# 1 Binary Phase Diagrams GLY 4200 Fall, 2012. 2 Binary Diagrams Binary diagrams have two components We therefore usually choose to plot both T (temperature)

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1 Binary Phase Diagrams GLY 4200 Fall, 2012

2 Binary Diagrams Binary diagrams have two components We therefore usually choose to plot both T (temperature) and X (composition) with pressure held constant P-X (T fixed) or P-T (X fixed) are also possible

3 Binary System Examples Binary solid solution - olivine, plagioclase feldspar Binary eutectic with congruent melting - potassium feldspar - silica Binary peritectic and eutectic with solid to solid conversion - leucite - Potassium feldspar - silica Binary minimum melting point - potassium feldspar - albite Binary minimum melting point with solvus - potassium feldspar - albite

4 Phase Rule for Binary Systems  f = c - p + 2 = 2 - p + 2 = 4 - p If two phases are present, there are two degrees of freedom (both T and X) If three phases are present, there is one degree of freedom (either T or X)

5 Binary Solid Solution Plagioclase Feldspar series, 39% of the earth’s crust

6 Phase Rule Application How many degrees of freedom are present at points 1,2, and 3?

7 Binary Eutectic Diagram Conventions Two immiscible components: such as CaAl 2 Si 2 O 8 (calcic plagioclase) and FeMgSiO 4 (olivine) plotted along the horizontal axis, OR olivine (isolated tetrahedra) and pyroxene (single chain tetrahedra), which are immiscible because they have different crystal structures One variable, temperature, plotted along the vertical axis. Pressure is held constant at 1 atmosphere. Three phases, crystal A, crystal B, and melt. Complete miscibility of the melt (magma)

8 Binary Eutectic Diagram Assumptions The system remains in equilibrium throughout its history, so that all reactions can take place and everything can come to stability Everything in the original melt remains in communication throughout the crystallization process

9 Binary Eutectic Diagram

10 Binary Eutectic Diagram – Intermediate Compositions

11 Binary Eutectic Crystallization

12 Binary Eutectic Melting

13 Melting A Rock With A 30/70 Eutectic

14 FractionationFractionation

15 Congruent Melting The previous case is an example of congruent melting Congruent melting means melting of a substance directly to a liquid that is of the same composition as the solid

16 Incongruent Melting Melting accompanied by decomposition or by reaction with the liquid, so that one solid phase is converted into another Melting to give a liquid different in composition from the original solid One example occurs in the forsterite-quartz system

17 Binary Eutectic with Incongruent Melting L = Liquid Fo is fosterite En is enstatite Qtz is quartz

18 Reaction MgSiO 3 + SiO 2 = Mg 2 SiO 4 En + Qtz = Fo

19 Fo- Qtz

20 Forsterite – Quartz at Higher T Two liquid phases are present on the right side of the diagram

21 Binary Minimum Melting Point

22 Albite - Orthoclase

23 Lever

24 Application of Lever Rule C = 65 weight% β

25 Point 2 Solid phase B starts to form with a composition of 96 weight% β

26 Point 3 C 1 = 58 weight% β and C 2 = 92 weight% β

27 Point 3 Calculations Fraction of solid b = (65 - 58) / (92 - 58) = 20 weight% Fraction of liquid = (92 - 65) / (92 - 58) = 80 weight%

28 Point 4 C 3 = 48 weight% β C 4 = 87 weight% β

29 Point 4 Calculations Fraction of solid with composition C 4 = (65 - 48) / (87 - 48) = 44 weight%. Fraction of liquid at eutectic = 56 weight%

30 Point 5 C 5 = 9 weight% β and C 6 = 91 weight% β

31 Point 5 Calculations Fraction of solid with composition C 6 = (65 - 9) / (91 - 9) = 68 weight% Fraction of solid with composition C 5 = (91 - 65) / (91 - 9) = 32 weight%

32 Effects of Pressure With increased pressure, from 1 atm to 7 kbar, En changes from incongruent to congruent melting behavior The field of liquid immiscibility, the 2L field on the 1 atm diagram, disappears at slightly elevated pressures and is no longer evident in the 3 kbar diagram.

33 Orthoclase – Albite at Low P

34 Orthoclase – Albite at 5 kbars

36 Points on Diagram Edge Points on the edge have only two components

37 Reading Sample Points Note that the scales are plotted increasing in a CCW directions

38 Ternary Rock Composition Diagram Ternary diagrams can be used to plot any three things

39 Texture Diagram Another use of ternary diagrams

40 Ternary System Sample ternary diagram

41 Silica Nepheline Kalsilite 10 20 0 0 0 30 40 50 60 70 80 90 100 ← % Nepheline % Silica ↑ % Kalsilite ↓

42 Real Plot

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