2 (Å–2)2ZnNiCuCo681012Figure 4|Extended X-ray absorption fine structure.EXAFS measured at Advanced Photon Source beamlime 12-BM after energy normalization and fitting.Note that the oscillations for each element occur with similar relative intensity and at similar reciprocal spacing.This suggests a similar local structural and chemical environment for each.X-ray diffraction,EXAFS and STEM–EDS probes are sensitive to 10s of nm,10s of Åand 1Ålength scales,respectively.While any single technique could be misinterpreted to conclude homogenous mixing,the combination of X-ray diffraction,EXAFS and STEM–EDS provide very strong evidence.We note,in particular,the similarity in EXAFS oscillations (both in amplitude and position)out to 12inverse angstroms.This similarly would be lost if local ordering or clustering were present.Consequently,we conclude with certainty that the cations are uniformly dispersed.DiscussionThe set of experimental outcomes show that the transition from multiple-phase to single phase in E1is driven by configurational entropy.To complete our thermodynamic understanding of this system,it is important to understand and appreciate the enthalpic penalties that establish the transition temperature.In so doing,the data set can be tested for self-consistency,and the present data are brought into the context of prior research on oxide solubility.First,we consider an equation relating the initial and final states of the proposed phase transition:MgO ðRS ÞþNiO ðRS ÞþCoO ðRS ÞþCuO ðT ÞþZnO ðW Þ¼Mg ;Ni ;Co ;Cu ;Zn ðÞO ðRS ÞFor MgO,NiO and CoO,the crystal structures of the initial and final states are identical.If we assume that solution of each into the E1rocksalt phase is ideal,the enthalpy for mixing is zero.For CuO and ZnO,there must be a structural transition to rocksalt on dissolution from tenorite and wurtzite,respectively.If we again assume (for simplicity)that the solution is ideal,the mixing energy is zero,but there is an enthalpic penalty associated with the structure transition.From Davies et al.and Bularzik et al.,we know the reference chemical potential changes for the wurtzite-to-rocksalt and the tenorite-to-rocksalt transitions of ZnO and CuO;they are 25and 22kJ mol À1,respectively 36,37.If we make the assumption that the transition enthalpies of ZnO(wurtzite)to ZnO(rocksalt E1)and CuO(tenorite)to CuO(rocksalt E1)are comparable,then the enthalpic penalty for solution into E1can be estimated.For ZnO and CuO,the transition to solid solution in a rocksalt structure involves an enthalpy change of (0.2)Á(25kJ mol À1)þ(0.2)Á(22kJ mol À1),a total of þ10kJ mol À1.This calculation is based on the productof the mol fraction of each multiplied by the reference transition enthalpy.This assumption is consistent with the report of Davies et al.who showed that the chemical potential of a particular cation in a particular structure is associated with the molar volume of that structure 36.Since the rocksalt phases of ZnO and CuO have molar volumes comparable to E1,their reference transition enthalpy values are considered suitable proxies.In comparison,the maximum theoretically expected config-urational entropy difference at 875°C (the temperature were we observe the transition experimentally)between the single species and the random five-species solid solution is B 15kJ mol À1,5kJ mol À1larger than the calculated enthalpy of transition.It is possible that the origins of this difference are related to mixing energy as the reference energy values for structural transitions to rocksalt do not capture that aspect.While the present phase diagrams that monitor T trans as a function of composition demonstrate rather symmetric behaviour about the temperature minima,it is unlikely that mixing enthalpies are zero for all constituents.Indeed,literature reports show that enthalpies of mixing between the constituent oxides in E1are finite and of mixed sign,and their magnitudes are on the same order as the 5kJ mol À1difference between our calculated predictions 36.This energy difference may be accounted for by finite and positive mixing enthalpies.Following this argument,we can achieve a self-consistent appreciation for the entropic driving force and the enthalpic penalties for solution formation in E1by considering enthalpies of the associated structural transitions and expected entropy values for ideal cation mixing.As a final test,these predictions can be compared with experiment,specifically by calculating the magnitude of the endotherm observed by DSC at the transition from multiple-phase to single-phase states.Doing so we find a value B 12kJ mol À1(with an uncertainty of ±2kJ mol À1).While we acknowledge the challenge of quantitative calorimetry,we note that this experimental result is intermediate to and in close agreement with the predicted values.Compared with metallic alloys,the pronounced impact of entropy in oxides may be surprising given that on a per-atom basis the total disorder per volume of an oxide seems be lower than in a high-entropy alloy,as the anion sublattice is ordered (apart from point defects).The chemically uniform sublattice is perhaps the key factor that retains cation configurational entropy.As an illustration,consider a comparison between random metal alloys and random metal oxide alloys.Begin by reviewing the case of a two-component metallic mixture A–B.If the mixture is ideal,the energy of interaction E A–B ¼(E A–A þE B–B )/2,there is no enthalpic preference for bonding,and entropy regulates solution formation.In this scenario,all lattice sites are equivalent and configurational entropy is maximized.This situation,however,never occurs as no two elements have identical electronegativity and radii values.Figure 6a illustrates a two-component alloy scenario A–B where species B is more electronegative than A.Consequently,the interaction energies E A–A ,E B–B and E A–B will be different.A random mixture of A–B will produce lattice sites with a distribution of first near neighbours,that is,species A coordinated to 4-B atoms,2-A and 2-B atoms,etc y Different coordinations will have different energy values and the sites are no longer indistinguishable.Reducing the number of equivalent sites reduces the number of possible configurations and S .Now consider the same two metallic ions co-populating a cation sublattice,as in Fig.6b.In this case,there is always an intermediate anion separating neighbouring cation lattice sites.Again,in the limiting case where only first near neighboursareFigure 5|STEM–EDS analysis of E1.(a )HAADF image.Panels labelled as Zn,Ni,Cu,Mg and Co are intensity maps for the respective characteristic X-rays.The individual EDS maps show uniform spatial distributions for each element and are atomically resolved.considered,every cation lattice site is ‘identical’because each has the same immediate surroundings:the interior of an oxygen octahedron.Differentiation between sites is only apparent when the second near neighbours are considered.From the configura-tional disorder perspective,if each cation lattice site is identical,and thus energetically similar to all others,the number of microstates possible within the macrostate will approach the maximum value.This crystallographic argument is based on the limiting case where first-near-neighbour interactions predominate the energy landscape,which is an imperfect approximation.Second and third near neighbours will influence the distribution of lattice site energies and the number of equivalent microstates—but the impact will be the same in both scenarios.A larger number of equivalent sites in a crystal with an intermediate sublattice will increase S and expand the elemental diversity containable in a single solid solution and to lower the temperature at which the transition to entropic stabilization occurs.We acknowledge the hypothesis nature of this model at this time,and the need for a rigorous theoretical exploration.It is presented currently as a possibility and suggestion for future consideration and testing.We demonstrate that configurational disorder can promote reversible transformations between a poly-phase mixture and a homogeneous solid solution of five binary oxides,which do not form solid solutions when any of the constituents are removed provided the same thermal budget.The outcome is representative of a new class of materials called ‘entropy-stabilized oxides’.While entropic effects are known for oxide systems,for example,random cation occupancy in spinels 30,order–disorder transfor-mations in feldspar 38,and oxygen nonstoichiometry in layered perovskites 39,the capacity to actively engineer configurational entropy by composition,to stabilize a quinternary oxide with a single cation sublattice,and to stabilize unusual cation coordination values is new.Furthermore,these systems provide a unique opportunity to explore the thermodynamics and structure–property relationships in systems with extreme configurational disorder.Experimental efforts exploring this composition space are important considering that such compounds will be challenging to characterize with computational approaches minimizing formation energy (for example,genetic algorithms)or with adhoc thermodynamic models (for example,CALPHAD,cluster expansion)6.We expect entropic stabilization in systems where near-neighbour cations are interrupted by a common intermediateanion (or vice versa),which includes broad classes of chalcogenides,nitrides and halides;particularly when covalent character is modest.The entropic driving force—engineered by cation composition—provides a departure from traditional crystal-chemical principles that elegantly predict structural trends in the major ternary and quaternary systems.A companion set of structure–property relationships that predict new entropy-stabilized structures with novel cation incorporation await discovery and exploitation.MethodsSolid-state synthesis of bulk materials .MgO (Alfa Aesar,99.99%),NiO (Sigma Aldrich,99%),CuO (Alfa Aesar,99.9%),CoO (Alfa Aesar,99%)and ZnO (Alfa Aesar 99.9%)are massed and combined using a shaker mill and 3-mm diameter yttrium-stabilized zirconia milling media.To ensure adequate mixing,all batches are milled for at least 2h.Mixed powders are then separated into 0.500-g samples and pressed into 1.27-cm diameter pellets using a uniaxial hydraulic press at 31,000N.The pellets are fired in air using a Protherm PC442tube furnace.Temperature evolution of phases .Ceramic pellets of E1are equilibrated in an air furnace and quenched to room temperature by direct extraction from the hot zone.Phase analysis is monitored by X-ray diffraction using a PANalytical Empyrean X-ray diffractometer with Bragg-Brentano optics including programmable diver-gence and receiving slits to ensure constant illumination area,a Ni filter,and a 1-D 128element strip detector.The equivalent counting time for a conventional point detector would be 30s per point at 0.01°2y increments.Note that all X-ray are collected using substantial counting times and are plotted on a logarithmic scale.To the extent knowable using a laboratory diffractometer,the high-temperature samples are homogeneous and single phase:there are no additional minor peaks,the background is low and flat,and peak widths are sharp in two-theta (2y )space.Temperature-dependent diffraction data are collected with PANalytical Empyrean X-ray diffractometer with Bragg-Brentano optics includingprogrammable divergence and receiving slits to ensure constant illumination area,a Ni filter,and a 1-D 256element strip detector.The samples are placed in a resistively heated HTK-1200N hot stage in air.The samples are ramped at a constant rate of 5°C min À1with a theta–two theta pattern captured every 1.5min.Calorimetry data are collected using a Netzsch STA 449F1Jupiter system in a Pt crucible at 5°C min À1in flowing air.Determining solvus lines .Five series of powders are mixed where the amount of one constituent oxide is varied from the parent mixture E1.Supplementary Table 2lists the full set of samples synthesized for this experiment.Each individual sample is cycled through a heat-soak-quench sequence at 25°C increments from 850°C up to 1,150°C.The soak time for each cycle is 2h,and samples are then quenched to room temperature in o 1min.After the quenching step for each cycle,samples are immediately analysed for phase identification using a PANalytical Empyrean X-ray diffractometer using the conditions identified above.If more than one phase is present,the sample would be put through the next temperature cycle.The temperature at which the structure is determined to be pure rocksalt,with no discernable evidence of peak splitting or secondary phases,is deemed the transition temperature as a function of composition.Supplementary Fig.1shows an example of the collected X-raypatterns after each cycle using the E1L series with þ10%MgO.Once single phase is achieved,the sample is removed from the sequence.Note that this entire experiment is conducted two times.Initially in 50°C increments and longer anneals,and to ensure accuracy of temperature values and reproducibility,a second time using shorter increments and 25°C anneals.Findings in both sets are identical to within experimental error bar values.In the latter case,error bars correspond to the annealing interval value of 25°C.In the main text relating to Fig.2a we note that in addition to small peaks from second phases,X-ray spectra for N ¼4samples with either NiO or MgO removed show anisotropic peak broadening in 2y and skewed relative intensities where I (200)/I (111)is less than unity.This ratio is not possible for the rocksalt structure.Supplementary Table 3shows the result of calculations of structure factors for a random equimolar rocksalt oxide with composition E1.Calculations show that the 200reflection is the strongest,and that the experimentally measured relative intensities of 111/200are consistent with calculations.We use this information as a means too best assess when the transition to single phase occurs since the most likely reason for the skewed relative intensity is an incomplete conversion to the single-phase state.This dependency is highlighted in Supplementary Fig.1.X-ray absorption fine structure .X-ray absorption fine structure (XAFS)is made possible through the general user programme at the Advanced Photon Source in Lemont,IL (GUP-38672).This technique provides a unique way to probe the local environment of a specific element based on the interference between an emitted core electron and the backscattering from surrounding species.XAFS makes no assumption of structure symmetry or elemental periodicity,making it an ideal means to study disordered materials.During the absorption process,coreelectronsBFigure 6|Binary metallic compared with a ternary oxide.A schematic representation of two lattices illustrating how the first-near-neighbour environments between species having different electronegativity (the darker the more negative charge localized)for (a )a random binary metal alloy and (b )a random pseudo-binary mixed oxide.In the latter,near-neighbour cations are interrupted by intermediate common anions.。

非富勒烯受体有机光伏体系的激发态动力学
张圣兵;张春峰
【期刊名称】《物理学进展》
【年(卷),期】2022(42)1
【摘要】受益于非富勒烯受体的不断发展,近年来有机光伏器件的性能得到长足进步。

