Petrology

Tulane University

Magmatic Differentiation

Chemical Variation in Rock Suites

Soon after geologists began doing chemical analyses of igneous rocks they realized that rocks emplaced in any given restricted area during a short amount of geologic time were likely related to the same magmatic event.  Evidence for some kind of relationship between the rocks, and therefore between the magmas that cooled to form the rocks came from plotting variation diagrams. 

1. Distinct melting events from distinct sources.
   
2. Various degrees of partial melting from the same source.
   
3. Crystal fractionation.
   
4. Mixing of 2 or more magmas.
   
5. Assimilation/contamination of magmas by crustal rocks.
   
6. Liquid Immiscibility.

Distinct Melting Events

One possibility that always exists is that the magmas are not related except by some heating event that caused melting.  In such a case each magma might represent melting of a different source rock at different times during the heating event.  If this were the case, we might not expect the chemical analyses of the rocks produced to show smooth trends on variation diagrams.  But, because variation diagrams are based on a closed set of numbers (chemical analyses add up to 100%), if the weight% of one component increases, then the weight percent of some other component must decrease.  Thus, even in the event that the magmas are not related, SiO₂ could increase and MgO could decrease to produce a trend.  The possibility of distinct melting events is not easy to prove or disprove.

Various Degrees of Partial Melting

We have seen in our study of simple phase diagrams that when a multicomponent rock system melts, unless it has the composition of the eutectic, it melts over a range of temperatures at any given pressure, and during this melting, the liquid composition changes.  Thus, a wide variety of liquid compositions could be made by various degrees of partial melting of the same source rock.

Fractional Melting
Note that it was stated above that some of the liquid must be left behind.  If all of the liquid is removed, then we have the case of fractional melting, which is somewhat different.

We saw in our discussion of how magmas are generated that it is difficult enough to get the temperature in the Earth above the peridotite solidus, let alone to much higher temperatures.  Thus, fractional melting is not very likely to occur in the Earth.

Trace Elements as Clues to Suites Produced by Various Degrees of Melting
Trace elements are elements that occur in low concentrations in rocks, usually less than 0.1 % (usually reported in units of parts per million, ppm).  When considering the rocks in the mantle, trace elements can be divided into incompatible elements, those that do not easily fit into the crystal structure of minerals in the mantle, and compatible elements, those that do fit easily into the crystal structure of minerals in the mantle.

• Incompatible elements - these are elements like K, Rb, Cs, Ta, Nb, U, Th, Y, Hf, Zr, and the Rare Earth Elements (REE)- La, Ce, Pr, Nd, Pm, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, & Lu. Most have a large ionic radius. Mantle minerals like olivine, pyroxene, spinel, & garnet do not have crystallographic sites for large ions.
  
  
• Compatible elements - these are elements like Ni, Cr, Co, V, and Sc, which have smaller ionic radii and fit more easily into crystallographic sites that normally accommodate Mg, and Fe.

When a mantle rock begins to melt, the incompatible elements will be ejected preferentially from the solid and enter the liquid. This is because if these elements are present in minerals in the rock, they will not be in energetically favorable sites in the crystals. Thus, a low degree melt of a mantle rock will have high concentrations of incompatible elements.  As melting proceeds the concentration of these incompatible elements will decrease because (1) there will be less of them to enter the melt, and (2) their concentrations will become more and more diluted as other elements enter the melt.  Thus, incompatible element concentrations will decrease with increasing % melting.

Rare Earth elements are particularly useful in this regard. These elements, with the exception of Eu, have a +3 charge, but their ionic radii decrease with increasing atomic number. i.e. La is largest, Lu is smallest.  Thus the degree of incompatibility decreases from La to Lu.   This is even more true if garnet is a mineral in the source, because the size of the heavy REEs (Ho - Lu) are more compatible with crystallographic sites in garnet.

Crystal Fractionation

In our discussion of phase diagrams we saw how liquid compositions can change as a result of removing crystals from the liquid as they form.  In all cases except a eutectic composition, crystallization results in a change in the composition of the liquid, and if the crystals are removed by some process, then different magma compositions can be generated from the initial parent liquid.  If minerals that later react to form a new mineral or solid solution minerals are removed, then crystal fractionation can produce liquid compositions that would not otherwise have been attained by normal crystallization of the parent liquid.

Bowen's Reaction Series
Norman L. Bowen, an experimental petrologist in the early 1900s, realized this from his determinations of simple 2- and 3-component phase diagrams, and proposed that if an initial basaltic magma had crystals removed before they could react with the liquid, that the common suite of rocks from basalt to rhyolite could be produced.  This is summarized as Bowen's Reaction Series.

