Bonding between Atoms [4]
¾ Free atom: equilibrium at attractive and repulsive electrostatic forces between nucleus and electrosphere.
• nucleus: protons (+) and neutrons • electrosphere: electrons (-) • electrical charge: 1.60 x 10-19 C • mass of proton: 1.67 x 10-24 g • mass of electron: 9.11 x 10-28 g
Carbon atom Z=6 M=12.01 g/mol R=70 pm
1> Bonding between Atoms
¾ Interatomic bonds: forces that hold atoms together which act like little springs, linking one atom to the next in the solid state.
¾ Interatomic Forces:
¾ attractive forces (Fa)
¾ repulsive forces (Fr) ¾ The Coulomb's law: http://matterandinteractions.org/index.html q : Charge of object 1 q1 ⋅q2 1 F = K ⋅ q : Charge of object 2 e 2 2 r r: Distance between the two objects 9 2 -2 Ke = 8.9875 x 10 N.m .C (Coulomb Constant) F: Force between the two objects. F > 0 implies a repulsive interaction, while F < 0 means an attractive interaction. 2> Bonding between Atoms
¾ Consider two isolated atoms:
– When the atoms are at large inter-atomic separation distance, the atoms do not exert any force on each other.
– When the distance is decreased, an attractive force FA starts to act pulling atoms closer.
– FA increases as the atoms gets closer. – But as the atoms get closer a repulsive force FR begin to act. – The net force FN between the two atoms is given by: FN = FA + FR
–At some inter-atomic distance ro, FR exactly equals FA and FN becomes Zero
FN = 0 = FA + FR
–ro is called the equilibrium inter-atomic separation distance at which atoms enter into bonding 3> Bonding between Atoms
¾ equilibrium spacing: A B F = − F = A r p R r q where A, B, p, q are constants; q > p
• When FA + FR = 0, equilibrium exists. • The centers of the atoms/ions will remain separated by the
equilibrium spacing xo.
4> Bonding between Atoms
¾ Force-Energy Relationship: dV F = − dr “Force is the negative gradient of potential energy”
¾ Energy calculation: r r V = F (r)dr + F (r)dr N ∫ A ∫ R ∞ ∞
¾ Equilibrium is reached by minimizing VN 5> Bonding between Atoms
¾ The energy of the crystal is lower than that of the free atoms by an amount equal to the energy required to pull the crystal apart into a set of free atoms. This is called the binding (cohesive) energy of the crystal.
¾ Examples: – NaCl is more stable than a collection of free Na and Cl. – Ge crystal is more stable than a collection of free Ge.
Cl Na NaCl
6> Bonding between Atoms
¾ Energy in Ball-Spring atomic bonding: The spring’s force is given by F = - k.x (k: spring constant), therefore the potential energy is given by: 1 V = −k r ⋅dr →V = ⋅k ⋅r 2 ∫ 2 ¾ Is this an appropriate potential to use to describe interatomic interactions under all conditions? ANSWER: No! Consider what happens to V as interatomic separation r →∞. This doesn’t make sense… bonding energy V should go to ZERO.
7> Energy Bonding between Atoms
¾ Lennard-Jones potential (1924): mathematically simple model that approximates the interaction between a pair of neutral atoms or molecules. σ ε 12 6 ⎡⎛ ⎞ ⎛σ ⎞ ⎤ V = 4 ⎢⎜ ⎟ − ⎜ ⎟ ⎥ ⎣⎢⎝ r ⎠ ⎝ r ⎠ ⎦⎥
Repulsive Attractive interaction interaction
where ε is the depth of the potential well, σ is the finite distance at which the inter-particle potential is zero and r is the distance between the particles.
http://en.wikipedia.org/wiki/Lennard-Jones_potential
8> Lennard-Jones potential
¾ This typical curve has a minimum at equilibrium V(R) distance R0
¾ R > R0 : – the potential Repulsive increases gradually, approaching 0 as 0 R R Æ ∞ 0 R – the force is attractive Attractive ¾ R < R : 0 R – the potential r increases very rapidly, approaching ∞ at small separation. – the force is repulsive 9> Potential Energy vs. Internuclear Distance
¾ Animation of 2 hydrogen atoms: Dr. Kumar (2013)
https://www.youtube.com/watch?v=Wl5QHeS2UXE 10> Bonding Forces and Energies
When FA + FR = 0, equilibrium exists. The centers of the atoms will remain separated by the
equilibrium spacing ro.
