Large deviations from the thermodynamic limit in globally coupled maps

第三章热力学第二定律前面，所学的热力学第一律，是以“能量守恒原理”为基础，建立了U和H两个热力学函数，通过对过程ΔU和ΔH的计算，解决了过程的热效应问题。

然而，在一定条件下，一过程能否自动进行，进行到什么程度，亦即，过程的方向和限度问题，第一定律无能为力，这恰恰是第二定律所要解决的问题。

人类经验表明：一切自然界的过程都是有方向性的。

大家都知道：自然界中存在朝一定方向自发进行的过程，例如：热自动从高温物体传向低温物体，直至两物体温度相等；气体自动地从高压区流向低压区，直至各处压力相同，相互接触的不同气体，总是自动的相互混合均匀；电流总是从高电流处流向低电流处直至各处电势相等：浓度不均匀的溶液，自动地变成浓度均匀一致。

等等，这些过程都是可以自动进行的，叫“自发过程”。

显然，一切自然界的过程都是有方向性及一定的进行限度。

从未发现哪一自发过程可自动恢复原状。

为什么自发过程的逆过程不能自动进行？这就是第二定律所要解决的中心问题—判断过程的方向和限度问题。

究竟什么因素决定自发过程的方向和限度？从表面上看，似乎不同的过程，有着不同的决定因素。

如，决定热传导方向和限度的是温度T；决定气体流动的是压力p；决定电流的是电势V；等等。

决定化学反应的是什么？这就要找出：决定一切自发过程方向和限度的共同因素，以此作为判断的共同根据。

寻找一切自发过程方向和限度的判据，这就要研究自发过程的共同特征，根据经验总结热功转化规律，找出反映自发过程本质特征的状态函数—S,以ΔS判断过程的方向和限度。

进而又S据判据在特殊条件下，推演出了A、G状态函数，从而，得到更方便更实用的判据ΔA、ΔG。

§3.1自发变化的共同特征—不可逆性前已述及，一切自发过程都是有方向性的，亦即，自发过程进行之后，系统不能自动恢复原状。

若要让其恢复原状，环境中有什么变化？若让环境也复原，需要什么条件？现举例说明。

1. 理想气体向真空膨胀过程。

这是一个自发过程，当气体向真空膨胀时，Q = 0，W = 0，ΔU=0，ΔT=0。

Remnant PbI2, an unforeseen necessity in high-efficiency hybrid perovskite-based solar cells?a)Duyen H. Cao, Constantinos C. Stoumpos, Christos D. Malliakas, Michael J. Katz, Omar K. Farha, Joseph T. Hupp, and Mercouri G. KanatzidisCitation: APL Materials 2, 091101 (2014); doi: 10.1063/1.4895038View online: /10.1063/1.4895038View Table of Contents: /content/aip/journal/aplmater/2/9?ver=pdfcovPublished by the AIP PublishingArticles you may be interested inParameters influencing the deposition of methylammonium lead halide iodide in hole conductor free perovskite-based solar cellsAPL Mat. 2, 081502 (2014); 10.1063/1.4885548Air stability of TiO2/PbS colloidal nanoparticle solar cells and its impact on power efficiencyAppl. Phys. Lett. 99, 063512 (2011); 10.1063/1.3617469High efficiency mesoporous titanium oxide PbS quantum dot solar cells at low temperatureAppl. Phys. Lett. 97, 043106 (2010); 10.1063/1.3459146Near-IR activity of hybrid solar cells: Enhancement of efficiency by dissociating excitons generated in PbS nanoparticlesAppl. Phys. Lett. 96, 073505 (2010); 10.1063/1.3292183Effects of molecular interface modification in hybrid organic-inorganic photovoltaic cellsJ. Appl. Phys. 101, 114503 (2007); 10.1063/1.2737977APL MATERIALS2,091101(2014)Remnant PbI2,an unforeseen necessity in high-efficiency hybrid perovskite-based solar cells?aDuyen H.Cao,1Constantinos C.Stoumpos,1Christos D.Malliakas,1Michael J.Katz,1Omar K.Farha,1,2Joseph T.Hupp,1,band Mercouri G.Kanatzidis1,b1Department of Chemistry,and Argonne-Northwestern Solar Energy Research(ANSER)Center,Northwestern University,2145Sheridan Road,Evanston,Illinois60208,USA2Department of Chemistry,Faculty of Science,King Abdulaziz University,Jeddah,Saudi Arabia(Received2May2014;accepted26August2014;published online18September2014)Perovskite-containing solar cells were fabricated in a two-step procedure in whichPbI2is deposited via spin-coating and subsequently converted to the CH3NH3PbI3perovskite by dipping in a solution of CH3NH3I.By varying the dipping time from5s to2h,we observe that the device performance shows an unexpectedly remark-able trend.At dipping times below15min the current density and voltage of thedevice are enhanced from10.1mA/cm2and933mV(5s)to15.1mA/cm2and1036mV(15min).However,upon further conversion,the current density decreases to9.7mA/cm2and846mV after2h.Based on X-ray diffraction data,we determinedthat remnant PbI2is always present in these devices.Work function and dark currentmeasurements showed that the remnant PbI2has a beneficial effect and acts as ablocking layer between the TiO2semiconductor and the perovskite itself reducingthe probability of back electron transfer(charge recombination).Furthermore,wefind that increased dipping time leads to an increase in the size of perovskite crys-tals at the perovskite-hole-transporting material interface.Overall,approximately15min dipping time(∼2%unconverted PbI2)is necessary for achieving optimaldevice efficiency.©2014Author(s).All article content,except where otherwisenoted,is licensed under a Creative Commons Attribution3.0Unported License.[/10.1063/1.4895038]With the global growth in energy demand and with compelling climate-related environmental concerns,alternatives to the use of non-renewable and noxious fossil fuels are needed.1One such alternative energy resource,and arguably the only legitimate long-term solution,is solar energy. Photovoltaic devices which are capable of converting the photonflux to electricity are one such device.2Over the last2years,halide hybrid perovskite-based solar cells with high efficiency have engendered enormous interest in the photovoltaic community.3,4Among the perovskite choices, methylammonium lead iodide(MAPbI3)has become the archetypal light absorber.Recently,how-ever,Sn-based perovskites have been successfully implemented in functional solar cells.5,6MAPbI3 is an attractive light absorber due to its extraordinary absorption coefficient of1.5×104cm−1 at550nm;7it would take roughly1μm of material to absorb99%of theflux at550nm.Further-more,with a band gap of1.55eV(800nm),assuming an external quantum efficiency of90%,a maximum current density of ca.23mA/cm2is attainable with MAPbI3.Recent reports have commented on the variability in device performance as a function of perovskite layer fabrication.8In our laboratory,we too have observed that seemingly identicalfilmsa Invited for the Perovskite Solar Cells special topic.b Authors to whom correspondence should be addressed.Electronic addresses:j-hupp@ and m-kanatzidis@2,091101-12166-532X/2014/2(9)/091101/7©Author(s)2014FIG.1.X-ray diffraction patterns of CH3NH3PbI3films with increasing dipping time(%composition of PbI2was determined by Rietveld analysis(see Sec.S3of the supplementary material for the Rietveld analysis details).have markedly different device performance.For example,when ourfilms of PbI2are exposed to MAI for several seconds(ca.60s),then a light brown coloredfilm is obtained rather than the black color commonly observed for bulk MAPbI3(see Sec.S2of the supplementary material for the optical band gap of bulk MAPbI3).23This brown color suggests only partial conversion to MAPbI3and yields solar cells exhibiting a J sc of13.4mA/cm2and a V oc of960mV;these values are significantly below the21.3mA/cm2and1000mV obtained by others.4Under the hypothesis that fully converted films will achieve optimal light harvesting efficiency,we increased the conversion time from seconds to2h.Unexpectedly,the2-h dipping device did not show an improved photovoltaic response(J sc =9.7mA/cm2,V oc=846mV)even though conversion to MAPbI3appeared to be complete.With the only obvious difference between these two devices being the dipping time,we hypothesized that the degree of conversion of PbI2to the MAPbI3perovskite is an important parameter in obtaining optimal device performance.We thus set out to understand the correlation between the method of fabrication of the MAPbI3layer,the precise chemical compositions,and both the physical and photo-physical properties of thefilm.We report here that remnant PbI2is crucial in forming a barrier layer to electron interception/recombination leading to optimized J sc and V oc in these hybrid perovskite-based solar cells.We constructed perovskite-containing devices using a two-step deposition method according to a reported procedure with some modifications.4(see Sec.S1of the supplementary material for the experimental details).23MAPbI3-containing photo-anodes were made by varying the dipping time of the PbI2-coated photo-anode in MAI solution.In order to minimize the effects from unforeseen variables,care was taken to ensure that allfilms were prepared in an identical manner.The composi-tions offinal MAPbI3-containingfilms were monitored by X-ray diffraction(XRD).Independently of the dipping times,only theβ-phase of the MAPbI3is formed(Figure1).9However,in addition to theβ-phase,allfilms also showed the presence of unconverted PbI2(Figure1,marked with*) which can be most easily observed via the(001)and(003)reflections at2θ=12.56◦and38.54◦respectively.As the dipping time is increased,the intensities of PbI2reflections decrease with a concomitant increase in the MAPbI3intensities.In addition to the decrease in peak intensities of PbI2,the peak width increases as the dipping time increases indicating that the size of the PbI2 crystallites is decreasing,as expected,and the converse is observed for the MAPbI3reflections.This observation suggests that the conversion process begins from the surface of the PbI2crystallites and proceeds toward the center where the crystallite domain size of the MAPbI3phase increases and that of PbI2diminishes.Interestingly,the remnant PbI2phase can be seen in the data of other reports, but has not been identified as a primary source of variability in cell performance.8,10 Considering that the perovskite is the primary light absorber within the device,we wantedto further investigate how the optical absorption of thefilm changes with increasing dipping timeFIG.2.Absorption spectra of CH3NH3PbI3films as a function of unconverted PbI2phase fraction.FIG.3.(a)J-V curves and(b)EQE of CH3NH3PbI3-based devices as a function of unconverted PbI2phase fraction.(Figure2).11,12The pure PbI2film shows a band gap of2.40eV,consistent with the yellow color of PbI2.As the PbI2film is gradually converted to the perovskite,the band gap is progressively shifted toward1.60eV.The deviation of MAPbI3’s band gap(1.60eV)from that of the bulk MAPbI3 material(1.55eV)could be explained by quantum confinement effects related with the sizes of TiO2and MAPbI3crystallites and their interfacial interaction.13,14Interestingly,we also noticed the presence of a second absorption in the light absorber layer,in which the gap gradually red shifts from1.90eV to1.50eV as the PbI2concentration is decreased from9.5%to0.3%(Figure2—blue arrow).Having established the chemical compositions and optical properties of the light absorberfilms, we proceeded to examine the photo-physical responses of the corresponding functional devices in order to determine how the remnant PbI2affects device performance.The pure PbI2based device remarkably achieved a0.4%efficiency with a J sc of2.1mA/cm2and a V oc of564mV (Figure3(a)).Upon progressive conversion of the PbI2layer to MAPbI3,we observe two different regions(Figure4,Table I).In thefirst region,the expected behavior is observed;as more PbI2is converted to MAPbI3,the trend is toward higher photovoltaic efficiency,due both to J sc and V oc, until1.7%PbI2is reached.The increase in J sc is attributable,at least in part,to increasing absorption of light by the perovskite.We speculate that progressive elimination of PbI2,present as a layer between TiO2and the perovskite,also leads to higher net yields for electron injection into TiO2and therefore,higher J values.For a sufficiently thick PbI2spacer layer,electron injection would occur instepwise fashion,i.e.,perovskite→PbI2→TiO2.Finally,the photovoltage increase is attributable toFIG.4.Summary of J-V data vs.PbI2concentration of CH3NH3PbI3-based devices(Region1:0to15min dipping time, Region2:15min to2h dipping time).TABLE I.Photovoltaic performance of CH3NH3PbI3-based devices as a function of unconverted PbI2fraction.Dipping time PbI2concentration a J sc(mA/cm2)V oc(V)Fill factor(%)Efficiency(%) 0s100% 2.10.564320.45s9.5%10.10.93352 4.960s7.2%13.40.96052 6.72min 5.3%14.00.964557.45min 3.7%14.70.995578.315min 1.7%15.1 1.036629.730min0.8%13.60.968648.51h0.4%12.40.938657.62h0.3%9.70.84668 5.5a Determined from the Rietveld analysis of X-ray diffraction data.the positive shift in TiO2’s quasi-Fermi level as the population of photo-injected electrons is higher with increased concentration of MAPbI3.The second region yields a notably different trend;surprisingly,below a concentration of2% PbI2,J sc,V oc,and ultimatelyηdecrease.Considering that the light-harvesting efficiency would increase when the remaining2%PbI2is converted to MAPbI3(albeit to only a small degree),then the remnant PbI2must have some other role.We posit that remnant PbI2serves to inhibit detrimental electron-transfer processes(Figure5).Two such processes are back electron transfer from TiO2to holes in the valence band of the perovskite(charge-recombination)or to the holes in the HOMO of the HTM(charge-interception).This retardation of electron interception/recombination observation is reminiscent of the behavior of atomic layer deposited Al2O3/ZrO2layers that have been employed in dye-sensitized solar cells.15–18It is conceivable that the conversion of PbI2to MAPbI3occurs from the solution interface toward the TiO2/PbI2interface and thus would leave sandwiched between TiO2and MAPbI3a blocking layer of PbI2that inhibits charge-interception/recombination.For this hypothesis to be correct,it is crucial that the conduction-band-edge energy(E cb)of the PbI2be higher than the E cb of the TiO2.19–21 The work function of PbI2was measured by ultraviolet photoelectron spectroscopy(UPS)and was observed to be at6.35eV vs.vacuum level,which is0.9eV lower than the valence-band-edge energy(E vb)of MAPbI3(see Sec.S7of the supplementary material23for the work function of PbI2);the E cb(4.05eV)was calculated by subtracting the work function from the band gap(2.30eV).solar cell.FIG.6.Dark current of CH3NH3PbI3-based devices as a function of unconverted PbI2phase fraction.The E cb of PbI2is0.26eV higher than the E cb of TiO2and thus PbI2satisfies the conditions of a charge-recombination/interception barrier layer.In order to probe the hypothesis that PbI2acts as a charge-interception barrier,dark current measurements,in which electronsflow from TiO2to the HOMO of the HTM,were made.Consistent with our hypothesis,Figure6illustrates that the onset of the dark current occurs at lower potentials as the PbI2concentration decreases.In the absence of other effects,the increasing dark current with increasing fraction of perovskite(and decreasing fraction of PbI2)should result in progressively lower open-circuit photovoltages.Instead,the photocurrent density and the open-circuit photovoltage bothincrease,at least until to PbI2fraction reaches1.7%.As discussed above,thinning of a PbI2-basedFIG.7.Cross-sectional SEM images of CH3NH3PbI3film with different dipping time.sandwich layer should lead to higher net injection yields,but excessive thinning would diminish the effectiveness of PbI2as a barrier layer for back electron transfer reactions.Given the surprising role of remnant PbI2in these devices,we further probed the two-step conversion process by using scanning-electron microscopy(SEM)(Figure7).Two domains of lead-containing materials(PbI2and MAPbI3)are present.Thefirst domain is sited within the mesoporous TiO2network(area1)while the second grows on top of the network(area2).Area2initially contains 200nm crystals.As the dipping time is increased,the crystals show marked changes in size and morphology.The formation of bigger perovskite crystals is likely the result of the thermodynamically driven Ostwald ripening process,i.e.,smaller perovskite crystals dissolves and re-deposits onto larger perovskite crystals.22The rate of charge-interception,as measured via dark current,is proportional to the contact area between the perovskite and the HTM.Thus,the eventual formation of large, high-aspect-ratio crystals,as shown in Figure7,may well lead to increases in contact