金属材料表面功函数的计算方法研究

功函数和费米能级的公式1 功函数的定义首先，我们先看一下功函数(又称功函、逸出功)是指要使一粒电子立即从固体表面中逸出，所必须提供的最小能量(通常以电子伏特为单位)。

这里“立即”一词表示最终电子位置从原子尺度上远离表面但从宏观尺度上依然靠近固体。

功函数不是材料体相的本征性质，更准确的说法应为材料表面的性质(比如表面暴露晶面情况和受污染程度)功函数是金属的重要属性。

功函数的大小通常大概是金属自由原子电离能的二分之一。

The work function W for a given surface is defined by the difference W = - eϕ - EFwhere −e is the charge of an electron, ϕ is the electrostatic potential in the vacuum nearby the surface, and EF is the Fermi level (electrochemical potential of electrons) inside the material. The term −eϕ is the energy of an electron at rest in the vacuum nearby the surface. In words, the work function is thus defined as the thermodynamic work required to remove an electron from the material to a state at rest in the vacuum nearby the surface.我们再看下IUPAC 官网的解释：The minimum work needed to extract electrons from the Fermi level of a metal M across a surface carrying no net charge. It is equal to the sum of the potential energy and the kinetic Fermi energy taken with the reverse sign:ϕM=−(Ve+εFe)ϕM=−(Ve+εeF)where $V_{e}$ is the potential energy for electrons in metals and $\varepsilon_e^ F$ is the kinetic energy of electrons at the Fermi level.2 VASP 计算功函数的过程从前面的定义中可以看出，计算功函数我们只需要得到体系的费米能级和电子所处的静电势能，然后求差即可。

