General Phase Diagram Sections Arthur D Pelton Centre
- Slides: 38
General Phase Diagram Sections Arthur D. Pelton Centre de Recherche en Calcul Thermochimique École Polytechnique de Montréal, Québec, CANADA General rules of construction of all true phase diagram sections; Proper choice of variables and constants to give a “true” phase diagram section (with a unique equilibrium state at each point); A general algorithm for calculating all true phase diagram sections. www. factsage. com
Ca. O-Mg. O: phase diagram www. factsage. com
Diagram: Ca. O-Al 2 O 3 -Si. O 2 www. factsage. com
C-Fe-W System at 5 wt% W www. factsage. com
A Phase Diagram for the Fe-Cr-V-C System www. factsage. com
Fe-Cr-V-C system at 1. 5 wt% Cr and 0. 1 wt% V www. factsage. com
P–T diagram for Al 2 Ti. O 5 www. factsage. com
Fe-O 2 System www. factsage. com
System Fe-Cr-O 2 www. factsage. com
SO 2 -Cu System at 1000 K www. factsage. com
Fe 2 O 3 -Mg. O-Si. O 2 -O 2 System Si. O 2/(Fe 2 O 3+ Mg. O + Si. O 2) = 0. 20 in air www. factsage. com
Fe-Cr-S-O System www. factsage. com
A Phase Diagram for the Fe-Cr-V-C System www. factsage. com
The Law of Adjoining Phase Regions «As a phase boundary line is crossed, one and only one phase appears or disappears. » www. factsage. com
(a 1 + a 2 + … + a n) + b (a 1 + a 2 + … + an) +g (a 1 + a 2 + … + a n) + b + g A node in a general true phase diagram section. www. factsage. com
Ca. O-Mg. O: phase diagram www. factsage. com
L a+b+L T a b+L b a+b A XB B An isobaric binary temperature-composition diagram with the eutectic “opened-up” to show that this is an infinitely narrow 3 -phase region. www. factsage. com
SO 2 -Cu System at 1000 K www. factsage. com
b a+b f 2 b+g a+b+g a a+g g f 1 A “potential-potential” phase diagram “opened-up” to show that the lines are infinitely narrow 2 -phase regions. www. factsage. com
• Potential Variables (the same for all phases at equilibrium) T (temperature) P (pressure) mi (chemical potential) • Extensive Variables (not the same for all phases at equilibrium) Xi (composition) V (volume) www. factsage. com
If only potential variables are held constant, then all tie-lines lie in the plane of the section. In this case, the compositions of the individual phases at equilibrium can be read from the diagram and the lever rule applies. www. factsage. com
Zero Phase Fraction (ZPF) Lines MC fcc bcc M 7 C 3 M 23 C 6 www. factsage. com
Zero Phase Fraction (ZPF) Lines a LIQUID Liqu idus us Solid LIQUID + a L+b SOLID b 2 SOLIDS vus (a + b ) Sol ne SOLID a line Solvus li b LIQUID www. factsage. com
Fe-S-O Predominance diagram (ZPF lines) www. factsage. com
Choice of variables to always give a true phase diagram (single-valued) everywhere www. factsage. com
N-Component System (A-B-C-…-N) Gibbs-Duhem: Phase Diagram www. factsage. com
Choice of variables N-component system (1) Choose n potentials: f 1, f 2, … , fn (2) From the non-corresponding extensive variables (qn+1, qn+2, … ), form (N+1 -n) independent ratios (Qn+1, Qn+2, …, QN+1). Example: [f 1, f 2, … , fn; Qn+1, Qn+2, …, QN+1] are then the (N+1) variables of which 2 are chosen as axes and the remainder are held constant. Phase Diagram www. factsage. com
Mg. O-Ca. O Binary System S T f 1 = T V -P f 2 = -P n. Mg. O m. Mg. O n. Ca. O m. Ca. O Phase Diagram www. factsage. com
Ca. O-Mg. O: phase diagram www. factsage. com
Fe-Cr-S-O System S T f 1 = T V -P f 2 = -P n. Fe m. Fe n. Cr m. Cr Phase Diagram www. factsage. com
Fe-Cr-S-O System www. factsage. com
Pressure vs. Volume diagram for H 2 O This is P NOT a true phase diagram. S+L L+G S+G V Phase Diagram www. factsage. com
Fe-Cr-C System S T V -P n. C m. C f 1 = T f 2 = -P f 3 = m. C (NOT OK) n. Fe m. Fe (OK) n. Cr m. Cr Requirement: Phase Diagram www. factsage. com
Fe-Cr-C system, T = 1300 K, XCr = n. Cr/(n. Fe+n. Cr+n. C) vs. (carbon activity) 1. 0 Mole fraction of Cr 0. 9 M 23 C 6 0. 8 0. 7 M 7 C 3 0. 6 This is NOT a true phase diagram. 0. 5 0. 4 0. 3 bcc 0. 2 0. 1 fcc 0 -3 -2 -1 0 log(ac) 1 cementite Phase Diagram 2 www. factsage. com
“Corresponding” phase diagrams of the Fe-O system Liquid iron + liquid oxide Liquid iron Temperature (K) Liquid iron Liquid oxide 1900 Liquid oxide d-Iron 1700 Wustite 1500 + Wustite 1300 1100 a-Iron + Wustite 900 Wustite + Magnetite a-Iron + Magnetite 700 0 0. 50 g-Iron Hematite + Magnetite g-Iron 0. 54 Mole fraction XO Magnetite a-Iron Hematite + Oxygen 0. 58 0. 62 Hematite -500 -400 -300 -200 -100 0 RT ln PO 2 (k. J) www. factsage. com
Other Sets of Extensive Variables and Corresponding Potentials Gibbs-Duhem: www. factsage. com
Mg-Si binary phase diagram www. factsage. com
Mg-Si, DH vs XSi phase diagram www. factsage. com