Unit 5 Crystallisation of Magma PDF

UNIT 5 CRYSTALLISATION OF MAGMA Structure______________________________________________ 5.1 Introduction 5.5 Lever Rule Expected Learning Outcomes 5.6 Binary Eutectic System 5.2 Phase Rule...

UNIT 5 CRYSTALLISATION OF MAGMA Structure______________________________________________ 5.1 Introduction 5.5 Lever Rule Expected Learning Outcomes 5.6 Binary Eutectic System 5.2 Phase Rule 5.7 Summary Phase Diagram 5.8 Activity Condensed Phase Rule 5.9 Terminal Questions 5.3 Unicomponent System 5.10 References Crystallisation behaviour of H2O System 5.11 Further/Suggested Readings Crystallisation behaviour of SiO2 System 5.12 Answers 5.4 Binary System Binary System with Complete Solid Solution of Two End Members 5.1 INTRODUCTION In Unit 4, we have already learnt that the magma consists of complex mixtures of solids, fluids and dissolved gases. Essentially, they are very hot silicate melts containing large quantities of water and varying amount of highly reactive fluids and gases in the solution. You have also learnt that the volatiles impart low viscosity to the magma. The minerals in igneous rocks crystallise at a range of different temperatures. You have read in Unit 4 that the sequence in which minerals crystallise out from the magma is studied under the Bowen reaction series. In this unit, you will study about unicomponent and bicomponent or binary systems, the application of phase rule and equilibrium crystallisation. Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… Expected Learning Outcomes________________________ After reading this unit you should be able to: ❖ define phase rule and phase diagrams; ❖ describe unicomponent and bicomponent/ binary systems; ❖ explain the application of phase rule; and ❖ discuss binary eutectic system. 5.2 PHASE RULE It is important for you to understand the contribution of each chemical constituent existing in any system of the universe. The effects that occur by the addition or subtraction of constituents in the system will also be considered. This will not only help us to understand each system better, but also enable us to study more complex systems in nature. The fundamental and simple approach for this is the Phase rule. Before reading about the phase rule, let us get familiar with a few terms. System: It is part of the universe that one can isolate (either physically or mentally) to study it. Types of system: 1) Open System: A system may be open, if it can transfer energy and matter to and from the surroundings. 2) Closed System: In a closed system, only energy, such as heat, may be exchanged with the surroundings. 3) Isolated System: Neither energy nor matter may be transferred with the surroundings. Surroundings: Surroundings can be considered the bit of the universe just outside the system. Phase: Phase is defined as a chemically and physically homogenous part of a system that is bounded by an interface with adjacent phases. System Components: Smallest number of chemical constituents needs to make up all phases in the system. Variance (also known as the Degrees of Freedom, expressed as "f"): Minimum number of variables that need to completely define the state of a system at equilibrium. The state of a system is described completely by defining macroscopic properties of the system, which include temperature, pressure, composition, mass, volume and other interdependent properties. Gibbs phase rule was formulated by American Chemist J. Willard Gibbs and so it is named after him. It is used in the determination of the variance or degrees of freedom of a system (f). Phase rule is applicable only to the heterogeneous reversible reactions which are in equilibrium, whereas other reversible reactions are studied using “law of action.” 110 Unit 5 Crystallisation of Magma ……………………………………………………………………………………………….….............