常见金属材料功函数金属材料是一类具有良好导电性、导热性和可塑性的材料，广泛应用于工业制造、建筑工程、电子技术等领域。

金属材料的功函数是指材料表面所需的最小能量，是表征材料电子行为的重要参数。

下面将介绍几种常见金属材料的功函数。

首先是铜(Cu)材料。

铜是一种常见的导电性和导热性优良的金属材料，常用于电子电路的导线和散热器。

铜的功函数约为4.72eV。

它的导电性和导热性使得铜成为优秀的材料选择。

接下来是铝(Al)材料。

铝是一种轻质金属材料，功函数约为 4.28eV。

铝具有优良的导电性和可塑性，被广泛应用于建筑工程和制造业，如制造飞机、汽车和包装材料等。

锡(Sn)是一种重要的金属材料。

锡的功函数约为4.26eV。

锡具有良好的可焊性和可塑性，广泛应用于电子电路的焊接和包装材料。

铁(Fe)是一种常见的金属材料，功函数约为4.5eV。

铁具有良好的导磁性和可塑性，广泛应用于建筑、机械制造和交通运输等领域。

镍(Ni)是一种重要的金属材料。

镍的功函数约为5.01eV。

镍具有良好的耐腐蚀性和磁性，被广泛应用于电子技术、航空航天和化工等领域。

铬(Cr)是一种常见的金属材料，功函数约为4.5eV。

铬具有良好的耐腐蚀性和磁性，广泛应用于建筑、车辆和石油化工等领域。

钛(Ti)是一种轻质金属材料，功函数约为4.95eV。

钛具有良好的耐蚀性和高强度，广泛应用于航空、航天、医疗和化工等领域。

除了以上所述的几种金属材料，还有许多其他常见的金属材料，如黄铜、锌、铅等，它们的功函数也各不相同，但都具有良好的导电性、导热性和可塑性。

综上所述，金属材料的功函数是表征材料表面最小能量的重要参数，不同的金属材料具有不同的功函数。

这些金属材料根据其导电性、导热性、可塑性等特性被广泛应用于各个领域。

对于选用合适金属材料的工程项目或实验研究来说，了解材料功函数是非常重要且必不可少的。

常见金属材料功函数金属材料的功函数是指其中一种金属表面上需要供给的最小能量，以将一电子从金属表面抽离出来的过程。

它是金属物理性质的重要参数，与金属的导电性、光电效应、表面反应等密切相关。

以下将介绍常见金属材料的功函数。

1.铜（Cu）铜是常见的金属材料之一，其功函数约为4.7eV。

因为铜的功函数较高，所以它对光电效应的响应较弱，对光源要求较高。

铜具有良好的导电性和热传导性能，广泛应用于电子器件、电线电缆等领域。

2.铁（Fe）铁是一种重要的金属材料，其功函数约为4.5eV。

铁具有良好的导磁性和机械性能，广泛用于制造机械设备、建筑结构和电磁器件。

因为铁的功函数较高，所以它对光电效应的响应较弱，对于阳光的利用较不理想。

3.铝（Al）铝是一种轻金属，其功函数约为4.1eV。

铝具有良好的导电性和热导性，广泛用于制造飞机、汽车、建筑等领域。

铝的功函数较低，所以它对光电效应的响应较好，对太阳光的利用效率比较高。

4.锌（Zn）锌是一种常见的金属材料，其功函数约为4.3eV。

锌具有良好的抗腐蚀性和导电性能，广泛应用于锌电池、镀锌钢板等领域。

锌的功函数较低，所以它对光电效应的响应较好，对太阳光的利用效率较高。

5.银（Ag）银是一种重要的金属材料，其功函数约为4.3eV。

银具有良好的导电性和热导性能，广泛应用于电子器件、化学催化剂等领域。

银的功函数较低，所以它对光电效应的响应较好，适用于光电器件制造。

6.铂（Pt）铂是一种贵金属，其功函数约为5.7eV。

铂具有优异的化学稳定性和催化性能，广泛应用于化工、电子等领域。

铂的功函数较高，所以它对光电效应的响应较弱，对光源要求较高。

以上是常见金属材料的功函数介绍。

不同金属的功函数差异较大，这使得它们在电子器件、光电器件、化学反应等方面具有不同的应用潜力。

更深入地研究金属材料的功函数及其影响因素，有助于开发和优化金属材料的性能，满足不同领域的需求。

金属氧化物材料的功函数和势垒调控研究金属氧化物材料作为一种新型的功能材料，在各个领域中有着广泛的应用。

它们具有高温稳定性、优异的力学性能、超硬度等特点，因此受到了越来越多科学家的关注。

其中，功函数和势垒调控技术是一种常见的手段，用于改变金属氧化物材料的表面性质，以满足广泛的应用需求。

一、功函数调控技术功函数是指材料表面电子动能与真空相离散能的差值，其大小影响着材料表面的可见光吸收和能带结构等性质。

在金属氧化物材料中，功函数往往是其表面电子能带结构和性质的关键参数之一。

因此，通过调整功函数可以实现对其表面性质的调节。

目前最常用的功函数调节方法是通过改变表面化学组成或加入杂质等方式。

例如，通过表面化学修饰的方法，实现了阳离子掺杂的LaNiO3薄膜的功函数调控。

研究表明，掺杂阳离子后，薄膜的功函数比未掺杂薄膜降低了0.37 eV左右，这使得其表面能带结构得到了优化。

同样地，通过改变Al2O3氧化物表面的羟基含量，也可以实现其功函数的调控。

具体而言，通过表面羟基化学反应，制备出具有不同羟基含量的Al2O3氧化物，实现了其对Li-Al-HO*的CO2选择性吸附的调控。

另外，利用表面自组装单分子膜修饰的方式，也可以实现对材料表面功函数的调节。

例如，在氮化硅表面修饰一层含有氟的自组装单分子膜可以大幅度降低功函数，这对于氮化硅的光电传感器等应用具有重要意义。

二、势垒调控技术势垒是指在光电化学反应过程中，光子与表面电子的相互作用所需克服的电势差。

势垒的高低影响着光电催化反应的效率和能带结构等性质。

通过调整势垒，可以实现对金属氧化物材料表面光电化学反应性能的调控。

目前最常用的势垒调节方法是通过吸附分子和表面修饰等方式实现的。

例如，有机分子修饰的CdS光催化剂的势垒调控。

通过在CdS表面修饰含有羟基的有机分子，可以改变CdS的势垒，并提高其光催化产氢的效率。

另外，也有研究显示，通过对Pt表面进行阴离子的修饰（如氧、硫、氮等），也可以实现其表面催化活性的调控。

金属逸出功公式
金属逸出功公式是描述金属表面电子逸出的一种数学公式。

在金属表面，电子受到金属原子的束缚，需要克服金属原子的吸引力才能逸出金属表面。

金属逸出功公式描述了电子逸出所需要的能量与金属表面的物理性质之间的关系。

金属逸出功公式可以表示为：
Φ = hν - E
其中，Φ表示金属的逸出功，h表示普朗克常数，ν表示光子的频率，E表示金属表面的功函数。

这个公式说明了金属表面电子逸出所需要的能量与光子的频率和金属表面的物理性质之间的关系。

金属逸出功公式的应用非常广泛。

在光电子学中，金属逸出功公式被用来描述光电效应。

当光子照射到金属表面时，如果光子的能量大于金属的逸出功，那么金属表面的电子就会逸出。

这个过程被称为光电效应。

金属逸出功公式可以用来计算光电效应的能量阈值。

金属逸出功公式还被用来描述金属表面的化学反应。

在化学反应中，金属表面的电子可以参与反应，但是需要克服金属原子的吸引力才能离开金属表面。

金属逸出功公式可以用来计算化学反应中电子逸出所需要的能量。

金属逸出功公式是描述金属表面电子逸出的一种数学公式。

它可以
用来计算光电效应的能量阈值和化学反应中电子逸出所需要的能量。

这个公式的应用非常广泛，对于研究金属表面的物理和化学性质非常重要。

金属功函数在固体物理的意义全文共四篇示例，供读者参考第一篇示例：金属功函数在固体物理中是一个重要的概念，它不仅可以帮助我们理解金属的物理性质，还有助于我们研究和设计新型金属材料。

金属功函数是指在金属表面上需要克服的电子与金属原子相互作用的能量障碍，它决定了电子在金属中运动的自由程度，也直接影响了金属的导电性、热导性等重要性质。

本文将探讨金属功函数在固体物理中的意义，并介绍金属功函数的计算方法和应用。

金属功函数在固体物理中的意义主要体现在以下几个方面：1. 解释金属的导电性：金属功函数体现了金属中电子的自由程度，即需要克服多大的能量障碍才能使电子逸出金属表面。