传统富勒烯受体有机光伏体系下建立起来的电荷拆分和能量损耗模型,不完全
适用于非富勒烯受体体系。

我们利用超快光谱学方法,发现在模型体系中,非富勒烯
受体畴内非局域激发态代替界面电荷转移态介导了电荷拆分的空穴转移通道,在很
小的驱动能下实现高效电荷拆分。

非富勒烯体系中双分子复合过程在能量损耗中扮演重要角色,分子氟化设计可以改变能级排列,抑制双分子复合产生的三线态,从而抑制损耗。

分子间相互作用调控关键能级位置,可用以调控非富勒烯光伏体系光电流
产生机制,有效抑制损耗通道,进一步提升有机光伏体系的效率。

【总页数】7页(P27-33)
【作者】张圣兵;张春峰
【作者单位】江苏省通州高级中学;南京大学物理学院
【正文语种】中文
【中图分类】TQ317;TM914.4
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伏性能4.GW/BSE级别下的非绝热动力学模拟揭示桥连化学键对调控酞菁锌-富勒烯给体-受体复合物激发态弛豫过程的重要作用5.非富勒烯有机光伏体系三线态损耗通道的分子氟化调控
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第４７卷㊀第４期２０２３年７月南京林业大学学报（自然科学版）ＪｏｕｒｎａｌｏｆＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅｓＥｄｉｔｉｏｎ）Ｖｏｌ．４７，Ｎｏ．４Ｊｕｌ．，２０２３㊀收稿日期Ｒｅｃｅｉｖｅｄ：２０２１⁃０８⁃０９㊀㊀㊀㊀修回日期Ａｃｃｅｐｔｅｄ：２０２２⁃０２⁃０６㊀基金项目：江苏省重点研发计划（现代农业）面上项目（ＥＢ２０２０３４３）；徐州市科技项目（ＫＣ２１３３６）㊂㊀第一作者：杨宏（１６２２８５１６４８＠ｑｑ．ｃｏｍ）㊂∗通信作者：伊贤贵（ｙｉｘｉａｎｇｕｉ＠ｎｊｆｕ．ｅｄｕ．ｃｎ），副教授，博士㊂㊀引文格式：杨宏，董京京，吴桐，等．基于ＭａｘＥｎｔ模型的迎春樱桃潜在适生区预测［Ｊ］．南京林业大学学报（自然科学版），２０２３，４７（４）：１３１－１３８．ＹＡＮＧＨ，ＤＯＮＧＪＪ，ＷＵＴ，ｅｔａｌ．ＰｒｅｄｉｃｔｉｏｎｏｆｐｏｔｅｎｔｉａｌｓｕｉｔａｂｌｅａｒｅａｓｏｆＣｅｒａｓｕｓｄｉｓｃｏｉｄｅａｉｎＣｈｉｎａｂａｓｅｄｏｎｔｈｅＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＪｏｕｒｎａｌｏｆＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ（ＮａｔｕｒａｌＳｃｉｅｎｃｅｓＥｄｉｔｉｏｎ），２０２３，４７（４）：１３１－１３８．ＤＯＩ：１０．１２３０２／ｊ．ｉｓｓｎ．１０００－２００６．２０２１０８０１４．基于ＭａｘＥｎｔ模型的迎春樱桃潜在适生区预测杨㊀宏，董京京，吴㊀桐，周华近，陈㊀洁，李㊀蒙，王贤荣，伊贤贵∗（南京林业大学，南方现代林业协同创新中心，南京林业大学生态与环境学院，南京林业大学樱花研究中心，江苏㊀南京㊀２１００３７）摘要：ʌ目的ɔ基于迎春樱桃（Ｃｅｒａｓｕｓｄｉｓｃｏｉｄｅａ）在当代（１９７０ ２０００年）及未来（２０５０ｓ，２０７０ｓ）气候变化下（ＲＣＰ２．６㊁ＲＣＰ４．５㊁ＲＣＰ８．５）适生区的面积变化研究，预测其潜在适生区为迎春樱桃的种质资源保护与利用提供参考依据㊂ʌ方法ɔ基于１９个气候变量和３个地形因子，结合迎春樱桃现有的５２条有效标本记录信息，利用最大熵ＭａｘＥｎｔ模型并结合地理信息系统软件（Ａｒｃ⁃ＧＩＳ），分析影响迎春樱桃分布的主要因素，预测迎春樱桃的潜在分布区㊂ʌ结果ɔ当前环境条件下迎春樱桃潜在适生区主要分布于长江中下游地区，影响物种分布的主要气候因子是最干季降水量（ｂｉｏ１７）㊁最冷月最低温（ｂｉｏ６）㊁季节性温度变化（ｂｉｏ４）和地形因子坡度（ｓｌｏ）㊂在未来气候（ＢＣＣ⁃ＣＳＭ１．１）条件下其适生区总面积呈减少趋势，但是在２０５０ｓ时期，温室气体中等浓度的排放条件下（ＲＣＰ４．５），物种总适生区面积出现最大值，为７．４９ˑ１０５ｋｍ２；而２０５０ｓ和２０７０ｓ时期低浓度（ＲＣＰ２．６）和中等浓度（ＲＣＰ４．５）温室气体的排放条件下，物种的中度适生区面积保持不变㊂ʌ结论ɔ迎春樱桃适生分布区主要分布于长江中下游地区，江西㊁安徽㊁湖北㊁江苏与浙江等低山地区为迎春樱桃种质资源分布的核心区域㊂关键词：迎春樱桃；适生区；ＭａｘＥｎｔ模型；种质资源中图分类号：Ｓ７１８㊀㊀㊀㊀㊀㊀㊀文献标志码：Ａ开放科学（资源服务）标识码（ＯＳＩＤ）：文章编号：１０００－２００６（２０２３）０４－０１３１－０８ＰｒｅｄｉｃｔｉｏｎｏｆｐｏｔｅｎｔｉａｌｓｕｉｔａｂｌｅａｒｅａｓｏｆＣｅｒａｓｕｓｄｉｓｃｏｉｄｅａｉｎＣｈｉｎａｂａｓｅｄｏｎｔｈｅＭａｘＥｎｔｍｏｄｅｌＹＡＮＧＨｏｎｇ，ＤＯＮＧＪｉｎｇｊｉｎｇ，ＷＵＴｏｎｇ，ＺＨＯＵＨｕａｊｉｎ，ＣＨＥＮＪｉｅ，ＬＩＭｅｎｇ，ＷＡＮＧＸｉａｎｒｏｎｇ，ＹＩＸｉａｎｇｕｉ∗（Ｃｏ⁃ＩｎｎｏｖａｔｉｏｎＣｅｎｔｅｒｆｏｒＳｕｓｔａｉｎａｂｌｅＦｏｒｅｓｔｒｙｉｎＳｏｕｔｈｅｒｎＣｈｉｎａ，ＣｏｌｌｅｇｅｏｆＢｉｏｌｏｇｙａｎｄｔｈｅＥｎｖｉｒｏｎｍｅｎｔ，ＣｅｒａｓｕｓＲｅｓｅａｒｃｈＣｅｎｔｅｒ，ＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，Ｎａｎｊｉｎｇ２１００３７，Ｃｈｉｎａ）Ａｂｓｔｒａｃｔ：ʌＯｂｊｅｃｔｉｖｅɔＢａｓｅｄｏｎＣｅｒａｓｕｓｄｉｓｃｏｉｄｅａｏｆｃｏｎｔｅｍｐｏｒａｒｙ（１９７０－２０００）ｓｕｉｔａｂｌｅａｒｅａｓａｎｄｔｈｅａｄａｐｔｉｖｅｒｅｇｉｏｎｏｆｔｈｅｆｕｔｕｒｅ（２０５０ｓ，２０７０ｓ）ｕｎｄｅｒｃｌｉｍａｔｅｃｈａｎｇｅ（ＲＣＰ２．６，ＲＣＰ４．５ａｎｄＲＣＰ８．５），ｔｈｅｓｅｒｅｓｕｌｔｓｐｒｏｖｉｄｅｄａｒｅｆｅｒｅｎｃｅｆｏｒｔｈｅｐｒｏｔｅｃｔｉｏｎａｎｄｕｔｉｌｉｚａｔｉｏｎｏｆＣ．ｄｉｓｃｏｉｄｅａｇｅｒｍｐｌａｓｍｒｅｓｏｕｒｃｅｓ．ʌＭｅｔｈｏｄɔＢａｓｅｄｏｎ１９ｃｌｉｍａｔｅｖａｒｉａｂｌｅｓａｎｄｔｈｒｅｅｔｏｐｏｇｒａｐｈｉｃｆａｃｔｏｒｓ，ｃｏｍｂｉｎｅｄｗｉｔｈ５２ｖａｌｉｄｓｐｅｃｉｍｅｎｓ，ｔｈｅｍａｘｉｍｕｍｅｎｔｒｏｐｙ（ＭａｘＥｎｔ）ｍｏｄｅｌａｎｄＡｒｃ⁃ＧＩＳｓｏｆｔｗａｒｅｗｅｒｅｕｓｅｄｔｏａｎａｌｙｚｅａｎｄｐｒｅｄｉｃｔｔｈｅｍａｉｎｆａｃｔｏｒｓａｎｄｔｈｅｉｒｐｏｔｅｎｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎａｒｅａｓｏｆｔｈｉｓｓｐｅｃｉｅｓ．ʌＲｅｓｕｌｔɔＵｎｄｅｒｃｕｒｒｅｎｔｅｎｖｉｒｏｎｍｅｎｔａｌｃｏｎｄｉｔｉｏｎｓ，ｔｈｅｐｏｔｅｎｔｉａｌｌｙｓｕｉｔａｂｌｅａｒｅａｓｆｏｒＣ．ｄｉｓｃｏｉｄｅａａｒｅｍａｉｎｌｙｄｉｓｔｒｉｂｕｔｅｄｉｎｔｈｅｍｉｄｄｌｅａｎｄｌｏｗｅｒｒｅａｃｈｅｓｏｆｔｈｅＹａｎｇｔｚｅＲｉｖｅｒ．Ｔｈｅｍａｉｎｃｌｉｍａｔｉｃｆａｃｔｏｒｓａｆｆｅｃｔｉｎｇｉｔｓｄｉｓｔｒｉｂｕｔｉｏｎｗｅｒｅｐｒｅｃｉｐｉｔａｔｉｏｎｏｆｔｈｅｄｒｉｅｓｔｑｕａｒｔｅｒ（ｂｉｏ１７），ｍｉｎｉｍｕｍｔｅｍｐｅｒａｔｕｒｅｏｆｔｈｅｃｏｌｄｅｓｔｍｏｎｔｈ（ｂｉｏ６），ｔｅｍｐｅｒａｔｕｒｅｓｅａｓｏｎａｌｉｔｙ（ｂｉｏ４），ａｎｄｓｌｏｐｅ（ｓｌｏ）．Ｉｎｔｈｅｆｕｔｕｒｅｃｌｉｍａｔｅ（ＢＣＣ⁃ＣＳＭ１．１），ｔｈｅｔｏｔａｌｓｕｉｔａｂｌｅａｒｅａｏｆｓｐｅｃｉｅｓｗｉｌｌｄｅｃｒｅａｓｅｄ，ｈｏｗｅｖｅｒ，ｉｎｔｈｅ２０５０ｓ，ｕｎｄｅｒｍｏｄｅｒａｔｅｇｒｅｅｎｈｏｕｓｅｇａｓｅｍｉｓｓｉｏｎｃｏｎｄｉｔｉｏｎｓ（ＲＣＰ４．５），ｔｈｅｔｏｔａｌｓｕｉｔａｂｌｅａｒｅａｏｆｓｐｅｃｉｅｓｗｉｌｌｒｅａｃｈａｍａｘｉｍｕｍｏｆ７．４９ˑ１０５ｋｍ２．Ｈｏｗｅｖｅｒ，ｕｎｄｅｒｔｈｅｃｏｎｄｉｔｉｏｎｓｏｆｌｏｗ（ＲＣＰ２．６）ａｎｄｍｏｄｅｒａｔｅ（ＲＣＰ４．５）ｇｒｅｅｎｈｏｕｓｅｇａｓｅｍｉｓｓｉｏｎｓｉｎｔｈｅ２０５０ｓａｎｄｔｈｅ２０７０ｓ，ｔｈｅｍｏｄｅｒａｔｅｌｙｓｕｉｔａｂｌｅａｒｅａｓｒｅｍａｉｎｅｄｕｎｃｈａｎｇｅｄ．ʌＣｏｎｃｌｕｓｉｏｎɔＴｈｅｓｕｉｔａｂｌｅｄｉｓｔｒｉｂｕｔｉｏｎａｒｅａｏｆＣ．ｄｉｓｃｏｉｄｅａｉｓｍａｉｎｌｙｉｎｔｈｅｍｉｄｄｌｅａｎｄｌｏｗｅｒｒｅａｃｈｅｓｏｆｔｈｅＹａｎｇｔｚｅＲｉｖｅｒ，ａｎｄｔｈｅｌｏｗｍｏｕｎｔａｉｎｏｕｓａｒｅａｓｏｆＪｉａｎｇｘｉ，Ａｎｈｕｉ，Ｈｕｂｅｉ，ＪｉａｎｇｓｕａｎｄＺｈｅｊｉａｎｇＰｒｏｖｉｎｃｅｓａｒｅｔｈｅｃｏｒｅａｒｅａｓｏｆｔｈｉｓｇｅｒｍｐｌａｓｍｒｅｓｏｕｒｃｅｓｄｉｓｔｒｉｂｕｔｉｏｎ．南京林业大学学报（自然科学版）第４７卷Ｋｅｙｗｏｒｄｓ：Ｃｅｒａｓｕｓｄｉｓｃｏｉｄｅａ；ｓｕｉｔａｂｌｅａｒｅａ；ＭａｘＥｎｔｍｏｄｅｌ；ｇｅｒｍｐｌａｓｍｒｅｓｏｕｒｃｅｓ㊀㊀樱花为世界著名观赏花木，隶属于蔷薇科（Ｒｏｓａｃｅａｅ）樱属（Ｃｅｒａｓｕｓ），广泛分布于北半球的温带与亚热带地区㊂我国拥有世界最丰富的樱属种质资源，野生樱花资源约４５种［１］，但极少数被推广利用㊂迎春樱桃（Ｃｅｒａｓｕｓｄｉｓｃｏｉｄｅａ）为我国特有的樱属种质资源，其树形优美，枝条纤细，先花后叶，花粉白色且密集而整齐，花期早，具有极高的观赏价值，是国产樱属资源中最具应用价值的早春观花树种之一㊂迎春樱桃主要分布于安徽㊁浙江㊁江西等省份［２］，喜光且喜温暖湿润的环境，天然分布于海拔２００ １１００ｍ的山谷或溪边［３］㊂气候变化对植被［４］㊁生态系统功能［５］㊁生物多样性［６］㊁植物物候节律［７－８］等产生重大影响，了解未来气候变化对物种分布及适生区的潜在变化，对物种保护利用及对策制定具有重要意义㊂近些年来陆续有樱属植物适生区的研究，如：赖铭婕等［９］通过对６种原产我国的野生樱桃（Ｃｅｒａｓｕｓｓｐｐ．）在广东的适生区进行预测和分析，表明年均温是６个种共同的主导气候限制因子；李蒙等［１０］通过对山樱花（Ｃｅｒａｓｕｓｓｅｒｒｕｌａｔａ）地理分布与水热环境的因子关系分析表明，山樱花热量分布范围整体偏低，影响其分布的重要环境因子为年均温㊁纬度㊁极端低温㊁１月均温和海拔；朱弘等［１１］进行了浙闽樱桃（Ｃｅｒａｓｕｓｓｃｈｎｅｉｄｅｒｉａｎａ）地理分布模拟及气候限制因子分析，发现年降水量㊁最湿季节降雨量㊁最暖季降雨量㊁温度季节变化方差等水热条件是影响浙闽樱桃当下适生区的气候限制因子㊂有关迎春樱桃的研究主要集中在形态标记［１２］与遗传多样性分析［１３］等方面，对其在大尺度的潜在适生区及影响因子等研究鲜见报道㊂生态位理论的模型主要是利用已有的物种分布资料和环境数据产生以生态位为基础的物种生态需求［８］，目前常用于生态位研究的模型有ＧＡＲＰ㊁ＭａｘＥｎｔ㊁ＥＮＦＡ㊁Ｂｉｏｃｌｉｍ和Ｄｏｍａｉｎ等５种，相较而言，ＭａｘＥｎｔ模型具有更好的预测精度［１４］㊂在猕猴桃（Ａｃｔｉｎｉｄｉａａｒｇｕｔａ）［１５－１６］㊁金钱松（Ｐｓｅｕｄｏｌａｒｉｘａｍａｂｉｌｉｓ）［１７］㊁桫椤（Ａｌｓｏｐｈｉｌａｓｐｉｎｕ⁃ｌｏｓａ）［１８－１９］㊁青钱柳［２０］㊁珙桐（Ｄａｖｉｄｉａｉｎｖｏｌｕｃｒａ⁃ｔａ）［２１－２２］等中国特有物种的适生区研究中取得良好预测结果，为目标物种的保护与利用提供了科学依据㊂本研究以迎春樱桃的地理分布数据及当代（１９７０ ２０００年）和未来（２１世纪５０ ７０年代）气候数据为基础，利用ＭａｘＥｎｔ模型预测当代和未来气候环境下迎春樱桃的潜在分布区，分析影响迎春樱桃分布的主要因素，以期更好地了解迎春樱桃在未来气候变化下的分布范围，为其种质资源的保护与利用提供理论依据㊂１㊀材料与方法１．１㊀数据来源１）标本数据收集㊂为了获得迎春樱桃在我国的地理分布数据，借助中国数字植物标本馆（ｈｔ⁃ｔｐｓ：／／ｗｗｗ．ｃｖｈ．ａｃ．ｃｎ／）查阅公开发表的相关资料，并对迎春樱桃分布点进行统计，对于查阅到的标本只有分布点描述记录而没有经纬度记录时借助ｌｏ⁃ｃａｓｐａｃｅｖｉｅｒ网站（ｈｔｔｐ：／／ｗｗｗ．ｌｏｃａｓｐａｃｅ．ｃｎ／）进行解析并确定经纬度㊂将收集到的数据储存于Ｅｘｃｅｌ表格中，运用ＤＶＩ⁃Ａｒｃ⁃ＧＩＳ进行筛选并剔除重复数据，最终获得５２条分布数据用于模型的构建（分辨率１ｋｍ）㊂２）环境数据的收集㊂研究选择的当代（１９７０ ２０００年）１９个气候因子数据和３个地形因子数据（海拔㊁坡度㊁坡向），均来自世界气候数据库（ｈｔｔｐｓ：／／ｗｗｗ．ｗｏｒｌｄｃｌｉｍ．ｏｒｇ／）；未来２个时段（２１世纪５０年代和７０年代，简称２０５０ｓ㊁２０７０ｓ）的数据来自政府间气候变化委员会（ＩＰＣＣ）第５次气候评估报告中的ＢＣＣ⁃ＣＳＭ１．１大气环流模型［２３］，以及３种典型浓度途径（ｔｈｅｒｅｐｒｅｓｅｎｔａｔｉｖｅｃｏｎｃｅｎ⁃ｔｒａｔｉｏｎｐａｔｈｗａｙｓ，ＲＣＰ２．６㊁ＲＣＰ４．５和ＲＣＰ８．５），共４套气候模拟数据㊂根据ＩＰＣＣ第５次评估报告中的数据，ＲＣＰ２．６表示在严格减排下将全球气候变化控制在高于工业化之前温度２ħ以内的情景，ＲＣＰ４．５表示温室气体在中等浓度的情况，ＲＣＰ８．５代表温室气体在较高排放的情况㊂上述气候数据空间分辨率均为３０ｓ（分辨率１ｋｍ）㊂地图数据以国家基础地理信息中心（ｈｔｔｐ：／／ｗｗｗ．ｎｇｃｃ．ｃｎ／ｎｇｃｃ／）提供的１ʒ４００万中国行政地图为底图［底图审图号：ＧＳ（２０１９）１８２２］㊂１．２㊀气候数据的处理将迎春樱桃的地理信息在Ｅｘｃｅｌ表格中保存（．ｃｓｖ文件），在世界气候数据库中下载的栅格数据导入Ａｒｃ⁃ＧＩＳ中，利用ＳｐａｔｉａｌＡｎａｌｙｓｔ中的提取分析工具，掩膜提取中国行政区以内的１９个生物数据以及３个地形数据（海拔㊁坡度㊁坡向），将提取好的生物栅格数据转换为ＡＳＣ格式并保存㊂１．３㊀ＭａｘＥｎｔ模型建立将收集好的迎春樱桃地理分布数据㊁１９个气２３１㊀第４期杨㊀宏，等：基于ＭａｘＥｎｔ模型的迎春樱桃潜在适生区预测候因子变量以及３个地形因子数据（表１）导入ＭａｘＥｎｔ模型中，勾选ｃｒｅａｔｒｅｓｐｏｎｓｅｃｕｒｖｅｓ㊁ｄｏｊａｃｋ⁃ｋｎｉｉｆｅｔｏｍｅａｓｕｒｅｖａｒｉａｂｉｅｉｍｐｏｒｔａｎｃｅ㊁ｏｕｔｐｕｔｆｏｒｍａｔ为ｌｏｇｉｓｔｉｃ［２４］，随机选取２５％的分布数据作为检验数据，其他为训练数据［２５］，重复１０次运算以排除随机因素的影响，其余则使用模型的默认数值㊂将模型运算输出结果设为ＡＳＣ，输出即为分布概率㊂以０．５为阈值，删除相关系数大且贡献率小的变量，最终按贡献率选取５个气候因子和１个地形因子（ｂｉｏ１７㊁ｂｉｏ６㊁ｂｉｏ４㊁ｓｌｏ㊁ｂｉｏ１９㊁ｂｉｏ９）用于最终的模型构建㊂将选取的５个气候因子和１个地形因子以及地理分布数据导入ＭａｘＥｎｔ模型中再次运算１０次（其余不变）得到分布概率㊂表１㊀用于ＭａｘＥｎｔ模型构建筛选出的环境因子Ｔａｂｌｅ１㊀ＥｎｖｉｒｏｎｍｅｎｔａｌｆａｃｔｏｒｓｆｉｌｔｅｒｅｄｏｕｔｆｏｒＭａｘＥｎｔｍｏｄｅｌｃｏｎｓｔｒｕｃｔｉｏｎ１．４㊀分布图的制作及模型精度的验证将ＭａｘＥｎｔ输出的ＡＳＣ文件导入Ａｒｃ⁃ＧＩＳ转化为栅格文件后进行重分类，根据Ａｒｃ⁃ＧＩＳ中的自然断点法将迎春樱桃的潜在适生区划为４个等级，依次为非适生区㊁低度适生区㊁中度适生区和高度适生区㊂模型精度验证以软件内建的变量分析㊁响应曲线和刀切法验证模型中变量对迎春樱桃适应性的影响㊂以受试者工作特征（ＲＯＣ）曲线下面积（ＡＵＣ）的数值大小对模型精度做出评价，取值范围为［０，１］［２６］，数值越大模型精度越高，表明模型预测效果越好㊂２㊀结果与分析２．１㊀迎春樱桃当代分布图和标本记录点由ＭａｘＥｎｔ输出的ＲＯＣ曲线（图１）可知，该模型的ＡＵＣ均值为０．９８０，标准差为０．００９６［２７］，预测结果很好，且精度很高，因此此次建模结果适用于迎春樱桃在中国潜在适生区的预测㊂根据ＭａｘＥｎｔ模型预测以及Ａｒｃ⁃ＧＩＳ中自带的自然断点法将适生区划为４个等级，结果见图２㊂由图２可知，迎春樱桃主要分布在华中和华东地图１㊀ＭａｘＥｎｔ模型的ＲＯＣ曲线及ＡＵＣ面积Ｆｉｇ．１㊀ＲＯＣｃｕｒｖｅａｎｄＡＵＣａｒｅａｏｆＭａｘＥｎｔｍｏｄｅｌ区，其中：高度适生区主要分布于浙江北部㊁安徽南部和西部㊁江西北部和湖北东南部等地；中度适生区主要分布于江西西部㊁中部和西南部㊁湖南中部㊁浙江南部与江苏等地区；低度适生区主要分布在湖南北部和西部㊁福建北部㊁江西南部等地㊂在当前气候环境下迎春樱桃的适生区面积占中国陆地面积的７．７％，为７．