… Phase Rule governs the number of phases that can co-exist in an equilibrium in the system and is expressed as: F=C-P+2 or F+P=C+2 Where, P= Number of phases present in a system F= Degree of Freedom C= Components 2= Two intensive parameters usually T (temperature) and P (pressure). As stated above, phase is physically distinct in a system (based on their composition, structure and/or state) that is mechanically separable from the rest. It may be a liquid or gas or solid. For example: Matter Number of Phases Ice 1 (solid phase) Ice + water 2 (liquid+solid) 2 piece of ice 1 (only different pieces) To understand a phase diagram, it is very important to know about its components. A component is defined as the minimum number of chemical species required to define a system and all its phases. It is generally expressed as proportion of oxides (SiO2, Al2O3, FeO, Fe2O3, H2O, CO2, CaO, MgO). If we consider ice and water, they have only 1 component (H2O) and 2 phases. To describe silica /quartz system (SiO2), we can describe it by 3 components (Si, O or SiO2) but only SiO2 is good enough to define it. So, number of components is “1”. Number of components depends upon: 1) the behaviour of the system and 2) the range of conditions over which it is studied. For example, at low temperature, calcite is treated as a single component (CaCO3) system, but at high temperature, it is a two-component system (CaO+CO2). 5.2.1 Phase Diagram The graphical presentation giving the conditions of pressure and temperature under which the various phases are existing and transform from one phase to another is known as the phase diagram of the system. A phase diagram consists of areas, curves or lines and points. These diagrams display stability fields of various phases, separated by lines representing conditions under which phase changes occur. They also represent relationship between melt and solids. Phase diagrams are those which show stability fields and relationship between different phases as a function of variables such as P, T and composition (X). Thus, the results of the phase equilibrium experiment which are performed in the laboratory to study the crystallisation and melting behaviour of a magma of definite composition under same P and T conditions are graphically represented by phase stability diagram. These diagrams show 111 Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… constitution of alloys as a function of temperature under equilibrium condition and are also known as phase equilibrium diagrams. Fig. 5.1: Phase diagram showing solid-liquid-gas behaviour of a substance. Fig. 5.2: Phase diagram of unicomponent system showing critical and triple point. In Figure 5.1, temperature is represented as T on Y-axis and composition on the X-axis. In general, at high temperature, the system is completely in the melt form and 100% melt field is separated from rest of the phase diagram by a boundary called liquidus. Liquidus line separates liquid from liquid + solid. The 100% melt exists above this line. Likewise, low temperature stability field for 100% solid is separated from high temperature condition by a phase boundary line called solidus. Solidus is the line below the liquidus line, where 100% solid exists. Solidus line separates solid from liquid + solid. In the intermediate T between solidus and liquidus, the system consists of 2 types of stable phases at an equilibrium i.e., both liquid and solid crystals. Figure 5.2 shows the phase diagram of a unicomponent 112 Unit 5 Crystallisation of Magma ……………………………………………………………………………………………….….............… system where temperature (T ºC) is represented on X-axis and pressure (P atm) on Y-axis. The three curves separate these phases, viz. solid, liquid and gas. Triple point is the point where the temperature and pressure at which the solid, liquid and vapour phases of the pure substance can exist together at equilibrium (Fig. 5.2). The end point of a phase equilibrium curve is known as critical point. It is defined as the point at which two phases of a substance initially become indistinguishable from one another. You have read in Unit 3 of BGYCT-131 course that the interior of the Earth is inaccessible. Geologists observe only a tiny fraction of the rocks that compose the Earth. A large portion of information about the Earth is indirect, coming from melts of subsurface material, geophysical studies or experiments conducted at elevated temperature and pressure. Thus, it is important to note that the P and T conditions of magma generation and modification can be deduced from the real melting of melt of minerals under laboratory conditions. 5.2.2 Condensed Phase Rule In cases, where either P or T is kept constant, one can apply the condensed phase rule with the formula: F=C-P+1 This is simply because the total number of variables within the system has now become 1, as only one of the two intensive properties of the system (P and T) is allowed to vary. The condensed phase rule is quite helpful in understanding isobaric T (temperature) – X (composition) or isothermal P (pressure) – X (composition) diagrams as well as experimental geochemistry where either P or T is kept constant to investigate the dependence of a system on the other intensive variable. 