Role of Thermodynamics in Ceramics Is to indicate Whether a system is stable What conditions (T, P) will cause it to change
Thermodynamics and Kinetics Can a reaction occur, given enough time? (The driving force for change) THERMODYNAMICS Can a reaction occur at a reasonable rate? (The speed of change) KINETICS
Laws of Thermodynamics Zeroth law, stating that thermodynamic equilibrium is the equivalence relation. If two thermodynamic systems are separately in thermal equilibrium with a third, they are also in thermal equilibrium with each other. If two thermodynamic systems are separately in thermal equilibrium with a third, they are also in thermal equilibrium with each other. First law, about the conservation of energy The change in the internal energy of a closed thermodynamic system is equal to the sum of the amount of heat energy supplied to the system and the work done on the system. Second law, about entropy The total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value. Third law, about absolute zero temperature As a system asymptotically approaches absolute zero of temperature all processes virtually cease and the entropy of the system asymptotically approaches a minimum value; also stated as: the entropy of all systems and of all states of a system is zero at absolute zero or equivalently it is impossible to reach the absolute zero of temperature by any finite number of processes.
1st Law of Thermodynamics For a closed system du = q dw = TdS - PdV - Heat is the transfer of energy between a hotter object and a colder object: energy in transit. - Energy is the capacity to do work or transfer heat. Internal Energy (U), the sum of all microscopic forms of energy of a system -The internal energy is the total energy of a system; the sum of the kinetic (translation, rotation, vibration of atoms) and potential (attraction or repulsion of atoms in crystals) energies of all components making up the system. - Cannot measure absolute internal energy but can only a change in the energy. - When a system changes from one state to another, its internal energy changes,
2nd Law of Thermodynamics A reaction is spontaneous (product-favored) if DS for the universe is positive. DS universe = DS system + DS surroundings DS universe > 0 for product-favored process Spontaneous changes tend to smooth out differences in temperature, pressure, density, and chemical potential that may exist in a system, and entropy is thus a measure of how far this smoothing-out process has progressed.
Concept of Entropy, S If System s Energy Useful Energy + Useless Energy Then, S Useless Energy When a system s energy is defined as the sum of its useful energy, (e.g., that is used to push a piston), and its useless energy, i.e., that energy which cannot be used for external work, then entropy may be visualized as the scrap or useless energy whose energetic prevalence over the total energy of a system is directly proportional to the absolute temperature of the considered system (Note TS in Gibbs free energy relation). Entropy is a function of a quantity of heat which shows the possibility of conversion of that heat into work. The increase in entropy is small when heat is added at high temperature and greater when heat is added at lower temperature. Thus for maximum entropy there is minimum availability for conversion into work.
Macroscopic Definition of Entropy (Class. Thermodynamics) The entropy of the thermodynamics system is a measure of how far the equalization has progressed. When the universe has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. dq DS T
Microscopic Definition of Entropy (Stat. Thermodynamics) The Concept of Entropy (S) Entropy refers to the state of order. Thermodynamics - Free Energy A change in order is a change in the number of ways of arranging the particles, and it is a key factor in determining the direction of a spontaneous process. more order less order solid liquid gas more order crystal + liquid more order crystal + crystal less order ions in solution less order gases + ions in solution 3
Thermodynamics - Free Energy 1877 Ludwig Boltzman S = k ln W where S is entropy, W is the number of ways of arranging the components of a system, and k is a constant (the Boltzman constant), R/N A (R = universal gas constant, N A = Avogadro s number. A system with relatively few equivalent ways to arrange its components (smaller W) has relatively less disorder and low entropy. A system with many equivalent ways to arrange its components (larger W) has relatively more disorder and high entropy. DS universe = DS system + DS surroundings > 0 This is the second law of thermodynamics. 6
Thermodynamics - Free Energy Figure 20.2 The number of ways to arrange a deck of playing cards 4
Calculating DS for a Reaction DS o = S o (products) - S o (reactants) 2 H 2 (g) + O 2 (g) 2 H 2 O(liq) DS o = 2 S o (H 2 O) - [2 S o (H 2 ) + S o (O 2 )] DS o = 2 mol (69.9 J/K mol) [2 mol (130.7 J/K mol) + 1 mol (205.3 J/K mol)] DS o = -326.9 J/K There is a decrease in S because 3 mol of gas give 2 mol of liquid.
