納米材料和納米結(jié)構(gòu)：Chapter 5 Characterization of Nano-sized Materials

1、Chapter 5Characterization of Nano-sized MaterialsOutline5.1 顆粒粒度分析5.2 結(jié)構(gòu)表征5.3 性能表征5.1 顆粒度分析5.1.1 電鏡觀察法5.1.2 激光粒度分析法5.1.3 沉降法粒度分析5.1.4 電超聲粒度分析法5.1.1 電鏡觀察法采用掃描電子顯微鏡 （Scanning Electron Microscope, SEM）和透射電子顯微鏡（Transmission Electron Microscope, TEM）兩種方式對納米顆粒的大小、形貌和形狀進行觀測。Scanning Electron MicroscopeSEM的

2、工作原理是用一束極細(xì)的電子束掃描樣品，在樣品表面激發(fā)出次級電子，次級電子的多少與電子束入射角有關(guān)，也就是說與樣品的表面結(jié)構(gòu)有關(guān)，次級電子由探測體收集，并在那里被閃爍器轉(zhuǎn)變?yōu)楣庑盘?，再?jīng)光電倍增管和放大器轉(zhuǎn)變?yōu)殡娦盘杹砜刂茻晒馄辽想娮邮膹姸龋@示出與電子束同步的掃描圖像。圖像為立體形象，反映了標(biāo)本的表面結(jié)構(gòu)。為了使標(biāo)本表面發(fā)射出次級電子，標(biāo)本在固定、脫水后，要噴涂上一層重金屬微粒，重金屬在電子束的轟擊下發(fā)出次級電子信號。S-3700N, Hitachi, JapanChamber of SEMTransmission Electron Microscope由電子槍發(fā)射出來的電子束，在真空通道中

3、沿著鏡體光軸穿越聚光鏡，通過聚光鏡將之會聚成一束尖細(xì)、明亮而又均勻的光斑，照射在樣品室內(nèi)的樣品上；透過樣品后的電子束攜帶有樣品內(nèi)部的結(jié)構(gòu)信息，樣品內(nèi)致密處透過的電子量少，稀疏處透過的電子量多；經(jīng)過物鏡的會聚調(diào)焦和初級放大后，電子束進入下級的中間透鏡和第1、第2投影鏡進行綜合放大成像，最終被放大了的電子影像投射在觀察室內(nèi)的熒光屏板上；熒光屏將電子影像轉(zhuǎn)化為可見光影像以供使用者觀察。CM300, Philips, Netherland電鏡觀察法是對樣品局部區(qū)域的觀測，有可能會造成較大的統(tǒng)計誤差，所以在進行粒度分布分析時，需要多幅照片的觀測，通過軟件分析得到統(tǒng)計的粒度分布。電鏡觀察法得到的一次粒度分

4、析結(jié)果一般很難代表實際樣品顆粒的分布狀態(tài)。對一些在強電子束轟擊下不穩(wěn)定甚至分解的納米顆粒以及制樣困難的生物和微乳等樣品則很難得到準(zhǔn)確的結(jié)果。電鏡觀察法一次粒度檢測結(jié)果通常作為其他分析方法結(jié)果的比照。5.1.2 激光粒度分析法激光是一種電磁波，它可繞過障礙物，并形成新的光場分布，稱為衍射現(xiàn)象。激光衍射法示意圖平行激光束照在直徑為D的球形顆粒上，在顆粒后可得到一個圓斑稱為Airy斑，Airy斑直徑d=2.44f/D，為激光波長，f為透鏡焦距，由此式可計算顆粒大小D。通常所說激光粒度分析儀是指利用衍射和散射原理的粒度儀。激光粒度測量儀的工作原理基于夫朗和費（Fraunhofer）衍射和米（Mie）氏

