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1、材料的表面与界面材料的表面与界面Surfaces and Interfaces Surfaces and Interfaces in Materialsin Materials任课教师：耿林教授任课教师：耿林教授哈尔滨工业大学材料科学与工程学院第第1章章 前言前言n主要参考文献：(1)李恒德，肖纪美，材料表面与界面，清华大学出版社。(2)叶恒强，材料界面结构与特性,科学出版社, 1999。(3)胡福增，陈国荣，杜永娟，材料表界面，华东理工大学出版社，2007。(4)James M. Howe, Interfaces in Materials, A Wiley-interscience Publ
2、ication,1997.(5)Hans Luth, Surfaces and Interfaces of Solid Materials, Springer, 1995.(6)D. Wolf and S. Yip, Materials Interfaces, Chapman & Hall, 1992.n固态界面的定义固态界面的定义: : A solid interface is defined as a small number of atomic layers that separate two solids in intimate contact with one another, wh
3、ere the properties differ significantly form those of the bulk materials it separates.1.1 序序n固态界面的特点固态界面的特点: : Some of the most important properties of materials in high-technology applications are strongly influenced or even controlled by the presence of solid interfaces. It is widely appreciated t
4、hat a highly interdisciplinary approach holds the greatest promise for providing novel insights into the fundamental physical, chemical, electronic, and mechanical processes at solid interfaces. The importance of interface materials is based primarily on their inherent inhomogeneity, i.e. the fact t
5、hat physical properties at or near an interface can differ dramatically from those of the nearby bulk material. An approach utilizing the complementary capabilities of computer simulation and experiment seems to be particularly promising in the investigation of structure-property correlations. n固态界面
6、的分类固态界面的分类: : One can imagine many ways of classifying interfacial systems, for example, by distinguishing commensurate from incommensurate system, coherent from incoherent interfaces, homophase (grain boundary) materials from heterophase (dissimilar- material) interfaces, or internal interfaces fro
7、m thin-film-type systems. The latter distinction between buried interfaces and systems composed of thin-film-type interfaces appears to be particularly meaningful for two reasons: first, because of the fundamentally different experimental techniques required for their investigation and second, becau
8、se the lattice parameter(s), and hence the physical properties in the interfacial region, depend strongly on whether or not the interface is embedded between bulk material. Fig.1-1 Distinction of three types of interfacial systems. Depending on whether the system is embedded in bulk material on both
9、 sides of the interface, on only one side or not at all, we distinguish “bulk”, “epitaxial”, and “thin-film” interfaces. A and B are generally different materials.Bulk perfectCrystal 2Bulk perfectCrystal 1Interfaceregion 2Interfaceregion 1Interface planeMaterial BXYZMaterial An固态界面的研究内容固态界面的研究内容: :
10、Relationship among interface energy, interface structure and interface properties. Formation and stability of the interfaces: Energy of the system, thermodynamic and kinetics of the interfaces.n固态界面的研究方法固态界面的研究方法: The experimental problems lie mainly in the extremely high spatial resolution, coupled
11、 with high detection sensitivity, which are required to identity minute amounts of chemical species, charge states of atoms and point defects, and different phases which may be present in the narrow interface region. Because the properties in the interfacial region are controlled by relatively few a
12、toms, electronic and atomic-level computer simulations can provide a close-up view of the most critical part of the material. The local nature of atomic bonding, the positions and movements of atoms, local stresses, etc., can be investigated by computer simulations. 1.2 Atomic structure and interato
13、mic bonding The binding energy is defined as the energy needed to transform one mole of solid or liquid into a gas at zero temperature and pressure. It is approximately the same magnitude as the energy of sublimation Hs when transforming a solid to a gas or the energy of vaporization Hv when transfo
14、rming a liquid to a gas, except that these are usually measured at 1 atm pressure. These quantities are often obtained at finite temperatures such as 298 K or at the boiling point , but this does not alter the binding energy or bond enthalpy, which is assumed to be independent of temperature. These
15、energies are related to a fundamental energy in materials, the interatomic potential energy between atoms.1.2.1 Interatomic potential and binding energy 1.2.2 Interatomic potential and binding energy 126/2/beerrrrr/.Fddr If the atoms are displaced toward one another, a repulsive force acts to increa
16、se the interatomic distance. This repulsive force is positive. The opposite occurs when the atoms are stretched apart. Hookes law The minimum potential energy corresponds to the equilibrium interatomic separation re. In solids, re can readily be measured by X-ray diffraction. The depth of the well i
17、s clearly proportional to the strength of the inter-atomic bond. b Lennard-Jones potential:1.2.2 Interatomic potential and binding energy In metals, attractive interaction between atoms is short-range with an r-6 dependence. Hence, the nearest-neighbor approximation works well for estimating the bin
18、ding energy for metals. In ionic solids, the attraction between the positive and negative ions is coulombic and much longer in range. The attractive coulombic potential is proportional to r-1, which decays slowly with increasing r. The repulsive potential may display an r-12 dependence, as with meta
19、ls, so the resulting profile looks like that shown in Fig.1-3 Fig.1-3 The broken curve shows the interatomic potential energy when the attractive interaction is long-range with an r-1 dependence 1.2.2 Interatomic potential and binding energy 刚性球模型：Clearly the repulsive interaction is very short-rang
