University of Southern California Dissertations and Theses

The Application Of Electrochemistry Of Solids

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The Application Of Electrochemistry Of Solids

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Content THE APPLICATION OP ELECTROCHEMISTRY OP SOLIDS by Daniel Ta-nien Yuan A Dissertation Presented to the FACULTY OP THE GRADUATE SCHOOL UNIVERSITY OP SOUTHERN CALIFORNIA In partial Fulfillment of the Requirement for the Degree DOCTOR OP PHILOSOPHY (Materials Science) January, 1971 72-3810 YUAN, Daniel Ta-nien, 1940- THE APPLICATION OF ELECTROCHEMISTRY' OF SOLIDS. University of Southern California, Ph.D;, 1971 Materials Science University Microfilms, A XEROX Company, Ann Arbor, Michigan THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED U N IV E R S IT Y O F S O U T H E R N C A L IF O R N IA TH E GRADUATE SCHO OL U N IV E R S ITY PARK LOS ANGELES, C A L IF O R N IA 9 0 0 0 7 This dissertation, written by Yuan................. under the direction of / z . J k § L Dissertation Com mittee, and approved by all its members, has been presented to and accepted by The Gradu ate School, in partial fulfillment of require ments of the degree of D O C T O R O F P H I L O S O P H Y .... f j Dean Date.J.^PP*PJ...l^?.l... DISSERTATION C O M M ITTEE PLEASE NOTE: Some Pages have in d is tin c t p rin t. Filmed as received. UNIVERSITY MICROFILMS ACKNOWLEDGMENT Thanks are due to the guidance of Professor E. A. Kroger, without him this thesis would not have materialized. ii ABSTRACT The Application of Electrochemistry of Solids The object of this work was to investigate various applications of electrochemical cells with solid electrolytes. Investigation shows that electrolytic cells based on stabilized zirconia as solid electrolyte may be used to remove oxygen from stationary or streaming gas. The minimum pressures that, can be accurately measured are limited by the onset of electronic con duction in the electrolyte. In buffered gases, the lowest pressure that can be attained is limited either by the capacity of the buffer or by the decomposition kinetics of the buffer molecules. Typical values of the oxygen pressures that can be reached when using commercial high-density sintered stabilized zirconia • Z Q q tubes as an electrolyte, are 1 x 10 atm at 530 C, 3 x 10-5° atm at 700°0, and 3 x atm at 800°C. Electromotive force measurements in a cell Ra/ Pyrex/ Ra,Sn, where Pyrex serves as a solid elec trolyte, lead to values for the sodium activity down to x.T_ = 1 x 10“3. Excess functions are inter preted on the "basis of the zero-order theory and the result is used to estimate the entropy of NaSn(s). Pyrex cells W,Na/Pyrex/pt,02; Pt,02/Pyrex/pt,02; and W,Na/Pyrex/c,S2 are found to give emf’s following, the Nernst formula. The emf is attributed to the formation of Na20 or Ua2S in the glass near the glass-gas interface. After strong polarization in either direction, the emf returns to the value for the unperturbed system. Energies and entropies of solution of Na20 in Pyrex are shown to be close to the corresponding values for the formation of NaSiO^. Thus, Pyrex cells can be used as 02 or S2 pressure gauges. Emf measurements on cells Cd/cdS-crystal/s2, where CdS serves as solid electrolyte, show that CdS is an electronic conductor in the temperature range of 500-700°C. TABLE OE CONTENTS Page j i ACKNOWLEDGEMENTS ±i | ABSTRACT iii | LIST OE TABLES vii j LIST OE ILLUSTRATIONS viii : CHAPTER | I. INTRODUCTION................................ 1 j II. THEORY....................................... 9 j 2.1 Imperfections in Crystal 2.2 Lattice Defects and Diffusion 2.3 Conductivity in Ionic Crystals 2.4 Electrochemical Cells with Solid Elec trolytes 2.5 Application of Solid Cells in Determining Thermodynamical Parameters 2.6 Solid State Batteries III. STABILIZED ZIRCONIA AS AN OXYGEN PUMP 25 3.1 Exp erimental 3.2 Results 3.3 Discussion IV. THE SODIUM ACTIVITY IN LIQUID SODIUM-TIN ALLOYS.................... 62 4.1 Experimental 4.2 results and Discussion V. AN ELECTROCHEMICAL OXYGEN AND SULFUR VAPOR GAUGE WITH PYREX AS SOLID ELECTROLYTE............................. 73 5.1 Experimental 5.2 Results and Discussion VI. CONDUCTION IN CdS................. 99 6.1 Experimental 6.2 Results and Discussion I " VII. CONCLUSION............................. 108 LIST OP REFERENCES ................................ 110 vi. LIST OP TABLES Table Page 1. Effects of Estimated Oxygen Leaks . 53 2. Partial Pressures of H^O and Hg Giving 10“58 atm 02 at 530°0 .................... 56 3. Values of -Log f^a at Various Concentrations and Temperatures gg 4. Thermochemical Data for NaSn .............. vii LIST OS’ ILLUSTRATIONS Figure . 1• Electrode Assembly for Oxygen Removal and Measurement of Oxygen Pressure .... 2. Experimental Results for Em ............ 3. Current Voltage Sequences of the 'Pumping Cell .... ........ 4. The Time lt__ ) Needed by the Measuring J7Q C • Cell to Revert Back to Its Pre-pumping emf ...... ...................... . tP0 Vin as £'unc' tion °£ Temperature .... 6. Em as Function of EpUffip ................. 7. J-E Characteristic for the Narrow Tube 8. Limitations to Em ........................ 9. t. as a Function of Log p„ .......... i u2 10. E„, as a Function of Log p~ ............. 2 11. Relation Between -Log. x^a and -Log a^a ... 12. The Na Electrode and the Procedure to Make It ............................. 13. Emf as f(.pn ) for a Cell Na/ Pyrex/ 09 .... 2. 14. Variation of the Emf with Time of an Oxygen Cell after Polarization .... 15. Emf as f(T) for an Oxygen Cell .... . 16. Emf of the Pt, 02/ Pyrex/ Pt, 02 Cell ... 17. Emf as f(T) for the Sodium-Sulfur Cell •• 18. Partial Pressure of S2 as f(T.) .......... 19. Pq Isobars of the Sodium-Sulfur Cell .... viii Page 30: 33 37 38: 43 45: 47 55 58. 59 66 78 83 86 87 91 92 94- -95 Figure Page 20. Emf Measurements of the Sodium/ Pyrex. / H^S Cell .see.s. 97 21. Apparatus Used in CdS Conduction Experiments ..... . '102 22. Emf Measured Against aT of the Qlwo Electrodes ....... 194 ix CHAPTER I Introduction Imperfections play an-important role in determining . the properties of solids. Practically all physical properties depend directly or indirectly on the pre sence of imperfections. One of the properties which depend essentially on the imperfections is the move ment of ions in solids(1; and all of them play a part in or can be used as a tool for the study of physical or chemical reactions. This work primarily deals with the movement of ions in solids for the transformation of electrical and chemical energy in electrochemical cells and for the determination of thermodynamic parameters by electrochemical methods. Historically, electrochemical cells with solid electrolytes were first used by Haber^2). He used glass and porcelain membranes in cells based on the reactions H2(g) + £ 02 t* H20(g) (.1-1) and 00(g) + 02 # C02(g;> (1-2). 1 later, Reinhold (3) studied thermocells as an outgrowth of his work on chemical equilibria between solid salts, likewise, Wagner used solid electrolytes in galvanic cells in his study on the conductance of solids (4-). In most of the earlier work, silver halides were used as solid electrolytes because of their relatively large con ductivities. The cell combination Ag; / Agl / I2 was first studied and reported to have an emf of 0.7 volts by Reinhold (5). However, because of difficulties associated o with operation of an Ig-electrode above 145 C which is the transition point above which Agl has a high ionic conductivity, this work was redirected towards AggS. AggS o is a relatively good conductor above 179 0, but at this temperature a large portion of the conductivity is elec tronic. Thus, although the free energy change corresponds to an emf of 0.2 volts, it is found (6) that an Ag / . ! o Ag2S / S2 cell above 179 C gave an emf of only 2-10 mv. The full 0.2 volt is obtained by inserting a layer of the nearly purely ionic conductor Agl (5) to suppress the electronic conduction. This is done in such a way that the Agl is the actual electrolyte of the cell. Other halides have also been used as solid electrolytes. Van der G-rinten (7) developed the cell Ag / AgBr / OuBr2 + C and Ag, / AgCl / CuCl2 + C. Ag2HgI^ was found to have a high ionic conduction at relatively low temperature (8j, and was used in the cell Ag / Ag2EgI4 / C, (9). The system Ta / Ta20^ / Mn02 has been used as a solid electrolyte capacitor (.1°)« When an anodic po tential is applied to a tantalum point contact to Mn02, the tantalum can be electroehemically oxidized by Mn02 in a solid state process which is analogous to the aqueous anodic oxidation process in a battery. Smyth (.11) found it exhibited an open-circuit voltage of only 1,mv o at 350 C. Although the emf is so small, yet it serves as an important 'healing’ mechanism in the Ta / Ta20^ / Mh02 solid electrolyte capacitor. For all the cells described so far, the voltages attained were under 1 volt. G-utmann et al.( . 12j reported a cell in which the cathode is an electronic charge— transfer complex of nitrogen or iodine; the anode is magnesium: Mg / organic complex / Pt. The voltage-pro— > ducing electrochemical reaction is the formation of the corresponding metal salt. This salt ( Mg^N2, Mgl^) is formed between the Mg and the complex and acts as the electrolyte of the cell. Open circuit voltages of 1.5-2.5 volt and current densities of up to 25 ma / cm were found at room temperature; the cell can be operated up o to at least 130 C. The exchange and self-diffusion of the sodium ion in ( 3 -Alumina with the composition Ha20-11A120^ (,13) .. 