The atomic mass (A) = mass of protons + mass of

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Chapter Outline Review of Atomic Structure • Electrons, Protons, Neutrons, Quantum mechanics of atoms, Electron states, The Periodic Table

• Atomic Bonding in Solids

  Bonding Energies and Forces

• Periodic Table

  Primary Interatomic Bonds • Ionic Covalent Metallic

• Secondary Bonding (Van der Waals)

  Three types of Dipole Bonds

• Molecules and Molecular Solids

  Understanding of interatomic bonding is the first step towards understanding/explaining materials properties University of Tennessee, Dept. of Materials Science and Engineering

  1 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Review of Atomic Structure

  Atoms = nucleus (protons and neutrons) + electrons

  Charges:

  Electrons (-) and protons (+) have negative and positive

• 19 charges of the same magnitude, 1.6 × 10 Coulombs.

  Neutrons are electrically neutral.

  Masses:

• 27 Protons and Neutrons have the same mass, 1.67 × 10 kg.
• 31

  Mass of an electron is much smaller, 9.11 × 10 kg and can be neglected in calculation of atomic mass.

  The atomic mass (A) = mass of protons + mass of neutrons # protons gives chemical identification of the element # protons = atomic number (Z) # neutrons defines isotope number

  University of Tennessee, Dept. of Materials Science and Engineering

  2

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Atomic mass units. Atomic weight.

  The atomic mass unit (amu) is often used to express

  atomic weight. 1 amu is defined as 1/12 of the atomic mass of the most common isotope of carbon atom that has 6 protons (Z=6) and six neutrons (N=6).

• 24

  ≈ M M = 1.66 x 10 g = 1 amu.

  proton neutron

12 The atomic mass of the C atom is 12 amu.

  The atomic weight of an element = weighted average of

  the atomic masses of the atoms naturally occurring isotopes. Atomic weight of carbon is 12.011 amu. The atomic weight is often specified in mass per mole.

  A mole is the amount of matter that has a mass in grams

  equal to the atomic mass in amu of the atoms (A mole of carbon has a mass of 12 grams).

  The number of atoms in a mole is called the Avogadro

  23 number , N = 6.023 × 10 . av N = 1 gram/1 amu. av

  Example: Atomic weight of iron = 55.85 amu/atom = 55.85 g/mol

  University of Tennessee, Dept. of Materials Science and Engineering

  3 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Some simple calculations

3 The number of atoms per cm , n, for material of density d

  3

  (g/cm ) and atomic mass M (g/mol): n = N × d / M

  av

  3 Graphite (carbon): d = 2.3 g/cm , M = 12 g/mol

  23

  3

  22

  n = 6×10 atoms/mol × 2.3 g/cm / 12 g/mol = 11.5 × 10

  3

  atoms/cm

  3 Diamond (carbon): d = 3.5 g/cm , M = 12 g/mol

  23

  3

  22

  n = 6×10 atoms/mol × 3.5 g/cm / 12 g/mol = 17.5 × 10

  3

  atoms/cm

3 Water (H O) d = 1 g/cm , M = 18 g/mol

  2

  23

  3

  22

  n = 6×10 molecules/mol × 1 g/cm / 18 g/mol = 3.3 × 10

  3

  molecules/cm

  22

  3 For material with n = 6 × 10 atoms/cm we can calculate 1/3

  mean distance between atoms L = (1/n) = 0.25 nm. the scale of atomic structures in solids – a fraction of 1 nm

  ‰ or a few A.

  University of Tennessee, Dept. of Materials Science and Engineering

  4

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Electrons in Atoms (I)

  The electrons form a cloud around the nucleus, of radius of 0.05 – 2 nm.

  This “Bohr” picture looks like a mini planetary system. But quantum mechanics tells us that this analogy is not correct: Electrons move not in circular orbits, but in odd shaped “orbitals” depending on their quantum numbers.

  Only certain “orbits” or shells of electron probability densities are allowed. The shells are identified by a principal

  quantum number n, which can be related to the size of the

  shell, n = 1 is the smallest; n = 2, 3 .. are larger. The second

  quantum number l, defines subshells within each shell. Two more quantum numbers characterize states within the subshells.

