## PHASE EQUILIBRIUM:

PE_1         How would you know the environmental conditions [Temperature (T), Pressure (P), composition (X), redox potential (Eh), acidity (pH), etc.] in which a mineral or groups of minerals were formed and are stable?

During the formation of minerals and rocks, the pressure and temperature conditions  are estimated by performing theoretical calculations and/or laboratory experiments.  Experiments are conducted by using pressure bombs.   Phase diagrams, which show stability fields of minerals are plotted from the pressure, temperature, and fluid conditions applied during the experiments.

Phase diagrams are graphical representation of stability fields of minerals and include:

A) T-X diagrams which show conditions of temperature and composition.

B) P-T diagrams which show conditions of pressure and temperature.
P-T diagrams help one determine the range of temperature and pressure within which a mineral or minerals are stable.
Sea also P-T-t  digrams and Eh-pH diagrams

PE_2 Assorted reinforcement questions:

Define.

1) phase, 2) component, 3) variable, 4) degrees of freedom, 5) phase rule, 6) invariant point (triple point), 7) univariant curve, 8) divariant field, 9) critical Point , 10) system

System: any part of the universe that is considered for an investigation. There are 3 types of systems.

Open system. system exchanges materials aand heat with its surrounding.

Closed system. system does not exchange maaterials with its surrounding, but heat may be.

Isolated System. This a system in which neither material nor heat is exchanged with the surrounding.

Phase: A homogeneous material that is mechanically separable from others. Nine pyrite crystals and 1 galena crystal are composed o two phases, namely pyrite and galena..

components : The smallest number of chemical species that are sufficient and necessary to define the reactions in a system. When dealing with a system in which the three phases of water, ice. and steam are to be investigated, we are dealing with a one component system, namely H2O.

Degrees of freedom (or variance): The smallest number of conditions or variables that may be changed without resulting in a change of the number or nature of phases in a system.

The Phase Rule : This relates the number of phases (P) that can be present in a system of a given number of components (C) undergoing a given set of changes (F= degrees of freedom) in that system.

F = C - P + 2

Conditions are unvariant when F = 1, divariant when F = 2, and invariant when F= 0.

The phase rule is derived from calculations of thermodynamics, which provides the laws that will help determine weather a reaction is spontaneous or not.  The free energy of reaction  D G (Gp-Gr), which is determine as the free energy of products minus the free energy of reactants is used to asses the condition of equilibrium reactions.D G is also determine from enthalpy and entropy values (D G = D H-TD S).  Note that the symbol D  = change of reaction)

If D G is negative (less than zero), the reaction should proceed forward as written, products are stable.
If D G is zero, an equilibrium condition is stable. there is an equal amount of forward and reverse reaction.
If D G is positive (greater than zero), the reverse reaction is preferred, the reactants are stable.

PE_3   Why do we need T-X diagrams?

T-X phase diagrams help one to:
1. determine the range of temperature at which minerals crystallize.
2. understand the role of degree of undercolling, and the types of texture, such as symplectic texture, glass that might ensue
3. understand concepts of congruent and incongruent melting or solidification
4. understand concepts of fractional crystallization, partial melting, degree of partial melting or bath melting.
5. explain textures such as zoning, reaction rimming, perthitic intergrowth.
6. understand concepts of compatible and incompatible minerals.
7. understand concepts of silica saturated and undersaturated magmas.

Materials:

Acontainer (bomb) to melt crystals at high temperatures, instruments  for measuring temperature, pressure, composition, and other constraints which we may wish to impose for the investigation.

3-a. What are the component oxides of anorthite, and in what ratio should these oxides be mixed?

(Answer: CaO, Al2O3, 2SiO2 ;   1:1:2)

* One may buy reagent grade lime, alumina, and silica, mix them in the proprtion of anorthite, place that in a suitable container to study the temperature at which anorthite melts or the anorthite melt solidifies.  At one atmospheric pressure, pure anorthite melts at 1553oC.

* Melt quartz. When a small amount begins to melt, or when the entire quartz has melted, the melt composition is the same as that of the quartz. Pure quartz melts at 1713oc, and the melt crystallized to give the cristobalite variety of silica.

* Note: for T-X diagrams, one uses the condensed phase rule :

F = C - P + 1

(Or one assumes that there is vapor in all fields and use F = C - P + 2)

PE_4

Cooling curves are determined from experimental runs of crystallization in pressure bombs.

* Crystallization (formation reaction) is commonly exothermic and liberates heat.