金属功函数越小，金属中电子的自由度越高，导电性就越好。

金属功函数可以用来解释不同金属的导电性差异，也可以作为研究金属导电机制的重要参数。

2. 影响金属的热导性：金属功函数还与金属的热导性密切相关。

通常情况下，具有较小金属功函数的金属也具有较高的热导性，因为功函数小意味着电子在金属中能够更自由地传递热量，从而增加了金属的热导率。

3. 金属的表面电子结构：金属功函数还可以揭示金属的表面电子结构，即表面电子与金属原子之间的相互作用。

金属功函数的大小与表面电子结构的稳定性直接相关，通过研究金属功函数可以更深入地了解金属的表面性质。

接下来，我们将介绍金属功函数的计算方法和应用：1. 计算方法：金属功函数的计算通常使用第一性原理计算方法，如密度泛函理论（DFT）等。

这些计算方法可以准确地模拟金属表面的电子结构和相互作用，从而得到金属功函数的数值。

通过这些计算方法，我们可以系统地研究不同金属的功函数和其导电性、热导性等性质之间的关系。

2. 应用领域：金属功函数的应用涉及到材料科学、表面科学、纳米技术等多个领域。

在材料设计中，金属功函数可以作为评估金属材料性能的重要参数，有助于设计更具导电性、热导性等优良性质的金属材料。

在表面科学领域，金属功函数可以用来研究金属表面的化学反应、吸附行为等过程。

钙钛矿铜的功函数钙钛矿（perovskite）是一种重要的材料，在太阳能电池等领域具有广阔的应用前景。

对于钙钛矿材料来说，了解其功函数是非常重要的，它可以影响材料的导电性和光电性能。

本文将深入分析钙钛矿铜的功函数，并探讨其测量方法和影响因素。

功函数是指材料表面电子的能级与真空能级之间的能量差，即引出电子的最小能量。

它是一个重要的物理量，用来描述材料的电子亲和力和导电性。

对于钙钛矿铜来说，其功函数是描述其电子将要脱离材料表面进入真空态所需的最小能量。

功函数通常用电子伏特（eV）作为单位来表示。

测量钙钛矿铜的功函数可以采用多种方法，其中比较常用的有光电子能谱（XPS）和紫外光电子能谱（UPS）。

XPS是一种通过测量材料表面电子发射能谱来分析材料表面组分和电子能级的方法。

UPS是通过测量材料表面电子随能量的变化来获得材料的功函数。

钙钛矿铜的功函数通常在4-5 eV之间，具体数值取决于实验条件和材料制备方法等因素。

实际测量中，功函数的值可以受到一些因素的影响，如材料的纯度、表面处理和环境条件等。

为了准确测量功函数，一般需要对材料进行严格的表面处理，以去除可能存在的杂质和氧化物等。

对钙钛矿铜的功函数进行调控可以通过一些方法实现。

例如，可以通过化学处理、表面修饰或合金化等方法来改变材料表面的化学性质和形貌，从而改变其功函数。

此外，钙钛矿铜可以与其他材料进行界面调控，通过调节界面的能带结构和电子结构来调控功函数。

在光电器件等应用中，了解钙钛矿铜的功函数对于优化器件性能和提高效率非常重要。

功函数的大小将影响材料的导电性和光电转换效率。

较低的功函数意味着更容易从钙钛矿铜材料中引出电子，提高了器件的载流子传输和电荷注入效率，有利于提高器件性能。

综上所述，钙钛矿铜的功函数对于电子能级和材料性能具有重要意义。

准确测量和调控功函数可以为相关领域的研究提供指导，并有助于优化钙钛矿材料的性能和应用。

PLEASE SCROLL DOWN FOR ARTICLEThis article was downloaded by: [Su, H. L.]On: 14 March 2011Access details: Access Details: [subscription number 934653370]Publisher Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UKPhilosophical Magazine Letters Publication details, including instructions for authors and subscription information:/smpp/title~content=t713695410Changes of hardness and electronic work function ofZr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 bulk metallic glass on annealing K. Luo a ; W. Li a ; H. Y. Zhang a ; H. L. Su aa Faculty of Material and Photoelectronic Physics, Key Laboratory of Low Dimensional Materials &Application Technology (Ministry of Education), Xiangtan University, Hunan, Xiangtan 411105, PRChina First published on: 02 February 2011To cite this Article Luo, K. , Li, W. , Zhang, H. Y. and Su, H. L.(2011) 'Changes of hardness and electronic work function of Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5 bulk metallic glass on annealing', Philosophical Magazine Letters, 91: 4, 237 — 245, First published on: 02 February 2011 (iFirst)To link to this Article: DOI: 10.1080/09500839.2010.539989URL: /10.1080/09500839.2010.539989Full terms and conditions of use: /terms-and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.Philosophical Magazine LettersVol.91,No.4,April 2011,237–245Changes of hardness and electronic work function ofZr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5bulk metallic glass on annealingK.Luo,W.Li *,H.Y.Zhang and H.L.SuFaculty of Material and Photoelectronic Physics,Key Laboratory of Low Dimensional Materials &Application Technology (Ministry of Education),Xiangtan University,Hunan,Xiangtan 411105,PR China(Received 5April 2010;final version received 9November 2010)The hardness and electronic work function (EWF)of a bulk metallic glass,namely Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5,have been studied experimentally,withan emphasis on the effect of heat treatments.The glass was annealed atdifferent time and temperatures,and its hardness and EWF measured usingthe Rockwell indentation technique and a scanning Kelvin probe system,respectively.It is found that the EWF decreases with annealing time andtemperature,whereas the hardness increases.This study shows a closerelationship between hardness and EWF,indicating that the EWF could bea sensitive parameter for characterising and investigating the mechanicalbehaviour of BMG at the electronic level.Keywords:bulk metallic glass;annealing;electronic work function;hardness1.Introduction There has been much interest in bulk metallic glasses (BMGs)because of their potential engineering applications [1,2].Compared with crystalline alloys,metallic glasses exhibit excellent mechanical properties including high compressive strengths and hardness values [1–4].Besides,they show high corrosion and wear resistance,aswell as good magnetic properties [5].Alloy systems,such as Zr–Ti–Cu–Ni–Be and Pd–Cu–Ni–P,have good glass-forming ability (cooling rates below 