2nd Law of Thermodynamics 2 H 2 (g) + O 2 (g) 2 H 2 O(liq) DS o system = -326.9 J/K DS o surroundings = q surroundings T = -DH system T Can calc. that DH o rxn = DH o system = -571.7 kj D S o surroundings = - (-571.7 kj)(1000 J/kJ) 298.15 K = +1917 J/K
2nd Law of Thermodynamics 2 H 2 (g) + O 2 (g) 2 H 2 O(liq) DS o system = -326.9 J/K DS o surroundings = +1917 J/K DS o universe = +1590. J/K The entropy of the universe is increasing, so the reaction is product-favored.
Thermodynamics Will the rearrangement of a system decrease its energy? If yes ( G<0), system is favored to react a product-favored system. Most product-favored reactions are exothermic. Often referred to as spontaneous reactions. Spontaneous does not imply anything about time for reaction to occur. G = H - T S
Product-Favored Reactions In general, product-favored reactions are exothermic. (Negative DH) In general, reactant-favored reactions are endothermic. (Positive DH)
Thermodynamics - Free Energy DG = DH - TDS 18
GIBB'S FREE ENERGY AND THE NATURE OF CHEMICAL REACTIONS 1. Introduction In a chemical reaction, some bonds are broken in the reactants in order to form bonds in the products and the equilibrium of reaction depends on the concentrations of reactants and products and the difference in energy between them. 1) Concentrations - The initial rate of product formation depends on the initial concentrations of reactants and products. - As product concentration increases, the rate of the reverse reaction increases. - When the rate of forward and reverse reactions become equal, the concentrations of reactants and products are constant, and the mixture is in chemical equilibrium. 2) Energy difference - Since breaking bonds requires energy (endothermic) and forming bonds releases energy (exothermic), the net energy of a chemical reaction will depend on the sum of energy absorbed and generated. - Eventually, the difference in energy between the reactants and products decreases as equilibrium is achieved.
2. Importance - We can estimate the direction and nature of a chemical reaction by quantifying the free energy of reactants and products. - We can understand how changes in energy are related to achieving chemical equilibrium. 3. Questions - How can we measure the energy of a chemical reaction? - How can we predict the direction of a chemical reaction? - How do properties of the reactants and products affect the net result of a chemical reaction? 4. Methods A measure of free energy, the potential energy of a reaction, can be used to predict properties of chemical reactions. The free energy (G), which depends on the concentration of reactant and product, of a system can be defined as G = H TS where H is the heat energy of the system, T is the temperature, and S is entropy. Heat energy (H) is a measure of the chemical bond energy and entropy (S) is a measure of the disorder in a system.
Every chemical reaction results in a change in free energy which we can measure as DG = G p - G r = H p - H r - T(S p - S r ) = DH TDS Thus, the free energy of a chemical reaction depends on the heat energy and entropy of the reactants and products. If the energy of the reactants is higher than the energy of the products, G r > G p, the reaction will occur spontaneously. In such a case, DG < 0, and the free energy of the system decreases with the reaction. In the opposite case, DG > 0, and energy is required for the reaction to occur. As the concentration of reactants decreases as products are formed in the chemical reaction, the difference in free energy decreases until the free energy of the products and reactants are equal. Therefore at chemical equilibrium, DG = 0. Free energy also depends on the concentration of reactants and products. This is because the movement of molecules from a more to less concentrated state can perform work.