5、散射理論相結(jié)合。顆粒對于入射光的散射服從經(jīng)典的米氏理論。Mie散射理論認(rèn)為顆粒不僅是激光傳播中的障礙物而且對激光有吸收部分透射和輻射作用，由此計算得光場分布稱為Mie散射，Mie散射適用任何大小顆粒。Mie散射對大顆粒的計算結(jié)果與夫瑯和費衍射基本一致。夫朗和費衍射只是嚴(yán)格米氏散射理論的一種近似，適用于當(dāng)被測顆粒的直徑遠(yuǎn)大于人射光的波長時的情況。Fraunhofer衍射理論的前提顆粒尺寸遠(yuǎn)大于激光的波長；不同尺寸的顆粒散射率相同；顆粒不透明，并且不透光。Mie散射理論的前提顆粒必須是球形的；顆粒必須具有光滑的表面；顆粒必須由單一組分的；必須預(yù)先知道分散顆粒用的液體或氣體的折射系數(shù)，以及顆粒本身的

6、折射系數(shù)；必須預(yù)先知道顆粒的吸收系數(shù)。Fraunhofer衍射理論無需考慮顆粒的光學(xué)參數(shù)，而且受顆粒形狀的影響較小，但是在實際情況下，F(xiàn)raunhofer衍射理論的條件有時得不到滿足，而Mie散射理論考慮了光的相互作用，可以準(zhǔn)確分析粒度范圍更大的樣品顆粒。Fraunhofer衍射適用的條件：儀器測量下限大于3 m，或被測顆粒是吸收型的且粒徑大于1 m。Mie衍射適用的條件：測量下限小于1 m的顆粒。激光粒度儀原理激光粒度儀是利用激光所特有的單色性、聚光性及容易引起衍射現(xiàn)象的光學(xué)性質(zhì)制造而成的。激光衍射式粒度測量儀一般由激光源，檢測器等組成。一般采用激發(fā)波長為632.8 nm的半導(dǎo)體激光器的單色

7、光作為激發(fā)源。當(dāng)分散在液體中的顆粒受到激光的照射時，就產(chǎn)生衍射現(xiàn)象，該衍射光通過付氏透鏡后，在焦平面上形成靶芯狀的衍射光環(huán)。衍射光環(huán)的半徑與顆粒的大小有關(guān)，衍射光環(huán)光的強度與相關(guān)粒徑顆粒的多少有關(guān)，通過放置在焦平面上的環(huán)型光電接受器陣列，就可以接受到激光對不同粒徑顆粒的衍射信號或光散射信號。Optical set up for the generation of diffraction patterns.Diffraction pattern of small spherical particles.亞微米和微米級顆粒的測試（0.1微米以上）納米顆粒的測試（0.1微米以下）理論激光衍射理論布朗

8、運動原理方法靜態(tài)激光衍射法動態(tài)激光散射法動態(tài)光散射法（Dynamic Light Scattering, DLS）微小顆粒在液體中的布朗運動，可以看作是顆粒在液體中的擴散。通過測量微粒在液體中的擴散速率來測試其顆粒度。布朗運動引起的顆粒位置變化出現(xiàn)在微秒至毫秒級的時間間隔中，由于微小顆粒的布朗運動，從而造成激光照射在它上面后所產(chǎn)生的散射光強是隨時間不斷地脈動。顆粒越大，顆粒位置的改變越慢，在探測器上得到的光強信號的改變也越慢。DLS，也稱為光子相關(guān)光譜法（Photon Correlation Spectroscopy, PCS）的原理就是根據(jù)這些光強信號的起伏變化來測定顆粒的尺寸。Advant

9、ages of DLS in Particle SizingFastPreciseReproducibleAbsoluteWide Size RangeAqueous/NonaqueousIntensity Weighting Emphasizes Onset of AggregationDisadvantages of DLS in Particle SizingLow Resolution PSD informationFew Large Particles May Cause ErrorsNot suitable for very broad PSDsIntensity Weightin