5.3 UNICOMPONENT SYSTEM In the above section you have studied about phase rule and phase diagram. Now let us discuss about unicomponent system. A system having only one component is called unicomponent system. The least number of phases possible in any system is one. Thus, according to phase rule, a one-component system should have a maximum of two degree of freedom. When C=1, P=1, So, F=C-P+2 =1-1+2 =2 Hence, a one component system requires a maximum of two variables (i.e. temperature and pressure) to be fixed in order to define the system completely. Phase diagram of one component system consist of points, curves or lines, areas, and represents a non-variant, univariant and bivariant systems respectively. SiO2 and H2O systems are examples of one component system. In the following section let us discuss H2O system of unicomponent system. 5.3.1 Crystallisation Behaviour of H2O System Water is a one component system which is chemically a single compound involved in the system. It constitutes a three phase (ice-solid, water-liquid and 113 Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… vapour-gaseous) and have the following equilibria that depends upon the conditions of temperature and pressure (variables): ice → vapour ice → water water → vapour If the values of vapour pressures at different temperatures are plotted against the corresponding temperatures, the phase diagram of the H2O System (Fig. 5.3) is obtained. It consists of three stable curves and one metastable curve. Water and vapour exist together in equilibrium along the vapour pressure curve of water OB. At point D, the vapour pressure of water becomes equal to the atmospheric pressure (100 ºC; boiling point of water). At temperature 374 ºC and pressure 218 atm, the curve OB finishes at B where the water and vapour are indistinguishable. The system has one phase and this point is the critical point. Applying phase rule on this curve, C=1, and P=2, F=C-P+2 =1-2+2 =1 Hence, the curve represents a univariant system, i.e. only one factor either temperature or pressure is sufficient to be fixed in order to define a system. Two phases ice and vapour exist together in equilibrium along sublimation curve of ice OA (Fig. 5.3). The lower end of the curve OA extends to absolute zero (-273 ºC) where no vapour exists. In Fig. 5.3 the areas AOC, COB and BOA represent following phases. Area Phase Component Area AOC ice H2O Area COB water H2O Area below BOA vapour H2O Thus, for every area when C=1 and P=1; Applying phase rule on areas F=C-P+2 =1-1+2 =2 Hence, each area is a bivariant system, where it becomes necessary to specify both the temperature and the pressure to define a one phase system. 114 Unit 5 Crystallisation of Magma ……………………………………………………………………………………………….….............… Fig. 5.3: Phase diagram of unicomponent system. 5.3.2 Crystallisation Behaviour of SiO2 System In one component system, e.g. silica polymorphs, where silica has number of polymorphs, each having a definite crystal structure and is stable under definite T and P range. The stability field represents the P and T conditions under which each mineral is stable and the phase boundaries define the limits of the stability field as well as the conditions under which phases in the adjoining fields are co- existing. There are various phases in the phase diagram. For any of the phases, we can freely vary P and T without affecting the nature of the phases. It is important to mention that phase rule does not provide any information on the number of phases that exist or are possibly produced in the system. A good example of unicomponent system is the SiO2 system that consists of many phases as shown in Fig. 5.4. At a point X, P=3 where high quartz, tridymite, cristobalite co-exist as the high quartz - tridymite, high quartz - cristobalite and tridymite-cristobalite phase boundaries intersect. Here component denoted by C=1(e.g. SiO2). So, when we apply phase rule it is expressed as: P+F=C+2 3+F=1+2 F=0 As F=0, X is an invariant point. i.e., at this point, 3 phases co-exist in equilibrium but, T and P are invariable, if 3 phases are co-existing. At the phase-stability boundaries e.g. Y on the Fig. 5.4 (univariate curve) P=2 (stishovite, coesite) and C=1, F=1+2-2=1 115 Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… F=1, indicating that the P and T are invariant independently. If, T increases, P must have to increase, and vice-versa, for the system to remain on the phase stability boundary, where these two phases co-exist. For any point within a phase stability field, Z marked on the Fig. 5.4 (bivariant field), P=1(low quartz) and C=1(SiO2). Fig. 5.4: P-T phase diagram for the SiO2 system (unicomponent system) where following phases are present: melt SiO2, low quartz (α-quartz), high quartz (β-quartz), tridymite, cristobalite, coesite, stishovite. Now F=2 indicating that this is a bivariant field and T and P can change independently without changing the phase stability. In the Fig. 5.4, the shaded portion represents high T condition under which silica is in liquid phase (melt). On cooling, at X (temperature 1650 ºC and at pressure 0.4GPa), cristobalite begins to crystallise. On further cooling, the system will be reaching the cristobalite-tridymite phase boundary at 1470 ºC and here cristobalite transforms into tridymite. On continuous cooling at tridymite- high quartz phase boundary, it will transform into high quartz. With further cooling, it reaches the low-quartz/high-quartz phase boundary, where high-quartz is converted into low quartz. Two phases will coexist only at phase boundary during phase transformation. On decompression and cooling, the high-pressure varieties of SiO2 such as, stishovite and coesite will be converted 116 Unit 5 Crystallisation of Magma ……………………………………………………………………………………………….….............… into lower polymorphs at suitable T and P ranges. SiO2 system explains an abundance of quartz as a rock forming mineral (as quartz is the stable polymorph of silica over a broad range of P-T conditions). The existence of coesite and stishovite associated with the meteorite impact and thermonuclear bombsites. Learners, you have learnt about the phase rule, phase diagram and crystallisation behaviour of unicomponent system. Before discussing about the binary system, spend few minutes to perform an exercise to check your progress. SAQ 1 a) A part of universe that one can isolate either physically or mentally to study is known as ____________. b) Equation ‘Liquid+Solid1=Solid2’ denotes ______________reaction. c) Define phase rule. d) Define triple and critical point. e) What are solidus and liquidus lines? 5.4 BICOMPONENT SYSTEM You have studied unicomponent system in the above section. Now, let us discuss about bicomponent/binary system. Systems having two components are described as bicomponent system. The binary phase relations are mainly of three different types, such as: a) crystallisation of two end members of a solid solution, b) eutectic crystallisation of two mineral components, and c) incongruent melting of a binary eutectics with the peritectic reaction. Generally, in nature, only three cases are possible when two components are mixed together. Mixed-crystals form which are miscible and form a solid solution series in indefinite proportions. Miscible crystals of composition 1 and composition 2 will be formed (due to eutectic reaction), which are of definite proportions. Two immiscible components form a crystal of intermediate composition by reaction only. 5.4.1 Binary System with Complete Solid Solution of Two End Members Minerals with very similar mineral lattice structures mix easily on the atomic scale. This phenomenon is defined as solid solution of one phase with the other phase. The most common example in the igneous petrology which shows such behaviour is of olivine and plagioclase minerals. Now, let us define the term mixed crystals and solid solution series. When the two components are isomorphous and miscible in all proportions in solid state, they form 117 Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… homogeneous crystals which are called as mixed crystals. Solid solution forms where both components are isomorphous and constituent ions have similar ionic radius and equal ionic charge. In this case, both the components in solid and melt phases change during equilibrium crystallisation and both the components mixed completely with each other. Fig. 5.5: Isobaric T-X phase diagram for Albite-Anorthite (Ab-An) system at atmospheric pressure. Now you will learn about binary system with complete solid solution of the two end