4 has heen reported (14). This compound was used as electrolyte in the cell Ua(l)//3 -AlgO^/ S(l) (15). This cell has an open circuit potential of 2.08 volt at 300°C until a composition corresponding to Na2S^ is reached. It then drops almost linearly to 1.76 volt at a compo sition corresponding to WagS^* Hever(l6; devised a solid-state electrochemical cell by using a ceramic ion conducting electrode, 1.3 0*2 Li20'10 A120^, and ceramic electrodes 1.3 K20*0.2 l\fa20*10( Fe^gTiQ -jO^) v/hich are mixed ionic and electronic conductors. The charge and dis charge of the cell occurs by oxidation-reduction pro cesses in the electrode ceramics without chemical phase change and the reaction of the cell to an electric current is therefore capacitive. Electrochemical measurements with galvanic cells using solid electrolytes makes possible the direct determination of the free energy of formation of chemical compounds at elevated temperature with a higher degree of accuracy. The pioneering work by Kiukkola and Wagner (17) has demonstrated the usefulness of this method by the 'open cell stacked pellet' technique. In this method the indicating, electrode consisted of a pelletized and sintered mixture of the metal-metal oxide system under investigation separated from the reference electrode by a pellet of the zirconia-calcia diaphragm. The reference 5 electrode was another metal-metal oxide system of known free energy of formation. These cells are usually ope rated under flow of inert gas, using the same gas for both electrode compartments. Rezukhina et al, (18) ope rated their cells under vacuum. Rapp (19) improved the technique by fabricating the electrolyte in an R-shape tube and fitting the sintered metal-metal oxide cylinders into each other. R.oeder and Smeltzer.. (20) mounted their cell independently from the fux-nace. assembly with the help of a compression spring inside a Pyrex cap. Steele and Alcock (21) developed a gas concentration cell in which the two electrode compartments are separated by pressing one side of the electrolyte against the open polished end of an alumina tube. Thus different oxygen activities may be maintained on two sides. Oharette and Flangas (22) used a ’closed cell’ designed to ope rate under truly equilibrium oxygen pressure condition to measure their data. The free energy of formation * ( } . - of many compounds have been determined with the aid of cells based on stabilized zirconia as solid electrolyte, e.g. those of NiO, CoO, Cu20 (17), TJyT3i.j Q2+x (23); RbO (18); Mo02 (19,24); FegTiO^, PegSiO^, FeTiO^, Co2T104, CoTiO^, Ri2SiO^ (,25); Fe^O^ (20), W02 (.24); • PbO (22,26), Ta205 (27); MnOx, FeOx, Ou^O (22) etc.. Other solid electrolytes were also used to determine the free energy of formation of chemical com- pounds. Thus Gal^ was used to measure the aG-'s of CaSiO^, CaTiO^, Ca4-Ti010(28j and ThE, 301^(29); SrE2 was used in measuring the a G»s of SrTiO^ and SrTi^010; MgE2 for MgAl20^(25.); Agl for AggS and Ag2Se(17); PbCl2 for PbS(17j; NaX for UI3(30); Th02-Y2C> 5 for Sn02(31) and Th02-Ia2C> 3 for r-Al205(32) etc. V/hen an electrochemical cell with MX as the solid electrolyte based on a reaction in which X is one of the reactants, then the emf measured is related to the ionic transference number t^ of the electrolyte and the chemicaL potential of X by the relation: Here E is the Earaday, n is the number of equivalents per mole, i.e. the number of charges that is trans ported by the ions when one mole of reaction product is formed5 I and II are the two electrodes of the cell; ti is the local transference number, is the transference number averaged over the cell. Thus if ag of a compound is known then by eq.(l-3) measurement of E gives ^ of that compound. Also, ^ may be found by using a concentration cell. Suppose we have a con centration cell of MX /(Px )jj > now part of II the mechanism of the reaction is the diffusion of X from a high activity to a low activity. In this case j i AG = rt m CpX2)i/(pX2;ii (1-4) I i 3nd E = ^i ST ln ^VX2)T ^ VX2^TL (1-5) | The transport numbers of many compounds have been determined in this manner, e.g. MgO(33j; BeO, GaO, Sr0(34); BaTi03(35j; Sr02(36;j RH4C1(.37); AgCl(38); Th02 and Th02-Y2C>3 mixture(39-42); Zr02(.Ca0)(42); Be0(43)j Nb203(44) and ice(,45). It is found from these experiments, that in general the transport num- 1 ber depends on the ambient as well as on temperature. The work described here, deals with several aspects of solid state electrochemistry. In Chapter II, the basic concepts of solid electrochemistry related to this work are presented. Chapter III deals with the ionic conduction in stabilized zirconia and the use of it as an oxygen pump. Chapters IV and V describe experiments in which pyrex is used as a sodium ion-specific membrane. Chapter IV describes the determination of the sodium activity in melted sodium-tin alloys as a function of temperature and composition. Chapter V deals with the measurement: of oxygen and sulfur activities. Chapter VI describe an experiment designed to determine the small ionic conductance in semiconducting CdS and Ga-doped CdS. In Chapter VII the various results obtained are summarized. CHAPTER II THEORY II.1 Imperfections in Crystals. Crystals may contain various types of lattice defects. Y/e shall mainly discuss those defects which are directly related to this work. A). .Atomic imperfections. There are three different types of atomic imperfections: a). Vacancies. Vacancies are sites in a crystal which should he occupied,:- hut which are unoccu pied ( . 46). b). Interstitials. Interstitials are atoms or ions occupying sites which in the ideal crystal should not he occupied. c). Misplaced atoms. Misplaced atoms are atoms occupying sites which in the ideal crystal are assigned to atoms of a different type. B). Electronic imperfections. In an ideal non-metallic crystal elec- | I trons are present in fully occupied states j in the valence hand. Any net movement of the electrons in an electric field is not possible! # in this case. Free electrons e' or holes h , however, may be introduced into those crystals in other ways, e.g. by the establishment of high electric field gradients near the surface; which inject or pull out electrons, or by the ; action of photons of ionizing radiations. C). Foreign imperfections. 7/hen foreign atoms represented by F are present, they tend to occupy the site occupied; by the atom to which they are closest in chemical behavior. If the number of valence electrons of F is greater than the valence electrons of the substituted atom, then F is a donor. If F has less valence electrons ; than the substituted one, then it acts as an acceptor. Imperfections will be represented by a major symbol indicating the type of imperfection considered | and a subscript indicating the site it occupies. The j entities indicated by the symbols are called 'struc- \ ture elements'. For examples, indicates a vacancy j 11 j at an A site, B- indicates an atom B: at an intersti- j tial site, and A-g indicates an atom A on a B site. ' Symbols without superscripts or with crosses as j superscripts (,e.g. B?; represent defects that are neutral relative to the ideal crystal. If the defects ■ occur in ionized form, i.e. have an effective charge relative to the ideal lattice, they are represented j by symbols like , V^' etc. for acceptors and F?, etc. for donors. Here the dashes indicate the effective negative charges on that specific defect, and the dots indicate the effective positive charges or the number of holes bound by that specific defect:. Normal lattice constituents may be represented by similar symbols as the imperfections, e.g. A^, B^ etc.(47) II.2 lattice Defects and Diffusion The existence of imperfections are found essen tial to the diffusion of atoms in solids. The most important, imperfections involved are vacancies and interstitials. ! Diffusion by a vacancy mechanism consists of ! movements of atoms from sites next to vacancies into ! these vacancies. More complicated defects such as ' vacancy pairs(,48; and vacancy-impurity atom complexes | 12 ; ! 49>> also may be involved. The mechanism of diffusion | by vacancies is well established as the dominant mechanism in fee metals and alloys, and has been | shown to be operative also in many ionic compounds j and oxides. j i Diffusion by an interstitial mechanism consists i of the passing of an ion from one interstitial site to one of the nearesx-neighbouring interstitial sites i without permanently displacing any of the matrix ions. , It is dominant in most non-metallic solids in which the diffusing interstitial does not distort the lattice too much. If the diffusing interstitial ion is almost as large as the ions on the normal lattice sites, then the distortion associated with this mechanism becomes too large, and vacancy mechanism or other diffusion mechanisms become dominant. A variant of interstitial diffusion is the so called interstitialcy mechanism of diffxision(50;, in which the diffusing ion may knock an adjacent ion from a lattice site into an intersti tial position, occupying the vacated site itself. The interstitialcy mechanism has been proved to be the I dominant diffusion mechanism for silver in AgBr: (51J* Still another variant of interstitial diffusion in volves the crowdion(52). The crowdion is a configura tion in which an extra ion is placed between two nearest neighbours of the lattice ions, thus displacing;! 13 several ions from their equilibrium positions. It resembles an edge dislocation in that its distortion is spread out along a line. It can glide in only one direction and the energy to move it is quite small. In general the movement of ions is related to the movement of point defects on a one to one basis, thus diffusion may be discussed either in terms of the ions or in terms of the imperfections. II. 3 Conductivity in Ionic Crystals The conductivity of" an ionic crystal is closely related to the diffusion coefficient D^ of mobile de fects in that compound. Diffusion is a drift resulting from the presence of a concentration gradient which introduces asymmetry in the thermal random motion of the defects. In conduction concentration gradients are usually absent; now a drift is superimposed on the random motion by an applied electric field. If the mobility of the diffusing particles is known indepen dently then the diffusion coefficient D^ and the corresponding mobility v^ are related by the Einstein relation: vt 'L . q D? “ F T ^2"1 ^r here v^ is the mobility of the imperfection i, which is related to the conductivity of that imperfection by H the equation G ~. = q.n.v. ; Z • q is the effective | charge of the imperfection, k is Boltzmann’s constant j and T is the absolute temperature. She total conduc- I tivity may contain contributions from more than one j type of imperfections, including electrons, so (T“ = 6 ~. . + ( y - n , ionic uelectronic i = 2± q ^ i (2-2 ) The concentration by one mechanism is often much in I excess of that of others, but it may happen that the contributions of various mechanisms are of the same ' order. Therefore it is necessary to determine by j additional experiments the ratio in which each me- i chanism contributes, which is called the transport number ■q = £ (2-3). II. '4 Electrochemical Cells with Solid Electrolytes If we consider a solid compound MaX^ which is present between a phase of pure M(metal) and a gaseous phase of pure X(non-metal), then the compo sitions and the activities of the components in the compound at the two boundaries are fixed but different: with each other. Lethave imperfections vjjjj', V^* ; e' and h*, with a/b = r/m, which is normally true, then v/e may express (M)co and (X)0 # in terms j of the chemical potentials of structure elements. At j the metal-compound interface I, v/e have i t I a M £ a M* + b v|* + br e1 (2-4; j so ! a-4«metal = aX < M>comp.I = + brACe'jj (2-5) | Similarly for the equilibrium compound-vapor at inter- | face II, we have i bX=bX^+auJ' + am h* (2-6) j and | b i((X)vapor = 13-^^x^comp.II | | b X(x£)i;[; + a X(vjJ' ) + am A{h* )1Z j (2-7; Thus the gradient in X(lvl) andxl(x; would lead to gra dients in -^(‘ Vjj1), M(Y^*;, M(e') andA((h*;. If we take the gradient ofM(X), then b [ ^(x^ - a w )x1} | j b [ X4(^;j_ -xl(X^;I;L] + aj\X(V^ )x _ X(v^ ! + am[^((h*;I -^(h*;IX) (2-8;.I Since 16 JX = m P + rt In a = Jl° + kT In £ vjj'] etc. (2-9) when [ J«1 and also distributed complete at random over the sites assigned to them, where the etc. are the site fraction of different species. Also, [X^] = 1 at both surfaces, so we may neglect the term and get h [M(X)1 - = kr f | a In [ 7^ ] j - a ln[v^ j + am^lnPj. - lnP^^ (2-10) If we assume Schottky equilibrium to be maintained, i. e. 0 = avjj' + bv|\ then a/KvjJ') + T^(v|' ) = 0; alsoK(h') + (e *) = 0 at each point in the layer. Therefore we may rewrite ea.