area and thereby contributes to the dark-current in Figure6.Regardless,we found that the formation of large perovskite crystals greatly decreased our success rate in constructing high-functioning,non-shorting solar cells.In summary,residual PbI2appears to play an important role in boosting overall efficiencies for CH3NH3PbI3-containing photovoltaics.PbI2’s role appears to be that of a TiO2-supported blocking layer,thereby slowing rates of electron(TiO2)/hole(perovskite)recombination,as well as decreasing rates of electron interception by the hole-transporting material.Optimal performance for energy conversion is observed when ca.98%of the initially present PbI2has been converted to the perovskite. Conversion to this extent requires about15min.Pushing beyond98%(and beyond15min of reaction time)diminishes cell performance and diminishes the success rate in constructing non-shorting cells.The latter problem is evidently a consequence of conversion of small and more-or-less uniformly packed perovskite crystallites to larger,poorly packed crystallites of varying shape and size.Finally,the essential,but previously unrecognized,role played by remnant PbI2 provides an additional explanation for why cells prepared dissolving and then depositing pre-formed CH3NH3PbI3generally under-perform those prepared via the intermediacy of PbI2.We thank Prof.Tobin Marks for use of the solar simulator and EQE measurement system. Electron microscopy was done at the Electron Probe Instrumentation Center(EPIC)at Northwestern University.Ultraviolet Photoemission Spectroscopy was done at the Keck Interdisciplinary SurfaceScience facility(Keck-II)at Northwestern University.This research was supported as part of theANSER Center,an Energy Frontier Research Center funded by the U.S Department of Energy, Office of Science,Office of Basic Energy Sciences,under Award No.DE-SC0001059.1R.Monastersky,Nature(London)497(7447),13(2013).2H.J.Snaith,J.Phys.Chem.Lett.4(21),3623(2013).3M.M.Lee,J.Teuscher,T.Miyasaka,T.N.Murakami,and H.J.Snaith,Science338(6107),643(2012).4J.Burschka,N.Pellet,S.J.Moon,R.Humphry-Baker,P.Gao,M.K.Nazeeruddin,and M.Gratzel,Nature(London) 499(7458),316(2013).5F.Hao,C.C.Stoumpos,D.H.Cao,R.P.H.Chang,and M.G.Kanatzidis,Nat.Photonics8(6),489(2014);F.Hao,C.C. Stoumpos,R.P.H.Chang,and M.G.Kanatzidis,J.Am.Chem.Soc.136,8094–8099(2014).6N.K.Noel,S.D.Stranks,A.Abate,C.Wehrenfennig,S.Guarnera,A.Haghighirad,A.Sadhanala,G.E.Eperon,M.B. 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学科代码学科名称A数理科学B化学科学C生命科学D地球科学E工程与材料科学F信息科学G管理科学A01数学A0101基础数学A010101数论A01010101解析数论A01010102代数数论A01010103丢番图分析A01010104超越数论A01010105模型式与模函数论A01010106数论的应用A010102代数学A01010201群论A01010202群表示论A01010203李群A01010204李代数A01010205代数群A01010206典型群A01010207同调代数A01010208代数K理论A01010209Kac-Moody代数A01010210环论A01010211代数(可除代数)A01010212体A01010213编码理论与方法A01010214序结构研究A010103几何学A01010301整体微分几何A01010302代数几何A01010303流形上的分析A01010304黎曼流形与洛仑兹流形A01010305齐性空间与对称空间A01010306调和映照及其在理论物理中的应用A01010307子流形理论A01010308杨--米尔斯场与纤维丛理论A01010309辛流形A010104拓扑学A01010401微分拓扑A01010402代数拓扑A01010403低维流形A01010404同伦论A01010405奇点与突变理论A01010406点集拓扑A010105函数论A01010501多复变函数论A01010502复流形A01010503复动力系统A01010504单复变函数论A01010505Rn中的调和分析的实方法A01010506非紧半单李群的调和分析A01010507函数逼近论A010106泛函分析A01010601非线性泛函分析A01010602算子理论A01010603算子代数A01010604泛函方程A01010605空间理论A01010606广义函数A010107常微分方程A01010701泛函微分方程A01010702特征与谱理论及其反问题A01010703定性理论A01010704稳定性理论、分支理论A01010705混沌理论A01010706奇摄动理论A01010707复域中的微分方程A01010708动力系统A010108偏微分方程A01010801连续介质物理与力学、及反应扩散等应用领域中A01010802几何与数学物理中的偏微分方程A01010803微局部分析与一般偏微分算子理论A01010804非线性椭圆（和抛物）方程研究中的新方法和新A01010805混合型及其它带奇性的方程A01010806非线性波、非线性发展方程和无穷维动力系统A010109数学物理A01010901规范场论A01010902引力场论的经典理论与量子理论A01010903孤立子理论A01010904统计力学A01010905连续介质力学等方面的数学问题A010110概率论A01011001马氏过程A01011002随机过程A01011003随机分析A01011004随机场A01011005鞅论A01011006极限理论A01011007概率论在调和分析、几何及微分方程等方面的应A01011008在物理、生物、化学管理中的概率论问题A01011009平稳过程A010111数理逻辑与数学基础A01011101递归论A01011102模型论A01011103证明论A01011104公理集合证A01011105数理逻辑在人工智能及计算机科学中的应用A0102应用数学A010201数理统计A01020101抽样调查与抽样方法A01020102试验设计A01020103时间序列分析及其算法研究A01020104多元分析及其算法研究A01020105数据分析及其图形处理A01020106非参数统计方法A01020107应用统计中的基础性工作A01020108统计线性模型A01020109参数估计方法A01020110随机过程的统计理论及方法A01020111蒙特卡洛方法 (统计模拟方法) A010202运筹学A01020201线性与非线性规划A01020202整数规划A01020203动态规划A01020204组合最优化A01020205随机服务系统A01020206对策论A01020207不动点算法A01020208随机最优化A01020209多目标规划A01020210不可微最优化A01020211可靠性理论A010203控制论A01020301有限维非线性系统A01020302分布参数系统的控制理论A01020303随机系统的控制理论A01020304最优控制理论与算法A01020305参数辨识与适应控制A01020306线性系统理论的代数与几何方法A01020307控制的计算方法A01020308微分对策理论A01020309稳健控制A010204若干交叉学科A01020401信息论及应用A01020402经济数学A01020403生物数学A01020404不确定性的数学理论A01020405分形论及应用A010205计算机的数学基础A01020501可解性与可计算性A01020502机器证明A01020503计算复杂性A01020504VLSI的数学基础A01020505计算机网络与并行计算A010206组合数学A01020601组合计数A01020602组合设计A01020603图论A01020604线性计算几何A01020605组合概率方法A0103计算数学与科学工程计算A010301偏微分方程数值计算A01030101初边值问题数值解法及应用A01030102非线性微分方程及其数值解法A01030103边值问题数值解法及其应用A01030104有限元、边界元数值方法A01030105变分不等式的数值方法A01030106辛几何差分方法A01030107数理方程反问题的数值解法A010302常微分方程数值解法及其应用A01030201二点边值问题A01030202STIFF 问题研究A01030203奇异性问题A01030204代数微分方程A010303数值代数A01030301大型稀疏矩阵求解A01030302代数特征值问题及其反问题A01030303非线性代数方程A01030304一般线性代数方程组求解A01030305快速算法A010304函数逼近A01030401多元样条A01030402多元逼近A01030403曲面拟合A01030404有理逼近A01030405散乱数据插值A010305计算几何A01030501曲面造型A01030502曲面光滑拼接A01030503曲面设计A01030504体素拼接A01030505几何问题的计算机实现A010306新型算法A01030601并行算法A01030602多重网格技术A01030603自适应方法A01030604区间分析法及其应用A02力学A0201一般力学A020101分析力学A020102动力系统的分岔、混沌A020103运动稳定性与控制A020104非线性振动与控制A020105多体动力学A020106转子动力学A020107弹道力学和飞行力学A020108理性力学A020109力学中的反问题A020110力学发展史学A0202固体力学A020201弹性力学与塑性力学A020202疲劳与断裂力学A020203损伤、破坏机理和微结构演化A020204本构关系A020205复合材料力学A020206新型材料的力学问题A020207极端条件下的材料和结构A020208微机电系统中的固体力学问题A020209岩体力学和土力学A020210冲击动力学A020211结构力学A020212结构振动与噪声A020213结构优化和可靠性分析A020214制造工艺力学A020215实验固体力学A020216计算固体力学A020217流固耦合作用A0203流体力学A020301流动的稳定性A020302湍流A020303水动力学A020304空气动力学A020305分层流A020306非平衡流A020307渗流A020308多相流A020309非牛顿流A020310内流A020311化工流体力学A020312工业空气动力学A020313微重力流体力学A020314微机电系统中的流体力学问题A020315流动噪声与控制A020316稀薄气体力学A020317实验流体力学A020318计算流体力学A0204交叉与边缘领域的力学A020401物理力学A020402爆炸力学A020403环境流体力学A020404生物力学A020405电磁流体力学和等离子体动力学A03天文学A0301宇宙学A0302星系和类星体A0303恒星物理与星际物质A0304太阳和太阳系A0305射电天文A0306空间天文A0307理论天体物理A0308天体测量和天文地球动力学A0309天体力学和人造卫星动力学A0310时间、频率A0311天文仪器A0312天文学史A0313其它A04物理学(Ⅰ)A0401凝聚态物性Ｉ：结构、力学和热学性质A040101液体和固体结构；晶体、非晶、准晶的物质结构A040102凝聚态物质的力学和声学性质A040103晶格动力学和晶体统计学A040104状态方程、相平衡和相变A040105凝聚态物质的热学性质A040106凝聚态物质的输运性质A040107量子流体和固体;液态氦和固态氦A040108表面和界面;薄膜和晶须；人工微结构（结构和 A0402凝聚态物性Ⅱ：电子结构、电学、磁学和光学性A040201电子态A040202凝聚态物质中的电子输运A040203表面.界面.薄膜和低维系统的电子结构及电学性A040204超导电性A040205磁学性质A040206凝聚态物质的磁共振和弛豫;穆斯堡尔效应A040207介电性质A040208光学性质、凝聚态物质的波谱学、物质与粒子的A040209液体和固体的电子发射和离子发射;碰撞现象A040210与凝聚态物理有关的交叉学科A0403原子和分子物理A040301原子和分子理论A040302原子光谱及原子与光子相互作用A040303分子光谱及分子与光子相互作用A040304原子和分子碰撞过程及相互作用A040305研究原子和分子性质的实验设备和技术A040306特殊原子和分子的研究A040307与原子、分子有关的其它物理问题和交叉学科A0404光学A040401光在均匀介质中的传播A040402光在非均匀介质中的传播A040403像的形成和分析A040404全息照相A040405量子光学A040406微波激射A040407激光发射过程A040408激光系统和激光与物质相互作用A040409非线性光学A040410光学材料中物理问题及固体发光A040411光源和光学标准A040412光学透镜和反射镜系统A040413光学器件的原理A040414与光学有关的其它物理问题和交叉学科A0405声学A040501普通线性声学A040502非线性声学和强声学A040503航空声学和大气声学A040504水声A040505超声、量子声学和声的物理效应A040506次声A040507噪声、噪声效应及其控制A040508建筑声学A040509声的信号处理A040510声全息照相A040511语言声学A040512乐声A040513声的测量及专用仪器A040514声的转换原理A040515与声学有关的其它物理问题和交叉学科A05物理学(Ⅱ)A0501基础物理学A050101物理教育学及物理学史A050102物理学中的数学问题A050103经典物理学和量子理论A050104相对论与引力A050105热力学与统计物理学 (含混沌)A050106测量科学、一般实验技术和测试系统A0502粒子物理学和场论A050201粒子基本特性及粒子物理一般问题A050202场论中的基本问题和新方法A050203对称性及对称破缺A050204量子色动力学、强相互作用和强子物理A050205电－弱相互作用及其唯象学A050206非标准模型及其唯象学A050207新粒子A050208粒子的延展体理论A050209宇宙射线和超高能现象A050210粒子物理与宇宙学A0503核物理A050301原子核特性A050302原子核结构模型的理论研究A050303原子核统计理论研究A050304原子核高激发态、高自旋态和超形变A050305带奇异数系统、奇异核和超核A050306核内非核子自由度A050307核力与少体系统A050308强子、轻子与核相互作用A050309核物质理论及核多体方法A050310核衰变、核裂变、核聚变A050311低能核反应与散射A050312重离子核物理A050313中高能核物理A050314核天体物理A050315核数据分析和计算机模拟A0504核技术及其应用A050401离子束与物质相作用和辐照损伤A050402核分析技术 ( RBS、PIXE、NRA )A050403穆斯堡尔谱学及其应用A050404正电子湮灭技术及其应用A050405中子衍射及其应用A050406扰动角关联及其应用A050407核磁共振及其应用A050408中子活化和同位素示踪技术A050409离子束材料改性A050410核技术在地学中的应用A050411核技术在医学中的应用A050412核技术在农业中的应用A050413核技术在工业中的应用A050414核科学和其它学科的交叉A0505粒子物理与核物理实验设备A050501加速器原理和关键技术A050502离子源和电子枪A050503预加速装置和加速器部件A050504束流输运和性能测量A050505真空和超高真空技术A050506反应堆A050507辐射探测方法A050508探测技术和谱仪A050509辐射剂量及其防护A050510核电子学A0506等离子体物理A050601等离子体中的基本过程与特性A050602等离子体的加热、约束和辐射A050603等离子体动力学与电磁流体力学A050604等离子体中的混沌、孤立波、湍流等非线性现象A050605等离子体的模拟、数值方法和软件A050607等离子体诊断技术A050608等离子体与固体相互作用A050609激光束、粒子束、微波与等离子体A050610低气压低温等离子体的应用A050611热平衡低温等离子体的应用A050612非中性等离子体A050613强耦合等离子体A050614空间等离子体B01无机化学B0101无机合成和制备化学B010101合成技术B010102合成化学B010103特殊聚集态制备B0102丰产元素化学B010201稀土化学B010202钨化学B010203钼化学B010204锡化学B010205锑化学B010206钛化学B010207钒化学B010208稀有碱金属化学B010209稀散元素化学B0103配位化学B010301固体配位化学B010302溶液配位化学B010303金属有机化学B010304原子簇化学B010305功能配合物化学B0104生物无机化学B010401金属酶化学及其化学模拟B010402金属蛋白化学及其化学模拟B010403生物体内微量元素的状态及功能、受体底物相互B010404金属离子与生物膜的作用及其机理B010405金属离子与核酸化学B0105固体无机化学B010501缺陷化学B010502固体反应B010503固体表面化学B010504无机固体材料化学B0106分离化学B010601萃取化学B010602无机色层B010603无机膜分离B0107物理无机化学B010701无机化合物结构与性质B010702理论无机化学B010703无机反应机制及反应动力学B010704熔盐化学及相平衡B0108同位素化学B010801同位素分离B010802同位素分析B010803同位素应用B0109放射化学B010901核燃料化学B010902超铀元素化学B010903裂片元素化学B010904放射性核素及其标记化合物的制备和应用B010905放射分析化学B010906放射性废物处理和综合利用B0110核化学B011001低能核化学B011002高能核化学B011003裂变化学B011004重离子核化学B011005核天体化学B02有机化学B0201有机合成B020101有机合成反应B020102新化合物和复杂化合物的设计与合成B020103高选择性有机合成试剂B020104不对称合成B0202金属有机及元素有机化学B020201有机磷化学B020202有机硅化学B020203有机硼化学B020204有机氟化学B020205金属有机化合物的合成及其应用B0203天然有机化学B020301甾体及萜类化学B020302糖类黄酮类化学B020303中草药有效成份B020304具有重要应用价值的天然产物的研究B0204物理有机化学B020401活泼中间体化学B020402化学动态学B020403有机光化学B020404立体化学B020405有机分子结构与活性关系B020406具有光、电、磁特性的化合物研究B020407计算有机化学B0205药物化学B020501新药物分子设计和合成B020502药物构效关系B0206生物有机化学B020601多肽化学B020602核酸化学B020603仿生及模拟酶B020604天然酶的化学修饰及应用B020605生物合成及生物转化B0207有机分析B020701新化合物和复杂化合物的结构研究B020702有机分析、分离新方法新技术研究B020703有机化合物结构波谱学B0208应用有机化学B020801除草剂B020802植物生长促进剂B020803害虫引诱剂、昆虫信息素B020804高效、低毒、低抗性农药B020805食品化学B020806香料化学B020807染料化学B03物理化学B0301结构化学B030101体相静态结构B030102表面结构B030103溶液结构B030104动态结构B030105谱学B030106结构化学方法和理论B0302量子化学B030201基础量子化学B030202应用量子化学B0303催化B030301多相催化B030302均相催化B030303人工酶催化B030304光催化B0304化学动力学B030401宏观反应动力学B030402分子动态学B030403反应途径和过渡态B030404快速反应动力学B030405结晶过程动力学B0305胶体与界面化学B030501表面活性剂B030502分散体系B030503流变性能B030504界面吸附现象B030505超细粉和颗粒B0306电化学B030601电极过程及其动力学B030602腐蚀电化学B030603熔盐电化学B030604光电化学B030605半导体电化学B030606生物电化学B030607表面电化学B030608电化学技术B030609电催化B0307光化学B030701激光闪光光解B030702激发态化学B030703电子转移光化学、光敏化B030704光合作用B030705大气光化学B0308热化学B030801热力学参数B030802相平衡B030803电解质溶液化学B030804非电解质溶液化学B030805生物热化学B030806量热学B0309高能化学B030901辐射化学B030902等离子体化学B030903激光化学B0310计算化学B031001化学信息的运筹B031002计算模拟B031003计算控制B031004计算方法的最优化B04高分子科学B0401高分子合成B040101催化剂、聚合反应及聚合方法B040102高分子设计和合成B040103新单体及单体的新合成方法B040104聚合反应动力学B040105高分子光化学、辐射化学、等离子体化学B040106微生物参与的聚合反应、酶催化聚合反应B0402高分子反应B040201高分子老化、降解、交联B040202高分子接枝、嵌段改性B040203高分子功能化改性B040204粒子注入、辐射、激光等方法对高分子的改性B0403功能高分子B040301吸附、分离、离子交换、螯合功能的高分子B040302用于有机合成、医疗、分析等领域的高分子试剂B040303医用高分子、高分子药物B040304液晶态高分子B040305有机固体电子材料、磁性高分子B040306储能、换能、敏感材料及高分子催化剂B040307高分子功能膜B040308微电子材料、分子组装材料及器件B0404天然高分子B0405高分子物理及高分子物理化学B040501高分子溶液性质和溶液热力学B040502高分子链结构B040503高分子流变学B040504高聚物聚集态结构B040505高分子结构与性能关系B040506高聚物测试及表征方法B040507高分子材料的传质理论、强度理论、破坏机理B040508高分子多相体系B0406高分子理论化学B040601高分子聚合、交联、聚集态统计理论B040602数学、计算机方法在高分子凝聚态、分子动态学B0407聚合物工程及材料B040701聚合工程反应动力学及聚合反应控制B040702聚合物成型理论及成型方法B040703塑料、纤维、橡胶及成型研究B040704涂料、粘合剂及高分子肋剂B040705可生物降解薄膜B040706高分子润滑材料B040707其它领域中应用的高分子材料B040708高分子资源的再生和综合利用B05分析化学B0501色谱分析B050101气相色谱B050102液相色谱B050103薄层色谱B050104离子色谱B050105超临界液体色谱B050106毛细管电泳B0502电化学分析B050201伏安法B050202极谱法B050203化学修饰电极B050204库伦分析B050205光谱电化学分析B050206电化学传感器B0503光谱分析B050301原子发射光谱（包括ICP）B050302原子吸收光谱B050303原子荧光光谱B050304X射线荧光光谱B050305分子发射光谱（包括荧光光谱、磷光光谱和化学B050306紫外和可见光谱B050307光声光谱B050308红外光谱B050309拉曼光谱B0504波谱分析B050401顺磁B050402核磁B0505质谱分析B050501有机质谱B050502无机质谱B0506化学分析B050601萃取剂、显色剂、特殊功能试剂B050602色谱柱固定相、分离膜B0507热分析B0508放射分析B050801活化分析B050802质子荧光B0509生化分析及生物传感B0510联用技术B0511采样、分离和富集方法B0512化学计量学B051201分析方法与计算机技术B051202分析讯号与数据解析B0513表面、微区、形态分析B051301表面分析B051302微区分析B051303形态分析B06化学工程及工业化学B0601化工热力学和基础数据B060101状态方程与溶液理论B060102相平衡B060103热化学B060104化学平衡B060105热力学理论模型和分子系统的计算机模拟B060106热力学数据和数据库B0602传递过程B060201化工流体力学和传递性质B060202传热过程及设备B060203传质过程B060204流变学B060205颗粒学及浆料化学B0603分离过程及设备B060301蒸馏B060302蒸发与结晶B060303干燥B060304吸收B060305萃取B060306吸附与离子交换B060307机械分离过程B060308膜分离B060309其他分离技术B0604化学反应工程B060401化学(催化)反应动力学B060402反应器原理及传递特性B060403反应器的模型化和优化B060404流态化技术和多相流反应工程B060405固定床反应工程B060406聚合反应工程B060407电化学反应工程B060408生化反应工程B060409催化剂工程B0605化工系统工程B060501化学过程的控制与模拟B060502化工系统的优化B060503化工过程动态学B0606无机化工B060601常规无机化工B060602工业电化学(电解、电镀、化学腐蚀与防腐)B060603精细无机(无机颜料、吸附剂及表面活性剂等) B060604核化工与放射化工B0607有机化工B060701工业有机化工B060702精细有机化工（染料、涂料、感光剂、粘合剂与B0608生物化工与食品化工B060801生化反应动力学及反应器B060802发酵物的提取和纯化B060803生化过程的化工模拟及人工器官B060804酶化工B060805天然产物和农副产品的化学改性及深度加工B060806生物医药工程B0609能源化工B060901煤化工B060902石油化工B060903燃料电池B060904其它能源化工B0610化工冶金B061001矿产资源的利用研究B061002化学选矿与浸出B061003湿法冶金物理化学B061004等离子体冶金B061005化学涂层B0611环境化工B061101环境治理中的物理化学原理B061102三废治理技术中的化工基础B061103环境友好的化工过程B061104可持续发展环境化工的新概念B07环境化学B0701环境分析化学B070101环境中微量生命元素及其化合物的分离、分析技B070102环境中微量有机污染物的分离、分析技术B0702环境污染化学B070201大气污染化学B070202水污染化学B070203土壤污染化学B070204固体废弃物及放射性核素污染化学B0703污染控制化学B070301化学控制、防治新工艺、新技术及其基础性研究B070302无害化工艺(原料、能源和资源的综合利用)B0704污染生态化学B0705理论环境化学B0706全球性环境化学问题C01基础生物学C0101微生物学C010101微生物分类学C01010101细菌分类C01010102放线菌分类C01010103真菌分类C010102微生物生理及生物化学C010103微生物遗传育种C010104微生物方法学C010105微生物资源与生态C010106应用微生物学基础C01010601工业微生物C01010602农业、土壤微生物C010107病毒学C01010701动物病毒C01010702植物病毒C01010703微生物病毒C010108医学与兽医微生物学C01010801病毒C01010802立克次氏体(含衣原体)C01010803病原细菌(含支原体与螺旋体)C01010804病原真菌C0102植物学C010201植物结构学C01020101植物形态解剖学C01020102植物形态发生C01020103植物胚胎学C010202植物系统学与分类学C01020201植物系统发育与演化C01020202种子植物分类C01020203孢子植物分类C01020204植物区系与地理学C010203植物生理学C01020301光合作用及固氮C01020302呼吸作用、采后生理及次生物质代谢C01020303矿质营养及有机物质运输C01020304水分生理及抗性生理C01020305植物激素、生长发育及生殖生理C010204植物资源学C01020401植物资源评价C01020402植物引种驯化C01020403植物种质保存C01020404资源植物化学C0103动物学C010301动物形态学C010302动物胚胎学C010303动物分类学C010304动物生理学C010305动物行为学C010306动物进化和动物遗传学C010307动物地理学C010309保护生物学C010310实验动物学C0104生物化学和分子生物学C010401生物分子的结构与功能、合成机理及调节过程C01040101蛋白质与肽C01040102核酸C01040103酶C01040104多糖及糖复合物C01040105激素C01040106天然产物化学C010402生物膜的结构与功能C010403无机生物化学C0105生物物理学与生物医学工程学C010501理论生物物理C01050101量子生物学C01050102生物信息论和生物控制论C01050103生物功能的计算机模拟、生物数学C01050104生命现象的生物物理理论阐述C010502环境生物物理C01050201电离辐射生物物理C01050202光生物物理C01050203电磁辐射生物物理C01050204声生物物理C01050205其它环境因素对生物的作用C01050206自由基生物学C010503生物组织的物理特性C01050301生物光学C01050302生物电磁学C01050303生物声学C01050304生物力学和生物流变学C01050305生物组织的其它物理特性C010504分子生物物理C01050401生物分子结构的运动性C01050402生物分子的相互作用C01050403生物分子中的能量传递与电子传递C010505膜与细胞生物物理C010506感官与神经生物物理C010507生物物理技术C010508生物物理学研究中的新概念和新方法C010509人工器官C010510生物医学信号处理C010511生物医学测量技术C010512生物系统的建模与应用C010513生物医学超声C010514生物医学传感技术C010515生物材料C010516生物医学图象C010517其它生物医学工程学研究C0106神经生物学C010601分子神经生物学C010602细胞神经生物学C010603系统神经生物学C010604高级神经生物学C010605比较神经生物学C010606发育神经生物学C010607感觉系统神经生物学C0107生理学C010701循环生理学C010702血液生理学C010703呼吸生理学C010704消化生理学C010705泌尿生理学C010706内分泌生理学C010707特殊环境生理学C010708生殖生理学C010709年龄生理学C0108心理学C010801心理学的基本过程研究C010802认知心理学C010803生物心理学C010804医学心理学(含精神卫生学)C010805工程心理学C010806发展与教育心理学C010807运动心理学C0109细胞生物学及发育生物学C010901细胞结构与功能C010902细胞增长、分裂与分化C010903模型动植物及实验体系的建立C010904细胞工程(生物技术和细胞培养) 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关于序列二次规划（SQP）算法求解非线性规划问题研究兰州大学硕士学位论文关于序列二次规划（SQP）算法求解非线性规划问题的研究姓名：石国春申请学位级别：硕士专业：数学、运筹学与控制论指导教师：王海明20090602兰州大学2009届硕士学位论文摘要非线性约束优化问题是最一般形式的非线性规划NLP问题，近年来，人们通过对它的研究，提出了解决此类问题的许多方法，如罚函数法，可行方向法，Quadratic及序列二次规划SequentialProgramming简写为SOP方法。