  University of Tennessee, Dept. of Materials Science and Engineering

  5 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Quantum Rules

• n can take any positive integer value
• l can take any integer value between

  0 and n-1. Therefore there are n possible values of l for a given n

• m can take any integer value

  l between - l and + l. Thus there are (2 l +1) values of m for a given l l

• m can take two values: ±1/2

  s

• Thus for any given value of l (an

  electron subshell) there are 2(2 l +1) electrons; for any given value of n (an electron shell) there are Σ2(2 l +1) electrons (add up all the subshells) University of Tennessee, Dept. of Materials Science and Engineering

  6

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  7 Recall Isotopes C

  12 where 12 = 6 Protons + 6 Neutrons C

  13 where 13 = 6 Protons + 7 Neutrons (Isotope) Isotopic abundance of C

  13 ≈ 1.1 %

  Carbon: 12.01 g/mol Atoms having the same atomic number but varying numbers of neutrons are isotopes

  Mass of basic particles: Particle Charge Mass (amu*) (1.66x10

• ^-24 or 1/N _av

  ) Proton +1 1.00814 (1.6734x10

• ^-24

  g) Neutron 0 1.00898 (1.675x10

• ^-24

  g) Electron -1 0.00055 (0.000911x10

• ^-24

  g) The atomic mass unit (amu) is the basic unit of measurement of an atom’s mass, one amu = (1/12)* ¹² C ₆ (1 amu = 1.660420 x 10

• ^-24

g) Atomic Structure

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  8 Electrons in Atoms (II) ¾ The quantum numbers arise from solution of Schrodinger’s equation ¾ Pauli Exclusion Principle: only one electron can have a given set of the four quantum numbers.

  The Number of Available Electron States in Some of the Electron Shells and Subshells

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Electrons in Atoms (III) 1s 2s sp 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p

  Subshells by energy: 1s,2s,2p,3s,3p,4s,3d,4s,4p,5s,4d,5p,6s,4f,…

  ¾ Electrons that occupy the outermost filled shell – the valence electrons – they are responsible for bonding. ¾ Electrons fill quantum levels in order of increasing energy (due to electron penetration)

  2

  2

  6

  2

  6

  6

  2 Example: Iron, Z = 26: 1s 2s 2p 3s 3p 3d 4s University of Tennessee, Dept. of Materials Science and Engineering

  9 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  10

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Draft of the periodic table, Mendeleev, 1869

  University of Tennessee, Dept. of Materials Science and Engineering

  11 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding General Periodic Table: Metals and Non- Metals

  Elements in the same column (Elemental Group) share similar properties. Group number indicates the number of electrons available for bonding.

  0: Inert gases (He, Ne, Ar...) have filled subshells: chem. inactive

  IA: Alkali metals (Li, Na, K…) have one electron in outermost occupied s subshell - eager to give up electron – chem. active

  VIIA: Halogens (F, Br, Cl...) missing one electron in outermost occupied p shell - want to gain electron - chem. active University of Tennessee, Dept. of Materials Science and Engineering

  12

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Periodic Table - Electronegativity The electronegativity values.

  Electronegativity - a measure of how willing atoms are to accept electrons Subshells with one electron - low electronegativity Subshells with one missing electron -high electronegativity Electronegativity increases from left to right Metals are electropositive – they can give up their few valence electrons to become positively charged ions

  University of Tennessee, Dept. of Materials Science and Engineering

  13 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Bonding Energies and Forces repulsion

  E gy, attraction

  Potential Ener equilibrium

  This is typical potential well for two interacting atoms The repulsion between atoms, when they are brought close to each other, is related to the Pauli principle: when the electronic clouds surrounding the atoms starts to overlap, the energy of the system increases abruptly.

  The origin of the attractive part, dominating at large distances, depends on the particular type of bonding.