(2-l0) as b [M(X)I -M(X)it1 = -kT j b ln[v^*) j . - b ln[v^*J jj- + br(ln n^ - In n^) or - dji((X) = kT d' ln[vj*] nrj (2-11) Owing to these gradients, the ions and electrons ( or holes; diffuse through the compound layer. As the concentrations and diffusion coefficients of the 17 species involved are different, so they lead to the formation of a space charge inside the crystal. The ! space charge gives rise to an electric field opposing | the separation of charges. Eventually a stationary state is reached in which the field d0/dx is just ; so that no net electric current flows. This potential j 0 is comparable to a diffusion potential in electro- I lytic solutions. The migrating species are under ! the influence of both the concentration gradient ! and the diffusion potential. According to Wagner(53) the number of particles of species i with concentration; c^ passing per second through a plane parallel to 2 the surface of the metal with an area of 1 cm would be d^i ^i " “ciBi c[x + Zi^ Hx (2-12) in which q is the elemental charge, x the ordinate perpendicular to the growing surface and Z^ the valency of the species i. is a sort of generalized mobility, related to as; Di _ Vi Bi “ Et " Z±q (2-135! and v^ being, respectively, the diffusion constant j 18 and the mobility of the species i. Thus the general form of the current equation in our case can be written as D j ~ " kT C 35^ M '+ Zq^} = - c M° + kT. ln[x] + Zq0j j = - c t + Z< 1 M ) (2-14)| i where c is the concentration of x in c.c. In order j to relate c to (.x], the site fraction, we define j a constant IP, so that c = IP (.x) (2-15;! in which IP is the total number of sites per c.c. Inserting eq.(2-15) into eq.(2-H), we have the current equation j = - j^n'Cx) cm jrryaiw + Zq d r_, .. df = _ PIP - [x] N * vx (2-16) as the general form, in which we have used eq.(2-1), the Einstein relation. The particle currents of all species then may be written in the same form, in this case we have imperfections of VjJj1, , e1 and h*, thus, iH- scvg') = - % ^ - 3 - [ tm is <2-17a> fr3(^-) = - D s ^ - 3 - TX i (2-17bJ |t 3( «’) = - De - E - +nTeil <2-17c> i r 5( h ’ ) = - “ h - a i - - p V ^ (2- i 7 d ) in which D*s and y's are the diffusion constant and the mobility of the respective species. As we know that there should be no net electric current flowing, 0(e«) + m jCvjJ') = 30i*; + r dCvJ*) (2-18) Inserting eqs.(2-17 a-d) into this expression and eli minating the D’s with the aid of eq.(2-1), we find v / h l ’J T v d n t o kl ^ dx M dx ecfx h S H = - Q. rvx[v|']+ Hiv^'j + ven + vhp _ kT ( d[VX*J dCVM J „ dn „ XT * j X~c[x " M--dx----e 33c h (2-19) in which 0" is the total conductivity of the compound. Let us introduce a transport number for each species, t _ ^ Te . t _ «>Th . t ^ e 0T~ » th UT~ » S i & ’ and rq[l£'] vY ------ • Introduction of these into eq.(2-19), gives: 20 _ k T f ^ X d l n t1 /x * ] d l n ^ ^ M j Hx ” q \r 35c ~ ra 35c " te din n . j . din n ' I . o ^5T“ + i h"tx } 12-20) Prom Schottky equilibrium and a/b = r/m, we know r dlnt,- ^ ) = -m dln[V^*] and dlnp: = - dlnn, so a 0 _ k i f ^ X %• din n\ 3 x q \ 'r~ r~^- 35E--- “ + V"35E---) _ kp [ A + din nl (n " ~q \ < ■ r * ----35c------ "Ux J t2_2l) in which we used the relationship Et^ = 1. Using again eq* (2—11 ), £ - * l + 1 # 1 ] **-**> where t^ = t^ + t^. Integration over the layer thick ness, gives *0 = 0jj_ - 0-£ = r^qjr *1 + q W ^ I I “ (2“-23) If we have two identical inert metal electrodes which transmit electronic current, only) attached to the grow ing compound at the boundaries I and II where it is in contact with the reacting elements, then potential differences arise at the contacts as a result of the equilibrium for the electron transfer between the elec trode and the compound. These so called contact poten- 21 tials can be found from the condition that in equili brium the electrochemical potential of the electrons 7j{e) in the two phases is equal: ^(e;electrode = ^compound* following lange(l54/ V. is defined by y\ =Ji + Zq$, so for electrons ^ = Jd - q0t and electrode " q^electrode = - u^e^I “ (2~24) The superscript I refers to electrode X, the subscribe I refer to the compound at the contact I. Similarily, ~ ^ (e ^ e le c tro d e " ^ e le c tr o d e ” Jn “ 4 ^ u (2 -2 5 ) S tn o e J H e )J le e t l.oae = M e ) g eoteode, s u b tr a c tio n o f eq. (2-2.5) from e q .( 2 - 2 4 ) gives T? = e ^electrode v electrode = ^ [Me)1 - JdCej^] + { . l & j j . - 0Z) (2-26;. Inserting 0ZZ - 0Z from eq. (2-25 0 into eq.(.2-2 6;, we find that the voltage difference Ee measured over a growing layer at inert electrodes is equal to Ee ( 2 " 2 '7 ) If t-^ do not vary markedly with X or JU(X), It can be replaced by its average value outside the integral, so Ee = 22 - SET ^ » n amq ^ 'II ^ ! i-.AS (2-28) I am q i If we want to work in terms of gram-molecules, a G j j becomes IT,, times larger ( }T ir being Avogadro's ! clv • cl v « I number) and eq.(2-28), may be replaced by j i I E " - \ HF (2-29) | where n = am and E is the Faraday. j II. 5 Application of Solid Cells in Determination | of Thermodynamical parameters In eq.(2-29;, if ^ = 1, then from the measured | 1 i l value E we may find the free energy of formation of j the compound involved. Also, from Maxwell's relation | we have i I ah = ag + T*S (2-30) | and (2-31) j Comparing these equations with eq.(2-29)» taking 1, we have nl?( |f)p = AS (2-32) | and a H = -nEE + nE T( §| )p (2-33) Thus from measurements of the emf of a cell at differ- 23 ! ! ent temperatures it is possible to calculate AG, aS j and AH. for the cell reaction provided = 1, II. 6 Solid State Batteries If the resistance of the cell discussed in | section II.4 can be made sufficiently low, if fur- j ther electrode effects can be eliminated and if leak- j age can be avoided, then such cells with electronic ; conductors as leads can be used as batteries. These ! ! cells have come into prominence because solid elec trolyte cells, as compared with liquid electrolyte i cells, have the advantage of simpler construction. By reducing their weight and size, batteries can be miniaturized. ; In order for a compound M„X. to be useful as cl D a suitable electrolyte for a solid state battery, it should fulfill the following requirements: a) A large decrease of the free energy, -ag, of the reaction aM + bX = ^a^b necessary f°r a high emf. b) The ionic transference number should be j much larger than the electronic transference number, j i.e. >> ^ , in which must of high absolute , value and (J^ of low absolute value. Since the emf | of the cell at zero current is » this condition i is necessary for a high short long shelf life ( . low leakage conditions). 24 circuit current and a under open circuit CHAPTER III Stabilized Zirconia as an Oxygen Pump Stabilized zirconia of tbe composition ZrQ g^- ^a0o15®1.85 crystallizes in the CaPg type structure i 4*2 4 - 4 . with the Oa and Zr ^ occupying the metal sites and | oxygen occupying the non-metal sites. The presence i of 15i » Ca gives rise to 7.5° j o vacant oxygen ion sites. (55>56) Electrical conduction in stabilized zirconia at high temperatures in air or oxygen is primarily due to the migration of oxygen ions through the | movement of doubly charged oxygen vacancies(55»57). At lower oxygen pressures electronic conduction sets in(58,59)» The value of the oxygen pressure at which t^, the ionic transference number, = 0.5 is a function of temperature(60) and varies from sample to sample, possibly as a result of the presence of donor impuri ties in different concentrations(60,6l). Stabilized zirconia can be used as a solid electrolyte in a galvanic cell with platinum contacts» I Such cells, when operated with different oxygen pres sures at two sides of the solid electrolyte and in 'the range of t^ = 1, can be used as a fuel cell(62). 25 26 : i Suppose we have (pA )T at one side and (pA at i ^2 X U2 XX i the other side of the electrolyte, then the voltage j measured across the electrolyte would he ! j •prn . j E = " W ln ^P02 ^I ^ ^p02 ^ n (5 -1 ) I On the other hand, if v/e operate with a known j oxygen pressure at one side and an unknown one at the other, then by using eq.(3-1), this cell can be used j to measure the unknown oxygen pressure(58). Similar : cells can be used to measure gas equilibrium constants or free energy of formation of oxides(63). in the range where stabilized zirconia is an I ionic conductor, the passing of current through the electrolyte would transfer oxygen from the cathode side to the anode side# As in the cathode the reaction would be & 02(I) + + 2 e o£ (3-2) ; and in the anode side °0 ~ 2 e' Y0 + * o2(IJ) (3-3) ; Thus the resultant of the above reactions is the transfer of oxygen from one side to the other. This has been used to adjust the stoichiometric composition of uranium oxides(64,65). It has also been used to ; pump oxygen gas from the cathode side to the anode i side, thus reducing the oxygen pressure at the cathode j 27 ] side in a known way. In experiments carried out by j i Heyne(66j the oxygen is removed from a closed system, i It has been indicated, however, that the same prin- ; ciple can be used to remove oxygen from streaming j i gas in an open system(67). Strickler etal. (68), ; recognizing the dependence of the ionic current on j | the activity of oxygen gas at the cathode, used this j dependence to determine t^ , but did not remove oxygen i j by passing current. j j It is the object of the work reported in this chapter to investigate the effectiveness of stabilized 1 zirconia as an oxygen pump. As we shall see, it is possible to reach oxygen pressures as low as 10”^® atm ; by pumping on a gas originally with a composition of 1 atm Ng + 10 atm 02 at a flow rate of 4.6 cnr/sec at 530°C. j III. 1 Experimental Ihe zirconia tubes used in the experiments were high density sintered