本文主要研究用序列二次规划SOP算法求解不等式约束的非线性规划问题。

SOP算法求解非线性约束优化问题主要通过求解一系列二次规划子问题来实现。

本文基于对大规模约束优化问题的讨论，研究了积极约束集上的SOP 算法。

我们在约束优化问题的s一积极约束集上构造一个二次规划子问题，通过对该二次规划子问题求解，获得一个搜索方向。

利用一般的价值罚函数进行线搜索，得到改进的迭代点。

本文证明了这个算法在一定的条件下是全局收敛的。

关键字：非线性规划，序列二次规划，积极约束集Hl兰州人学2009届硕二t学位论文AbstractNonlinearconstrainedarethemostinoptimizationproblemsgenericsubjectsmathematicalnewmethodsareachievedtosolveprogramming．Recently,Manyasdirectionit，suchfunction，feasiblemethod，sequentialquadraticpenaltyprogramming??forconstrainedInthisthemethodspaper,westudysolvinginequalityabyprogrammingalgorithm．optimizationproblemssequentialquadraticmethodaofSQPgeneratesquadraticprogrammingQPsequencemotivationforthisworkisfromtheofsubproblems．OuroriginatedapplicationsinanactivesetSQPandSQPsolvinglarge-scaleproblems．wepresentstudyforconstrainedestablishontheQPalgorithminequalityoptimization．wesubproblemsactivesetofthesearchdirectionisachievedQPoriginalproblem．AbysolvingandExactfunctionsaslinesearchfunctionsubproblems．wepresentgeneralpenaltyunderobtainabetteriterate．theofourisestablishedglobalconvergencealgorithmsuitableconditions．Keywords：nonlinearprogramming，sequentialquadraticprogrammingalgorithm，activesetlv兰州大学2009届硕士学位论文原创性声明本人郑重声明：本人所呈交的学位论文，是在导师的指导下独立进行研究所取得的成果。