When the concentrations of reactants and products are variable, DG is where R is gas constant, and C p, C r are the initial concentrations of the products and reactants and DG o is the standard free energy of a reaction when temperature is 298 K, pressure is 1 atm, ph is 7.0, and initial concentrations of reactants and products are equal. Ex 1.) Plot of DG vs C p /C r For chemical reaction of photosynthesis which has DG o = + 686 kcal/mol for 6CO 2 + 6H 2 O glucose + 6O 2 and the reverse reaction has DG o = - 686 kcal/mol. C 6 H 12 O 6
1) Photosynthesis For C p /C r << 1, DG is negative so the reaction progresses spontaneously. As the amount of product increases, however, DG quickly becomes positive and this reaction is not spontaneous, and energy is required for the chemical reaction to occur. 2) Reverse reaction For C p /C r << 1, the reaction progresses spontaneously and the reaction approaches a chemical equilibrium where DG = 0, as the concentration of product increases. Ex 2.) Effect of DG o on K eq 1) For a reaction of DG o < 0 Majority of reactant is converted to product spontaneously (large K eq ). 2) For a reaction of DG o > 0 Very little of the reactant may be converted to product without the input of additional energy into the system.
제 4 장상평형과반응 1. 열역학자연의변화를에너지변환의과정으로보는학문. 2. 열역학제 1 법칙어떠한자연변화에있어외부와계의에너지총합은일정하게보존된다. - 에너지보존의법칙. 1) 내부에너지, U 계가 q 만큼의열을받아 w 만큼의일을했을때계의전체에너지또는내부에너지의변화 du 는 du dq dw (1) - 계로에너지가유입시 : + (endothermic) - 계로부터에너지가방출시 : - (exothermic)
일 (w) 은압력 (P) 을가했을때체적 (V) 의변화이며 dw 의일이외부에행해졌을때 식 (1) 은 dw PdV du dq PdV (2) (3) 식 (3) 이열역학제 1 법칙의표현이다. 2) Heat Capacity, C 어떤물질이 dq 만큼의열을받아 dt 만큼온도가올라갈때그비를 heat capacity(c) 라고한다. dq C (4) dt dq 는상태함수 (state function) 가아니라서그값은반응경로에따라달라진다. 3) 엔탈피, H 에너지양 (energy content) 을엔탈피 (enthalpy, H) 라고하며반응경로에따라달라지는 dq 를경로에무관한열량의변화 (dh) 로설명한다. H U PV (5) dh du PdV VdP 식 (3) 으로부터 dh dq PdV PdV VdP (6) (7)
일정한압력하에서 dp=0 이므로 dh=dq p 즉, 엔탈피는일정한압력하에서물질이흡수하거나방출하는열을의미한다. 식 (4) 에서일정압력하의 heat capacity (Cp) 식 (8) 로부터 dh Cp dt P (8) T T 298 H H CpdT 298 (9) H 298 는 298K 의표준상태 (standard state) 에서의 formation enthalpy 로원소상태에서는 0 이다. 예제 ) 298-932K 에서 Al 의 Cp 는 Cp = 20.7 + 0.0124 T 이고, 298-1800K 에서 Al 2 O 3 의 Cp 는 Cp = 106.6 + 0.0178T 2,850,000T -2 이며원소로부터알루미나의 298K 에서 formation enthalpy 는 1675.7 kj/mol 이다. 298K 와 900K 에서 Al 과 Al 2 O 3 의엔탈피량을계산하라. 풀이 ) 1 원소 Al 의 298K 에서엔탈피량은정의에의해 0 이다. 900K 에서는
