1. : Atomic Systems and Bonding :
R. R. Lindeke, Ph.D.
ME 2105– Lecture Series 2

2. ISSUES TO ADDRESS... The Structure of Matter What Promotes Bonding?
A Quick Review from chemistry
What Promotes Bonding?
What type of Bonding is Possible?
What Properties are Inferred from Bonding?

3. Their FINAL PROPERTIES
Just as before:
How the atoms are arranged
& how they bond
GREATLY AFFECTS
Their FINAL PROPERTIES
& therefore use
ATOMIC Structure
Electron configurations
Primary & secondary
BONDING

4. Structure of Matter:
Atoms are the smallest particle in Nature that exhibits the characteristics of a substance
The radius of a typical atom is on the order of meter and cannot be studied without very powerful microscopes
Pictured here is an “Electron Microscope” It can greatly magnify materials but can’t resolve individual atom – we need a TEM or STP for that

5. Structure of Matter: A molecule consists of 2 or more atoms bound together
In a common glass of water “upon closer examination” we would find a huge number of Water “Molecules” consisting of 1 atom of Oxygen and 2 atoms of hydrogen

6. Atomic Structure (Freshman Chem.)
atom – electrons – x kg  protons neutrons
atomic number = # of protons in nucleus of atom = # of electrons of neutral species
A [=] atomic mass unit = amu = 1/12 mass of 12C   Atomic wt = wt of x 1023 molecules or atoms   1 amu/atom = 1g/mol
C H etc.
( x kg)
} 1.67 x kg
Atomic Weight is rarely a whole number – it is a weighted average of all of the natural isotopes of an “Element”

7. What is this in weight or mass in “Real Terms”
Example 1:

8. What is this in weight or mass in “Real Terms”

9. Structure of Matter – an Element
Any material that is composed of only one type of atom is called a chemical element, a basic element, or just an element.
Every element has a unique atomic structure.
Scientists know of only about 109 basic elements at this time. (This number has a habit of changing!)
All matter is composed of combinations of one or more of these elements.
Ninety-one of these basic elements occur naturally on or in the Earth (Hydrogen to Uraninum).
These elements are pictured in the “Periodic Table”

10. The Periodic Table of the Elements

11. Structure of Matter
Each of the “boxes” in the periodic table help us to understand the details of a given elements
Here we see atomic Number (# of Electrons or Protons) and Atomic Weight
Some tables provide information about an elements “Valance State” or the ability to gain or shed their outermost electrons when they form molecules or “Compounds”

12. Structure of Matter
These outermost or Valence electrons determine all of the following properties concerning an element:
Chemical
Electrical
Thermal
Optical

13. Schematic Image of Atoms:
Atomic number is 29

14. Electronic Structure
Electrons have wavelike and particulate properties.
This means that electrons exist in orbitals defined by a probability. – Boer coupled w/ Schrödinger models
Each orbital is located at a discrete energy level determined by quantum numbers.
Quantum # Designation
n = principal (energy level/shell) K, L, M, N, O (1, 2, 3, etc.)
l = subsidiary (orbitals) s, p, d, f (0, 1, 2, 3,…, n -1)
ml = magnetic 1(s), 3(p), 5(d), 7(f)
ms = spin ½, -½

15. Electron Energy States
• have discrete energy states
• tend to occupy lowest available energy state.
Electrons 1s 2s 2p
K-shell n = 1
L-shell n = 2 3s 3p
M-shell n = 3 3d 4s 4p 4d
Energy
N-shell n = 4
Can hold up to 32 electrons
Can hold up to 18 Electrons
Can hold up to 8 electrons
Can hold up to 2 electrons
Adapted from Fig. 2.4, Callister 7e.

16. More exhaustively:

17. SURVEY OF ELEMENTS
• For Most elements: This Electron configuration not stable.
Electron configuration
(stable)
... 1s 2 2s 2p 6 3s 3p 3d 10 4s 4p
Atomic # 18 36
Element 1
Hydrogen
Helium 3
Lithium 4
Beryllium 5
Boron
Carbon
Neon 11
Sodium 12
Magnesium 13
Aluminum
Argon
Krypton
• Why? Valence (outer) shell usually not filled completely so the electrons can ‘move out’!