第４０卷第１７期２０２０年９月生态学报ＡＣＴＡＥＣＯＬＯＧＩＣＡＳＩＮＩＣＡＶｏｌ．４０，Ｎｏ．１７Ｓｅｐ．，２０２０基金项目：国家自然科学基金项目（３１６００３９５）；云南省高原湿地科学创新团队项目（２０１２ＨＣ００７）收稿日期：２０１９⁃０５⁃１７；㊀㊀修订日期：２０２０⁃０３⁃１８∗通讯作者Ｃｏｒｒｅｓｐｏｎｄｉｎｇａｕｔｈｏｒ．Ｅ⁃ｍａｉｌ：ｚｈａｎｇｙｕｎｃｏｏｌ＠１６３．ｃｏｍＤＯＩ：１０．５８４６／ｓｔｘｂ２０１９０５１７１０１９曹仁杰，尹定财，田昆，肖德荣，李志军，张绪岗，李泽辉，张贇．丽江老君山海拔上限长苞冷杉（Ａｂｉｅｓｇｅｏｒｇｅｉ）和云南铁杉（Ｔｓｕｇａｄｕｍｏｓａ）径向生长对气候变化的响应．生态学报，２０２０，４０（１７）：６０６７⁃６０７６．ＣａｏＲＪ，ＹｉｎＤＣ，ＴｉａｎＫ，ＸｉａｏＤＲ，ＬｉＺＪ，ＺｈａｎｇＸＧ，ＬｉＺＨ，ＺｈａｎｇＹ．ＲｅｓｐｏｎｓｅｏｆｒａｄｉａｌｇｒｏｗｔｈｏｆＡｂｉｅｓｇｅｏｒｇｅｉａｎｄＴｓｕｇａｄｕｍｏｓａｔｏｃｌｉｍａｔｅｃｈａｎｇｅａｔｕｐｐｅｒｄｉｓｔｒｉｂｕｔｉｏｎａｌｌｉｍｉｔｓｏｎＬａｏｊｕｎＭｏｕｎｔａｉｎ，Ｌｉｊｉａｎｇ，Ｙｕｎｎａｎ，Ｃｈｉｎａ．ＡｃｔａＥｃｏｌｏｇｉｃａＳｉｎｉｃａ，２０２０，４０（１７）：６０６７⁃６０７６．丽江老君山海拔上限长苞冷杉（Ａｂｉｅｓｇｅｏｒｇｅｉ）和云南铁杉（Ｔｓｕｇａｄｕｍｏｓａ）径向生长对气候变化的响应曹仁杰１，尹定财１，田㊀昆１，肖德荣１，李志军２，张绪岗２，李泽辉２，张㊀贇１，∗１西南林业大学国家高原湿地研究中心，昆明㊀６５０２２４２大理剑川剑湖湿地省级自然保护区管护局，剑川㊀６７１３００摘要：基于树木年轮学方法，利用丽江老君山海拔上限长苞冷杉（Ａｂｉｅｓｇｅｏｒｇｅｉ）和云南铁杉（Ｔｓｕｇａｄｕｍｏｓａ）树轮宽度资料，构建差值年表，运用响应函数和滑动响应分析研究树木径向生长与气温和降水的相关关系及其稳定性，进而阐明影响该区域２个针叶树种径向生长的主要气候要素㊂结果表明：２个树种对降水累积效应的响应较为一致，对逐月气候因子的响应存在差异，相关关系较为稳定，具体表现为（１）上年１１月平均温升高和当年生长季盛期（７ ８月）降水增加有利于老君山海拔上限长苞冷杉生长；（２）云南铁杉径向生长与当年３月㊁树木休眠期（１ ３月）㊁生长季盛期（７ ８月）的降水表现为显著正相关关系，与上年７月与当年５月的气温及当年生长季末期（９ １０月）降水呈显著负相关；（３）上述相关关系的稳定性较强，在全部或大部分分析时段（１９５１ ２０１７）内达到显著相关，云南铁杉的稳定性更强㊂研究结果可为气候变化背景下滇西北高原树木生长的管理及森林生态系统的保护提供理论依据㊂关键词：树木年轮；气候响应；海拔上限；滇西北高原ＲｅｓｐｏｎｓｅｏｆｒａｄｉａｌｇｒｏｗｔｈｏｆＡｂｉｅｓｇｅｏｒｇｅｉａｎｄＴｓｕｇａｄｕｍｏｓａｔｏｃｌｉｍａｔｅｃｈａｎｇｅａｔｕｐｐｅｒｄｉｓｔｒｉｂｕｔｉｏｎａｌｌｉｍｉｔｓｏｎＬａｏｊｕｎＭｏｕｎｔａｉｎ，Ｌｉｊｉａｎｇ，Ｙｕｎｎａｎ，ＣｈｉｎａＣＡＯＲｅｎｊｉｅ１，ＹＩＮＤｉｎｇｃａｉ１，ＴＩＡＮＫｕｎ１，ＸＩＡＯＤｅｒｏｎｇ１，ＬＩＺｈｉｊｕｎ２，ＺＨＡＮＧＸｕｇａｎｇ２，ＬＩＺｅｈｕｉ２，ＺＨＡＮＧＹｕｎ１，∗１ＮａｔｉｏｎａｌＰｌａｔｅａｕＷｅｔｌａｎｄｓＲｅｓｅａｒｃｈＣｅｎｔｅｒ，ＳｏｕｔｈｗｅｓｔＦｏｒｅｓｔｒｙＵｎｉｖｅｒｓｉｔｙ，Ｋｕｎｍｉｎｇ６５０２２４，Ｃｈｉｎａ２ＤａｌｉＪｉａｎｃｈｕａｎＪｉａｎｈｕＷｅｔｌａｎｄＰｒｏｖｉｎｃｉａｌＮａｔｕｒｅＲｅｓｅｒｖｅ，Ｊｉａｎｃｈｕａｎ６７１３００，ＣｈｉｎａＡｂｓｔｒａｃｔ：Ｂａｓｅｄｏｎｔｈｅｄｅｎｄｒｏｃｈｒｏｎｏｌｏｇｉｃａｌｍｅｔｈｏｄ，ｔｒｅｅｗｉｄｔｈｄａｔａｏｆＡｂｉｅｓｇｅｏｒｇｅｉａｎｄＴｓｕｇａｄｕｍｏｓａａｔｔｈｅｉｒｕｐｐｅｒｄｉｓｔｒｉｂｕｔｉｏｎａｌｌｉｍｉｔｉｎＬａｏｊｕｎＭｏｕｎｔａｉｎｗｅｒｅｕｓｅｄｔｏｄｅｖｅｌｏｐｔｒｅｅ⁃ｒｉｎｇｒｅｓｉｄｕａｌｃｈｒｏｎｏｌｏｇｉｅｓ．Ｉｎｏｒｄｅｒｔｏｃｌａｒｉｆｙｔｈｅｍａｉｎｃｌｉｍａｔｉｃｆａｃｔｏｒｓａｆｆｅｃｔｉｎｇｔｈｅｒａｄｉａｌｇｒｏｗｔｈｏｆｔｗｏｃｏｎｉｆｅｒｓｐｅｃｉｅｓ，ｗｅｕｓｅｄｒｅｓｐｏｎｓｅｆｕｎｃｔｉｏｎａｎｄｍｏｖｉｎｇｉｎｔｅｒｖａｌａｎａｌｙｓｉｓｔｏｓｔｕｄｙｒｅｌａｔｉｏｎｓｈｉｐｓｂｅｔｗｅｅｎｃｈｒｏｎｏｌｏｇｉｅｓａｎｄｔｅｍｐｅｒａｔｕｒｅａｎｄｐｒｅｃｉｐｉｔａｔｉｏｎ，ａｎｄｔｈｅｓｔａｂｉｌｉｔｙｏｆｔｈｅｒｅｌａｔｉｏｎｓｈｉｐｓ．Ｔｈｅｒｅｓｕｌｔｓｓｈｏｗｅｄｔｈａｔｔｈｅｒｅｓｐｏｎｓｅｏｆｔｈｅｔｗｏｔｒｅｅｓｐｅｃｉｅｓｗａｓｃｏｎｓｉｓｔｅｎｔｉｎｃｕｍｕｌａｔｉｖｅｅｆｆｅｃｔｓｏｆｐｒｅｃｉｐｉｔａｔｉｏｎ，ｂｕｔｄｉｆｆｅｒｅｎｔｉｎｍｏｎｔｈｌｙｃｌｉｍａｔｉｃｆａｃｔｏｒｓ，ａｎｄｔｈｅｒｅｌａｔｉｏｎｓｈｉｐｓｗｅｒｅｓｔａｂｌｅ．Ｔｈｅｄｅｔａｉｌｒｅｓｕｌｔｓｗｅｒｅａｓｆｏｌｌｏｗｓ：（１）Ｎｏｖｅｍｂｅｒｍｅａｎｔｅｍｐｅｒａｔｕｒｅｉｎｌａｓｔｙｅａｒａｎｄｇｒｏｗｉｎｇｓｅａｓｏｎ（Ｊｕｌｙ Ａｕｇｕｓｔ）ｐｒｅｃｉｐｉｔａｔｉｏｎｉｎｃｕｒｒｅｎｔｙｅａｒｐｒｏｍｏｔｅｄｔｈｅｒａｄｉａｌｇｒｏｗｔｈｏｆＡ．ｇｅｏｒｇｅｉａｔｔｈｅｕｐｐｅｒｄｉｓｔｒｉｂｕｔｉｏｎａｌｌｉｍｉｔ．（２）ＴｈｅｒａｄｉａｌｇｒｏｗｔｈｏｆＴ．ｄｕｍｏｓａｗａｓｓｉｇｎｉｆｉｃａｎｔｌｙａｎｄｐｏｓｉｔｉｖｅｌｙｃｏｒｒｅｌａｔｅｄｗｉｔｈｔｈｅｐｒｅｃｉｐｉｔａｔｉｏｎｉｎＭａｒｃｈ，ｔｈｅｄｏｒｍａｎｔｐｅｒｉｏｄ（Ｊａｎｕａｒｙ Ｍａｒｃｈ）ａｎｄｇｒｏｗｉｎｇｓｅａｓｏｎｏｆｃｕｒｒｅｎｔｙｅａｒ，ｂｕｔｔｈｅｇｒｏｗｔｈｗａｓ８６０６㊀生㊀态㊀学㊀报㊀㊀㊀４０卷㊀ｓｉｇｎｉｆｉｃａｎｔｌｙａｎｄｎｅｇａｔｉｖｅｌｙｃｏｒｒｅｌａｔｅｄｗｉｔｈＪｕｌｙｔｅｍｐｅｒａｔｕｒｅｉｎｌａｓｔｙｅａｒ，Ｍａｙｔｅｍｐｅｒａｔｕｒｅａｎｄｐｏｓｔ ｇｒｏｗｉｎｇｓｅａｓｏｎ（Ｓｅｐｔｅｍｂｅｒ Ｏｃｔｏｂｅｒ）ｐｒｅｃｉｐｉｔａｔｉｏｎｉｎｃｕｒｒｅｎｔｙｅａｒ．（３）Ｔｈｅｒｅｌａｔｉｏｎｓｈｉｐｓｂｅｔｗｅｅｎｒａｄｉａｌｇｒｏｗｔｈａｎｄｃｌｉｍａｔｉｃｆａｃｔｏｒｓｗｅｒｅｓｔａｂｌｅｂｙｐｒｅｓｅｎｔｉｎｇｓｉｇｎｉｆｉｃａｎｔｃｏｒｒｅｌａｔｉｏｎｓｉｎｍｏｓｔｏｒｗｈｏｌｅａｎａｌｙｓｉｓｐｅｒｉｏｄｓ（１９５１ ２０１７），ａｎｄｔｈｅｓｔａｂｉｌｉｔｙｏｆＴ．ｄｕｍｏｓａｗａｓｓｔｒｏｎｇｅｒｔｈａｎＡ．ｇｅｏｒｇｅｉ．ＴｈｅｒｅｓｕｌｔｏｆｔｈｉｓｐａｐｅｒｃａｎｐｒｏｖｉｄｅａｔｈｅｏｒｅｔｉｃａｌｂａｓｉｓｆｏｒｔｈｅｐｒｅｄｉｃｔｉｏｎｏｆｔｒｅｅｇｒｏｗｔｈａｎｄｔｈｅｍａｎａｇｅｍｅｎｔａｎｄｐｒｏｔｅｃｔｉｏｎｏｆｆｏｒｅｓｔｅｃｏｓｙｓｔｅｍｓｉｎｔｈｅｎｏｒｔｈｗｅｓｔｅｒｎＹｕｎｎａｎＰｌａｔｅａｕｕｎｄｅｒｔｈｅｂａｃｋｇｒｏｕｎｄｏｆｃｌｉｍａｔｅｃｈａｎｇｅ．ＫｅｙＷｏｒｄｓ：ｔｒｅｅ⁃ｒｉｎｇ；ｃｌｉｍａｔｅｒｅｓｐｏｎｓｅ；ｔｈｅｕｐｐｅｒｄｉｓｔｒｉｂｕｔｉｏｎａｌｌｉｍｉｔ；ＮｏｒｔｈｗｅｓｔｅｒｎＹｕｎｎａｎＰｌａｔｅａｕ气候变化已经从局地㊁区域和全球等不同空间尺度上影响着树木生长［１⁃４］㊂树木生长受遗传和环境因子的共同影响，是多种生态因子共同作用的结果，运用树木年轮学方法筛除树种原生遗传因子和生长趋势等非气候因子影响后，年轮宽度指数将保留对应年份的气候信息［５］，因此树木年轮已广泛应用于树木生长对气候变化的响应研究［６⁃８］和古气候的重建［５］㊂海拔上限的自然环境恶劣，是树木垂直分布的界限㊂因而该区域树木生长对环境变化敏感，以往研究结果表明气温是影响海拔上限树木径向生长的主要气候因子［９⁃１０］，但受地区限制因子差异及局地环境影响，这一规律存在局限性㊂例如：刘敏等发现影响长白山自然保护区内高海拔红松（Ｐｉｎｕｓｋｏｒａｉｅｎｓｉｓ）径向生长的主要气候因子是当年生长季帕尔默干旱指数和降水［１１］㊂曹宗英等发现祁连山中段海拔上限青海云杉（Ｐｉｃｅａｃｒａｓｓｉｆｏｌｉａ）径向生长受降水和气温共同影响［１２］㊂宋文琦等发现影响青藏高原都兰地区高海拔祁连圆柏（Ｓａｂｉｎａｐｒｚｅｗａｌｓｋｉｉ）主要受降水的影响［１３］㊂杨绕琼等发现玉龙雪山高海拔限制云南松（Ｐｉｎｕｓｙｕｎｎａｎｅｎｓｉｓ）径向生长的主要气候因子为夏季降水［１４］㊂因而海拔上限树木径向生长和气候因子关系的研究，有助于揭示不同地区树木生长对气候变化的响应规律㊂滇西北高原地处青藏高原东南缘，生物多样性丰富［１５］，是典型的气候敏感区，适合开展树木年轮学研究，前人已在白马雪山㊁石卡雪山㊁普达措国家公园㊁哈巴雪山㊁玉龙雪山等地开展了较多海拔上限的树轮研究工作㊂Ｆａｎ等发现白马雪山海拔上限长苞冷杉（Ａｂｉｅｓｇｅｏｒｇｅｉ）径向生长主要受夏季气温影响［１６］㊂张贇等发现石卡雪山海拔上限长苞冷杉径向生长仅受７月气温影响，高山松（Ｐｉｎｕｓｄｅｎｓａｔａ）径向生长受上年１０月平均温影响［１７⁃１８］，普达措国家公园海拔上限长苞冷杉与丽江云杉（Ｐｉｃｅａｌｉｋｉａｎｇｅｎｓｉｓ）径向生长仅受气温影响［１９］，哈巴雪山海拔上限长苞冷杉径向生长主要受上年１１月气温和当年９月降水的影响，大果红杉（Ｌａｒｉｘｐｏｔａｎｉｎｉｉ）受当年９月降水的影响［２０］，玉龙雪山海拔上限处长苞冷杉与丽江云杉受气温和降水的共同影响［２１］㊂上述研究表明，滇西北高原海拔上限树木生长对气候的响应存在差异，这种差异既表现在不同地区的同一树种，也存在于同一地区的不同树种㊂在由北至南的纬度梯度上，由单一气温影响转变为气温与降水共同作用㊂老君山是滇西北高原南部生态系统保存完好的一座典型高山，该地区已开展表层土壤花粉与植被关系研究［２２］㊁植物景观资源开发与保护研究［２３］，但对于树木径向生长和环境因子关系的相关研究较少㊂长苞冷杉与云南铁杉（Ｔｓｕｇａｄｕｍｏｓａ）是丽江老君山的主要树种［２２］，也是滇西北亚高山森林的主要组成㊂长苞冷杉耐荫寒㊁喜湿润，云南铁杉喜温凉㊁不耐旱［２４］㊂对生物学习性不同的树种开展树木年轮研究，更有助于揭示影响该地区树木生长的关键气候因子及其响应机制㊂本文以老君山为研究地点，选取长苞冷杉和云南铁杉为研究对象，根据树木年轮学方法建立２个树种海拔上限的树轮差值年表，通过相关分析研究其对气温和降水的响应特征及其稳定性，从而阐明影响老君山２个树种径向生长的关键气候要素，为老君山树木生长管理和森林保护提供科学依据㊂１㊀材料与方法１．１㊀研究区域概况老君山位于玉龙纳西族自治县㊁剑川县与兰坪白族普米族自治县等交界处，地理坐标介于２６ʎ３８ᶄ２７ʎ１５ᶄＮ，９９ʎ０７ᶄ １００ʎ００ᶄＥ之间（图１），海拔２１００ ４５１５ｍ，总面积约为１３２４ｋｍ２［２２］㊂其地处滇西北高原山系南段云岭主脉中支纵谷区㊁世界自然遗产 三江并流 带的南端㊂区内植物区系地理成分复杂，植物种类丰富，森林类型多样，是滇西北高原生物多样性热点地区的腹地，也是中国原生生态系统保存最为完好和全球最具代表性的生态系统之一［２５］㊂图１㊀研究区域位置Ｆｉｇ．１㊀ＬｏｃａｔｉｏｎｏｆｓｔｕｄｙａｒｅａｉｎｔｈｅＬａｏｊｕｎＭｏｕｎｔａｉｎｏｆＬｉｊｉａｎｇ，ＹｕｎｎａｎＡｂｉ：长苞冷杉，Ａｂｉｅｓｇｅｏｒｇｅｉ；Ｔｓｕ：云南铁杉，Ｔｓｕｇａｄｕｍｏｓａ老君山植被垂直地带性显著，依次为落叶阔叶林㊁针阔混交林㊁常绿阔叶林㊁亚高山针叶林［２２］㊂云南铁杉生长在海拔２５００ ３５００ｍ的针阔混交林［２３］，长苞冷杉生长在海拔３０００ ４０００ｍ的亚高山针叶林［２２］㊂研究区气候受印度洋西南季风㊁太平洋东南季风和青藏高原气团的交错影响㊂根据云南丽江气象站（２６．８７ʎＮ，１００．２２ʎＥ，海拔２３９３ｍ）１９５１ ２０１７年气象资料显示，区域年平均温１２．７５ħ，最热月６月平均温１８．１７ħ，最冷月１月平均温６．１０ħ㊂区域年平均降水量９６４．６８ｍｍ，季节分布不均，主要集中于６ ９月，占全年降水的８０．８２％（图２）㊂１．２㊀样品采集与年表建立２０１８年６月，在老君山２个树种的海拔上限分别设立样点开展年轮采集工作㊂样点设置在未受人为干扰的森林群落，用生长锥在每棵树胸高位置（距离地面１．３ｍ处）采集树芯，即沿山坡平行方向钻取２个样芯，装入事先准备好的塑料管内，对同一颗树的２棵样芯配对打包并标记，分别取样２８棵长苞冷杉和３２棵云南铁杉（表１）㊂表１㊀采样点概况Ｔａｂｌｅ１㊀Ｄｅｓｃｒｉｐｔｉｏｎｏｆｓａｍｐｌｉｎｇｓｉｔｅｓ树种Ｓｐｅｃｉｅｓ采样时间Ｓａｍｐｌｉｎｇｄａｔｅ海拔／ｍＡｌｔｉｔｕｄｅ／ｍ经度／ＥＬｏｎｇｉｔｕｄｅ／Ｅ纬度／ＮＬａｔｉｔｕｄｅ／Ｎ样本量（树／样芯）Ｎｏ．（ｔｒｅｅ／ｃｏｒｅ）长苞冷杉Ａｂｉｅｓｇｅｏｒｇｅｉ２０１８．０６３８１０９９ʎ４４ᶄ２６ʎ３８ᶄ２８／５３云南铁杉Ｔｓｕｇａｄｕｍｏｓａ２０１８．０６３５０２９９ʎ４８ᶄ２６ʎ３３ᶄ３２／６２９６０６㊀１７期㊀㊀㊀曹仁杰㊀等：丽江老君山海拔上限长苞冷杉和云南铁杉径向生长对气候变化的响应㊀０７０６㊀生㊀态㊀学㊀报㊀㊀㊀４０卷㊀图２㊀云南丽江气象站气象资料（１９５１ ２０１７）Ｆｉｇ．