calcia-stabilized zirconia, obtained from the Zirconium Company of America. It has the composition (Zr02)Q g(CaQ)0 ^ and x-ray analy- I sis shows it to consist of two phases, the major phase ; being calcia-stabilized cubic zirconia, the minor I one being monoclinic zirconia. One of the tubes has an inner diameter of 5mm, the other of 12mm, both j having a wall thickness of 0.5mm* Inner and outer electrodes were made with the I aid of Hanovia platinum paste. This is a fluxless I mixture of 0.1X platinum powder and resinous material suspended in an organic solvent; it is marketed in the United States hy Engelhard Industries, East Newark,! New Jersey. The inner electrode(I) is a continuous j porous layer, a few microns thick, extending over a length of about 22 cm. It was made by pulling a cotton : wool plug, wetted with Pt paste, through the tube, followed by heating to 500°C in air. It is found that three times of the wetting and drying are required in order to make a good continuous layer. This process * of heating burns off all the organic resinous material ; and leaves only platinum metal particles on the zir conia surface. This inner electrode is grounded. The outer electrode consists of three sections. One (II), the 'pump’ section, made again with the aid of Pt paste in the manner described above, is 14 cm long. The others (.III, IV) are about 5 cm each in length j and consists platinum foil and 0.05 in. platinum i wire wound around it, placed, respectively, 2 and j 6 cm away from the edge of II. Figure 1 shows the ! electrode arrangement. An additional Pt-Rh wire welded to the Pt contact wire at contact III forms a thermo- I couple which makes it possible to measure the tempera- | 29 1 ture. The whole assembly is placed in an electric I furnace, the temperature of which is kept constant within - 2°C. Tank nitrogen were introduced into the zirconia tube through pyrex tube ( with rubber tube j connections at the ends) and then through a flow meter in order to know the flow rate. The outside of j the tube is kept in air. Application of a positive j voltage at II relative to I. leads to the removal of Og fffom the inside of the tube. The effectiveness of ! this 'pumping' is determined by measuring the emf Em of the cells III-I and IV-I., one being further removed ; from the pumping cell than the other. This is done with the object of determining whether pumping affects the gas over the entire cross section, or only over a thin layer near the surface. Currents are measured with a Simpson meter,,and voltages with a Keithley 610 B high impedance voltmeter. III. 2 Results Initial experiments with no externally applied voltage, using eq.(3-1; for Em , showed that the tank —6 nitrogen contained 1 atm Ng and 2x10 ^ atm 02* The cell showed the temperature dependence as required by eq.(3-1j. No appreciable emf was observed in symmetri- j cal situations, i.e., with nitrogen, air or oxygen Pt paste Pt wire ►AIR ______ / _ _ Y ___________ . y "\- — n2+so2 « ■ ---- 14cm -----►2cm■•4cm* I (Zr,Ca) o PtPh Fig. 1. Electrode assembly for oxygen removal (II, 1} and measurement of oxygen pressure (III, I and IV, I). o flowing both in and outside the tube. j The results of pumping experiments at 530°G, using i the narrow tube with a nitrogen flow rate of 4*6 cm^/ - i sec. inside and with air outside are shown in Fig.2. ! I The values of the voltage Em over the measuring j cells III.-I and IV-I are stationary state values, measured with the Keithley voltmeter without compen- I sation. Em is seen to increase with increasing current passing the pumping section II-I. A sharp increase of I Em occurs at pumping current JpUmp between 0.7 and j 2 ina. In this current range the removal of oxygen from the nitrogen passing the tube approaches completion. The current at which complete oxygen removal is ex- : pected at the given flow rate and the oxygen content -5 of 2 x 10 atm as determined at Jpump = 0, should the ionic transference number of the zirconia remain i 1, is JpUmp - 0.6- ma. The measuring cells III-I and IV-I, placed at different distances downstream from the pumping section give similar results, but the values of IV-I are systematically almost 3$ lower than j those of III-I. The fact that the two voltages are so | close indicates that oxygen is not just removed from a thin layer at the inner surface, maintained by j laminar flow, but that there is depletion of oxygen over the entire cross section of the tube. This view finds support in an estimate of the diffusion length 1. For oxygen at 530°C, the diffusion coefficient 2 D ~ 0.9 cm /sec (69;, and using a transit time t^U.1 sec given by the time it takes the gas to flow from the right hand of II to III at a flow rate of 4.6 3 / i cm /sec in the tube with d = 0.5 cm, we find 1 = (^DtJ3 - 0.3 cm = r, the radius of the tube. Since diffusion starts well before the edge of II is reached, t may be 2-4 times larger. Accordingly diffusion will effectively even out the concentration over the cross section. As will be shown in a latter discussion sec tion, the small difference between cells III-I and IV-I is probably due to back diffusion from the end of the tube, as contact IV being closer to the end than III. Curve 1-4 of Fig.2 correspond to different conditions of the experiment. For curve 1 the nitrogen was dried by passing it through a liguid air trap. This leads to the highest voltage ( = lowest residual oxygen pressure ) attained: Em = 1.5v, corresponding ■ f c o (Prt*!,.--^ = 10'36 atm. ( Here the p£ indicates l# 2 in in 2 pressure values calculated from eq.(3-1). As we shall see later, more nearly correct values, given as- Pq without an asterisk are calculated using a more general: equation. Using nitrogen directly from the tank (curve 2 ) gives E_ = 1.4v, (p = 10~3^ atm. Since this 1 in £ m m i Fig. 2. Experimental results for Em and the • X * values of pn calculated from it with Eq.(2-1) 2 and : (2-4-) as a function of the pumping current with air as the outside atmosphere and an inner atmosphere consisting of: 1. U2 + 2 x 10 ^ Og passed through a liquid nitrogen trap; 2, Kg +2 x 10-5 Og direct from the tank; 3#Ng+2x10> 0g passed through water at 25°C; -5 4r. wet or dry Ng + 4 x 10 CC>2* Inner diameter of tube: 5mm; flow rate: 4*6' cnr /sec. Temperature: 530°C. Note the difference in scale for J>and<1ma. 33 — o Contacts I - I I Contacts 1 - W . - 1 , 8 -1.6 40_ 30 — 25“ -1.0 ^ 2 0 “ - log Po* (atm.) 10- - 0.8 -0.4 5- (mA) pump 25,C 1 7 , 0 2 1 , 0 1 3 . 0 9,0 0 .0 08 1 , 0 5,0 0,4 35 suggests a dependence on the water pressure, a third experiment was carried out with nitrogen saturated with water at 25°C (curve 3), Now the minimum pressure P 0 obtained is considerably higher, = 10 atm. In the fourth and fifth experiment the oxygen present in the nitrogen was transformed into a mixture of GO and 002 by passing the tank nitrogen gas over graphite at 650? ; For the fourth experiment, tank nitrogen was used as such. For the fifth experiment the gas was predried j by means of a liquid air trap. No difference was observed between these two experiments (curve 4J. , The removal of oxygen in this manner leads to a rela tively high Em without pumping. On the other hand, pumping has little effect on Em . The no-pumping value of Em is considerably lower than is expected, should the mixture of C02 formed by passing the N2 + 02 mixture over graphite at 650°C correspond to their thermodynamic equilibrium. We shall return to this point later. Instead of plotting Em as a function of JpUmp as shown in Fig. 2, we might plot Em as a function of the pumping voltage, EpUmp» There are, however, com plications resulting from a time dependence of the 3 6 I _ e character: Jpump“BpUmp curves obtainedoby mea suring JpnTnp different, times after application of the voltage, are different for Ep^p^ 4 volt. This is demonstrated in fig. 3> where 1-2-3-4 and i*-2,-3f-4' represent two different current-voltage sequences. In the first sequence EpUmp.ls increased rapidly to 6 volt and held for two hours before decreasing the voltage to 3 volt. In the second sequence, Epump is kept for five minutes at 9 volt. In both cases, but especially in the second sequence, lowering the voltage to 3 volt leaves a small excess current as compared to that in the cell in its initial state. The change of Jpump with time indicates that at these voltages the ziaBConia of the pumping section is irreversibly changed. This effect is also indicated by the recovery time of the signal of the measuring cell. This recovery time is the time it takes the measuring cell to come back to its original, low, no-pumping value after interruption of the pumping current, indicating that the gas in the tube is again of the original compo sition- As shown in Pig. 4 for EpUmp>4T, this time de pends on the time during which the pumping has taken place, the recovery time increasing with increasing pum ping time. This dependence is stronger for larger EpUmp» The semi-permanent changes in the zirconia of the pump ing; section are related to its decomposition by electro- 2 ' T 5 Min Imi) 2hrs. (V) "pump 3 C*CU?X6H"U VOXXcl^B S6 QuexiOtJo ! “V * t . . v . of°the pumping cell (II-I) for different times of operation. ^ Pig. 4 The time(t rec. ) needed by the measuring cell ( , III-I) 5/q to revert back to its pre-pumping emf. 1;. For interruption of the pumping current immediately after its being established; and . 