Phase transitions

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<p>Classification of Phase Transitions</p> <p>Phase TransitionsBy Saurav Chandra SarmaCRYSTALLOGRAPHY AND ITS APPLICATIONSOutlineIntroductionClassification of Phase TransitionKinetics of Phase TransitionMartensitic TransformationBaTiO3 Phase TransitionGlass TransitionOther ExamplesConclusionIntroductionAphase transitionis the transformation of athermodynamicsystem from onephaseorstate of matterto another one byheat transfer.</p> <p>During a phase transition of a given medium certain properties of the medium change, often discontinuously, as a result of the change of some external condition, such as temperature, pressure, or others</p> <p>For example, a liquid may become gas upon heating to theboiling point, resulting in an abrupt change involume.Classification of Phase TransitionsClassification of Phase TransformationsMechanismThermodynamicsBased onEhrenfest, 1933Buerger, 1951Order of a phase transformationBAEhrenfests ClassificationFirst order phase transition: Discontinuity in the first derivative of Gibbs Free Energy,G.Second order phase transition: Continuous first derivative but discontinuity in the second derivative of G.</p> <p>Lambda Transition:</p> <p>Buergers ClassificationReconstructive Transition: Involves a major reorganization of the crystal structure.E.g: Graphite DiamondDisplacive Transition: Involves distortion of bond rather than their breaking and the structural changes.</p> <p>E.g: Martensitic Transformation</p> <p>Diffusional or CivilianMilitaryTransformation involving first coordination Reconstructive (sluggish)DiamondGraphite Dilatational (rapid)Rock saltCsCl</p> <p>Transformation involving second coordination Reconstructive (sluggish)QuartzCristobalite Displacive (rapid)LowHigh Quartz</p> <p>Transformations involving disorder Substitutional (sluggish)LowHigh LiFeO2 Rotational (rapid)FerroelectricParaelectric NH4H2PO4</p> <p>Transformations involving bond type (sluggish)GreyWhite SnBuergers Classification: full listLiquid Solid phase transformationSolid (GS)Liquid (GL)TmT G TGLiquid stableSolid stableT - Undercooling tFor sufficientUndercooling On cooling just below Tm solid becomes stable But solidification does not start E.g. liquid Ni can be undercooled 250 K below TmG veG +veNucleationof phaseTrasformation +Growthtill is exhausted=1nd ordernucleation &amp; growthKinetics of Phase Transition:13Phase TransformationsNucleation nuclei (seeds) act as templates on which crystals growfor nucleus to form rate of addition of atoms to nucleus must be faster than rate of lossonce nucleated, growth proceeds until equilibrium is attainedDriving force to nucleate increases as we increase Tsupercooling (eutectic, eutectoid)superheating (peritectic)</p> <p>Small supercooling slow nucleation rate - few nuclei - large crystals</p> <p>Large supercooling rapid nucleation rate - many nuclei - small crystals</p> <p>13Heterogeneous nucleationNucleation occur at the interface between two phases or at the grain boundary.Homogeneous nucleationNucleation occur without any preferential nucleation sites.</p> <p>Occurs spontaneously and randomly but it requires superheating or supercooling.</p> <p>An example of supercooling: Pure water freezes at 42C rather than at its freezing temperature of 0C. The crystallization into ice may be facilitated by adding some nucleation seeds: small ice particles, or simply by shaking15</p> <p>r* = critical nucleus: for r &lt; r* nuclei shrink; for r &gt;r* nuclei grow (to reduce energy) Adapted from Fig.10.2(b), Callister &amp; Rethwisch 8e.Homogeneous Nucleation &amp; Energy EffectsDGT = Total Free Energy = DGS + DGV Surface Free Energy - destabilizes the nuclei (it takes energy to make an interface)</p> <p>g = surface tensionVolume (Bulk) Free Energy stabilizes the nuclei (releases energy)</p> <p>1516Solidification</p> <p>Note: Hf and are weakly dependent on T r* decreases as T increasesFor typical T r* ~ 10 nmHf = latent heat of solidificationTm = melting temperatureg = surface free energyDT = Tm - T = supercoolingr* = critical radius16Avirami equation:Transformations are often observed to follow a characteristic S-shaped, or sigmoidal.</p> <p>Initial Slow rate time reqd. for forming a significant no. of nuclei of the new phase.</p> <p>Intermediate fast rate nuclei grow in size and cross the critical radius</p> <p>Final slow rate particles already existing begin to touch each other, forming a boundary where growth stops.