Huajing Song (Wilson) Supervisor: Dr. JJ Hoyt

Transcription

1 Huajing Song (Wilson) Supervisor: Dr. JJ Hoyt

2 Introduction Previous works Theory Approach Results and discussion Conclusion & future research 1

3 1184 K 1665 K α Υ δ Ferrite Austenite Melting point 1809 K BCC FCC BCC Figure [1] 2

4 In all the experiments, solid drag is added to slow down the interface movement. The effect of the interstitial content should be studied and one should in general use the lowest possible impurity contents -----M. Hillert (2006) How much does the drag slow down movement? What happen in a pure iron case? At present, simulation by means of molecular dynamics (MD) seems to be one of the best methods available to acquire information in these transformation for the pure iron case. 3

5 Adding solid drag (C, Ni, Mn) Fe alloy M=0.035exp( /RT) m*mol/js [1] Speich and Szirmae (1969) Fe-C M = 0.058exp( /RT) m*mol/js [2] GP. Krielaart and J. Sietsma (1997) Fe-Ni M = 2.4exp( /RT) m*mol/js [3] Wits et al. (2000) Activation energy was identified around 140 kj/mol. Can t use the pure iron as the experimental element. 4

6 M. Hillert (2006) New information on the mobility of a/c interfaces obtained from the massive transformation. (+):Υ-α in Fe, Liu et al. [4],( ):Υ-α in Fe Co and ( ):Υ-α in Fe Mn, Liu et al. [5], ( ):Υ-α in Fe Ni, ( ):α-υ in Fe Ni,( ):α-υ in Fe Mn and ( ):Υ-α in Fe Mn [6]. Mobility around 10-6 to 10-9 m * mol/j-s 5

7 Not full periodic boundary. At least one pair of the boundaries which is perpendicular to the interface is not periodic. Concluded that there was not transformation in the full periodic boundary case (NOT TRUE). Figure C. Bos[2] and J. Sietsma (2006) 6

8 C. Bos and J. Sietsma (2006) 7

9 A kind of composition-invariant nucleation-andgrowth formation of a solid phase from another solid phase M. Hillert Basic model of interface movement: v = M 0 exp( Q RT ) G (1) v interface velocity Q- activation energy R gas constant T temperature G - free energy different between fcc & bcc - Pre-exponential factor of mobility M 0 8

10 The whole exponential term can consider as the mobility of the interface. M = M 0 exp( Q RT ) (2) M = v G (3) In order to calculate the mobility M, the interface velocity v and the driving force ΔG have to be identified 9

11 Equation (4) was developed to calculate the moving speed of solid-liquid interface in the solidification of Ni. v = 1 2a H m /Ω de dt (4) a area of the interface (Å 2 ) ΔH m latent heat or Potential Energy different between BCC & FCC (ev/atom) Ω -the volume per atom de/dt Slope of total Potential Energy Vs time for the whole system. 10

12 G T = T H s (T) H L m (T) dt (5) T T 2 Graph [1] 11

13 Using the embedded atom method (EAM) iron alloy potential. Under this potential, the pure iron has the melting point 2358K for BCC phase and 2236K for FCC phase. 5 temperatures are choose (600, 800, 1000, 1200 and 1400 K) to do the simulation. The free energy different between the Austenite (FCC) and Ferrite (BCC) is the main driving force for the transformation. 12

14 Y x BCC fcc Lattice parameter: Å fcc(111) // bcc(110); fcc[1-1 0] // bcc[-1 1 0] At T=800K Spacing(x, y, z): Å, Å, Å No. unit cell(x,y,z): 60, 15, 15 Box size(x,y,z): Å, 85.89Å, 78.31Å Ave spacing in x: Å Interface area: Å 2 Stress FCC Stress BCC bcc Lattice parameter: Å Spacing(x, y, z): Å, Å, Å No. unit cell(x,y,z): 8, 21, 27 Box size(x,y,z): 32.68Å, 85.79Å, 78.00Å Ave spacing in x: å Interface area: Å 2 The different between the interface area around 0.89% Figure [3] 13