• The continuous reaction series is composed of the plagioclase feldspar solid solution series.  A basaltic magma would initially crystallize a Ca- rich plagioclase and upon cooling continually react with the liquid to produce more Na-rich plagioclase.  If the early forming plagioclase were removed, then liquid compositions could eventually evolve to those that would crystallize a Na-rich plagioclase, such as a rhyolite liquid.
  
         
  

• The discontinuous reaction series consists of minerals that upon cooling eventually react with the liquid to produce a new phase.  Thus, as we have seen, crystallization of olivine from a basaltic liquid would eventually reach a point where olivine would react with the liquid to produce orthopyroxene.  Bowen postulated that with further cooling pyroxene would react with the liquid, which by this time had become more enriched in H₂O, to produce hornblende.  The hornblende would eventually react with the liquid to produce biotite.  If the earlier crystallizing phases are removed before the reaction can take place, then increasingly more siliceous liquids would be produced.
  

This generalized idea is consistent with the temperatures observed in magmas and with the mineral assemblages we find in the various rocks.  We would expect that with increasing SiO₂ oxides like MgO, and CaO should decrease with higher degrees of crystal fractionation because they enter early crystallizing phases, like olivines and pyroxenes. Oxides like H₂O, K₂O and Na₂O should increase with increasing crystal fractionation because they do not enter early crystallizing phases.  Furthermore, we would expect incompatible trace element concentrations to increase with fractionation, and compatible trace element concentrations to decrease.  This is generally what is observed in igneous rock suites.   Because of this, and the fact that crystal fractionation is easy to envision and somewhat easy to test, crystal fraction is often implicitly assumed to be the dominant process of magmatic differentiation.

Graphical Representation of Crystal Fractionation
The effects on chemical change of magma (rock) compositions that would be expected from crystal fractionation can be seen by examining some simple variation diagrams.

In a simple case imagine that we have two rocks, A and B, with their SiO₂ and MgO concentrations as shown in the diagram. Also plotted is the analysis of olivine contained in rock A.  Removal of olivine from Rock A would drive the liquid composition in a straight line away from A. (This is the same idea we used in phase diagrams). If rock B were produced from rock A by  fractionation of olivine, then the composition of rock B should lie on the same line.

%Olivine Fractionated = [y/(x + y)]*100

If olivine fractionation were the process responsible for the change from magma A to magma B, then these proportions would have to be the same on all other variation diagrams as well.

In a more complicated case, we next look at what happens if two phases of different composition were involved in the fractionation.  Again the rules we apply are the same rules we used in phase diagrams.

     %solids fractionated = [z/(w + z)]*100

This works well for small steps in the fractionation sequence.  In the real world we find that many minerals expected to crystallize from a magma are solid solutions whose compositions will change as the liquid evolves and temperature drops.  We can see how this would affect things with the following example. In this case we look at what happens if an Mg-Fe solid solution mineral is removed as temperature falls.

The initial magma has high MgO and low SiO₂. The solid crystallizing from this magma also has high MgO and low SiO₂. Taking the fractionation in small increments, the second magma produced by removing the solids from the original magma will have higher SiO₂ and lower MgO. 

But, the second liquid will be crystallizing a solid with lower MgO and higher, SiO₂, so it will evolve along a different path.  The net result will be that the variation will show a curved trend on a variation diagram.  Thus, a generalization we can make is that in natural magmas we expect the variation to be along smooth curved trends since most of the minerals that crystallize from magmas are solid solutions.  Note that different minerals fractionated will produce different trends, but they will still be smooth and curved.

Another complication arises if there is a change in the combination of minerals that are fractionating. 

Thus, sudden changes in the trends on variation diagrams could mean that there has been a change in the mineral assemblage being fractionated.  

Trace Elements and Crystal Fractionation
As we might expect, elements that are excluded from crystals during fractionation should have their concentrations increase in the fractionated magmas.  This is true for trace elements as well.  The concentration of incompatible trace elements should thus increase with increasing crystal fractionation, and the concentration of compatible trace elements should decrease with fractionation.  To see how this works with incompatible trace elements, we'll look at the REEs.  The diagram shows how the REEs behave as calculated from theoretical equations for trace element distribution. 

Note that the REE patterns produced by higher percentages of crystal fractionation show higher concentrations, yet the patterns remain nearly parallel to one another.  Thus, a suite of rocks formed as a result of crystal fractionation should show nearly parallel trends of REE patterns.