4-a. Why is the surface of a lava hotter than the interior?

Answer.  Due to cooling, rocks (composed of minerals) form at the surface of a lava, and formation reactions liberate heat.

(Exothermic reaction is the reason why one's mouth may burn when one breathes from an oxygen can one carries around one's waist when breathing  inside some parts of a mine in which there is methane or carbon monoxide.  Oxygen combines with carbon to form carbondioxide, and liberates heat in the process.)

4-b. What do inflection points on cooling curves indicate?

Answer.  They indicate the beginning  of crystallization, or exothermic reaction.  * Examine cooling curves.  Change in slope of curve (from steep to gentle indicates crystallization at the liquidus.   Where the curve is horizontal, it indicates eutectic, or peritectic reaction).

Describe Unary phase diagrams?

In a unary phase diagram, the number of components is 1.

For example, water, ice, and steam are 3 separate phases (P) composed of one component (c), H2O.
The  P-T space diagrams for  H2water  has a triple point at 0.006 bars and 0.001oC; a critical pressure at 221 bars and a critical temperature at 374 oC.
We use the Phase Rule to determine invariant point ( F = 0), univariant line (F= 1), and bivariant field (F =2).

The triple point is an invariant point, with zero degrees of freedom (F), and at which all 3 phases (P =3) are present.

a. Why do people that skate on ice actually do so on water?

Answer.  The univariant ice-water curve has a negative slope, so that with increased pressure, one goes from solid to liquid field water  . Note that isobaric decompression results in the change of water to ice, which is abnormal the angle between H-h bonds and O expands from 105 in water to 109.5° in ice) for in most other cases isobaric decompression results in melting.

b. What is a supercritical fluid?

Answer.  It is a fluid that carries dissolved ions like a liquid, but bounces around like gas.  Above the critical temperature of 374 oC, and critical pressure above 221 bars, H2O is a supercritical fluid.

Another unary phase diagram is that of quartz, ( many phases: from high temperature to low : Cristobalite, tridymite, and normal quartz; high pressure forms include coesite, stishovite, p.58 )

a. Isobaric decompression for temperatures above 1713 results in producing a magma.  Decompression for temperatures below 1713°C may result in metastable coesite being rimmed by  b-quarta and included in garnet. for details see below.

[Further relationships may be determined by superposing the work of Schreyer, 1999 ( p.72 Hutton's Bicentennial volume) on the P-T for quartz, p.58. Notice that the ensuing diagram is a petrogentic grid and not a unary phase diagram.  First draw a vertical line at 1200oC line, and a horizontal line at 5. GPa. From the intersection point of this two lines, draw a line to the origin, i.e., 0oc 0 GPa- that line is a 5oC/km geothermal line.  From the B-Quartz and coesite boundary line draw a vertical line at about 800oC down to its intersection with the 5oC/Km line.  This line is a univariant curve separating low temperature phase kynite from higher temperature pyrope, a relationship that is present for depth below 99 Km or 3 GPa.  Coesite that might have been enclosed by pyrope might persist as an inclusion even when  exhumed to the surface of the earth by tectonic forces and erosion.  The outer surface of  compact and dense coesite might invert to the less dense and more open a -quartz, forming a rim around coesite and cracking the enveloping garnet. Such texture indicates origin of rock at the mantle.]

Yet, another unary  phase diagram (for metamorphic reactions) is the alumino - silicates, KAS minerals (triple point at 3.2 Kbars, and about 500oC).  {Note that the diagram, p.472,  also shows other univariant curves.  Hence it is a petrogentic grid.]

a. What are the likely T and P values for the formation of a metamorphic rock in which andalusite, kyanite, and sillimanite coexist in equilibrium (are coeval)?

b. Differentiate between coeval minerals and mineral assemblages?

Answer.  Coeval minerals formed at the same time and implies equilibrium conditions.  Assemblage refers to all minerals found in a rock, unless it is specified that we are dealing with an equilibrium assemblage or coeval minerals.

c. What is metastability? considering the high affinity of carbon for oxygen, why should Lady Rebecca have a diamond ring?

Answer.  Metastable means that the mineral should not be found at the given pressure and temperature conditions.  (Diamond being a high pressure mineral, it should convert to carbon.  However, the rate of change (kinetics) is extremely slow and it persists metastably.)  If kyanite is found in the field of andalusite, kynaite is a metastable in that P-t regime.

d. Would jadeite and andalusite be found in the same metamorphic rock?

