The Fundamentals of Materials Science

Transcription

1 The Fundamentals of Materials Science An Introduction to Materials Science Chapter 2: Atomic Structure & Interatomic Bonding Shengjuan Li Office: Room 201 in School of MSE School of Materials Science and Engineering

2 Chapter 2: Atomic Structure & Interatomic Bonding Material (Substance) is composed of atoms. The electronic structures of atoms are the most concerned, and the nature of the interatomic bonding. Determine: Classification metals, ceramics, polymers, Property --- mechanical, electrical, thermal, School of Materials Science and Engineering

3 Learning Objectives 1. Name the two atomic models cited, and note the differences between them. 2. Describe the important quantum-mechanical principle that relates to electron energies. 3. (a) Schematically plot attractive, repulsive, and net energies versus interatomic separation for two atoms or ions. (b) Note on this plot the equilibrium separation and the bonding energy. 4. (a) Briefly describe ionic, covalent, metallic, hydrogen, and van derwaals bonds. (b) Note which materials exhibit each of these bonding types. School of Materials Science and Engineering

4 The structure of materials: Composition, Structure----Properties, Performance The structure of materials: (five different levels) 1. macrostructure; (>100000nm, 100 um, 0.1 mm) 2. microstructure; ( nm) 3.nanostructure; (1-100 nm) 4.short- and long-range atomic arrangements; 5. atomic structure.

5 Football 22cm flea meter millimeter micron nanometer angstrom 1. macrostructure; (> nm, 100 um, 0.1 mm) 2. microstructure; ( nm) 3.nanostructure; (1-100 nm) 4.short- and long-range atomic arrangements; 5. atomic structure.

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7 Atomic Structure: atom electrons 9.11 x kg protons neutrons } 1.67 x kg atomic number(z) = No. of protons in nucleus of atom = No. of electrons of neutral species A [=] atomic mass unit = amu = 1/12 mass of 12 C Atomic mass (A) --- the sum of the masses of protons and neutrons within the nucleus. Atomic wt. = wt. of x molecules or atoms 1 amu/atom (or molecule) = 1g/mol C , H etc.

8 Atomic Structure: In 1879, J.J Thomson( English physicist), Discovery of electron In 1904,proposed plum pudding model of atom, (1906,Nobel prize) In 1911, E.Rutherford (British physicist), the father of nuclear physics Discovery of atomic nucleus (Rutherford model) In 1913, N.Bohr(Danish physicist), understanding atomic structure and quantum theory, (1922,Nobel Prize ) Bohr was also a philosopher and a promoter of scientific research. Bohr atomic model

9 Electrons in atoms: Bohr atomic model (simple quantum-mechanical model) Electrons are assumed to revolve around the atomic nucleus in discrete orbitals, and the position of any particular electron is more or less well defined in terms of its orbital. The energies of electrons are quantized; that is, electrons are permitted to have only specific values of energy. An electron may change energy, but in doing so it must make a quantum jump either to an allowed higher energy (with absorption of energy) or to a lower energy (with emission of energy). School of Materials Science and Engineering

10 Electrons in atoms: Wave-mechanical model The electron is considered to exhibit both wavelike and particle-like characteristics. With this model, an electron is no longer treated as a particle moving in a discrete orbital; rather, position is considered to be the probability of an electron s being at various locations around the nucleus. In other words, position is described by a probability distribution or electron cloud. School of Materials Science and Engineering

11 In 1924 the wave model of the atom was introduced by Louis de Broglie (a French physicist who made groundbreaking contributions to quantum theory. ) Nobel Prize in physics (1929)

12 Bohr Model Quantum Model Probability wave School of Materials Science and Engineering

13 Quantum numbers: Every electron in an atom is characterized by four parameters called quantum numbers. The size, shape, and spatial orientation of an electron s probability density are specified by three of these quantum numbers. Bohr energy levels separate into electron subshells, and quantum numbers dictate the number of states within each subshell. Shells are specified by a principal quantum number n; sometimes these shells are designated by the letters K, L, M, N, O,, which correspond, respectively, to n =1, 2, 3, 4, 5,... Second quantum number( orbital ), l, (subshell), denoted by a lowercase letter an s, p, d, or f, related to the shape of the electron subshell, is restricted by the magnitude of n. School of Materials Science and Engineering

14 Quantum numbers: The number of energy states for each subshell is determined by the third quantum number, m l. For an s subshell, there is a single energy state, whereas for p, d, and f subshells, three, five, and seven states exist, respectively. In the absence of an external magnetic field, the states within each subshell are identical. However, when a magnetic field is applied these subshell states split, each state assuming a slightly different energy. Associated with each electron is a spin moment, which must be oriented either up or down. Related to this spin moment is the fourth quantum number, m s, for which two values are possible ( ), one for each of the spin orientations. School of Materials Science and Engineering