  University of Tennessee, Dept. of Materials Science and Engineering

  14

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  15 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  16 But what does it mean?? Bonding Behavior (a) High melting temperature, high elastic modulus, low thermal expansion coefficient (b) Low melting temperature, low elastic modulus, high thermal expansion coefficient

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Relevant Equations Coulombic Attraction Force – Oppositely Charged Ions

2 F = K/ , r = atomic separation distance between c r

  ion centers

• -19 K = - k (Z q)(Z q), q = 1.6 x 10 coulomb/unit

  1

  2 charge Z = valence of the ion (+1,+2,+3,-1,-2,-3…)

  2 ∴F = - [k (Z q)(Z q)] / r c

  1

2 Repulsive Force

• -a/p F = λe λ,p are constants R At equilibrium: F = 0 = F + F = 0, ∴ F = - N A R A F R University of Tennessee, Dept. of Materials Science and Engineering

  17 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding The electron volt (eV) – energy unit convenient for description of atomic bonding

  Electron volt - the energy lost / gained by an electron when it is taken through a potential difference of one volt.

  × V E = q

• 19

  For q = 1.6 x 10 Coulombs V = 1 volt

• -19 1 eV = 1.6 x 10 J University of Tennessee, Dept. of Materials Science and Engineering

  18

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Types of Bonding - Primary bonding : e are transferred or shared Strong (100-1000 KJ/mol or 1-10 eV/atom)

  ¾ Ionic: Strong Coulomb interaction among negative atoms (have an extra electron each) and positive atoms

  (lost an electron). Example - Na Cl ¾ Covalent: electrons are shared between the molecules, to saturate the valency. Example - H

  2

  ¾ Metallic: the atoms are ionized, loosing some electrons from the valence band. Those electrons form a electron sea, which binds the charged nuclei in place

• - Secondary Bonding : no e transferred or shared

  Interaction of atomic/molecular dipoles Weak (< 100 KJ/mol or < 1 eV/atom)

  ¾ Fluctuating Induced Dipole (inert gases, H , Cl …)

  2

  2

  ¾ Permanent dipole bonds (polar molecules - H O, HCl...)

  2

  ¾ Polar molecule-induced dipole bonds (a polar molecule like induce a dipole in a nearby nonpolar atom/molecule)

  University of Tennessee, Dept. of Materials Science and Engineering

  19 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Ionic Bonding (I)

  Formation of ionic bond:

  1. Mutual ionization occurs by electron transfer (remember electronegativity table)

• Ion = charged atom
• Anion = negatively charged atom
• Cation = positively charged atom

  2. Ions are attracted by strong coulombic interaction

• Oppositely charged atoms attract
• An ionic bond is non-directional (ions may be attracted to one another in any direction

  Example: NaCl

  17 Protons Cl

11 Protons Na Electron Configuration? Electron Configuration? Na (metal) Cl (nonmetal) unstable unstable electron - Na (cation) + Cl (anion) stable stable Coulombic Attraction University of Tennessee, Dept. of Materials Science and Engineering

  20

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

• Na
• Cl
• Ionic bonds: very strong, nondirectional bonds
• Electron transfer reduces the energy of the system of atoms, that is, electron transfer is energetically favorable
• Note relative sizes of ions: Na shrinks and Cl expands

  21 Ionic Bonding (II)

  Na Cl e

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  22 Predominant bonding in Ceramics Give up electrons Acquire electrons

^He

^-

^Ne

^-

^Ar

^-

^Kr

^-

^Xe

^-

^Rn

^-

^{F 4.0 Cl 3.0 Br 2.8 I 2.5 At 2.2 Li 1.0 Na 0.9 K 0.8 Rb 0.8 Cs 0.7 Fr 0.7 H 2.1 Be 1.5 Mg 1.2 Ca 1.0 Sr 1.0 Ba 0.9 Ra 0.9 Ti 1.5 Cr 1.6 Fe 1.8 Ni 1.8 Zn 1.8 As 2.0} CsCl

  MgO CaF2 NaCl _{O 3.5} Adapted from Fig. 2.7, Callister 6e. (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.}

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Ionic Bonding (III) Crystal Structures in Ceramics with predominantly ionic bonding

  Crystal structure is defined by ¾ Magnitude of the electrical charge on each ion. Charge

• 2+

  balance dictates chemical formula (Ca and F form CaF ).

