MSE 360 Exam 1 Spring 011 105 Points otal Name(print) ID number No notes, books, or information stored in calculator memories may be used. he NCSU academic integrity policies apply to this exam. As such, by taking this exam you are implicitly agreeing with the statement: I have neither given nor received unauthorized aid on this test. All work must be written on these pages and turned in. o receive full or partial credit on numerical problems, you must show your calculations in step-by-step fashion. Units must be shown when applicable and plots must have labeled axes. Be sure that you read and answer all parts of each question. Constants, equations, and data are given at the end of the exam. 1-13.) (3 Points Each-39 Points otal) Multiple Choice 1. See the figure on the right, which represents the Gibbs free energy along a reaction path for a single phase to transform from state 1 to state. he reaction kinetics can be expressed by A) rate C exp(-δg 1 /R), B) rate C exp(-δg /R). With increasing temperature and constant pressure, the Gibbs free energy of a single phase A) increase, B) decrease 3. he internal energy of a system consists of and 4. A regular solution will likely form an ordered atomic structure if: d.) Ω 0 b.) Ω > 0 c.) Ω < 0 5. From the Gibbs phase rule for a -component system, at constant pressure, within a -phase region of the equilibrium phase diagram: a.) and composition can be independently varied b.) choosing a fixes the equilibrium compositions c.) neither nor composition can be varied d.) phases cannot be in equilibrium 6. Concerning the vacancy concentration, and the equilibrium concentration of a dilute solute atom B where ΔH mix is >>0: a.) for both cases, entropy favors mixing, while enthalpy discourages mixing b.) for both cases, the equilibrium concentration is dependent c.) for both cases, enthalpy favors mixing d.) both a) and b) e.) both b) and c) 7 With increasing melting point, the activation enthalpy for diffusion generally becomes A. higher B. lower C. same 8. he Gibbs phase rule is written as P+F C+. his is valid under the following conditions A) Constant pressure 1
B) Constant temperature C) Binary alloy system D) Single element system E) Varying temperature and pressure F) Constant temprature and pressure 9. Which of the following is not an example of a high-diffusivity pathway: a.) Diffusion along Grain Boundaries b.) Diffusion along Dislocation Defects c.) Diffusion along Vacancy Defects d.) Diffusion along Free-Surfaces e.) All are High Diffusivity Pathways 10. Comparing the substitutional diffusion relative to the vacancy diffusion in a single element system: a.) Both have the same magnitude of diffusion flux b.) Both have the same diffusion coefficient c.) Both a) and b) 11. he mechanism of diffusion for a dilute solute atom of small atomic radius compared to the host material would be best described by: a.) Substitutional diffusion b.) Interstitial diffusion c.) Vacancy diffusion d.) all of the above 1 During a non-steady state diffusion, A. the concentration behavior does not change with time B. the concentration behavior changes with time C. the diffusion process can be described by Fick s Second Law D. both B and C 13. he driving force of the diffusion process is A. the gradient in Gibbs free energy B. the gradient in chemical composition C. the gradient in stress field D. the gradient in electrical field 14 (10 points): Estimate the change in equilibrium melting temperature of Cu caused by a change of pressure of 50 MPa. he molar volume of Cu is 8.0x10-6 m 3 for the liquid and 7.6x10-6 m 3 for the solid phase. ΔH m 13.05 kj/mol, m 1085 C.
15 (6 points): Assuming B atom has a solubility of 0.1% at 400 C, and 0.8% at 900 C. What is its solubility at 700 C? 16 (1 points): See the Ag-Cu phase diagram. Draw schematically the Gibbs free energy curves of all phases at 900 C, 779 C, and 700 C. 3
17. (15 Points) Regular Solution Problem. a.) Write here, and explain the general meaning of (one sentence), the equation for the ideal entropy of mixing for a solution comprised of N A atoms of type A, and N B atoms of type B. b.) Calculate the ΔS mix (with units) for an ideal solution at 800K with X B 0.5. c.) Assume the enthalpy of mixing term exactly offsets the entropy of mixing term (in the expression for ΔG mix ) at a composition of X B 0.5 and temperature of 800K. Calculate the for ΔG mix at 500K. 18 (10 points). A 3 mm long Cu rod is welded to a 7 mm long Zn rod and the rod is heated to 400 C to allow diffusion to proceed. Draw schematically the phase/composition along the rod during the diffusion. 4
19 (5 points) he diffusion coefficient can be written as DD 0 exp(-q/r). What is the meaning of Q in terms of thermodynamics? Hint: ΔG ΔH - ΔS. 0 (8 points). For the carbonization of steel at 800 C, it takes hours to reach a C concentration of 0.4% at a depth of 100 µm. Assuming that the diffusion coefficient does not change with composition. If the carbonization time is increased to 6 hours, Calculate the depth at which the C concentration reaches 0.4%. Answer Key for 1-13: 1A, B, 3 Potential energy & kinetics energy, 4C, 5B, 6D, 7A, 8E, 9C, 10A, 11B, 1D, 13A 5
Constants and Equations N A 6.0 x 10 3 mole -1 k (or R) 8.6 x 10-5 ev/atom-k (or 8.31 J/mol K) K C +73 10 9 nm 1 m 10 cm 1 m P + F C + P + F C + 1 G H S HU+PV du ds - PdV G X aga + X bgb ΔGmix H C p " C p d S d 0 dp d ΔH V 0 eq eqδ Δ ΔH m S m L m Δ G LΔ m ω conf ( N a N a + N b )!! N! b 1 "S mix #R(X a ln X a + X b ln X b ) Δ ε ε AB ( ε AA ε BB ) Ω zδε N a H mix ΩX a X b Δ "G mix "H mix # "S mix γvm γvm γvm Δ Gγ ΔPVm X r X exp X (1 + ) r Rr Rr ΔGv Qv nv exp N exp X e B Ae " Q R k k J number area time dc d C D dt dx dc J D dx x C(x,t) C s " #C erf (" Dt ) $ C C + " 0 sin #x ' % &! ( ) * exp +t, l [ ] where: τ π D Qd ΔS D D0 exp( ) D 1 d d 0 zν exp k 6 K 6
7