４ˑ１０５ｋｍ２，其中：高度适生区面积为１．０６ˑ１０５ｋｍ２，占１．１％；中度适生区面积为２．２１ˑ１０５ｋｍ２，占２．３％；低度适生区面积为３３１南京林业大学学报（自然科学版）第４７卷底图审图号：ＧＳ（２０１９）１８２２㊂下同㊂Ｔｈｅｓａｍｅｂｅｌｏｗ．图２㊀迎春樱桃在中国的当代适生区和标本记录点Ｆｉｇ．２㊀ＣｏｎｔｅｍｐｏｒａｒｙｓｕｉｔａｂｌｅｇｒｏｗｉｎｇａｒｅａｓａｎｄｓｐｅｃｉｍｅｎｒｅｃｏｒｄｐｏｉｎｔｓｏｆＣｅｒａｓｕｓｄｉｓｃｏｉｄｅａｉｎＣｈｉｎａ４ １３ˑ１０５ｋｍ２，占４．３％㊂但是高度适生区面积占比较小，说明迎春樱桃的生长范围比较狭窄，如果受到人为因素的干扰，其栖息地更容易遭到破坏导致种群数量减少㊂ａ．最干季降水量响应曲线ｐｒｅｃｉｐｉｔａｔｉｏｎｉｎｔｈｅｄｒｉｅｓｔｓｅａｓｏｎｒｅｓｐｏｎｓｅｃｕｒｖｅ；ｂ．最冷月最低温响应曲线ｍｉｎｔｅｍｐｅｒａｔｕｒｅｏｆｔｈｅｃｏｌｄｅｓｔｍｏｎｔｈｒｅｓｐｏｎｓｅｃｕｒｖｅ；ｃ．季节性温度变化响应曲线ｓｅａｓｏｎａｌｃｈａｎｇｅｏｆｔｅｍｐｅｒａｔｕｒｅｒｅｓｐｏｎｓｅｃｕｒｖｅ；ｄ．坡度响应曲线ｓｌｏｐｅｒｅｓｐｏｎｓｅｃｕｒｖｅ㊂图４㊀主要环境因子响应曲线Ｆｉｇ．４㊀Ｒｅｓｐｏｎｓｅｃｕｒｖｅｓｏｆｍａｊｏｒｅｎｖｉｒｏｎｍｅｎｔａｌｆａｃｔｏｒｓ２．２㊀环境因子对迎春樱桃适生区的影响２．２．１㊀环境变量分析刀切法检验结果可以反映不同环境变量对迎春樱桃潜在分布的影响，根据输出的Ｊａｃｋｎｉｆｅ图（图３）横坐标表示每次规范训练的结果，条带数值越大说明环境对其影响越大㊂由图３可知，最干旱季度的降水（ｂｉｏ１７）和最冷季度的降水量（ｂｉｏ１９）两个环境变量对迎春樱桃的适生区分布影响最大也是最重要的㊂说明如果预测中不包含这两个环境变量将对迎春樱桃适生区的预测产生极大的影响㊂此外温度和坡度对迎春樱桃分布的影响较大［２８］，这也说明迎春樱桃适宜生活在降水量丰沛且温暖的地区㊂预测结果与物种分布地点相符㊂图３㊀基于刀切法的环境变量分析Ｆｉｇ．３㊀Ａｎａｌｙｓｉｓｏｆｅｎｖｉｒｏｎｍｅｎｔａｌｖａｒｉａｂｌｅｓｂａｓｅｄｏｎｋｎｉｆｅ⁃ｃｕｔｔｉｎｇｍｅｔｈｏｄ２．２．２㊀环境变量贡献率分析根据ＭａｘＥｎｔ模型预测结果可知，温度㊁降水和坡度都不同程度影响迎春樱桃的适生区分布㊂从贡献率来看ｂｉｏ１７最干季降水贡献率最高达到７３ ４％，其次为最冷月最低温度（ｂｉｏ６）㊁季节性温度变化（ｂｉｏ４）㊁坡度（ｓｌｏ），其贡献率分别为９ ４％㊁５ ７％㊁５ ３％㊂其中最干季降水（ｂｉｏ１７）和最冷月最低温度（ｂｉｏ６）的合计贡献率超过８０％，说明这两个因子对迎春樱桃的分布范围影响最大，其次为ｂｉｏ４和ｓｌｏ，两者占比超过１０％，且ｂｉｏ４和ｓｌｏ两个环境变量在模型中的贡献率要高于重要性，说明环境因子增加了模型的可信度［２９］㊂２．２．３㊀环境变量响应曲线分析根据迎春樱桃环境变量（ｂｉｏ１７㊁ｂｉｏ６㊁ｂｉｏ４㊁ｓｌｏ）与对应的物种存在概率，可获得迎春樱桃环境变量主要响应曲线（图４），以存在概率＞０．５为适宜范围［３０］，则迎春樱桃适宜生长的最干季降水量在１３０ １７０ｍｍ，其中最适宜的降水量为１５０ｍｍ；最冷月最低温在－４ ２ħ，最适宜的温度为０ħ上下；坡度在３ʎ ２７ʎ，其中４ʎ为最适宜的坡度㊂这也从侧面证实了迎春樱桃适宜生长在温暖㊁降水量适宜的缓坡地上㊂若最冷月温度过低或最干季降水量过少都将不利于迎春樱桃的生长㊂４３１㊀第４期杨㊀宏，等：基于ＭａｘＥｎｔ模型的迎春樱桃潜在适生区预测２．３㊀未来气候条件下迎春樱桃潜在的适生区根据ＭａｘＥｎｔ模型预测结果，在未来气候条件下迎春樱桃的适生区有向高纬度迁移的趋势，其中广东㊁福建的适生区面积呈减少趋势（图５）㊂由图５可知，未来迎春樱桃适生区面积总体上呈减少的态势，但是在２０５０ｓ⁃ＲＣＰ４ ５时总适生区面积达到最大值为７．４９ˑ１０５ｋｍ２，且高度适生区面积有所增加；而在ＲＣＰ２．６（低浓度）和ＲＣＰ４．５（中等浓度）温室气体排放条件下，迎春樱桃的中度适生区面积增加，但在（ＲＣＰ８．５）高浓度温室气体排放条件下中度适生区面积减少；同时在未来气候条件下低度适生区的总体面积也呈减少趋势（表２）㊂图５㊀迎春樱桃未来在中国的适生区Ｆｉｇ．５㊀ＴｈｅｆｕｔｕｒｅｓｕｉｔａｂｌｅｇｒｏｗｉｎｇａｒｅａｏｆＣ．ｄｉｓｃｏｉｄｅａｉｎＣｈｉｎａ表２㊀未来气候条件下迎春樱桃的潜在适生区面积及占当代适生区面积的比例Ｔａｂｌｅ２㊀ＴｈｅｐｏｔｅｎｔｉａｌｓｕｉｔａｂｌｅａｒｅａｏｆＣ．ｄｉｓｃｏｉｄｅａｉｎｔｈｅｆｕｔｕｒｅｃｌｉｍａｔｅａｎｄｉｔｓｐｒｏｐｏｒｔｉｏｎｔｏｔｈｅａｒｅａｏｆｃｏｎｔｅｍｐｏｒａｒｙｓｕｉｔａｂｌｅａｒｅａ情景及年代ｓｃｅｎａｒｉｏａｎｄｅｒａ总适生区ｔｏｔａｌｓｕｉｔａｂｌｅａｒｅａ高度适生区ｈｉｇｈｌｙｓｕｉｔａｂｌｅａｒｅａ中度适生区ｍｏｄｅｒａｔｅｓｕｉｔａｂｌｅａｒｅａ低度适生区ｌｏｗｓｕｉｔａｂｌｅａｒｅａ面积／ˑ１０５ｋｍ２ａｒｅａ占比／％ｐｅｒｃｅｎｔａｇｅ面积／ˑ１０５ｋｍ２ａｒｅａ占比／％ｐｅｒｃｅｎｔａｇｅ面积／ˑ１０５ｋｍ２ａｒｅａ占比／％ｐｅｒｃｅｎｔａｇｅ面积／ˑ１０５ｋｍ２ａｒｅａ占比／％ｐｅｒｃｅｎｔａｇｅ当代ｃｕｒｒｅｎｔ７．４０ １．０６ ２．２１ ４．１３ ＲＣＰ２．６２０５０ｓ７．０１９４．７３１．２５１１７．９２２．４０１０８．６０３．３６８１．３６２０７０ｓ７．２０９７．３０１．０６１００．００２．４０１０８．６０３．７４９０．５６ＲＣＰ４．５２０５０ｓ７．４９１０１．２２１．５４１４５．２８２．４０１０８．６０３．５５８５．６０２０７０ｓ７．３０９８．６５１．２５１１７．９２２．４０１０８．６０３．６５８８．３８ＲＣＰ８．５２０５０ｓ６．９１９３．３８１．２５１１７．９２２．１１９５．４８３．５５８５．６０２０７０ｓ６．９１９３．３８１．３４１２６．４２２．０２９１．４０３．５５８５．６０㊀㊀根据预测结果可知，迎春樱桃的总适生面积变化趋势主要取决于低度适生区面积的变化㊂在２０５０ｓ ２０７０ｓ时期的高强度温室气体排放条件下（ＲＣＰ８．５），迎春樱桃总适生区面积出现最小值为６．９１ˑ１０５ｋｍ２，占当代适生区面积的９３．３８％，而在（ＲＣＰ４．５）中等浓度温室气体排放条件下，２０５０ｓ时５３１南京林业大学学报（自然科学版）第４７卷期物种高度适生区面积达到最大值１．５４ˑ１０５ｋｍ２，为当代适生区面积的１４５．２８％；在低等浓度（ＲＣＰ２．６）和中等浓度温室气体排放条件下（ＲＣＰ４．５），同一时期物种的中度适生区面积都保持不变，为２．４０ˑ１０５ｋｍ２，占当代适生区面积的１０８ ６０％；在低等浓度温室气体排放条件下（ＲＣＰ２ ６）２０５０ｓ时期的低度适生区面积出现最小值，为３ ３６ˑ１０５ｋｍ２，占当代低度适生区面积的８１ ３６％㊂这也说明随着全球气候变暖，水热条件发生改变，使得一些地区不再适宜迎春樱桃的生长，适生区缩小，物种生存压力和种间竞争力加大，物种有趋向濒危的风险㊂３㊀讨㊀论迎春樱桃潜在适生区和高度适生区分别占全国陆地面积的７．７％和１．１％，主要分布于安徽㊁江苏㊁浙江和江西４省，且最干季降水量对迎春樱桃的潜在分布影响最大，其次为温度，该物种能忍受的最冷月温度为－４ ２ħ，低于－４ħ时不能正常生长㊂环境因子中，坡度对其影响较大，结合野外调查情况，表明此物种适宜生长在光照良好的低山丘陵山地㊂基于ＭａｘＥｎｔ模型，结合气候㊁地理因子与迎春樱桃分布数据计算其适生区面积，通过交叉验证等得出迎春樱桃的适生区主要集中于华中和华东地区，其中高度适生区主要分布于浙江北部㊁安徽南部和西部㊁江西北部和湖北东南部等地；中度适生区主要分布于江西西部㊁中部和西南部㊁湖南中部㊁浙江南部等地区；低度适生区主要分布在湖南北部和西部㊁福建北部㊁江西南部等地㊂当代适生区的分析与南程慧等［３１］㊁商韬等［１３］所记录的分布范围高度吻合，并与‘中国植物志“［２］关于这一物种分布地点的描述一致㊂武夷山地区樱属植物资源丰富，但在长期调查中未发现有迎春樱桃的分布，推测原因与武夷山低度适生区模拟结果及其小乔木树型的性状相关，在发育良好的常绿阔叶林地带性植被中该物种无竞争优势㊂‘中国植物志“［２］与‘江苏植物志“［３２］都未记录迎春樱桃在江苏地区的分布，但实地调查发现，在江苏南部的宜溧山区（１１９ʎ４１ᶄ３５．１２ᵡＥ，３１ʎ１３ᶄ０５．４２ᵡＮ；１１９ʎ３１ᶄ０２．９７ᵡＥ，３１ʎ１０ᶄ１９．０７ᵡＮ）及江苏北部的云台山地区（１１９ʎ２６ᶄ３６．３０ᵡＥ，３４ʎ４２ᶄ４９．８０ᵡＮ）有分布，这与江苏南部宜溧山区为迎春樱桃中度适生区模拟结果一致㊂湖北和湖南地区有着众多的野生樱属资源，但‘湖北植物志“［３３］中没有迎春樱桃分布的记录，推测可能在之前的调查中因交通不便或高山阻隔导致其未被发现㊂根据前人对迎春樱桃系统发育的研究［３４－３６］表明，其与尾叶樱桃㊁山樱花和浙闽樱桃具有较近的遗传关系，同时这些类群地理分布相似，均广泛分布于华中㊁华东一带㊂通过对山樱花㊁浙闽樱桃和尾叶樱桃的适生区研究发现，影响它们分布范围的限制条件为水热条件，这与本研究结果相一致㊂前人对尾叶樱桃的适生区模拟分析［３７－３８］发现其有向东扩展的趋势，而本研究显示迎春樱桃的适生区有向高纬度扩张的趋势，表明樱属植物对水分和热量条件的要求较宽泛；笔者推测迎春樱桃对江苏北部等暖温带地区的次生落叶阔叶林具有较强的竞争优势与适应性，这也是迎春樱桃未来高度适生区朝东北方向扩张的主要原因㊂本研究中选取了３个地形因子结合１９个气候因子数据，发现地形因子也是影响樱属植物的重要因素之一㊂安徽㊁江苏㊁浙江和江西位于中国东部季风区及长江中下游地区，迎春樱桃主要分布于该区的低山丘陵山地，良好的水热条件以及低山环境为迎春樱桃提供了良好的生存环境，模拟结果显示，该区域也是未来气候条件下迎春樱桃的高度适生区㊂在此次模拟中西藏部分地区出现了迎春樱桃的潜在适生区，而查阅当前资料和野外调查暂未发现该地区有天然分布，推测山脉的阻隔以及传播路径过长影响了迎春樱桃在此区域的群体扩张㊂近年来，ＭａｘＥｎｔ模型广泛应用于物种分布方面的预测，本研究利用该模型较好地预测了迎春樱桃在中国的潜在分布区，分析了未来气候条件下迎春樱桃适生区面积的变化趋势㊂迎春樱桃适生区面积总体呈减少趋势，而人为干扰与生境破碎化等问题导致迎春樱桃种群更新与扩张困难㊂随着全球温室效应的加剧以及树种所处生存群落的不断发育，迎春樱桃在群落中将丧失竞争优势，种群数量将不断减少并极易导致其退出现有分布区，未来应注重其种质资源收集㊁引种繁殖及推广利用等方面的研究㊂参考文献（ｒｅｆｅｒｅｎｃｅ）：［１］陈涛，胡国平，王燕，等．我国野生樱属植物种质资源调查㊁收集与保护［Ｊ］．植物遗传资源学报，２０２０，２１（３）：５３２－５４１．ＣＨＥＮＴ，ＨＵＧＰ，ＷＡＮＧＹ，ｅｔａｌ．Ｓｕｒｖｅｙ，ｃｏｌｌｅｃｔｉｏｎａｎｄｃｏｎｓｅｒ⁃ｖａｔｉｏｎｏｆｗｉｌｄＣｅｒａｓｕｓＭｉｌｌ．ｇｅｒｍｐｌａｓｍｒｅｓｏｕｒｃｅｓｉｎＣｈｉｎａ［Ｊ］．ＪＰｌａｎｔＧｅｎｅｔＲｅｓｏｕｒ，２０２０，２１（３）：５３２－５４１．ＤＯＩ：１０．１３４３０／ｊ．ｃｎｋｉ．ｊｐｇｒ．２０１９０７１６００１．［２］中国科学院中国植物志编辑委员会．中国植物志：第３８卷［Ｍ］．北京：科学出版社，１９８６：５２．ＥｄｉｔｏｒｉａｌＣｏｍｍｉｔｔｅｅｏｆＣｈｉｎｅｓｅＦｌｏｒａ，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ．ＦｌｏｒａｏｆＣｈｉｎａ：６３１㊀第４期杨㊀宏，等：基于ＭａｘＥｎｔ模型的迎春樱桃潜在适生区预测Ｖｏｌｕｍｅ３８［Ｍ］．Ｂｅｉｊｉｎｇ：ＳｃｉｅｎｃｅＰｒｅｓｓ，１９８６：５２．［３］严春风，徐梁，赵绮，等．我国原生樱属植物资源的分类研究［Ｊ］．江苏林业科技，２０１７，４４（３）：３５－４０．ＹＡＮＣＦ，ＸＵＬ，ＺＨＡＯＱ，ｅｔａｌ．ＣｌａｓｓｉｆｉｃａｔｉｏｎｒｅｓｅａｒｃｈｏｆＣｈｉｎｅｓｅｎａｔｉｖｅＣｅｒａｓｕｓｒｅｓｏｕｒｃｅｓ［Ｊ］．ＪＪｉａｎｇｓｕＦｏｒＳｃｉＴｅｃｈｎｏｌ，２０１７，４４（３）：３５－４０．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１００１－７３８０．２０１７．０３．００９．［４］李茂华，都金康，李皖彤，等．１９８２ ２０１５年全球植被变化及其与温度和降水的关系［Ｊ］．地理科学，２０２０，４０（５）：８２３－８３２．ＬＩＭＨ，ＤＵＪＫ，ＬＩＷＴ，ｅｔａｌ．ＧｌｏｂａｌｖｅｇｅｔａｔｉｏｎｃｈａｎｇｅａｎｄｉｔｓｒｅｌａｔｉｏｎｓｈｉｐｗｉｔｈｐｒｅｃｉｐｉｔａｔｉｏｎａｎｄｔｅｍｐｅｒａｔｕｒｅｂａｓｅｄｏｎＧＬＡＳＳ⁃ＬＡＩｉｎ１９８２－２０１５［Ｊ］．ＳｃｉＧｅｏｇｒＳｉｎ，２０２０，４０（５）：８２３－８３２．ＤＯＩ：１０．１３２４９／ｊ．ｃｎｋｉ．ｓｇｓ．２０２０．０５．０１７．［５］傅伯杰，牛栋，赵士洞．全球变化与陆地生态系统研究：回顾与展望［Ｊ］．地球科学进展，２００５，２０（５）：５５６－５６０．ＦＵＢＪ，ＮＩＵＤ，ＺＨＡＯＳＤ．Ｓｔｕｄｙｏｎｇｌｏｂａｌｃｈａｎｇｅａｎｄｔｅｒｒｅｓｔｒｉａｌｅｃｏｓｙｓｔｅｍｓ：ｈｉｓｔｏｒｙａｎｄｐｒｏｓｐｅｃｔ［Ｊ］．ＡｄｖＥａｒｔｈＳｃｉ，２００５，２０（５）：５５６－５６０．ＤＯＩ：１０．３３２１／ｊ．ｉｓｓｎ：１００１－８１６６．２００５．０５．０１１．［６］何远政，黄文达，赵昕，等．气候变化对植物多样性的影响研究综述［Ｊ］．中国沙漠，２０２１，４１（１）：５９－６６．ＨＥＹＺ，ＨＵＡＮＧＷＤ，ＺＨＡＯＸ，ｅｔａｌ．Ｒｅｖｉｅｗｏｎｔｈｅｉｍｐａｃｔｏｆｃｌｉｍａｔｅｃｈａｎｇｅｏｎｐｌａｎｔｄｉｖｅｒｓｉｔｙ［Ｊ］．ＪＤｅｓｅｒｔＲｅｓ，２０２１，４１（１）：５９－６６．ＤＯＩ：１０．７５２２／ｊ．ｉｓｓｎ．１０００－６９４Ｘ．２０２０．００１０４．［７］付永硕，李昕熹，周轩成，等．全球变化背景下的植物物候模型研究进展与展望［Ｊ］．中国科学：地球科学，２０２０，５０（９）：１２０６－１２１８．ＦＵＹＳ，ＬＩＸＸ，ＺＨＯＵＸＣ，ｅｔａｌ．Ｐｒｏｇｒｅｓｓｉｎｐｌａｎｔｐｈｅｎｏｌｏｇｙｍｏｄｅｌｉｎｇｕｎｄｅｒｇｌｏｂａｌｃｌｉｍａｔｅｃｈａｎｇｅ［Ｊ］．ＳｃｉＳｉｎ（Ｔｅｒｒａｅ），２０２０，５０（９）：１２０６－１２１８．［８］张文秀，寇一翾，张丽，等．采用生态位模拟预测濒危植物白豆杉５个时期的适宜分布区［Ｊ］．生态学杂志，２０２０，３９（２）：６００－６１３．ＺＨＡＮＧＷＸ，ＫＯＵＹＸ，ＺＨＡＮＧＬ，ｅｔａｌ．Ｓｕｉｔａｂｌｅｄｉｓ⁃ｔｒｉｂｕｔｉｏｎｏｆｅｎｄａｎｇｅｒｅｄｓｐｅｃｉｅｓＰｓｅｕｄｏｔａｘｕｓｃｈｉｅｎｉｉ（Ｃｈｅｎｇ）Ｃｈｅｎｇ（Ｔａｘａｃｅａｅ）ｉｎｆｉｖｅｐｅｒｉｏｄｓｕｓｉｎｇｎｉｃｈｅｍｏｄｅｌｉｎｇ［Ｊ］．ＣｈｉｎＪＥｃｏｌ，２０２０，３９（２）：６００－６１３．ＤＯＩ：１０．１３２９２／ｊ．１０００－４８９０．２０２００２．０２８．［９］赖铭婕，吴保欢，崔大方．基于ＤＩＶＡ⁃ＧＩＳ的广东适生樱花预测分析［Ｊ］．广东园林，２０２０，４２（４）：３７－４１．ＬＡＩＭＪ，ＷＵＢＨ，ＣＵＩＤＦ．ＰｒｅｄｉｃｔｉｏｎａｎｄａｎａｌｙｓｉｓｏｆｓｕｉｔａｂｌｅＣｅｒａｓｕｓｓｐｐ．ｉｎＧｕａｎｇｄｏｎｇＰｒｏｖｉｎｃｅｂａｓｅｄｏｎＤＩＶＡ⁃ＧＩＳ［Ｊ］．ＧｕａｎｇｄｏｎｇＬａｎｄｓｃＡｒｃｈｉｔ，２０２０，４２（４）：３７－４１．［１０］李蒙，伊贤贵，王华辰，等．山樱花地理分布与水热环境因子的关系［Ｊ］．南京林业大学学报（自然科学版），２０１４，３８（增刊）：７４－８０．ＬＩＭ，ＹＩＸＧ，ＷＡＮＧＨＣ，ｅｔａｌ．ＳｔｕｄｉｅｓｏｎｔｈｅｒｅｌａｔｉｏｎｓｈｉｐｂｅｔｗｅｅｎＣｅｒａｓｕｓｓｅｒｒｕｌａｔａｄｉｓｔｒｉｂｕｔｉｏｎｒｅｇｉｏｎａｎｄｔｈｅｅｎｖｉｒｏｎｍｅｎｔａｌｆａｃｔｏｒｓ［Ｊ］．ＪＮａｎｊｉｎｇＦｏｒＵｎｉｖ（ＮａｔＳｃｉＥｄ），２０１４，３８（Ｓ１）：７４－８０．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１０００－２００６．２０１４．Ｓ１．０１６．［１１］朱弘，尤禄祥，李涌福，等．浙闽樱桃地理分布模拟及气候限制因子分析［Ｊ］．热带亚热带植物学报，２０１７，２５（４）：３１５－３２２．ＺＨＵＨ，ＹＯＵＬＸ，ＬＩＹＦ，ｅｔａｌ．Ｍｏｄｅｌｉｎｇｔｈｅｇｅｏｇｒａｐｈｉｃａｌｄｉｓｔｒｉ⁃ｂｕｔｉｏｎｐａｔｔｅｒｎａｎｄｃｌｉｍａｔｉｃｌｉｍｉｔｅｄｆａｃｔｏｒｓｏｆＣｅｒａｓｕｓｓｃｈｎｅｉｄｅｒｉａｎａ［Ｊ］．