Phases Diagrams Of Ceramics Third Stage - 2-3-1 The lever rule
2-3-2 The Binary Eutectic : The eutectic reaction is an isothermal three-phase reaction in which a liquid is in equilibrium with two crystalline phases.
EENS 2110 Mineralogy Tulane University Prof. Stephen A. Nelson
7 févr. 2011 TWO COMPONENT (BINARY) PHASE DIAGRAMS. Experimental Determination of ... (Fo and liquid in this case) can similarly be found by applying the lever ...
Lecture 17: 11.07.05 Free Energy of Multi-phase Solutions at
11 juin 2005 Figure by MIT OCW. •. This is the simplest form a binary phase diagram can take. Tie lines and the lever rule on ...
Binary Phase Diagrams A binary phase is a two component system
The lever rule is used to find the fractions of liquid phase and solid phase in the binary alloy in the two-phase state at equilibrium. The rule can be obtained
Pseudo-binary phase diagram for Zr-based in situ Я phase composites
5 and 6 demonstrate the Я phase volume fraction will be gov- erned by the lever rule between compositions M and B. However
Module 19 Solidification & Binary Phase Diagrams II Lecture 19
Weight % α & % β at any given temperature (say 0°C) can be estimated from the phase diagram using the lever rule. Binary Peritectic system. L a b p α + L α +
Chapter Outline: Phase Diagrams
lever rule to find the relative fractions of primary α phase. (18.3 wt% Sn) The Gibbs phase rule – example of a binary system. 2Ph. CF. +. −. = 1Ph. CF. +.
Lecture 18: 11.09.05 Binary systems: miscibility gaps and eutectics
11 sept. 2005 Two-phase equilibrium introduces the phase fraction determined by the lever rule: ... Free energy diagrams directly relate to binary phase ...
Binary Phase Diagrams
The relative proportions of two phases in equilibrium may be determined from the bulk composition of the system the lever rule
Drude Theory of Metals
Most solid-state phase diagrams are at 1 atm simplest binary diagram for solids ... Lever rule: the fractional amounts of two phases are inversely.
Chapter Outline: Phase Diagrams
A binary alloy contains two components a ternary Phase diagrams for binary systems ... The lever rule is a mechanical analogy to the mass balance.
Chapter 9: Phase Diagrams
The Cu-Ni and binary phase diagram (Figure 10.3) is the simplest type of binary Here we must use the lever rule to calculate the mass fraction of each.
Diffusion and Kinetics Lecture: Binary phase diagrams and Gibbs free
Relative proportion of phases (tie lines and the lever principle). • Development of microstructure in isomorphous alloys. • Binary eutectic systems (limited
Teach Yourself Phase Diagrams and Phase Transformations
Mar 11 2009 Building a simple binary diagram
Lecture 17: 11.07.05 Free Energy of Multi-phase Solutions at
Jun 11 2005 Figure by MIT OCW. •. This is the simplest form a binary phase diagram can take. Tie lines and the lever rule on ...
Binary Phase Diagrams
Igneous Phase Rule for Binary. Systems. • Phase rule: calculates the variability of a Lever Rule (Tie Line Rule) ... Binary Eutectic Phase Diagram.
Chapter 9: Phase Diagrams
Diagrams of Binary Nickel Alloys P. Nash diagram. Phase Diagrams: # and types of phases. • Rule 1: If we know T and Co
Chapter 11: Phase Diagrams
Rothery rules) suggesting high mutual solubility. diagram. Isomorphous Binary Phase Diagram. • Phase diagram: Cu-Ni system. ... The Lever Rule.
CHAPTER 9 PHASE DIAGRAMS PROBLEM SOLUTIONS 9.17 A 90
Ag-75 wt% Cu alloy (at 775°C). In order to do this it is necessary to employ the lever rule using a tie line that extends entirely across the ? + ? phase
Phase Equilibria
Reading: West 7
433PHASE DIAGRAMS
Also called equilibrium or constitutional diagramsPlots of temperature vs. pressure, orT or P vs.