members with the help of Albite (NaAlSi3O8) - Anorthite (CaAl2Si2O8) (Ab- An) system. In Ab-An system, solid solution coupled with Na+1 and Si+4 substitution for Ca+2 + Al+3 in a constant AlSi2O8 reference framework is involved. In the above Fig. 5.5, pure albite (Ab) is taken on the right end and the pure anorthite (An) on the left end of the X axis. These two pure systems behave like a typical isobaric one component system. In this system, solid-melt that coexists in a single phase at a fixed temperature in equilibrium (P=2). When applied in the phase rule (F=C-P+2), it is expressed as F =1-2+1 F =0 (invariant point) Pure Ab and An melts at 1118 ºC and 1153 ºC at X and Y points respectively. Now, let us examine what happens when we add a component on either of the pure systems. In the experiment, when we add Ab component to pure An component, the melting point lowers down. In case of addition of pure Ab, melting point rises. Now, let us use the phase rule to analyse the behavior of melt of an intermediate composition. 118 Unit 5 Crystallisation of Magma ……………………………………………………………………………………………….….............… Now, first consider a melt of a composition ‘a’ in Fig. 5.5 at 1600 ºC (An60Ab40), we take it as the bulk composition (X bulk) of the system. At about 1600 ºC, liquid composition is An60. In this case, the liquid composition is equal to the bulk composition as the system is entirely of liquid composition. Thus, in this case P=1(liquid) and C=2. Applying phase rule (F=C-P+2), we have F = (2+1-1) = 2 This means that for a single two component liquid at a constant pressure, F =2. The two most realistic intensive variables that we can take to define the system include: 1) temperature, and 2) composition (X liqAn or X liqAb). After cooling the system to point ‘b’ (An60Ab40) in Fig. 5.5 at about 1475 ºC, plagioclase of composition ‘c’ (An87), which is different from that of the melt beings to crystallise indicating that the initial crystal is An-rich. The line connecting b and c i.e., the composition of the co-existing phases at a definite temperature is called a ‘Tie line’. Now, with the help of a phase rule, at any point on the liquidus curve, P=2 (co- existing liquid and solid) and C=2. So, F=2-2+1 = 1 Here, only one intensive variable is sufficient to define a system completely. With continuous cooling, both liquid and solid vary in compositions. The liquid composition changes along the liquidus from b to g in Fig. 5.5 and the plagioclase changes from c to h indicating that with continuous cooling, both crystal and liquid become more sodic (Ab rich). In this case, the reaction is represented by: Liquid1 + plagioclase1= liquid2 + plagioclase2 Such reactions having at least one degree of freedom that occur by exchange of components over a range of temperature and or pressure are called continuous reaction and form a series of mixed crystals.  Watch the following video to learn more about solidus and liquidus curves. Exsolution Intergrowth Link: https://youtu.be/7SnfV0nJMvk 5.5 LEVER RULE Now let us study about lever rule. In addition to their mineralogical compositions, a phase diagram also furnishes information related to the modal proportions of phases. The technique used to find out this information is known as lever rule. It can be used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. Using the length of a tie line at any specific 119 Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… temperature, we can calculate the relative amount of phases in a system. The tie line in the two-phase regions is analogous to a lever balance on a fulcrum. This geometric approach is called “Lever rule”. Let’s consider the tie-line ‘df’ (Fig. 5.6) we can represent it as- Fig. 5.6: Graphical representation of the abundance of components in a binary mixture. According to lever’s rule: Liquid % = length of line segment (e-f) * 100/ df Plagioclase % = length of d-e * 100/ df We can define lever rule as the amount of a given phase in a system is proportional to the length of segment on opposite side of the bulk composition. The closer a phase to the bulk composition, the more predominant it is. In order to understand lever rule, take help of Fig. 5.5. Using this at 1445 ºC, ef= An82- An60 = 22 and de= An60- An48 = 12, thus Liquid % = 22*100/(82-48)= 22*100/34 = 64.70 wt% Solid % = 12*100/34 = 35.29 wt% If we continue the cooling, with a constant bulk composition, ‘ef’ becomes larger, whereas ‘de’ becomes smaller which is a natural phenomenon, i.e., the % of solid increases with the decrease % in the melt. As the temperature approaches to 1340 ºC, the corresponding solid composition of melt ‘g’ (An22) will be at ‘h’ which is equal to the bulk composition (An60). With continuous cooling, the tiny amount of liquid (An22) is consumed immediately. Here F= 2-1+1 = 2, so we must specify both T and a compositional variable, like in case of liquidus to specify the system. Petrographic Significance of Ab-An system As solid is always rich in An-component with respect to corresponding liquid, ‘Ca’ becomes more refractory than ‘Na’. Compositional zoning can be defined by this system. 5.6 BINARY EUTECTIC SYSTEM In a binary system, when two mineral components crystallises or melts simultaneously at a particular or fixed temperature, the temperature is called eutectic temperature and the process is called eutectic crystallisation. 120 Unit 5 Crystallisation of Magma ……………………………………………………………………………………………….….............… Opposite to the case, when a mixture of two minerals is heated at a fixed pressure a melt of fixed composition is formed. The temperature at which two minerals are melted is called eutectic melting temperature and the process is called eutectic melting. Fig. 5.7: Binary system (Diopside-Anorthite) without solid solution relation. Fig. 5.7 represents a simple type of Diopside –Anorthite binary system without solid solution relation (as the Diopside –Anorthite posses different mineral structure, Diopside-single chain inosilicate, Anorthite-tectosilicate). In this case, both the mineral components crystalises out simultaneously only at a particular temperature or a point called eutectic point in a particular fixed proportion. Crystallisation behaviour on the left side of the eutectic point: Consider a melt of ‘a’ (Di30An70) composition above the liquidus, P= 1 (only liquid) and C=2, so applying phase rule F= 2+1-1= 2 Here two variables, temperature and composition (T, XliqAn or XliqDi) are required to define the system. With cooling, when the melt (Di30An70) touches the liquidus at a point ‘b’ at 1450 ºC, pure Di begin to crystallise. So above liquidus, as F= 2+1-2= 1, only one variable (temperature or composition) is needed to define the system. With further cooling, more and more Di crystals are formed and liquid composition will move away from b towards point d. At point d (1274 ºC), anorthite joins diopside and both (Di and An) the mineral components crystalises out simultaneously at a fixed eutectic temperature and in a fixed eutectic proportion. Cooling to the point ‘g’ (1450 ºC), crystallisation of pure ‘Di’ will begin and at that point, F will be = 2-2+1= 1. Here, we have to fix one variable (generally ‘T’). With continuous cooling, the liquid composition changes along the liquidus line from ‘g’ towards ‘d’ and pure anorthite crystals continue to form. This crystallisation of ‘An’ from melt is also a continuous reaction which may be represented by: 121 Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… Liquid1 = solid + liquid2 With continuous cooling, at the eutectic point (1274 ºC), where both the liquidus converge, there are 3 phases that coexist, and degree of freedom F= 0. This eutectic reaction is a type of equilibrium crystallisation. At eutectic point, we can apply the lever's rule to determine the relative amount of solid and liquid. It has been found that with the progress of time, ratio of solid to liquid that increases. Learners, you have learnt about the binary system with complete solid solution of two end members and binary eutectic system. Now, spend few minutes to perform an exercise to check your progress.  Watch the following video to know more about eutectic point. Igneous Textures, Processes and Pathways: Volcaniclastics Link: SAQ 2 a) The point at which two liquidus lines meets is known as ___________. b) When the two mineral components are isomorphous and miscible in all proportions in solid state, they form a homogeneous crystal and are called as __________. c) ____________ is used to determine the fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. 