ＪＴｒｏｐＳｕｂｔｒｏｐＢｏｔ，２０１７，２５（４）：３１５－３２２．ＤＯＩ：１０．１１９２６／ｊｔｓｂ．３７０２．［１２］南程慧．迎春樱居群变异与繁殖生物学研究［Ｄ］．南京：南京林业大学，２０１２．ＮＡＮＣＨ．Ｓｔｕｄｙｏｎｐｏｐｕｌａｔｉｏｎｖａｒｉａｔｉｏｎａｎｄｒｅ⁃ｐｒｏｄｕｃｔｉｖｅｂｉｏｌｏｇｙｏｆＣｅｒａｓｕｓｄｉｓｃｏｉｄｅａＹüｅｔＬｉ［Ｄ］．Ｎａｎｊｉｎｇ：ＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，２０１２．［１３］商韬，王贤荣，南程慧，等．基于ＳＳＲ标记的迎春樱自然居群遗传多样性分析［Ｊ］．甘肃农业大学学报，２０１３，４８（６）：１０４－１０９，１１５．ＳＨＡＮＧＴ，ＷＡＮＧＸＲ，ＮＡＮＣＨ，ｅｔａｌ．ＧｅｎｅｔｉｃｄｉｖｅｒｓｉｔｙｉｎｎａｔｕｒａｌｐｏｐｕｌａｔｉｏｎｓｏｆＣｅｒａｓｕｓｄｉｓｃｏｉｄｅａｂａｓｅｄｏｎＳＳＲｍａｒｋｅｒｓ［Ｊ］．ＪＧａｎｓｕＡｇｒｉｃＵｎｉｖ，２０１３，４８（６）：１０４－１０９，１１５．ＤＯＩ：１０．１３４３２／ｊ．ｃｎｋｉ．ｊｇｓａｕ．２０１３．０６．０２１．［１４］曹向锋，钱国良，胡白石，等．采用生态位模型预测黄顶菊在中国的潜在适生区［Ｊ］．应用生态学报，２０１０，２１（１２）：３０６３－３０６９．ＣＡＯＸＦ，ＱＩＡＮＧＬ，ＨＵＢＳ，ｅｔａｌ．ＰｒｅｄｉｃｔｉｏｎｏｆｐｏｔｅｎｔｉａｌｓｕｉｔａｂｌｅｄｉｓｔｒｉｂｕｔｉｏｎａｒｅａｏｆＦｌａｖｅｒｉａｂｉｄｅｎｔｉｓｉｎＣｈｉｎａｂａｓｅｄｏｎｎｉｃｈｅｍｏｄｅｌｓ［Ｊ］．ＣｈｉｎＪＡｐｐｌＥｃｏｌ，２０１０，２１（１２）：３０６３－３０６９．ＤＯＩ：１０．１３２８７／ｊ．１００１－９３３２．２０１０．０４３１．［１５］张童，黄治昊，彭杨靖，等．基于ＭａｘＥｎｔ模型的软枣猕猴桃在中国潜在适生区预测［Ｊ］．生态学报，２０２０，４０（１４）：４９２１－４９２８．ＺＨＡＮＧＴ，ＨＵＡＮＧＺＨ，ＰＥＮＧＹＪ，ｅｔａｌ．Ｐｒｅｄｉｃｔｉｏｎｏｆｐｏ⁃ｔｅｎｔｉａｌｓｕｉｔａｂｌｅａｒｅａｓｏｆＡｃｔｉｎｉｄｉａａｒｇｕｔａｉｎＣｈｉｎａｂａｓｅｄｏｎＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＡｃｔａＥｃｏｌＳｉｎ，２０２０，４０（１４）：４９２１－４９２８．ＤＯＩ：１０．５８４６／ｓｔｘｂ２０１９０９１６１９２１．［１６］王茹琳，王明田，罗家栋，等．基于ＭａｘＥｎｔ模型的美味猕猴桃在中国气候适宜性分析［Ｊ］．云南农业大学学报（自然科学），２０１９，３４（３）：５２２－５３１．ＷＡＮＧＲＬ，ＷＡＮＧＭＴ，ＬＵＯＪＤ，ｅｔａｌ．ＴｈｅａｎａｌｙｓｉｓｏｆｃｌｉｍａｔｅｓｕｉｔａｂｉｌｉｔｙａｎｄｒｅｇｉｏｎａｌｉｚａｔｉｏｎｏｆＡｃｔｉｎｉｄｉａｄｅｌｉｃｉｏｓａｂｙｕｓｉｎｇＭａｘＥｎｔｍｏｄｅｌｉｎＣｈｉｎａ［Ｊ］．ＪＹｕｎｎａｎＡｇｒｉｃＵｎｉｖ（ＮａｔＳｃｉ），２０１９，３４（３）：５２２－５３１．ＤＯＩ：１０．１２１０１／ｊ．ｉｓｓｎ．１００４－３９０Ｘ（ｎ）．２０１７１１０３９．［１７］王国峥，耿其芳，肖孟阳，等．基于４种生态位模型的金钱松潜在适生区预测［Ｊ］．生态学报，２０２０，４０（１７）：６０９６－６１０４．ＷＡＮＧＧＺ，ＧＥＮＧＱＦ，ＸＩＡＯＭＹ，ｅｔａｌ．ＰｒｅｄｉｃｔｉｎｇＰｓｅｕｄｏｌａｒｉｘａｍａｂｉｌｉｓｐｏｔｅｎｔｉａｌｈａｂｉｔａｔｂａｓｅｄｏｎｆｏｕｒｎｉｃｈｅｍｏｄｅｌｓ［Ｊ］．ＡｃｔａＥｃｏｌＳｉｎ，２０２０，４０（１７）：６０９６－６１０４．ＤＯＩ：１０．５８４６／ｓｔｘｂ２０１９０７０２１３９０．［１８］杨启杰，李睿．桫椤的潜在适生区及其变化［Ｊ］．应用生态学报，２０２１，３２（２）：５３８－５４８．ＹＡＮＧＱＪ，ＬＩＲ．Ｐｒｅｄｉｃｔｉｎｇｔｈｅｐｏ⁃ｔｅｎｔｉａｌｓｕｉｔａｂｌｅｈａｂｉｔａｔｓｏｆＡｌｓｏｐｈｉｌａｓｐｉｎｕｌｏｓａａｎｄｔｈｅｉｒｃｈａｎｇｅｓ［Ｊ］．ＣｈｉｎＪＡｐｐｌＥｃｏｌ，２０２１，３２（２）：５３８－５４８．ＤＯＩ：１０．１３２８７／ｊ．１００１－９３３２．２０２１０２．０１５．［１９］许斌，朱文泉，李培先．不同气候条件下桫椤在中国的潜在适生区分布［Ｊ］．生态学报，２０２０，４０（１７）：６１０５－６１１７．ＸＵＢ，ＺＨＵＷＱ，ＬＩＰＸ．ＰｏｔｅｎｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｓｏｆＡｌｓｏｐｈｉｌａｓｐｉｎｕｌｏｓａｕｎｄｅｒｄｉｆｆｅｒｅｎｔｃｌｉｍａｔｅｓｉｎＣｈｉｎａ［Ｊ］．ＡｃｔａＥｃｏｌＳｉｎ，２０２０，４０（１７）：６１０５－６１１７．ＤＯＩ：１０．５８４６／ｓｔｘｂ２０１９０７２４１５６５．［２０］刘清亮，李垚，方升佐．基于ＭａｘＥｎｔ模型的青钱柳潜在适宜栽培区预测［Ｊ］．南京林业大学学报（自然科学版），２０１７，４１（４）：２５－２９．ＬＩＵＱＬ，ＬＩＹ，ＦＡＮＧＳＺ．ＭａｘＥｎｄｍｏｄｅｌ⁃ｂａｓｅｄｉｎｄｅｎｔｉｆｉｃａｔｉｏｎｏｆｐｏｔｅｎｔｉａｌＣｙｃｌｏｃａｒｙａｐａｌｉｕｒｕｓｃｕｌｔｉｖａｔｉｏｎｒｅｇｉｏｎｓ［Ｊ］．ＪＮａｎｊｉｎｇＦｏｒｅＵｎｉｖ（ＮａｔＳｃｉＥｄ），２０１７，４１（４）：２５－２９．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１０００－２００６．２０１６０８０１０．［２１］王雨生，王召海，邢汉发，等．基于ＭａｘＥｎｔ模型的珙桐在中国潜在适生区预测［Ｊ］．生态学杂志，２０１９，３８（４）：１２３０－１２３７．ＷＡＮＧＹＳ，ＷＡＮＧＺＨ，ＸＩＮＧＨＦ，ｅｔａｌ．ＰｒｅｄｉｃｔｉｏｎｏｆｐｏｔｅｎｔｉａｌｓｕｉｔａｂｌｅｄｉｓｔｒｉｂｕｔｉｏｎｏｆＤａｖｉｄｉａｉｎｖｏｌｕｃｒａｔａＢａｉｌｌｉｎＣｈｉｎａｂａｓｅｄｏｎＭａｘＥｎｔ［Ｊ］．ＣｈｉｎＪＥｃｏｌ，２０１９，３８（４）：１２３０－１２３７．ＤＯＩ：１０．１３２９２／ｊ．１０００－４８９０．２０１９０４．０２４．［２２］陈俪心，和梅香，王彬，等．基于ＭａｘＥｎｔ模型的凉山山系珙桐种群适宜生境分布及其影响因素分析［Ｊ］．四川大学学报（自然科学版），２０１８，５５（４）：８７３－８８０．ＣＨＥＮＬＸ，ＨＥＭＸ，ＷＡＮＧＢ，ｅｔａｌ．Ａｎａｌｙｓｉｓｏｆｓｕｉｔａｂｌｅｈａｂｉｔａｔｄｉｓｔｒｉｂｕｔｉｏｎａｎｄｉｔｓｉｎ⁃ｆｌｕｅｎｃｅｆａｃｔｏｒｓｏｆＤａｖｉｄｉａｉｎｖｏｌｕｃｒａｔａｉｎＬｉａｎｇｓｈａｎＭｏｕｎｔａｉｎｓｂａｓｅｄｏｎＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＪＳｉｃｈｕａｎＵｎｉｖ（ＮａｔＳｃｉＥｄ），２０１８，５５（４）：８７３－８８０．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．０４９０－６７５６．２０１８．０４．０３５．７３１南京林业大学学报（自然科学版）第４７卷［２３］沈永平，王国亚．ＩＰＣＣ第一工作组第五次评估报告对全球气候变化认知的最新科学要点［Ｊ］．冰川冻土，２０１３，３５（５）：１０６８－１０７６．ＳＨＥＮＹＰ，ＷＡＮＧＧＹ．ＫｅｙｆｉｎｄｉｎｇｓａｎｄａｓｓｅｓｓｍｅｎｔｒｅｓｕｌｔｓｏｆＩＰＣＣＷＧＩｆｉｆｔｈａｓｓｅｓｓｍｅｎｔｒｅｐｏｒｔ［Ｊ］．ＪＧｌａｃｉｏｌＧｅｏｃｒｙｏｌ，２０１３，３５（５）：１０６８－１０７６．ＤＯＩ：１０．７５２２／ｊ．ｉｓｓｎ．１０００－０２４０．２０１３．０１２０．［２４］齐国君，陈婷，高燕，等．基于Ｍａｘｅｎｔ的大洋臀纹粉蚧和南洋臀纹粉蚧在中国的适生区分析［Ｊ］．环境昆虫学报，２０１５，３７（２）：２１９－２２３．ＱＩＧＪ，ＣＨＥＮＴ，ＧＡＯＹ，ｅｔａｌ．ＰｏｔｅｎｔｉａｌｇｅｏｇｒａｐｈｉｃｄｉｓｔｒｉｂｕｔｉｏｎｏｆＰｌａｎｏｃｏｃｃｕｓｍｉｎｏｒａｎｄＰ．ｌｉｌａｃｉｎｕｓｉｎＣｈｉｎａｂａｓｅｄｏｎＭａｘＥｎｔ［Ｊ］．ＪＥｎｖｉｒｏｎＥｎｔｏｍｏｌ，２０１５，３７（２）：２１９－２２３．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１６７４－０８５８．２０１５．０２．１．［２５］邹天娇，倪畅，郑曦．基于ＭａｘＥｎｔ模型的北京浅山区珍稀植物适生区预测及管理［Ｊ］．中国城市林业，２０２０，１８（４）：１７－２２．ＺＯＵＴＪ，ＮＩＣ，ＺＨＥＮＧＸ．ＰｒｅｄｉｃｔｉｏｎａｎｄｍａｎａｇｅｍｅｎｔｏｆｒａｒｅｐｌａｎｔｓｕｉｔａｂｌｅａｒｅａｉｎｈｉｌｌｙａｒｅａｓｏｆＢｅｉｊｉｎｇｂａｓｅｄｏｎＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＪＣｈｉｎＵｒｂａｎＦｏｒ，２０２０，１８（４）：１７－２２．ＤＯＩ：１０．１２１６９／ｚｇｃｓｌｙ．２０１９．０３．２７．０００１．［２６］柳晓燕，李俊生，赵彩云，等．基于ＭａｘＥｎｔ模型和ＡｒｃＧＩＳ预测豚草在中国的潜在适生区［Ｊ］．植物保护学报，２０１６，４３（６）：１０４１－１０４８．ＬＩＵＸＹ，ＬＩＪＳ，ＺＨＡＯＣＹ，ｅｔａｌ．Ｐｒｅｄｉｃｔｉｏｎｏｆｐｏ⁃ｔｅｎｔｉａｌｓｕｉｔａｂｌｅａｒｅａｏｆＡｍｂｒｏｓｉａａｒｔｅｍｉｓｉｉｆｏｌｉａＬ．ｉｎＣｈｉｎａｂａｓｅｄｏｎＭａｘＥｎｔａｎｄＡｒｃＧＩＳ［Ｊ］．ＪＰｌａｎｔＰｒｏｔ，２０１６，４３（６）：１０４１－１０４８．ＤＯＩ：１０．１３８０２／ｊ．ｃｎｋｉ．ｚｗｂｈｘｂ．２０１６．０６．０２３．［２７］孙蓉，刘影．基于ＭａｘＥｎｔ模型的江西省白桂木生境适宜性评价［Ｊ］．南方林业科学，２０２０，４８（２）：２３－２７．ＳＵＮＲ，ＬＩＵＹ．ＨａｂｉｔａｔｓｕｉｔａｂｉｌｉｔｙｅｖａｌｕａｔｉｏｎｏｆＡｒｔｏｃａｒｐｕｓｈｙｐａｒｇｙｒｅｕｓＨａｎｃｅｉｎＪｉａｎｇｘｉＰｒｏｖｉｎｃｅｂａｓｅｄｏｎＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＳｏｕｔｈＣｈｉｎａＦｏｒＳｃｉ，２０２０，４８（２）：２３－２７．ＤＯＩ：１０．１６２５９／ｊ．ｃｎｋｉ．３６－１３４２／ｓ．２０２０．０２．００５．［２８］樊信，盘金文，何嵩涛．气候变化背景下基于ＭａｘＥｎｔ模型的刺梨潜在适生区分布预测［Ｊ］．西北植物学报，２０２１，４１（１）：１５９－１６７．ＦＡＮＸ，ＰＡＮＪＷ，ＨＥＳＴ．ＰｒｅｄｉｃｔｉｏｎｏｆｔｈｅｐｏｔｅｎｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｏｆＲｏｓａｒｏｘｂｕｒｇｈｉｉｕｎｄｅｒｔｈｅｂａｃｋｇｒｏｕｎｄｏｆｃｌｉｍａｔｅｃｈａｎｇｅｂａｓｅｄｏｎＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＡｃｔａＢｏｔＢｏｒｅａｌｉＯｃｃｉｄｅｎｔａｌｉａＳｉｎ，２０２１，４１（１）：１５９－１６７．ＤＯＩ：１０．７６０６／ｊ．ｉｓｓｎ．１０００－４０２５．２０２１．０１．０１５９．［２９］姚祺，李佶芸，赵垦田．基于ＭａｘＥｎｔ模型的巨柏青藏高原生态适宜性研究［Ｊ］．高原农业，２０２１，５（２）：１０９－１１４．ＹＡＯＱ，ＬＩＪＹ，ＺＨＡＯＫＴ．ＲｅｓｅａｒｃｈｏｎｅｃｏｌｏｇｉｃａｌｓｕｉｔａｂｉｌｉｔｙｏｆｇｉａｎｔｃｙｐｒｅｓｓｏｎＱｉｎｇｈａｉ⁃ＴｉｂｅｔＰｌａｔｅａｕｂａｓｅｄｏｎＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＪＰｌａｔｅａｕＡｇｒｉｃ，２０２１，５（２）：１０９－１１４．ＤＯＩ：１０．１９７０７／ｊ．ｃｎｋｉ．ｊｐａ．２０２１．０２．００１．［３０］王广，张莹，张娇，等．基于ＭａｘＥｎｔ模型的半夏潜在适宜分布研究［Ｊ］．武汉轻工大学学报，２０１８，３７（６）：３５－４０．ＷＡＮＧＧ，ＺＨＡＮＧＹ，ＺＨＡＮＧＪ，ｅｔａｌ．ＰｏｔｅｎｔｉａｌｄｉｓｔｒｉｂｕｔｉｏｎｏｆＰｉｎｅｌｌｉａｔｅｒｎａｔａｂａｓｅｄｏｎＭａｘＥｎｔｍｏｄｅｌ［Ｊ］．ＪＷｕｈａｎＰｏｌｙｔｅｃｈＵｎｉｖ，２０１８，３７（６）：３５－４０．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．２０９５－７３８６．２０１８．０６．００５．［３１］南程慧，伊贤贵，王华辰，等．迎春樱群落主要种群生态位研究［Ｊ］．南京林业大学学报（自然科学版），２０１４，３８（增刊）：８９－９２．ＮＡＮＣＨ，ＹＩＸＧ，ＷＡＮＧＨＣ，ｅｔａｌ．ＳｔｕｄｙｏｎｔｈｅｎｉｃｈｅｏｆｔｈｅｍａｉｎｐｏｐｕｌａｉｔｉｏｎｉｎＣｅｒａｓｕｓｄｉｓｃｏｉｄｅａｃｏｍｍｕｎｉｔｙ［Ｊ］．ＪＮａｎｊｉｎｇＦｏｒＵｎｉｖ（ＮａｔＳｃｉＥｄ），２０１４，３８（Ｓ１）：８９－９２．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１０００－２００６．２０１４．Ｓ１．０１８．［３２］江苏省植物研究所．江苏植物志：上册［Ｍ］．南京：江苏人民出版社，１９７７．ＪｉａｎｇｓｕＩｎｓｔｉｔｕｔｅｏｆＢｏｔａｎｙ．ＦｌｏｒａｏｆＪｉａｎｇｓｕ：Ｖｏｌｕｍｅ１［Ｍ］．Ｎａｎｊｉｎｇ：ＪｉａｎｇｓｕＰｅｏｐｌｅ ｓＰｕｂｌｉｓｈｉｎｇＨｏｕｓｅ，１９７７．［３３］傅书遐．湖北植物志［Ｍ］．武汉：湖北科技出版社，２００２．ＦＵＳＸ．ＦｌｏｒａＨｕｂｅｉｅｎｓｉｓ［Ｍ］．Ｗｕｈａｎ：ＨｕｂｅｉＳｃｉｅｎｃｅａｎｄＴｅｃｈｎｏｌｏｇｙＰｒｅｓｓ，２００２．［３４］ＬＩＭ，ＳＯＮＧＹＦ，ＳＹＬＶＥＳＴＥＲＳＰ，ｅｔａｌ．ＣｏｍｐａｒａｔｉｖｅａｎａｌｙｓｉｓｏｆｔｈｅｃｏｍｐｌｅｔｅｐｌａｓｔｉｄｇｅｎｏｍｅｓｉｎＰｒｕｎｕｓｓｕｂｇｅｎｕｓＣｅｒａｓｕｓ（Ｒｏｓａ⁃ｃｅａｅ）：ｍｏｌｅｃｕｌａｒｓｔｒｕｃｔｕｒｅｓａｎｄｐｈｙｌｏｇｅｎｅｔｉｃｒｅｌａｔｉｏｎｓｈｉｐｓ［Ｊ］．ＰＬｏＳＯｎｅ，２０２２，１７（４）：ｅ０２６６５３５．ＤＯＩ：１０．１３７１／ｊｏｕｒｎａｌ．ｐｏｎｅ．０２６６５３５．［３５］ＹＡＮＪＷ，ＬＩＪＨ，ＹＵＬ，ｅｔａｌ．ＣｏｍｐａｒａｔｉｖｅｃｈｌｏｒｏｐｌａｓｔｇｅｎｏｍｅｓｏｆＰｒｕｎｕｓｓｕｂｇｅｎｕｓＣｅｒａｓｕｓ（Ｒｏｓａｃｅａｅ）：ｉｎｓｉｇｈｔｓｉｎｔｏｓｅｑｕｅｎｃｅｖａｒｉａｔｉｏｎｓａｎｄｐｈｙｌｏｇｅｎｅｔｉｃｒｅｌａｔｉｏｎｓｈｉｐｓ［Ｊ］．ＴｒｅｅＧｅｎｅｔＧｅｎｏｍｅｓ，２０２１，１７（６）：５０．ＤＯＩ：１０．１００７／ｓ１１２９５－０２１－０１５３３－８．［３６］朱弘，伊贤贵，朱淑霞，等．基于叶绿体ＤＮＡａｔｐＢ⁃ｒｂｃＬ片段的典型樱亚属部分种的亲缘关系及分类地位探讨［Ｊ］．植物研究，２０１８，３８（６）：８２０－８２７．ＺＨＵＨ，ＹＩＸＧ，ＺＨＵＳＸ，ｅｔａｌ．ＡｎａｌｙｓｉｓｏｎｒｅｌａｔｉｏｎｓｈｉｐａｎｄｔａｘｏｎｏｍｉｃｓｔａｔｕｓｏｆｓｏｍｅｓｐｅｃｉｅｓｉｎＳｕｂｇ．ＣｅｒａｓｕｓＫｏｅｈｎｅｗｉｔｈｃｈｌｏｒｏｐｌａｓｔＤＮＡａｔｐＢ⁃ｒｂｃＬｆｒａｇｍｅｎｔ［Ｊ］．ＢｕｌｌＢｏｔＲｅｓ，２０１８，３８（６）：８２０－８２７．ＤＯＩ：１０．７５２５／ｊ．ｉｓｓｎ．１６７３－５１０２．２０１８．０６．００４．［３７］朱弘．尾叶樱桃（Ｃｅｒａｓｕｓｄｉｅｌｓｉａｎａ）系统分类地位与种群生物地理学研究［Ｄ］．南京：南京林业大学，２０２０．ＺＨＵＨ．ＰｈｙｌｏｇｅｎｅｔｉｃｐｏｓｉｔｉｏｎａｎｄｐｏｐｕｌａｔｉｏｎｂｉｏｇｅｏｇｒａｐｈｙｏｆＣｅｒａｓｕｓｄｉｅｌ⁃ｓｉａｎａ（Ｒｏｓａｃｅａｅ）［Ｄ］．Ｎａｎｊｉｎｇ：ＮａｎｊｉｎｇＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，２０２０．［３８］朱弘，伊贤贵，朱淑霞，等．中国亚热带特有植物尾叶樱桃的研究进展［Ｊ］．中国野生植物资源，２０２０，３９（１）：３５－４０．ＺＨＵＨ，ＹＩＸＧ，ＺＨＵＳＸ，ｅｔａｌ．ＲｅｓｅａｒｃｈｐｒｏｇｒｅｓｓｏｆＣｅｒａｓｕｓｄｉｅｌｓｉａｎａ，ａｎｅｎｄｅｍｉｃｐｌａｎｔｓｆｒｏｍｓｕｂｔｒｏｐｉｃａｌＣｈｉｎａ［Ｊ］．ＣｈｉｎＷｉｌｄＰｌａｎｔＲｅ⁃ｓｏｕｒ，２０２０，３９（１）：３５－４０．ＤＯＩ：１０．３９６９／ｊ．ｉｓｓｎ．１００６－９６９０．２０２０．０１．００９．（责任编辑㊀郑琰燚）８３１。