(Answer. No. p.496. Andalusite is low pressure "spark plug" mineral or an aluminosilicate (Al2SiO5), while Jadeite (Na2Si2O6) is a high pressure pyroxene.  Note that this P-T space is a petrogentic grid.)

PE_5   Describe Binary phase diagrams?

A) Simple Binary with a eutectic
B) Binary with a peritectic
C) binary with a single loop (solid solution)
D) Binary with two loops

Unary phase diagrams (e. g., quartz, KAS, which were mentioned above) are displayed on P-T space.  In contrast, binary phase diagrams are displayed on T-X space.

Cooling curves are determined from experimental runs of crystallization in pressure bombs to determine the liquidus and solidus boundary cures and  eutectic and /or peritectic points.

Define:  liquidus,  solidus,  eutectic,  peritectic

Liquidus = boundary curve which separates a temperature field of all liquid from that of liquid plus solid.

Solidus = boundary curve which separates a high temperature field of of liquid plus solid from a lower temperature field of all solid.

Eutectic = The temperature below which there is no melt.

Peritectic = The temperature at which incongruent solidification produces a melt and a solid phase (crystals)  different in composition from the parent melt.

4-c. Why do eutectic or peritectic reactions yield horizontal sectors on a cooling curve?

(Answer: Although external temperature may be lowered, exothermic reactions supply heat and hold the temperature within the test tube at a certain level for some time.)

4-d. Why is the melting temperature of a mixture of two solids lower than that of the pure end members?

( Why does salt reduce the boiling point of soup? common ion effect?).

5-A *Examine simple binary with a eutectic, for example, the albite- quartz system. Identify divariant phases, liquidus, solidus, eutectic, proportions of mole fractions (X) , lever rule.

Crystals will form as parent magma cools below its liquidus. From the lever rule, we can determine the amount of liquid that has been used to form crystals. We can also determine the composition of the residual melt. Example, use page 63 of Raymond's book.   At 1200 o C, a tie line (a line connecting phases that are in equilibrium with each other, l¥ and T¥) can be used to see the application of the lever rule by using the lengths in the phase diagram.

Amount  liquid left (residual magma) at 1200°C      = {g to Tg/ (lg  tog )}* 100  = {(100-60)/(100-43)}*100 = 70.2 %  [or  {l / l +s)* 100}  in the diagram on the web.]
Composition of the liquid left         = Ab57, Q 43

Equilibrium crystallization and equilibrium melting.  The crystallization or melting proceeds without removing any melt from the initial magma chamber.  Equilibrium melting follows exactly the opposite path of equilibrium crystallization.  Thus, in an albite-quartz system, if a liquid of 60% quartz at 1600oC begins to cool, tridymite begins to crystallize as the liquids is intersected at about 1370 oC.  Tridymite continues to form until at 1062oC it is joined by the crystallization of albite.  Both albite and tridymite continue to form as the exothermic reaction holds the temperature at 1062oC until the last melt is used up.   At the eutectic, the amount of quartz is 32% and 68% albite.   After that ,the rock simply cools down. The overall composition of the rock is 60% quartz.

Similarly, in equilibrium melting of a rock with 60% quartz, the first melt of albite and quartz begins at 1062oC. The first melt would be that of pure albite (0% Q).  The melt t temperature does not increase with increasing temperature until the melt has  a composition of 32% quartz. Thus,  if the melting continues until the last albite melts, the temperature will still be at 1062oC. For temperatures higher than 1062oC, increase in temperature will cause a change in liquidus composition up the liquidus toward tridymite, and the rock will have melted when the liqidus has a composition of 60% quartz,1370 oC., (Tg).

Thus, equilibrium melting is just the opposite of equilibrium crystallization

Note that  NaAl Si O4 (nepheline) and quartz  are incompatible minerals.  Examine the composition bar of  NaAlSiO4 (nepheline, a feldspathoid), Na Al Si2O6  (jadeitic pyroxene),  NaAl SiO3O8 (albite), and SiO2 (quartz)

Fractional crystallization (FC)

Disequilibrium condition yield fractional crystallization (FC), e.g., in the albite-quartz system (US the AB-uartz system, p. 63, in the text book).  Upon cooling a 60% quartz liquid (a- parental magma), which was at 1600oC, tridymite begins to form after 1370oC at b.  Continued cooling produces more tridymite .  At  Tg, 1200 °C , from the lever rule, we find that 70.2% of magma a is liquid lg, while 29.8% has crystallized to tridymite.  Let us separate the liquid ,lg, and squirt it  to a place where it cools. This residual liquid  gives tridymite until at the the eutectic where both tridymite and albite crystallize together.   Thus, different rocks can form from an original magma by fractional crystallization.   IN FC the crystal paths have compositional breaks.