10、g Overshadows Small Particles in DistributionDelsaNano S, Beckmam, U.S.A.注意事項利用激光粒度儀對納米體系進行粒度分析時，必須對被分析體系的粒度范圍事先有所了解，否則分析結(jié)果將不會準(zhǔn)確。另外，激光法粒度分析的理論模型是建立在顆粒為球形、單分散條件上的，而實際中被測顆粒多為不規(guī)則形狀并呈多分散性。5.1.3 沉降法粒度分析沉降法粒度分析方法是通過顆粒在液體中沉降速度來測量粒度分布的方法。主要有重力沉降式和離心沉降式兩種光透沉降粒度分析方式，適合納米顆粒度分析的主要是離心式分析方法。Gravity sedimentation

11、(Stokes equation, 1891)DParticle diameter,Liquid viscosity,vSedimentation velocity,Particle density,0Liquid density,gAcceleration due to gravity.把樣品放到某種液體中制成一定濃度的懸浮液，懸浮液中的顆粒在重力或離心力作用下將發(fā)生沉降。大顆粒的沉降速度較快，小顆粒的沉降速度較慢，沉降速度與粒徑的關(guān)系有Stokes定律來描述。從Stokes定律中我們看到，沉降速度與顆粒直徑的平方成正比。Centrifugal sedimentation由于離心轉(zhuǎn)速都在數(shù)百

12、轉(zhuǎn)以上，離心加速度2r g，所以vc v。就是說在相同的條件下，顆粒在離心狀態(tài)下的沉降速度遠(yuǎn)遠(yuǎn)大于在重力狀態(tài)下的沉降速度，因此離心沉降情況下的Stokes表達式中不考慮重力加速度。Schematic structure of a disc centrifuge particle size analysis system.BI-DCP, Brookhaven, U.S.A.5.1.4 電超聲粒度分析法（Acoustic particle size analysis）電超聲粒度分析法是最新出現(xiàn)的粒度分析方法，粒度測量范圍為10 nm-100 m。當(dāng)聲波在樣品內(nèi)部傳導(dǎo)時，儀器能在一個寬范圍超聲波頻率

13、內(nèi)分析聲波的衰減值，通過測得的聲波衰減譜，計算出衰減值與粒度的關(guān)系。分析中需要粒子和液體的密度、液體的黏度、粒子的質(zhì)量分?jǐn)?shù)等參數(shù)，對乳液或膠體中的柔性粒子，還需要粒子的熱膨脹參數(shù)。這種獨特的電超聲原理優(yōu)點在于它可測高濃度分散體系和乳液的特性參數(shù)，不需要稀釋，避免了激光粒度分析法不能分析高濃度分散體系粒度的缺陷，且精度高，粒度分析范圍更寬。APS-100, Matec Applied Science, U.S.A.NIMBUS, Sympatec, GermanyNIMBUS, Sympatec, Germany電鏡觀察法不同pH值對納米顆粒形成過程的影響（TEM粒度分析）pH2pH3pH4pH

14、5pH6pH8激光粒度分析GarnetCaCO3沉降粒度分析KaolinTungsten carbideAcoustic particle size analysisSiO2 (Standard sample for calibration)TiO25.2 結(jié)構(gòu)表征5.2.1 電子顯微鏡分析5.2.2 振動光譜技術(shù)和核磁共振5.2.3 X射線結(jié)構(gòu)分析技術(shù)5.2.4 X射線光電子能譜5.2.5 掃面隧道顯微術(shù)5.2.6 原子力顯微術(shù)5.2.1 電子顯微鏡分析電子顯微分析優(yōu)點：可做形貌觀察且具有高空間分辨率（透射電子顯微鏡分辨率高達1 ，掃描電子顯微鏡分辨率高達0.6 ）；可做結(jié)構(gòu)分析（選區(qū)電子衍

15、射，微衍射，會聚束衍射）；可做成分分析（X射線能譜、X射線波譜、電子能量損失譜）；可觀察材料的表面與內(nèi)部結(jié)構(gòu)；可同時研究材料的形貌、結(jié)構(gòu)與成分，這是其他微結(jié)構(gòu)研究方法無法做到的。電子顯微分析的局限性在于：儀器價格昂貴，結(jié)果分析較困難，儀器操作復(fù)雜，樣品制備較復(fù)雜。電子顯微鏡的主要種類有：透射電子顯微鏡（TEM），掃描電子顯微鏡（SEM）電子探針顯微分析（EPMA）和掃描透射電子顯微鏡（STEM）。透射電子顯微鏡（TEM）(a) bright-field and (b) dark-field images of Pt nanocrystals, showing a ring shape cont

