ELEC-D Principles of materials science- Thermodynamics and diffusion. ELEC-D Principles of materials science
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1 Thu 3.3 Mon 7.3 ELEC-D Principles of materials science- Thermodynamics and diffusion Thu 10.3 Exercise 5 Mon 14.3 Thu 17.3 Exercise 6 Mon 21.3 Thermodynamics - Principles (T,xi) equilibrium diagrams I (T,xi) equilibrium diagrams II Diffusion Thu 24.3 Exercise 7 Mon 28.3 Easter holiday Thu 31.3 Exercise 8 Mon 4.4 Thu 7.4 Course recap, Metals and ceramics in electronics and biomedical applications Intermediate examination II Thermodynamics Learning outcomes ELEC-D Principles of materials science The interpretation of thermodynamic stability diagrams Especially T-x i diagrams i.e. binary phase diagrams Global equilibria Local equilibria AuSn+Au 5 Sn T=250 C T=25 C Au80Sn20 wt-% Au71Sn29 at-% T=400 C 1
2 ELEC-D Principles of materials science Thermodynamics Learning outcomes The interpretation of thermodynamic stability diagrams Especially T-x i diagrams i.e. binary phase diagrams Global equilibria Local equilibria T=60 C T=60 C, t=1h Au80Sn20 wt-% Au71Sn29 at-% ELEC-D Principles of materials science Thermodynamics - Learning outcomes Terms and definitions System, state, phase Entropy, Enthalpy, Free energy (G, F) Laws of thermodynamics (0 th, 1 st, 2 nd, 3 rd ) Basic thermodynamic equations Chemical potential Equilibria g-x i diagrams => T-x i diagrams 2
3 Multimaterial structures - energetics: G = G(T, p, x i ) [J/mol] i) System and it s state: In thermodynamics the system is the macroscopic volume in space that is clearly defined and the surrounding space (which is interacting with the system) is defined as it s environment.. There is a physical boundary over which the system can be in a) mechanical, b) thermal, or c) chemical interactiom with the environment. System is open, when it can exchange both energy and matter with the environment. Other systems are closed (dm = 0) ja isolated system (dq = dw = dm = 0). Open system The ocean or cup of coffee are examples of an open system 3
4 Multimaterial structures - energetics: G = G(T, p, x i ) [J/mol] Other systems are closed (dm = 0) ja isolated system (dq = dw = dm = 0). i) System (material) is either homogeneous, i.e. all properties are identical through the material or heterogeneous. ii) Homogeneous system is phase (), which can be either pure material i.e. component (element or chemical compound) or solution, which contains one or more components [matrix and alloying elements]. Pure Gold Ice NaCl -brass (CuZn alloy) 4
5 iii) Heterogeneous system is composed of multiple homogeneous systems i.e. phase mixture +β-brass (Cu60Zn40 wt-% alloy) Bronze (Cu80Sn20 wt-% alloy) Ice water iv) Defining the state of the system = defining the variables, which are properties of the system like T, p and composition (x i ). Consept of solubility Why materials (components) tend to dissolve into each other? Answer: Due to increase in entropy. The increase in entropy drives different components to mix in all weight/atom ratios (like gases) but the mutual interactions (attractive or repulsive) limit the mutual I.e.: Solubility (to solid or liquid) depends on the nature and extent of mutual interactions (L ij ), which are dependent on both temperature and pressure (N.B. quite often pressure is constant, 1 atm!). 5
6 The solubility is defined (atom fraction, weigh fraction, ) at constant temperature (and pressure) by the maximum entropy i.e. minimum Gibbs free energy of the system: G G min e x i Entropy law (Boltzmann S = klnw) follows from the experimental fact, that matter is composed of ever moving and interacting particles (electrons, atoms, molecules, ) which continuously tend to mix both matter and energy. Therefore, entropy is defined as the mixed-upness, (Gibbs) or disorder of matter and energy (Planck). According to Guggenheimin entropy is the measure of spread in energy and matter or lack of information (Shannon). 6
7 Laws of thermodynamics (i) Zeroth law: The definition of temperature (ii) First law: Internal energy E Isolated system in equilibrium can be defined with E being constant (de = Q + W) Only the change (de) can be inspected, not the absolute value. Laws of thermodynamics 7