Batch melting. Again,use the albite-quartz system. Imagine that a rock which is composed of 60% quartz and 40% albite is melted. As the temperature is increased to 1062 a melt of pure albite begins to form.  Increasing the external temperature continues to increase the amount of the melt, the internal temperature is maintained at 1062oC until the last albite is melted. Suppose the melt (batch 1) when the last albite is melted is squirted out by filter press action to another place, and the reaming rock is allowed to melt by increasing temperature. Since  pure quartz will not melt below 1713, what would happen is that , firstly there will be a phase transformation from tridymite to cristobalite at 1470oC, then the cristobalite melts at 1713oC. This liquid (batch 2) is that of pure quartz and is different from batch 1, which is 32% quartz and 68% albite.  The point is that different batches of magmas may be generated by batch melting (BM).  In BM the liquid paths have compositional breaks

Thus, fractional crystallization is not the opposite of batch melting.

Different degrees of partial melting.
Consider the albite-quartz system, and a rock unit composed of 60% quartz.  Consider melting this rock to 1062oC.  That gives one type of magma, 32% quartz.

How about if instead the rock unit was melted to 1270oC?  That would give a magma of about 50% quartz.

How about if the rock was melted to 1500oC?  That would give a magma of 60% quartz.

Clearly different degrees of partial melting of the same rock can give different magmas.  (In batch melting, the parent rock is melted up to some point, and the melt is separated from the parental rock followed by melting the residual rock, which  gives  a magma of another composition.)

Degree of undercooling.
Consider the albite-quartz system, and a magma composed of 60%  quartz, but at 1100oC.

Such a magma would have tridymite crystals (phenocrysts) in it.

Suppose vapor unmixes from the melt (either due to crystallization induced degassing or due to decompression in a partly evacuated chamber), the crystallization temperature (Tc) will be lower than the magma temperature (Tm) or the liquidus.  Supposing the under cooling involved a reduction of 38oC, (i.e., the eutectic temperature of 1062oC is reached), a complex intergrowth between albite and quartz called a symplectic texture will result. If the quartz nucleates on phenocrysts it may show optical continuity with the quartz in the symplectite. This particular symplectite, where the albite is intergrown with qaurtz, is  a type called  myrmekitic texture, whereas if kspar was intergrown with quartz it would be called granophyric texture.

5-B: *Binary with a peritectic. Example: Leucite-quartz system,. Enstatite-quartz system. Identify peritectic.

5-B1. Define: a). silica undersaturated magma, b). incompatible minerals, c). peritectic temperature.

Answer. a). Quartz will not crystallize from a silica undersaturated melt, or if it does there is a reaction rim between quartz and the incompatible minerals such as leucite or enstatite. b). Minerals do not occur in the same rock or if they do they do not touch each other, e.g., leucite and quartz are incompatible; magnesian olivine (forsterite) and quartz are incompatible. C) The temperature at which there is incongruent melting or crystallization.

* Melt potassic feldspar (Kspar - KAlSi3O8). When a small amount begins to melt, some of the Kspar is altered to leucite (K2AlSi2O6) an a melt which is silicic compared to Kspar is evolved. This is a case of incongruent melting at the peritectic temperature.

When all the Kspar has melted, if the early melt (l1) has not been removed, then the composition of the final melt is the same as that of kspar.  Note:  if l1 was removed and the remaining crystal continued to melt, then the final melt (l2) will be different from l1. Other examples include enstatite (pyroxene), which upon melting initially changes to olivine crystals as a melt which is more siliceous than enstatite is evolved.

Note how different melt composition can be derived by removing early melt (l1) from the melting crystal, and continuing the melting of the remaining crystal (l2).  Basically, this is called batch melting.

What is corona texture or reaction rim texture?

Answer: When a crystal is in disequilibrium with the melt, the crystal is resorbed.  Incomplete resorption leads to the crystal being armored by another, which is in equilibrium with the melt.  This texture is developed at peritectic reactions.  Thus, feldspar rims leucite, and enstatite rims forsterite under disequilibrim cooling conditions.  Other, reaction rims have been observed and include amphibole rimming pyroxene, biotite rimming amphibole.  Such reaction rims were among the reasons why Bowen called olivine, pyroxene, amphibole, and biotite discontinuous Series minerals.

