제 4 장 3성분계 상태도
4.1 조성읽기 (성분 분률)
( )%A-( )%B-( )%C ( )%A-( )%B-( )%C
( )% A - ( )% B - ( )% C Fig. 4-1 3성분계 성분분률(1).
What is the composition for the points shown (% A,B,C):
※ Note the composition always sums to 100%
i) ( ), ( ), ( ) ii) ( ), ( ), ( ) iii) ( ), ( ), ( ) iv) ( ), ( ), ( )
v) ( ), ( ), ( )
Fig. 4-2 3성분계 성분분률(2).
4.2 3성분계 지렛대 원리 (상 분률)
( ) ( ) Fraction A = --- Fraction A = --- ( x + y + z) ( x + y ) ( ) ( ) Fraction B = --- Fraction B+C = --- ( x + y + z) ( x + y )
( ) ( ) ( ) Fraction C = --- Fraction B = --- × --- ( x + y + z) ( x + y ) ( z + w ) ( ) ( ) Fraction C= --- × --- ( x + y ) ( z + w )
Fig. 4-3 3성분계 상분률(1).
A 점
성분 조성 MgO ( ) % Al2O3 ( ) % SiO2 ( ) %
상 조성 MgO
(Periclase) ( ) % MgAl2O4
(Spinel) ( ) % Mg2SiO4
(Forsterite) ( ) %
B 점
성분 조성 MgO ( ) % Al2O3 ( ) % SiO2 ( ) %
상 조성 Mg2SiO4
(Forsterite) ( ) % MgAl2O4
(Spinel) ( ) % 2MgO․2Al2O3․5SiO2
(Cordierite) ( ) % Fig. 4-4 3성분계 성분 및 상분률.
4.3 Mole%, Wt%, Compositions and Projections in Ternary Diagram(Homework)
Consider the minerals/fluids listed in Table 1, at the end of this handout.
1. Calculate the mole % of each element in each phase and fill in the table.
2. Calculate the weight % of each element in each phase and fill in the table.
(If I were doing this, I would use Excel or Quattro or some other spreadsheet. If you setup the spreadsheet it will save you a lot of button pushing on your calculator. And you will not make errors. But, hey, it's a fee country – do it as you wish.)
3. Answer question 4 before doing this: For those phases that do not contain water: Plot their compositions on the two triangular diagrams provided later on in this handout, and label the points with the phase abbreviations. One plot uses mole% values, the other uses wt%.
4. BUT WAIT! BEFORE YOU DO THE PLOTTING, ANSWER THIS QUESTION:
Make a prediction -- What do you think the differences will be between the two plots. Will they be the same? If so, why? If not, will they be completely different? Or, only a little different? Why? Explain.
5. For plotting mineral compositions and thinking about how they compare and mineral reactions, etc., which kind of plot do you think would be most valuable: mole% plots or weight% plots? Why?
6. Under what circumstance would the other kind of plot be useful?
7. Now redo the mole% diagram you just plotted but add the phases that include H2O as well.
The problem is that we now have four components. Must come up with a plan. What to do?
BEFORE YOU START PLOTTING AGAIN, PREDICT WHAT YOU WILL FIND. YOU ARE GOING TO MAKE FOUR PLOTS (READ BELOW): WILL THE FOUR PLOTS COME OUT TO BE SIMILAR, DIFFERENT, OR SOMEWHERE BETWEEN?
Try plotting the compositions (use mole%) ignoring H2O. Just add up the other three and normalize (multiply by a fudge factor) so they total 100%. Then plot. (The ones you plotted before will not move because they already total 100% - they contain no H2O.) By ignoring a component, you are creating a projection. The idea is that if H2O (or something else) is unimportant, we can just ignore it for plotting purposes.
Try plotting the compositions, projecting from (ignoring) CaO.
Try plotting the compositions, projecting from (ignoring) Al2O3. Try plotting the compositions, projecting from (ignoring) SiO2.
8. How do the four plots you just made compare? Very similar, different, close.?
Which do you think would be most valuable when considering mineral compositions, reactions, etc.?
9. What do you think about using projections to plot 3-D compositions on a 2-D piece of paper? Is this useful, misleading, hairy, fun, etc.? Discuss, briefly.
Plotting the minerals that do not contain H2O.
Mole % ==>
Wt % ==>
Fig. 4-5 3성분계 몰%, 무게% 및 성분분률.
4.4 Ternary eutectic system with crystallization spaces separated
Fig. 4-6 3성분계 공간모식도.
Fig. 4-7. Ternary eutectic system with crystallization spaces separated.
8 Spaces or Volumes
1. 액상 공간 ( Liquid Space )
① 액상연 위의 영역이며 액상만으로 이루어짐
2. 3개의 초정출 공간 ( 3 Spaces of Primary Crystallization) ② A + 액체
③ B + 액체 ④ C + 액체
초정출 공간 상부 표면은 액상 표면에 의해 제한되어 있음
하부 표면은 다음 방식으로 형성됨 (예) 초정출 공간 A +액체를 생각하면 ㉠ 연필과 같은 가느다란 막대기를 한 끝은 수직선 Aw에 접촉하는 점 m에 그리고 다른 한 끝은 경계선 gf에 접촉하는 점 g에 수명한 위치로 놓음
㉡ 만일 막대기 왼쪽 끝이 m에서부터 a 로 미끌어지는 한편
수평으로 유치되면서 경계선 gE에 접촉하며 오른쪽 끝이 점 E 까지 미끄러진다면 ㉢ 형성된 표면들은 초정출 공간 A의 하부제한 표면의 일부임
㉣ 하부표면의 나머지는 막대기를 경계선 fE와 접촉을 유지하면서 q에서부터 a까지 수평으로 미끌어 뜨림으로써 형성됨
이 공간의 모든 조성-온도 점들은 결정 A와 조성이 액상면 wfEg 위에 놓이는 액체들 사이의 평형을 나타냄
3. 3개의 이원 정출 공간 ( 3 Spaces of Binary crystallization ) ⑤ A + B + 액체
⑥ A + C + 액체 ⑦ B + C + 액체
이원 정출 공간 상부 표면은 초정출 공간들의 하부표면들에 의해 제한되어 있음 하부 표면은 공정점 E를 지닌 수평면 abc에 의해 제한되어 있음
이 공간 안의 모든 조성-온도 점들은 두 결정상들과 조성이 적절한 경계선(gE, fE 또는 hE) 상에 놓인 액체 사이의 평형을 나타냄
예를들면, 이원 정출 공간 A + C + 액체 안에서, 모든 액체 조성은 경계선 gE상에 놓임
이 공간들의 하부 수직외부표면들은 2원 고상선 온도 이하의 온도에서의 2원계 안에 놓이며 따라서 두 결정상들만을 지님
4. 결정상들만 포함한 공간 ( Space of 3 Solids ) ⑧ 결정 A + B + C
평면 abc 아래의 공간