4/0 2;. for interruption of the pumping current J>0 min. after its being established. * Epump(voStS) 39 lysis and/or its becoming polarized when no oxygen is available at the cathode. Thermodynamic data for ZrO£ and OaO indicate, respectively, decomposition voltages for formation of the pure metal and oxygen at 1 atm. of 2.52 and 2.84 Y at 530°Cj; in the solid solution employed, the value may be expected to be somewhat higher. The values given correspond to thermodynamic equilibrium. If currents are drawn, the applied voltage will be high er by the ohmic voltage drop. This brings the expected value for the voltage at which electrolysis occurs close to 4Y» At voltages smaller than that required for elec trolysis, polarization occurs, which gives rise to a change in the stoichiometric composition in the direction of metal excess at the non-reversible cathode. This in turn represents a change in the activity of the compo nents of the compound at this electrode, the metal activity being increased, the oxygen activity being, decreased. Note that polarization and electrolysis are closely related: electrolysis occurs when the polariza tion is so strong that the metal activity reaches the value at which pure metal may be formed. In the strong ly polarized state the zirconia assumes a dark color(70, 7 . - 1 j and becomes partly electronically conductive (,58,6o)» The theory of the polarization process and its conse quences as far as electronic conduction is concerned is essentially the one given by Wagner for AgSr ('72,-73)* A decision as to whether polarization and electro lysis both occur, or whether only polarization occurs, can he reached on the basis of the time dependence of the pumping current. Electrolysis should give a con tinuously increasing current. Polarization, on the other hand, requires a current approaching asymptoti cally a certain final value. Our data for voltages > 4v, indicate that electrolysis occurs. On the basis of these arguments we expect a situa tion in which we have ionically conducting zirconia in the outer and central sections of the tube, elec tronically and ionically conducting zirconia below the inner surface, and zirconium (and calcium) metal at the inner surface. Since application of a strong field tends to give rise to polarization as well as electrolysis, an initial concentration of the field at certain points, e.g. at grain boundaries or dis locations tends to give rise to the local formation of metal and electronically conducting zirconia, which in turn tends to strengthen locally the field across the less affected part of the cross section. Thus both effects favor dendrite formation. Such dendrites have been observed with zirconia used as an electrode in magnetohydrodynamic power generators(70, 71). Electrolysis occurs only at the pumping section 41 i which, is affected directly by the pumping current. | The oxygen-poor, partly decomposed inner surface goes on acting as a pump after interruption of the pumping ! current until it is reoxidized by the oxygen of the gas. If the oxygen content of the gas is low, as in our experiments, this may take a long time. This ex plains the long recovery time (measured with the measuring cell) plotted in Fig.4. The material of the mmeasuring cell is affected i only through the reduced 02 activity in the gas. If ^ this activity is sufficiently low, it will lead to an oxygen poor, electronically conducting material over part of the cross section. Decomposition with the ; formation of metallic zirconium will not occur: the lowest oxygen pressure that can be reached corresponds to the coexistence of oxygen-poor zirconia and metallic: zirconium, and this does not represent a driving force for the nucleation and formation of metallic zirconium required for electrolysis. Normally, Em was measured with the Keithley volt meter without compensation. It was found that the i I same results are obtained for measurement of Em with ; compensation, using the Keithley meter as a zero indi- j cator. This indicates that the small current drawn by the meter does not upset the measurement. ! In Fig.5 the minnmum values of pn reached by i 2 pumping are compared with (pQ )Q^ , the oxygen pressure of the Zr02-Ca0 diffusion cell calculated ! from equation (3-1) for , which also represents ! the oxygen pressure at which zirconia has equal ionic and electronic conductivities - Schmalzried1s PQ(75). I It is seen from Fig.5 that the values of ^p0 )minj are close -g o the values of (,p0 )Q ^ found hy Yanagida (76; for a tube of the same material as used by us. Yanagida’s values were arrived at by comparing the emf of the cell Al, AlgO^ / (Zr,CajC>2 / 02 with the theoretical emf which can be calculated from the known Gibbs free energy of formation of AlgO^ : E0.5 = ln (p02j0.5 Etb. " ^0Z>A1,1CLZ03 ’ ^p02^Al,A120^ being the pressure of oxygen over Al in equilibrium with A120^ and may be changed by change the temperature. At 800°C Yanagida’s and our values O M for Eq ^ correspond to (pQ ^ = 5 x ‘ \'3~ atm. Other reported values are considerable lower. Schmalzried’s CM O CL O O' O 50 r 40 Pig. 5. (p0 )min# as f(T) compared to the oxygen pressures (Pq2 -^0.5 at wilicla stabilized zirconia is .50^ electronic conductor according to Yanagida(76j. 30 j 20 10 x (po2 )min. ° (Po2)05'according to Yanagida -6 * Temp °C 500 600 700 800 900 1000 1100 - P = * data(75; lead to (Po^^o.S = ^ x 10""^ atm. Patterson et al.(60; found values of 10~"^ atm from conductivity! _ X Q measurements, and 10 atm from polarization experi- I ments. These differences are partly due to differences! (and possibly errors; in the measuring techniques, but differences may also result from differences in the composition of the zirconia used. It is known(6l; that (pA ; is sensitive to the presence of trace 2 * donor concentrations. This point deserves further study. Pig.6 compares Em as f( Epump ) for the wide tube (curve 2) and the narrow tube (curve ' [ ) at equal flow rates. As expected, the wide tube is less effi cient, though the performance is still satisfactory. Attempts to measure the pumping efficiency at higher flow rates were complicated by temperature changes, fast flowing gas tending to cool the tube. Although pumping still takes place, uncertainties in the temperature make a quantitative evaluation more difficult. Por this reason this line of investigation was not pursued any further. Instead of removing oxygen from the gas in the tube, we can add oxygen by passing current through the pumping section in the opposite direction. Due to the Pig. 6. Em as f(KpUmpJ for a gas flow of 4.6 cm5/sec at 530 C for tubes with different inner diameter d: pump -1,4 - 0,8 - 0,6 -0,4 XV) pump' 46 relatively small pumping currents employed, for flowing gas the effect of oxygen addition is not very spectacu lar, Fig,7 shows the complete J-E characteristic inclu ding. both types of operation. As mentioned before, the right-hand part, of the characteristic at E ^ 4v is time dependent; the curve given corresponds to t^ 1 min. The characteristic differs from that measured on a point electrode by Kleitz(67) because the various sec tions of the pumping, cell operate in different oxygen pressures. At voltages where the cell acts as a pump, the section near the edge where the flowing'gas enters operate in the original pressure, whereas sections fur ther down operate in an oxygen free environment. Since a change of the oxygen pressure shifts the zero current point of a cell, the total characteristic arises as the sum of contributions from cells, the characteristics of which are shifted relative to each other. As a result the marked S-character of the individual characteristics is largely lost — though some is still observable. III. 3 Discussion It has been shown that under favorable conditions (narrow tube and reasonably low flow rates) stabilized zirconia may be used to reach extremely low oxygen pressures in flowing as well as stationary gases. Two points need closer examination. The first is that, as has been found, the value of (pn*attained by n i i n pumping is independent, oh the presence of water vapor 0,8 (mA) 0,6 0,4 0.2 0,2 pump 0,4 0,6 0,8 Oxygen removal Oxygen addition Fig. 7. J-E characteristic for the narrow tube at 530°G. Oxygen addition and removal refer to the inside of the tube. 48 and/or C02, high partial pressures of these gases limit ing the lowest oxygen presstires that can he attained. The second point that needs examination is that values of Em corresponding to values of p„ as low as reported can u2 he measured at all. The first effects are due to the capacity of H20 and C02 "bo produce oxygen hy dissociation: H20 = Eg + & 02 p§2 = K ^ 0 . p^Q / 002 = GO + i 02 Pq^ = . pco^ /pco with ^KH20^530°G = 6x10 14 atm^» and ^kco2^530°g‘= 1.2x10“14atiA (77) After the removal of the free oxygen originally present, dissociation of H20 and/or C02 established a certain residual oxygen pressure. This residual pressure is lowered as more oxygen is removed and as more H2 ox: GO is formed. The value actually attained in the rela tively short time that the gas passes through the pump ing cell depends on the rate of oxygen removal, on the rate of decomposition of the buffer molecules, or on the buffering capacity of the gas for oxygen removal. This buffering capacity must be expected to be greater when more H^O or 002 is present. In the case of water-satu rated gas, in which water (and thus oxygen; has been added to the gas, it may well be the increased buffering .49 capacity that is responsible for the decreased pumping efficiency.' For the gas mixture made by passing the oxygen-containing nitrogen over graphite at 650°C, no additional oxygen was added. Therefore, in this case the rate of decomposition of the buffer molecule CC;02) must limit the pumping rate. This view is supported by results obtained by Kleitz ^67) with stabilized zirconia in contact with Pt in a mixture of oxygen and 002 (Fig. 60, pp. 97 of that reference). Also note that Karpachev et al. (78;, investigating the working of the Pt/zirco- nia electrode in CO, found rate limitation of the oppo site process, the oxidation of CO to CO2. Oxidation of graphite at T.< 1000°C leads to partial pressures of CO2 and CO determined by the kinetics of oxidation rather than by equilibrium (79). The emf of the measuring cell ^ —22 when no pumping is taking place indicates pA = 10“ z 2 - 5 atm., corrsponding to pCQ /pco = 10 . Hence, p^Q = 2x10 2 atm. (the original oxygen pressure; and p^Q = 2x1u“ atm. The buffering capacity - but now against oxygen addition - must also be involved to explain why we can measure without compensation pressures as low as the ones found in the measurements. The main difficulty lies in the possibility of oxygen leaking back into the tube. There are three ways in which this may occur, viz: 1) by counter stream diffusion from the open end of the tube, 2) by diffusion through the tube wall, and 3) as 50 a result of the measuring current. Let us look at these three processes a little more closely. 