２㊀ＣｌｉｍａｔｅｄａｔｅｆｒｏｍＹｕｎｎａｎＬｉｊｉａｎｇＭｅｔｅｏｒｏｌｏｇｉｃａｌＳｔａｔｉｏｎ（１９５１ ２０１７）将样本带回实验室，从塑料管内取出树芯，并用白乳胶固定在定制的木槽内，待其自然风干后，依次用由粗到细的砂纸对树芯进行打磨，直到用肉眼可以清晰分辨出年轮㊂先将样芯放在双筒显微镜下进行目视定年，后置于ＥＰＳＯＮＳｃａｎ（Ｅｓｐｒｅｓｓｉｏｎ１１０００ＸＬ）扫描仪中进行扫描并对样芯编号，扫描仪参数设定为专业模式图像类型２４位全彩，分辨率为３２００ｄｐｉ，扫描后的图像利用ＣＤｅｎｄｒｏａｎｄＣｏｏＲｅｃｏｒｅｒｖｅｒ７．３［２６］软件测量年轮宽度，精度为０．００１ｍｍ㊂进一步用ＣＯＦＥＣＨＡ程序［２７］将测量结果进行检验，剔除断裂㊁破损等质量较差的样本，最终保留５０根长苞冷杉和６１根云南铁杉树芯进入主序列㊂运用ＡＲＳＴＡＮ程序建立年表，拟合采用步长为样本长度６７％的样条函数，去除树木本身个体差异的影响（例如遗传因子和干扰竞争）㊂最终建立了丽江老君山长苞冷杉和云南铁杉的标准年表（ＳＴＤ），差值年表（ＲＥＳ，图３）和自回归年表（ＡＲＳ）㊂通过对比统计特征值，确定本研究采用拥有更多高频信息的差值年表［２８］，并与主要气候要素（气温和降水）进行相关分析㊂１．３㊀气象资料的获取在中国气象科学数据共享网（ｈｔｔｐ：／／ｄａｔａ．ｃｍａ．ｃｎ／）获取距离老君山最近的丽江气象站（２６．８７ʎＮ，１００．２２ʎＥ，海拔２３９３ｍ，直线距离９５ｋｍ左右）的气候信息，资料时段为１９５１ ２０１７年，包括月平均气温和月平均降水㊂根据以往该区域树木年轮学研究成果Ｐａｎｔｈｉ等［２４］㊁Ｌｉａｎｇ等［２９］㊁Ｆａｎ等［３０］㊁徐宁等［３１］，气象站数据能够较好的应用于海拔梯度上树木生长对气候变化的响应研究，本文亦利用丽江气象站数据进行老君山长苞冷杉和云南铁杉与气候因子的相关分析，选用气温和降水２个气候指标分析与年表的相关性㊂１．４㊀数据分析因为气候对树木生长具有滞后效应［３２］，所以本次研究选取上年７月至当年１０月的平均气温和降水与２个树种的差值年表进行逐月响应分析，同时研究树木不同生长季（１ ３月为树木休眠期，４ ６月为生长季图３㊀树轮宽度差值年表Ｆｉｇ．３㊀Ｒｅｓｉｄｕａｌｔｒｅｅ⁃ｒｉｎｇｃｈｒｏｎｏｌｏｇｙ早期，７ ８月为树木生长季盛期，９ １０月为树木生长季末期）对气温和降水的响应㊂响应函数对气候要素先提取主成分量再进行回归分析，能够更加准确的反映出样本数据受环境因子的影响程度，分析软件选用ＤｅｎｄｒｏＣｌｉｍ２００２软件完成㊂同时运用ＤｅｎｄｒｏＣｌｉｍ２００２中的ＥｖｏｌｕｔｉｏｎａｒｙａｎｄＭｏｖｉｎｇＲｅｓｐｏｎｓｅａｎｄＣｏｒｒｅｌａｔｉｏｎ模块，窗口年限选择３２年，分别选向前和向后滑动，分析两个树种径向生长与气温和降水的动态关系，以确定树木径向生长与气候要素响应关系间的稳定性㊂绘图由ＳｉｇｍａＰｌｏｔ１０．０完成㊂２㊀结果与分析２．１㊀年表的统计特征长苞冷杉和云南铁杉年表统计参数及公共区间所示（表２），建立的长苞冷杉和云南铁杉差值年表均对２个气候要素具有较高敏感性，公共区间（１９５１ ２０１７年）统计量中平均敏感度分别为０．１３和０．１４，信噪比为１２．３９％和２０．３８％，第一主成分的方差解释量为３１．７２％和３４．７５％，样本总体代表性为０．９３和０．９５（都高于０．８５），表明建立的长苞冷杉和云南铁杉的差值年表质量较好，适合用于与气候要素的分析㊂表２㊀年表统计参数及公共区间分析Ｔａｂｌｅ２㊀Ｓｔａｔｉｓｔｉｃｓｏｆｒｉｎｇ—ｗｉｄｔｈｃｈｒｏｎｏｌｏｇｉｅｓａｎｄｃｏｍｍｏｎｉｎｔｅｒｖａｌａｎａｌｙｓｉｓ统计特征Ｓｔａｔｉｓｔｉｃｃｈａｒａｃｔｅｒｓ长苞冷杉Ａｂｉｅｓｇｅｏｒｇｅｉ云南铁杉Ｔｓｕｇａｄｕｍｏｓａ样本量（树／样芯）Ｎｏ．（ｔｒｅｅ／ｃｏｒｅ）２８／５０３２／６１序列长度Ｔｉｍｅｓｐａｎ／Ａ．Ｄ１７６１ ２０１７１８１２ ２０１７ＥＰＳ＞０．８５起始年样芯数ＹｅａｒｓｉｎｃｅＥＰＳ＞０．８５／ｃｏｒｅｓ１８４５／１７１８９６／１３平均敏感度Ｍｅａｎｓｅｎｓｉｔｉｖｉｔｙ０．１３０．１４公共区间（１９５１ ２０１７年）统计量Ｃｏｍｍｏｎｉｎｔｅｒｖａｌａｎａｌｙｓｉｓ（１９５１ ２０１７）标准差Ｓｔａｎｄａｒｄｄｅｖｉａｔｉｏｎ０．１１０．１２信噪比Ｓｉｇｎａｌ⁃ｔｏ⁃ｎｏｉｓｅｒａｔｉｏ１２．３９％２０．３８％样本总体代表性Ｅｘｐｒｅｓｓｅｄｐｏｐｕｌａｔｉｏｎｓｉｇｎａｌ０．９３０．９５第一主成分方差解释量Ｖａｒｉａｎｃｅｉｎｆｉｒｓｔｅｉｇｅｎｖｅｃｔｏｒ／％３１．７２％３４．７５％２．２㊀径向生长对气候要素的响应长苞冷杉和云南铁杉差值年表与逐月气温和降水的响应分析结果表明（图４），长苞冷杉径向生长与上年１１月平均气温呈显著正相关，云南铁杉径向生长与上年７月㊁当年５月气温呈显著负相关，与当年３月降水呈显著正相关㊂与生长季气候要素的响应分析结果表明，长苞冷杉径向生长与当年生长季盛期降水呈显著正相关，云南１７０６㊀１７期㊀㊀㊀曹仁杰㊀等：丽江老君山海拔上限长苞冷杉和云南铁杉径向生长对气候变化的响应㊀铁杉径向生长与当年休眠期㊁生长季盛期㊁生长季末期降水表现出显著相关关系，当年休眠期和生长季盛期降水促进其生长，当年生长季末期降水则抑制生长㊂图４㊀差值年表与气候因子的相关关系Ｆｉｇ．４㊀ＲｅｌａｔｉｏｎｓｈｉｐｓｂｅｔｗｅｅｎｒｅｓｉｄｕａｌｃｈｒｏｎｏｌｏｇｉｅｓａｎｄｃｌｉｍａｔｉｃｆａｃｔｏｒｓＰ：上年；∗：达到０．０５水平的显著相关；ＰＰＧ：上年生长季末期，ｐｒｅｖｉｏｕｓｐｏｓｔ⁃ｇｒｏｗｉｎｇｓｅａｓｏｎ；ＤＧ：休眠期，ｄｏｒｍａｎｔｇｒｏｗｉｎｇｓｅａｓｏｎ；ＥＧ：生长季前期，ｅａｒｌｙｇｒｏｗｉｎｇｓｅａｓｏｎ；Ｇ：生长季盛期，ｇｒｏｗｉｎｇｓｅａｓｏｎ；ＰＧ：生长季末期，ｐｏｓｔ⁃ｇｒｏｗｉｎｇｓｅａｓｏｎ２．３㊀径向生长与气候要素的动态关系滑动分析结果表明，海拔上限处长苞冷杉径向生长与上年１１月气温㊁当年生长季盛期降水的响应关系稳定，在分析时段内均达到显著正相关㊂长苞冷杉对当年生长季盛期降水的稳定性有明显的上升趋势，响应系数从１９５１年的０．１３５上升至２０１７年的０．３３９㊂云南铁杉径向生长与休眠期和生长季末期降水有非常强的稳定性，分析时段内均达到显著正相关㊂与休眠期降水的显著正相关呈下降趋势（响应系数从１９５１年的０．２７８降至２０１７年的０．１２９）；与生长季末期降水的显著负相关关系加强（响应系数从１９５１年的 ０．１２７降至２０１７年的 ０．１８４）；与上年７月气温㊁当年５月的气温㊁生长期降水的稳定性较强，在大部分的时间内达到显著相关；与当年３月降水的稳定性相对较弱，在部分时间段内达到显著正相关（图５）㊂３㊀讨论３．１㊀２个树种径向生长对气候响应的共性２个树种径向生长都与当年生长季盛期降水呈显著正相关关系，这是因为夏季是树木生长的旺季，生长季充足的降水能够保证夏季土壤具有良好的水分状况，有利于树木进行光合作用并提供生长所需的有机物［３３］㊂生长季降水量与树木径向生长通常呈正相关［３４］，较高的含水量为植物组织提供较好的生理代谢环境［３５］㊂在邻近区域川西亚高山森林岷江冷杉（Ａｂｉｅｓｆａｘｏｎｉａｎａ）的树木年轮学研究中也有相似结果［３６］㊂２７０６㊀生㊀态㊀学㊀报㊀㊀㊀４０卷㊀图５㊀树轮宽度差值年表与气候要素的滑动响应分析Ｆｉｇ．５㊀Ｍｏｖｉｎｇｉｎｔｅｒｖａｌｒｅｓｐｏｎｓｅａｎａｌｙｓｉｓｂｅｔｗｅｅｎｔｈｅｒｅｓｉｄｕａｌｃｈｒｏｎｏｌｏｇｉｅｓａｎｄｃｌｉｍａｔｉｃｆａｃｔｏｒｓａ：长苞冷杉与上年１１月气温；ｂ：云南铁杉与上年７月气温；ｃ：云南铁杉与当年５月气温；ｄ：云南铁杉与当年３月降水；ｅ：长苞冷杉与生长季盛期降水；ｆ：云南铁杉与休眠期降水；ｇ：云南铁杉与生长季盛期降水；ｈ：云南铁杉与生长季末期降水当年休眠期降水的增加有利于长苞冷杉和云南铁杉径向生长，这种作用在云南铁杉上更为突出（在３月及１ ３月都表现出显著性）㊂老君山１ ３月降水以降雪为主，降雪多积雪厚，可形成保温层，客观上保护了树木根系，有利于树木度过冻害期，并在气温回暖后更好的生长［３７］㊂另一方面积雪融化后会给树木生长季前期提供充足的水分储备［３８］，在相邻的玉龙雪山不同海拔云南铁杉㊁长苞冷杉与丽江云杉［２９，３９］㊁香格里拉普达措海拔上限大果红杉［２０］㊁川西王朗自然保护区的岷江冷杉树轮研究中也有类似发现［２１，４０］，说明冬季降雪在３７０６㊀１７期㊀㊀㊀曹仁杰㊀等：丽江老君山海拔上限长苞冷杉和云南铁杉径向生长对气候变化的响应㊀４７０６㊀生㊀态㊀学㊀报㊀㊀㊀４０卷㊀该区域树木生长中的重要保护作用㊂另外，在日本中部亚高山林线［４１］㊁美国北卡斯克德山脉的亚高山针叶林［４２］㊁欧洲奥地利亚高山树线［４３］也有同样结论，表明冬季降雪是海拔上限树木生长的重要影响因子㊂２个树种还与当年生长季末期降水呈负相关关系（其中云南铁杉表现出显著性），生长季末期气温下降速度快，降雨常常伴随着低温且云量增大，导致太阳辐射减弱，降低树木的光合作用速率，有机物产量减少，不利于树木径向生长［１６］㊂相似结果在其他冷杉属植物及相邻地区的树轮研究中有所报道，例如西藏林芝的喜马拉雅冷杉（Ａｂｉｅｓｐｉｎｄｒｏｗ）［４４］㊁神农架的巴山冷杉（Ａｂｉｅｓｆａｒｇｅｓｉｉ）［４５］㊁哈巴雪山的大果红杉［２０］㊁王朗自然保护区的紫果云杉（Ｐｉｃｅａｐｕｒｐｕｒｅａ）［４６］等研究中也有同样结论㊂３．２㊀２个树种径向生长对气候响应的差异长苞冷杉表现出与上年１１月平均气温的显著正相关，这可能与上年生长季末期气温升高增强光合作用速率有关［４７］㊂丽江１１月的气温较低，树木已基本停止生长，但仍有较弱的生理活动，此时的高温能够提高长苞冷杉光合作用速率，促进有机物质的合成与储存，为下年的树木生长创造有利条件［１９］㊂１１月的高温客观上延长了长苞冷杉的生长季，使其有更多的时间贮存养分，以供来年生长［２１］㊂在相邻白马雪山的长苞冷杉［２９］㊁石卡雪山的高山松［４８］㊁川西亚高山岷江冷杉［３６］都有同样结论，说明上年１１月平均气温是影响老君山海拔上限长苞冷杉径向生长的关键气候要素㊂云南铁杉表现出与上年７月㊁当年５月气温的显著负相关，７月气温升高在促进光合作用的同时，也消耗了大量有机物，不利于营养物积累［４９］，从而影响来年生长季初期云南铁杉的生长㊂与当年５月气温的显著负相关，表明当年生长季前期气温升高不利于云南铁杉的径向生长㊂在一些水分受到限制的区域，生长季前期的气温升高将会增强植物的蒸散作用，降低水分可利用性，形成水分胁迫，从而限制树木生长［５０］，甚至增加树木的死亡率［５１］㊂老君山５月气温高，降水相对较少，增加了蒸发速率，造成干旱，因此树木径向生长受到影响㊂这与相邻玉龙雪山云南铁杉［５２］以及川西米亚罗林区南方铁杉（Ｔｓｕｇａｃｈｉｎｅｎｓｉｓ）［５３］的树轮学研究结果一致，说明铁杉容易受春季干旱的不利影响㊂３．３㊀２个树种径向生长与气候要素的稳定性分析总体而言，２个树种与气候因子关系的稳定性较强，在全部或大部分分析时段内能达到显著相关，说明２个树种对气候变化较为敏感，是树木年轮学研究的适宜树种㊂同时，短期气候变化也会对树木生长产生影响，例如：１９５１年以来生长季盛期降水的增加促进了长苞冷杉生长，尤其是１９６７ ２００２年降水显著增加时期（图６），相关系数数值上升趋势更为明显㊂而１９９２ ２０１２年时间段内，休眠期降水的持续下降（图６）减弱了其与云南铁杉的显著正相关关系㊂图６㊀与稳定性相关的气候数据Ｆｉｇ．６㊀Ｃｌｉｍａｔｅｄａｔａｒｅｌａｔｅｄｔｏｓｔａｂｉｌｉｔｙ４㊀结论老君山海拔上限长苞冷杉和云南铁杉的径向生长受上年和当年的气温和降水共同影响，这与高海拔树木生长主要受气温影响的传统认识不同，因而可为不同地区高海拔树木生长与气候因子关系研究提供参考㊂２个树种对降水累积效应的响应共性较好，逐月气候因子的响应差异明显，表明２个树种树轮年表中既包含了共同气候信息，也因树种生物学习性不同存在生长响应差异㊂云南铁杉对气候变化更为敏感（显著相关的气候因子更多）且相关关系的稳定性较强，说明老君山云南铁杉径向生长能够反映出更多的气候信息㊂本研究是对滇西北高原树轮研究的有利补充，可为区域内针叶树种生长应对气候变化提供科学依据，也为高海拔地区不同树种径向生长对气候响应差异的研究提供参考㊂参考文献（Ｒｅｆｅｒｅｎｃｅｓ）：［１］㊀ＧｉｒａｒｄｉｎＭＰ，ＨｏｇｇＥＨ，ＢｅｒｎｉｅｒＰＹ，ＫｕｒｚＷＡ，ＧｕｏＸＪ，ＣｙｒＧ．Ｎｅｇａｔｉｖｅｉｍｐａｃｔｓｏｆｈｉｇｈｔｅｍｐｅｒａｔｕｒｅｓｏｎｇｒｏｗｔｈｏｆｂｌａｃｋｓｐｒｕｃｅｆｏｒｅｓｔｓｉｎｔｅｎｓｉｆｙｗｉｔｈｔｈｅａｎｔｉｃｉｐａｔｅｄｃｌｉｍａｔｅｗａｒｍｉｎｇ．ＧｌｏｂａｌＣｈａｎｇｅＢｉｏｌｏｇｙ，２０１６，２２（２）：６２７⁃６４３．［２］㊀ＣｈａｒｎｅｙＮＤ，ＢａｂｓｔＦ，ＰｏｕｌｔｅｒＢ，ＲｅｃｏｒｄＳ，ＴｒｏｕｅｔＶＭ，ＦｒａｎｋＤ，ＥｎｑｕｉｓｔＢＪ，ＥｖａｎｓＭＥＫ．Ｏｂｓｅｒｖｅｄｆｏｒｅｓｔｓｅｎｓｉｔｉｖｉｔｙｔｏｃｌｉｍａｔｅｉｍｐｌｉｅｓｌａｒｇｅｃｈａｎｇｅｓｉｎ２１ｓｔｃｅｎｔｕｒｙＮｏｒｔｈＡｍｅｒｉｃａｎｆｏｒｅｓｔｇｒｏｗｔｈ．ＥｃｏｌｏｇｙＬｅｔｔｅｒｓ，２０１６，１９（９）：１１１９⁃１１２８．［３］㊀ＬｉｕＨＹ，ＷｉｌｌｉａｍｓＡＰ，ＡｌｌｅｎＣＤ，ＧｕｏＤＬ，ＷｕＸＣ，ＡｎｅｎｋｈｏｎｏｖＯＡ，ＬｉａｎｇＥＹ，ＳａｎｄａｎｏｖＤＶ，ＹｉｎＹ，ＱｉＺＨ，ＢａｄｍａｅｖａＮＫ．Ｒａｐｉｄｗａｒｍｉｎｇａｃｃｅｌｅｒａｔｅｓｔｒｅｅｇｒｏｗｔｈｄｅｃｌｉｎｅｉｎｓｅｍｉ ａｒｉｄｆｏｒｅｓｔｓｏｆＩｎｎｅｒＡｓｉａ．ＧｌｏｂａｌＣｈａｎｇｅＢｉｏｌｏｇｙ，２０１３，１９（８）：２５００⁃２５１０．