This spacing also corresponds to the minimum of the potential energy curve. The bonding energy that would be required to separate two atoms to an infinite separation is Eo 11> Physical Properties vs. Bonding Forces
¾ Melting Temperature, Tm ¾ Elastic modulus, E Energy (r) E = slope of the F-r curve at ro. E ~ curvature of E-r curve at ro.
ro Energy r unstretched length smaller Tm ro r larger Tm smaller Elastic Modulus Tm is larger if Eo is larger. • At room temperature, solids formed larger Elastic Modulus for large bonding energies, whereas for small energies the gaseous state is favored, liquids prevail when E is larger if Eo is larger. energies are of intermediate magnitude. 12> Physical Properties vs. Bonding Forces
¾ Coefficient of thermal expansion, α
length, Lo Δ unheated, T1 L ΔL = α (T2-T1) Lo heated, T2
Energy ¾ α ~ symmetry at ro.
ro r α is larger if Eo is smaller. larger α
smaller α
13> Physical Properties vs. Bonding Forces
Metal (Z) melting temperature Young’s modulus 0C GPa Pb (82) 327 14 Zn (30) 420 43 Mg (12) 649 45 Al (13) 660 71 Ag (47) 962 76 Au (79) 1064 82 Cu (29) 1085 124 Ni (28) 1455 214 Fe (26) 1538 196 Cr (24) 1863 289 Mo (42) 2623 324 W(74) 3422 411
14> Types of Atomic & Molecular Bonds
¾ Primary Atomic Bonds (strong) – Ionic Bonds – Covalent Bonds – Metallic Bonds
¾ Secondary Atomic & Molecular Bonds (weak) – Permanent Dipole Bonds – Fluctuating Dipole Bonds
15> Types of Atomic & Molecular Bonds
16> Ionic Bonding
¾Large inter-atomic forces are created by the “coulombic” effect produced by positively and negatively charged ions. ¾Ionic bonds are “non-directional”. ¾The “cation” has a + charge and the “anion” has the - charge. ¾The cation is much smaller than the anion. ¾ Properties: generally large bonding energies (600-1500 kJ/mol) and thus high melting temperatures, hard, brittle, and electrically and thermally isolative. 17> Ionic Bonding
¾ Chemistry: What is an Ionic Bond?
https://www.youtube.com/watch?v=dqW7H7c7M4A 18> Ionic Bonding
Ionic bond: metal + nonmetal
donates accepts electrons electrons
Dissimilar electronegativities ex: MgO Mg 1s2 2s2 2p6 3s2 O1s2 2s2 2p4
Mg2+ 1s2 2s2 2p6 O2- 1s2 2s2 2p6
19> Ionic Bonding
Periodic Table - electronegativities
Give up electrons Acquire electrons
Ionic compounds: NaCl, MgO, CaF2, CsCl, e.g. 20> Sodium Chlorine (NaCl)
¾ Notice that when sodium loses its one valence electron it gets smaller in size, while chlorine grows larger when it gains an additional valence electron. After the reaction takes place, the charged Na+ and Cl- ions are held together by electrostatic forces, thus forming an ionic bond.
21> Some characteristics of ionic compounds
Property Explanation The melting and boiling points of ionic Melting point compounds are high because a large amount of and boiling point thermal energy is required to separate the ions which are bound by strong electrical forces. Solid ionic compounds do not conduct electricity when a potential is applied because there are Electrical no mobile charged particles. conductivity No free electrons causes the ions to be firmly bound and cannot carry charge by moving. Most ionic compounds are hard; the surfaces of their crystals are not easily scratches. This is Hardness because the ions are bound strongly to the lattice and aren't easily displaced. Most ionic compounds are brittle; a crystal will shatter if we try to distort it. This happens Brittleness because distortion cause ions of like charges to come close together then sharply repel. 22> Covalent Bonding
¾ Large inter-atomic forces are created by the sharing of electrons to form directional bonds. ¾ Covalent bonding takes place between atoms with small differences in electronegativity which are close to each other in periodic table (between non-metals and non- metals). ¾ The covalent bonding is formed by sharing of outer shell electrons (i.e., s and p electrons) between atoms rather than by electron transfer. ¾ This bonding can be attained if the two atoms each share one of the other’s electrons. So the noble gas stable electron configuration can be attained. ¾ Number of covalent bonds for a particular molecule is determined by the number of valence electrons. ¾ Rarely are compounds purely ionic or covalent but are a percentage of both.
