P (atm) T (K) a, solid crystal V, vapor L, liquid V + L a + L a + V a + L + V Po TM TVġ1 Single phase (a, L, V) stability regions are 2-D, an area.Ĭont…. a, solid crystal L, liquid a + L V + L a + L + V V, vapor a + VĬonsider phase stability and phase transformation at a constant pressure, Po, eg. P (atm) T (K) a, solid crystal V, vapor L, liquid V + L a + L a + V Show regions of stability of phases in terms of the state variables T & P. 1 P - T Diagram -Unary, Single Component Phase Diagram Example CO2 or H2O Homogeneous system - consists of a single phase Heterogeneous system - consists of more than one phase All the elements may exists in at least 3 distinct states of matter or phase- solid, liquid and gasĨ Cont… Many element exhibit more than one phase form in solid state-called Allotropes Example : BCC and FCC structures are allotropic forms of iron The BCC phase change to FCC iron at 910oC, 1 atm pressure-called allotropic transformation In general, Phase Transformation- any change in the phase form of a system Example : melting or fusion-which change solid to liquid boiling or vaporization-which change from liquid to vapourĩ 3. Phase transitions occur with a decrease (spont.) or no change (equil.) in Gibbs energy.Ī system is considered to be unary if it consists of a single chemical component for the range of states under study. The conversion of one phase to another is a phase transition. A slight change in temperature or pressure will favor one phase over others. At some conditions of temperature and pressure, two or more phases may exist in equilibrium. Usually, only one phase of a given substance is stable at any given temperature and pressure.
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For example, for transformation occurring at constant T and P the relative stability of the phases in a system is determined by their Gibbs free energies, ∆G = Gfinal - Ginitial = ∆ H - T ∆ S ∆G process is allowed ∆G > 0 => process is forbidden ∆G = 0 => equilibriumĦ Cont…. Thermodynamics can be used to predict weather the system is in equilibrium and to analyze the phase stability and phase transformations.
They can be used to describe gas - liquid – solid transitions, polymorphic solid-to-solid transitions, stable phases in alloys of different composition, etc. Phase diagrams arise from minimizing free energies for each phase. 2 Content 1.0 Introduction 2.0 Thermodynamically stable phaseģ.0 Unary Heterogeneous Systems 3.1 P - T Diagram -Unary, Single Component Phase Diagram 3.2 logP – 1/T Diagram -Unary, Single Component Phase Diagram 3.3 Conclusion-Unary p - T Diagrams 3.4 G-T Phase Diagrams G - T Diagram - Unary, Single Component Phase Diagram – V T Diagram - Unary, Single Component Phase Diagram - L, V T Diagram - Unary, Single Component Phase Diagram-a, L,V T Diagram - Single Component Phase Diagram -a, b, L, Vģ 3.5 Metastability 3.6 Chemical Potential and Gibbs Free Energy of Single Component Phases 3.7 Enthalpy & Entropy of Transformation 3.8 Compute Phase Equilibria from Free Energy Relations 4.0ěinary System 4.1 Binary liquid system 4.2 Binary solutions with total solid solubility 4.3 Binary systems without solid solution 5.0ğree Energy-Composition (G-X) Diagram 5.1 Free energy diagrams of total solubility systems 5.2 Free energy diagram for binary solutions with a miscibility gap 5.3 Free energy diagram of binary systems without solid solution (eutectic system) 6.0 Phase boundary CalculationsĤ 1.0 Introduction A phase diagram is a graphical representation of all the equilibrium phases as a function of temperature, pressure, and composition.
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