  2

  ¾ Relative sizes of the cations and anions. Cations wants maximum possible number of anion nearest neighbors and vice-versa. Stable ceramic crystal structures: anions surrounding a cation are all in contact with that cation. For a specific coordination number there is a critical or minimum cation- anion radius ratio r /r for which this contact can be

  C A maintained.

  University of Tennessee, Dept. of Materials Science and Engineering

  23 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Covalent Bonding (I)

  In covalent bonding, electrons are shared between the molecules, to saturate the valency. The simplest example is the H molecule, where the electrons spend more time in

  2 between the nuclei than outside, thus producing bonding.

  Formation of covalent bonds:

• Cooperative sharing of valence electrons
• Can be described by orbital overlap
• Covalent bonds are HIGHLY directional
• Bonds - in the direction of the greatest orbital overlap
• Covalent bond model: an atom can covalently bond with at most 8-N’, N’ = number of valence electrons

  2

  2

  6

  2

  

5

Example: Cl molecule. Z =17 (1S

  2S

  2P

  3S

  3P )

2 Cl

  → can form only one covalent bond N’ = 7, 8 - N’ = 1

  University of Tennessee, Dept. of Materials Science and Engineering

  24

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Covalent Bonding (II) Whereas the metallic and ionic CN is based on size and hard sphere Packing, covalent bonding is based on a different set of rules. Hard sphere model r/R CN (ionic, metallic) 0.732 ≤r/R<1

  8 r/R = 1

  12

• Covalent bond model: 8-N, N = number of valence electrons

  El. Config. X’tal structure # valence e 8-N

• ^- ₂
_{2 2} C (1S) ₂

  2S ₂

  2P diamond cubic

  4

  

4

Si ..3S

  3P diamond cubic _{2 1}

  4

  

4

GaAs Ga ..4S ₂

  4P zinc blend 4 average ₃

  

4

As.. 4S

  4P University of Tennessee, Dept. of Materials Science and Engineering

  25 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Covalent Bonding (III)

  2

  2

  2 Example: Carbon materials. Z = 6 (1S

  2S

  2P )

  c

  → can form up to four covalent bonds N’ = 4, 8 - N’ = 4 ethylene molecule: polyethylene molecule: ethylene mer diamond: (each C atom has four covalent bonds with four other carbon atoms)

  University of Tennessee, Dept. of Materials Science and Engineering

  26

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

• Diamond if covalently-bonded carbon
• Expected CN=12 (if ionic, equal sizes, r/R = 1)
• Observed CN=4 (“tetrahedral” coordination)
• Outer shell electrons 2s and 2p hybridize to form 4equally-spaced orbitals
• Reason: greater orbital overlap possible

  27 Example: Hybridization

  Explanation: directional bonding

  Covalent Bonding (IV) Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  

F2

_{Si 1.8 Ga 1.6} GaAs ^{Ge 1.8 O 2.0} colum n

   IVA Sn _{1.8 Pb 1.8} Adapted from Fig. 2.7, Callister 6e. (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.}

  EXAMPLES: COVALENT BONDING

• ^- 28 ^{He Ne - Ar - Kr - Xe - Rn - F}
^{4.0 Cl 3.0 Br 2.8 I 2.5 At 2.2 Li 1.0 Na 0.9 K 0.8 Rb 0.8 Cs 0.7 Fr 0.7 H 2.1 Be 1.5 Mg 1.2 Ca 1.0 Sr 1.0 Ba 0.9 Ra 0.9 Ti 1.5 Cr 1.6 Fe 1.8 Ni 1.8 Zn 1.8 As 2.0} SiC C(diamond) H2O _{C 2.5} H2

Cl2

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Metallic Bonding (I)

  Valence electrons are detached from atoms, and spread in an 'electron sea' that "glues" the ions together.