15 J.M. Rigsbee and H.I. Aaronson (1978) fcc(111) // bcc(110); fcc[1-1 0] // bcc[-1 1 0] C. Bos and J. Sietsma (2006) 14

16 5.26 rotation about plane normal: (110) BCC // (111) FCC and [001] BCC // [1-1 0] FCC X Y Z Fix the Z-axis and rotate the Coordinate on the X-Y plane for 5.26 Cross product the rotation matrix Y [3 3-7] FCC X [7 7 6] Figure [4] 15

17 J.M. Rigsbee and H.I. Aaronson (1978) Figure [5] First of all, this structure has the most matching atoms in each ledge. It makes a good initial state for activating the transformation 16

18 BCC nucleus FCC BCC FCC BCC BCC FCC Figure [6] Similar to the solidification of silicon, austenite ferrite transformation is under a layer-by-layer process. 17

19 BCC FCC BCC 800K Figure [7] 18

20 19

21 800K de dt Graph [2] Using the 800K system as a example. de/dt is the slope of the best fit line. y = x

22 600K 1000K 1200K 1400K Graph [3] T (K) M (m*mol/j-s) 3.089E E E E E-03 v (m/s) ΔG (ev/atom) Table [1] 21

23 y= x Base on the equation [3] and the mobility data in five different temperature. The activation energy is identified as Q=15.96kJ/mole and M 0 =7.19E-03 m*mole/j-s 22

24 Around 800K Our results (simulation) Sietsma s results (simulation) Experimental results (M. Hillert 2006) Velocity (m/s) Mobility (m*mol/j-s) Activation energy (kj/mol) N/A The activation energies obtained from atomistic simulations were invariably significantly smaller than those found in experiments (even in high purity materials) [7 10]. 23

25 Base on FCC(111)//BCC(110) grain boundary. Change the rotation degree to increase the ledge length. Create a vacancy or adding impurity. compare the mobility and activated energy with the model without the vacancy or adding. And check the position of the vacancy or impurity atoms to see if it diffuse during the transformation or be frozen in its original position. Using new orientation to set up the simulation box. 24

26 A method for study pure iron austenite ferrite transformation has been demonstrated. A steps ledge structure is required to keep the transformation automatically and continuously. The velocity and mobility are obtained (600 to 1400K) Activation energy is calculated base on this result to be 16kJ/mole Further research start to focus on creating vacancy and adding impure atoms (solid drag) to the system 25

27 1. Speich GR, Szirmae A. Trans Metall Soc, AIME 245:1063 (1969). 2. Krielaart GP, Sietsma J, van der Zwaag S. Mater Sci Eng A 237:216, (1997). 3. Wits JJ, Kop TA, van Leeuwen Y, Seitsma J, van der Zwaag S. Mater Sci Eng A 283:234, (2000). 4. M. Hillert, L. Höglund. Scripta Mater v54, (2006) 5. SM. Foiles, J.J. Hoyt, Acta Materialia, v54,n1, (2006). 6. C. Bos, J. Sietsma, B. J. Thijsse. Phys Rev B, 73, (2006). 26

28 7. Scho nfelder B, Wolf D, Phillpot SR, Furtkamp M. Interface Sci v5, 245. (1997). 8. Zhang H, Mendelev MI, Srolovitz DJ. Acta Mater n52, (2004) 9. Mendelev MI, Srolovitz DJ, Han S, Ackland GJ, Morris JR. Phys Rev B (2004) 10. SM. Foiles, J.J. Hoyt, Acta Materialia, v54,n1, (2006). 11. Zhang H, Mendelev MI, Srolovitz DJ. Acta Mater v52, 2569 (2004). 27

29 Take the logarithm of the mobility function, got a linear function of 1/T Vs logm. The slope of the function is the Q/R, and the Y-intercept is the logm 0. (3) 28

30 In a simulation, the potential energy of an atom, i, is given by E = F ( ρ (r )) + 1 φ ( r ), i α α ij 2 αβ ij i j i j where r ij is the distance between atoms i and j, φ αβ is a pair-wise potential function, ρ α is the contribution to the electron charge density from atom j at the location of atom i, and F is an embedding function that represents the energy required to place atom i of type α into the electron cloud. 29