23> Covalent Bonding
¾ Chemistry: What is a Covalent Bond?
https://www.youtube.com/watch?v=ZxWmyZmwXtA 24> Covalent Bonding
Pure element - silicon (Si): 2003 Brooks/Cole Publishing / Thomson Learning™ © Si (Z=14): 1s22s22p63s23p2
Covalent bonding requires that electrons be shared between atoms in such a way that each atom has its outer sp orbital filled. In silicon, with a valence of four, four covalent bonds must be formed. 25> Covalent Bonding 2003 Brooks/Cole Publishing / Thomson Learning™ © Silicon (Si):
Covalent bonds are directional. In silicon, a tetrahedral structure is formed, with angles of 109.5° required between each covalent bond 26> Covalent Bonding
Dissimilar compound - methane (CH4):
27> Some Properties of Covalent Bonding
Property Explanation Very high melting points because each atom is bound by strong covalent bonds. Many covalent Melting point bonds must be broken if the solid is to be melted and boiling point and a large amount of thermal energy is required for this.
Electrical Poor conductors because electrons are held either conductivity on the atoms or within covalent bonds. They cannot move through the lattice.
They are hard because the atoms are strongly Hardness bound in the lattice, and are not easily displaced.
Covalent network substances are brittle. If sufficient force is applied to a crystal, covalent bond are Brittleness broken as the lattice is distorted. Fracture failure occurs rather than deformation of a shape. 28> Comparison of Ionic and Covalent Bonding
29> Ionic-Covalent Mixed Bonding
¾ Calculation of % Ionic Character (IC): ⎡ ⎛ ()X − X 2 ⎞⎤ ⎜ A B ⎟ %IC = ⎢1− exp⎜− ⎟⎥ ⋅100 ⎣⎢ ⎝ 4 ⎠⎦⎥ where XA and XB are Pauling electronegativities.
¾ Example: MgO XMg = 1.3 XO = 3.5 ⎡ ⎛ ()3.5 −1.3 2 ⎞⎤ ⎜ ⎟ %IC = ⎢1− exp⎜− ⎟⎥ ⋅100 = [][]1− exp()−1.21 ⋅100 = 1− 0.298 ⋅100 = 70.2% ⎣⎢ ⎝ 4 ⎠⎦⎥
¾ Example: NaCl XNa = 0.9 XCl = 3.0 ⎡ ⎛ ()3.0 − 0.9 2 ⎞⎤ ⎜ ⎟ %IC = ⎢1− exp⎜− ⎟⎥ ⋅100 = [][]1− exp()−1.10 ⋅100 = 1− 0.332 ⋅100 = 66.8% ⎣⎢ ⎝ 4 ⎠⎦⎥
30> Coordination Number and Ionic Radii
rcation ¾ Coordination Number (CN) increases with ranion To form a stable structure, how many anions can surround a cation? r cation CN ZnS ranion (zinc blende) < 0.155 2 linear
0.155 - 0.225 3 triangular NaCl (sodium 0.225 - 0.414 4 tetrahedral chloride)
0.414 - 0.732 6 octahedral CsCl (cesium chloride) 0.732 - 1.0 8 cubic
31> Example - Cation-Anion Radius Ratio
¾ Determine maximum rcation/ranion for an octahedral site (C.N. = 6) a Measure the radii (blue 2ranion + 2rcation = 2a and yellow spheres)
Substitute for “a” in the a = 2ranion above equation
2 ranion + 2rcation = 22ranion
r anion + rcation = 2ranion r cation = (2−1) ranion r cation = 2 −1= 0.414 ranion 32> Metallic Bonding
¾ Metallic bonding is the type of bonding found in metal elements. This is the electrostatic force of attraction between positively charged ions and delocalized outer electrons. The weakness of the bonding actions in a metal is due to the enlargement of the internuclear spacing. ¾ All valence electrons in a metal combine to form a “sea” of electrons that move freely between the atom cores. A metal may be described as a cloud of free electrons. So, metals have high electrical and thermal conductivity. ¾ This type of bonding is nondirectional and is rather insensitive to structure. As a result we have a high ductility of metals - the “bonds” do not “break” when atoms are rearranged – metals can experience a significant degree of plastic deformation. ¾ The metallic bond is weaker than the ionic and the covalent bonds. 33> METALLIC BONDING 2003 Brooks/Cole Publishing / Thomson Learning™ ©
The metallic bond forms when atoms give up their valence electrons, which then form an electron sea. The positively charged atom cores are bonded by mutual attraction to the negatively charged electrons
34> Metallic Bonding
¾ Chemistry: What is a Metal?