1.) Counter Stream Diffusion An estimate of the importance of counter stream diffusion may he made hy calculating the oxygen pressure, built up a certain distance 1 up-stream away from the end in the time t required hy flowing gas to cover the distance 1, if we start at t = 0 with an oxygen pressure step profile with p_ = 0 inside the tuhe, and pn =0.2 2 2 atm. outside. ^p02>l,t = °*2 h - erf t . For. the distance as shown in Fig. 1, with contacts III and IT respectively 6.7 and 2.7 cm. from the end, the times involved are 0.33 and 0.14 sec. respectively. p —1 Talcing again (Dq ^550oC ^ cm seG* » we (Po^III *= 2x10“1^atm. and (pQ )j^/= 10“8atm.. These figures have heen arrived at with the aid of the tables of error functions given in ref. The relatively large leak at electrode IT due to this mechanism can he largely removed hy the use of a somewhat longer tuhe. 2.; Diffusion Through the Tuhe Wall In the well-sintered tuhe as used in our experi ments, diffusion hy neutral species is negligible. The only diffusion of importance involves charged species, 5 -1 moving, through the bulk of the crystals. Such diffusion requires the simultaneous diffusion of ionic and elec tronic defects, e.g. vacancies and electrons and/or holes. If the permeation is diffusion controlled, its rate is given by an expression similar to the one de - scribing the rate of oxidation of a metal according to Wagner's theory of oxidation ^66,81) pm rP0 (outside; growth- \ v ^i^el^11 -^0 (3-2; 6 8F d J p.. (inside) 1 el °2 2 Here O ' is the total conductivity, tg^ = 1-t^ = the total transference number for electrons^tg) and holes(t^jjand d the thickness of the wall of the tube. Heyne (.66) measured the permeation of stabilized zirconia (157® CaO) at 730°C from oxygen to vacuum, conditions under which only t^:.is appreciable. Interpretation on the basis of the formula given above gave t^ = 3x10”^, smaller by a factor 7 from the value 2x10 , arrived at by extrapolating to this temperature conductivity data by Patterson et al. (60), a second check can be made by comparing calculated values of jd and experimental results by Smith et al. (82;. At 300°C, from 25 torr. 1 o to high vacuum, (36.)ca^c = 2x10“ g-mole/cm,sec. where- — * 1 A. as (D^Q^g =10“ ^g-mole/cm,sec. i Thus in both cases the calculated value is smaller than the observed one. This indicates that the permeation is not entirely 52 diffusion controlled, Taut is determined to some extent by surface processes. In any case, the formula may be used to find an upper bound to the permeation. Carrying out the integration with = O'g + c r h = 4.6x107 pQ -"^exp (-4.3 eV/ki; + 8,8x10^ pn exp (-2.l2eV/kI) 2 as found by Patterson et al. (62;, with outer and inner oxygen pressures of 0.2 and 10“^8atm., and 1 = 530°C, we find 3 = 3e + = 5.2x10-* 17 + 2. 6x 10-17 _ 1 7 P = 7.8x10 g-mole/cm ,sec.. permeation occurs through the wall section between the pumping section and the measuring electrodes with an 2 2 area of 3.14 cm for contact III and 9.42 cm for con tact IV. She times involved are 0,1 sec. for III, 0.3 sec. for IV. At a gas flow rate of 4.6 cm^/sec., the permeated gas flows into a gas volume of 0.46, and 1.38 3 cm respectively for the two cases and gives rise to —12 12 (p0 )jjj = 3x10 atm. and ^pQ = 9x10 atm.. Since this is an upper bound, the actual values may be some what smaller. 3. Permeation as a Result of the Measuring current The Keithley 61 OB electrometer used for the mea surements has an entrance impedance of ^ 10 There fore a current of 10~^ amp. flows at E = 1V. It flows 53 in a direction opposite to that required for pumping, and represents a hack flow of oxygen into the system —20 of 2x10 g-moles per second. At the rate of flow of 4.6 cnr/sec. this corresponds to a partial pressure — 1 fi of 2x10 atm. of oxygen added to the gas in the>tube. Table X summarizes the effect of the various estimated oxygen leaks at electrodes III and IV. Table I Electrode III Electrode IV Counter Stream Diffusion 2x10“^ atm 1x10”® atm — 12 -1 2 Permeation 3 x10 atm 9x10 atm * 1 £ 1 c Monitor Current 2x10” atm 2x10” atm The fact that in all cases appreciably lower values are indicated by the voltage of the measuring cells must be due to the removal of the back diffusing oxy gen by a buffer. Actually, the emf measured indicates an oxygen activity maintained by the buffer system rather than a real oxygen pressure. We use pressures only as a convenient way to express these activities. For the water system, the buffering action consists of the reaction of oxygen with hydrogen; for the OO2/CO system it involves reaction with CO. In the latter case, the calculated p is well in excess of GO the oxygen back flow so that the measurement will not affect the results. In the water system the buffer ing capacity depends on the presence of B2* If no H2 is present in the h2 initially, all the H2 active in the measuring section must be formed by decomposition of water in the pumping period. The pressures required though large relative to the extremely low oxygen pressures involved, are small when considered on an absolute basis; therefore formation of the required amount of during pumping is not unacceptable. Fig.8 shows the relation between pA and possible values of 2 p„ and p„ A at 530 C in the gas after it has passed 2 2 the pumping section, calculated under the assumption that equilibrium is attained. Oxygen pressures of • 7 0 « —1 1 k 10"-’ atm. are seen to be possible for p„ ^ 10 — ftp — — 8 — 16 atm. and p^, A between 10 and 10“ atm.. If the Hp 2 has been created by the pumping, the initial water pressures must have been equal to CPjj q )initial = ^EbjO ^residual + Table II shows a few combinations of partial giving pA = 10-38 an(j 2 corresponding (s2^initial* ^ c- ^ ue these 70 combinations was actually present when pA = 10' atm. 2 was measured atcontact III lies in the increase of —36 the measured oxygen pressure to pA = 10 atm. at 2 contact IV which must result from the counter current diffusion leak of 10“8 atm.. Such an effect is to be pressures p„ Q and p^. -34 Pig. 8 Relation between and possible values of p and -22 - l o g P H ( a t m ) -18 expected if the hydrogen pressure, which determines the buffering capacity, is of the same order as the back flow leak, e.g.-p^ = 2x1cT8 atm., (pH20)residual —14. R = 7x10 * atm., and thus (p^0initial = 2x10~ atra* This last value is much higher than the equilibrium pressure of ice at liquid air temperature. However, it is probable that a single stage trap does not remove water vapor down to this theoretical limit, and a resi- — R dual water pressure of ^ 10“ atm. is not unlikely. Under these conditions, all the other leaks are small relative to the buffering capacity and therefore the buffering is practically complete. Table II Combination of partial pressures of H20 and in equilibrium with p„ = 10“^® atm. at 530°C. 2 (units : atm.) pH2 (pH20^initial 57 Values of Em actually measured are affected and ultimately limited by the occurrence of electronic con duction in the solid electrolyte of low oxygen pressures, The transition from t^ = 1 to t^ = 0 is a gradual one. Por, whereas the ionic conductivity is approximately 1, constant, the electronic conductivity gcC p“4 (60-62). 1 As a consequence t± = ■ = - j + & requires a range of ^ 10 orders of magnitude in pA to change from 2 t^ = 0.95 to t^ = 0.05. Pig. 9 demonstrates this for (p0 )q 5 = 10-56 atm. as observed at 530°C by Yanagida (76) and O' as given by eq.(3-3;« The variation of t. in turn affects the value of the measured emf as shown in Chapter 2: Tjm fP0o(inside). ^ = - i jn2 *i"“ Poa <■**> p02(outside) This equation is equivalent to eq.(3-1) only if t^ = 1. If we apply eq.C3-4) to our case in which (,P0 )outside = 1/5 atm., under which condition t^ = 1, we find Em as a function of pn by carrying out the integration 2 using t.as a function of log pA as shown in Pig.9. 2 The result is given in Pig. 10. The shape of the curve is as discussed by Schmalzried (.76;, the slope at each t. 0,5 -log (Pop) 0,5 ■**-log PoJatm.)! 44 42 40 38 36 34 32 . 30 28 J?ig. 9. as a function of log pQ for (?:= constant, (Tocp 26 and ^ 0.5 = 10 -36 ui 00 atm. - 1 . 6 ^°2^0.5 Fig. 10. Em as a function of log p for the 2 electrolyte characterized by Fig. 9 with (Po^outside^ 1/5 at,n and 1 = 53°°C. Em =0 at -log Po2 = 0,7 28i 30i 32. 341 -log Po2(atm.) 36i 38i 40. 4 2 ! VJ1 T orn w w point being equal to 2.3 t^. Since the curve t^ versus log p.. shows inversion symmetry with respect 2 to the point t^ = 0.5, the maximum contribution of the range with t^< 0; .5 to the integral in eq.(3-4) is just equal to the loss of voltage in the range where 1> t^> 0.5 (.the two contributions being propor tional to the shaded areas in Pig. 9)* Therefore, when the oxygen pressure inside the tube approaches zero, Em approaches asymptotically the value calculated from eq. (3-1) at ( p ^ ) ^ . —30 Evidently for p,. « 10 atm., the point where 2 * t. starts to drop, values of the oxygen pressure pA 2. deduced from Em using eq. ( . 3-1) are considerably too high. The actual oxygen pressures reached in our pump ing experiments may be found with the aid of eq. (.3-4; or Pig. 10. in Pig. 2. these are given as pn ; the 2 minimum value, (Pq )raj _ n = 10~^® atm. is indeed markedly lower than the corresponding p£ • Obviously the non- 2 linearity of E^ versus log pQ near (pQ ;0 5 has ' fco be taken into account when the oxygen pump is used in experiments where the oxygen pressure must be exactly known. It should be pointed out that the results for (pQ )min shown in Pig. 10 and Pig. 2 are based on tPo2;0 5 as measured by Yanagida (.77) on a tube similar to ours, and on cr■ cc pn 4 as reported in the literature j 2 i | j (60). In case such pumps are to he used in applications j I where exact knowledge of pn is necessary, it is ! ! ! prudent to either restrict the applications to ranges j i where eq.(3-1) holds» Otherwise one should measure j (Pn )n c and as f(Pn ) for tube to be used and deduce a curve of the type of Pig.10 for this tube. Chapter IT The Sodium Activity in liquid Sodium-Tin Alloys Experimental investigations of the thermodynamic properties of many intermetallic solutions have shown large deviations from ideal "behavior, dilute solutions "behaving as/ 'simple' mixtures (83). Hauffe and Tierk (84) and Delimarskii and Kolotti (85) measured the activity of sodium in liquid Na-Sn alloys at Ha con centrations >0.1 mol a / a and found markedly nonideal behavior (Figure 11). The work reported in this chapter extends the measurements to lower concentrations. IT*. 