• Crystal Settling/Floating - In general, crystals forming from a magma will have different densities than the liquid.
  
  
  • If the crystals have a higher density than the liquid, they will tend to sink or settle to the floor of the magma body. The first layer that settles will still be in contact with the magma, but will later become buried by later settling crystals so that they are effectively removed from the liquid.
    
    
  • If the crystals have a lower density in the magma, they will tend to float or rise upward through the magma.  Again the first layer that accumulates at the top of the magma body will initially be in contact with the liquid, but as more crystals float to the top and accumulate, the earlier formed layers will be effectively removed from contact with the liquid. 
    

• Inward Crystallization - Because a magma body is hot and the country rock which surrounds it is expected to be much cooler, heat will move outward away from the magma.   Thus, the walls of the magma body will be coolest, and crystallization would be expected to take place first in this cooler portion of the magma near the walls.  The magma would then be expected to crystallize from the walls inward.  Just like in the example above, the first layer of crystals precipitated will still be in contact with the liquid, but will eventually become buried by later crystals and effectively be removed from contact with the liquid.
  

• Filter pressing - this mechanism has been proposed as a way to separate a liquid from a crystal-liquid mush.  In such a situation where there is a high concentration of crystals the liquid could be forced out of the spaces between crystals by some kind of tectonic squeezing that moves the liquid into a fracture or other free space, leaving the crystals behind.  It would be kind of like squeezing the water out of a sponge.   This mechanism is difficult to envision taking place in nature because (1) unlike a sponge the matrix of crystals is brittle and will not deform easily to squeeze the liquid out, and (2) the fractures required for the liquid to move into are generally formed by extensional forces and the mechanism to get the liquid into the fractures involves compressional forces.  Filter pressing is a common method used to separate crystals from liquid in industrial processes, but has not been shown to have occurred in nature.
  

Magma Mixing

If two or more magmas with different chemical compositions come in contact with one another beneath the surface of the Earth, then it is possible that they could mix with each other to produce compositions intermediate between the end members.  If the compositions of the magmas are greatly different (i.e. basalt and rhyolite), there are several factors that would tend to inhibit mixing.

• Temperature contrast - basaltic and rhyolitic magmas have very different temperatures.  If they come in contact with one another the basaltic magma would tend to cool or even crystallize and the rhyolitic magma would tend to heat up and begin to dissolve any crystals that it had precipitated.
  

• Density Contrast- basaltic magmas have densities on the order of 2600 to 2700 kg/m³, whereas rhyolitic magmas have densities of 2300 to 2500 kg/m³.   This contrast in density would mean that the lighter rhyolitic magmas would tend to float on the heavier basaltic magma and inhibit mixing.
  

• Viscosity Contrast- basaltic magmas and rhyolitic magmas would have very different viscosities.  Thus, some kind of vigorous stirring would be necessary to get the magmas to mix. 

Despite these inhibiting factors, there is evidence in rocks that magmas do sometimes mix.  The smaller the difference in chemical composition between two magmas, the smaller will be the contrasts in temperature, density, and viscosity.

If magmas of contrasting composition come in contact and begin to mix some kind of stirring mechanism would first be necessary.  Such stirring could be provided by convection, with the hotter magma rising through the cooler magma.

Evidence for Mixing

• Mingling of magmas. If, in the initially stages of such mixing, the magma were erupted, then we might expect to find rocks that show a "marble cake" appearance, with dark colored mafic rock intermingled with lighter colored rhyolitic rock.  This, however, is mingling of magmas. Note that differences in color are not always due to differences in composition, so even in rocks that show this banding, mingling of magmas may not have occurred.

• Disequilibrium Mineral Assemblages. If convective stirring progresses beyond the point of mingling, some evidence might still be preserved if the crystals present in one of the magmas does not completely dissolve or react.  This might leave disequilibrium mineral assemblages.  For example, if a basaltic magma containing Mg-rich olivine mixed with a rhyolite magma containing quartz, and the magma was erupted before the quartz or olivine could be redissolved or made over into another mineral, then we would produce a rock containing mineral that are out of equilibrium. 
   
