1. Reaction Series and Melting Behavior GLY 4310 - Spring, 2016
Petrology Lecture 5
Reaction Series and Melting Behavior
GLY Spring, 2016
The connection between the application of laboratory research and petrological observations in the field was demonstrated extremely strongly by the work of Norman Levi Bowen.

2. Norman Levi Bowen
Canadian geologist who was one of the most important pioneers in the field of experimental petrology
Widely recognized for his phase-equilibrium studies of silicate systems as they relate to the origin of igneous rocks
Reaction principle. He recognized two types of reaction, continuous and discontinuous. (1922)
More information at:
Mineralogical Society of America, fellow, president
Geological Society of America, vice-president, president
1928, The Evolution of the Igneous Rocks. The work was based on a series of lectures Bowen gave to students at Princeton University in the spring of 1927.
He developed an idea which he called the reaction principle. He recognized two types of reaction, continuous and discontinuous. These ideas were first published in 1922.

3. Continuous Reaction
The first reaction involves the conversion of one mineral to another by reaction with the melt, and with a change in the melt chemistry. These take place whenever solid solution series, such as olivine or plagioclase, exist. The second type occurs whenever a mineral begins to crystallize. If C>2, these reactions may involve more than one mineral.

4. Discontinuous Reaction
The second reaction was seen before in the phase diagrams shown in mineralogy
What was that type of reaction called?
The crystallization of diopside and anorthite from a melt is an example of the first type of reaction. The second is the familiar peritectic situation, which we saw in:

5. Name of reaction? This was the reaction
These reactions are common in magmas undergoing crystallization, and more reactions may occur simultaneously. The sequence of reactions in a melt is known as a reaction series. Bowen proposed the first of these based in 1922, on his studies of basaltic magmas.
The reaction is called incongruent melting.

6. Bowen’s Reaction Series
Although Bowen was working on basaltic magmas, his Reaction Series is much more generally applicable. However, it is based on equilibrium thermodynamics, and nature often does not maintain equilibrium. Thus, it can used as a very useful guide, while remembering that many exceptions or modifications exist.
General Observations
Initial crystallization involves Mg-Fe rich material on the discontinuous side, and Ca -rich material on the continuous side. This depletes the magma in these elements. As crystallization proceeds, the magma becomes more silicic and more alkalic. Fractional crystallization will produce a liquid phase enriched in SiO2, Al2O3, Na2O, and K2O. Partial melting involves the lowest melting minerals, and we expect these melts to be enriched in the same elements.
Factors not considered in Bowen’s work can play a big role. Oxygen fugacity is one. Fugacity is a measure of the reactivity of an element. It is a corrected “partial pressure” for the element in question. In many igneous systems, fO2= to When fO2 is low, the iron is ferrous ion, substituting freely for Mg2+ in silicate phases. When fO2 is elevated, the iron is oxidized to ferric iron, which forms Fe-Ti-oxide phases. The removal of iron increases the Mg:Fe ratio, inhibiting the formation of lower temperature mafic silicates. This changes the sequence of minerals crystallizing from melt.
Image Source:

7. Gibbs Free Energy Definition
We can formulate a differential equation to represent changing geologic conditions:
Review of thermodynamics
The Gibbs Free Energy may be defined:
In igneous petrology, we are most often interested in the conditions involved at the liquid-solid phase boundary

8. Solid-Liquid Reaction
Considering a reaction between a solid and a liquid (S ↔ L) we can rewrite the previous equation as
Δ represents a change as the result of a reaction - here, going from solid to liquid or vice versa

9. ΔV
Since most solids are denser than their liquids at the melting point, ΔV is positive on going from solid to liquid
Water is a notable exception

10. Melting Reaction Schematic P-T diagram of a melting reaction
This figure shows the behavior of an arbitrary phase
In the region labeled “Solid” the solid phase is stable, because GS < GL
In the region labeled “Liquid” the liquid phase is stable, because GS > GL

11. Isobaric System
Because Sliquid > Ssolid, the slope of G vs. T is greater for the liquid than the solid
At low temperatures the solid phase is more stable, but as temperature increases, the liquid phase becomes stable
For an isobaric system (P = constant), we can rewrite the equation as a partial derivative:
Entropy is positive (above 0 K) so the slope of (δG/δT) is negative. Plotting Gphase vs. P gives:

12. Equilibrium Temperature
Relationship between Gibbs Free Energy and temperature for the solid and liquid forms of a substance at constant pressure.
Teq is the equlibrium temperature
For an isothermal (T = constant) system, this becomes:

13. Isothermal System
Because Vliquid > Vsolid, the slope of G vs. P is greater for a liquid than a solid
The liquid phase has lower G, and is thus more stable, at low pressure, but the solid phase is more stable at higher pressure
This is why the inner core is solid
V is positive, and therefore the slope of (δG/δP) is positive.
Plotting Gphase versus T gives:

14. Equilibrium Presssure
V is positive, and therefore the slope of (δG/δP) is positive.

15. Equilibrium Curve
Any two points on the equilibrium curve for a solid-liquid interface must have ΔG = 0, and therefore dΔG = 0
Substituting gives

16. Clapeyron Equation Rearranging the previous equation gives:
How pressure affects melting behavior
The Clapeyron equation shows that the slope of the melting curve DP/DT, is positive for most solids of geologic interest. Increasing the pressure will increase the melting point for almost any mineral, but the rate of increase depends on δP/δP, and is thus different for each mineral. The effect of this is to shift the curves seen in phase diagrams, for example, a binary eutectic.

17. Diopside – Anorthite System
Eventually, a phase may become unstable, and it will be replaced by another phase. At high pressure,
Feldspars → Na-Al pyroxenes and/or Ca-Al garnets (Eclogite)
How fluids affect melting behavior
In the atmosphere, at any given temperature, the air can hold so much moisture per unit volume. The relative humidity tells us how much moisture is actually present, relative to the maximum possible amount. If relative humidity = 100%, the dew point is reached. The dew point corresponds to fluid saturation. The same thing can happen in a melt.
Figure 6-11.Isobaric T-X phase diagram at atmospheric pressure. After Bowen (1915), American Journal of Science, 40,

18. Fluid Saturation
A fluid-saturated melt contains the maximum amount of dissolved volatile species possible at a given set of P-T-X conditions
Any increase in volatile content will produce one or more additional phases

19. Fluid Pressure
The fluid pressure (Pf) is used to define the state of volatiles in a melt
If Pf = Ptotal, the melt is saturated with volatiles
If Pf = 0, the system does not contain volatiles, and is often called “dry”

20. Le Châtlier’s Principle
Any change imposed on a system at equilibrium will drive the system in the direction that reduces the imposed change

21. Melting of Hydrous Minerals
Adding water to the system should cause melting, according to Le Châtlier’s Principle
Adding water drives the reaction from left to right
Removing water, such as by loss of volatiles near the surface, should cause crystallization
The melting of hydrous minerals involves a fluid phase:

22. H2O Solubility
Solubility of H2O at 1100°C in three natural rock samples and albite
After Burnham (1979)
Applying this principle we can examine real data for several systems under different pressure and Pf conditions. As pressure increases, water solubility goes up, rapidly at first, than slower at higher pressures. This is because ΔV between gas and free liquid is large at low pressures, but much smaller when the gas is under high pressure. Water molecules are capable of inserting themselves at the bridging oxygen (the one linking two SiO4 tetrahedra).
Thus, water solubility is greater in felsic minerals like feldspar and quartz, which have bridging oxygens, than in olivine, which doesn’t. Thus water is least soluble in basalt, and most soluble in granite, which is felsic.

23. Albite – H2O Effect of H2O saturation on the melting of albite
After Burnham and Davis, 1974
Dry melting curve from Boyd and England, 1963
Experimental petrologists have examined some systems to see how fluids affect melting behavior. The albite-H2O is one classic example.
When PH2O = 0, the system is dry, and the curve shown on the right is obtained. The melting point increase with increasing pressure, as expected. When PH2O = Ptotal (fluid saturation, or “wet”) the melting point is depressed with increasing pressure. The effect is large initially, and then gradually becomes less significant at higher pressures. Why?

24. Melting of Albite
This reaction has a large negative ΔV on going from left to right, thus stabilizing the liquid phase and lowering the melting point
At higher pressures, ΔV is less negative, and the slope of the line is less

25. Application of Clapeyron Equation
For the dry case, ΔV is positive, and the slope of the melting curve is positive
For the wet case, ΔV is negative, and the slope of the melting curve is negative (melting point is depressed with increasing pressure)
The Clapeyron equation allows us to reach the same conclusion more quickly:

26. Effect of H2O saturation on the melting of gabbro (Burnham and David, 1974)
Dry melting curve from Boyd and England (1963)
Melting of Gabbro
This idea can be applied in a more useful way. Basalts and gabbros have the same chemical makeup. Basalts are usually dry, whereas gabbro may be wet. The dry case behaves as expected. The wet case does at lower pressures. Above 1.5GPa, the slope of the solidus line reverses, and above about 3.5GPa, the slope of the liquidus line reverses as well.

