材料物理导论-Chapter 4

1、1. Diffusion phenomenon、essence、 study method 2. Diffusion condition for solid metals lHigh Temperature (T) : High temperature leads to a large diffusion activation energy to overcome the binding of the around atoms. Fe: diffusion temperature: 500oC; C diffusion temperature in Fe: 100oClLong time (t

2、):the longest diffusion distance of atoms in crystal lattice very time 0.30.5 nm，1 nm distance require about one hundred million of transportation lAtoms Soluted in metals:a solid solubility for the atoms in the metals required for diffusion lDiffusion driven force:the directional diffusion need a d

3、iffusion driven force3. Diffusion types lSelfdiffusion：diffusion in pure matter, no concentration change, independent on d/dx, relative with thermal vibration, only in pure metals and uniform solid solutions e.g. crystal grain growth in pure metals；grain growth in uniform solutioslmutual/chemical di

4、ffusion：concentration change, mutual diffusion depends on the different atom solution, the diffusion between the different atoms e.g. chemical heat treatment; materials composition uniformity lDownhill diffusion：diffusion along concentration decrease, concentration uniformity e.g. uniformity anneali

5、ng, chemical heat treatment lUphill diffusion:diffusion along concentration increase, concentration change along two directions decided by chemical grads： a) Effect of elasticity stress. uphill diffusion decrease the energy induced by elasticity deformation.。 b) Absorb at interface. Decrease the fre

6、e energy of the whole system c) Different chemical potential. Dominating factor d) Forming compouds. e.g. Fe3C e) Special condition. e.g. eletric field, magnetic field。 e.g. eutectic transformation for liquid alloy; new phase formation and growth in solution solidscrystal lattice invariable, no new

7、phaseelement concentration of the metals exceeding the solubility limit, new phase formation. An interface occur between the new phase and the mother phase, the new phase may be interphase or solid solution. e.g. the new phase for the iron nitrified at 520C can be identified for the FeN phase diagra

8、ms, different WN,different new phase. phase：N in Fe form interstitial solid solution WN RCu, shift only110，due to the different diffusion velocity for the two atoms lDefining：the symbol surface shift induced by different diffusion flux of the two elements due the different diffusion velocity of the

9、atoms。Brass：W(Zn) = 30%l Discussion：diffusion in substitutional solid solute determined by Kirkendall and Darken effects excursion velocity V =(D2-D1)dx2/dx =(D1-D2)dx1/dx Darken suppose the nonintervention between the constituent element diffusion and the vacancy concentration invariable, the first

10、-law for diffusion is obtained： J1 = Dd1/dx J2 = Dd2/dx Here DD1x2D2x1 -diffusion coefficient x1、x2 are the mol fraction for element 1 and 2. Replacing the diffusion coefficient by the mutual diffusion coefficients, and the directions for the two diffusion flux are different. l Application：measure t

11、he mutual diffusion coefficient at a given temperature and the marked shift velocity v and d/dx，the diffusion coefficient for the two types of atoms D1 and D2 can be determined Darken calculated the diffusion coefficient of the marked place of the brass and copper, DCu=2.2x10-13 m2/S, DZn=5.1x10-13

12、m2/S,DZn/DCu= 2.3 fromDD1x2D2X1，when x2 near 0，X near 1， mutual diffusion coefficient: D D2. Only in subtlety substitutional solid solute, mutual diffusion coefficient similar to intrinsic diffusion coefficient, their difference increase with the increase of the concentration of solute atoms.4.2 The

13、rmodynamics analysis of diffusion Diffusion driven force is chemical potential grads / x, which can be obtained as following： F= - i/ x l i(chemical potential)：the free energy for very i atom （i G/ ni),ni is the atom number for element il minus present the driven force along the decrease of the chem

14、ical potential Migration rate（B)：atomic diffusion velocity under unit driven force D = kTBi1( lnri / lnxi)（ri-activity coefficient ，xi= i/p） l for the solid solution with ri=1 or ri=const,D=kTBi，that is NernstEinstein, the diffusion velocity for different elements only determined by migration rate l

15、 the conclusion is also right for the practical solid solution：DBi,1( lnri / lnxi) is thermodynamic factor 1( lnri/ lnxi)0，D0 downhill diffusion 1( lnri / lnxi)0, D0 uphill diffusion Uphill diffusion happens under the following conditions:l Elasticity stress effect. elasticity stress gradient leads

16、to that atoms with larger radius move to the lattice elongate part and those with smaller radius move to the pressed part, resulting in the nonuniformity. l Absorbed in interface. energy of the interface higher than that of the crystal interior , atoms at interface arrange anomaly，if solute atoms at

17、 interface can reduce the system energy, the atoms diffuse to interface preferentially leading to a high concentration at the interfacel The diffusion direction can also be affected by a large electric field or a temperature gradient 4.3 Atomic theory for diffusionMechanism of diffusion:lExchange me

18、chanism: diffusion by change position of the neighbouring atoms. change ways：direct exchange and cyclic exchange lInterstitial mechanism： a) interstitial atoms move from one place to another b) Mechanism for interstitial diffusion ： interstitialcy mechanism crowdion configuration Diffusion mechanism

