2.2 differences in atomic scale boning create macroscopic property differences in materials

you can plot bond length vs forces or energy to get

• equilibirum bond length

• elastic modulus

• melting point

• CTE

Attractive force (Fa)

Coulombic attraction

Fa=|Z1Z2|q²/4pie0x²

• strength of charges/distance between charges

• Z- valency

• q- charge of an electron

repulsive force (Fr)

coulmbic repulsion

Fr=-B/x^12

Fnet=

Fa + Fr

when is net force at an equilibrium

FA=FR

Ionic bonds

sum of forces

Fnet=A/x² - B/x^12

ionic bonds on a graphj

Axes- Force is the y ; x is distance between atomic centers

When graph is positive, there is net attraction

when graph is negative, net repulsion

Graph=0—> equilibirum. From the 0 to that point is equilibrium bond length

as the graph goes to infinity what happens?

become non-bonded

Ionic Bond, Bond Energy on a Bond length vs force graph

The area under the curve

• net repulsive is positive energy

• net attractive is negaitve energy

When force is at equilibrium aka 0

energy is at is minimum

bond energies, bonds can either

compress or expand

bonding and stiffness

• take slope at equilibirum

• curve with steeper slope has higher stiffness

  • more curvature, stiffer

  • if you add energy, how far does each compress at that energy, the one that compresses less is the stiffer one

can think of energy as the amount of

thermal energy

if T>0K and KBT>0

thermal energy and atomic vibrations

if T=0 and KBT-0

no thermal energy nor vibrations, only equilibriuym x0 allowed

Higher melting temperatuer

Deeper energy well, higher melting points, need more thermal energty to melt/break the bonds

Higher CTE

• more asymetrical→ higher CTE

• more symetric→ lower CTE

• looking at the middle of the hump vs the middle of the given temperature lines,

• less symetric will spend more time expanding than a sykmetric one

deper energy wells () usually are

• Higher melting point

• more symetric, lower CTES

• + higher curvature aka more stiff