100K/s)and can be prepared using recent developments [6,7].However,these glasses are extremely brittle [8,9],which compromises their potential engineering applications.Despite all the virtues of BMGs,the disadvantage of low plasticity,arising from their disordered atomic structure [10],needs further investigation.To investigate the disordered atomic structure,the glass transition of BMGs has attracted much attention,because it impinges on the development of new systems of BMGs as well as being of intrinsic interest.The glass transition,i.e.the transition from a state of internal equilibrium (supercooled liquid)into a non-equilibrium state (glass)and back,is associated with a change in enthalpy;see for example [11,12].In the study of BMGs,the glass transition temperature,T g ,is one of the most *Corresponding author.Email:wenl@ualberta.caISSN 0950–0839print/ISSN 1362–3036onlineß2011Taylor &FrancisDOI:10.1080/09500839.2010.539989D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011important characteristic parameters.When a glass is annealed at a temperature 5T g ,structural relaxation (so-called physical ageing)takes place [11,12].In this process,the molecular mobility changes and there is a decrease in enthalpy and free volumes [13].The decrease in free volume during the annealing process makes plastic deformation more difficult and thus embrittlement occurs [14,15].Characterisation of the mechanical properties of BMGs is very important for structural applications.Hardness,as a measure of resistance to permanent deformation and thus to wear,is an important parameter for applications.The Rockwell hardness (HR)test is the most widely used mechanical method for determining hardness.The HR test,introduced in the 1920s,was developed based on force and displacement calibrations [16,17].Its measurement uncertainties have been largely reduced in recent years by new methods,such as the employment of stylus and laser interferometry techniques [17].In order to achieve a fundamental understanding of the mechanical properties of BMGs,it is necessary to take investigations to the electron level.As a fundamental characteristic of solid surfaces,the electronic work function (EWF)is a promising parameter suitable for such studies.The EWF of a metal is defined as the difference between the electrochemical potential inside the metal and the electrostatic potential just outside it [18].It can be easily determined using the scanning Kelvin probe (SKP)technique [19].The measurement system consists of a digital oscillator,a data acquisition unit and a sample translation device,controlled by a host PC.On account of its inherent high surface sensitivity and lateral resolution,it can be employed more powerfully for the analysis of a wider range of materials,at different temperatures and pressures,than any other surface analysis techniques [18,19].In this letter,we report the measurements of hardness and EWF of BMG samples,which were heat treated for different annealing times and temperatures.The aim is to establish a relationship between the hardness and the EWF,which can be useful when investigating the microstructure of BMGs.2.Experimental detailsThe material used in this study has a composition of Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5,which can be prepared by mature processing technology and has shown promising applications.Alloy ingots were prepared by arc melting mixtures of pure metal elements in a titanium-gettered argon atmosphere,followed by suction casting into a copper mould at about 1atm pressure.BMG samples with dimensions of 12Â3Â2mm 3(the size of the copper mould)were annealed in a resistance furnace for times of 30and 60min,and at four temperatures,320 C,360 C,380 C and 450 C,during both annealing periods.The crystalline structures of the as-cast and annealed samples were characterised by X-ray diffraction.Thermal analysis was performed by differential scanning calorimetry (DSC)under an argon atmosphere at a heating rate of 0.33K/s.Rockwell indentation experiments were conducted using a Wilson indenter ( ¼60 ).Both geometrical and non-geometrical factors affect the hardness performance of the indenters.Geometrical properties include the mean tip radius and the maximum and minimum radii,profile peak and profile valley deviations,the238K.Luo et al.D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011mean cone angle as well as the maximum and minimum cone angles,the cone flank straightness,any holder axis alignment error,surface roughness and surface defects.Non-geometrical factors include the mechanical properties of the diamonds and the soldering of the diamond prism into the holder.Here,the maximum loads (F max )were chosen as 10,20,30,40and 50N for the Rockwell test.The loading rate and the holding time at the maximum load were controlled at 0.02N/s and 100s,respectively.Prior to the indentation tests,the samples were polished in successive steps to 1m m finish using diamond pastes.The EWF was measured using an SKP system,which was provided by KP Technology Ltd.