15 Quantum numbers: The principal quantum number n(shell)- 主量子数 The energy of the electron, n =1, 2, 3, 4, 5,... Designated by the letters K, L, M, N, O,, The second(orbital)quantum number l - 轨道动量量子数, 角量子数, 轨道角动量的量子数 The shape of the electron subshell, l=0,1, 2, 3, 4, 5,...n-1 Designated by the letters s, p, d, or f,, The third(magnetic) quantum number m l 磁量子数 The spatial orientation of the electron cloud, m l = 0,±1, ±2,,±l The fourth(spin) quantum number m s - 自旋角动量量子数 The spin orientation of the electron, m s =. School of Materials Science and Engineering

16 n =1, 2, 3, 4, 5,.. l=0,1, 2, 3, 4, 5,...n-1 m l = 0,±1, ±2,,±l

17 The smaller the principal quantum number, the lower the energy level; Within each shell, the energy of a subshell level increases with the value of the l quantum number. There may be overlap in energy state in one shell with states in an adjacent shell, which is especially true of d and f states. Figure 2.4 Schematic representation of the relative energies of the electrons for the various shells and subshells. School of Materials Science and Engineering

18 Electronic Structure Electrons have wavelike and particulate properties. This means that electrons are in orbitals defined by a probability. Each orbital at discrete energy level is determined by quantum numbers. Quantum numbers n = principal (energy level-shell) l = second (orbitals) m l = magnetic Designation m s = spin ½, -½ K, L, M, N, O (1, 2, 3, etc.) s, p, d, f (0, 1, 2, 3,, n-1) 0,±1, ±2,,±l

19 Electron Energy States Electrons... have discrete energy states tend to occupy lowest available energy state. Energy 4p 4d 3d 4s N-shell n = 4 3p M-shell n = 3 3s 2p 2s 1s L-shell n = 2 K-shell n = 1

20 Electron configurations: Pauli exclusion principle 泡利不相容原理 (quantum-mechanical concept) Each electron state can hold no more than two electrons, which must have opposite spins. Thus, s, p, d, and f subshells may each accommodate, respectively, a total of 2, 6, 10, and 14 electrons. Not all possible states are filled with electrons. For most atoms, the electrons fill up the lowest possible energy states in the electron shells and subshells, two electrons (having opposite spins) per state. When all the electrons occupy the lowest possible energies in accord with the foregoing restrictions, an atom is said to be in its ground state ( 基态 ). School of Materials Science and Engineering

21 The electron configuration or structure of an atom represents the manner in which these states are occupied. In the conventional notation the number of electrons in each subshell is indicated by a superscript after the shell subshell designation. For example, the electron configurations for sodium(na): 1s 2 2s 2 2p 6 3s 1

22 Significance of electron configurations : First, the valence electrons ( 价电子 )are those that occupy the outermost shell. These electrons are extremely important; as will be seen, they participate in the bonding between atoms to form atomic and molecular aggregates. Furthermore, many of the physical and chemical properties of solids are based on these valence electrons. In addition, some atoms have what are termed stable electron configurations ; that is, the states within the outermost or valence electron shell are completely filled.these elements (Ne-neon, Ar-argon, Kr-krypton, and He-helium) are the inert, or noble, gases, which are virtually unreactive chemically School of Materials Science and Engineering

23 Valence The number of electrons in an atom that participate in bonding or chemical reactions. The number of electrons in the outer s and p energy levels. The valence of an atom is related to the ability of the atom to enter into chemical combination with other elements. magnesium aluminum germanium Valence also depends on the environment surrounding the atom or the neighboring atoms available for bonding. Ex: phosphorus(p): valence =3, combine with oxygen valence =5, react with hydrogen Manganese (Mn): valence = 2,3,4,6,or 7

24 SURVEY OF ELEMENTS Most elements: Electron configuration not stable. Element Hydrogen Helium Lithium Beryllium Boron Carbon... Neon Sodium Magnesium Aluminum... Argon... Krypton Atomic # Electron configuration 1s 1 1s 2 (stable) 1s 2 2s 1 1s 2 2s 2 1s 2 2s 2 2p 1 1s 2 2s 2 2p s 2 2s 2 2p 6 1s 2 2s 2 2p 6 3s 1 1s 2 2s 2 2p 6 3s 2 1s 2 2s 2 2p 6 3s 2 3p 1... (stable) 1s 2 2s 2 2p 6 3s 2 3p 6 (stable)... 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 4s 2 4p 6 (stable) Adapted from Table 2.2, Callister & Rethwisch 8e. 24 Why? Valence (outer) shell usually not filled completely.