1 Experimental Starting materials were Mallinckrodt pro analysis sodium and tin which were used without further purifi cation. Sodium activities were determined by emf mea surements on cells Fe/Na/Pyrex glass/Ha,Sn/Fe, in which a pyrex glass tube acts as an Ua+ ion-specific membrane. Iron wires are used as electrodes. The sodium was cut under toluene and then transferred in an atmosphere into the inside of the tube. Mixtures of measured amo unts of sodium and tin "were introduced into the outer electrode compartment, protected from the air by a 62 63 ! j second glass tube; here also nitrogen was used as an j atmosphere. The whole cell was then placed inside a j I furnace and heated under dried nitrogen gas until the metals melted forming a homogeneous liquid alloy. Tem peratures were regulated to within + 2°C. A chromel- ! alumel thermocouple was used in measuring the tempera tures. The cell emf was measured with a Keithley 610B high-impedance voltmeter. In order to obtain steady ' readings, it was necessary to season the cell for about 10 hours after filling. | The temperature dependence of the emf was deter mined between 350°0 and 500°G by measuring the emf at 50°C intervals both with increasing and decreasing temperatures. The values obtained in the two cases agreed with each other within 1 of their readings, indicating that equilibrium was attained. A large number of alloys of different composition were needed for the investigation. Rather than preparing each alloy from pure sodium and tin, a few standard alloys were made as described above. Then the sodium concentration in these alloys was varied (i) by adding more tin to the mixtyire or (ii) by applying a voltage across the cell and passing a certain number of cou- ' lombs. This transfers a known amount of sodium between the ty/o electrode compartments and thus changes the alloy composition in a known way. At low sodium concentration, oxidation may lead to erroneous irreproducible results that seem to indicate abnormally low activities. Only the repro ducible results will be presented. IV. 2 Results and Discussion The net reaction of our cell is the transfer of sodium from a higher activity ( pure sodium) to a lower activity (Sn-Na alloy;. She measured emf is equal to RI,. ^ a ^ I _ RT -,„•/„ » ^ F F ^a^II (4-1) where ^ajjja)j = 1, is the activity of the pure sodium and ^a^;^ is the activity of sodium in the Sn-Na alloy. Figure 11 shows a plot of the logarithm of the sodium concentration x^a versus the logarithm of the sodium activity for I = 500°C. The figure contains our data as well as those by others^84,85;. The agree- - 1 - 5 ment is satisfactory. For x^a between 10 and 3x10 » the measured emf varied from 485 to 710 mV. The acti vity points lie on a line that is very nearly parallel to the line with unit slope representing ideal be havior. In this range the activity coefficient f^a defined by aNa = fNa x ^ is approximately constant, ; for here we have 91n f^/aln x^a = 0. This is the ' behavior to be expected for a simple solution(83)« ! Fig. 11. Relation between -log x^a and -log a^a according to data by Hauffe and Vierk (84;, Delimarskii and Kolotti(85), and this paper, and the relation expected on the basis of eq.(4-3;• j r3 a Hauffe and Vierk o Delimanskii and Kolotti X This paper -2 Unit slope equation . . — ^ Hog AN a 67 Since Xexc(Na) = R31 In fNa , and also ^exc = GQXC = Eexc " TSexC(83;’ tlms» H — f P - c5 In f = -J®22 exc s Wa RI ' exc In the zero order theory(86) -^L^ClTa) = x G cXC DU 1 C He*c - < 0 ^ 1 - ^ a )2 , th u s K TS 1 ln fua = ---— (1 - W 2 | and ^ ln fl^a _ 2g8xc /1 } j ? In x.T “ RT ^'“^ a ^ a j « 2xNa*exc j RT which goes to zero for x^a - » 0, f^& approaching asympto-- tically to the value &°XC/RE. (G°xc ^ H°xc and S°XQ used i in these equations are the excess functions for the sodium under standard conditions corresponding to ^ ^ila/^ * ^Na increases with increasing x^a to become equal to one for x^a = 1. In this range the zero-order approximation gives a rather poor description of fjja« At x^a < 3 x 10"3, the activity coefficient appears to decrease strongly with decreasing x^. It is most probably that in this range the emf is no ■ i longer determined by sodium in the lla-Sn alloy but | i by the small amount of sodium in the pyrex glass. A ! similar effect - though occurring at 5UX lower concen- tration - was observed by Stern(87; with, the cell j Ag/AgCl, NaCl/glass/AgCl/Ag. Table III shows the tem- j perature dependence of f^a» A least-square analysis I leads to j In = - (.5237 * 120;/T + (1 .925 ± 0.185; (4-5; | i Equating this with the exact expression for lnf^ in j eq.(4—2), it is seen that the true excess enthalpy a = -10,474 + 24u cal/mole and the true excess entropy S__. =• -3*85 + 0.37 cal/deg-raole. i | i i Table III I Values of -Log f^a at Various ! Concentrations and Temperatures | Temp. °C i , ^ a 623 675 723 773 0.020 2.85 2.55 2.28 2.13 0.013 2.83 2.57 2.33 2.12 0.0082 - 2.81 2.55 2.31 2.09 0.0061 2.82 2.56 2.34 2.14 69 Note that, as pointed out by Guggenheim (83.), Sexc ^ ^exc and Sexc are due of Na-Sn bonds from Na-Na and Sn-Sn bonds. The negative value of H0__ indicates that the Na-Sn bonds ai-e strong- “ AU er than the Ha-Ha and the Sn-Sn bonds. Accordingly, the vibrational frequencies will be higher, and fewer vibra tions are thermally excited. This accounts for S_„_< 0 @ x c as found. At low concentrations of sodium, the great majority of sodium atbms have tin neighbors only. If the coodination of the sodium in the concentrated alloys is the same as in the dilute ones, the situation around each sodium is similar to that in molten HaSn, and we expect a similar enthalpy and entropy of formation. In order to check this, we must relate &exc toAGjjagn Dissolving 1 mol of Ha into liquid Sn involves the bond reaction ibiH. , , _ . ( Ha-Ha) + £nH „(Sn-Sn) — ► nv Av nffAvOsra-Sn); &exG (4-7; Here n is the coordination number, HAvis Avogadro’s number, and the entities in brackets indicate the type of bonds involved. On the other hand, the formation of HaSn according to the reaction Ha(l) + Sn(l) HaSn(l); A (%aSn (4-8) when written in terms of their bonds, is again repre sented by eq.(4-7;. Hence 70 J AGHaSn “ &exc “ nNAv*gbond (.4-9) Sable I# shows the calculation of the thermodynamic parameters of the reaction shown in eq.(4-8) at 500°C. from thermodynamical data (88). Since the heat of fusion of HaSn is not known, the value reported for HaPb is used instead (89,90).. Further, it is assumed that Cp(UaSn) = Cp(H.a) + Cp(Sn). We find A % aSn> 7?5 = -10440 cal/mol whereas we had = (-10474 + 240) cal/mol, 6XC an unexpectedly good agreement. The entropy for HaSn is not known. Assuming the agreement between AH^a. Sn and H_„_ to not entirely fortuitous, we assume a simi- 63CC lar correspondence for the entropy, i.e., ^Sjjagn ^73 = S = (-3*85 + 0.37) cal/deg-mol. This then leads to an estimated value of a Sjjagn 298 = “5*35 cal/mol-deg as shown in Table I1T in brackets. Owing to the specu lative nature of the procedure, we do not indicate limits of error for these figures. Since the approach followed here is essentially identical with the zero-order approximtion mentioned earlier, the degree of agreement here should corres pond with that between -logfjja as determined experi mentally and by the zero-order expression. As is seen in Figure 11, at x^a = 0.5 there is a disagreement 7-1 Sable 17 Thermodynamical Data for HaSn a K a s S kcal/mol cal/deg-mol Ha(s;2g8 + Sn(s;298^ HaSn(s;2g8 -12 + 0.8 (-3.35; Ha(s;^Y-| ^®C®)'298 -a Na(i;^,^| Na(sj^Y^ -0.62 -1.68 ^ ( 1^77-3 Na(l 1^71 -b Sn(s;5o5; ^ Sn(s ;2g8 -d Sn(i;^o5 Sn(s)5Q5- -C: Su.(l;77^ Sn(l;^0^ -1.72 -3.41 NaSn(s)2g8 . v\ NaSn(s;Yy^ a+b+c+d* NaSn(s; ^NaSn(i; 3.9** 4.6 Ha(ljyY^ + Sn(l^YY^— NaSn^.1 Jryry™ -1.0.44 + 0.8 (—3*85 115 “ +0.37) * Assuming Cp(NaSn; = Cp(Ha) + Cp(Sn;. ** Assuming the value reported for DaPb (89,90;. 72 "between these two quantities by a factor of approxima tely 1.8. Therefore the Data of lable II compared to experiment should show a similar disagreement. The factor 1.8 corresponds to a correction of -1.2 cal/ deg-mol in aS or of 900 cal/mol in AH. The latter is almost accounted for by the experimental error in ABi>faSh indioa' fce(3- irL Table IY. The entropy was unknown, and thus a different value can be introduced without any interference. Since we do not know the degree to which the two factors contribute, we shall not attempt to correct the data in Table IY. Chapter V An Electrochemical Oxygen and Sulfur Vapor Gauge with Pyrex as Solid Electrolyte L ' Glass has been used:as solid electrolyte in the cell H^/glass/^ for measuring the emf's due to the formation of water from oxygen and hydrogen(91-93)• Pyrex, a horosilicate glass(94), has been used as a sodium ion specific membrane in contact with molten sodium salts(95), or liquid sodium alloys as in Chapter IV of this work, to measure sodium activities. The Ea+ conductor Na-JJA^O^ has been used as a solid electrolyte in a cell based on the reaction Ea(l) + S(l) -* Na2S.(96) It is of interest to see whether Pyrex can also be used to measure the oxygen and sulfur pressure in gases. To this end emf measurements were carried out on cells of the types W,-Na(l) / Pyrex / Pt,02(g) (5-1). W, l\Ta(l) / Pyrex / C, S2(g) (5-2) and Pt, 02(X) / Pyrex / Pt, 02(II). (5-3). The reaction underlying a possible emf are 2Na(l; + i 02(.g) -► Ua20 (glass); G° (Ea20, glass) (5-4-) IT 2Na(l) + i S2(g) • * Na2S(glass;; G° (Na2S, glass) (5-5; and °2^p02^I ** °2^p02^II (5-6) Na20(glass) and Na2S(glass; indicate the state of the compounds as they are present in the glass at the glass -gas interface. If the activity of Na20 in the glass is a^a q , then the free enthalpy of Na20 in the glass is Gr°(Na20, glass; = G° (Na20) + EE In a^ Q (5-7) G°(Na20) being the standard free enthalpy of Ua20(s). A similar expression holds for G°(,Na2S, glass). A value of a^a q ^ 1 must be expected to result partly from the heat and vibrational entropy of solution of Na20 in the glass (.&exc# = - ^exc.^ partly from configurational entropy due to the distribution of the Na20 or its components in the glass (a^a 0 config^ Thus RE ln = RE In a ^ ^ config. + &exc.ox. (5-8) 75 For simple solution* a ^ O , config.= ^ N a ^ n depen ding on the atomic structure of the solution. We expect n=1 for incorporation of Na20 in a manner in which only one defect is formed, the two Na's being close together: Na Na 0 0 N ' S ' Si Si N n = 2, if two defects are formed in concentrations larger than the native disorder: Na 0 0" x Si Si s + Nat , 0 ^ and n = 3 if there are three defects formed: 0" 0" Si Si + 2NaT . 0 Alternatively v/e may have configurations involving boron: Na x /Bn (n = 1), or ^ B + Na± (n = 2) The expected emf's are for cell (1J: 76 -El = ^ [ a^ua^o; + ®exo.ox. + El ln a^a^Qt Config. -0^ 1 15-9) a^a being the activity of Na in the melt at the left hand side, and p„ the oxygen pressure in the gas at 2 the right hand side. Similarly for cells (.2): "E2 = W C G°(Na2S) + Gexc<sulf. + ln ajja2gf config. PSg^a 3 (5-10) Cells (3) should follow the Nernst expression a 5 v ^Op^IX ' -E 3 - w ln,“ --- (5-11;. ' ' po2;r Since G° = H° - fS° and Gexc# = Hexc< - M exo. f Eqs. (5-9) and (5-10) can be rewritten as -Eox. = 2sr{La°(Ha20) + Hexo>ox.) - l[s°(Ka20) S a p0; ,1 + S— + * ln ^o,config.1) l5-12) ani “Esulf.= Sf{[H°(I,a2s^ + Hexc.sulf. “ l 'Ke'23' ) aNa p0| ^ + S , . + E In ------------ ]> (5-13) exc.sulf. ^jfapS, config. J 77 If we neglect the temperature dependence of H and S, eqs.5-12j and (5-13) indicate that the emf's of cells (1) and {2) are of the form E = EQ - BT« A plot of the emf as a function of temperature is a straight line, with EQ , the intercept at T = 0°K, equal to “^ a 20 + Hexc.ox.)/2F and the sl°Pe B' » ea- ual to 2 ^ a Na P0 + sexc.ox.