상평형도 Chemographics refers to the graphical representation of the chemistry of mineral assemblages A simple example: the plagioclase system as a linear C = 2 plot: = 100 An/(An+Ab)
상평형도 3-C mineral compositions are plotted on a triangular chemographic diagram x, y, z, xz, xyz, and yz 2
Suppose that the rocks in our area have the following 5 assemblages: x-xy-x 2 z xy-xyz-x 2 z xy-xyz-y xyz-z-x 2 z y-z-xyz Figure 24-2. Hypothetical three-component chemographic compatibility diagram illustrating the positions of various stable minerals. Minerals that coexist compatibly under the range of P-T conditions specific to the diagram are connected by tie-lines. After Best (1982) Igneous and Metamorphic Petrology. W. H. Freeman. 공존선 Tie-line
Note that this subdivides the chemographic diagram into 5 sub-triangles, labeled (A)-(E) x-xy-x 2 z xy-xyz-x 2 z xy-xyz-y xyz-z-x 2 z y-z-xyz
Common point corresponds to 3 phases, thus P = C Figure 24-2. Hypothetical three-component chemographic compatibility diagram illustrating the positions of various stable minerals. Minerals that coexist compatibly under the range of P-T conditions specific to the diagram are connected by tie-lines. After Best (1982) Igneous and Metamorphic Petrology. W. H. Freeman.
What happens if you pick a composition that falls directly on a tie-line, such as point (f)? P = 2 Figure 24-2. Hypothetical three-component chemographic compatibility diagram illustrating the positions of various stable minerals. Minerals that coexist compatibly under the range of P-T conditions specific to the diagram are connected by tie-lines. After Best (1982) Igneous and Metamorphic Petrology. W. H. Freeman.
상평형도 확실한다이어그램은일부변성지역에서 P-T conditions 의특정영역을표현하기도함. P 와 T 가변화하면광물들의안정성과그것들의조합이변함. 서로다른변성정도에서다이어그램은다음과같이변화함. 특정광물들이안정하게됨. 동일한광물들의서로다른배열 ( 서로다른 tie-lines 서로다른공존상 -mineral- 과연결됨 )
일부광물들이 solid solution ( 고용체 ) 를나타내는다이어그램의사례 Figure 24-2. Hypothetical three-component chemographic compatibility diagram illustrating the positions of various stable minerals, many of which exhibit solid solution. After Best (1982) Igneous and Metamorphic Petrology. W. H. Freeman.
만일공존선상에 X bulk 가존재 (f) Figure 24-2. Hypothetical three-component chemographic compatibility diagram illustrating the positions of various stable minerals, many of which exhibit solid solution. After Best (1982) Igneous and Metamorphic Petrology. W. H. Freeman.
X bulk in 3-phase triangles F = 2 (P & T) so X min fixed Figure 24-2. Hypothetical three-component chemographic compatibility diagram illustrating the positions of various stable minerals, many of which exhibit solid solution. After Best (1982) Igneous and Metamorphic Petrology. W. H. Freeman.
변성암에서상평형도 가장일반적인자연상태의암석 : SiO 2, Al 2 O 3, K 2 O, CaO, Na 2 O, FeO, MgO, MnO, H 2 O 으로구성 (C = 9) 2 차원적으로쉽게생각할수있는최대성분의개수 : 3 성분 (C=3) 그렇다면올바른성분의선택은???? 가장단순한방법을고려 ( 암석의주성분의랭킹 )
1) 간단하게무시되는성분미량원소 오로지하나의광물에만들어가는원소 이동성이좋은성분 2) 같이결합하는원소 (Combine components) 고용체에서서로간치환을해주는성분 (Fe + Mg)
3) 암석의타입을제한하는원소 Ex) 석회암 : CaO 4) 일부투영법을이용하는경우도있음 Biotite on AFM diagram
The ACF Diagram 염기성암석 에서변성광물조합을묘사한간단한 3-C 삼각다이어그램 변성작용동안출현하고사라지는광물들에만집중함. 따라서변성정도를지시하는지시자로사용됨. A =Al2O3, C=CaO, F=FeO???? NO!!!!!