25 Electron Configurations Valence electrons those in unfilled shells Filled shells more stable Valence electrons are most available for bonding and tend to control the chemical properties example: C (atomic number = 6) 1s 2 2s 2 2p 2 valence electrons Isotopes of carbon are atomic nuclei that contain six protons plus a number of neutrons 25 (varying from 2 to 16).

26 Electronic Configurations ex: Fe - atomic # =26 1s 2 2s 2 2p 6 3s 2 3p 6 3d 6 4s 2 4d 4p 3d 4s N-shell n = 4 valence electrons Energy 3p M-shell n = 3 3s 2p 2s L-shell n = 2 1s K-shell n = 1 26 Adapted from Fig. 2.4, Callister & Rethwisch 8e.

27 Electron configurations : Some atoms of the elements that have unfilled valence shells assume stable electron configurations by gaining or losing electrons to form charged ions, or by sharing electrons with other atoms. This is the basis for some chemical reactions, and also for atomic bonding in solids. give up 1e - inert gases H Li give up 2e - Be Na Mg K Ca give up 3e - Sc Oaccept 2e- S Se accept 1e - F Cl Br He Ne Ar Kr Rb Sr Y Te I Xe Cs Fr Ba Ra School of Materials Science and Engineering Po At Rn

28 The Periodic Table: All the elements have been classified according to electron configuration in the periodic table. give up 1e - give up 2e - give up 3e - inert gases H Li Be Oaccept 2e- accept 1e - F He Ne Na Mg S Cl Ar K Ca Sc Se Br Kr Rb Sr Y Te I Xe Cs Ba Po At Rn Fr Ra Electropositive elements: Readily give up electrons to become + ions. Electronegative elements: Readily acquire electrons to become - ions. Adapted from Fig. 2.6, Callister & Rethwisch 8e.

29 inert gases Electronegativity the tendency of an atom to gain an electron. almost completely filled outer energy levels: chlorine(cl),strongly electronegative empty outer levels: sodium(na): low electronegativity. High atomic number elements low electronegativity. Because: the out electrons are at a greater distance from the positive nucleus, are not as strongly attracted to the atom. give up 1e - H Li give up 2e - Be give up 3e - Oaccept 2e- Na Mg S accept 1e - He F Ne Cl Ar K Ca Sc Se Br Kr Rb Sr Y Te I Xe Cs Ba Po At Rn Fr Ra

30 Electronegativity Large values: tendency to acquire electrons. Ranges from 0.7 to 4.0, Larger electronegativity Smaller electronegativity Adapted from Fig. 2.7, Callister & Rethwisch 8e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University. School of Materials Science and Engineering

31 The Periodic Table

32 Atomic bonding in solids Bonding forces and energies The interatomic forces that bind the atoms together. At large distances, the interactions are negligible, but as the atoms approach, each exerts forces on the other. These forces are of two types, attractive and repulsive, and the magnitude of each is a function of the separation or interatomic distance.

33 Potential energies between two atoms Equilibrium spacing, r 0, corresponds to the separation distance at the minimum of the potential energy curve. The bonding energy for these two atoms, E 0, corresponds to the energy at this minimum point.

34 r 0 - Equilibrium distance (spacing) ; F A + F R = 0 E 0 -Bonding energy r = r 0, r 0 0.3nm (3Å)

35 The magnitude of this bonding energy and the shape of the energy-versus interatomic separation curve vary from material to material, and they both depend on the type of atomic bonding. A number of material properties depend on E 0, the curve shape, and bonding type. Large bonding energies high melting temperatures The mechanical stiffness (or modulus of elasticity) of a material is dependent on the shape of its force-versus interatomic separation curve. stiff material --steep curve at equilibrium spacing

36 giv give u accept accept ine Primary interatomic bonds H give up 3e - (1) Ionic Li Be Bonding Na Mg S Occurs between + and - ions. K Ca Sc Requires electron transfer. Rb Sr Y Large Cs difference Ba in electronegativity required. Example: Fr Ra NaCl (sodium chloride) O Se Te Po F Cl Br I At He Ne Ar Kr Xe Rn Na (metal) unstable Na (cation) stable electron + - Coulombic Attraction Cl (nonmetal) unstable Cl (anion) stable

37 (1)Ionic Bonding The attractive bonding forces are coulombic force; that is, positive and negative ions, by virtue of their net electrical charge, attract one another. A, B, n: constants, depend on the particular ionic system. The value of n is approximately 8. Ionic bonding is termed nondirectional; that is, the magnitude of the bond is equal in all directions around an ion. Bonding energies, which generally range between 600 and 1500 kj/mol, are relatively large, as reflected in high melting temperatures. Ionic materials are characteristically hard and brittle and, furthermore, electrically and thermally insulative.