18. Lets Try one: Here we have Iron ‘Fe’ (w/ Atomic Number 26)
ex: Fe - atomic # = 1s 2s 2p
K-shell n = 1
L-shell n = 2 3s 3p
M-shell n = 3 3d 4s 4p 4d
Energy
N-shell n = 4
1s2 2s2 2p6 3s2 3p6
3d 6 4s2

19. Electron Configurations
Valence electrons – those in unfilled shells
Filled shells are more stable
Valence electrons are most available for bonding and tend to control the chemical properties
example: C (atomic number = 6)
1s2 2s2 2p2
valence electrons

20. Matter (or elements) Bond as a result of their Valance states
give up 1e
give up 2e
give up 3e
inert gases
accept 1e
accept 2e O Se Te Po At I Br He Ne Ar Kr Xe Rn F Cl S Li Be H Na Mg Ba Cs Ra Fr Ca K Sc Sr Rb Y
Electropositive elements:
Readily give up electrons to become + ions.
Electronegative elements:
Readily acquire electrons
to become - ions.

21. Molecular/Elemental Bonding
Bonding is the result of the balance of the force of attraction and the force of repulsion of the electric nature of atoms (ions)
Net Force between atoms: FN = FA + FR and at some equilibrium (stable) bond location of separation, FN = 0 or FA = FR
From Physics we like to talk about bonding energy where:

22. Bonding Energy r A B EN = EA + ER =
Equilibrium separation (r0) is about .3 nm for many atoms
Energy – minimum energy most stable
Energy balance of attractive and repulsive terms r A n B
EN = EA + ER = -
Attractive energy EA
Net energy EN
Repulsive energy ER
Interatomic separation r
n is 7-9 for most ionic pairs

23. Here: A, B and n are “material constants”
EN = EA + ER = -

24. Figure Net bonding force curve for a Na+−Cl− pair showing an equilibrium bond length of a0 = 0.28 nm.

25. Bonding Energy, the Curve Shape, and Bonding Type
Properties depend on shape, bonding type and values of curves: they vary for different materials.
Bonding energy (minimum on curve) is the energy that would be required to separate the two atoms to an infinite separation.
Modulus of elasticity depends on energy (force) versus distance curve: the slope at r = r0 position on the curve will be quite steep for very stiff materials, slopes are shallower for more flexible materials.
Coefficient of thermal expansion depends on E0 versus r0 curve: a deep and narrow trough correlates with a low coefficient of thermal expansion

26. Bonding Types of Interest:
Ionic Bonding: Based on donation and acceptance of valance electrons between elements to create strong “ions” – CaIONs and AnIONs due to large electro-negativity differences
Covalent Bonding: Based on the ‘sharing’ of valance electrons due to small electro negativity differences
Metallic Bonding: All free electrons act as a moving ‘cloud’ or ‘sea’ to keep charged ion cores from flying apart in their ‘stable’ structure
secondary bonding: van der wahl’s attractive forces between molecules (with + to – ‘ends’)
This system of attraction takes place without valance electron participation in the whole
Valence Electrons participate in the bonding to build the molecules not in ‘gluing’ the molecules together

27. Ionic bond – metal + nonmetal
donates accepts electrons electrons  
Dissimilar electronegativities  
ex: MgO Mg 1s2 2s2 2p6 3s O 1s2 2s2 2p4
[Ne] 3s2 
Mg2+ 1s2 2s2 2p O2- 1s2 2s2 2p6
[Ne] [Ne]
Note: after exchange we have a stable (albeit ionic) electron structure for both Mg & O!

28. Examples: Ionic Bonding
• Predominant bonding in Ceramics
NaCl
MgO
Give up electrons
Acquire electrons
CaF 2
CsCl

29. Ionic Bonding – a Closely held Structure of +Ions and –Ions (after this Valence exchange)
These structure a held together by Coulombic Bonding forces after the Atoms exchange Valance Electrons to form the stable ionic cores:
It the solid state these ionic cores will sit at highly structured “Crystallographic Sites”
We can compute the coulombic forces holding the ions together – it is a balance between attraction force (energy) due to the ionic charge and repulsion force (energy) due to the nuclear cores of the ions
These forces of attraction and repulsion compete and will achieve a energy minimum at some inter-ion spacing

30. Figure 2.10 Formation of an ionic bond note effect of ionization on atomic radius. The cation (Na+) becomes smaller than the neutral atom, while the anion (Cl−) becomes larger than the neutral atom

31. Example: Using these energy issues
Here, ‘r0’ equals the sum of the ionic radii of each and represents the r in the energy balance equations!

