# 工程材料
###### tags: `academy`

## Chapter 9: Phase Diagrams
### Issues to address
- resulting equilibrium state when combining two elements
- specify `composition(%數)`、`temperature(T)`，then
- how many phases form?
- what is the composition of each phase?
- what is the amount of each phase?
- 

### Phase Equilibria: Solubility Limit
> 相平衡: 溶解度極限
#### 溶液vs混合物
- Solution: solid, liquid, gas solutions, single phase
- Mixture: more than one phase
- Solubility Limit:
- Maximum concentration for which only a single phase solution exists
-
- Question:
> What is the solubility limit for sugar in water at 20ºC
> 
- Answer:
> 65wt% sugar
> At 20ºC, if C<65 wt% sugar: syrup
> At 20ºC, if C>65 wt% sugar: syrup + sugar
### Components and Phases
- Components:
- The elements or compounds(化合物) which are present in the alloy
- Phases:
- The physically and chemically distinct material regions that form(e.g. $\alpha$ and $\beta$)
### Effect of Tempearture & Composition
### Criteria for Solid Solubility
- Simple system (e.g.Ni-Cu solution)
- Both have the same crystal structure(FCC) and have similar electronegativities and atomic radii suggesting high mutual solubility.
- Ni and Cu are totally soluble in one another for all properties
### Phase Diagram
- Indicate phases as afunction of T, C, and P
- For this course
- binary system: just 2 components
- independent variables: T and C (P=1 atm is almost always used)

#### Isomorphous(同構的) Binary Phase Diagram
- Phase Diagram: Cu-Ni system
- System:
- Binary
> 2 components
- isomorphous(同構)
> complete solubility of one component in another, $\alpha$ phase field extends from 0 to 100 wt% Ni.
#### Determination of phase(s) present
- Rule 1: If we know T and C~o~
> which phase(s) is (are) present
- Examples
- A(1100ºC, 60 wt% Ni): 1 phase $\alpha$
- B(1250ºC, 35 wt% Ni): 2 phases L+$\alpha$
#### Determination of phase compositions
- Rule 2: If we know T and C~0~
> the composition of each phase
- Examples
> Consider C~0~ = 35 wt% Ni
- At T~A~ = 1320ºC:
- Only Liquid(L) present
- C~L~ = C~0~ (=35 wt%)
- At T~D~ = 1190ºC:
- Only solid($\alpha$) present
- $C_\alpha$=C~0~(=35 wt%)
- At T~B~ = 1250ºC:
- Both $\alpha$ and L present
- C~L~ = 32$ wt% Ni
- $C_\alpha$~ = 43 wt% Ni
#### Determination of phase weight fractions
- Rules 3: If we know T and C~0~
> can determine weight fraction of each phase
- Examples:
> Consider C~0~ = 35 wt% Ni
- At T~A~: Only Liquid
- $W_L=1.00, \ W_\alpha = 0$
- At T~D~: Only Solid($\alpha$)
- $W_L=0, \ W_\alpha = 1.00$
- At T~B~: Both Liquid and Solid
- $W_L = \dfrac{S}{R+S}$ = 0.73
- $W_\alpha = \dfrac{R}{R+S}$ = 0.27
- $R,S$為B到boundary的wt距離
### The Lever Rule
- Tie line: connects the phases in equilibrium with each other
- also sometimes called an isotherm(等溫線)
### Cored vs Equilibrium Structures
- $C_\alpha$ changes as we solidfy
- Cu-Ni case:
- First $\alpha$ to solidify has $C_\alpha$ = 46 wt% Ni
- Last $\alpha$ to solidify has $C_\alpha$ = 35 wt% Ni
- Slow rate of cooling: Equilibrium structure
- Fast rate of cooling: Cored structure
### Mechanical Properties: Cu-Ni System
- Effect of solid solution strengthening on:
### Binary-Eutectic Systems
> Eutectic: has a spectial composition with a min. melting T
Ex. Cu-Ag system
- 3 single phase regions(L, $\alpha$, $\beta$)
- Limited solubility
- $\alpha$: mostly Cu
- $\beta$: mostly Ag
- $T_E$: No liquid below $T_E$
- $C_E$: Composition at temperature $T_E$
- Eutectic reaction:
- $L(C_E) \leftrightharpoons \alpha (C_{\alpha E}+\beta (C_{\beta E}))$
:::warning
例題看ppt動畫
ask: phase present, phase compositions, relative amount of each phase
:::
### Microstructural Developments in Eutectic
#### System I
- For alloys for which C~0~ < 2 wt% Sn
- Result: at room temperature
- polycrystalline with grains of $\alpha$ phase having composition C~0~
#### System II
- For alloys for which 2 wt% Sn < C~0~ <18.3 wt% Sn
- Result: at temperature in $\alpha + \beta$ range
- polycrystalline with $\alpha$ grains and small $\beta$-phase particles
#### System III
- For alloy of composition C~0~ = C~E~
- Result: Eutectic microstructure (lamellar struc)
- alternating layers(lamellae) of $\alpha$ and $\beta$ phases
#### System IV
- For alloys for which 18.3 wt% Sn < C~0~ < 61.9 wt% Sn
- Result: $\alpha$ phase particles and a eutectic microconstituent
### **Hypoe**utectic & **Hyper**eutectic
### Eutectic, Eutectoid, Peritectic
- Eutectic: liquid transforms to two solid phases
- Eutectoid: one solid phase transforms to two other solid phases
- Peritectic: liquid and one solid phase transform to a second solid phase
:::warning
Hypoeutectoid Steel & Hypereutectoid Steel 看PPT動畫解釋
例題也看PPT
:::
### Summary
- Phase diagrams are useful tools to determine
- the number and types of phases present
- the composition of each phase
- and the weight fraction of each phase
- The microstructure of an alloy depends on
- its composition
- whether or not cooling rate allows for maintenance of equilibrium
- Important phase diagram phase transformations include