Semi-Heusler合金NiCrP和NiVAs半金属铁磁性稳定特性的第一性原理研究姚仲瑜【摘要】采用基于密度泛函理论的全势能线性缀加平面波方法对semi-Heusler 合金NiCrP和NiVAs的电子结构进行自旋极化计算.semi-Heusler合金NiCrP和NiVAs处于平衡晶格常数时都具有半金属性质,它们自旋向下子能带的带隙分别是0.59 eV和0.46eV,合金分子的总磁矩分别为3.00/formula和2.00/formula.在晶体相对于平衡晶格发生各向同性形变的情况下,计算semi-Heusler合金NiCrP和NiVAs的电子结构.计算结果表明,在相对于平衡晶格的各向同性形变分别为-6%～2%和-2%～4%时,semi-Heusler合金NiCrP和NiVAs的总磁矩稳定,并且能保持其半金属铁磁性.【期刊名称】《海南师范大学学报（自然科学版）》【年(卷),期】2011(024)001【总页数】5页(P47-51)【关键词】第一性原理;NiCrP;NiVAs;半金属铁磁性【作者】姚仲瑜【作者单位】海南师范大学物理与电子工程学院,海南海口571158【正文语种】中文【中图分类】O562.1半金属半铁磁体（half-metallic ferromagnet）是指一个自旋子能带（一般为自旋向上子能带）是金属性的，而另一个自旋子能带是半导体性或绝缘体性的铁磁性物质.这一性质是de Groot等人在1983年对半霍伊斯勒（semi-Heusler）合金NiMnSb和Pt⁃MnSb进行能带计算时首次发现的[1].之后，已经有许多化合物在理论上被预言[2-7]或在实验上被证实具有半金属的性质[8-11]，本文将要研究的semi-Heu⁃sler合金NiCrP和NiVAs就具有这一性质[12-13].半金属铁磁体是制作自旋电子学器件（spin⁃tronci device）的关键性材料[14].半霍伊斯勒（semi-Heusler）合金NiMnSb和PtMnSb的晶格具有C1b结构（空间群编号：216）.作为制作自旋电子学器件的材料，半霍伊斯勒合金具有以下两方面的优势：1）它们具有相对较高的居里温度（Tc）[15-16]，例如，半霍伊斯勒（semi-Heusler）合金NiMnSb的居里温度为730 K[15]；2）它们与已在工业上广泛使用的闪锌矿相二元半导体（如ZnS、GaAs和GaP）的结构相似（空间群编号同为：216），因而半霍伊斯勒合金半金属与二元半导体有较好的晶格相容性，它有利于在二元半导体基底上外廷生长出半霍伊斯勒合金半金属（单层或多层）薄膜而制成自旋电子学器件，因此，半霍伊斯勒合金半金属是制作自旋电子学器件的理想候选材料.半霍伊斯勒合金NiCrP和NiVAs是铁磁性半金属，它们可能成为制作自旋电子学器件的备选材料.制作自旋电子学器件的方法通常是在器件的基底上外延生长半金属性质的薄膜.一般情况下，半金属材料的晶格与基底晶格是不同的（晶格结构和/或晶格常数），这种晶格失配（lattice mismatch）现象普遍存在于器件的制作之中，这必将导致与器件基底接触的NiCrP和NiVAs合金表面膜层晶格发生畸变.在晶体晶格发生形变的情况下，半霍伊斯勒合金NiCrP和NiVAs是否具有半金属性，这是一个有待于进一步研究的问题.经检索现有的文献资料，未见相关问题的研究报道，因此，本文将对这一问题进行研究.本文将通过使晶体晶格发生各向同性形变的方式来研究半霍伊斯勒合金NiCrP和NiVAs的半金属及其磁性的稳定性.具有C1b结构的半霍伊斯勒合金NiCrP和Ni⁃VAs的晶体晶格是由3个次面心结构套构而成，其空间群为（空间群编号：216）.半霍伊斯勒合金NiCrP晶格中对应原子的分数坐标位置分别是：Ni（1/4，1/4，1/4）、Cr（1/2，1/2，1/2），P（0，0，0），其空间结构图见图1.所有的电子结构都采用WIEN2K[17]计算程序软件包计算.在WIEN2K程序计算中，采用以Kohn-Sham密度泛函理论为基础的全势能线性缀加平面波（full-potential linearized augmented plane wave,FP_LAPW）方法.该方法将晶胞划分为非重叠的muffin-tin球区和剩余的间隙空间区.在muf⁃fin-tin球区内，电荷密度和势能函数按球谐函数展开，基函数为原子径向和球谐部分的乘积；在间隙区，由于势场变化比较平缓，电荷密度、势函数和基函数则采用平面波展开.交换-相关势采用广义梯度近似（GGA）下的Perdew-Burke-Ernzerhof’96方法处理[18].波矢积分采用四面体网格法，在第一布里渊区k点网格取10×10×10.在半霍伊斯勒合金NiCrP 和 NiVAs中，Ni、Cr、V、P 和 As原子的 muf⁃fin-tin 模型球半径 Rmt分别取为 2.1 a.u.，2.0 a.u.，2.0 a.u.，1.8 a.u.和2.1 a.u.（1a.u.=0.052 9177 nm）.取截断参数：Rmt×Kmax=8，其中，Rmt是分子中最小的muffin-tin球半径，Kmax是平面波展式中最大的倒格子矢量.自洽计算的收敛精度取为1×10-4e/cell.对半霍伊斯勒合金NiCrP和NiVAs的电子结构进行自旋极化计算，得到它们在平衡体积时（平衡晶格常数a0分别为5.59 Å[12]和5.85 Å[13]）的电子能带结构图见图2.从图中可看出，半霍伊斯勒合金NiCrP和NiVAs自旋向上的分能带是金属性的，而自旋向下分能带呈现明显的非导体性质，因此，它们是半金属性的.从计算结果可以看出，它们自旋向下的自旋子能带中费米能附近的能带带隙分别为0.59 eV和0.46 eV.为了研究晶体各向同性形变对半霍伊斯勒合金NiCrP和NiVAs半金属性的影响，在不改变晶体空间群结构的情况下改变其晶格常数，并对它们的电子结构进行自旋极化计算.我们用（a0为晶体平衡时的晶格常数，a为变化后的晶格常数，Δa=a-a0）表示晶体相对于平衡晶格的各向同性形变.在晶体相对于平衡晶格发生各向同性形变的条件下，我们计算半霍伊斯勒合金NiCrP和NiVAs的电子结构，并研究了它们的半金属性和磁性的稳定性.半霍伊斯勒合金NiCrP晶体相对于平衡晶格的各向同性形变为-6%和+2%时的电子态密度（density of states,DOS）分布在图3中给出.在图3中，当Δa/a0=-6%时，自旋向上子能带是金属性的，费米能恰好位于自旋向下子能带带隙的最右端，而当Δa/a0=+2%时，自旋向上子能带也是金属性的，费米能恰好位于自旋向下子能带带隙的最左端.半霍伊斯勒合金NiVAs晶体相对平衡晶格的各向同性形变为-2%和+4%的电子态密度分布在图4中给出.当Δa/a0=-2%时，自旋向上子能带是金属性的，费米能恰好位于自旋向下子能带带隙的最右端，而当Δa/a0=+4%时，自旋向上子能带也是金属性的，费米能恰位于自旋向下子能带带隙的最左端.从图3和图4可以看出，当Δa/a0增大时，费米能在自旋向下子能带带隙中的位置是会发生变化的，都有向左移动的趋势.为了进一步详细研究各向同性形变对半霍伊斯勒合金NiCrP和NiVAs的半金属性的稳定性的影响，将相对于平衡晶格的各向同性形变Δa/a0的变化步长减小为1%，并计算半霍伊斯勒合金NiCrP和NiVAs的电子结构.计算结果表明，半霍伊斯勒合金NiCrP和NiVAs在相对平衡晶格的各向同性形变从-8%变化到+8%的过程中其自旋向上子能带始终是金属性，因此，它们是否具有半金属性完全取决于自旋向下子能带的性质.从已得到的计算结果中将半霍伊斯勒合金NiCrP和NiVAs自旋向下费米能附近的DOS空白区域分别绘于图5中.从图5中可看出，当相对平衡晶格各向同性形变分别为-6%～2%和-2%～4%时，半霍伊斯勒合金NiCrP和NiVAs的费米能位于自旋向下DOS空白区内，因此，它们在上述形变范围内具有半金属性质.自旋磁矩的计算结果表明，当半霍伊斯勒合金NiCrP和NiVAs处于平衡体积时，它们的总磁矩分别为3.00 μB/formula和2.00 μB/formula.它们的整数总磁矩符合关系式[19]：M=（Z-18）μB，其中，Z为分子中各原子价电子之和（在Ni、Cr、V、P和As原子中，它们的价电子数分别为10、6、5、5和5），M为分子总磁矩（单位为μB）.在NiCrP合金中，Ni原子、Cr原子和P原子上的磁矩分别为0.048 3 μB、2.88 μB和-0.128 μB.NiCrP合金的总磁矩主要由Cr原子贡献，P原子的磁矩为负值而且相对而言很小，所以,半霍伊斯勒合金NiCrP是铁磁性的.在NiVAs合金中，分子总磁矩为2.00 μB，Ni、V 和 As原子的磁矩分别为0.0153 μB、1.68 μB、和-0.0730 μB，总磁矩主要来源于V原子，As原子的磁矩为负值而且相对而言很小，半霍伊斯勒合金NiVAs也是铁磁性的.整数总磁矩是半霍伊斯勒合金NiCrP和NiVAs的铁磁性特征之一.为了研究半霍伊斯勒合金NiCrP和NiVAs铁磁性的稳定性，我们仍以1%的变化步长改变相对于平衡晶格的各向同性形变Δa/a0来计算它们的总磁矩，并将所得的计算结果在图6中给出.从图6中可以看出，在相对于平衡晶格的各向同性形变分为-6%～2%和-2%～4%时，半霍伊斯勒合金NiCrP和NiVAs的总磁矩分别稳定于3.00 μB/formula和2.00 μB/formula.综合以上分析结果，半霍伊斯勒合金NiCrP和NiVAs相对于平衡晶格的各向同性形变分别在-6%～2%和-3%～4%的范围内具有稳定的半金属铁磁性.基于密度泛函理论的全势能线性缀加平面波（FP_LAPW）方法，计算了半霍伊斯勒合金NiCrP和NiVAs的电子结构.计算结果表明，半霍伊斯勒合金NiCrP和NiVAs处于平衡晶格常数时是半金属性的，并且它们自旋向下分能带上分别有0.59 eV和0.46 eV的能带带隙，它们的总磁矩分别为3.00 μB/formula和2.00 μB/formula.在晶体相对于平衡晶格发生各向同性形变的条件下，当相对平衡晶格的各向同性形变分别为-6%～2%和-2%～4%时，半霍伊斯勒合金NiCrP和NiVAs具有稳定的半金属铁磁性.【相关文献】[1]de Groot R A,Mueller F M,van Engen P G,et al.New Class of Materials:Half-Metallic Ferromagnets[J].Phys Rev Lett,1983,50:2024.[2]Yanase A,Siratori K.Band Structure in the High Tempera⁃ture Phase of Fe3O4[J].J Phys Soc Japan,1984,53:312-317.[3]Zhang M,Dai X F,Hu H N,et al.Search for new half-metallic ferromagnets in semi-Heusler alloys 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See discussions, stats, and author profiles for this publication at: /publication/229595062 Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloysARTICLE in JOURNAL OF APPLIED PHYSICS · MAY 2011Impact Factor: 2.19 · DOI: 10.1063/1.3587228CITATIONS 80DOWNLOADS143VIEWS4104 AUTHORS, INCLUDING:Sheng GuoChalmers University of Technology29 PUBLICATIONS 329 CITATIONSSEE PROFILEAvailable from: Sheng GuoRetrieved on: 16 September 2015Effect of valence electron concentration on stability of fcc or bcc phase in high entropy alloysSheng Guo,1Chun Ng,1Jian Lu,2and C.T.Liu1,a)1Department of Mechanical Engineering,The Hong Kong Polytechnic University,Hung Hom,Kowloon,Hong Kong,People’s Republic of China2College of Science and Engineering,City University of Hong Kong,Kowloon,Hong Kong(Received8March2011;accepted3April2011;published online16May2011)Phase stability is an important topic for high entropy alloys(HEAs),but the understanding to it isvery limited.The capability to predict phase stability from fundamental properties of constituentelements would benefit the alloy design greatly.The relationship between phase stability andphysicochemical/thermodynamic properties of alloying components in HEAs was studiedsystematically.The mixing enthalpy is found to be the key factor controlling the formation of solidsolutions or compounds.The stability of fcc and bcc solid solutions is well delineated by thevalance electron concentration(VEC).The revealing of the effect of the VEC on the phase stabilityis vitally important for alloy design and for controlling the mechanical behavior of HEAs.V C2011American Institute of Physics.[doi:10.1063/1.3587228]I.INTRODUCTIONHigh entropy alloys(HEAs)constitute a new type of metallic alloys for structural and particularly high-tempera-ture applications,due to their high hardness,wear resistance, high-temperature softening resistance and oxidation resist-ance.1–3HEAs are typically composed of more thanfive me-tallic elements in equal or near-equal atomic ratios,and interestingly they tend to form solid solution structure (mainly fcc and/or bcc)rather than multiple intermetallic compounds as expected from general physical metallurgy principles.They were termed as HEAs because the entropy of mixing is high when the alloying elements are in equia-tomic ratio,and it was initially believed that the high entropy of mixing leads to the formation of the solid solution struc-ture rather than intermetallic compounds.The generally used alloying elements in HEAs are fcc-type Cu,Al,Ni,bcc-type Fe,Cr,Mo,V and hcp-type Ti,Co (crystal structure at ambient temperature).When these alloy-ing elements are mixed with different combination,or with same combination but different amount of certain elements, fcc,bcc or mixed fcc and bcc structures may form.For example,cast CoCrCuFeNi(in atomic ratio,same after-wards)has the fcc structure while AlCoCrCuFeNi has the fccþbcc structure;4and the amount of Al in the Al x CoCrCu-FeNi system can tune the crystal structure from fcc to fccþbcc and to fully bcc4.The structure directly affects the mechanical properties,and to take again the Al x CoCrCuFeNi system as an example:with increasing x,the structure changes from fcc to fccþbcc andfinally to bcc;the hardness and strength increase with the increasing amount of bcc phases but the alloys get brittle.4,5Although the embrittle-ment mechanism by bcc phases still needs further explora-tion,it is certainly important to be able to control the formation of bcc phases.The target of this work is hence to find out the physical parameters that control the stability for the fcc and bcc phases in HEAs.II.ANALYSISWang et al.briefly discussed the reason of addition of Al in the Al x CoCrCu1Àx FeNiTi0.5system causing the struc-tural transition from fcc to bcc.6They claimed that the alloy-ing of larger Al atoms introduces the lattice distortion energy,and the formation of a lower atomic-packing-effi-ciency structure,such as bcc,can decrease this distortion energy.This does make sense but is far away from being sat-isfactory;besides,it can not quantitatively predict when the bcc structure will form as a function of Al additions.Ke et al.claimed that,in the Al x Co y Cr z Cu0.5Fe v Ni w system,Ni and Co are fcc stabilizers and Al and Cr are bcc stablizers;1.11Co is equivalent to Ni as the fcc stablizers and2.23Cr is equivalent to Al for the bcc stablizers.Furthermore,if the equivalent Co%is greater than45at.%,the alloy has an fcc structure,and the alloy has a bcc structure if the equivalent Cr%is greater than55at.%.7This empirical rule is useful but it has no scientific merits and is valid only for the specific alloy systems.The establishment of scientific principles to control the crystal structures in HEAs can also contribute to the alloy design of HEAs with desirable properties.For example,we can use less expensive Ni to partially or com-pletely replace more expensive Co;or we can reduce the amount of Cu which is known to cause segregation issue because the mainly positive enthalpy of mixing between Cu and other alloying elements.4As a test to the equivalency of Ni and Co as fcc stabil-izers,we prepared a series of Al x CrCuFeNi2(0.2x 1.2) alloys to study the effect of Al amount on the phase stability in this alloy system,in comparison to the well studied Al x CoCrCuFeNi system.The alloys were prepared by arc-melting a mixture of the constituent elements with purity better than99.9%in a Ti-gettered high-purity argon atmos-phere.Repeated melting was carried out at leastfive times toa)Author to whom correspondence should be addressed.Electronic mail:mmct8tc@.hk.0021-8979/2011/109(10)/103505/5/$30.00V C2011American Institute of Physics109,103505-1JOURNAL OF APPLIED PHYSICS109,103505(2011)improve the chemical homogeneity of the alloy.The molten alloy was drop-cast into a10mm diameter copper mold.The phase constitution of the alloy was examined by X-ray dif-fractometer using Co radiation(Bruker AXS D8Discover). The X-ray diffraction patterns are shown in Fig.1where it is clear that at x0.8,the alloys have a single fcc structure and the bcc phase starts to appear at x¼1.0.In the Al x CoCrCu-FeNi system,fully fcc structure is obtained at x0.5and bcc phase starts to appear at x>0.8.4The experimental results indicate that Co is not necessarily required in obtain-ing the solid solution structure in HEAs,which is good foralloy design from economy concerns.This new alloy systemalso provides more data to study the phase stability in HEAs,ideally from the consideration of the fundamental propertiesof constituent alloying elements.Zhang et al.studied the relationship between the phasestability and the atomic size difference,d(¼100ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP Ni¼1c ið1Àr i=rÞ2q,r¼P ni¼1c i r i,where c i and r i areatomic percentage and atomic radius of the i th component),and also the mixing enthalpy,D H mix(¼P ni¼1;i¼jX ij c i c j,X ij¼4D AB mix,where D AB mix is the mixing enthalpy of binaryliquid AB alloys)for multi-component alloys.8They foundthat the solid solution tends to form in the region delineatedbyÀ15KJ/mol D H mix5KJ/mol and1d 6.Therequirement of atomic size difference for formation of thesolid solution structure is not surprising as basically it is inline with the well established Hume-Rothery rule.9Othertwo requirements from the Hume-Rothery rule to form thesolid solution are electronegativity and electron concentra-tion.Fang et al.defined the electronegativity difference in amulti-component alloy system as D v(¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP ni¼1c iðv iÀvÞ2q,v¼P ni¼1c i v i,where v i is the Pauling electronegativity forthe i th component).10The effect of electron concentration isa little bit more complex.There are basically two definitionsof the electron concentration:average number of itinerantelectrons per atom,e/a,and the number of total electronsincluding the d-electrons accommodated in the valenceband,valence electron concentration or VEC.11,12e/a orVEC for a multi-component alloy can be defined as theweighted average from e/a or VEC of the constituent compo-nents:e/a¼P ni¼1c iðe=aÞi or VEC¼P ni¼1c iðVECÞi,where(e/a)i and(VEC)i are the e/a and VEC for the individual ele-ment.Hume-Rothery rule works with the e/a definition ande/a has clear effect on the crystal structure for the so-calledelectron compounds or Hume-Rothery compounds.9How-ever,the HEAs comprise mainly transition metals(TMs)ande/a for TMs are very controversial.11Very recently,Mizutanireviewed the various definitions of e/a for TMs and con-cluded that e/a for TMs are small positive numbers.11Unfortunately,not all e/a for TMs have been determined ande/a for a TM element even varies in different environment.For convenience,VEC was used here to study the electronconcentration effect on the phase stability in HEAs.III.RESULTSFollowing Zhang et al.’s method,8the atomic size dif-ference,d,and the mixing enthalpy,D H mix for the Al x CoCr-CuFeNi4and Al x CrCuFeNi2systems are plotted in Fig.2.The electronegativity difference,D v,and VEC are also plot-ted to show how these factors referred in the Hume-Rotheryrule affect the solid solution formation.D H mix,D v and VECare all plotted as a function of d in Fig.2for convenience,and this does not indicate these parameters are mutually de-pendent.For comparison,d,D H mix,D v and VEC for threeadditional systems of HEAs[CoCrCuFeNiTi x(see Ref.13),Al0.5CoCrCuFeNiTi x(see Ref.14),Al0.5CoCrCuFeNiV x(see Ref.15)],where compounds will form in the originallyfcc-typed alloy by increasingly doping the amount of onealloying element(Ti or V),are also plotted in Fig.2.The cal-culation required physicochemical and thermodynamicFIG.1.(Color online)X-ray diffraction patterns for Al x CrCuFeNi2alloys(x¼0.2$1.2).FIG.2.(Color online)Relationship between the mixing enthalpy,D H mix(a),the Electronegativity,D v(b)and the valence electron concentration,VEC,(c),and the atomic size difference,d,forfive HEA systems:Al x CoCrCu-FeNi,CoCrCuFeNiTi x,Al0.5CoCrCuFeNiTi x,Al0.5CoCrCuFeNiV x,andAl x CrCuFeNi2.Note on the legend:fully closed symbols for sole fcc phases;fully open symbols for sole bcc phase;top-half closed symbols for mixes fccand bcc phases;left or right-half closed symbols for phases containing atleast one compound phase(left or right half simply indicates different typesof compounds).parameters for the constituent alloying elements are from Refs.16–19and some of them are listed in Table I .As seen from Fig.2,using the definitions of atomic size difference,mixing enthalpy,valence electron concentration and electronegativity defined here,D H mix is the only effec-tive parameter that can predict the formation of sole solid solutions (hence no formation of compounds)in HEAs.Solid solution form when À5KJ/mol D H mix 5KJ/mol,and compounds would form once D H mix is more negative.On the other hand,d ,D v and VEC all fail to effectively predict the formation of solid solution phases or compounds.Figure 2provides some clues to obtain the solely solid solution struc-ture in HEAs based simply on the fundamental properties of constituent elements.This is certainly useful but from Fig.2it is still unclear when the bcc phase will form and what is the determining factor controlling the bcc phase formation.A careful examination of Fig.2,however,suggests that bcc phases start to form when VEC reaches $8.0[Fig.2(c)].The other three parameters,D H mix ,d ,and D v do not behave such a clear indicator function.To make the point clearer,VEC for three HEA systems,Al x CoCrCuFeNi (see Ref.4),Al x CoCrCu 0.5FeNi (see Ref.7),and Al x CoCrCuFeNi 2(this work)in which increasingly doping of the same element Al would cause phase constitution from sole fcc to mixed fccand bcc,are plotted in Fig.3.Figure 3clearly shows that VEC can be used to quantitatively predict the phase stability for fcc and bcc phases in HEAs:at VEC !8.0,sole fcc phase exists;at 6.87 VEC <8.0,mixed fcc and bcc phases will co-exist and sole bcc phase exists at VEC <6.87.Note that at the boundary VEC ¼8.0,sometimes bcc phases also form but they are minor phases (see Fig.1and Ref.4).Although there is one exception for the Al x CoCrCu 0.5FeNi alloy where 6.87 VEC <8.0but the stable phase is sole bcc (not fcc þbcc),we suspect this VEC -defined phase stability shall work effectively for most cases.To prove this,VEC for more HEA systems with fcc,fcc þbcc,or bcc structure containing other alloying elements like Ti,V,Mn,Nb,Mo,Ta,W even metalloid B and C,are plotted in Fig.4(data are from litera-tures in Ref.7and 20–24).Although there are still some exceptions,the fcc/bcc phase boundary can clearly be delineated by VEC .With a note to those exceptions,the VEC -defined fcc/bcc phase boundary seems to work unsatis-factorily for Mn-containing HEA systems.TABLE I.Physiochemical properties for commonly used elements in HEAs.Element Atom radius (A˚)Pauling electronegativityVEC Al 1.4321.613B 0.8202.043C 0.773 2.554Co 1.251 1.889Cr 1.249 1.666Fe 1.241 1.838Mn 1.350 1.557Mo 1.363 2.166Nb 1.429 1.65Ni 1.246 1.9110Ta 1.430 1.505Ti 1.462 1.544V 1.316 1.635W1.3672.366FIG.3.(Color online)Relationship between VEC and the fcc,bcc phase sta-bility for three HEA systems:Al x CoCrCuFeNi,Al x CrCuFeNi 2and Al x CoCr-Cu 0.5FeNi.Note on the legend:fully closed symbols for sole fcc phases;fully open symbols for sole bcc phase;top-half closed symbols for mixes fcc and bccphases.FIG. 4.(Color online)Relationship between VEC and the fcc,bcc phase sta-bility for more HEA systems further to Fig.3.Note on the legend:fully closed symbols for sole fcc phases;fully open symbols for sole bcc phase;top-half closed symbols for mixes fcc and bcc phases.IV.DISCUSSIONThe effect of the VEC on the phase stability has been studied before by the current authors for the intermetallic compounds only.One example is on the(Fe,Co,Ni)3V inter-metallic alloys with long-range-ordered(LRO)structures.25 We found that these LRO alloys are characterized by specific sequences of stacked close-packed ordered layers and the stacking character can be altered systematically by control-ling the VEC of these alloys.With the decreasing VEC by partial substitution of Co and Ni by Fe,the LRO changes from purely hexagonal,to L12-type cubic ordered structure, through different ordered mixtures of hexagonal and cubic layers.As the hexagonal structure exhibits brittle fracture while the cubic ordered structures are ductile,the control of VEC can hence be used to tune the mechanical properties of LRO alloys.We also investigated the role of VEC in the phase stability of NbCr2-based transition-metal Laves phase alloys.26It was found that when the atomic size ratios were kept nearly identical,the VEC is the dominant factor in con-trolling the phase stability(C14,hexagonal or C15,cubic)in this type of high-temperature structural alloys.Our results in the present work prove that VEC also plays a decisive role in the stability of fcc and bcc solid solution phases in the multi-component HEAs.Mizutani has shown that VEC is crucial in determining the Fermi level whenfirst-principles band calcu-lations are carried out to study the band structure.11In the first-principles band calculations,the integration of the den-sity of states(DOS)actually results in VEC,which includes not only s-and p-electrons but also d-electrons forming the valence band.11Mizutani emphasized that the parameter VEC,instead of e/a,should be used in realistic electronic structure calculations to take into account the d-electron con-tribution.11More theoretical work needs to be carried out to understand the physical basis for the mechanism behind the VEC rule on the phase stability,for example from the VEC-electronic structure-bind structure energy perspective.27 Two issues need to be emphasized here for the discussion of the VEC rule on the phase stability.First,the VEC ranges for different phases to be stable might overlap and these ranges also vary depending on the specific alloy systems.A very close example is in some ternary Mg alloys that possess typical Laves structures.9It was found that the electron con-centration(e/a though)ranges for MgCu2-type(cubic,with packing ABCABCABC),MgNi2-type(hexagonal,with pack-ing ABACABAC)and MgZn2-type(hexagonal,with packing ABABAB)structures differ in various alloy systems,and the e/a ranges for MgNi2-type structure and MgZn2-type struc-ture overlap for the Mg-Cu-Al system.This can probably explain the exceptions that appear in Figs.3and4.Second, the phases referred in this work are all identified in the as-cast state and they are hence very possibly in the metastable state. However,evidences have shown that these metastable phases have quite good thermal stability28–31and can hence be regarded as very close to the stable phases.This gives confi-dence to the general applicability of the VEC rule,consider-ing it works so well for such an extended series of various alloy systems.More work is certainly needed to further verify this.Admitting these two issues mentioned above,one solid result out of our study is that,in HEAs the bcc phase is stable at lower VEC while the fcc phase is stable at higher VEC. This trend already sheds some light on the alloy design,and the fact that most HEA alloy systems satisfying the VEC (<6.87,bcc;!8,fcc)rule even simplifies the process.As the VEC rule on the phase stability between the fcc and bcc phases is tested only for the HEAs in this work,its applicabil-ity to other alloy systems other than the nearly equiatomic HEAs(i.e.,in the traditional alloys where only one or two pri-mary elements dominate),awaits further analysis.In addition, it would be interesting to know whether this VEC rule can be used to predict the phase stability for other structured phases, like the hcp-typed phases.More work along these directions is under way.V.CONCLUSIONSIn summary,the phase stability in HEAs and its relation-ship to the physicochemical and thermodynamic properties of constituent alloying elements are systematically studied. The mixing enthalpy determines whether the solid solution phases or compounds form in the nearly equiatomic multi-component alloy systems.Most importantly the VEC is found to be the physical parameter to control the phase sta-bility for fcc or bcc solid solutions.Fcc phases are found to be stable at higher VEC(!8)and instead bcc phases are sta-ble at lower VEC(<6.87).This work provides valuable input for understanding of the phase stability and to design ductile crystal structures in HEAs. ACKNOWLEDGMENTSThis research was supported by the internal funding from HKPU.1B.Cantor,I.T.H.Chang,P.Knight,and A.J.B.Vincent,Mater.Sci. 