Fully Miscible Solution Simple solution system (e.g., Ni-Cu solution) Crystal Structure electroneg r (nm) Ni FCC 1.9 0.1246 Cu FCC 1.8 0.1278 Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume Rothery rules) suggesting high mutual solubility. Ni and Cu are totally miscible at all mixture compositions isomorphous Copper-Nickel Binary Equilibrium Phase Diagram Solid solutions are typically designated by lower case Greek letters: etc. Liquidus line separates liquid from two phase field Solidus line separates two phase field from a solid solution Pure metals have melting points Alloys have melting ranges
What do we have? Whats the composition? The Lever Rule Draw Tie line connects the phases in equilibrium with each other - essentially an isotherm T(C) 1300 tie line dus i l i qu L (liquid) B TB 1200 + L s L 20 + R S (solid) (1) W + WL = 1 (2)
WC + WLCL = Co Let W = mass fraction (amount of phase) 30C C 40 C L o wt% Ni WL us d i l o Derived from Conservation of Mass: 50 Adapted from Fig. 9.3(b), Callister 7e. ML S C C0 ML M R S C CL W R C CL 0 R S C CL Example Calculation Co = 35 wt% Ni
At T B: W T(C) Both and L S 43 35 73 wt % WL R + S 43 32 R = 27 wt% R +S Cu-Ni system 1300 L (liquid) 20 id sol CLCo us (solid) + L 3 032 35 us
+ L B R S TB 1200 tie line liquid 4403 C 50 wt% Ni Equilibrium Cooling in a Cu-Ni Binary Phase diagram: Cu-Ni system. System is: --binary i.e., 2 components: Cu and Ni. --isomorphous i.e., complete solubility of one component in another; phase field extends from 0 to 100 wt% Ni. Consider Co = 35 wt%Ni. Cored vs Equilibrium Phases
C changes as we solidify. Cu-Ni case: First to solidify has C = 46 wt% Ni. Last to solidify has C = 35 wt% Ni. Fast rate of cooling: Cored structure Slow rate of cooling: Equilibrium structure First to solidify: 46 wt% Ni Last to solidify: < 35 wt% Ni Uniform C : 35 wt% Ni Mechanical Properties: Cu-Ni System Effect of solid solution strengthening on: --Ductility (%EL,%AR) 400 TS for pure Ni 300 TS for pure Cu 200 0 20 40 60 80 100 Cu Ni Composition, wt% Ni --Peak as a function of Co Elongation (%EL) Tensile Strength (MPa)
--Tensile strength (TS) 60 %EL for pure Cu %EL for pure Ni 50 40 30 20 0 20 Cu 40 60 80 100 Ni Composition, wt% Ni --Min. as a function of Co Consider Pb-Sn System Simple solution system (e.g., Pb-Sn solution) Crystal Structure electroneg r (nm) Pb FCC 1.8
0.175 Sn Tetragonal 1.8 0.151 13.7% W. Hume Rothery Rules: Atomic size is within 15% Same electronegativity Do not have same crystal structure Will have some miscibility, but will not have complete miscibility Binary-Eutectic System Liquidus From Greek eut ktos, easily melted Solidus Eutectic Point Solvus Eutectic Reaction: L(CE) (CE) + (CE) Microstructural Evolution in Eutectic T(C) Consider (1): Co < 2 wt% Sn Result: --at extreme ends --polycrystal of grains
i.e., only one solid phase. L: Co wt% Sn 400 L L 300 200 L + (Pb-Sn System) : Co wt% Sn TE 100 + 0 Co 10 20 30 Co , wt% Sn 2 (room T solubility limit)
Microstructural Evolution in Eutectic Consider (2): 2 wt% Sn < Co < 18.3 wt% Sn L: Co wt% Sn T(C) 400 L L 300 Result: Initially liquid + then alone finally two phases polycrystal fine -phase inclusions L + 200 : Co wt% Sn TE 100 + 0 10
20 Pb-Sn system 30 Co Co , wt% 2 (sol. limit at T room ) 18.3 (sol. limit at TE) Sn Microstructural Evolution in Eutectic Consider (3): Co = CE Result: Eutectic microstructure (lamellar structure) --alternating layers (lamellae) of and crystals. T(C) L: Co wt% Sn 300 Pb-Sn system L+ 200 L 100 0 L
183C TE 20 18.3 40 Micrograph of Pb-Sn eutectic microstructure : 97.8 wt% Sn : 18.3 wt%Sn 60 CE 61.9 80 100 97.8 C, wt% Sn 160 m Lamellar Eutectic Structure Microstructural Evolution in Eutectic Consider (4): 18.3 wt% Sn < Co < 61.9 wt% Sn T(C) L: Co wt% Sn 300 L
L Pb-Sn system L L+ 200 R TE S R 100 L+ S + primary eutectic eutectic 0 20 18.3
40 60 61.9 80 Co, wt% Sn 100 97.8 Result: crystals and a eutectic microstructure Hypoeutectic vs Hypereutectic 300 L T(C) 200 L+ L+ TE + 100 0 20 40
hypoeutectic: Co = 50 wt% Sn 60 80 100 eutectic 61.9 (Pb-Sn System) Co, wt% Sn hypereutectic: (illustration only) eutectic: Co = 61.9 wt% Sn 175 m 160 m eutectic micro-constituent
Reversal with "QP" Deposit. If you choose to set the Q on the Tax Detail screen manually and set the client preference to 'N' all accounts with a Q will be divided regardless of qualifications met when BMI 1228 runs...
Times New Roman Wingdings Symbol Arial Default Design Microsoft Excel Worksheet Mills on Suburbanization Explanations of Suburbanization Looking at Decentralization. What do we want? Functions We expect 1. Why? Regressions What does this mean?
Self-Awareness in the Work World: 4 Primary Attributes (Traits) Knows own personality, strengths, and areas of knowledge, skills, or habits that can be improved. Looks for work opportunities that would be a good match for personal strengths and skills.
Arial Calibri Tahoma Wingdings Bauhaus 93 Baskerville Old Face Berlin Sans FB Demi Algerian Dutch801 Rm BT Times New Roman Book Antiqua Arial Narrow Verdana Office Theme 1_Office Theme 2_Office Theme Visio INTRODUCTION ECONOMICS THEORY Slide 2 Slide 3 Slide...
Scaling is the mathematical process which provides a basis for comparing performance in Stage 2 SACE subjects which have different objectives, content and assessment practices. They come from the assessment results used by the SACE Board - the final subject...