［４］㊀ＷｉｌｌｉａｍｓＡＰ，ＡｌｌｅｎＣＤ，ＭａｃａｌａｄｙＡＫ，ＧｒｉｆｆｉｎＤ，ＷｏｏｄｈｏｕｓｅＣＡ，ＭｅｋｏＤＭ，ＳｗｅｔｎａｍＴＷ，ＲａｕｓｃｈｅｒＳＡ，ＳｅａｇｅｒＲ，Ｇｒｉｓｓｉｎｏ ＭａｙｅｒＨＤ，ＤｅａｎＪＳ，ＣｏｏｋＥＲ，ＧａｎｇｏｄａｇａｍａｇｅＣ，ＣａｉＭ，ＭｃＤｏｗｅｌｌＮＧ．Ｔｅｍｐｅｒａｔｕｒｅａｓａｐｏｔｅｎｔｄｒｉｖｅｒｏｆｒｅｇｉｏｎａｌｆｏｒｅｓｔｄｒｏｕｇｈｔｓｔｒｅｓｓａｎｄｔｒｅｅｍｏｒｔａｌｉｔｙ．ＮａｔｕｒｅＣｌｉｍａｔｅＣｈａｎｇｅ，２０１３，３（３）：２９２⁃２９７．［５］㊀刘敏，毛子军，厉悦，孙涛，李兴欢，黄唯，刘瑞鹏，李元昊．不同纬度阔叶红松林红松径向生长对气候因子的响应．应用生态学报，２０１６，２７（５）：１３４１⁃１３５２．［６］㊀ＧｅｏｒｇｅＳＳ．Ａｎｏｖｅｒｖｉｅｗｏｆｔｒｅｅ⁃ｒｉｎｇｗｉｄｔｈｒｅｃｏｒｄｓａｃｒｏｓｓｔｈｅＮｏｒｔｈｅｒｎＨｅｍｉｓｐｈｅｒｅ．ＱｕａｔｅｒｎａｒｙＳｃｉｅｎｃｅＲｅｖｉｅｗｓ，２０１４，９５：１３２⁃１５０．［７］㊀ＷｉｌｍｋｉｎｇＭ，ＪｕｄａｙＧＰ，ＢａｒｂｅｒＶ，ＺａｌｄＨＳＪ．ＲｅｃｅｎｔｃｌｉｍａｔｅｗａｒｍｉｎｇｆｏｒｃｅｓｃｏｎｔｒａｓｔｉｎｇｇｒｏｗｔｈｒｅｓｐｏｎｓｅｓｏｆｗｈｉｔｅｓｐｒｕｃｅａｔｔｒｅｅｌｉｎｅｉｎＡｌａｓｋａｔｈｒｏｕｇｈｔｅｍｐｅｒａｔｕｒｅｔｈｒｅｓｈｏｌｄｓ．ＧｌｏｂａｌＣｈａｎｇｅＢｉｏｌｏｇｙ，２００４，１０（１０）：１７２４⁃１７３６．［８］㊀ＢｏｒｇａｏｎｋａｒＨＰ，ＳｉｋｄｅｒＡＢ，ＲａｍＳ．Ｈｉｇｈａｌｔｉｔｕｄｅｆｏｒｅｓｔｓｅｎｓｉｔｉｖｉｔｙｔｏｔｈｅｒｅｃｅｎｔｗａｒｍｉｎｇ：Ａｔｒｅｅ⁃ｒｉｎｇａｎａｌｙｓｉｓｏｆｃｏｎｉｆｅｒｓｆｒｏｍＷｅｓｔｅｒｎＨｉｍａｌａｙａ，Ｉｎｄｉａ．ＱｕａｔｅｒｎａｒｙＩｎｔｅｒｎａｔｉｏｎａｌ，２０１１，２３６（１／２）：１５８⁃１６６．［９］㊀ＹｕＤＰ，ＷａｎｇＧＧ，ＤａｉＬＭ，ＷａｎｇＱＬ．ＤｅｎｄｒｏｃｌｉｍａｔｉｃａｎａｌｙｓｉｓｏｆＢｅｔｕｌａｅｒｍａｎｉｉｆｏｒｅｓｔｓａｔｔｈｅｉｒｕｐｐｅｒｌｉｍｉｔｏｆｄｉｓｔｒｉｂｕｔｉｏｎｉｎＣｈａｎｇｂａｉＭｏｕｎｔａｉｎ，ＮｏｒｔｈｅａｓｔＣｈｉｎａ．ＦｏｒｅｓｔＥｃｏｌｏｇｙａｎｄＭａｎａｇｅｍｅｎｔ，２００７，２４０（１／３）：１０５⁃１１３．［１０］㊀曹受金．南岭山地松科树种径向生长与气候因子关系及气候重建研究［Ｄ］．长沙：中南林业科技大学，２０１５．［１１］㊀刘敏，毛子军，厉悦，夏志宇．不同径级红松径向生长对气候变化的响应．应用生态学报，２０１８，２９（１１）：３５３０⁃３５４０．［１２］㊀曹宗英，勾晓华，刘文火，高琳琳，张芬．祁连山中部青海云杉上下限树轮宽度年表对气候的响应差异．干旱区资源与环境，２０１４，２８（７）：２９⁃３４．［１３］㊀宋文琦，朱良军，张旭，王晓春，张远东．青藏高原东北部不同降水梯度下高山林线祁连圆柏径向生长与气候关系的比较．植物生态学报，２０１８，４２（１）：６６⁃７７．［１４］㊀杨绕琼，范泽鑫，李宗善，温庆忠．滇西北玉龙雪山不同海拔云南松（Ｐｉｎｕｓｙｕｎｎａｎｅｎｓｉｓ）径向生长对气候因子的响应．生态学报，２０１８，３８（２４）：８９８３⁃８９９１．［１５］㊀ＭｙｅｒｓＮ，ＭｉｔｔｅｒｍｅｉｅｒＲＡ，ＭｉｔｔｅｒｍｅｉｅｒＣＧ，ＤａＦｏｎｓｅｃａＧＡＢ，ＫｅｎｔＪ．Ｂｉｏｄｉｖｅｒｓｉｔｙｈｏｔｓｐｏｔｓｆｏｒｃｏｎｓｅｒｖａｔｉｏｎｐｒｉｏｒｉｔｉｅｓ．Ｎａｔｕｒｅ，２０００，４０３（６７７２）：８５３⁃８５８．［１６］㊀ＦａｎＺＸ，ＢｒäｕｎｉｎｇＡ，ＣａｏＫＦ，ＺｈｕＳＤ．Ｇｒｏｗｔｈ⁃ｃｌｉｍａｔｅｒｅｓｐｏｎｓｅｓｏｆｈｉｇｈ ｅｌｅｖａｔｉｏｎｃｏｎｉｆｅｒｓｉｎｔｈｅｃｅｎｔｒａｌＨｅｎｇｄｕａｎＭｏｕｎｔａｉｎｓ，ｓｏｕｔｈｗｅｓｔｅｒｎＣｈｉｎａ．ＦｏｒｅｓｔＥｃｏｌｏｇｙａｎｄＭａｎａｇｅｍｅｎｔ，２００９，２５８（３）：３０６⁃３１３．［１７］㊀毕迎凤．滇西北地区五种植物径向生长与气候变化的研究 兼论铁杉空间分布模拟［Ｄ］．昆明：中国科学院大学，２０１３．［１８］㊀ＺｈａｎｇＹ，ＹｉｎＤＣ，ＳｕｎＭ，ＷａｎｇＨ，ＴｉａｎＫ，ＸｉａｏＤＲ，ＺｈａｎｇＷＧ．Ｖａｒｉａｔｉｏｎｓｏｆｃｌｉｍａｔｅ ｇｒｏｗｔｈｒｅｓｐｏｎｓｅｏｆｍａｊｏｒｃｏｎｉｆｅｒｓａｔｕｐｐｅｒｄｉｓｔｒｉｂｕｔｉｏｎａｌｌｉｍｉｔｓｉｎＳｈｉｋａＳｎｏｗＭｏｕｎｔａｉｎ，ｎｏｒｔｈｗｅｓｔｅｒｎＹｕｎｎａｎＰｌａｔｅａｕ，Ｃｈｉｎａ．Ｆｏｒｅｓｔｓ，２０１７，８（１０）：３３７．［１９］㊀张贇，尹定财，张卫国，岳海涛，杜杰次丹，李秋平，杨荣，田昆．普达措国家公园２个针叶树种径向生长对温度和降水的响应．生态学报，２０１８，３８（１５）：５３８３⁃５３９２．［２０］㊀张贇，尹定财，田昆，肖德荣，孙梅，王行，张卫国．滇西北海拔上限大果红杉径向生长对气候变化的响应．应用生态学报，２０１７，２８（９）：２８０５⁃２８１２．［２１］㊀张贇，尹定财，田昆，和荣华，和茂珍，李玉春，孙大成，张卫国．玉龙雪山东坡不同海拔长苞冷杉径向生长与气候因子的关系．应用生态学报，２０１８，２９（７）：２３５５⁃２３６１．［２２］㊀李永飞，贺杰，李春海，许斌，谢贤健．云南丽江老君山表土花粉与植被关系的研究．微体古生物学报，２０１８，３５（１）：５１⁃６４．５７０６㊀１７期㊀㊀㊀曹仁杰㊀等：丽江老君山海拔上限长苞冷杉和云南铁杉径向生长对气候变化的响应㊀６７０６㊀生㊀态㊀学㊀报㊀㊀㊀４０卷㊀［２３］㊀杨桂芳，郑鹏，和继光．丽江老君山国家公园植物景观资源的开发与保护．林业调查规划，２０１４，３９（５）：３６⁃３９．［２４］㊀ＰａｎｔｈｉＳ，ＢｒäｕｎｉｎｇＡ，ＺｈｏｕＺＫ，ＦａｎＺＸ．ＧｒｏｗｔｈｒｅｓｐｏｎｓｅｏｆＡｂｉｅｓｇｅｏｒｇｅｉｔｏｃｌｉｍａｔｅｉｎｃｒｅａｓｅｓｗｉｔｈｅｌｅｖａｔｉｏｎｉｎｔｈｅｃｅｎｔｒａｌＨｅｎｇｄｕａｎＭｏｕｎｔａｉｎｓ，ｓｏｕｔｈｗｅｓｔｅｒｎＣｈｉｎａ．Ｄｅｎｄｒｏｃｈｒｏｎｏｌｏｇｉａ，２０１８，４７：１⁃９．［２５］㊀余艳红．景观格局指数在生态环境影响评价中的应用 以丽江至香格里拉铁路生态影响评价为例．环境科学导刊，２０１０，２９（２）：８２⁃８５，１０８⁃１０８．［２６］㊀ｈｔｔｐｓ：／／ｗｗｗ．ｃｙｂｉｓ．ｓｅ／ｃｂｅｅｗｉｎｇ／ＣＲｅｃｏｒｄｅｒ／ｈａｎｄｂｏｋ．ｈｔｍ［２７］㊀ＬＨＲ．Ｃｏｍｐｕｔｅｒ⁃ａｓｓｉｓｔｅｄｑｕａｌｉｔｙｃｏｎｔｒｏｌｉｎｔｒｅｅ⁃ｒｉｎｇｄａｔｉｎｇａｎｄｍｅａｓｕｒｅｍｅｎｔ．Ｔｒｅｅ⁃ＲｉｎｇＢｕｌｌｅｔｉｎ，１９８３，４３（１）：６９⁃７５．［２８］㊀邵雪梅，吴祥定．华山树木年轮年表的建立［Ｊ］．地理学报，１９９４（０２）：１７４⁃１８１．［２９］㊀ＬｉａｎｇＥＹ，ＷａｎｇＹＦ，ＸｕＹ，ＬｉｕＢＭ，ＳｈａｏＸＭ．ＧｒｏｗｔｈｖａｒｉａｔｉｏｎｉｎＡｂｉｅｓｇｅｏｒｇｅｉｖａｒ．ｓｍｉｔｈｉｉａｌｏｎｇａｌｔｉｔｕｄｉｎａｌｇｒａｄｉｅｎｔｓｉｎｔｈｅＳｙｇｅｒａＭｏｕｎｔａｉｎｓ，ｓｏｕｔｈｅａｓｔｅｒｎＴｉｂｅｔａｎＰｌａｔｅａｕ．Ｔｒｅｅｓ，２０１０，２４（２）：３６３⁃３７３．［３０］㊀ＦａｎＺＸ，ＢｒäｕｎｉｎｇＡ，ＣａｏＫＦ．ＡｎｎｕａｌｔｅｍｐｅｒａｔｕｒｅｒｅｃｏｎｓｔｒｕｃｔｉｏｎｉｎｔｈｅｃｅｎｔｒａｌＨｅｎｇｄｕａｎＭｏｕｎｔａｉｎｓ，Ｃｈｉｎａ，ａｓｄｅｄｕｃｅｄｆｒｏｍｔｒｅｅｒｉｎｇｓ．Ｄｅｎｄｒｏｃｈｒｏｎｏｌｏｇｉａ，２００８，２６（２）：９７⁃１０７．［３１］㊀徐宁，王晓春，张远东，刘世荣．川西米亚罗林区不同海拔岷江冷杉生长对气候变化的响应．生态学报，２０１３，３３（１２）：３７４２⁃３７５１．［３２］㊀赵志江，谭留夷，康东伟，刘琪璟，李俊清．云南小中甸地区丽江云杉径向生长对气候变化的响应．应用生态学报，２０１２，２３（３）：６０３⁃６０９．［３３］㊀ＲｏｌｌａｎｄＣ．Ｔｒｅｅ⁃ｒｉｎｇａｎｄｃｌｉｍａｔｅｒｅｌａｔｉｏｎｓｈｉｐｓｆｏｒＡｂｉｅｓａｌｂａｉｎｔｈｅｉｎｔｅｒｎａｌＡｌｐｓ．Ｔｒｅｅ ＲｉｎｇＳｏｃｉｅｔｙ，１９９３，５３：１⁃１１．［３４］㊀ＧｅｒｖａｉｓＢＲ．Ａｔｈｒｅｅ ｃｅｎｔｕｒｙｒｅｃｏｒｄｏｆｐｒｅｃｉｐｉｔａｔｉｏｎａｎｄｂｌｕｅｏａｋｒｅｃｒｕｉｔｍｅｎｔｆｒｏｍｔｈｅＴｅｈａｃｈａｐｉＭｏｕｎｔａｉｎｓ，ＳｏｕｔｈｅｒｎＣａｌｉｆｏｒｎｉａ，ＵＳＡ．Ｄｅｎｄｒｏｃｈｒｏｎｏｌｏｇｉａ，２００６，２４（１）：２９⁃３７．［３５］㊀赖志华．长苞铁杉幼苗对极端温度和外源钙的适应与响应机制［Ｄ］．厦门：厦门大学，２００７．［３６］㊀赵志江．川西亚高山岷江冷杉与紫果云杉对气候的响应［Ｄ］．北京：北京林业大学，２０１３．［３７］㊀ＺｈａｎｇＹ，ＢｅｒｇｅｒｏｎＹ，ＺｈａｏＨＸ，ＤｒｏｂｙｓｈｅｖＩ．Ｓｔａｎｄｈｉｓｔｏｒｙｉｓｍｏｒｅｉｍｐｏｒｔａｎｔｔｈａｎｃｌｉｍａｔｅｉｎｃｏｎｔｒｏｌｌｉｎｇｒｅｄｍａｐｌｅ（ＡｃｅｒｒｕｂｒｕｍＬ．）ｇｒｏｗｔｈａｔｉｔｓｎｏｒｔｈｅｒｎｄｉｓｔｒｉｂｕｔｉｏｎｌｉｍｉｔｉｎｗｅｓｔｅｒｎＱｕｅｂｅｃ，Ｃａｎａｄａ．ＪｏｕｒｎａｌｏｆＰｌａｎｔＥｃｏｌｏｇｙ，２０１５，８（４）：３６８⁃３７９．［３８］㊀ＶａｇａｎｏｖＥＡ，ＨｕｇｈｅｓＭＫ，ＫｉｒｄｙａｎｏｖＡＶ，ＳｃｈｗｅｉｎｇｒｕｂｅｒＦＨ，ＳｉｌｋｉｎＰＰ．ＩｎｆｌｕｅｎｃｅｏｆｓｎｏｗｆａｌｌａｎｄｍｅｌｔｔｉｍｉｎｇｏｎｔｒｅｅｇｒｏｗｔｈｉｎｓｕｂａｒｃｔｉｃＥｕｒａｓｉａ．Ｎａｔｕｒｅ，１９９９，４００（６７４０）：１４９⁃１５１．［３９］㊀张贇，尹定财，田昆，张卫国，和荣华，和文清，孙江梅，刘振亚．玉龙雪山不同海拔丽江云杉径向生长对气候变异的响应．植物生态学报，２０１８，４２（６）：６２９⁃６３９．［４０］㊀ＺｈａｏＺＪ，ＥａｍｕｓＤ，ＹｕＱ，ＬｉＹ，ＹａｎｇＨＷ，ＬｉＪＱ．ＣｌｉｍａｔｅｃｏｎｓｔｒａｉｎｔｓｏｎｇｒｏｗｔｈａｎｄｒｅｃｒｕｉｔｍｅｎｔｐａｔｔｅｒｎｓｏｆＡｂｉｅｓｆａｘｏｎｉａｎａｏｖｅｒａｌｔｉｔｕｄｉｎａｌｇｒａｄｉｅｎｔｓｉｎｔｈｅＷａｎｇｌａｎｇＮａｔｕｒａｌＲｅｓｅｒｖｅ，ｅａｓｔｅｒｎＴｉｂｅｔａｎＰｌａｔｅａｕ．ＡｕｓｔｒａｌｉａｎＪｏｕｒｎａｌｏｆＢｏｔａｎｙ，２０１２，６０（７）：６０２⁃６１４．［４１］㊀ＴａｋａｈａｓｈｉＫ，ＴｏｋｕｍｉｔｓｕＹ，ＹａｓｕｅＴＫ．Ｃｌｉｍａｔｉｃｆａｃｔｏｒｓａｆｆｅｃｔｉｎｇｔｈｅｔｒｅｅ⁃ｒｉｎｇｗｉｄｔｈｏｆＢｅｔｕｌａｅｒｍａｎｉｉａｔｔｈｅｔｉｍｂｅｒｌｉｎｅｏｎＭｏｕｎｔＮｏｒｉｋｕｒａ，ｃｅｎｔｒａｌＪａｐａｎ．ＥｃｏｌｏｇｉｃａｌＲｅｓｅａｒｃｈ，２００５，２０（４）：４４５⁃４５１．［４２］㊀ＰｅｔｅｒｓｏｎＤＷ，ＰｅｔｅｒｓｏｎＤＬ．ＥｆｆｅｃｔｓｏｆｃｌｉｍａｔｅｏｎｒａｄｉａｌｇｒｏｗｔｈｏｆｓｕｂａｌｐｉｎｅｃｏｎｉｆｅｒｓｉｎｔｈｅＮｏｒｔｈＣａｓｃａｄｅＭｏｕｎｔａｉｎｓ．ＣａｎａｄｉａｎＪｏｕｒｎａｌｏｆＦｏｒｅｓｔＲｅｓｅａｒｃｈ，１９９４，２４（９）：１９２１⁃１９３２．［４３］㊀ＯｂｅｒｈｕｂｅｒＷ．ＩｎｆｌｕｅｎｃｅｏｆｃｌｉｍａｔｅｏｎｒａｄｉａｌｇｒｏｗｔｈｏｆＰｉｎｕｓｃｅｍｂｒａｗｉｔｈｉｎｔｈｅａｌｐｉｎｅｔｉｍｂｅｒｌｉｎｅｅｃｏｔｏｎｅ．ＴｒｅｅＰｈｙｓｉｏｌｏｇｙ，２００４，２４（３）：２９１⁃３０１．［４４］㊀刘晓宏，秦大河，邵雪梅，任贾文，王瑜．西藏林芝冷杉树轮稳定碳同位素对气候的响应．冰川冻土，２００２，２４（５）：５７４⁃５７８．［４５］㊀赵志江，康东伟，李俊清．川西亚高山不同年龄紫果云杉径向生长对气候因子的响应．生态学报，２０１６，３６（１）：１７３⁃１７９．［４６］㊀侯鑫源．湖北神农架自然保护区不同海拔高度巴山冷杉径向生长对气候的响应［Ｄ］．南京：南京大学，２０１５．［４７］㊀姚启超，王晓春，肖兴威．小兴安岭红皮云杉年轮 气候关系及其衰退原因．应用生态学报，２０１５，２６（７）：１９３５⁃１９４４．［４８］㊀张贇，尹定财，孙梅，李丽萍，田昆，张卫国．滇西北石卡雪山２个针叶树种森林上限径向生长对温度和降水的响应．生态学报，２０１８，３８（７）：２４４２⁃２４４９．［４９］㊀王婷，于丹，李江风，马克平．树木年轮宽度与气候变化关系研究进展．植物生态学报，２００３，２７（１）：２３⁃３３．［５０］㊀吴普，王丽丽，黄磊．五个中国特有针叶树种树轮宽度对气候变化的敏感性．地理研究，２００６，２５（１）：４３⁃５２．［５１］㊀ＬｉａｎｇＥＹ，ＬｅｕｓｃｈｎｅｒＣ，ＤｕｌａｍｓｕｒｅｎＣ，ＷａｇｎｅｒＢ，ＨａｕｃｋＭ．Ｇｌｏｂａｌｗａｒｍｉｎｇ ｒｅｌａｔｅｄｔｒｅｅｇｒｏｗｔｈｄｅｃｌｉｎｅａｎｄｍｏｒｔａｌｉｔｙｏｎｔｈｅｎｏｒｔｈ ｅａｓｔｅｒｎＴｉｂｅｔａｎｐｌａｔｅａｕ．ＣｌｉｍａｔｉｃＣｈａｎｇｅ，２０１６，１３４（１／２）：１６３⁃１７６．［５２］㊀ＧｕｏＧＡ，ＬｉＺＳ，ＺｈａｎｇＱＢ，ＭａＫＰ，ＭｕＣＬ，ＰｕｍｉｊｕｍｎｏｎｇＮ，ＺｈａｎｇＱＢ，ＥｃｋｓｔｅｉｎＤ，ＢａａｓＰ．ＤｅｎｄｒｏｃｌｉｍａｔｏｌｏｇｉｃａｌｓｔｕｄｉｅｓｏｆＰｉｃｅａｌｉｋｉａｎｇｅｎｓｉｓａｎｄＴｓｕｇａｄｕｍｏｓａｉｎＬｉｊｉａｎｇ，Ｃｈｉｎａ．ＩＡＷＡＪｏｕｒｎａｌ，２００９，３０（４）：４３５⁃４４１．［５３］㊀郭明明，张远东，王晓春，刘世荣．川西米亚罗林区主要树木生长对气候响应的差异．应用生态学报，２０１５，２６（８）：２２３７⁃２２４３．。