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More informationPhase Noise and Frequency Stability in OscillatorsPresenting a comprehensive account of oscillator phase noise and frequency stability,this practical text is both mathematically rigorous and accessible.An in-depth treatmentof the noise mechanism is given,describing the oscillator as a physical system,andshowing that simple general laws govern the stability of a large variety of oscillatorsdiffering in technology and frequency range.Inevitably,special attention is given to am-plifiers,resonators,delay lines,feedback,andflicker(1/f)noise.The reverse engineeringof oscillators based on phase-noise spectra is also covered,and end-of-chapter exercisesare given.Uniquely,numerous practical examples are presented,including case studiestaken from laboratory prototypes and commercial oscillators,which allow the oscillatorinternal design to be understood by analyzing its phase-noise spectrum.Based on tuto-rials given by the author at the Jet Propulsion Laboratory,international IEEE meetings,and in industry,this is a useful reference for academic researchers,industry practitioners,and graduate students in RF engineering and communications engineering.Additional materials are available via /rubiola.Enrico Rubiola is a Senior Scientist at the CNRS FEMTO-ST Institute and a Professorat the Universit´e de Franche Comt´e.With previous positions as a Professor at theUniversit´e Henri Poincar´e,Nancy,and in Italy at the University Parma and thePolitecnico di Torino,he has also consulted at the NASA/Caltech Jet PropulsionLaboratory.His research interests include low-noise oscillators,phase/frequency-noisemetrology,frequency synthesis,atomic frequency standards,radio-navigation systems,precision electronics from dc to microwaves,optics and gravitation.More informationThe Cambridge RF and Microwave Engineering SeriesSeries EditorSteve C.CrippsPeter Aaen,Jaime Pl´a and John Wood,Modeling and Characterization of RF andMicrowave Power FETsEnrico Rubiola,Phase Noise and Frequency Stability in OscillatorsDominique Schreurs,M´a irt´ın O’Droma,Anthony A.Goacher and Michael Gadringer,RF Amplifier Behavioral ModelingFan Y ang and Y ahya Rahmat-Samii,Electromagnetic Band Gap Structures in AntennaEngineeringForthcoming:Sorin V oinigescu and Timothy Dickson,High-Frequency Integrated CircuitsDebabani Choudhury,Millimeter W aves for Commercial ApplicationsJ.Stephenson Kenney,RF Power Amplifier Design and LinearizationDavid B.Leeson,Microwave Systems and EngineeringStepan Lucyszyn,Advanced RF MEMSEarl McCune,Practical Digital Wireless Communications SignalsAllen Podell and Sudipto Chakraborty,Practical Radio Design TechniquesPatrick Roblin,Nonlinear RF Circuits and the Large-Signal Network AnalyzerDominique Schreurs,Microwave Techniques for MicroelectronicsJohn L.B.Walker,Handbook of RF and Microwave Solid-State Power AmplifiersPhase Noise and Frequency Stability in OscillatorsENRICO RUBIOLAProfessor of Electronics FEMTO-ST Institute CNRS and Universit´e de Franche Comt´e Besanc ¸on,FranceMore informationMore informationCAMBRIDGE UNIVERSITY PRESSCambridge,New Y ork,Melbourne,Madrid,Cape Town,Singapore,S˜a o Paulo,DelhiCambridge University PressThe Edinburgh Building,Cambridge CB28RU,UKPublished in the United States of America by Cambridge University Press,New Y orkInformation on this title:/9780521886772C Cambridge University Press2009This publication is in copyright.Subject to statutory exceptionand to the provisions of relevant collective licensing agreements,no reproduction of any part may take place withoutthe written permission of Cambridge University Press.First published2009Printed in the United Kingdom at the University Press,CambridgeA catalog record for this publication is available from the British LibraryISBN978-0-521-88677-2hardbackCambridge University Press has no responsibility for the persistence oraccuracy of URLs for external or third-party internet websites referred toin this publication,and does not guarantee that any content on suchwebsites is,or will remain,accurate or appropriate.More informationContentsForeword by Lute Maleki page ixForeword by David Leeson xiiPreface xv How to use this book xviSupplementary material xviii Notation xix 1Phase noise and frequency stability11.1Narrow-band signals11.2Physical quantities of interest51.3Elements of statistics91.4The measurement of power spectra131.5Linear and time-invariant(LTI)systems191.6Close-in noise spectrum221.7Time-domain variances251.8Relationship between spectra and variances291.9Experimental techniques30Exercises33 2Phase noise in semiconductors and amplifiers352.1Fundamental noise phenomena352.2Noise temperature and noisefigure372.3Phase noise and amplitude noise422.4Phase noise in cascaded amplifiers492.5 Low-flicker amplifiers522.6 Detection of microwave-modulated light62Exercises65 3Heuristic approach to the Leeson effect673.1Oscillator fundamentals673.2The Leeson formula72More informationvi Contents3.3The phase-noise spectrum of real oscillators753.4Other types of oscillator824Phase noise and feedback theory884.1Resonator differential equation884.2Resonator Laplace transform924.3The oscillator964.4Resonator in phase space1014.5Proof of the Leeson formula1114.6Frequency-fluctuation spectrum and Allan variance1164.7 A different,more general,derivation of the resonatorphase response1174.8 Frequency transformations1215Noise in delay-line oscillators and lasers1255.1Basic delay-line oscillator1255.2Optical resonators1285.3Mode selection1305.4The use of a resonator as a selectionfilter1335.5Phase-noise response1385.6Phase noise in lasers1435.7Close-in noise spectra and Allan variance1455.8Examples1466Oscillator hacking1506.1General guidelines1506.2About the examples of phase-noise spectra1546.3Understanding the quartz oscillator1546.4Quartz oscillators156Oscilloquartz OCXO8600(5MHz AT-cut BV A)156Oscilloquartz OCXO8607(5MHz SC-cut BV A)159RAKON PHARAO5MHz quartz oscillator162FEMTO-ST LD-cut quartz oscillator(10MHz)164Agilent10811quartz(10MHz)166Agilent noise-degeneration oscillator(10MHz)167Wenzel501-04623(100MHz SC-cut quartz)1716.5The origin of instability in quartz oscillators1726.6Microwave oscillators175Miteq DRO mod.D-210B175Poseidon DRO-10.4-FR(10.4GHz)177Poseidon Shoebox(10GHz sapphire resonator)179UWA liquid-N whispering-gallery9GHz oscillator182More informationContents vii6.7Optoelectronic oscillators185NIST10GHz opto-electronic oscillator(OEO)185OEwaves Tidalwave(10GHz OEO)188 Exercises190Appendix A Laplace transforms192References196Index202More informationForeword by Lute MalekiGiven the ubiquity of periodic phenomena in nature,it is not surprising that oscillatorsplay such a fundamental role in sciences and technology.In physics,oscillators are thebasis for the understanding of a wide range of concepts spanningfield theory and linearand nonlinear dynamics.In technology,oscillators are the source of operation in everycommunications system,in sensors and in radar,to name a few.As man’s study ofnature’s laws and human-made phenomena expands,oscillators have found applicationsin new realms.Oscillators and their interaction with each other,usually as phase locking,and withthe environment,as manifested by a change in their operational parameters,form thebasis of our understanding of a myriad phenomena in biology,chemistry,and evensociology and climatology.It is very difficult to account for every application in whichthe oscillator plays a role,either as an element that supports understanding or insight oran entity that allows a given application.In all thesefields,what is important is to understand how the physical parametersof the oscillator,i.e.its phase,frequency,and amplitude,are affected,either by theproperties of its internal components or by interaction with the environment in whichthe oscillator resides.The study of oscillator noise is fundamental to understanding allphenomena in which the oscillator model is used in optimization of the performance ofsystems requiring an oscillator.Simply stated,noise is the unwanted part of the oscillator signal and is unavoidablein practical systems.Beyond the influence of the environment,and the non-ideality ofthe physical elements that comprise the oscillator,the fundamental quantum nature ofelectrons and photons sets the limit to what may be achieved in the spectral purity of thegenerated signal.This sets the fundamental limit to the best performance that a practicaloscillator can produce,and it is remarkable that advanced oscillators can reach it.The practitioners who strive to advance thefield of oscillators in time-and-frequencyapplications cannot be content with knowledge of physics alone or engineering alone.The reason is that oscillators and clocks,whether of the common variety or the advancedtype,are complex“systems”that interact with their environment,sometimes in waysthat are not readily obvious or that are highly nonlinear.Thus the physicist is needed toidentify the underlying phenomenon and the parameters affecting performance,and theengineer is needed to devise the most effective and practical approach to deal with them.The present monograph by Professor Enrico Rubiola is unique in the extent to which itsatisfies both the physicist and the engineer.It also serves the need to understand bothMore informationx Forewordsthe fundamentals and the practice of phase-noise metrology,a required tool in dealingwith noise in oscillators.Rubiola’s approach to the treatment of noise in this book is based on the input–output transfer functions.While other approaches lead to some of the same results,this treatment allows the introduction of a mathematical rigor that is easily tractable byanyone with an introductory knowledge of Fourier and Laplace transforms.In particular,Rubiola uses this approach to obtain a derivation,fromfirst principles,of the Leesonformula.This formula has been used in the engineering literature for the noise analysisof the RF oscillator since its introduction by Leeson in1966.Leeson evidently arrivedat it without realizing that it was known earlier in the physics literature in a differentform as the Schawlow–Townes linewidth for the laser oscillator.While a number ofother approaches based on linear and nonlinear models exist for analyzing noise inan oscillator,the Leeson formula remains particularly useful for modeling the noisein high-performance oscillators.Given its relation to the Schawlow–Townes formula,it is not surprising that the Leeson model is so useful for analyzing the noise in theoptoelectronic oscillator,a newcomer to the realm of high-performance microwave andmillimeter-wave oscillators,which are also treated in this book.Starting in the Spring of2004,Professor Rubiola began a series of limited-timetenures in the Quantum Sciences and Technologies group at the Jet Propulsion Labo-ratory.Evidently,this can be regarded as the time when the initial seed for this bookwas conceived.During these visits,Rubiola was to help architect a system for themeasurement of the noise of a high-performance microwave oscillator,with the sameexperimental care that he had previously applied and published for the RF oscillators.Characteristically,Rubiola had to know all the details about the oscillator,its principleof operation,and the sources of noise in its every component.It was only then that hecould implement the improvement needed on the existing measurement system,whichwas based on the use of a longfiber delay in a homodyne setup.Since Rubiola is an avid admirer of the Leeson model,he was interested in applyingit to the optoelectronic oscillator,as well.In doing so,he developed both an approachfor analyzing the performance of a delay-line oscillator and a scheme based on Laplacetransforms to derive the Leeson formula,advancing the original,heuristic,approach.These two treatments,together with the range of other topics covered,should makethis unique book extremely useful and attractive to both the novice and experiencedpractitioners of thefield.It is delightful to see that in writing the monograph,Enrico Rubiola has so openlybared his professional persona.He pursues the subject with a blatant passion,andhe is characteristically not satisfied with“dumbing down,”a concept at odds withmathematical rigor.Instead,he provides visuals,charts,and tables to make his treatmentaccessible.He also shows his commensurate tendencies as an engineer by providingnumerical examples and details of the principles behind instruments used for noisemetrology.He balances this with the physicist in him that looks behind the obvious forthe fundamental causation.All this is enhanced with his mathematical skill,of which healways insists,with characteristic modesty,he wished to have more.Other ingredients,missing in the book,that define Enrico Rubiola are his knowledge of ancient languagesMore informationForewords xi and history.But these could not inform further such a comprehensive and extremelyuseful book on the subject of oscillator noise.Lute MalekiNASA/Caltech Jet Propulsion Laboratoryand OEwaves,Inc.,February2008More informationForeword by David LeesonPermit me to place Enrico Rubiola’s excellent book Phase Noise and Frequency Stabilityin Oscillators in context with the history of the subject over the pastfive decades,goingback to the beginnings of my own professional interest in oscillator frequency stability.Oscillator instabilities are a fundamental concern for systems tasked with keeping anddistributing precision time or frequency.Also,oscillator phase noise limits the demod-ulated signal-to-noise ratio in communication systems that rely on phase modulation,such as microwave relay systems,including satellite and deep-space parablyimportant are the dynamic range limits in multisignal systems resulting from the mask-ing of small signals of interest by oscillator phase noise on adjacent large signals.Forexample,Doppler radar targets are masked by ground clutter noise.These infrastructure systems have been well served by what might now be termedthe classical theory and measurement of oscillator noise,of which this volume is acomprehensive and up-to-date tutorial.Rubiola also exposes a number of significantconcepts that have escaped prior widespread notice.My early interest in oscillator noise came as solid-state signal sources began to beapplied to the radars that had been under development since the days of the MIT RadiationLaboratory.I was initiated into the phase-noise requirements of airborne Doppler radarand the underlying arts of crystal oscillators,power amplifiers,and nonlinear-reactancefrequency multipliers.In1964an IEEE committee was formed to prepare a standard on frequency stability.Thanks to a supportive mentor,W.K.Saunders,I became a member of that group,whichincluded leaders such as J.A.Barnes and L.S.Cutler.It was noted that the independentuse of frequency-domain and time-domain definitions stood in the way of the develop-ment of a common standard.To promote focused interchange the group sponsored theNovember1964NASA/IEEE Conference on Short Term Frequency Stability and editedthe February1966Special Issue on Frequency Stability of the Proceedings of the IEEE.The context of that time included the appreciation that self-limiting oscillators andmany systems(FM receivers with limiters,for example)are nonlinear in that theylimit amplitude variations(AM noise);hence the focus on phase noise.The modestfrequency limits of semiconductor devices of that period dictated the common usage ofnonlinear-reactance frequency multipliers,which multiply phase noise to the point whereit dominates the output noise spectrum.These typical circuit conditions were secondnature then to the“short-term stability community”but might not come so readily tomind today.More informationForewords xiii Thefirst step of the program to craft a standard that would define frequency stabilitywas to understand and meld the frequency-and time-domain descriptions of phaseinstability to a degree that was predictive and permitted analysis and optimization.Bythe time the subcommittee edited the Proc.IEEE special issue,the wide exchange ofviewpoints and concepts made it possible to synthesize concise summaries of the workin both domains,of which my own model was one.The committee published its“Characterization of frequency stability”in IEEE Trans.Instrum.Meas.,May1971.This led to the IEEE1139Standards that have served thecommunity well,with advances and revisions continuing since their initial publication.Rubiola’s book,based on his extensive seminar notes,is a capstone tutorial on thetheoretical basis and experimental measurements of oscillators for which phase noiseand frequency stability are primary issues.In hisfirst chapter Rubiola introduces the reader to the fundamental statistical de-scriptions of oscillator instabilities and discusses their role in the standards.Then in thesecond chapter he provides an exposition of the sources of noise in devices and circuits.In an instructive analysis of cascaded stages,he shows that,for modulative or parametricflicker noise,the effect of cascaded stages is cumulative without regard to stage gain.This is in contrast with the well-known treatment of additive noise using the Friisformula to calculate an equivalent input noise power representing noise that may originateanywhere in a cascade of real amplifiers.This example highlights the concept that“themodel is not the actual thing.”He also describes concepts for the reduction offlickernoise in amplifier stages.In his third chapter Rubiola then combines the elements of thefirst two chapters toderive models and techniques useful in characterizing phase noise arising in resonatorfeedback oscillators,adding mathematical formalism to these in the fourth chapter.Inthefifth chapter he extends the reader’s view to the case of delay-line oscillators suchas lasers.In his sixth chapter,Rubiola offers guidance for the instructive“hacking”ofexisting oscillators,using their external phase spectra and other measurables to estimatetheir internal configuration.He details cases in which resonatorfluctuations mask circuitnoise,showing that separately quantifying resonator noise can be fruitful and that devicenoisefigure and resonator Q are not merely arbitraryfitting factors.It’s interesting to consider what lies ahead in thisfield.The successes of today’sconsumer wireless products,cellular telephony,WiFi,satellite TV,and GPS,arise directlyfrom the economies of scale of highly integrated circuits.But at the same time thisintroduces compromises for active-device noise and resonator quality.A measure ofthe market penetration of multi-signal consumer systems such as cellular telephonyand WiFi is that they attract enough users to become interference-limited,often fromsubscribers much nearer than a distant base station.Hence low phase noise remainsessential to preclude an unacceptable decrease of dynamic range,but it must now beachieved within narrower bounds on the available circuit elements.A search for new understanding and techniques has been spurred by this requirementfor low phase noise in oscillators and synthesizers whose primary character is integrationand its accompanying minimal cost.This body of knowledge is advancing througha speculative and developmental phase.Today,numerical nonlinear circuit analysisMore informationxiv Forewordssupports additional design variables,such as the timing of the current pulse in nonlinearoscillators,that have become feasible because of the improved capabilities of bothsemiconductor devices and computers.Thefield is alive and well,with emerging players eager tofind a role on the stage fortheir own scenarios.Professionals and students,whether senior or new to thefield so ablydescribed by Rubiola,will benefit from his theoretical rigor,experimental viewpoint,and presentation.David B.LeesonStanford UniversityFebruary2008More informationPrefaceThe importance of oscillators in science and technology can be outlined by two mile-stones.The pendulum,discovered by Galileo Galilei in the sixteenth century,persistedas“the”time-measurement instrument(in conjunction with the Earth’s rotation period)until the piezoelectric quartz resonator.Then,it was not by chance that thefirst inte-grated circuit,built in September1958by Jack Kilby at the Bell Laboratories,was aradio-frequency oscillator.Time,and equivalently frequency,is the most precisely measured physical quantity.The wrist watch,for example,is probably the only cheap artifact whose accuracy ex-ceeds10−5,while in primary laboratories frequency attains the incredible accuracy ofa few parts in10−15.It is therefore inevitable that virtually all domains of engineeringand physics rely on time-and-frequency metrology and thus need reference oscillators.Oscillators are of major importance in a number of applications such as wireless com-munications,high-speed digital electronics,radars,and space research.An oscillator’srandomfluctuations,referred to as noise,can be decomposed into amplitude noise andphase noise.The latter,far more important,is related to the precision and accuracy oftime-and-frequency measurements,and is of course a limiting factor in applications.The main fact underlying this book is that an oscillator turns the phase noise of itsinternal parts into frequency noise.This is a necessary consequence of the Barkhausencondition for stationary oscillation,which states that the loop gain of a feedback oscillatormust be unity,with zero phase.It follows that the phase noise,which is the integral ofthe frequency noise,diverges in the long run.This phenomenon is often referred to asthe“Leeson model”after a short article published in1966by David B.Leeson[63].Onmy part,I prefer the term Leeson effect in order to emphasize that the phenomenon isfar more general than a simple model.In2001,in Seattle,Leeson received the W.G.Cady award of the IEEE International Frequency Control Symposium“for clear physicalinsight and[a]model of the effects of noise on oscillators.”In spring2004I had the opportunity to give some informal seminars on noise in oscil-lators at the NASA/Caltech Jet Propulsion Laboratory.Since then I have given lecturesand seminars on noise in industrial contexts,at IEEE symposia,and in universities andgovernment laboratories.The purpose of most of these seminars was to provide a tuto-rial,as opposed to a report on advanced science,addressed to a large-variance audiencethat included technicians,engineers,Ph.D.students,and senior scientists.Of course,capturing the attention of such a varied audience was a challenging task.The stimu-lating discussions that followed the seminars convinced me I should write a workingMore informationxvi Prefacedocument1as a preliminary step and then this book.In writing,I have made a seriouseffort to address the same broad audience.This work could not have been written without the help of many people.The gratitudeI owe to my colleagues and friends who contributed to the rise of the ideas containedin this book is disproportionate to its small size:R´e mi Brendel,Giorgio Brida,G.JohnDick,Michele Elia,Patrice F´e ron,Serge Galliou,Vincent Giordano,Charles A.(Chuck)Greenhall,Jacques Groslambert,John L.Hall,Vladimir S.(Vlad)Ilchenko,LaurentLarger,Lutfallah(Lute)Maleki,Andrey B.Matsko,Mark Oxborrow,Stefania R¨o misch,Anatoliy B.Savchenkov,Franc¸ois Vernotte,Nan Yu.Among them,I owe special thanks to the following:Lute Maleki for giving me theopportunity of spending four long periods at the NASA/Caltech Jet Propulsion Labora-tory,where I worked on noise in photonic oscillators,and for numerous discussions andsuggestions;G.John Dick,for giving invaluable ideas and suggestions during numerousand stimulating discussions;R´e mi Brendel,Mark Oxborrow,and Stefania R¨o misch fortheir personal efforts in reviewing large parts of the manuscript in meticulous detail andfor a wealth of suggestions and criticism;Vincent Giordano for supporting my effortsfor more than10years and for frequent and stimulating discussions.I wish to thank some manufacturers and their local representatives for kindness andprompt help:Jean-Pierre Aubry from Oscilloquartz;Vincent Candelier from RAKON(formerly CMAC);Art Faverio and Charif Nasrallah from Miteq;Jesse H.Searles fromPoseidon Scientific Instruments;and Mark Henderson from Oewaves.Thanks to my friend Roberto Bergonzo,for the superb picture on the front cover,entitled“The amethyst stairway.”For more information about this artist,visit the website.Finally,I wish to thank Julie Lancashire and Sabine Koch,of the Cambridge editorialstaff,for their kindness and patience during the long process of writing this book.How to use this bookLet usfirst abstract this book in one paragraph.Chapter1introduces the language ofphase noise and frequency stability.Chapter2analyzes phase noise in amplifiers,includ-ingflicker and other non-white phenomena.Chapter3explains heuristically the physicalmechanism of an oscillator and of its noise.Chapter4focuses on the mathematics thatdescribe an oscillator and its phase noise.For phase noise,the oscillator turns out to bea linear system.These concepts are extended in Chapter5to the delay-line oscillatorand to the laser,which is a special case of the latter.Finally,Chapter6analyzes indepth a number of oscillators,both laboratory prototypes and commercial products.Theanalysis of an oscillator’s phase noise discloses relevant details about the oscillator.There are other books about oscillators,though not numerous.They can be divided intothree categories:books on radio-frequency and microwave oscillators,which generallyfocus on the electronics;books about lasers,which privilege atomic physics and classical1E.Rubiola,The Leeson Effect–Phase Noise in Quasilinear Oscillators,February2005,arXiv:physics/0502143,now superseded by the present text.PrefacexviideeperreadingbasictheoreticaladvancedtheoreticallegendexperimentalistlecturerdeeperreadingFigure1Asymptotic reading paths:on the left,for someone planning lectures on oscillatornoise;on the right,for someone currently involved in practical work on oscillators.optics;books focusing on the relevant mathematical physics.The present text is uniquein that we look at the oscillator as a system consisting of more or less complex interactingblocks.Most topics are innovative,and the overlap with other books about oscillatorsor time-and-frequency metrology is surprisingly small.This may require an additionaleffort on the part of readers already familiar with the subject area.The core of this book rises from my experimentalist soul,which later became con-vinced of the importance of the mathematics.The material was originally thought anddrafted in the following(dis)order(see Fig.1):3Heuristic approach,6Oscillator hack-ing,4Feedback theory,5Delay-line oscillators.Thefinal order of subjects aims at amore understandable presentation.In seminars,I have often presented the material in the3–6–4–5order.Y et,the best reading path depends on the reader.T wo paths are suggestedin Fig.1for two“asymptotic”reader types,i.e.a lecturer and experimentalist.Whenplanning to use this book as a supplementary text for a university course,the lecturer More information。