(Caithness,UK).The system had high resolution (550m eV)and the probe spacing could be controlled within 40nm.A three-axis microstepper positioner permitted high-resolution sample positioning (0.4m m/step).In this study,a gold tip with a diameter equal to 1mm was used and the oscillation frequency of the Kelvin probe was set as 173Hz.The tested samples were then lightly polished using a slurry containing aluminium oxide powder (0.05m m).After polishing,the samples were ultrasonically cleaned in reagent-grade acetone (10min)and reagent alcohol (5min).All tests were carried out on the polished surfaces without etching in order to reduce the probability of formation of surface films.For the EWF measurement,the surface under study was scanned line by line by the Kelvin probe over an area of 1Â1mm which covered 10Â10¼100points.Each measured value is therefore an average over 100measurements,which is statistically more precise than that of a measurement at a single point.In this study,all presented EWF values were obtained by averaging four measurements.3.Results and discussion Figure 1shows DSC thermograms of the as-cast and the isothermal annealed samples.They exhibit an endothermic feature characteristic of the glass transition.Here,T g is defined as the onset temperature of the glass transition,T x is the onset temperature of the crystallisation event.D T ,defined as T x ÀT g ,is referred to as the supercooled liquid region.The DSC trace of the as-cast alloy reveals that the glasstransition temperature is 623K and the supercooled liquid region spans 80K before the onset of crystallisation at 703K.A comparison between the DSC scans obtained from the as-cast and the annealed samples shows no obvious difference.However,closer examination of the glass transition regime (indicated by the dotted box in Figure 1a,and shown magnified in Figure 1b)reveals subtle but systematic changes at about 650K.A sharp exothermic peak is observed for the as-cast glass prior to the endothermic reaction caused by the glass transition,and the exothermal enthalpy is about 18J/g.With increasing annealing temperature,the height of exothermic peak reduces gradually.After 523K (12h),573K (12h),593K (1h)and 633K (1h)annealings,the exothermal enthalpy values are 13,7.2,8.4and 2.7J/g,respectively.This means that annealing at 633K for 1h leads to a reduction in the exothermal enthalpy by 85%with respect to that of the as-cast sample.The exothermic peak prior to T g during the DSC measurements is known to be caused by structural relaxation well below the glass transition temperature [20–24].It has been well-documented that the exothermic enthalpy is the result of annihilation Philosophical Magazine Letters 239D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011of excess free volume,D v f .The reduction in the free volume D v f gives rise to a heat release D H ,when the glass sample is heated in DSC,and D H is proportional to D v f[20–24].Hence,it is possible to estimate the free-volume changes that occur during annealing by monitoring D H [20–24].From Figure 1b,it can be seen that DHFigure 1.(a)DSC curves of the as-cast and annealed samples and (b)enlarged view of the glass transition regime.240K.Luo et al.D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011gradually decreases on account of the reduction of free volume upon structural relaxation annealing.So,we choose the proper annealing temperatures for low-temperature heat treatment based on the result of DSC to investigate the microstructure of the metallic glass.The result of the latter experiment can be interpreted by the free-volume theory.The as-cast and annealed samples were studied by scanning electron microscopy (SEM).Shallow wells on the surface of the BMGs were seen (Figure 2)after 60min of annealing.They became more obvious although the amount of them was unchanged as the annealing temperature became higher.These changes were attributed to structural relaxation in the annealing process according to the analysis of Cernoskov et al.