https://www.youtube.com/watch?v=vOuFTuvf4qk 35> Secondary Bonding or van der Walls Bonding
¾ Also known as physical bonds ¾ Weak in comparison to primary or chemical bonds ¾ Exist between virtually all atoms and molecules ¾ Arise from atomic or molecular dipoles ¾ bonding that results from the coulombic attraction between the positive end of one dipole and the negative region of an adjacent one ¾ a dipole may be created or induced in an atom or molecule that is normally electrically symmetric
36> Secondary Bonding or van der Walls Bonding
¾Fluctuating Induced Dipole Bonds – A dipole (whether induced or instantaneous) produces a displacement of the electron distribution of an adjacent molecule or atom and continues as a chain effect – Liquefaction and solidification of inert gases – Weakest Bonds – Extremely low boiling and melting point
Atomic nucleus Atomic nucleus Instantaneous Electron cloud Electron Fluctuation cloud 37> Secondary Bonding or van der Walls Bonding
¾ Polar Molecule-Induced Dipole Bonds – Permanent dipole moments exist by virtue of an asymmetrical arrangement of positively and negatively charged regions – Polar molecules can induce dipoles in adjacent nonpolar molecules – Magnitude of bond greater than for fluctuating induced dipoles Atomic nucleus Electron Cloud + -
Polar Induced Molecule Dipole 38> Secondary Bonding or van der Walls Bonding
¾Permanent Dipole Bonds – Stronger than any secondary bonding with induced dipoles – A special case of this is hydrogen bonding: exists between molecules that have hydrogen as one of the constituents
Hydrogen Bond
HCl HCl
39> Secondary Bonding or van der Walls Bonding ¾Permanent Dipole Bonds:
¾Hydrogen bonds in water Solid
Many molecules do not have a symmetric Liquid distribution/arrangement of positive and negative
charges (e.g. H2O, HCl, NH3)
40> Bonding Energy - Summary
41> Atomic Bonding - Summary
Type Bond Energy Comments Ionic Large! Nondirectional (ceramics)
Covalent Variable Directional large-Diamond (semiconductors, ceramics small-Bismuth polymer chains)
Metallic Variable large-Tungsten Nondirectional (metals) small-Mercury Secondary smallest Directional inter-chain (polymer) inter-molecular 42> References
¾ CALLISTER JR, W. D. AND RETHWISCH, D. G. Materials Science and Engineering: An Introduction, 9th edition. John Wiley & Sons, Inc. 2014, 988p. ISBN: 978-1-118-32457-8. ¾ ASHBY, M. and JONES, D. R. H. Engineering Materials 1: An Introduction to Properties, Applications and Design. 4th Edition. Elsevier Ltd. 2012, 472p. ISBN 978-0-08-096665-6. ¾ CALLISTER JR, W. D. AND RETHWISCH, D. G. Fundamentals of Materials Science and Engineering: An Integrated Approach, 4th ed. John Wiley & Sons, Inc. 2012, 910p. ISBN 978-1-118-06160-2. ¾ ASKELAND, D. AND FULAY, P. Essentials of Materials Science & Engineering, 2nd Edition. Cengage Learning. 2009, 604p. ISBN 978-0-495-24446-2. ¾ http://matterandinteractions.org/index.html
Nota de aula preparada pelo Prof. Juno Gallego para a disciplina Ciência dos Materiais de Engenharia. ® 2015. Permitida a impressão e divulgação. http://www.feis.unesp.br/#!/departamentos/engenharia-mecanica/grupos/maprotec/educacional/ 43