16、rast in the dark-field image.HERM（TEM）HRTEM images of cubic Pt nanocrystals oriented along (a) 001 and (b) 110.HRTEM images of Pt crystals having twin and stacking fault structures.A series of in-situ TEM images recorded at different specimen temperature, displaying the shape and structural transfor

17、mation of Pt nanocrystals.電子衍射圖A 非晶B 單晶C 多晶D 會聚束掃描透射電子顯微鏡（STEM）High-resolution secondary electron images of silver nanoparticles deposited onto clean surfaces of (a) MgO and (b) -alumina crystals.High-resolution secondary electron image of a large MgO cube.掃描電子顯微鏡（SEM）Ground Konjac particlesNano-siz

18、ed particles of CeO2Nano-sized fibers of TiO2Carbon nanotubes環(huán)境掃描電子顯微鏡（Environmental Scanning Electron Microscope, ESEM）一般的SEM只能在高真空下工作，無法觀察含水或揮發(fā)性的樣品。ESEM的樣品室和需要保持高真空度的電子槍、鏡筒部分分開。ESEM可在低真空下工作，可以觀察含水或揮發(fā)性的樣品，另外還可以做動態(tài)試驗，如加熱樣品，觀察樣品在加熱、結(jié)晶、熔解時的變化。ESEM image of wetting: (a) uncoated fibres and (b) sputter

19、coated fibres (10 min).NaAlH4 milled with 2% TiCl3: A) before, and B) after heating in an ESEM.X射線能譜儀（Energy Dispersive X-ray Spectroscopy, EDS）X-rays emitted from atoms represent the characteristics of the elements and their intensity distribution represents the thickness-projected atom densities i

20、n the specimen.EDS systems can detect X-rays from all the elements in the periodic table above beryllium, Z-4, if present in sufficient quantity. The minimum detection limit (MDL) for elements with atomic numbers greater than Z - 11 is as low as 0.02 % wt., if the peaks are isolated and the spectrum

21、 has a total of at least 2.5 105 counts. In practice, the MDL is about 0.1 % wt. because of a high background count and broad peaks.Under conditions in which the peaks are severely overlapped, the MDL may be only 1 - 2 % wt. For elements with Z 10, the MDL is usually around 1 - 2% wt. under the best

22、 conditions, especially in electron-beam instruments.Standard output of an EDS spectrumThe horizontal axis is the energy scale.The vertical axis is the number of photons per energy interval. The X-ray identification, element and lines, is indicated in the vicinity of the peaks.The EDS unit is often

23、attached in electron column instruments such as the scanning electron microscope (SEM), the electron probe microanalyzer (EPMA), and transmission electron microscopes (TEM). TEMs are further classified as conventional transmission (CTEM) or scanning transmission (STEM) instruments, depending on whet

24、her scanning is the primary imaging mode. Microscopic images and elemental maps of a W/Si double layer TEM sample. (a) The sample SEM image and (b) the enlarged STEM image. The upper layer corresponds to the Si area, while the lower layer corresponds to the W area. The sample is glued on an Au foil.

25、 Elemental maps of (c) W, (d) Si, and (e) Au, and (f) a montage map.X射線波譜儀（X-ray WavelengthDispersive Spectroscopy, WDS）A beam of highly accelerated electrons strikes a small surface (approximately1 m2) of the specimen. The emerging X-rays are then selected on the basis of their wavelength, using Br

26、agg diffraction conditions on an adapted crystal. The peak positions on the spectrometer obey the Bragg law. The peak positions of X-rays from atoms excited by the electron beam are used to identify elements EDSWDS探測效率高低峰值分辨率差好分析元素范圍4Be 92U4Be 92U探測精度0.01%0.001%定性分析快慢定量分析差好設(shè)備維護難，需要液氮容易，不需要液氮樣品制備無嚴(yán)格要