It has also been observed that pyroxene armors quartz, which is in disequilibrium with a melt. But there is no peritectic reaction that would explain this texture.  More likely, this texture indicates magma mixing so that the resultant hybrid magma is in disequilibrium with early formed quartz.  (Quartz is a xenocryst, with a rounded outline-  Harker 1904 has described such rocks at Marsco, and at Glamaig in the Island of Sky, Scotland, where he saw gabbroic ground mass containing course un-etched feldspars and rounded quartz.  This might have resulted from a gabbroic magma dissolving a granitic rock. The observation at Sky  is for rocks formed at a divergent boundary setting).  more typically, hybridization occurs above a subduction zone where magmas formed from partial melting of the over riding plate mix with magmas that originate from the mantle wedge between the upper and the subducted lithosphere

Suppose a rock contains leucite phenocrysts, does that mean the rock is silica saturated?

(Answer. It may not be true if leucite crystal is surrounded by a reaction rim of potassic feldspar. if there is a reaction-rimmed leucite, it is posssible for the fine-grained groundmass to contain quarts and alkali feldspar. What it might mean is that disequilibrium cooling has resulted in fractional crystallization.)
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5-C: *Binary with solid solution of one loop. Example: plagioclase, olivine. Examine liquidus and solidus

* Melt plagioclase. When a small amount begins to melt, the melt is enriched in Na, causing the remaining solid to be comparatively more enriched in Ca. Basically, the sodium behaves as a solute that is preferentially mobile. When all the plagioclase has melted, in a condition where the early melt (l1) has not been removed, the composition of the final melt is identical to the composition of the original solid. This is true of all minerals which exhibit solid solution.  Note., If l1 were removed, and the melting of plagioclase is continued, the final melt (l2) will be different from l1.  This is another example of fractional crystallization. Another example that shows solid solution would be olivine.

5-C1. Does the Na/Ca ratio in plagioclase depend on temperature?  Why?

(Answer.  Yes. It has to do with vibration of atoms and the number of Si that are replaced by Al)

5-C2. Why does a plagioclase which crystallized at high temperature have a high Ca/Na ratio than another which crystallized at low temperature?

(Answer.  At high temperature, more Si ions are replaced by Al, and Ca is used to charge balance compounds. Thus, at high temperature 2 of the 4 in a Silicate tetrahedron are replaced by Al and one Ca is used to bring a charge balance for anorthite. At low temperature only 3 of the 4 Si are replaced by Al and 2 Na ions can be used to balance the charge in Albite)

5-C3. What is normal zoning? What is reverse zoning?
Answer: To begin with zoning indicates disequilibrium cooling or fractional crystallization of the magma.
In normal zoned plagioclase, the Ca/Na ratio decreases from core to rim.  In reversely zoned Plagioclase, the Ca/Na ratio increases from core to rim.  The question becomes, why would reverse zoning develop?  The answer includes a) changes in magmatic pressure as it ascends and cools, which would change the plagioclase liquidus and solidus temperatures.  It also might arise from magmatic assimilation of limestone country rock as the magma cools.

There is another type of zoning, and it refers to the presence of internal unconformity within the zoned plagioclase.  This would imply magma mixing or hybridization.  Oxygen isotope studies of such plagioclases have indicated that the plagioclase layers have sampled two different sources of magma.

5-C4. Give the names of plagioclase minerals.

5-D. *Binary with two solid solution loops.  Example, the alkali feldspar system. Identify minimum of alkali feldspars .

5-D1. What is the role of vapor pressure on the alkali feldspar system?

(Answer:  Increased vapor pressure lowers the crystallization temperatures of anhydrous phased.  Thus, the crystallization temperatures of pure albite and orthoclase, respectively, are 1118 and  1520 at 1 kb; 800 and 900 at 3 kb, and 758 and 876 at 5 kb (p. 74, Raymond's book).  Also note that the solidus for Ab-Or system intersects the solvus, and solid solution minimum becomes a eutectic , thereby allowing for two separate feldspars to crystallize simultaneously.  Thus, at vapor pressures above 5 Kb, two feldspars precipitate at the eutectic.  This give rise to subsolvus rocks.- i.e., rocks that crystallized at high PH20 pressure or low temperature of crystallization, will have two feldspar types.  Generally, high PH20 corresponds to great depth, and the lowering of  temperature due to presence of vapor pressure.

5-D2. Define: 10. solvus, 11. Perthite, 12, antiperthite, 13. perthitic texture, 14. subsolvus granite.