5.7 SUMMARY Let us summarise what we have learnt in this unit: Phase Rule governs the number of phases that can co-exist in an equilibrium in any system and expressed as F=C-P+2. Where, P= number of phases present in a system; F=degree of freedom; C=components; and 2= two intensive parameters usually T and P. A component is defined as the minimum number of independent chemical species required to define a system and all its phases. It is generally expressed as a proportion of oxides (SiO2, Al2O3, FeO, Fe2O3, H2O, CO2, CaO, MgO). Minimum number of components depends upon: a) behaviour of the system, and b) the range of conditions over which it is studied. Phase diagrams show stability fields and relationship between different phases as a function of such variables as P, T and composition (X). In case, where either P or T is held constant, one can apply the condensed phase rule with the formula: P+F=C+1. A system having only one component is called unicomponent system. For example: silica polymorphs, where silica have number of polymorphs, each having a definite crystal structure and stable under define set of T and P range. 122 Unit 5 Crystallisation of Magma ……………………………………………………………………………………………….….............… Two phases will co-exist only at a particular phase boundary during phase transformation. System having two components is described as binary system. Generally, in nature, only three cases are possible when two components are mixed. i) mixed crystal form which are miscible (solid solution) in any proportion, ii) mixed crystals of composition 1 and composition 2 formed as result of Eutectic reaction, miscible at a fixed proportion, and iii) two components will be immiscible and a crystal of intermediate composition is formed by reaction only. Lever rule is used to determine fraction of liquid and solid phases for a given binary composition and temperature that is between the liquidus and solidus line. In a binary eutectic system, a new melting point is called the eutectic point that occurs when melt of a fixed composition called eutectic composition is formed by mixture of two mineral components is heated at a fixed pressure. The temperature at which eutectic melting occurs is called the eutectic temperature. 5.8 ACTIVITY Redraw and discuss the phase diagram for water system and albite-anorthite (Ab-An) system as given in section 5.3. 5.9 TERMINAL QUESTIONS 1. What do you understand by phase diagram and phase rule? 2. Explain the crystallisation behaviour of SiO2 system. 3. Explain binary system with complete solid solution. 4. Explain the principle of lever rule. Audio/Video Material-Based Questions: What is eutectic point? Define liquidus and solidus curve. 5.10 REFERENCES Best, M.G. (1982) Igneous and Metamorphic Petrology: W.H. Freeman and Company, San Francisco, 630p. Singh Devender and Vats Satish Kumar (2010) Comprehensive engineering chemistry. I.K. International Pvt. Ltd, 356p. Tyrell, G. W. (1973) The principles of Petrology. John Wiley & Sons. ISBN 0470894806, 9780470894804, 349p. Winter J.D. (2014) Principles of Igneous and Metamorphic Petrology. Second Edition. Pearson Education Limited, Edinburgh Gate, Harlow, 728p. 123 Block 2 Igneous Petrology-II ……………………………………………………………………………………………….…............… 5.11 FURTHER/SUGGESTED READINGS Best, M.G. (1982) Igneous and Metamorphic Petrology: W.H. Freeman and Company, San Francisco, 630p. Mukherjee, P.K. (2000) A Text Book of Geology. The World Press, Kolkata, ISBN:81-87567-09-0, 638p. Philpotts, Anthony R., & Ague, Jay J. (2009). Principles of igneous and metamorphic petrology, Second edition. Cambridge University Press. ISBN: 0521880068, 978-0521880060, 498p. Ragland, P.C. (1989) Basic Analytical Petrology: Oxford University Press, New York, 369p. 5.12 ANSWERS Self Assessment Questions 1 a) System b) Peritectic c) Triple point is the point where the temperature and pressure at which the solid, liquid and vapour phases of the pure substance can exist together at equilibrium. The end point of a phase equilibrium curve is known as critical point. d) The liquidus is represented by a line on a phase diagram that separates a liquid phase from a solid + liquid phase region. A system must be heated above the liquidus temperature to become completely liquid. The solidus is represented by a line on a phase diagram that separates a solid phase from a solid + liquid phase region. The system is not completely solid until it cools below the solidus temperature. 2 a) Eutectic point. b) Mixed crystal. c) Lever rule. Terminal questions 1. Refer to section 5.2 and subsection 5.2.1. 2. Refer to section 5.3. 3. Refer to section 5.4. 4. Refer to section 5.5 124