38 Examples: Ionic Bonding Predominant bonding in Ceramics NaCl MgO CaF 2 CsCl Give up electrons Acquire electrons Adapted from Fig. 2.7, Callister & Rethwisch 8e. (Fig. 2.7 is adapted from Linus Pauling, The Nature of the Chemical Bond, 3rd edition, Copyright 1939 and 1940, 3rd edition. Copyright 1960 by Cornell University.

39 (2) Covalent Bonding In covalent bonding, stable electron configurations are assumed by the sharing of electrons between adjacent atoms. Two atoms that are covalently bonded will each contribute at least one electron to the bond, and the shared electrons may be considered to belong to both atoms. Ex. Methane, CH 4 C: has 4 valence e -, needs 4 more H: has 1 valence e -, needs 1 more Electronegativities are comparable. CH4 shared electrons from carbon atom shared electrons from hydrogen atoms Hydrogen atom---acquire a helium(he) electron configuration (two 1s valence electrons) Carbon atom--- acquire the electron structure of neon(ne). H H C H H

40 (2) Covalent Bonding similar electronegativity share electrons bonds determined by valence s & p orbitals dominate bonding. The covalent bond is directional; that is, it is between specific atoms and may exist only in the direction between one atom and another that participates in the electron sharing. The number of covalent bonds that is possible for a particular atom is determined by the number of valence electrons. Covalent bonds may be very strong, as in diamond, which is very hard and has a very high melting temperature, > 3550 or they may be very weak, as with bismuth(bi), which melts at about 270.

41 giv give u accept accept give up 3e - ine It is possible H to have interatomic bonds that are partially He ionic and Li partially Be covalent. O F Ne Na Mg For a compound, the degree of either bond type depends on K Ca Sc Se Br Kr the relative Rb Sr positions Y of the constituent atoms Te in I the Xe periodic Cs Ba table or the difference in their Po At Rn Fr Ra electronegativities. The wider the separation (both horizontally and vertically) from the lower left to the upper-right-hand corner (i.e., the greater the difference in electronegativity), the more ionic the bond. Conversely, the closer the atoms are together (i.e., the smaller the difference in electronegativity),the greater the degree of covalency. S Cl Ar

42 Ionic-Covalent Mixed Bonding % ionic character = 1 e ( X A X 4 B ) 2 ( 100 %) where X A & X B are Pauling electronegativities Ex: MgO X Mg = 1.2 X O = 3.5 (3.5 % ionic character 1 e ) x (100%) 73.4% ionic

43 (3) Metallic Bonding Final primary bonding type, is found in metals and their alloys. Metallic materials have one, two, or at most, three valence electrons. These valence electrons are not bound to any particular atom in the solid and are more or less free to drift throughout the entire metal. These valence electrons may be thought of as belonging to the metal as a whole, or forming a sea of electrons or an electron cloud. The remaining nonvalence electrons and atomic nuclei form ion cores

44 Secondary bonding or van der Waals bonding Secondary, van der Waals, or physical bonds are weak in comparison Hydrogen to bonding, the primary a or special chemical type ones. of secondary bonding, Arises from is interaction found to exist between between dipoles some 偶极子 molecules that Fluctuating have hydrogen dipoles as one of the constituents. Permanent dipoles-molecule induced -general case: -ex: polymer asymmetric electron clouds secondary bonding H ex: liquid H 2 H2 H2 H H H secondary bonding + - secondary + - bonding Dipole interactions occur between induced dipoles, -ex: liquid HCl H Cl secondary between induced dipoles and H Cl bonding polar molecules (which have permanent dipoles), and between polar molecules. secondary bonding

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46 Summary: Bonding Type Ionic Covalent Metallic Secondary Bond Energy Large! Variable large-diamond small-bismuth Variable large-tungsten(w) small-mercury(hg) smallest Comments Primary interatomic bonding, chemical bonding Nondirectional (ceramics) Directional (semiconductors, ceramics polymer chains) Hydrogen bonding,in between the two types Secondary bonding, Physical bonding, Nondirectional (metals) Directional inter-chain (polymer) Van der Waals bonding inter-molecular

47 Properties From Bonding: T m Bond length, r r Melting Temperature, T m Energy Bond energy, E o Energy ro smaller T m r ro unstretched length E o = bond energy r larger T m T m is larger if E o is larger. 47

48 Properties From Bonding : a Coefficient of thermal expansion, a length, L o unheated, T 1 heated, T 2 DL coeff. thermal expansion DL = a (T 2 -T 1 ) L o a ~ symmetric at r o Energy E o E o 48 unstretched length r o larger a smaller a r a is larger if E o is smaller.

49 Summary: Primary Bonds Ceramics (Ionic & covalent bonding): Metals (Metallic bonding): Polymers (Covalent & Secondary): Large bond energy large T m large E small a Variable bond energy moderate T m moderate E moderate a Directional Properties Secondary bonding dominates small T m small E large a 49

50 That s all for today, thanks!