• A metallic bond is non-directional (bonds form in any

  → atoms pack closely direction) Electron cloud from valence electrons

  ion core University of Tennessee, Dept. of Materials Science and Engineering

  29 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Metallic Bonding (II) University of Tennessee, Dept. of Materials Science and Engineering

  30

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Secondary Bonding (I)

  Secondary = van der Waals = physical (as opposed to

• chemical bonding that involves e transfer) bonding results from interaction of atomic or molecular dipoles and is weak, ~0.1 eV/atom or ~10 kJ/mol.

  Arises from interaction between dipoles • Fluctuating dipoles asymmetric electron ex: liquid H 2 clouds H2 H2 - - H H + H H + secondary secondary bonding bonding • Permanent dipoles -molecule induced secondary -general case: + - - + bonding secondary -ex: liquid HCl H Cl H Cl bonding -ex: polymer seconda ry bondin g University of Tennessee, Dept. of Materials Science and Engineering

  31 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Secondary Bonding (II)

  Example: hydrogen bond in water. The H end of the molecule is positively charged and can bond to the negative side of another H O molecule (the O side of the

2 H O dipole)

  2 O H H

• - + + Dipole

  “Hydrogen bond” – secondary bond formed between two permanent dipoles in adjacent water molecules.

  University of Tennessee, Dept. of Materials Science and Engineering

  32

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  33 Secondary Bonding (III)

  Hydrogen bonding in liquid water from a molecular-level simulation

  Molecules: Primary bonds inside, secondary bonds

  among each other

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding University of Tennessee, Dept. of Materials Science and Engineering

  34 Secondary Bonding (IV)

  The Crystal Structures of Ice Hexagonal Symmetry of Ice Snowflakes

  Figures by Paul R. Howell

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding PROPERTIES FROM BONDING: T

  M

  Bond length , r • _{F F} Melting Temperature , T • m Energy (r) r r o • Bond energy , E o

r

Energy (r) smaller Tm larger Tm unstretched length r o r Eo= “bond energy” T m is larger if E o is larger. ₁₅ University of Tennessee, Dept. of Materials Science and Engineering

  35 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding PROPERTIES FROM BONDING: E

  Elastic modulus , E • Elastic modulus cross sectional F ∆L length, Lo = E area Ao A L o o undeformed ∆L deformed F o • E ~ curvature at r Energy unstretched length r o r smaller Elastic Modulus larger Elastic Modulus o E is larger if E is larger. ₁₆ University of Tennessee, Dept. of Materials Science and Engineering

  36

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding PROPERTIES FROM BONDING: α

  α Coefficient of thermal expansion , • length, coeff. thermal expansion Lo unheated, T1

  ∆L

∆L

T T ) = α ( -

  2

1 Lo heated, T2

  α ~ symmetry at r

• • o Energy r o r larger α

  α smaller

  α is larger if E o is smaller. ₁₇ University of Tennessee, Dept. of Materials Science and Engineering

  37 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding SUMMARY: PRIMARY BONDS

  Ceramics Large bond energy large T m (Ionic & covalent bonding): large E small α

  Metals Variable bond energy moderate T m (Metallic bonding): moderate E moderate α

  Directional Properties Polymers Secondary bonding dominates (Covalent & Secondary): small T small E large α seconda ry b ₁₈ University of Tennessee, Dept. of Materials Science and Engineering

  38

  Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Summary (II) University of Tennessee, Dept. of Materials Science and Engineering

  39 Introduction To Materials Science, Chapter 2, Atomic Structure -Interatomic Bonding Summary (III)

  Make sure you understand language and concepts: ¾ Atomic mass unit (amu) ¾ Atomic number ¾ Atomic weight ¾ Bonding energy ¾ Coulombic force ¾ Covalent bond ¾ Dipole (electric) ¾ Electron state ¾ Electronegative ¾ Electropositive ¾ Hydrogen bond ¾ Ionic bond ¾ Metallic bond ¾ Mole ¾ Molecule ¾ Periodic table ¾ Polar molecule ¾ Primary bonding ¾ Secondary bonding ¾ Van der Waals bond ¾ Valence electron

  University of Tennessee, Dept. of Materials Science and Engineering

  40