27. Melting Curves H2O saturated curves are solid
H2O free curves are dashed
Mafic rocks have higher melting points than felsic rocks
Figure 7-21 shows the effect of water in depressing the melting points of peridotite (ultramafic), basalt (mafic) and granodiorite (intermediate). The effect is greatest for granodiorite, because it has the highest felsic content. In granites, melting can begin just above 600̊C. This means that during high-grade metamorphism partial melting of a granitic phase is possible. The depression of basalt, almost matching the granodiorite, has been attributed to OH- forming complexes with Al ions in Ca aluminosilicates, but this has not been confirmed.

28. Albite – H2O System
Pressure-temperature projection of the melting relationships in the system albite – H2O
After Burnham and Davis, 1974
In many systems, there is insufficient water to completely crystallize the entire melt. Melting will proceed under “wet” conditions until the water is substantially exhausted. Figure 7-22 illustrates the system albite-H2O. This is a calculation for this system, based on thermodynamic data.
The sub-horizontal (blue) lines represent the contours for the amount of water in mol percent for water-saturated albite. At any given T-P conditions, albite may contain only a certain amount of water
The sub-vertical (red) lines represent melting of albite with fixed amounts of water available. Notice that as the amount of available water decreases, the melting behavior approaches that of the dry case.
Where a red line intersects a blue line, we have conditions for water saturated melting.
Red curves = melting for a fixed mol % water in the melt (Xw)
Blue curves tell the water content of a water-saturated melt

29. Albite Melting Percentage
An example may help to clarify the use of Figure Assume we have a system starting at 670̊C and 0.6 GPa, with 10 mol % water. The system is heated, but does not begin to melt until 770̊C (point f on F7-22).
At point f, a water saturated melt would contain 65 mol % water (interpolate between the sub-vertical lines). Since it has only 10 mol %, only 15% (10/65) can melt.
By 905̊C, (point g) a water saturated melt would contain only 50 mol % water, so the system is 20% melted (10/50).
This can be shown graphically (Figure 7-23). Melting starts slowly, and the initial temperature had to rise from 770̊C to 1120̊C, or 350̊C to melt half the liquid. The final half melts in the next 60̊C, as the system gets close to the dry solidus. Thus, although water depresses the melting point, then amount of water present may limit the extent to which melting can proceed.
Note: This system represents the case where PH2O = Pfluid < Ptotal.
At point h (1120̊C) the system is 50% melted (10/20). Finally, at point i (1180̊C) the system will be 100% melted (10/10).
Percentage of melting for albite with 10 mol % H2O at 0.6 GPa as a function of temperature along traverse e-i

30. Albite – H2O System
Pressure-temperature projection of the melting relationships in the system albite – H2O
After Burnham and Davis, 1974
Using figure 7-22 again, we can examine the properties of melts from another angle. At point a, the system is a 1 GPa and has 50 mol % water. Most of the system (96%, or 50/52) will have melted.
If the melt forms a diapir and rises rapidly enough that the system remains isothermal, what happens? At point b, the system is now completely melted (50/50). The now completely molten diapir rises more, at temperatures increasing above the melting point.
At point c, the diapir crosses the line at which a 50 mol % solution is a water saturated melt. Water begins to leave the melt to form a separate phase. As the diapir rises further, more and more water is released.
When the system reaches the H2O-saturated melting curve at about 0.05 GPa and about 30 mol % water, the melt crystallizes entirely to albite, and all the remaining water is expelled into the vapor phase.
Thus rising hydrous melts reach H2O saturation and expel water. and expel even more water at final crystallization. They also are likely to fully crystallize before reaching the surface. This applies to granitic melts. On the other hand, a dry melt (like basalt) is not likely to intersect the positively sloped anhydrous solidus, and thus are unlikely to crystallize before reaching the surface.