ARTICLEOPENReceived11Dec2012|Accepted16May2013|Published14Jun2013A solid with a hierarchical tetramodalmicro-meso-macro pore size distributionYu Ren1,Zhen Ma2,3,Russell E.Morris1,Zheng Liu1,Feng Jiao4,Sheng Dai3&Peter G.Bruce1Porous solids have an important role in addressing some of the major energy-related pro-blems facing society.Here we describe a porous solid,a-MnO2,with a hierarchical tetramodalpore size distribution spanning the micro-,meso-and macro pore range,centred at0.48,4.0,18and70nm.The hierarchical tetramodal structure is generated by the presence ofpotassium ions in the precursor solution within the channels of the porous silica template;thesize of the potassium ion templates the microporosity of a-MnO2,whereas theirreactivity with silica leads to larger mesopores and macroporosity,without destroying themesostructure of the template.The hierarchical tetramodal pore size distribution influencesthe properties of a-MnO2as a cathode in lithium batteries and as a catalyst,changingthe behaviour,compared with its counterparts with only micropores or bimodalmicro/mesopores.The approach has been extended to the preparation of LiMn2O4with ahierarchical pore structure.1EaStCHEM,School of Chemistry,University of St Andrews,St Andrews KY169ST,UK.2Shanghai Key Laboratory of Atmospheric Particle Pollution and Prevention(LAP3),Department of Environmental Science and Engineering,Fudan University,Shanghai200433,China.3Chemical Sciences Division,Oak Ridge National Laboratory,Oak Ridge,T ennessee37831,USA.4Department of Chemical and Biomolecular Engineering,University of Delaware,Newark,Delaware19716,USA.Correspondence and requests for materials should be addressed to P.G.B.(email:p.g.bruce@).P orous solids have an important role in addressing some of the major problems facing society in the twenty-first century,such as energy storage,CO2sequestration,H2 storage,therapeutics(for example,drug delivery)and catalysis1–8. The size of the pores and their distribution directly affect their ability to function in a particular application2.For example, zeolites are used as acid catalysts in industry,but their micropores impose severe diffusion limitations on the ingress and egress of the reactants and the catalysed products9.To address such issues, great effort is being expended in preparing porous materials with a bimodal(micro and meso)pore structure by synthesizing zeolites or silicas containing micropores and mesopores10–17,or microporous metal–organic frameworks with ordered mesopores18.Among porous solids,porous transition metal oxides are particularly important,because they exhibit many unique properties due to their d-electrons and the variable redox state of their internal surfaces8,19–22.Here we describe thefirst solid(a-MnO2)possessing hierarchical pores spanning the micro,meso and macro range, centred at0.48,4.0,18and70nm.The synthesis method uses mesoporous silica as a hard template.Normally such a template generates a mesoporous solid with a unimodal23–31or,at most,a bimodal pore size distribution32–38.By incorporating Kþions in the precursor solution,within the silica template,the Kþions act bifunctionally:their size templates the formation of the micropores in a-MnO2,whereas their reactivity with silica destroys the microporous channels in KIT-6comprehensively, leading to the formation of a-MnO2containing large mesopores and,importantly,macropores,something that has not been possible by other methods.Significantly,this is achieved without destroying the silica template by alkaline ions.The effect of the tetramodal pore structure on the properties of the material is exemplified by considering their use as electrodes for lithium-ion batteries and as a catalyst for CO oxidation and N2O decomposition.The novel material offers new possibilities for combining the selectivity of small pores with the transport advantages of the large pores across a wide range of sizes.We also present results demonstrating the extension of the method to the synthesis of LiMn2O4with a hierarchical pore structure.ResultsComposition of tetramodal a-MnO2.The composition of the synthesized material was determined by atomic absorption ana-lysis and redox titration to be K0.08MnO2(the K/Mn ratio of the precursor solution was1/3).The material is commonly referred to as a-MnO2,because of the small content of Kþ19.N2sorption analysis of tetramodal a-MnO2.The tetramodal a-MnO2shows a type IV isotherm(Fig.1a).The pore size dis-tribution(Fig.1b)in the range of0.3–200nm was analysed using the density functional theory(DFT)method applied to the adsorption branch of the isotherm39–42,as this is more reliable than analysing the desorption branch43;note that this is not the DFT method used in ab initio electronic structure calculations. Plots were constructed with vertical axes representing ‘incremental pore volume’and‘incremental surface area’.Large (macro)pores can account for a significant pore volume while representing a relatively smaller surface area and vice versa for small(micro)pores.Therefore,when investigating a porous material with a wide range of pore sizes,for example,micropore and macropore,the combination of surface area and pore volume is essential to determine the pore size distribution satisfactorily (Fig.1b).Considering both pore volume and surface area, significant proportions of micro-,meso-and macropores are evident,with distinct maxima centred at0.70,4.0,18and70nm.To probe the size of the micropores more precisely than is possible with DFT,the Horvath–Kawazoe pore size distribution analysis was employed44.A single peak was obtained at0.48nm(Fig.1c),in good accord with the0.46-nm size of the2Â2channels of a-MnO2 (refs.19,21).The relatively small Brunauer–Emmett–Teller(BET) surface area of tetramodal a-MnO2(79–105m2gÀ1; Supplementary Table S1)compared with typical surface areas of mesoporous metal oxides(90–150m2gÀ1)45is due to the significant proportion of macropores(which have small surface areas)and relatively large(18nm)mesopores—a typical mesoporous metal oxide has only3–4nm pores.TEM analysis of tetramodal a-MnO2.Transmission electron microscopic(TEM)data for tetramodal a-MnO2,Fig.2, demonstrates a three-dimensional pore structure with a sym-metry consistent with space group Ia3d.From the TEM data,an a0lattice parameter of23.0nm for the mesostructure could be extracted,which is in good agreement with the value obtained from the low-angle powder X-ray diffraction(PXRD)data, a0¼23.4nm(Supplementary Fig.S1a).High-resolution TEM images in Fig.2c–e demonstrate that the walls are crystalline with a typical wall thickness of10nm.The lattice spacings of0.69,0.31 and0.35nm agree well with the values of6.92,3.09and3.46Åfor the[110],[310]and[220]planes of a-MnO2(International Centre for Diffraction Data(ICDD)number00-044-0141), respectively.The wide-angle PXRD data matches well with the PXRD data of bulk cryptomelane a-MnO2(Supplementary Fig. S1b),confirming the crystalline walls.The various pores in tetramodal a-MnO2can be observed by TEM directly:the0.48-nm micropores are seen in Fig.2e(2Â2 tunnels with dimensions of0.48Â0.48nm in the white box);the 4.0-nm pores are shown in Fig.2b–d;the18-nm pores are shown in Fig.2a;the70-nm pores are evident in Fig.2b(highlighted with white circles).Li intercalation.Li can be intercalated into bulk a-MnO2 (ref.46).Therefore,it is interesting to compare Li intercalation into bulk a-MnO2(micropores only)and bimodal a-MnO2 (micropores along with a single mesopore of diameter3.6nm,see Methods)with tetramodal a-MnO2(micro-,meso-and macropores).Each of the three a-MnO2materials was subjected to Li intercalation by incorporation as the positive electrode in a lithium battery,along with a lithium anode and a non-aqueous electrolyte(see Methods).The results of cycling(repeated intercalation/deintercalation of Li)the cells are shown in Fig.3. Although all exhibit good capacity to cycle Li at low rates of charge/discharge(30mA gÀ1),tetramodal a-MnO2shows sig-nificantly higher capacity(Li storage)at a high rate of 6,000mA gÀ1(corresponding to charge and discharge in3min). The tetramodal a-MnO2can store three times the capacity(Li) compared with bimodal a-MnO2,and18times that of a-MnO2 with only micropores,at the high rate of intercalation/deinter-calation(Fig.3).The superior rate capability of tetramodal a-MnO2over microporous and bimodal forms may be assigned to better Liþtransport in the electrolyte within the hierarchical pore structure of tetramodal a-MnO2.The importance of elec-trolyte transport in porous electrodes has been discussed recently35,47,48and the results presented here reinforce the beneficial effect of a hierarchical pore structure.Catalytic studies.CO oxidation and N2O decomposition were used as reactions to probe the three different forms of a-MnO2as catalysts(Supplementary Fig.S2).As shown in Supplementary Fig.S2a,tetramodal a-MnO2demonstrates better catalytic activity compared with only micropores or bimodal a-MnO2;thetemperature of half CO conversion (T 50)was 124°C for tetra-modal a -MnO 2,whereas microporous and bimodal a -MnO 2exhibited a T 50value of 275°C and 209°C,respectively.In the case of N 2O decomposition,a -MnO 2with only micropores demonstrated no catalytic activity in the range of 200–400°C,in accord with a previous report 49.Tetramodal and bimodal a -MnO 2showed catalytic activity and reached 32%and 20%of N 2O conversion,respectively,at a reaction temperature of 400°C.The differences in catalytic activity are related to the differences in the material.A detailed study focusing on the catalytic activity alonewould be necessary to demonstrate which specific features of the textural differences (pore size distribution,average manganese oxidation state,K þand so on)between the different MnO 2materials are responsible for the differences in behaviour.However,the preliminary results shown here do illustrate that such differences exist.Porous LiMn 2O 4.To demonstrate the wider applicability of the synthesis method,LiMn 2O 4with a hierarchical pore structurewas1801601401201008060402000.00.20.40.60.81.0V (c m 3 g –1)Pore diameter (nm)0.0120.0100.0080.0060.0040.0020.000I n c r e m e n t a l p o r e v o l u m e (c m 3 g –1)Pore width (nm)I n c r e m e n t a l s u r f a c e a r e a (m 2 g –1)I n c r e m e n t a l s u r f a c e a r e a (m 2 g –1)P /P 0Figure 1|N 2sorption analysis of tetramodal a -MnO 2.(a )N 2adsorption–desorption isotherms,(b )DFT pore size distribution and (c )Horvath–Kawazoe pore size distribution from N 2adsorption isotherm for tetramodal a -MnO 2.Figure 2|TEM images of tetramodal a -MnO 2.TEM images along (a )[100]direction,showing 18nm mesopores (scale bar,50nm);(b )4.0and 70nm pores (70nm pores are highlighted by white circles;scale bar,100nm);(c –e )high-resolution (HRTEM)images of tetramodal a -MnO 2showing 4.0and 0.48nm pores (scale bar,10nm).Inset is representation of a -MnO 2structure along the c axis,demonstrating the 2Â2micropores as shown in the HRTEM (white box)in e .Purple,octahedral MnO 6;red,oxygen;violet,potassium.synthesized in a way similar to that of tetramodal a -MnO 2.The main difference is the use of LiNO 3instead of KNO 3(see Methods).In this case,Li þreacts with the silica template col-lapsing/blocking the microporous channels in the KIT-6and resulting in the large mesopores and macropores (17and 50nm)in the LiMn 2O 4obtained.The use of Li þinstead of the larger K þdeters the formation of micropores because Li þis too small.TEM analysis illustrates the hierarchical pore structure of LiMn 2O 4(Supplementary Fig.S3):4.0nm pores are evident in Supplementary Fig.S3b;17nm pores in Supplementary Fig.S3a;and 50nm pores in Supplementary Fig.S3b (highlighted with white circles).The d-spacing of 0.47nm in the high-resolution TEM image (Supplementary Fig.S3c)is in good accordance with the values of 0.4655nm for the [111]planes of LiMn 2O 4(ICDD number 00-038-0789)and with the wide-angle PXRD data (Supplementary Fig.S4).The original DFT pore size distribution analysis from N 2sorption (adsorption branch)gives three pore sizes in the range of 1–100nm centred at 4.0,17and 50nm (Supplementary Fig.S5).A more in-depth presentation of the results for LiMn 2O 4will be given in a future paper;preliminary results presented here illustrate that the basic method can be applied beyond a -MnO 2.DiscussionTurning to the synthesis of the tetramodal a -MnO 2,the details are given in the Methods section.Hard templating using silica templates,such as KIT-6,normally gives rise to materials with unimodal or,at most,bimodal mesopore structures,and in the latter case the smaller mesopores dominate over the larger mesopores 8,32,35.Alkali ions are excellent templates for micropores in transition metal oxides 19,21,but they have been avoided in nanocasting from silica templates because of concerns that they would react with and,hence,destroy thesilica20018016014012010080604020D i s c h a r g e c a p a c i t y (m A h g –1)0Cycle numberx in Li x MnO 2Figure 3|Electrochemical behaviour of different a -MnO 2.Capacity retention for tetramodal a -MnO 2cycled at 30(empty blue circles)and 6,000mA g À1(filled blue circles);bulk a -MnO 2cycled at 30(empty red squares)and 6,000mA g À1(filled red squares);bimodal a -MnO 2cycled at 30(empty black triangle)and 6,000mA g À1(filled blacktriangles).18 nm pores70 nm poresTwo sets of mesoporeschannels connecting both sets of mesoporesEtching of silica Etching of silica Etching of silica template2discontinuously within one set of the KIT-6mesoporesFigure 4|Formation mechanism of meso and macropores in tetramodal a -MnO 2.When both KIT-6mesochannels are occupied by a -MnO 2and then the silica between them etched away,the remaining pore is 4nm (centre portion of figure).When a -MnO 2grows in only one set of mesochannels and then the KIT-6is dissolved away,the remaining metal oxide has 18nm pores (upper portion of figure).The comprehensive destruction of the microchannels in KIT-6by K þleads to a -MnO 2growing in only a proportion of one set of the KIT-6mesochannels,resulting in the formation of B 70nm pores (lower portion of figure).template50.Here,not only have alkali ions been used successfully in precursor solutions without destroying the template mesostructure but they give rise to macropores in the a-MnO2, thus permitting the synthesis of a tetramodal,micro-small,meso-large,meso-macro pore structure.Synthesis begins by impregnating the KIT-6silica template with a precursor solution containing Mn2þand Kþions.On heating,the Kþions template the formation of the micropores in a-MnO2,as the latter forms within the KIT-6template.KIT-6 consists of two interpenetrating mesoporous channels linked by microporous channels51–53.The branches of the two different sets of mesoporous channels in KIT-6are nearest neighbours separated by a silica wall of B4nm53;therefore,when both KIT-6mesochannels are occupied by a-MnO2and the silica between them etched away,the remaining pore is4nm(see centre portion of Fig.4).It has been shown previously,by a number of authors,that by varying the hydrothermal conditions used to prepare the KIT-6,the proportion of the microchannels can be decreased to some extent,thus making it difficult to simultaneouslyfill the neighbouring KIT-6mesoporous channels by the precursor solution of the target mesoporous metal oxide33–35.As a result,the target metal oxide grows in only one set of mesochannels of the KIT-6host but not both.When the KIT-6is dissolved away,the remaining metal oxide has B18nm pores,because the distance between adjacent branches of the same KIT-6mesochannels is greater than between the two different mesochannels in KIT-6.Here we propose that the Kþions have a similar effect on the KIT-6to that of the hydrothermal synthesis,but by a completely different mechanism.Reaction between the Kþions in the precursor solution with the silica during calcination results in the formation of Kþ-silicates,which cause collapse or blocking of the microporous channels in KIT-6,such that the a-MnO2grows in one set of the KIT-6mesochannels,giving rise to18nm pores in a-MnO2when the silica is etched away,see top portion of Fig.4. However,the reaction between Kþand the silica is more severe than the effect of varying the hydrothermal treatment.In the former case,the KIT-6microchannels are so comprehensively destroyed that the proportion of the large(18nm)to smaller (4nm)mesopores is greater than can be achieved by varying hydrothermal conditions.The comprehensive destruction of the microchannels in KIT-6by Kþ,perhaps augmented by some minor degradation of parts of the mesochannels,leads to a-MnO2 growing in only a proportion of one set of the KIT-6 mesochannels,resulting in the formation of B70nm pores in a-MnO2,see lower portion of Fig.4.In summary,the Kþreactivity with the silica goes beyond what can be achieved by varying the conditions of hydrothermal synthesis and is responsible for generating the tetramodal pore size distribution reported here. The mechanism of pore formation in a-MnO2by reaction between Kþand the silica template is supported by several findings.First,by the lower K/Mn molar ratio of thefinal tetramodal a-MnO2product(0.08)compared with the starting materials(0.33)implies that some of the Kþions in the impregnating solution have reacted with the silica.Second, support for collapse/blocking of the microporous channels in KIT-6due to reaction with Kþwas obtained by comparing the texture of KIT-6impregnated with an aqueous solution contain-ing only KNO3and calcined at300and500°C.The micropore volume in KIT-6is the greatest,with no KNO3in the solution;it then decreases continuously as the calcination temperature and calcination time is increased,such that after2and5h at500°C the micropore volume has decreased to zero(Supplementary Fig. S6).Third,we prepared tetramodal a-MnO2using a similar synthetic procedure to that described in the Methods section, except that this time we used a covered tall crucible for the calcination step.Sun et al.54have shown that using a covered,tall crucible when calcining results in porous metal oxides with much larger particle sizes.If the70-nm pores had arisen simply from the gaps between the particles,then the pore size would have changed;in contrast,it remained centred at70nm, Supplementary Fig.S7,consistent with the70-nm pores being intrinsic to the materials and arising from reaction with the Kþas described above.Fourth,if the synthesis of MnO2is carried out using the KIT-6template but in the absence Kþions,then the DFT pore size distribution shown in Supplementary Fig.S8is obtained.The0.48-and70-nm pores are now absent,but the4-and18-nm pores remain.This demonstrates the key role of Kþin the formation of the smallest and largest pores and,hence,in generating the tetramodal pore size distribution.The absence of Kþmeans that there is nothing to template the0.48nm pores and so a-MnO2is not formed;the b-polymorph is obtained instead.The absence of Kþalso means that the microchannels in the KIT-6template remain intact,resulting in no70nm pores and the dominance of the4-nm pores compared with the 18-nm pores.The hierarchical pore structure can be varied systematically by controlling the synthesis conditions,in particular the Kþ/Mn ratio of the precursor solution.A range of Kþ/Mn ratios,1/5,1/3and1/2,gave rise to a series of pore size distributions,in which the pore sizes remained the same but the relative proportions of the different pores varied (Supplementary Table S1).The higher the Kþ/Mn ratio,the greater the proportion of macropores and large mesopores.This is in accord with expectations,as the higher the Kþconcentra-tion in the precursor solution the greater the collapse/blocking of the microporous channels in the KIT-6(as noted above),and hence the greater the proportion of macropores and large mesopores.Indeed,these results offer further support for the mechanism of pore size distribution arising from reaction between Kþand the silica template.In conclusion,tetramodal a-MnO2,thefirst porous solid with a tetramodal pore size distribution,has been synthesized.Its hierarchical pore structure spans the micro,meso and macropore range between0.3and200nm,with pore dimensions centred at 0.48,4.0,18and70nm.Key to the synthesis is the use of Kþions that not only template the formation of micropores but also react with the silica template,therefore,breaking/blocking the micro-porous channels in the silica template far more comprehensively than is possible by varying the hydrothermal synthesis conditions, to the extent that macropores are formed,and without destroying the silica mesostructure by alkali ions,as might have been expected.The resulting hierarchical tetramodal structure demon-strates different behaviours compared with microporous and bimodal a-MnO2as a cathode material for Li-ion batteries,and when used as a catalyst for CO oxidation and N2O decomposi-tion.The method has been extended successfully to the preparation of hierarchical LiMn2O4.MethodsSynthesis.Tetramodal a-MnO2(surface area96m2gÀ1,K0.08MnO2)was pre-pared by two-solvent impregnation55using Kþand mesoporous silica KIT-6as the hard template.KIT-6was prepared according to a previous report (hydrothermal treatment at100°C)51.In a typical synthesis of tetramodal a-MnO2, 7.53g of Mn(NO3)2Á4H2O(98%,Aldrich)and1.01g of KNO3(99%,Aldrich)were dissolved in B10ml of water to form a solution with a molar ratio of Mn/K¼3.0. Next,5g of KIT-6was dispersed in200ml of n-hexane.After stirring at room temperature for3h,5ml of the Mn/K solution was added slowly with stirring.The mixture was stirred overnight,filtered and dried at room temperature until a completely dried powder was obtained.The sample was heated slowly to500°C (1°C minÀ1),calcined at that temperature for5h with a cover in a normal crucible unless is specified54and the resulting material treated three times with a hot aqueous KOH solution(2.0M),to remove the silica template,followed by washing with water and ethanol several times,and then drying at60°C.Bimodal a-MnO2(surface area58m2gÀ1,K0.06MnO2)with micropore and a single mesopore size of3.6nm was prepared by using mesoporous silica SBA-15as a hard template.The SBA-15was prepared according to a previous report56.Bulk a-MnO2(surface area8m2gÀ1,K0MnO2)was prepared by the reaction between325mesh Mn2O3(99.0%,Aldrich)and6.0M H2SO4solution at80°C for 24h,resulting in the disproportionation of Mn2O3into a soluble Mn2þspecies and the desired a-MnO2product46.Treatment of KIT-6with KNO3was carried out as follows:1.01g of KNO3was dissolved in B15ml of water to form a KNO3solution.Five grams of mesoporous KIT-6was dispersed in200ml of n-hexane.After stirring at room temperature for 3h,5ml of KNO3solution was added slowly with stirring.The mixture was stirred overnight,filtered and dried at room temperature until a completely dried powder was obtained.The sample was heated slowly to300or500°C(1°C minÀ1), calcined at that temperature for5h and the resulting material was washed with water and ethanol several times,and then dried at60°C overnight.The synthesis method for hierarchical porous LiMn2O4was similar to that of tetramodal a-MnO2.The main difference was to use1.01g of LiNO3instead of KNO3.After impregnation into KIT-6,calcination and silica etching,porous LiMn2O4was obtained.Characterization.TEM studies were carried out using a JEOL JEM-2011, employing a LaB6filament as the electron source,and an accelerating voltage of 200keV.TEM images were recorded by a Gatan charge-coupled device camera in a digital format.Wide-angle PXRD data were collected on a Stoe STADI/P powder diffractometer operating in transmission mode with Fe K a1source radiation(l¼1.936Å).Low-angle PXRD data were collected using a Rigaku/MSC,D/max-rB with Cu K a1radiation(l¼1.541Å)operating in reflection mode with a scintillation detector.N2adsorption–desorption analysis was carried out using a Micromeritics ASAP2020.The typical sample weight used was100–200mg. The outgas condition was set to300°C under vacuum for2h,and all adsorption–desorption measurements were carried out at liquid nitrogen tem-perature(À196°C).The original DFT method for the slit pore geometry was used to extract the pore size distribution from the adsorption branch usingthe Micromeritics software39–42.A Horvath–Kawazoe method was used to extract the microporosity44.Mn and K contents were determined by chemical analysis using a Philips PU9400X atomic adsorption spectrometer.The average oxidation state of framework manganese in a-MnO2samples was determined by a redoxtitration method57.Electrochemistry.First,the cathode was constructed by mixing the active material (a-MnO2),Kynar2801(a copolymer based on polyvinylidenefluoride),and Super S carbon(MMM)in the weight ratio80:10:10.The mixture was cast onto Al foil (99.5%,thickness0.050mm,Advent Research Materials,Ltd)from acetone using a Doctor-Blade technique.After solvent evaporation at room temperature and heating at80°C under vacuum for8h,the cathode was assembled into cells along with a Li metal anode and electrolyte(Merck LP30,1M LiPF6in1:1v/v ethylene carbonate/dimethyl carbonate).The cells were constructed and handled in anAr-filled MBraun glovebox(O2o0.1p.p.m.,H2O o0.1p.p.m.).Electrochemical measurements were carried out at30°C using a MACCOR Series4200cycler.Catalysis.Catalytic CO oxidation was tested in a plug-flow microreactor(Alta-mira AMI200).Fifty milligrams of catalyst was loaded into a U-shaped quartz tube (4mm i.d.).After the catalyst was pretreated inflowing8%O2(balanced with He) at400°C for1h,the catalyst was then cooled down,the gas stream switched to1% CO(balanced with air)and the reaction temperature ramped using a furnace(at a rate of1°C minÀ1above ambient temperature)to record the light-off curve.The flow rate of the reactant stream was37cm3minÀ1.A portion of the product stream was extracted periodically with an automatic sampling valve and was analysed using a dual column gas chromatograph with a thermal conductivity detector.To perform N2O decomposition reaction testing,0.5g catalyst was packed into a U-shaped glass tube(7mm i.d.)sealed by quartz wool,and pretreated inflowing 20%O2(balance He)at400°C for1h(flow rate:50cm3minÀ1).After cooling to near-room temperature,a gas stream of0.5%N2O(balance He)flowed through the catalyst at a rate of60cm3minÀ1,and the existing stream was analysed by a gas chromatograph(Agilent7890A)that separates N2O,O2and N2.The reaction temperature was varied using a furnace,and kept at100,150,200,250,300,350 and400°C for30min at each reaction temperature.The N2O conversion determined from GC analysis was denoted as X¼([N2O]in—[N2O]out)/[N2O]inÂ100%.References1.Corma,A.From microporous to mesoporous molecular sieve materials andtheir use in catalysis.Chem.Rev.97,2373–2419(1997).2.Davis,M.E.Ordered porous materials for emerging applications.Nature417,813–821(2002).3.Taguchi,A.&Schu¨th,F.Ordered mesoporous materials in 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[推荐][名词委审定]汉英力学名词(1993)[翻译与翻译辅助工具] [回复] [引用回复] [表格型] [跟帖] [转发到Blog] [关闭] [浏览930 次] 用户名: westbankBZ反应||Belousov-Zhabotinski reaction, BZ reactionFPU问题||Fermi-Pasta-Ulam problem, FPU problemKBM方法||KBM method, Krylov-Bogoliubov-Mitropolskii methodKS[动态]熵||Kolmogorov-Sinai entropy, KS entropyKdV 方程||KdV equationU形管||U-tubeWKB方法||WKB method, Wentzel-Kramers-Brillouin method[彻]体力||body force[单]元||element[第二类]拉格朗日方程||Lagrange equation [of the second kind][叠栅]云纹||moiréfringe; 物理学称“叠栅条纹”。