19、 in crystals1-direct exchange, 2-cyclic exchange, 3- vacancy, 4-interstice, 5-fill, 6-pilelvacancy mechanism ：the opposite migration of the diffusion atoms and vacancies leads to Kirkendall effect(Zn atomic diffusion speed larger than Cu atoms require copper to produce vacancy). the most popular dif

20、fusion mechanism lInterface diffusion and surface diffusion Interior diffusion Dl interface diffusion Db surface diffusion DslDislocation diffusion：diffusion through dislocation, also named short circuit diffusion In short, diffusions in metal or alloy mainly depend on crystal defectslJump frequency

21、 that at the temperature of T the numbers of the molecule (jump A critical energy barrier has to been overcame for the atom diffusion, G =G2G1，only the atoms with a free energy larger than the barrier can carry out the jump migration It can be concluded probability)n/N can be deduced ： n/N = exp（G/k

22、T） For interstitial solid solution, diffusion of the solute atoms by jumping from one interstitial position to the neighboring oneRelations between the free energy and position of atoms In a crystal containing n atoms, in dt time the atoms jump m times, the jumping times at unit time of every atom (

23、jump frequency)为：为： = m/ndt The figure presents two parallel neighboring crystal faces with interstitial atoms, the probability P for the atoms jumping from face 1 to face 2 and from face 2 to face 1 D = Pd Pd determined from the solid solution structure， is relative with the character of the materi

24、al and temperature, e.g., C in -Fe at 1198 K, =1.7x109/s, at room temperature =2.1x10-9/s。 The above equation can also be used to substitutional solid solutionInterstitial atom jump of adjacent crystal planelDiffusion coefficient For the interstitial diffusion, substitutional diffusion and self-diff

25、usion in pure metals, D can be deduced ： Do: diffusion coefficient constant and relative withS Q: activation energy of diffusion per mol atoms. For interstitial diffusion ,Q is the migration energy U for atom jump；for substitutional diffusion and self-diffusion, Q includes the U and the formation en

26、ergy of vacancy Uv。 R: gas constant, R =8.31J/（mol.K）；）；T: absolute temperature（K） For different diffusion mechanism, the equations are the same, but the D and Q values are different4.4 Diffusion activation energy Different diffusion mechanism with different diffusion activation energy which can be

27、obtained by following： lnD = lnDoQ/(RT) The relation of lnD and 1/T can be determined by experiment.IflnD1/T have a line relation, lnDo can be determined by extrapolation, the slope of the line isQ/R， Q=Rtg Do has no relation with Q and T4.5 Effect factors of diffusion The diffusion speed depends on

28、 D, while D is relative with T and Q： D = Doexp（Q / RT） So the diffusion can be tailored by T or the factors who can change the Temperature(T)：T increases, D increases, D and T have index relations For example: C diffusion in -Fe，at 927，D = 1.6110-11 m2/s，at 1027，D = 4.7410-11 m2/s。When temperature

29、increase from 927 to 1027，diffusion coefficient increase by 3 times，Therefore, for the manufacture the processes controlled by diffusion are affected by temperature Types of solid solution： Q for the formation of the interstitial solid solution is much smaller than that for the substitutional solid

30、solution, diffusion much quicker For example：C inFe, at 1200K Dc=1.6110-11 m2/s Ni inFe, at 1200K DNi=2.0810-17 m2/s For different metal matrix, D0 and Q are differentRules:-Fe (melting at 1809K)、V(melting at 2108K)、Nb(melting at 2793K)、W( melting at 3653K), the diffusion activation energy Q are 103

31、、114、159、169(kJ/mol). For different structures of one metal, the diffusion coefficients are different, the higher the density, the smaller the D；the stronger the binding force between the atoms, the larger the Q, the symmetry of the crystal also have effects on D. For example:900the diffusion coeffi

32、cient of C in-Fe(bcc) and -Fe(fcc) are：1.610-10 m2/s and 8.710-12 m2/s demonstrating that C diffusion in-Fe easer than in-Fe at the same temperature. ：the larger the lattice distortion induced by the diffusion element, the smaller the diffusion activation energy, the larger the diffusion coefficient

33、 and the easier the diffusion For example: the diffusion of the interstitial atom of N、C、B in-Fe (see following table). The point, line and face defects all have effects on diffusion coefficient. The increase of the defect density leads to the increase of the diffusion coefficient. Diffusion ways：in

34、terior diffusion（Ql、Dl）、）、interface diffusion（Qb、Db）、）、surface diffusion（Qs、Ds）。）。 Rules lnD1/T exhibits the line relation (see the following figure) It can be seen：(1) the coefficient of the single crystals shows interior diffusion; the D for polycrystals demonstrates the interior and interface dif

35、fusion (2) For Ag, at more than 700 C, DsingleDpoly；lower than 700C， Dsingle Dpoly 。(3) anisotropy for interface diffusion (4) interface diffusion much quicker than interior diffusion (5) surface diffusion quicker than interface diffusion. Crystal defects play the role of quick routeway, that is lD

36、is relative with the character of constituent element. The self-diffusion Q for different metals is relative with the atomic binding force of the lattice, e.g., high Tm, large Q lD is relative with solute concentrationlThe third constituent element(or impurity) can also affect the diffusion of duality alloy, but very complex Stress:a) stress field in the alloy provides the driven force F,the larger the stress, the higher F V=BF b) the elastic stress gradient induced by stress can promot