(Answer: The solvus is a  curve within the solid field.  It separates regions of one solid solution phase from that of  two phases. One mineral inverts to two minerals below the solvus, as a minor phase exsolves along cleavage planes of a major phase.  The exsolution lamellae of albite in a major orthoclase phase develop perthites.  In contrast, exsolution lamellae of orthoclase in a major albite phase are antiperthites.  Such perthitic texture indicate hypersolvus or supersolvus rocks-- i.e., rocks that crystallized at low H20 pressure or high temperature will have one (perthitic) feldspar type.)

5-D4.  give the names of alkali feldspars?

(Answer:  Or 0 to 10 %= albite;  Or 10 to 35 %  = anorthoclase;  Or 35 to 100 % = sanadine at high temperature or orthoclase at low temperature.)

5-D4. What is peristerite or the plagioclase jump which corresponds to the garnet zone of metamorphism?

(Answer: There is a solvus beneath the solidus in the plagioclase system.See page 586, Hyndman's book.  At the garnet isograd there are two plagioclases one < An 5, and anothergreater than An 21.)

Go to list of questions

PE_6. Describe Ternary phase diagrams.

Three binaries compose the sides of a ternary.  The ternary is a triangular cut for a particular temperature?

6-A. How do you read information from ternary diagrams?

Three components are plotted at the apexes of a triangle.  The temperature must be plotted in another dimension, from which temperature contours are projected on the triangle.  Pressure is held constant.  The sides of the ternary are binaries.  Each binary eutectic heads a thermal valley, marked by a cotectic line, representing a temperature-composition curve along which two solid phases crystallize. (See page 75 of text by Raymond). The lowest temperature point in the ternary is a ternary eutectic. A peritectic in a binary becomes a subtraction line in a ternary, as in the SiO2-Fo-An- system for basalt, Bowen, 1928.

6-A-  Ternary bounded with three simple binaries.  (p. 75). From melt a, crystal a forms.  With reduction in temperature, the melt composition goes directly away from a toward ß at the cotectic.  With continued cooling, both A and B crystallize and the melt moves down the cotectic toward the ternary Eutectic, E.  At E all three minerals, A, B, and C crystallize until all liquid is used up.  Further lowering of temperatures merely cools the rock.

6-B. * a) Basalt Ternary-  albite, anorthite, diopside system (p. 77. Fig 4-17)  Only the Ab-An side is a binary with solid solution.  The other two sides are simple binaries.  Also, note that the  liquidus and solidus temperatures of the plagioclase loop are lowered when diopside is present in the melt.  In this system, the temperatures,  at which the cotectic is reached, and when it is used up during cooling, are determined from experiment.
b) In the SiO2-Fo-An- system for basalt, Bowen, 1928, a subtraction curve of the ternary peritectic line separates silica saturated magma from others.  Silica under-saturated basalts (alkali basalts) would not reach the ternary eutectic under equilibrium cooling conditions.

If olivine is added, one deals with the basalt quaternary from which an olivine-diopside-plagioclase ternary may be obtained..

6- C. Petrogeny's residua system (p.78- Fig. 4-19):  Inspect the SiO2 -feldspathoid ternary, which is separated by a temperature ridge of the feldspars.  Determine where leucite and nepheline lie on that ternary.  Notice that this ternary is separable into a feldspathoidal quadrilateral and the SiO2- Ab- Or Ternary.   The SiO2- Ab- Or Ternary (p.77), also called petrogeney's  residua system and is useful for showing relationships in silica saturated rocks.   Notice how  the QAP plots of 1269 rocks matches with ternary minimum in Figure 4.21 on p.77.

6-D. Ternary diagrams for classification purposes.

* QAPF scheme or Streckeisen's diagram for classifying igneous rocks

* Ternary for classifying clastic sedimentary rocks

* AFM, ACF diagrams for metamorphic rocks.

6**. What is the difference between ternary diagrams and ternary phase diagrams?

PE_7  Describe a quaternary diagram?

Quaternary Phase diagrams are bounded by ternaries.

Other quaternary diagrams include:

7-A) Basalt Diagram. This is based normative minerals such as olivine clino -and ortho-pyroxenes, plagioclase and quartz. The diagram is useful for distinguishing between tholeiites and alkali basalts.

7-B) Pyroxene quadrilateral. This is basically a cut on the pyroxene triangle. It is a useful diagram. It helps remember the common pyroxene mineral compositions. It also depicts coexisting pyroxenes.