Figure 24-4. After Ehlers and Blatt (1982). Petrology. Freeman. And Miyashiro (1994) Metamorphic Petrology. Oxford.
The ACF Diagram The three pseudo-components are all calculated on an atomic basis: A = Al 2 O 3 + Fe 2 O 3 - Na 2 O - K 2 O C = CaO - 3.3 P 2 O 5 F = FeO + MgO + MnO
The ACF Diagram A = Al 2 O 3 + Fe 2 O 3 - Na 2 O - K 2 O 왜뺄까? 일반적인염기성암석에서 Na, K 는전형적으로정장석과조장석 (Albite) 를만들기위해 Al 과결합함. ACF diagram 에서, 장석류를제외한다른 K-bearing metamorphic minerals 만존재 장석에서 Al 2 O 3 : Na 2 O or K 2 O 비율은 1:1, 따라서 1:1 비율만큼장석을형성한다가정하고빼주는것임.
The ACF Diagram C = CaO - 3.3 P 2 O 5 F = FeO + MgO + MnO
특정 P 와 T 영역에관련된전형적인 ACF diagram (the kyanite zone in the Scottish Highlands) Figure 24-5. After Turner (1981). Metamorphic Petrology. McGraw Hill.
The AKF Diagram 이질퇴적암 (Pelitic sedimentary rocks) 이 Al 2 O 3 와 K 2 O 를많이함유하고상대적으로 CaO 를적게갖기때문에 Eskola 가제안한새로운다이어그램. K2O 를갖는광물조합이포함됨. AKF diagram 에서, 세가지성분 : A = Al 2 O 3 + Fe 2 O 3 - Na 2 O - K 2 O - CaO K = K 2 O F = FeO + MgO + MnO
Figure 24-6. After Ehlers and Blatt (1982). Petrology. Freeman.
AKF compatibility diagram (Eskola, 1915) illustrating paragenesis of pelitic hornfelses, Orijärvi region Finland Figure 24-7. After Eskola (1915) and Turner (1981) Metamorphic Petrology. McGraw Hill.
변성니질암에서가장일반적인광물 3 종 : andalusite, muscovite, and microcline. 이광물들은 AKF 다이어그램에서별개의지점으로존재 And & Ms 는 ACF diagram 에서같은지점에존재. 그리고미사장석은없음. 따라서 ACF diagram 이질암류에서는부적절함 (rich in K and Al) Figure 24-7. After Ehlers and Blatt (1982). Petrology. Freeman.
투영법고찰 : 상평형도에서투영 왜 ACF / AKF diagram 에서 SiO 2 는배제할까? What that subtraction was all about in calculating A and C It will also help you to better understand the AFM diagram and some of the shortcomings of projected metamorphic phase diagrams
상평형도에서투영 Example- the ternary system: CaO-MgO-SiO 2 ( CMS ) Straightforward: C = CaO, M = MgO, and S = SiO 2 none of that fancy subtracting business! Let s plot the following minerals: Fo - Mg 2 SiO 4 Per - MgO En - MgSiO 3 Qtz - SiO 2 Di - CaMgSi 2 O 6 Cc - CaCO 3
상평형도에서투영 Fo - Mg 2 SiO 4 Per - MgO En - MgSiO 3 Qtz - SiO 2 Di - CaMgSi 2 O 6 Cc - CaCO 3
The line intersects the M-S the side at a point equivalent to 33% MgO 67% SiO 2 Note that any point on the dashed line from C through Di to the M-S side has a constant ratio of Mg:Si = 1:2
상평형도에서투영 Fo - Mg 2 SiO 4 Per - MgO En - MgSiO 3 Qtz - SiO 2 Di - CaMgSi 2 O 6 Cc - CaCO 3 Pseudo-binary Mg-Si diagram in which Di is projected to a 33 Mg - 66 Si + Cal MgO SiO 2 Per Fo En Di' Q
Could project Di from SiO 2 and get C = 0.5, M = 0.5 상평형도에서투영 MgO + Qtz Per, Fo, En Di' Cal CaO
상평형도에서투영 MgO SiO 2 Per Fo En Di' Q 광물학적인상률 (P = C) 과연관지으면아래의 2-phase 광물조합이위의 2-component system에서적용됨. Per + Fo Fo + En En + Di Di + Q
상평형도에서투영 ACF and AKF diagrams 에서 SiO 2 배제 : 석영으로부터투영 가장간단한이유 : 어떤정점으로부터투영되는성분은성분에서배제한다. 이방식의결점은이러한투영이어떠한크기 ( 차원 ; dimension) 을없애면서까지진정한상관관계를묘사한다는점이다.
