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The binary eutectic phase diagram explains the chemical behavior of two immiscible unmixable crystals from a completely miscible mixable melt, such as olivine and pyroxene, or pyroxene and Ca plagioclase. Here we are going to generalize to two minerals, A and B, or P and Q. We want to observe the behavior of this system under two conditions, one of complete equilibrium during crystallization when all chemical reactions can run to completion, and the second of disequilibrium when fractionation occurs and igneous rocks evolve.
The conventions for the phase diagram include the following illustration below: They 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 The assumptions are: 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. Organization of the Binary Eutectic Phase Diagram. This path is the same any time the composition of B is greater than the eutectic value. Now, imagine the process stops just at the point the last crystal of A has melted, and all the melt is removed fractionated from the system.
As the temperature continues to rise, B will remain unmelted until the T B of about o is reached. By this process the original rock has been split into two fractions. Of course, the separation could occur at any time in the process, before all A has melted, or after A has all melted and some of B as well.
The resulting two fractions will differ depending on the circumstances. Once all of Q is gone then the system can leave the eutectic. With further rise in temperature the systems just follows the red line up to the top of the diagram. Now, imagine the process stops just at the point the last crystal of P has melted, and all the melt is removed fractionated from the system.
As the temperature continues to rise it will remain unmelted until the TQ of about o is reached. Of course, the separation could occur at any time in the process, before all Q has melted, or after Q has all melted and some of P as well.
NOTE the following about reading the diagram: NOTE that the solidus and liquidus lines are experimental, they have been determined by melting and cooling many melts at different percent compositions. The eutectic is the point at which all three phases can exist simultaneously, A, B, and melt. For pure A far left of diagram the melting crystalizing temperature is T A about o. For pure B far right of diagram the melting crystalizing temperature is T B about o.
The more B we add the lower the melting temperature becomes; that is, it moves down the liquidus line toward the eutectic. Any mixture of A and B lowers the melting crystallizing temperature. The First Crystal numbers on phase diagram correspond with numbers below 1. Cool melt to liquidus line along red arrow. Only B crystals form at about o B is immiscible with A. Removing crystallizing B changes the melt composition making in richer in A.
Therefore the melt composition begins to migrate to the left, but down the liquidus line toward the eutectic point. The system must stay on the liquidus line since going above it would raise the temperature high enough to melt everything. We can reverse the process and begin with a rock, heating it slowly until it melts. In this case the diagram is read the reverse of the crystallization steps following the numbers below.
It is slowly heated until it reaches the solidus line. At the solidus line the system shifts laterally to the eutectic point. Melting is always at the ratio of the eutectic, regardless of the starting composition. Melting at the eutectic is always at the ratio of the eutectic, regardless of the starting composition. This time we will fractionate the system, the first 3 steps are the same as last time but are repeated here. As with fractional melting what is required is separating the crystal from the melt before complete crystallization has occurred.
Give it a try. See if you understand. Cool and fractionate the system until just at the point all the least abundant mineral melts. What is the composition of the two fractions, and at what temperature will this occur?
And since in both cases it is the fraction lower on the reaction series which melts preferentially, the effect of both fractionations is to produce a melt which is lower on the reaction series than the original rock.
The actual fractionation of a rock is more complex than the simple phase diagrams indicate. First, an igneous rock may have 3, 4, 5, or more minerals, all of which interact in complex ways.
Second, many phases have partial miscibility and require more elaborate phase diagrams. Phase diagrams have been worked out for all the combinations and permutations you can think of: