What’s unique about Materials Science and Engineering?

We start with several examples to illustrate the subjects unique to Materials Science and Engineering.

• Thermodynamically versus Kinetically controlled processes and phenomena in materials

• Phase transformation and rate control Diffusional vs. Diffusionless(Martensitic) transformation

1st order (Nucleation & growth) vs. 2nd order (volume transformation) Displacive vs. reconstructive transformation

• Kinetic rate equations and driving force(s) in materials

• Thermodynamic legitimate questions in materials

• Rate equations

Kinetics versus Thermodynamics

Kinetics Describes reaction speed, whether it is at equilibrium and what factors effect the speed of the reaction

Tells you if it will get there in a reasonable amount of time.

Thermodynamics Predicts distribution of chemical species and phases if reactions get to equilibrium (or final state of a system)

Says nothing about speed of reaction, nor predict what can happen, but predict what cannot happen.

•  Melting and Crystallization are Thermodynamic Transitions -Discontinuous changes in structure and properties and Tm

-Structures are �thermodynamically controlled� and described by the �Phase Diagram�

•  The Glass Transition is a Kinetic Transition – Continuous changes in structure and properties

– Structure and properties are continuous with temperature

– Structures and properties can be changed continuously by changing the kinetics of the cooling liquid �kinetically controlled�

glass

Super cooled liquid

Thermodynamically vs. Kinetically controlled phenomena

Example (1): Glass Transition

Temperature

Volu

me liquid

crystal

Tm αliquid

αcrystal

αliquid >>αcrystal

Tm Tg

Thermodynamics of Crystal and Glass

Stable versus Unstable

Stable

Meta-stable

Un-stable

Crystal is �stable� or �meta-stable� Glass is �unstable�

Immiscible Phase Separation and Spinodal Decomposition

Polymer phase separation Inorganic phase separation Pyrex glass Vycor glass

These are all “diffusional” process

Chemically durable (outside of spinode)

Thirsty glass (inside of spinode)

(inside of spinode)

vs

“Diffusion-less” process (next)

Al2Au AlAu

AlAu2

Al2Au5

AlAu4

733K(460C)

473K(200C)

AlAu4 Al2Au

150C 100C

Example (2): Al-Au Bulk vs Thin Film

Bulk couple

Thin film couple

Thermodynamically vs. Kinetically controlled phenomena

• Annealed at 460C for 100min: All 5 compounds in correct order • Annealed at 200C for 100min: AuAl2 and AuAl are missing, other present

Why are AlAu and Al2Au5 not seen?

Reaction depends on thickness of each material

Example (3): Ni-Si Bulk vs Thin Film Bulk bonding at 850C

Thin Film at 250C

Thermodynamically vs. Kinetically controlled phenomena

• Ni on Si Ni2Si first ,followed by NiSi after consumption of Ni, after then NiSi2 vs • Si on Ni Ni2Si first, but the subsequent phases are different and are rich in Ni.

Phase diagram • The phase in equilibrium with Si should be NiSi2 (based on the thermodynamics), yet the first phase formed is Ni2Si.

• Cannot predict the phase sequence just looking at the phase diagram, since phase formation is a kinetic phenomenon.

Ni2Si

RBS(Rutherford Backscattering Spectroscopy)

Two examples: • To melt materials, need heat; “Melting” is endothermic.

• Point defect formation: To remove atoms from solid (i.e. vacancy), you need to break the bonds, which is endothermic.

Then why melting an vacancies do form, even it costs energy?

Thermodynamics Legitimate Questions

Simple answer: At the equilibrium, we must consider the �free-energy� rather than the �enthalpy�, then minimize the free-energy. The �entropy� changes associated with the formation of the melting and defect formation can reduce the free energy of the �system�, since G=H-TS, where H is always positive; G could become negative at some T.

G = H - TS

€

S = kB ln Ωminimum

Eq. *

Equation above

Equation above minimum

€

ΔG =Gdef −Gperf = nν

For constant T

Magic of the “entropy”

1. Instruction: Remove an atom from the bulk of a crystal, then place it on the surface,

then consider the energy difference between initial and final state conditions.

5. Note: This approach is not strictly orthodox: since Gperf cannot be calculated on an absolute scale; however, the approach is still valid such the final result is reached that the energy will be subtracted from Gdef.

Remove from the bulk then place on the surface

2. Legitimate Removing atoms means creating broken bonds. This is �endothermic�. question: Then, a question is why the vacancies do form, even it costs energy.

3. Answer: At the equilibrium, we must consider the �free-energy� rather than the �enthalpy�, so we need to minimize the free-energy.

4. How: The �entropy� changes associated with the formation of the defects must be taken into account, then �vacancies� becomes thermodynamically more favorable than �perfect crystal�.

G = H - TS

Thermodynamics of Point Defects Formation in Elemental Crystals

Use Standard Procedure of Evaluating �Thrmodynamics��

1.  Consider free energy of perfect versus defected crystal situations.

vs

2. Calculate Gperfect = (H - TS )perfect for perfect crystal 3.  Calculate Gdefected = (H - TS )defected for defected crystal 4.  Entropy part S consists of two parts: Configurational entropy Sconf

and Vibrational entropy Svib

5.  Difference of free energy (ΔG) between �perfect� and �defected� situations ΔG = Gperfect - Gdefected

6.  Try to minimize the difference of free energy with respect to # of defect

7. Find the # of defects, ndefect.

perfecdt defected Gperfect Gdefect

€

∂ΔG∂n

= 0

Difference of Gibb�s Free energy before and after defect formation

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ΔG =Gdef −Gperf = nν hd + kTnνζ lnν '

ν+ kT N ln N

nν + N+ nν ln

nνnν + N

&

' (

)

* +

• This is an important result because it says that the free-energy changes upon the introduction of nv

• Defects in an otherwise perfect crystal is a function of both nv and T.

minimum Eq. *

Equation above

Equation above minimum

€

ΔG =Gdef −Gperf = nν

For constant T

Free energy becomes minimum at certain concentration of the defects! But it is temperature dependent.

Vapor Pressure vs. Temperature of Various Materials

z

Cu

Al

Rate equation = ß F ß: a system constant (diffusion constant, etc.)

F: is the driving force