31. Melting Relationships
Pressure-temperature projection of the melting relationships in the system albite – H2O with curves representing constant activity of H2O
After Burnham and Davis, 1974
Another system that needs to be examined is the case where PH2O < Pfluid = Ptotal. This occurs when there are two or more species contributing to the fluid phase. The water concentration is no longer fixed. Instead, the activity of water is fixed.
Figure 7-24 shows a revised plot of the albite-water system, showing the solidus curve as a function of the activity of water.
Water solubility varies from mineral to mineral. Thus, the effect of water on a binary eutectic system will be to depress the melting point, and to shift the eutectic toward the more felsic mineral (since water is more soluble in these minerals).

32. Diopside-Anorthite Liquidus
The affect of H2O on the diopside-anorthite liquidus
Figure 7-25 illustrates the effect for diopside-anorthite. In systems with minimum melting points, the minimum melting point will shift toward the silicic rich mineral as the water pressure is increased (blue line to green). Anorthite is more felsic than diopside, a pyroxene. Increasing total pressure, under dry conditions, raises the melting point (red line to blue). Systems like pyroxene-feldspar show this behavior. In the mantle, such a system will produce more siliceous melts than would occur under anhydrous conditions. There is experimental evidence that confirms this behavior.
The other principal fluid phase in most systems is carbon dioxide. Carbon dioxide has no hydrogen bonds. Instead, it has strong covalent-ionic bonds. It does not dissociate, nor does it attack bridging oxygens. The small, highly charged carbon ion does not bond stablely to oxygens adjacent to Si4+ cations. Carbon dioxide solubility is thus quite limited in silicate melts. Carbon dioxide is often treated mainly as a dilutant for water, reducing the effect of water.

33. Albite Melting with Fluids
Experimentally determined melting of albite
Dry
H2O saturated
In presence of fluid containing 50% each of H2O and CO2
Figure 7-26 shows the system albite-water-carbon dioxide. Comparing figures 7-26 and 7-24, we see that the plot for aH2O = 0.5 is similar to the middle curve in At the highest pressures, particularly above 1 GPa, carbon dioxide does begin to dissolve. Eggler investigated the solubility of carbon dioxide and found that solubilities of 4-5% were possible in silicate melts, and that more mafic melts had higher carbon dioxide solubilities than more felsic melts, opposite to the effect of water. The addition of water to the system greatly increased carbon dioxide solubilities in mafic systems, but not in felsic.

34. CO2 Solubility System Pressure CO2 Solubility Albite-H2O-CO2 2 GPa
5-6%
Enstatite-H2O-CO2
18%
Diopside-H2O-CO2
35%
Mysen and Virgo (1980) suggested that the carbon dioxide dissolves by forming carbonate complexes in silicate melts, particularly when calcium is available to form CaCO3. The carbon dioxide steals one oxygen, and converts another to a bridging oxygen. Carbon dioxide thus tends to increase the polymerization of melts, again opposite to the effect of water. It should raise the viscosity of melts it is dissolved in. Since carbon dioxide is soluble in less polymerized melts, it becomes obvious why water increases carbon dioxide solubility. The water reduced polymerization, enhancing CO2 solubility. Since carbon dioxide is most effective in mafic melts under high pressures, its influence should be greatest in the mantle.

35. Ternary Eutectic Ne Fo En Ab
SiO2
Oversaturated
(quartz-bearing)
tholeiitic basalts
Highly undesaturated
(nepheline-bearing)
alkali olivine
basalts
Undersaturated
CO2
H2O
dry
P = 2 GPa
Effect of volatiles on ternary eutectic in the system Forsterite – Nepheline – Silica at 2 Gpa
Water moves the (2 GPa) eutectic toward higher silica, while CO2 moves it to more alkaline types
Figure 7-27 shows the effect of water and CO2 on the ternary eutectic in the system Fo-Neph-Silica. Increased water shifts the eutectic toward the silica, whereas increased CO2 shifts it towards nepheline. Saturation in the diagram refers to silica saturation, not carbon dioxide or water.

36. Ternary Eutectic
Effect of Pressure on the position of the eutectic in the basalt system
Increased pressure moves the ternary eutectic (first melt) from silica-saturated to highly undersat.alkaline basalts Ne Fo En Ab
SiO2
Oversaturated
(quartz-bearing)
tholeiitic basalts
Highly undesaturated
(nepheline-bearing)
alkali olivine
basalts
Undersaturated
3GPa
2GPa
1GPa
1atm
Volatile-free
Increased pressure moves the ternary eutectic (first melt) from silica-saturated to highly undersaturated alkaline basalts