  

• Reverse Zoning in Minerals. When a mineral is placed in an environment different than the one in which it originally formed, it will tend to react to retain equilibrium.  Instead of dissolving completely or remaking their entire composition, solid solution minerals may just start precipitating a new composition that is stable in the new chemical environment or at the new temperature.  This can result in zoned crystals that show reversals of the zoning trends. For Example:

Mg-Fe solid solution minerals normally zone from Mg-rich cores to Fe-rich rims. If a Fe-rich olivine or pyroxene is mixed into a Mg-rich magma that is precipitating Mg-rich olivine or pyroxene, it may precipitate the more Mg-rich composition on the rims of the added crystals. Analyses of such crystals would reveal a reversal in zoning. Similarly, if a Na-rich plagioclase originally crystallizing from a rhyolitic magma were mixed into a basaltic magma precipitating a Ca-rich plagioclase, a Ca-rich rim may be added to the Na-rich plagioclase.

• Glass Inclusions. Crystal growth from liquids is sometimes not perfect.   Sometimes the crystal grows incompletely trapping liquid inside.  If that liquid is quenched on the surface and a thin section is cut through the crystal this trapped liquid will be revealed as glass inclusions in the crystal.

Since the glass inclusions should represent the composition of the magma that precipitated the crystal, chemical analysis of glass inclusions give us the composition of the liquid in which the crystal formed.  The groundmass may also contain glass representing the composition of the liquid in which the crystal resided at eruption. If the composition of glass inclusions is different from glass in the groundmass, and if the groundmass composition is not what is expected from normal crystallization of the minerals present, this provides evidence of magma mixing.

• Chemical Evidence. If the mixing process proceeds to the point where other evidence is erased, evidence for mixing will still be preserved in the composition of the mixed magmas.  On oxide-oxide variation diagrams mixtures will lie along a straight line. Thus if diagrams show a group of rocks that lie along the same straight line, and the proportional distances are the same on all diagrams, one could hypothesize that the chemical variation resulted from magma mixing.

Crustal Assimilation/Contamination

Because the composition of the crust is generally different from the composition of magmas which must pass through the crust to reach the surface, their is always the possibility that reactions between the crust and the magma could take place.  If crustal rocks are picked up, incorporated into the magma, and dissolved to become part of the magma, we say that the crustal rocks have been assimilated by the magma.  If the magma absorbs part of the rock through which it passes we say that the magma has become contaminated by the crust.  Either of these process would produce a change in the chemical composition of the magma unless the material being added has the same chemical composition as the magma.

In a sense, bulk assimilation would produce some of the same effects as mixing, but it is more complicated than mixing because of the heat balance involved.  In order to assimilate the country rock enough heat must be provided to first raise the country rock to its solidus temperature where it will begin to melt and then further heat must be added to change from the solid state to the liquid state. The only source of this heat, of course, is the magma itself.

dH/dT = C_p or

ΔH =  C_p (T_m - T_i)  

As stated above the heat required for this process must be supplied by the magma.  In our example we'll take a simple case where the magma has a eutectic composition and therefore melts at a single temperature.   This time we'll assume that the magma is at a temperature, T_L, somewhat above its melting Temperature, T_m.           

In order to provide the heat for assimilation it would first have to cool.  The amount of heat it would give up would then be:

ΔH =  C_pLiquid (T_m - T_i)

Once it reached T_m the only other source of heat must be provided by crystallization to release the latent heat of crystallization, ΔH_c.   Note that in the case shown here, the total heat released by the magma in cooling to T_m and crystallizing is still not enough to melt the country rock.

Furthermore, in this process the magma has completely crystallized, so assimilation cannot take place.  There are two ways to overcome this problem:  (1) If the initial temperature of the magma were much higher, then it could provide the heat by simply cooling to its melting temperature.  This is unrealistic, however, because magmas are probably relatively close to or below their liquidus temperature after having passed through cooler country rocks.  (2)  If the country rock had an initial temperature closer to its melting temperature, less heat would have to be provided by the magma.  This could happen if there were successive batches of magma passing through and releasing heat into the country rock.

Nevertheless, this heat budget analysis illustrates the difficulty involved in bulk assimilation of country rock by magmas, and makes the process less attractive as a process to explain the chemical diversity of a suite of rocks.  Note also that the heat budget will still likely involve crystallizing some of the magma, so if assimilation takes place it will likely involve a combined process of crystal fractionation and assimilation.

Evidence for Assimilation/Contamination
As magma passes upward through the crust pieces of the country rock through which it passes may be broken off and assimilated by the magma.  Just as in magma mixing, various stages of this process may be preserved in the magma and rock that results.  Xenoliths (meaning foreign rock) are pieces of rock sometimes found as inclusions in other rocks.  The presence of xenoliths does not always indicate that assimilation has taken place, but if the xenoliths show evidence of having been disaggregated with their minerals distributed thought the rest of the rock it is likely that some contamination of the magma has taken place.  This may result in disequilibrium mineral assemblages and reversely zoned minerals, just as in the case of magma mixing.  And, if the assimilation goes to completion, with all of the xenoliths being dissolved in the magma, the only evidence left may be chemical, and again similar to the straight line mixing patterns produced by mixing.

Perhaps the best evidence of assimilation/contamination comes from studies of radiogenic isotopes.  Here we give an example using the systematics of the Rb - Sr system.

• ⁸⁷Rb is a radioactive isotope that decays to ⁸⁷Sr with a half life of 47 billion years.
  
  
• Because Rb is an incompatible element, it has been extracted from the mantle by magmas and added to the crust.  Thus the concentration of Rb in the crust (avg. about 100 ppm) is much higher than it is in the mantle (avg. about 4 ppm).
  
  
• ⁸⁶Sr is a stable, non radiogenic isotope whose concentration does not change with time.
  
  
• Because ⁸⁷Rb decays to produce ⁸⁷Sr and because there is more Rb in the crust than in the mantle, the ⁸⁷Sr/ ⁸⁶Sr of the crust has, over time, changed to much higher values than the ⁸⁷Sr/⁸⁶Sr ratio in the mantle.
  
  
• The ⁸⁷Sr/⁸⁶Sr ratio of the mantle is generally in the range between 0.702 - 0.705.  Thus, rocks derived from melting of the mantle should have ⁸⁷Sr/⁸⁶Sr ratios in this range.
  
  
• ⁸⁷Sr/⁸⁶Sr ratios of crustal rocks will depend on their age and concentration of Rb.  Older crustal rocks will have high values of ⁸⁷Sr/⁸⁶Sr in the range 0.705 - 0.720, younger crustal rocks having been recently derived from the mantle will ⁸⁷Sr/⁸⁶Sr ratios more similar to the mantle.
  
  
• If mantle derived magmas assimilate or are contaminated by older crustal rocks, then we would expect to find ratios of ⁸⁷Sr/⁸⁶Sr in these contaminated rocks that are higher than those found in the mantle and extend up to values found in older crustal rocks.

Liquid Immiscibility

Liquid immiscibility is where liquids do not mix with each other.  We are all familiar with this phenomenon in the case of oil and water/vinegar in salad dressing.  We have also discussed immiscibility in solids, for example in the alkali feldspar system.  Just like in the alkali feldspar system, immiscibility is temperature dependent.

This points out two important properties of immiscible liquids. 

1. If immiscible liquids are in equilibrium with solids, both liquids must be in equilibrium with the same solid compositions.
   
2. Extreme compositions of the two the liquids will exist at the same temperature.
   

Liquid immiscibility was once thought to be a mechanism to explain all magmatic differentiation.  If so, requirement 2, above, would require that siliceous liquids and mafic liquids should form at the same temperature.  Since basaltic magmas are generally much hotter than rhyolitic magmas, liquid immiscibility is not looked upon favorably as an explanation for wide diversity of magmatic compositions.  Still, liquid immiscibility is observed in experiments conducted on simple rock systems.

1. Sulfide liquids may separate from mafic silicate magmas.

2. Highly alkaline magmas rich in CO₂ may separate into two liquids, one rich in carbonate, and the other rich in silica and alkalies.  This process may be responsible for forming the rare carbonatite magmas
3. Very Fe-rich basaltic magmas may form two separate liquids - one felsic and rich in SiO₂, and the other mafic and rich in FeO.

Combined Processes

As pointed out previously, if any of these process are possible, then a combination of the process could act to produce chemical change in magmas.  Thus, although crystal fractionation seems to be the dominant process affecting magmatic differentiation, it may not be the only processes. As we have seen, assimilation is likely to accompanied by crystallization of magmas in order to provide the heat necessary for assimilation.   If this occurs then a combination of crystal fraction and assimilation could occur.   Similarly, magmas could mix and crystallize at the same time resulting in a combination of magma mixing and crystal fractionation.  In nature, things could be quite complicated.

Examples of questions on this material that could be asked on an exam

1. Define the following: (a) magmatic differentiation, (b) fractional melting, (c) fractional crystallization, (d) latent heat of fusion, (e) Bowen's Reaction Series.
   
   
2. Name 5 processes that might cause the chemical composition of a magma to change.
   
   
3. Discuss the mechanisms by which crystal fractionation could occur in nature.
   
   
4. What kind of evidence would one look for to determine if any of the following processes have operated to change the composition of magmas and resulting igneous rocks (a) crystal fractionation, (b) magma mixing, (c) crustal assimilation.

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