Chapter 2: Atomic Structure/Bonding

Elements in Structure

1. Atomic structure (s, p, d)

   • Affects bonding and certain properties (Elastic/Young’s modulus E, coefficient of thermal expansion CTE, and melting temperature Tm)

2. Crystal Structure (FCC, BCC, HCP, BCT)

   • affecting mechanical and physical properties (elastic and plastic properties)

3. Microstructure (grain size, phases, defects)

   • affects mechanical and physical properties (hardness, strength, ductility, electrical/thermal conductivity)

4. Macrostructure (pores, cracks - seen visually)

   • affects mechanical and physical properties (fatigue strength, fracture toughness, strength, ductility)

Electrons and Configuration

Every electron in an atom is characterized by 4 quantum numbers:

1. Principal quantum number n = 1,2,3,4,5 (K,L,M,N,O) - shell designation

   • number of electrons per shell: 2,8,18,32

2. Secondary quantum number l = s,p,d,f - subshell

   • number of electrons per subshell: 2,6,10,14

3. Tertiary quantum number m_l (number of energy states when magnetic field is applied, 1,3,5,7)

4. Quaternary quantum number m_s (spin moment +1/2, -1/2)

Elements in Structure

1. Atomic structure (s, p, d)

   • Affects bonding and certain properties (Elastic/Young’s modulus E, coefficient of thermal expansion CTE, and melting temperature Tm)

2. Crystal Structure (FCC, BCC, HCP, BCT)

   • affecting mechanical and physical properties (elastic and plastic properties)

3. Microstructure (grain size, phases, defects)

   • affects mechanical and physical properties (hardness, strength, ductility, electrical/thermal conductivity)

4. Macrostructure (pores, cracks - seen visually)

   • affects mechanical and physical properties (fatigue strength, fracture toughness, strength, ductility)

Electrons and Configuration

Every electron in an atom is characterized by 4 quantum numbers:

1. Principal quantum number n = 1,2,3,4,5 (K,L,M,N,O) - shell designation

   • number of electrons per shell: 2,8,18,32

2. Secondary quantum number l = s,p,d,f - subshell

   • number of electrons per subshell: 2,6,10,14

3. Tertiary quantum number m_l (number of energy states when magnetic field is applied, 1,3,5,7)

4. Quaternary quantum number m_s (spin moment +1/2, -1/2)

Pauli Exclusion Principle - The Aufbau Principle

s,p,d,f subshells may each accommodate, respectively, a total of 2,6,10,14 electrons

Periodic Table

• Transition metals: partially filled d electron states and one or two electrons in the next higher energy shell

• Electropositive elements: readily give up electrons to become + ions

• Electronegative elements: readily acquire electrons to become - ions

Primary Bonds

• All atoms have the tendency to form stable or inert gas electron configurations

• This can be achieved by: gaining, losing, or sharing electrons

• Primary bonding types:

  1. Ionic bonding

  2. Covalent bonding

  3. Metallic bonding

Ionic Bonding

• Metal/non-metal

• Atoms of a metallic (donor) element easily give up their valence electrons to the nonmetallic (recipient) atoms

• In the process, all the atoms acquire stable or inert gas configurations (ie completely filled orbital shells)

Covalent Bonding

• nonmetals, metal + nonmetal, metal

• sharing

• directional bonding

Metallic bonding

• Primary bonding for metals and metal alloys

• Arises from a sea of donated valence electrons (1, 2, or 3 from each atom)

• The electrons are shared among all

• These free electrons act as a “glue” to hold the ion cores together

Mixed Bonding

• Ionic-covalent mixed bonding

• % iconic character = [1-e^{-(X_A-X_B)²/4}](100%)

• X_A and X_B are electro-negativities of elements A and B

• For two elements with different electro-negativities, there will be some % of ionic bond between them

Bonding Tetrahedron

Sometimes it is illustrative to represent the four bonding types - ionic, covalent, metallic, and van der Waals - on what is called a bonding tetrahedron.

Secondary Bonding

• aka van der Waals bonding

• arises from interaction between dipoles

  • Fluctuating dipoles - asymmetric electron clouds

  • Permanent dipoles - molecule/geometry induced

Hydrogen Bond

HF, H₂O, NH₃

• F, O, and N strongly pull single electron from H leaving a bare proton which bonds strongly

• Strongest secondary bonding type

• Permanent dipoles - molecule induced (due to asymmetrical arrangement of positive and negative regions)

Ionic Bonding Summary

• Bond energy

  • Large

• Found in

  • Ceramics

Covalent Bonding Summary

• Bond energy:

  • Variable

  • Large - diamond

  • Small - bismuth

  • Tm = 270*C

• Found in:

  • Semiconductors

  • Ceramics

  • w/in polymer chains

Metallic Bonding Summary

• Bond energy:

  • Variable

  • Large - Tungsten

  • Small - Mercury

• Found in:

  • Metals

Secondary Bonding Summary

• Bond energy:

  • Smallest

• Found in:

  • Inter-chain (polymer)

  • Inter-molecular

Bonding Energy, E₀

Energy balance of attractive (-) and repulsive (+) terms

(at equilibrium spacing)

E_N = E_A + E_R = -A/r + B/rⁿ

E_N = Net energy

E_A = attractive energy

E_R = repulsive energy

Importance:

• Stiffness

• melting point

• coefficient of thermal expansion of pure substances

Bonding Energy/Elastic Modulus

Bonding Energy/Melting Temp

Bonding Energy/Elastic CTE α

Ceramic Material Class Summary

• Bonding type

  • Ionic

  • Covalent

• Properties

  • Large bond energy

  • large T_m

  • Large E

  • Small α

Metals Material Class Summary

• Bonding type

  • Metallic

• Properties

  • Variable bond energy

  • Moderate T_m

  • Moderate E

  • Moderate α

Polymers Material Class Summary

• Bonding type

  • Co

• Properties

  • Directional properties

  • Secondary bonding dominates

  • Small T_m

  • Small E

  • Large α