[叠栅]云纹法||moirémethod[抗]剪切角||angle of shear resistance[可]变形体||deformable body[钱]币状裂纹||penny-shape crack[映]象||image[圆]筒||cylinder[圆]柱壳||cylindrical shell[转]轴||shaft[转动]瞬心||instantaneous center [of rotation][转动]瞬轴||instantaneous axis [of rotation][状]态变量||state variable[状]态空间||state space[自]适应网格||[self-]adaptive meshＣ0连续问题||C0-continuous problemＣ1连续问题||C1-continuous problemＣＦＬ条件||Courant-Friedrichs-Lewy condition, CFL conditionＨＲＲ场||Hutchinson-Rice-Rosengren fieldＪ积分||J-integralＪ阻力曲线||J-resistance curveＫＡＭ定理||Kolgomorov-Arnol'd-Moser theorem, KAM theoremＫＡＭ环面||KAM torusｈ收敛||h-convergenceｐ收敛||p-convergenceπ定理||Buckingham theorem, pi theorem阿尔曼西应变||Almansis strain阿尔文波||Alfven wave阿基米德原理||Archimedes principle阿诺德舌[头]||Arnol'd tongue阿佩尔方程||Appel equation阿特伍德机||Atwood machine埃克曼边界层||Ekman boundary layer埃克曼流||Ekman flow埃克曼数||Ekman number埃克特数||Eckert number埃农吸引子||Henon attractor艾里应力函数||Airy stress function鞍点||saddle [point]鞍结分岔||saddle-node bifurcation安定[性]理论||shake-down theory安全寿命||safe life安全系数||safety factor安全裕度||safety margin暗条纹||dark fringe奥尔-索末菲方程||Orr-Sommerfeld equation奥辛流||Oseen flow奥伊洛特模型||Oldroyd model八面体剪应变||octohedral shear strain八面体剪应力||octohedral shear stress八面体剪应力理论||octohedral shear stress theory巴塞特力||Basset force白光散斑法||white-light speckle method摆||pendulum摆振||shimmy板||plate板块法||panel method板元||plate element半导体应变计||semiconductor strain gage半峰宽度||half-peak width半解析法||semi-analytical method半逆解法||semi-inverse method半频进动||half frequency precession半向同性张量||hemitropic tensor半隐格式||semi-implicit scheme薄壁杆||thin-walled bar薄壁梁||thin-walled beam薄壁筒||thin-walled cylinder薄膜比拟||membrane analogy薄翼理论||thin-airfoil theory保单调差分格式||monotonicity preserving difference scheme 保守力||conservative force保守系||conservative system爆发||blow up爆高||height of burst爆轰||detonation; 又称“爆震”。