투영법 (4 성분계 ) Two compounds plot within the ABCQ compositional tetrahedron, x (formula ABCQ) y (formula A 2 B 2 CQ) Figure 24-12. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
투영법 (4 성분계 ) x = ABCQ y = A 2 B 2 CQ Figure 24-12. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
투영법 (4 성분계 ) x = ABCQ y = A 2 B 2 CQ Figure 24-12. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
투영법 (4 성분계 ) x plots as x' since A:B:C = 1:1:1 = 33:33:33 y plots as y' since A:B:C = 2:2:1 = 40:40:20 x = ABCQ y = A 2 B 2 CQ Figure 24-13. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
투영법 (4 성분계 ) If we remember our projection point (q), we conclude from this diagram that the following assemblages are possible: (q)-b-x-c (q)-a-x-y (q)-b-x-y (q)-a-b-y (q)-a-x-c The assemblage a-b-c appears to be impossible Fig. 24-13
투영법 (4 성분계 ) Fig. 24-13
A(K)FM Diagram 변성니질암류를위한 AKF 다이어그램의확장버전 비록 AKF 다이어그램이충분하긴하지만, Thompson (1957) 은 Fe 와 Mg 가대부분의암석에포함되어있는염기성광물들 ( 석류석, 흑운모, 근청석, 십자석등 ) 에서똑같은비율로들어가지않는것을관찰함.
Figure 24-17. Partitioning of Mg/Fe in minerals in ultramafic rocks, Bergell aureole, Italy After Trommsdorff and Evans (1972). A J Sci 272, 423-437. A(K)FM Diagram
A(K)FM Diagram A = Al 2 O 3 K = K 2 O F = FeO M = MgO
A(K)FM Diagram Project from a phase that is present in the mineral assemblages to be studied Figure 24-18. AKFM Projection from Mu. After Thompson (1957). Am. Min. 22, 842-858.
(a) A simplified petrogenetic grid and (b) pseudosection constructed using the Gibbs program (Spear, 1989) and the dataset of Holland and Powell (1998) (in Cheong, 2008)
At high grades muscovite dehydrates to K-feldspar as the common high-k phase Then the AFM diagram should be projected from K-feldspar When projected from Kfs, biotite projects within the F-M base of the AFM triangle A(K)FM Diagram Figure 24-18. AKFM Projection from Kfs. After Thompson (1957). Am. Min. 22, 842-858.
A(K)FM Diagram A = Al 2 O 3-3K 2 O (if projected from Ms) = Al 2 O 3 - K 2 O (if projected from Kfs) F = FeO M = MgO
A(K)FM Diagram Biotite (from Ms): KMg 2 FeSi 3 AlO 10 (OH) 2 A = 0.5-3 (0.5) = - 1 F = 1 M = 2 To normalize we multiply each by 1.0/(2 + 1-1) = 1.0/2 = 0.5 Thus A = -0.5 F = 0.5 M = 1
A(K)FM Diagram Figure 24-20. AFM Projection from Ms for mineral assemblages developed in metapelitic rocks in the lower sillimanite zone, New Hampshire After Thompson (1957). Am. Min. 22, 842-858. Mg-enrichment typically in the order: cordierite > chlorite > biotite > staurolite > garnet
Figure 27-6. AFM projections showing the relative distribution of Fe and Mg in garnet vs. biotite at approximately 500 o C (a) and 800 o C (b). From Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1. MSA. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
절적한상평형도의선택 예를들어, 특정지역에서이질암류를연구한다고가정한다면, 이이질암류의시스템은 9 종류의기본적인성분을포함한다. (SiO 2, Al 2 O 3, FeO, MgO, MnO, CaO, Na 2 O, K 2 O, and H 2 O) 어떻게우리는이 9 가지성분중에서의미있고유용한다이어그램을얻어낼수있을까?