H 900 900 0 (20.7 0.0124 T) dt 298 16.93 kj / mol 2 298K 에서 Al 2 O 3 의엔탈피량은 formation enthlpy 로 1675.7kJ/mol 이다. 900K 에서는 900 900 2 H 1675.7 (106.6 0.0178T 2,850,000 T ) dt 298 1605.0 kj / mol HW 19) 1600K 에서 Al 2 O 3 가갖고있는열량을계산하라 3. 열역학제 2 법칙제 1 법칙에의해일어나는자연변화의변화방향을결정하는것으로계가일정한온도 T 를유지하도록계에 dq 의열량이가역적으로가해지면엔트로피 (entropy, S) 가증가하며증가의크기 ds 는 ds 비가역적일때 dq rev T (10) ds dq rev T (11) 엔트로피의개념도입을통해 자발적으로일어나는변화는계의자유에너지를감소시키는방향이다 라는것이열역학제 2 법칙이다. 예제 ) 금속이나세라믹스의용융현상
4. 열역학의기초방정식 식 (3) 과 (10) 으로부터 du TdS PdV (12) 보조함수로 H U PV A U TS A: Hermholt free energy G H TS G : Gibbs free energy 5. 자유에너지및평형평형상태를정의하는열역학적함수는엔탈피나엔트로피가아니라자유에너지함수인식 (15) 의 Gibbs 자유에너지로, 어떤반응이나상변태에서일어나는자유에너지의변화는 평형은 DG DH TDS DG 일때일어난다. (13) (14) (15) (16) 0 (17) 평형을식 (15) 로부터표현하면 dg dh TdS SdT (18)
식 (13) 으로부터 dh du PdV VdP (19) 식 (12) 와 (19) 로부터식 (17) 은 dg TdS VdP TdS SdT VdP SdT (20) 평형에서압력과온도의변화가없으므로 dp=0, dt=0 따라서평형조건은 dg 0 (21)
6. 상률 (Phase rule) 평형상태에서존재하는상, 성분, 자유도 ( 압력, 온도, 조성 ) 의수사이의관계식 F C 2 P (22) F : degree of freedom ( 평형상태에있는계를정확하게정의하는데필요한변수의수 ) C : components P : phases 상태도는평형상태를나타내므로상률은상태도를설명하는데유용하다. 7. 1 성분계 (One-component systems) 1 성분계에서 F 는조성에따라 2(C), 1(B), 또는 0(A) 를갖는다.( 그림 4.4 참조 )
1) Polymorphism ( 동질이상 ) i) Reconstructive transformation - 결합의붕괴와재배치에의해일어남. - 핵생성 (nucleation) 과성장 (growth) 에의해진행 - 상전이속도는느림 - 석영의상전이를예로들수있음. ii) Displacive transformation - 결합의붕괴없이원자면의이동에의해일어남 - 반응은신속히일어남. - 상전이된미세구조는일반적으로심한 twin ( 쌍점 ) 을보임. - 2 상에관련된 enthalpy 보다는열적 entropy 의역할이큼 - 일반적으로고온상의부피가저온상보다큼 ( 예외 : ZrO 2 ). 큰부피의구조는높은열적 entropy 를가짐.
Ex) 1 ZrO 2 단사정 (monoclinic) 정방정 (tetragonal) 입방정 (cubic) 액상 (liquid) 1170 C 2370 C 2680 C 2 BaTiO 3 능면정 (rhombohedral) 사방정 (orthorhombic) tetragonal cubic -90 C 0 C 130 C 0-130 C 에서 BaTiO 3 는 Ti 의위치가중심에서벗어난변형된 perovskite 구조를가짐으로 capacitor 로응용됨. 3 SiO 2
8. 2 성분계 (Binary Systems) 세라믹스나금속에서상평형시대부분압력은 1 기압에고정되므로 F 는조성에따라 2, 1, 0 을갖는다. 1) 2 성분계내고체고용도 (solid solubility) 의종류 i) 전율고용도 (complete solid solubility) ii) 중간화합물 (intermediate phase) 의생성이없는부분고체고용도 iii) 중간화합물이생성된부분고체고용도 2) Solid Solution 의종류 i) Substitutional Solid Solutions - 2 상의양이온이용매양이온또는 2 상의음이온이용매음이온을치환하는경우 NiO O Ni MgO x o x Mg ii) Interstitial Solid Solutions - 2 상이온이용매결정의격자간 (interstitial) 이온자리에고용됨. - 2 상이온의크기가작아야하고용매결정구조의격자간이온자리의크기가넓어야함. ex) Rock salt 구조보다는 fluorite 구조에서 (octahedral site) 쉽게일어남. YF Y F 2F 3 2 CaF 2 2 3 g ' x ca i F 2ZrO 2Zr 3O O YO g x " Y o i HW 20) 1) (Mg 0.5 Ni 0.5 )O 고용체의단위격자형태를그려라 2) CaF 2 에 YF 3 가 0.25mol 첨가된고용체의단위격자형태를그려라
3) 전율고용형상태도 전율고용을위해두가지성분은다음과같은조건을만족해야한다. i) Structure type : 두성분의결정구조가동일해야함. SiO 2 와 TiO 2 는전율고용을할수없음. ii) Valency factor : 두성분양이온의산화수가동일해야함. 그렇지않을경우용매고체내부에전하중립을유지하기위한결함이생성됨. iii) Size factor : 이온반경차이는 15% 이하야하며이보다클경우 strain energy 가커져전율고용을방해함. iv) Chemical affinity : 두성분의 chemical affinity 가상대성분에대해커서는안됨. 클경우중간화합물을형성하여계의자유에너지를낮출수있음.