27、求，可分析不平樣品要求平行度較好，表面光滑分析區(qū)域大小小，約50 大，約2000 多元素同時分析容易難用于TEM可以不可以5.2.2 振動光譜技術(shù)和核磁共振（Vibrational Spectroscopies and NMR）Fourier Transform Infrared spectroscopy, FTIR Raman SpectroscopySolid State Nuclear Magnetic Resonance, NMRThe molecules and crystals can be thought of as systems of balls (atoms) connec

28、ted by springs (chemical bonds).振動光譜是指物質(zhì)受光的作用，引起分子或原子基團的振動，從而產(chǎn)生對光的吸收。產(chǎn)生振動吸收的必要條件是振動的頻率與光波的某頻率相等，即光波中的某一波長與分子中的某一個基本振動形式的波長相等，吸收這一波長的光，可以把它的能級從基態(tài)激發(fā)到激發(fā)態(tài)。Each atom has 3 vibrational degrees of freedom. Linear molecules have 3N-5 degrees of vibrational modes. Nonlinear molecules have 3N-6 degrees of vib

29、rational modes.As an example H2O, a non-linear molecule, will have 33-6 = 3 degrees of vibrational freedom, or modes.振動模式可分為兩大類：伸縮振動和彎曲振動。伸縮振動指鍵合原子沿鍵軸方向的振動，這是鍵的長度因原子的伸縮運動而變化，它又可分為對稱伸縮振動和反對稱伸縮振動。彎曲振動是指原子沿垂直于鍵軸方向的振動，它又分為變形振動、搖擺振動和卷曲振動三類。SymmetricalstretchingAntisymmetricalstretchingScissoring RockingW

30、aggingTwisting 分子的振動能級只是分子的運動總能量（包括移動、轉(zhuǎn)動、振動和分子內(nèi)的電子運動）的一部分，其所對應(yīng)的能級間隔介于0.05至1.0 eV之間，它所吸收的輻射主要是中紅外區(qū)。Fourier Transform Infrared spectroscopy, FTIRIn FTIR a broad band source of IR radiation is reflected from the sample (or transmitted, for thin samples). The wavelengths at which absorption occurs are i

31、dentified by measuring the change in intensity of the light after reflection (transmission) as a function of wavelength. These absorption wavelengths represent excitations of vibrations of the chemical bonds and are specific to the type of bond and the group of atoms involved in the vibration.The in

32、frared portion of the electromagnetic spectrum is usually divided into three regions: the far-infrared, approximately 400-10 cm1 (1000-30 m), the mid-infrared, approximately 4000-400 cm1 (30-2.5 m), the near-infrared, approximately 14000-4000 cm1 (2.5-0.8 m) .Quantification is difficult, but with su

33、itable standards 5-10% accuracy in concentrations are achievable.The FTIR spectrum of the oxide of silicon (thin film deposited by CVD). (a) asymmetric stretching mode of vibration; (b) bending mode of vibration; (c) rocking mode of vibration.Spectral parameters typically used in band shape analysis

34、 of an FTIR spectrum: peak position, integrated peak area, and FWHM.Raman SpectroscopyA spectroscopic technique used to study vibrational, rotational, and other low-frequency modes in a system. Rely on inelastic scattering, or Raman scattering, of monochromatic light, usually from a laser in the vis

35、ible, near infrared, or near ultraviolet range.Raman scatteringAn intense monochromatic light beam impinges on the sample. The electric field of the incident radiation distorts the electron clouds that make up the chemical bonds in the sample, storing some energy. When the field reverses as the wave

36、 passes, the distorted electron clouds relax and the stored energy is reradiated. Most of the stored energy is reradiated at the same frequency as that of the incident exciting light. This component is known as the Rayleigh scattering and gives a strong central line in the scattering spectrum. A sma

37、ll portion of the stored energy is transferred to the sample itself, exciting the vibrational modes. The Raman lines appear in the spectrum at frequencies less than that of the incident beam. Scattering geometries appropriate to (a) liquids in capillaries or glass fibers; (b) powder pellets, solid s