[12].One can see from Figure 2that the graininess is in existence both before and after annealing.This means that crystallisation has not taken place,thus allowing the study of microstructural changes during low-temperature annealing in this study.Figure 3shows the variations in the EWF of annealed Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5samples with respect to annealing temperature and annealing time.From Figure 3a,one can see that the EWF decreased as the annealing temperature increased.When the annealing temperature increased below the onset of crystallisation at 430 C (703K),both curves decreased gradually following an approximate linear relation-ship,and then decreased further when the annealing temperature reached 445 C.Moreover,by comparing the two curves in Figure 3a,one can see that the EWF of the 60min annealed samples was lower that of the 30min annealed ones at each annealing temperature,with an approximately constant decrement,except for the point at 450 C.As can also be seen in Figure 3b from another perspective,the EWF decreased as the annealing time increased while the as-cast sample and a 10min annealed sample were added for comparison,for an annealing temperature of 380 C.The decrease in the EWF becomes more gradual as the annealing time is continuously increased.These results indicate that the annealing treatment lowers the minimum energy required to extract an electron from the inside of a bulk solid to the outside.This may arise from a falling free volume in the annealed BMG.Wigner and Bardeen [25]proposed that the work function can be expressed as¼À þD ¼À Àep "0:ð1ÞFigure 2.SEM micrographs of the (a)as-cast,(b)360 C annealed (t ¼60min)and (c)450 C annealed (t ¼60min)alloys.Philosophical Magazine Letters 241D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011The first term in Equation (1)is the bulk chemical potential of the electrons relative to the mean electrostatic potential in the metal interior,and the second term corresponds to the energy necessary to penetrate the dipole barrier D at the surface.The surface dipole barrier is formed by the redistribution of electron density on the surface and the chemical potential is a parameter that is inversely proportional to the free volume [26].Since is inversely proportional to the free volume of the bulk[27],Figure 3.Variations of the EWF of the annealed samples treated during (a)isochronal annealing and (b)isothermal annealing.242K.Luo et al.D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011the EWF decrease as the free volume is decreased by annealing is consistent with the EWF results.Therefore,when the free volume decreases gradually by low-temperature isochronal annealing,the EWF decreases approximately linearly as shown in Figure 3a.The decline became more obvious when the annealingtemperature lies beyond the onset of crystallisation temperature,which results in the annihilation of excess free volume.Similarly,the EWF decreases as the annealing time increases,which also has a positive effect on the decline of free volume.Figure 4shows the variation of hardness of 60min annealed Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5BMG with respect to various annealing temperatures,and compared with the work function curve.It can be seen that the hardnessincreases with the annealing temperature during low-temperature annealing because of structural relaxation,which is consistent with previous studies [26,28–30].The hardness displays an obvious rise in the first period of increasing annealing temperature,after which the curve becomes smoother when the annealing temper-ature exceeds the onset of crystallisation temperature.An increase in hardness with annealing has been reported for a wide variety of BMGs [31].In most cases,the hardness increase is linear with the crystalline volume fraction and this is attributed to micromechanisms in the nanocrystalline phase [32].It has also been suggested that solute enrichment in the amorphous phase arising from primary crystallisation could be responsible for the continuous increase in the hardness even when the crystalline phase is softer [32].Structural relaxation occurs through the