</p> <p>The parameter n depends on shape of -phase particles (the Dimension): </p> <p>Spherical n=3 (3D) Disk-shaped n=2 (2D) Rod-shaped n=1 (1D)Rate of Phase TransformationAvrami equation =&gt; y = 1- exp (-kt n)</p> <p>k &amp; n are transformation specific parameters</p> <p>transformation complete log tFraction transformed, yFixed Tfraction transformedtime0.5By convention rate = 1 / t0.5Adapted from Fig. 10.10, Callister &amp; Rethwisch 8e.maximum rate reached now amount unconverted decreases so rate slowst0.5rate increases as surface area increases &amp; nuclei grow18S.A. = surface areaTemperature Dependence of Transformation RateFor the recrystallization of Cu, since</p> <p>rate = 1/t0.5</p> <p>rate increases with increasing temperature Rate often so slow that attainment of equilibrium state not possible!Adapted from Fig. 10.11, Callister &amp; Rethwisch 8e.(Fig. 10.11 adapted from B.F. Decker and D. Harker, "Recrystallization in Rolled Copper", Trans AIME, 188, 1950, p. 888.)</p> <p>135C119C113C102C88C43C11010210419 The martensitic transformation occurs without composition change The transformation occurs by shear without need for diffusion The atomic movements required are only a fraction of the interatomic spacing The shear changes the shape of the transforming region results in considerable amount of shear energy plate-like shape of Martensite The amount of martensite formed is a function of the temperature towhich the sample is quenched and not of time Hardness of martensite is a function of the carbon content but high hardness steel is very brittle as martensite is brittle</p> <p>1) Martensitic Transformation:Example??</p> <p>Martensite</p> <p>FCCAusteniteFCCAusteniteAlternate choice of CellTetragonal MartensiteAustenite to Martensite 4.3 % volume increasePossible positions of Carbon atomsOnly a fraction ofthe sites occupiedBain distortion20% contraction of c-axis12% expansion of a-axisIn Pure Fe after the Matensitic transformationc = aC along the c-axis obstructs the contraction</p> <p>What happens actually???</p> <p>MartensiteAustenite2) BaTiO3 Phase transition</p> <p>&gt;120oCClick me</p> <p>Cubic Structure(Paraelectric)Tetragonal Strucure(Ferroelectric)Experimental Techniques:DSCEXAFS (Extended X-ray absorption fine structure)XANES (X-ray absorption near-edge structure)PDF (Pair Distribution Function)- To undertand local structure distortion.</p> <p>Change in hysteresis loop patternSource: Ferroelectricity, domain structure and phase transition of Barium Titanate, Reviews of Modern Physics, 22,3 (1950)</p> <p>Source: Ferroelectricity, domain structure and phase transition of Barium Titanate, Reviews of Modern Physics, 22,3 (1950)</p> <p>In the high-symmetry cubic phase, no reflections are split. In the tetragonal phase, (222) remains a single peak whereas the (400) reflection is divided into (400/ 040) and (004) peaks with an intensity ratio of 2:1Source: J. AM. CHEM. SOC.,130, 22, (2008) </p> <p>Tetragonal system: 10 Raman active modes but 18 observed due to LO-TO splitting.Cubic system: Should be Raman inactive but 2 modes observed due to displace Ti position Raman Spectra:</p> <p>Glass forming liquids are those that are able to by-pass the melting point, Tm</p> <p>Liquid may have a high viscosity that makes it difficult for atoms of the liquid to diffuse (rearrange) into the crystalline structure</p> <p>Liquid maybe cooled so fast that it does not have enough time to crystallizeTemperatureMolar Volumeliquidsupercooledliquidglass2) Glass transition:Examples of Poor Glass Formers:Why is water, H2O, found to be a very weak glass former</p> <p>Requires cooling the liquid faster than 1,000,000 oC/min</p> <p>300 to 150K in 9 millisecondsH2ONo bonding between molecules and molecules can easily flow by each otherExamples of Good Glass Formers:Why is silica, SiO2, found to be a very strong glass former?</p> <p>Can be cooled at 10-10C/min and still by-pass Tm without crystallizing</p> <p>2,000 oC to 1,000 oC in 20 million years!!</p> <p>SiO2Each Si is tetrahedrally bonded to O, each O is bonded to two Si. Si and O atoms cannot move unless other neighboring atoms also move</p> <p>Typical DSC thermogram</p> <p>Determination of Glass Transition temperature by dilatometry</p> <p>Other Examples:</p> <p>Tetragonal OrthorhombicConclusionExperimental techniques used to understand the phase transition depends on the type of phase transition.</p> <p>Depending on the type of transition, it shows various type of complexity.</p> <p>Understanding of phase diagram is must to deal with phase transition.</p>