38、labs of ceramic or rock, or films on substrates; and (c) oriented single crystals.Nuclear Magnetic Resonance, NMRThe spin states of those nuclei that have either an odd mass or odd atomic number are excited by a strong magnetic field (1-12 Tesla) in a NMR instrument. Excitation between these magneti

39、c levels is performed by absorption of radiofrequency (RF) radiation. By measuring the energy at which the absorptions occur (the resonance energies) the energy differences between the spin (magnetic) states are determined. NMR spectroscopy is one of the principal techniques used to obtain physical,

40、 chemical, electronic and structural information about molecules.A powerful technique that can provide detailed information on the topology, dynamics and three-dimensional structure of molecules in solution and the solid state.5.2.3 X射線結(jié)構(gòu)分析技術(shù)（X-ray characterization）X-rays is a form of electromagneti

41、c radiation, another form of light. X-rays have a wavelength in the range of 0.25 to 0.05 nm.The X-ray diffraction was observed by Von Laue in 1912.X-ray diffraction (XRD)Base on wide-angle elastic scattering of X-rays.The single most important technique for determining the structure of materials ch

42、aracterized by long-range order.Extended X-ray Absorption Fine Structure (EXAFS)Probe the local environment of a particular element without the necessity of long-range order in the materials by exploiting the energy-dependence of X-ray absorption due to interference effects in the individual photoel

43、ectron scattering process.Small-angle elastic X-ray scattering (SAXS)Used for the determination of the microscale or nanoscale structure of particle systems.Shape and size of macromolecules, characteristic distances of partially ordered materials, pore sizes, and other data. LimitationMacromolecules

44、 between 5 and 25 nm.Repeat distances in partially ordered systems of up to 150 nm.USAXS (ultra-small angle X-ray scattering) can resolve even larger dimensions.600 oC下焙燒時間對LaCoO3納米粉體平均顆粒度和晶粒度的影響焙燒時間/h1468平均顆粒度/nm1015152020252530平均晶粒度/nm9.6513.013.713.7納米材料介孔結(jié)構(gòu)的測定納米薄膜的分析納米材料合成中的物相結(jié)構(gòu)分析5.2.4 X射線光電子能譜（

45、X-ray Photoelectron Spectroscopy, XPS）Also known as Electron Spectroscopy for Chemical Analysis, ESCAThe most broadly applicable general surface analysis technique.XPS can detect all elements except hydrogen and helium.Identify the elements present from their Binding Energies.Detect elemental compos

46、ition, empirical formula, chemical state and electronic state of the elements.The relative concentrations of the different elements present can be determined from relative peak intensities.The depth of the solid material sampled varies from the top 2 atomic layers to 15-20 layers.The area examined c

47、an be as large as 1 cm x 1 cm or as small as 70 m x 70 m (10-m diameter spots may be achieved with very specialized equipment).The absolute sensitivity depending on the element: 0.01-0.3% at. (0.1 at% = 1 part per thousand = 1000 ppm). Basic components of a monochromatic XPS system.5.2.5 掃描隧道顯微術(shù) (Sc

48、anning Tunneling Microscopy, STM)STM developed by Dr. Gerd Binnig and his colleagues in 1981 at the IBM Zurich Research Laboratory, Rueschlikon, Switzerland, is the first instrument capable of directly obtaining three-dimensional images of solid surfaces with atomic resolution.Binnig and Rohrer rece

49、ived a Nobel Prize in Physics in 1986 for their discovery.The STM is based on the concept of quantum tunneling. When a conducting tip is brought very near to the surface to be examined, a bias (voltage difference) applied between the two can allow electrons to tunnel through the vacuum between them.