有序点集与无序点集的曲面重构方法比较
钟华颖
【期刊名称】《新建筑》
【年(卷),期】2011(000)003
【摘要】曲面重构在逆向工程领域是指利用物体表面的点集重新构建物体形状的操作,这一技术对于非标准建筑设计同样适用.从已知排列顺序的点集(有序点集)和未知排列顺序的点集(无序点集)出发,对自由曲面进行重构是曲面重构的两种基本方法.本文对此进行了对比研究,并由这两种出发点,生成包含表皮及支撑结构的双层曲面系统,验证了该技术在建筑设计领域应用的可行性.
【总页数】3页(P96-98)
【作者】钟华颖
【作者单位】东南大学建筑学院,南京,210096
【正文语种】中文
【中图分类】TU-05
【相关文献】
1.曲面模型重构方法比较及误差分析 [J], 莫海军;周佳军;林志生
2.基于点云数据的曲面重构方法及其比较 [J], 李红莉;邢渊
3.多约束的平面点集形状重构方法 [J], 朱杰;孙毅中
4.从点集重构曲面网格方法综述 [J], 王静;薛为民;毋茂盛
5.3D散列点集构造光滑曲面新方法 [J], 崔汉国;胡瑞安
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磁共振平衡式自由稳态序列原理哎，说到磁共振成像（MRI），你是不是也曾好奇过那些看似神秘的扫描背后到底有什么原理？比如，咱们今天说的这个“平衡式自由稳态序列”，听起来是不是有点高大上？别急，别急，我跟你说，这玩意儿其实并不像你想的那么复杂，反而还挺有意思的。