annealing treatment and the free volume decreases.Thus,the two curves in Figure 4show an inverse relationship.A higher EWF value corresponds to a lower hardness.In summary,structural relaxation of the BMG,caused by an increase in the annealing temperature or the time,decreases the free volume,resulting in an increase in the Figure 4.Variations of the EWF and hardness of 60min annealed samples with respect to annealing temperatures.Philosophical Magazine Letters 243D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011EWF and a decrease in the hardness.The relationship between EWF and hardness indicates that the EWF is a very promising parameter for fundamental understand-ing of the mechanical properties of BMG.4.ConclusionsIn this study,we have investigated the effects of isochronal and isothermal annealing treatments on the hardness and the EWF of a BMG with a composition of Zr 41.2Ti 13.8Cu 12.5Ni 10Be 22.5.The experimental results show that the EWF of the metallic glass decreases with an increase in the annealing time and temperature while the hardness increases with an increase in the annealing temperature.Moreover,there is a relation between the variation of EWF and hardness,namely if the annealing temperature is below the glass transition temperature (430 C),the EWF decreases and the hardness increases gradually,whereas if the annealing temperature is above 445 C,the decrease in EWF and the increase in hardness both become significantly greater.Such results can be interpreted using the concept of structural relaxation and free-volume theory.The relationship between hardness and EWF indicates that the latter is closely related to mechanical properties and could thus be used a sensitive parameter for characterising and investigating the mechanical behaviour of BMGs.Acknowledgements The authors acknowledge the financial support of the Natural Science Foundation of China (Reference Nos.10972190,10872177and 20973146245),and the State Key Laboratory of Advanced Metals Materials 246(Reference No.EG512677781CN).The project is also sponsored by the Scientific Research Foundation for Returned Overseas Chinese Scholars,State Education Ministry.References[1]A.Inoue,B.L.Shen,A.R.Yavari and A.L.Greer,J.Mater.Res.18(2003)p.1487.[2]V.Keryvin,V.H.Hoang and J.Shen,Intermetallics 17(2009)p.211.[3]C.J.Gilbert,R.O.Ritchie and W.L.Johnson,Appl.Phys.Lett.71(1997)p.476.[4]J.Das,W.Lo ser,U.Ku hn,J.Eckert,S.Roy and L.Schultz,Appl.Phys.Lett.82(2003)p.4690.[5]J.F.Loffler,Intermetallics 11(2003)p.529.[6]T.Waniuk,J.Schroers and W.Johnson,Appl.Phys.Lett.78(2001)p.1213.[7]Y.Gao,J.Shen,J.Sun,D.Chen,G.Wang,H.Wang,D.Xing,H.Xian and B.Zhou,Mater.Lett.57(2003)p.2341.[8]P.Hess,S.Poon,G.Shiflet and R.Dauskardt,J.Mater.Res.20(2005)p.783.[9]X.Gu,S.Poon and G.Shiflet,J.Mater.Res.22(2007)p.344.[10]X.H.Lin and W.L.Johnson,J.Appl.Phys.78(1995)p.6514.[11]I.M.Hodge,J.Non-Cryst.Solids 169(1994)p.211.[12]E.Cernoskov,Z.Cernosek,J.Holubov and M.Frumar,J.Non-Cryst.Solids 284(2001)p.73.[13]M.Yan,J.F.Sun and J.Shen,J.Alloys Compds.381(2004)p.86.244K.Luo et al.D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011[14]N.Nagendra,U.Ramamurty,T.T.Goh and Y.Li,Acta Mater.48(2000)p.2603.[15]P.Murali and U.Ramamurty,Acta Mater.53(2005)p.1467.[16]G.Barbato,S.Desogus and R.Levi,VDI Ber.(1978)p.97.[17]J.F.Song,S.Low,D.Pitchure,A.Germak,S.DeSogus,T.Polzin,H.-Q.Yang and H.Ishida,Measurement 24(1998)p.197.[18]W.Li and D.Y.Li,Wear 253(2002)p.746.[19]W.Li and D.Y.Li,J.Chem.Phys.122(2005)p.064708.[20]F.Spaepen,Acta Metall.25(1977)p.407.[21]A.van den Beukel and S.Radelaar,Acta Metall.31(1983)p.419.[22]S.S.Tsao and F.Spaepen,Acta Metall.33(1985)p.881.[23]A.van den Beukel and J.Sietsma,Acta Metall.38(1990)p.383.[24]A.Slipenyuk and J.Eckert,Scr.Mater.50(2004)p.39.[25]E.Wigner and J.Bardeen,Phys.Rev.48(1935)p.84.[26]G.He,J.Eckert and M.Hagiwara,Mater.Lett.60(2006)p.656.[27]W.J.Wright,T.C.Hufnagel and W.D.Nix,J.Appl.Phys.93(2003)p.1432.[28]J.Gutierrez,J.M.Barandiar,P.Minguez,Z.Kaczkowski,P.Ruuskanen,G.Vlas,P.Svec and P.Duhaj,Sens.Actuators A Phys.106(2003)p.69.[29]J.Gutierrez,J.M.Barandiaran and Z.Kaczkowski,Mater.Sci.Eng.370(2004)p.392.[30]J.Filipecki and A.V.D.Beukel,J.Mater.Sci.Lett.9(1990)p.1169.[31]J.Basu,N.Nagendra,Y.Li and U.Ramamurty,Phil.Mag.83(2003)p.1747.[32]A.L.Greer,Mater.Sci.Eng.A 304–306(2001)p.68.Philosophical Magazine Letters245D o w n l o a d e d B y : [S u , H . L .] A t : 01:20 14 M a r c h 2011。