composition, showing relative quantities of phases at equilibriumPressure influences phase structure
Remains virtually constant in most applications
Most solid-state phase diagrams are at 1 atm
Note: metastablephases
do not appear on equilibrium phase diagrams 434FeFe3C
phase diagramPHASES
A phase is a homogeneous portion of a system with uniform physical and chemical characteristics, in principle separable from the rest of the system. e.g., salt water, molten Na2O-SiO2 gaseous state seemingly only one phase occurs (gases always mix) liquid state often only one phase occurs (homogeneous solutions) solid state crystalline phases: e.g., ZnO and SiO2= two phases polymorphs: e.g., wurtzite and sphalerite ZnS are different phases solid solutions= one phase (e.g., Al2O3-Cr2O3solutions) A difference in eitherphysical or chemical properties constitutes a phase two immiscible liquids (or liquid mixtures) count as two phases 435PHASE EQUILIBRIA
The equilibrium phase is always the one with the lowest free energyG = H TS
The driving force for a phase
change is the minimization of free energyEquilibriumĺstate with
minimum free energy under some specified combination of temperature, pressure, and composition e.g., melting metastable unstable equilibrium state436 GGIBBS PHASE RULE
GibbsP + F = C + 2
P: number of phases present at equilibrium
C: number of components needed to describe the system F: number of degrees of freedom, e.g. T, P, composition The number of components(C) is the minimum number of chemically independent constituents needed to describe the composition of the phases present in the system. e.g., salt water. C = 2 (NaCl and water) solid magnesium silicates. C = 2 (MgO and SiO2) solid MgAl silicates. C = 3 (MgO, Al2O3, SiO2) The degrees of freedom (F) is the number of independent variables that must be specified to define the system completely.437F = C P + 2
-78ONE COMPONENT PHASE DIAGRAMS
P + F = C + 2
with C = 1P + F = 3
Composition is fixed,
only T and P can varyThree possibilities:
3 1 " ) 2 NLYMULMQP SOMVH field)
3 2 " ) 1 XQLYMULMQP SOMVH curve)
3 3 " ) 0 LQYMULMQP SOMVH point)
F=0 F=2 F=1 438P + F = C + 2
C = 1 (water)
P = 2 (vapor + liquid)
F = 1 (either T or P,
but not both)ĺcoexistence curve
F=1EXAMPLE: BOILING WATER
*once we specify either T or P of our boiling water, the other variable is specified automatically 439v s vv ss dT dP dd dPvdTsd dPvdTsd 12 12 21
222
111
P P P T hs ' VT H dT dP
From a to b, starting from Gibbs-Duhemequation:
CLAUSIUS-CLAPEYRON EQUATION
Expresses the pressure dependence of phase transitions as a function of temperature (gives slopes of coexistence curves). derived ~1834Slope of the coexistence curves:
VT H dT dP ' H positive along arrows (melt, sublime, vaporize) V negative only for melting *Ice less dense than water 441ONE COMPONENT PHASE DIAGRAMS
Carbon
442Gemesis, GE, Sumitomo Electric, and De Beers
More than 100 tons of synthetic diamonds are
produced annually worldwide by firms like Diamond Innovations (previously part of General Electric),Sumitomo Electric, and De Beers.
ONE COMPONENT PHASE DIAGRAMS
SiO24.287 g/cm3
P42/mnm
C2/c2.93 g/cm3
P31212.65 g/cm3
there are also many metastable phases (not shown)444OTHER EXAMPLES
Ice ²18 different crystalline phases!
445hex ice
OTHER EXAMPLES
CO2 446OTHER EXAMPLES
Sulfur
447TWO COMPONENT (BINARY) DIAGRAMS
with C = 2Composition is now variable: T, P, and
composition can varyP + F = C + 1
When vapor pressures are
negligible and nearly constant:Condensed phase rule:
P + F = C + 2
Pressure is no longer a variable: only T and composition matterP + F = 3
Three possibilities (as before):
3 1 " ) 2 NLYMULMQP SOMVH field)
3 2 " ) 1 XQLYMULMQP SOMVH curve)
3 3 " ) 0 LQYMULMQP SOMVH point)448
SIMPLE EUTECTIC SYSTEMS
simplest binary diagram for solids P=1 F=2P + F = 3
(liquid) P=2 F=1 P=2 F=1 P=2 F=1 (solid) 449no compounds/solid solutions in solid state only single phase liquid at high temperatures partial melting at intermediate temperatures 450
First, specify overall compositionof the system
Second, pick a temperature.
ĺThe compositions of the phases (1 or 2) are then fixedLiquid
1490°C
70% A30% B
isotherme.g., start with liquid at a certain composition isopleth 451
now, slowly cool liquid crystals of A begin to form Liquidus curve:specifies the maximum temperature at which crystals can co-exist with the melt in thermodynamic equilibrium452
Maximum T at which crystals can exist.
akaSaturation Solubility CurveMelting point
depression: the effect of a soluble impurity on the melting point of pure compounds.LIQUIDUS CURVE
453For example, consider salty ice:
MGG VMOP IUHH]LQJ SRLQP IMOOV"454
keep cooling more crystals of A form, depleting melt of A the system is now a mixture of crystals of pure A and the melt of composition y P=2 F=1 455Y YXf Along the isotherm XfY, the relative amountsof the phases A and melt vary but the compositionof the individual phases does not vary. Along XfY, the two phases are pure Aand melt of ~60% A & 40% B. 457
YXf
7OH UHOMPLYH MPRXQPV RI POH PRR SOMVHV ´phase compositionµ ŃMQ NH
determined by using the lever rulealong the tie line XfY:Amount of A = fY/XY and amount of liquid = Xf/XY.
tie line cool more note that liquid becomes richer in B We can use the phase diagram to determine the phase composition, the relative amounts of A and melt at a certain T and bulk comp.PHASE COMPOSITION AND LEVER RULE
Lever rule: the fractional amounts of two phases are inversely proportional to their distances along the tie line (isotherm) from the bulk composition axis XYf1 1 2 2f L f L
L1 = XfL2 = fY
1 1 22 1 11
f f L f f L 2 1 12 fY XY LfLLPhase 1
Phase 2
´NMOMQŃH POH PHHPHU-PRPPHUµ
459XYf
Phase 1
Phase 2
Overall CompositionFraction of liquid
fI··
Xf· C;K 10
Xf/XY = 60%
Xf·· C;K 8D
460last of the liquid solidifies as crystals of A and B cool some more Solidus curve:gives the lowest temperature at which liquids can exist in equilibrium over a given compositional range fraction A: fe/Xe melt fraction: Xf/Xe just above solidus: Xf passing through the solidus is called the eutectic reaction:
Liq. e + A AEA + B
461sample is now mixture of A and B crystals cool some more not much interesting happens below the solidus line. The solid just further cools with no change in composition. fraction A constant at fY/XY fraction B constant at Xf/XY below solidus: fXYP=2 F=1 462
crystals of B precipitate first (B primary) crystals of A precipitate firstquotesdbs_dbs9.pdfusesText_15
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