你要知道，MRI的那些“秘密”就像一台高端的料理机，里面有一堆精密的机制，但只要你知道它是怎么转动的，食物最后能变成美味，就很简单了。

就拿这个“平衡式自由稳态序列”来说吧，其实就是一种磁共振技术，让我们能看得更清楚，甚至让我们能“冻结”那些瞬间的变化，轻松搞定一些复杂的影像扫描任务。

说白了，这个“平衡式自由稳态序列”是MRI用来捕捉图像的“套路”之一。

它不依赖于传统的扫描方法那种像扫雷一样的逐一扫描，而是采取一种“稳稳的，稳稳的，别急”的方法，把整个过程都调成一个“持续稳定”的状态。

这就像咱们生活中有时候会慢慢地适应一个新环境，找到一个“舒服”的平衡点，哪里都不急，什么都不慌，最后反而事半功倍。

MRI也是这个道理，它通过“平衡式”方式确保成像过程中的各个步骤都能自如进行，而不会因为过度的能量波动而导致图像不清晰或失真。

而这个“平衡”的意思，也就跟我们生活中的“平衡”差不多，明白吧？它讲的就是一个“不轻不重，不急不躁”的中庸之道。

你想，普通的扫描方式，有时候会对身体产生一定的干扰，可能会影响成像质量。

而“平衡式自由稳态序列”这种方式就很聪明，它通过合理调节磁场、射频信号和梯度场，保持一种长期稳定的状态，这样即便身体内外有一点小波动，它也能很快恢复，反而成像更精准。

而且啊，这个序列其实还挺适合用来做一些特殊的影像诊断，比方说对比度很低的组织，或者是那些结构不太清晰的地方，它能通过精妙的“操作”把细节给突出出来。

这就好比你在一个黑暗的房间里，拿着手电筒照亮某个角落，虽然周围是漆黑的，但那个角落的细节却因为光线的精确聚焦，变得格外清晰。

嘿，你想过没有，其实MRI的每一次扫描就像一次静谧的“舞蹈”。