32. Another Example (working backward with Coulomb’s Law):

33. The largest number of ions of radius R that can coordinate an atom of radius r is 3 when the radius ratio r/R = 0.2. (Note: The instability for CN = 4 can be reduced, but not eliminated, by allowing a three-dimensional, rather than a coplanar, stacking of the larger ions.) – to keep the ionic characteristic in balance!

34. The minimum radius ratio, r/R, that can produce threefold coordination is 0.155

36. Covalent Bonding CH 4 C: has 4 valence e-, needs 4 more
similar electronegativity  share electrons
bonds determined by valence – s & p orbitals dominate bonding
Example: CH4
C: has 4 valence e-,
needs 4 more
H: has 1 valence e-,
needs 1 more
Electronegativities
are comparable.
Adapted from Fig. 2.10, Callister 7e.
shared electrons
from carbon atom
from hydrogen
atoms H C CH 4

37. Three-dimensional structure of bonding in the covalent solid, carbon (diamond). Each carbon atom (C) has four covalent bonds to four other carbon atoms. Note, the bond-line schematic of covalent bonding is given a perspective view to emphasize the spatial arrangement of bonded carbon atoms.

38. Tetrahedral configuration of covalent bonds with carbon
Tetrahedral configuration of covalent bonds with carbon. The bond angle is 109.5°.

40. During Polymerization, We break up one “double bond” (must supply 162 kcal/mole) and add two single bonds (releases 2*88 = 176 kcal/mole) which requires a catalyst to start but will be self-sustaining (releasing heat!) once the process begins

41. “Electro-negativity” Values for determining Ionic vs
“Electro-negativity” Values for determining Ionic vs. Covalent Bond Character
Give up electrons
Acquire electrons

42. Primary Bonding %) 100 ( x Ex: MgO XMg = 1.2 XO = 3.5
Ionic-Covalent Mixed Bonding
% ionic character =  
where XA & XB are ‘Pauling’ electronegativities %)
100 ( x
Ex: MgO XMg = XO = 3.5

43. Metallic Bonding:
In a metallic bonded material, the valence electrons are “shared” among all of the ionic cores in the structure not just with nearest neighbors!

44. Considering Copper:
It valance electrons are far from the nucleus and thus are not too tightly bound (making it easier to ‘move out’)
outside shell had only one electron
When the valence electron in any atom gains sufficient energy from some outside force, it can break away from the parent atom and become what is called a free electron
Atoms with few electrons in their valence shell tend to have more free electrons since these valence electrons are more loosely bound to the nucleus. In some materials like copper, the electrons are so loosely held by the atom and so close to the neighboring atoms that it is difficult to determine which electron belongs to which atom!
Under normal conditions the movement of the electrons is truly random, meaning they are moving in all directions by the same amount.
However, if some outside force acts upon the material, this flow of electrons can be directed through materials and this flow is called electrical current in a conductor.

45. SECONDARY BONDING
Arises from interaction between “electric” dipoles
• Fluctuating dipoles
Adapted from Fig. 2.13, Callister 7e.
asymmetric electron
clouds + -
secondary
bonding H 2
ex: liquid H
• Permanent dipoles-molecule induced
-general case:
-ex: liquid HCl
-ex: polymer
Adapted from Fig. 2.14,
Callister 7e. H Cl
secondary
bonding + -
secondary bonding

46. Summary: Bonding Type Bond Energy Comments Ionic Covalent Metallic
Secondary
Bond Energy
Large!
Variable
large-Diamond
small-Bismuth
large-Tungsten
small-Mercury
smallest
Comments
Nondirectional (ceramics)
Directional
(semiconductors, ceramics
polymer chains)
Nondirectional (metals)
inter-chain (polymer)
inter-molecular

47. Properties From Bonding: Tm
• Melting Temperature, Tm
• Bond length, r r o
Energy r
• Bond energy, Eo Eo =
“bond energy”
Energy r o
unstretched length
smaller Tm
larger Tm
Tm is larger if Eo is larger.

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

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