50、 The resulting tunneling current is a function of tip position, applied voltage, and the local density of states (LDOS) of the sample.Information is acquired by monitoring the current as the tips position scans across the surface, and is usually displayed in image form. 100100 nm2 STM images for Au

51、deposited at room temperature on the 11 TiO2 (110) surface: (a) 0.013 ML Au; (b) 0.08 ML Au; (c) 0.2ML Au. A set of consecutive STM images from an LEESR/STM processed area on a native Si oxide/Si surface. (a) 170 s, (b) 448 s, (c) 644 s, and (d) 837 s after the LEESR etching. STM images of evaporate

52、d C60 film on a gold-coated freshly-cleaved mica using a mechanically sheared Pt-Ir (80-20) tip in constant height mode.5.2.6 掃描探針顯微術(shù)（Scanning Probe Microscopy, SPM）Based on the design of the STM, in 1985, Dr. Gred Binnig et al. developed an Atomic Force Microscope (AFM) to measure ultra-small force

53、s (less than 1 N) present between the AFM tip surface and the sample surface.Unlike the STM, A conductive surface of sample is not the necessary condition for SPM.Atomic force microscopy (AFM) or scanning force microscopy (SFM) is a very high-resolution type of scanning probe microscopy.AFMThe AFM c

54、onsists of a cantilever with a sharp tip (probe) at its end that is used to scan the specimen surface. The cantilever is typically silicon or silicon nitride with a tip radius of curvature on the order of nanometers. When the tip is brought into proximity of a sample surface, forces between the tip

55、and the sample lead to a deflection of the cantilever according to Hookes law. Depending on the situation, forces that are measured in AFM include mechanical contact force, van der Waals forces, capillary forces, chemical bonding, electrostatic forces, magnetic forces, Casimir forces, solvation forc

56、es, etc. Typically, the deflection is measured using a laser spot reflected from the top surface of the cantilever into an array of photodiodes. Other methods that are used include optical interferometry, capacitive sensing or piezoresistive AFM cantilevers. Principles of operation of (a) a commerci

57、al small sample AFM, and (b) a large sample AFM.AFM (used) cantilever SEM micrographs of a square-pyramidal PECVD Si3N4 tip (a), a square pyramidal etched singlecrystal silicon tip (b), and a three-sided pyramidal natural diamond tip (c).Typical AFM images of freshly-cleaved (a) highly-oriented pyro

58、lytic graphite and (b) mica surfaces taken using a square pyramidal Si3N4 tip.(a) Topographic AFM image of an array of 50 nm width and 125 nm periodicity grooves on Si(001) surface. (b) SEM image of the cut Si tip used for tribological measurement.AFM image of sepiolite fibers(a and b) SEM images fr

59、om the historical glass A (medieval type) at different magnifications, (c) AFM image from the historical glass A, (d) AFM image from the model glass A.5.3 性能表征5.3.1 力學(xué)性能5.3.2 熱學(xué)性質(zhì)5.3.3 光學(xué)性質(zhì)5.3.4 磁性5.3.5 電學(xué)性質(zhì)5.3.6 擴散問題5.3.1 力學(xué)性能納米結(jié)構(gòu)材料力學(xué)性能的研究仍處于研究階段，尚未形成成熟的理論，可就以下幾個方面進行探討： 1) Hall-Petch關(guān)系 2) 模量 3) 超塑性

60、 4) 強度、硬度、韌性和塑性1) Hall-Petch關(guān)系Hall-Petch關(guān)系描述多晶材料的屈服應(yīng)力（或硬度）與晶粒尺寸的關(guān)系；建立在位錯塞積理論基礎(chǔ)上，經(jīng)過大量實驗的證實，總結(jié)得到；y 0.2屈服應(yīng)力；0移動單個位錯所需克服的點陣磨擦力；K常數(shù)，與材料種類相關(guān)；d平均晶粒尺寸。如果用硬度表示，則經(jīng)驗規(guī)律，適用于各種粗晶材料（K為正值）；對于不同種類的納米材料，K可能為正值或負(fù)值。納米晶體材料Fe，Pd，Cu，Ni的維氏硬度與d-1/2的關(guān)系納米晶體材料Nb3Sn，TiO2和Ni-P的維氏硬度與d-1/2的關(guān)系電沉積納米晶Ni的維氏硬度與d-1/2的關(guān)系界面在納米結(jié)構(gòu)材料中數(shù)量龐大，可從