8 (iii) Second law: Entropy In isolated system, entropy can never decrease i.e. d i S 0, (reversible or irreversible process) In real (irreversible) processes the entropy of isolated system always increase and achieves it s maximum value at equilibrium. Laws of thermodynamics Laws of thermodynamics (iv) Third law: The entropy of the system has such a property that S S 0, when T 0, in which S 0 is constant independent of the structure of the system. At temperature T = 0 K all pure, defect free crystalline elements have same entropy value S 0, which is agreed as zero. 8
9 Gibbs free energy and thermodynamic properties 1. Gibbs free energy is an extensive (i.e. dependent on the amount of material) variable, which is a function of independent variables (T, p ja n i ). Gibbs free energy can be divided into two parts: the enthalpy and the entropy of the system: G = (E + pv TS) = H - TS 2. If G of the system is known all the other thermodynamic properties can be calculated from it. 3. Gibbs free energy and useful work w : -(G) p,t w' = i n i + A + zfu +..., in which i n i is chemical work, is interfacial work and zfu is electrochemical work Useful equations G H TS Equilibrium ds C T p G 0 dt S H T S G H (1 ) T sp, p, s) S( T, p, s) ( T2 1 T 2 T 1 C p ( s) dt T T sp dh C pdt H ( T, p, s ) H ( T 2 1, p, s ) C dt p T T 2 1 9
10 Gibbs free energy and chemical potential If the Gibbsin energy, G, of the phase is known as a function of p, T ja n i (tor µ i ) all thermodynamic properties of the phase can be presented with G and its derivatives! Since G = G(p,T,n i ), dg = (G/T) p,nj dt + (G/p) T,nj dp + (G/n i ) T,p,nj dn i By combining the 1 st and 2 nd laws G = - SdT + Vdp + µ i dn i, it follows (G/T) p,nj =-S, (G/p) T,nj =V (G/n i ) T,p,nj =µ i which is the chemical potential (partial molar Gibbs free energy) of component i Partial molar properties- volume Mixtures of water (A) and methanol (B) at 25 C and 1bar (a) Mean molar volume as a function of x B. The dashed line is the tangent to the curve at x B = (b) Molar volume of mixing as a function of x B. The dashed line is the tangent to the curve at x B = (c) Partial molar volumes as functions of x B. The points at x B =0.307 (open circles) are obtained from the intercepts of the dashed line in either (a) or (b). 10
11 Gibbs free energy and chemical potential of solution phase Solution phase ( =..,l)containssolvent (i.e. matrix) and solute atoms, which can either replace the solvent atoms or locate in interstitials (octahedral or tetrahedral) between solvent atoms in crystalline materials. When we have one mole of, g = x i i = x io i + RTx i lna i, where i o i + RTlna i, = o i +RTlnx i +RTln i, Function o i (T,p) is the standard chemical potential of pure component i (crystal structure,and i = f(t,p,x i ) is the activity coefficient g=x io i +RTx i lnx i + RTx i ln i Equilibria between phases I Complete global equilibria: * ci 0 (a i 0) * T0 * Level rule can be applied on the whole system II Stabile local equilibria at interfaces: * Phase diagram is valid only on interfaces III Metastable local equilibria at interfaces: * Stabile phase does not nucleate or grow quickly enough * Metastable phase diagram depicts the equilibria at interfaces 11
12 Phase diagram Pb +L Sn + L Pb + Sn Gibbs free energy of mixing g = x io i + RTx i lnx i + RTx i ln i = 0 T = constant Crystal structure o A o B Standard state 12
13 Gibbs free energy of mixing g = x io i + RTx i lnx i + RTx i ln i 0 L AB > 0 Ideal solution o o g x x RT x ln x L x x A A B B i i i AB A B 13
14 Molar Gibbs free energy of phase mixture: g(t, x i, p = 1) (g,x i )-diagram s basic property: Phase mixture (A,B) + (A,B), which temperature is T, pressurep(= 1) and composition x Bo, the Gibbs energy g lies on the line (common tangent) defined by the solution phases g (x B )andg (x B )" g g g o B A g B = 0 A A x B y x B o Atomiosuus B y x B B Gibbs energy and phase diagram dg SdT Gibbs energy [J/mol] Vdp T=100 0 C g g liq g Atom-fraction of Bi idn i i Effect of temperature! Temperature ( o C) Gibbs energy [J/mol] 232 Sn o G Sn liq G Sn (E) A A Liq B E Atom-fraction of Bi g g B G g liq m E 271 T TFB Bi o G Bi = 0 liq G Bi (E) G Bi Sn liq G Bi (A/B) Atom-fraction of Bi 14
15 Gibbs energy and phase diagrams Gibbs energy and phase diagrams 15
16 Gibbs energy and phase diagrams What is the difference to the previous eutectic system? Gibbs energy and phase diagrams 16
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