20、e, whereas the attractive interaction is somewhat longer. This strong repulsive interaction makes it often realistic to represent atoms as “hard spheres”.最近邻假设：When the interatomic distance is twice the equilibrium distance (i.e., ), the potential energy decreases by a factor of 32. Thus, one can la
21、rgely ignore the interaction energy beyond the nearest neighbors and approximate the binding energy by considering only the nearest-neighbor bonds. 1.2.3 Correlation of binding energy and interatomic potential with physical and mechanical properties Binding Energy and Enthalpy of Sublimation If we d
22、efine z as the coordination number (the number of nearest neighbors) of an atomin a solid or liquid, then the binding energy of 1 mole of atoms is given by:Where NAis Avogadros number and the factor of 1/2 arises because we have counted each bond twice in the produce zNA if one assumes that the bind
23、ing energy per mole of solid is equal to the enthalpy ofSublimation per mole at low pressure, thensH2/bsAHzN Eb = 1/2z zNAeb1.2.3 Correlation of binding energy and interatomic potential with physical and mechanical properties Binding Energy and Enthalpy of Sublimation (/)sH kJ mol/beV atompair*/vHkj
24、 mol/beV atompairTable 1-1. Comparison of the interatomic potential energies of copper, silver and gold calculated from the heats of sublimation and vaporization using Eq.( 1.4)ElenentCuAgAu3362843680.580.490.64300.5250.6324.40.570.470.61*Heats of vaporization are usually specified at the boiling po
25、int, not at 0 K.1.2.3 Correlation of binding energy and interatomic potential with physical and mechanical properties Interatomic Potential and Theoretical Strength If we apply an external tensile force to a solid, the external force is defined as :Fex = +d/drwhere a positive sign is used to reflect
26、 the fact that an external tensile force (or stress) tends to lengthen the solid and increase the interatomic distance. On the basis of the sign convention established in Fig.1-2c, the force that increases the interatomic distance is positive and hence the tensile force (or stress) is positive. An e
27、xternal compressive force (or stress) which tends to shorten the solid is negative. The relationship among the interatomic potential, the external force and the sign of the force, are shown schematically in Fig.1-4.Fig.1-4. (a) Interatomic potential function plotted versus interatomic distance. (b)
28、Applied force plotted versus atomic displacement. (c) The direction and sign of the applied force ac-cording to the established convention. 1.2.3 Correlation of binding energy and interatomic potential with physical and mechanical properties Interatomic Potential and Theoretical Strength We can defi
29、ne a point Fmax as the maximum force that corresponds to the dissociative distance rd of the material. Fmax is thus the maximum tensile force needed to pull the solid apart because the force needed to increase the interatomic distance beyond rd is less than Fmax. We can regard Fmax as the theoretica
30、l strength of the solid. To calculate Fmax, we require that 220rat r = rd. If we assume that the solid obeys the Lennard-Jones potential and that the function is given by : 86222121370beeerrrrrr 126/2/beerrrrrwe obtain at r = rd 1.11derr1.2.3 Correlation of binding energy and interatomic potential w
31、ith physical and mechanical properties Interatomic Potential and Theoretical Strength 1.11derr Theoretically, the solid can be strained approximately 11% before it breaks. Furthermore, if stretched just below that strain, it would return to its original condition. We know that experimentally these c
32、onditions are not found. Most polycrystalline metals, whether they obey the Lennard-Jones potential or not, have an elastic limit of only 0.2%. After that, plastic deformation sets in. It is interesting to estimate the magnitude of the energy involved in elastic strain. Consider the case at the limi
33、t. The elastic energy is given by21/ 2elEdeYewhere is the stress, e is the strain and Y is Youngs modulus. To estimate the elastic energy, lets select one of the stiffest materials, steel, with Y = 2.01011 Pa and use 8.41022 atoms/cm3 to convert to electron volts per atom. If we take e =0.2%, then25
34、51/24 103 10/elaEYePeV atom 1.2.3 Correlation of binding energy and interatomic potential with physical and mechanical properties Interatomic Potential and Theoretical Strength This value of the elastic energy per atom is several orders of magnitude smaller than the binding energy of a metal or comp
35、ound, which is on the order of 3.5 eV/atom, as in Table 1-1. Therefore, the effects of elastic stress on the enthalpy of compound formation are often negligible. The potential energy corresponding to a strain of 0.2% is still very close to the binding energy. (/)sH kJ mol/beV atompair*/vHkj mol/beV
36、atompairTable 1-1. Comparison of the interatomic potential energies of copper, silver and gold calculated from the heats of sublimation and vaporization using Eq.( 1.4)ElenentCuAgAu3362843680.580.490.64300.5250.6324.40.570.470.611.2 Atomic structure and interatomic bondingProblems: 1 Using the Lenna
37、rd-Jones potential with n = 81022 atoms/cm3, Eb = 0.6eV/atom and re = (1/n)1/3:(1) Calculate the maximum force Fmax.(2) Assume the solid is in the linear elastic region and calculate Youngs modulus Y.(3) What is the elastic energy Eel at Fmax?2 For the Lennard-Jones potential, discuss the influence of increasing the attractive interaction while keeping the repulsive interaction fixed. How will this effect the equilibrium separation re and the pair potential Eb? 126/2/beerrrrr