절적한상평형도의선택 MnO 는 FeO + MgO 와같이생각하거나배제 ( 함량이상대적으로매우낮거나또는 FeO and MgO 를따라서고용체로행동 ) 이질암류에서 Na 2 O 는일반적으로사장석에서만중요하다. 따라서이것을배제하거나조장석을기준으로투영한다. H 2 O 는상당히이동성이좋으며배제하는성분임.
절적한상평형도의선택 Common high-grade mineral assemblage: Sil-St-Mu-Bt-Qtz-Plag Figure 24-20. AFM Projection from Ms for mineral assemblages developed in metapelitic rocks in the lower sillimanite zone, New Hampshire After Thompson (1957). Am. Min. 22, 842-858.
절적한상평형도의선택 Figure 24-21. After Ehlers and Blatt (1982). Petrology. Freeman.
Figure 24-21. After Ehlers and Blatt (1982). Petrology. Freeman. 절적한상평형도의선택
Choosing the Appropriate Chemographic Diagram 무수한상평형도가다양한변성암의종류에서성인적인관계를분석하기위하여제안되어왔음. 대부분이삼성분 ( 삼각다이어그램 ) 임 일부자연상에서존재하는시스템은 3-component system 에적절함. 결과적인변성상도 (metamorphic phase diagram) 는광물조합의형식에엄격하게적용됨.
Metapelites Figure 28-3. Greenschist facies AKF diagrams (using the Spear, 1993, formulation) showing the biotite-in isograd reaction as a tie-line flip. In (a), below the isograd, the tie-lines connecting chlorite and K-Feldspar shows that the mineral pair is stable. As grade increases the Chl-Kfs field shrinks to a single tie-line. In (b), above the isograd, biotite + phengite is now stable, and chlorite + K-feldspar are separated by the new biotite-phengite tie-line, so they are no longer stable together. Only the most Al-poor portion of the shaded natural pelite range is affected by this reaction. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-4. A series of AKF diagrams (using the Spear, 1993, formulation) illustrating the migration of the Ms-Bt-Chl and Ms-Kfs-Chl sub-triangles to more Al-rich compositions via continuous reactions in the biotite zone of the greenschist facies above the biotite isograd. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-5. AFM projection for the biotite zone, greenschist facies, above the chloritoid isograd. The compositional ranges of common pelites and granitoids are shaded. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-6. AFM projection for the upper biotite zone, greenschist facies. Although garnet is stable, it is limited to unusually Fe-rich compositions, and does not occur in natural pelites (shaded). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-7. AFM projection for the garnet zone, transitional to the amphibolite facies, showing the tie-line flip associated with reaction (28-8) (compare to Figure 28-6) which introduces garnet into the more Fe-rich types of common (shaded) pelites. After Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-9. AFM projection in the lower staurolite zone of the amphibolite facies, showing the change in topology associated with reaction (28-9) in which the lower-grade Cld-Ky tie-line (dashed) is lost and replaced by the St-Chl tie-line. This reaction introduced staurolite to only a small range of Al-rich metapelites. After Spear (1993) Metamorphic Phase Equilibria and Pressure-Temperature-Time Paths. Mineral. Soc. Amer. Monograph 1. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-10. AFM projection in the staurolite zone of the amphibolite facies, showing the change in topology associated with the terminal reaction (28-11) in which chloritoid is lost (lost tie-lines are dashed), yielding to the Grt-St-Chl sub-triangle that surrounds it. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-11. AFM diagram for the staurolite zone, amphibolite facies, showing the tie-line flip associated with reaction (28-12) which introduces staurolite into many low-al common pelites (shaded). After Carmichael (1970) J. Petrol., 11, 147-181. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-14. AFM projection for the kyanite zone, amphibolite facies, showing the tie-line flip associated with reaction (28-15) which introduces kyanite into many low-al common pelites (shaded). After Carmichael (1970) J. Petrol., 11, 147-181. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-15. AFM projection above the sillimanite and staurolite-out isograds, sillimanite zone, upper amphibolite facies. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-16. AFM diagram (projected from K-feldspar) above the cordierite-in isograds, granulite facies. Cordierite forms first by reaction (29-14), and then the dashed Sil-Bt tie-line is lost and the Grt-Crd tie-line forms as a result of reaction (28-17). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Figure 28-17. AFM diagrams (projected from muscovite) for low P/T metamorphism of pelites. a. Cordierite forms between andalusite and chlorite along the Mg-rich side of the diagram via reaction (28-23) in the albite-epidote hornfels facies. b. The compositional range of chloritoid is reduced and that of cordierite expands as the Chl- Cld-And and And-Chl-Crd subtriangles migrate toward more Fe-rich compositions. Andalusite may be introduced into Al-rich pelites. c. Cordierite is introduced to many Al-rich pelites via reaction (28-24) in the lowermost hornblende hornfels facies. (d) Chlorite is lost in Msbearing pelites as a result of reaction (28-25). Created using the program Gibbs (Spear, 1999) Geol. Materials Res., 1, 1-18. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall. Metapelites
Metapelites Figure 28-18. a. The stability range of staurolite on Figure 28-2 (red). b. AFM projection in the hornblende hornfels facies in the vicinity of 530-560 o C at pressures greater than 0.2 GPa, in which staurolite is stable and may occur in some high-fe-al pelites (shaded). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-19. AFM diagrams (projected from Kfs) in the lowermost pyroxene hornfels facies. a. The compositional range of cordierite is reduced as the Crd-And-Bt sub-triangle migrates toward more Mg-rich compositions. Andalusite may be introduced into Al-rich pelites b. Garnet is introduced to many Al-rich pelites via reaction (28-27). Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-20. Veins developed in pelitic hornfelses within a few meters of the contact with diorite. The vein composition contrasts with that of the diorite, and suggests that the veins result from localized partial melting of the hornfelses. Onawa aureole, Maine. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Figure 28-21. High-temperature petrogenetic grid showing the location of selected melting and dehydration equilibria in the Na 2 O-K 2 O- FeO-MgO-Al 2 O 3 -SiO 2 -H 2 O (NKFMASH) system, with sufficient sodium to stabilize albite. Also shown are some equilibria in the KFASH (orange) and KMASH (blue) systems. The medium and low P/T metamorphic field gradients from Figure 28-2 (broad arrows) are included. The Al 2 SiO 5 triple point is shifted as shown to 550 o C and 0.45 GPa following the arguments of Pattison (1992), allowing for the coexistence of andalusite and liquid. V = H 2 O-rich vapor, when present in fluid-saturated rocks. After Spear et al. (1999).
Metapelites Figure 28-22. Some textures of migmatites. a. Breccia structure in agmatite. b. Netlike structure. c. Raft-like structure. d. Vein structure. e. Stromatic, or layered, structure. f. Dilation structure in a boudinaged layer. g. Schleiren structure. h. Nebulitic structure. From Mehnert (1968) Migmatites and the Origin of Granitic Rocks. Elsevier. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
Metapelites Figure 28-23. Complex migmatite textures including multiple generations of concordant bands and cross-cutting veins. Angmagssalik area, E. Greenland. Outcrop width ca. 10 m. Winter (2001) An Introduction to Igneous and Metamorphic Petrology. Prentice Hall.
More complex migmatite textures. Metapelites