Lever Rule mol 비와중량비 - 몰비를중량비로전환 30 mol% AO 와 70 mol% BO 를섞었을때 AO 와 BO 의중량비는 AO 와 BO 의분자량이각각 m A, m B 일때다음과같다. 0.3mAO wt% AO x 100 0.3m 0.7m AO wt% BO 100 wt% AO - 중량비를몰비로전환 40 wt% AO 와 60 wt% BO 를각각의몰비로표시하면 BO 40/ mao mol% AO x 100 40/ m 60/ m AO mol% BO 100 mol% AO HW 21) 3 mol% Y 2 O 3 가첨가된 ZrO 2 고용체 1kg 을제조하기위해 Y 2 O 3 와 ZrO 2 는각각얼마씩을섞어야하나? HW 22) 그림 4.8 에서공정 (eutectic) 조성을 mol% 로표시하라. BO
4) 중간화합물이없는 2 성분계상태도 i) 공정반응 (eutectic reaction) L ( s) ( s) ii) 포정반응 (peritectic reaction) L ( s) ( s)
5) 중간화합물이있는 2성분계상태도두성분 AO 와 BO 의 chemical affinity 가큰경우다음반응을통해 A x B y O 2 화합물이생성된다. xao ybo A B O 1/ x 1/ y x y 2
이것은화합물생성에관련된자유에너지변화가 AO 와 BO 두성분의고용체를만들기위한단순혼합에관련된자유에너지변화보다크기때문이다. 중간화합물은두성분에대한고용도가없는경우와있는경우두가지이다. i) Congruently melting intermediate phase 화합물이용융될때중간화합물의조성에변화가없는경우 ex) Na O 2SiO Na O 2 SiO liq. 2 2 2 2 Na O SiO Na O SiO liq. 2 2 2 2 MgO Al O spinel liq. 2 3 ii) Incongruently melting intermediate phase 중간화합물이용융될때먼저액상과또다른조성의고상으로분리되는경우 ex) 2SiO 3 Al O( mullite) Al O liq.(60 mol% SiO 40 mol% Al O ) 2 2 2 3 2 2 3 2 Na O SiO Na O liq. 2 2 2
Attitude The longer I live, the more I realize the impact of attitude on life. Attitude, to me, is more important than facts. It is more important than the past, the education, the money, than circumstances, than failure, than successes, than what other people think or say or do. It is more important than appearance, giftedness or skill. It will make or break a company... a church... a home. The remarkable thing is we have a choice everyday regarding the attitude we will embrace for that day. We cannot change our past... we cannot change the fact that people will act in a certain way. We cannot change the inevitable. The only thing we can do is play on the one string we have, and that is our attitude. I am convinced that life is 10% what happens to me and 90% of how I react to it. And so it is with you... we are in charge of our Attitudes. - Chuck Swindoll -