ito与al的功函数ITO功函数：ITO（Indium Tin Oxide）是一种透明导电氧化物材料，具有优异的光电性能，广泛应用于透明导电薄膜、光电器件等领域。

ITO功函数指的是ITO材料的功函数特性，即表征电子在物质表面的能量状态。

ITO功函数的大小与ITO材料的性能密切相关。

ITO薄膜通常用于透明导电膜，作为太阳能电池、液晶显示、触摸屏等器件的电极材料。

在这些应用中，ITO薄膜需要具有较低的电阻、高的可见光透过率和较高的电子功函数，以确保其在光电器件中的优良性能。

ITO材料的功函数主要与其表面的能带结构有关。

一般来说，ITO材料表面具有斜坡状的能带结构，其带底位于导带底，带顶位于导带顶。

而ITO的功函数则是通过相对电势差来表示。

在ITO中，n型掺杂的锡离子（Sn4+）代替一部分铟离子（In3+），形成导带，带电子浓度增加。

ITO表面带有氧空位，可以吸附氧分子，进一步提高导电性能。

这使得ITO具有较高的电导率，同时保持较高的光透过率。

ITO功函数的大小通常通过光电流-电压（I-V）曲线来测量，其中光电流是光照射下电极之间的电流，电压是施加在电极之间的电压。

通过测量不同光照强度下的I-V曲线，可以推导得到ITO的功函数。

Al功函数：Al（aluminum）是一种常见的金属材料，具有良好的导电性和导热性。

Al功函数指的是Al材料的功函数特性，即表征电子在物质表面的能量状态。

与ITO不同，Al是一种金属材料，其表面具有自由电子。

在真空中，Al表面自由电子浓度较高，内部能带结构和表面能带结构相近。

因此，Al的表面功函数通常等于其体内功函数。

Al的功函数通常在真空或气体环境下通过光电子能谱（XPS）仪器测量得到。

光电子能谱通过照射光子束，使表面电子脱离材料，测量电子的能量分布。

通过测量不同光子能量下逸出电子的能量分布，可以得到Al的功函数。

通常，Al的功函数在4.1-4.3eV之间。

虽然Al的功函数对不同的表面处理，如氧化或涂覆其他材料可能有一些变化，但这些变化通常是很小的。