+ H in ^ Q 2 > , with similar expressions for the sulfur case. IF. 1 Experimental Sealed sodium-filled glass cells were made as indicated in Pig.12. The sodium was Mallinckrodt pro analysis sodium, used without further purification. As electrodes and leads, pure tungsten wires were used at the Na-side, Pt-wire and Pt-paste at the oxygen sides £ cells (1) and (3)] and graphite yarn and graphite powder at the sulfur side (cell (2)3* The sodium cell was placed inside another Pyrex tube which serves as a protection against the out side atmosphere, and the combination was mounted inside a furnace. Temperature fluctuations were kept within - 2°C by operating the furnace on a constant Pig. 12. The Na electrode (a) and the procedure to make it (b). 1) Introduce Na protected by toluene into A. 2) Evacuate A, B, G through D. 3) Close D. 4; Cool B to -180°C, and distill the toluene from A to B. 5) Melt Na in argon and pre-heat the capillary rod. 6) Let in argon at D and press the Na from A to C. 7) Evacuate through D. 8 j Melt off at E. T9 Pump W or Fe Pyrex No Pt paste (a) Three way stopper Argon gas Capillary silicone A Pig. 12 '80 voltage transformer. A ohromel-alumel thermocouple was used in measuring the temperatures. The cell emf's were measured hy a Cary 31CY vibrating reed electro meter which serves as a high impedance voltmeter. When different electrode materials were used, the emf values were corrected for the small thermoelectric power of the couples these materials constitute. In the polari zation experiments, outside voltages were supplied by constant voltage dry batteries and currents were mea sured with a Simpson meter. A digesting period is necessary for each measurement at the desired tempera ture in order to reach a steady state. Several gases were used to establish different oxygen activities, —3 —7 such as N2 + 10 ^atm.02 and Ar + 10 'atm. For lower oxygen activities, CO/CO2 and I-Ig/l^O buffer systems were used. For the Hg/H^O system, tank hydrogen gas is passed through water at known temperature so that the hydrogen gas is saturated with water vapor at that temperature. For the CO/COg system, tank nitrogen —5 (containing 10 Og) is passed over graphite which transforms the oxygen into a mixture of CO and CO2 in the same way as in Chapter III. The graphite was in a pyrex tube inside another furnace. Different ratios of CO/GO2 can be established by keeping the graphite at different temperatures. The "N2 + H2" mixture point was achieved by passing. ST2( containing —5 10 02) and H2 in a 1:1 ratio through an air trap to remove water, and then through a furnace at 700°0 to transform the oxygen into water v?ipor. The oxygen pressure can be calculated from the H2/h20 ratio, the latter being known if it is assumed that all the 02 in N2 is turned into H20. In all cases but the latter, the oxygen pressure was determined with the aid of a cell with calcia-stabilized zirconia as solid electrolyte. For nN2 + H^", the 02 pressure falls outside the range where the electrolyte has an ionic transference number equal to one, and there fore we have to rely on the calculated pressure. In the sulfur cells, sulfur pressures were established by various methods. In a first set of experiments, solid or liquid sulfur was present in the outer com partment of the cell and the temperatures of the sul fur and the cell were the same. In a second set of experiments, the sulfur and the cell were at different temperatures. Use of two separately controlled sec tions of the furnace makes it possible to vary the temperature of the sulfur source and the cell indepen 82 dently, i.e. we can study the properties of the cell at constant l1 under varying sulfur pressures. In order to transfer the sulfur vapor from one compartment to the other, pure argon was used as a carrier gas. Finally in a third series of experiments, HgS and mixtures of ^2 + ^2^ were used to establish low sulfur activities. V. 2 Results and Discussion Figure 13 shows the emf of the oxygen cells at 500°C as a function of the oxygen activity. All the points except the "Rg + Hg" point are close to the line showing the Og pressure dependence required by Eq. (5-9). This indicates that the interpretation of the cell emf as based on the formation of NagO is correct.: formation of Rag^j? would give a dependence =<-Vq • In order to find the reason for the deviation of the "Rg + Hg" point, let us consider the theoretical low- pressure limit for the operation of the cell. This limit is different for buffered and for non-buffered gases. The ulimit for buffered gas is set by the oxygen pressure at which liquid sodium with a^a = 1 is formed. In this case the cell (1) becomes identical with a cell. Ra(l)/Pyrex/Ra(l) with E = 0. Extrapolation of the Hernst line in Fig. 13 to E - 0 gives (Pq, , buffer = 10“ atm., a value well below the 10-^atm. value of C X , I a t m . fa » im 2 +io"5 o 2 Ar + I0 '70 T = 500°C C0/C0 2 buffer o > H2/H 2 0 buffer j#ir 13 unbuffered E im f'a a f(pQ ; operation limit c=ifor a cell tf,*Ja(l ;/p,yrex/pt,0, at 5UO°o. The line gives the pressure dencndence according to Sq.(5-9; [\L+hL ♦ - loo p0 (atm) 2 5 i 10 _i_ 1 5 _i _ 20 25 30 i 35 4 0 i 00 the "Wg + H2 1 1 point. In non-buffered gases we expect j the cell to be limited by the dissociative evaporation | of Na20: ! H'a20(glass; -* 2ha(g) + £ CM.g) ; Gevap.ox. | and P0J ' ex® <- ®evap.ox (5-15) with &evap.ox= "G-° (Na20, glass j + 2G°(Na1_>g;. Go(Na20, glass; is given by the emf E1 = 2.52 V of cell (1; i | with pure Na(l) on one side and 1 atm. 02 at the other at 5U0°G: G°(Na20, glass; = -2PE-, = - 116.2 k cal/mole. : G°(Nai^g) = 25.7 k cal/mole(77;, and thus G°vap.ox = 167.6 k cal/mole and exp t “&e vap. ox/Ra? ^ = 2,7 x 10~48 5/2 atm ' . At the sublimation point p^a = 4 Pq ; then eq(5-15) leads to (Pq2 unbuffered = 3*1 x 10 2° atm. This is much larger than the value = 10“3® atm the Nernst line indicated for the "ir2 + H2" point and | shows that the H2/h20 buffer is still active. This is i to be expected: since only reaction of H2 with 02 is ' involved, this H20-poor buffer should perform as well as the mixtures with more water. The deviation of the “N2 + H2 " point can therefore not he explained by a deviating oxygen activity in the gas phase, hut must he due to a different chemical reaction having hecome potential determining - possibly nitride formation. Further work is necessary to solve this problem. In any case, the cell is shown to he reliable down to —■•52 ! a pressure of 10 v atm. C > 2» i [ j In order to check the stability and reproducibi- i I S lity of the cell, it was polarized for several hours I | with a voltage of 12 volts with a Na-electrode either positive or negative. Fig. 14 shows the relaxation of the cell emf measured after removal of the polarizing j field. For both directions of polarization, the cell returns to its original emf in 1.5 to 2 hours. Fig.15 shows the emf of the oxygen cells as a function of temperature. The lines 1(a) and 2 represent — 5 the equilibrium emf's for N2 + 10 ^ atm C>2 and pure O2 > respectively. Lines 1(b) and 1(c) are obtained after polarization with a field of 12 volts at the corresponding temperature for several hours until the readings did not change with further polarization. For 1(b) the Na-side of the cell was negative, i.e. sodium ions were drawn inside from the outer surface. For E (volts) 3 . 2 Fig. 14. Variation of the emf with time for 300°C 0 ( b ) ] an oxygen cell after polarization 3.0 28 500°C [1(b)] 2 . 6 2.4 2 . 0 500°C [1(c)] 20 30 40 50 60 (min) 70 80 90 100 t recovery E (volts) 4.0r 3.5 Kb) 3.0 2.5 1(c) 2.0 i.i —i 200 400 500 100 300 -100 -200 Pig. 15 n=— Temp °C H a)» Pq = 1u atm; unpolarized. 1(b). as2(a), "but polarized (Na+ pulled inwards). 1(c). as (a), but polarized (Na+ pulled outwards). 3 2. p =1 atm. 2 Emf as f(T) for a cell w, Na(l)/ Pyrex /pt,02 • 1(c) the same voltage was applied in the opposite direction, i.e. sodium ions were drawn to the outer surface. In both cases the final values, taken appro ximately 30 seconds after removal of the polarizing field, are independent of the time of polarization and the voltage used for polarization. This indepen dence suggests for 1(h) that electrolysis has taken place with formation of a new phase (Ea20 or Na2SiO^) at the outer surface. Yet, as shown in Fig.14, the original emf is restored in a comparatively short time, which suggests that true polarization, without second phase formation has occurred, or, at least, that the formation of a second phase does not affect the emf- This is also indicated by the fact that 1(b) and 1(c) extrapolate to the same T=0 value in the equilibrium lines. For all four cases though with considerable scatter for 1(b) and 1(c) the emf is a linear func- | I tion of T: E = EQ - BT. The equilibrium lines 1 and 2 fit the relation E = 3.80 - 1.75 x 10"5T - §§ In a^a pQJ (5-16) Interpretation- of EQ = 3.80 V on the basis of eq(5-12); by neglecting the temperature dependence of H and S, leads to H0^ + Hexo-ox-= -173 k oal/mole; with I I ^ R°~m20,2 9 Q~ -'I00*6 k cal/mole (77), this gives H = -72.4 k cal/mole (Since we have neglected 6XC#OX« | I the temperature dependence of H and S in the inter- i pretation of EQ and B, so there is no point in dis- i | tinguishing between H^gg and , the enthalpy of I | the reaction-, and A32g8 and AS2g8 , the entropy diffe- ! rence of the reaction.) somewhat more negative than | the enthalpy effect of the reaction | ha20 + Si02 Na2Si05 (5-17) with H2gg = -56.5 k cal/mole, and = -40 cal/deg.mole. i The slope B for cell (2) is 1.75 x 10”^ v / ° j l . The quantity 2BB = 80.7 cal/deg.mole can be identified with - S (Na20) + sexc,ox# - R In config. ! by comparing with eq(5-12). By taking the value for | Na20 made from liquid sodium, we have AS°(ua20) = - 37 cal/deg.mole. Inserting this value into 2FB, we have Sexc.ox“ R ln aWfi = -41 cal/deg.mole. config. 9-a Sexcoxsll0Ul^ dose to as of reaction (5-17). There fore R In ^a^QjConfig. m u s ' fc tie very small. Figure 16 shows the emf measurements of cell(3), with oxygen at different pressures at two sides. The readings of the emf's have an uncertainty of + or - 5mv, the flow of gas through the cell making the temperature some what unsteady. The readings, however, are close to the calculated values of eq.(5-11). It may he concluded that Pyrex glass cells may he used as an oxygen activity sensor. Since the large value of Eq for the sodium cell introduces a consi derable source of error, it is preferable to use a cell of type (3) provided temperature effects can he eliminated. The sodium-oxygen cell can also he used to determine the NagO activity in sodium glasses. Figure 17 shows the emf of sulfur cells of type (2; as a function of temperature of the cell for various sulfur pressures. The curve for saturated sulfur vapor corresponds to the case that the sulfur source and the cell are at the same temperature. For the other curves, the sulfur source was at temperatures different from that of the cell, \7hen sulfur vapors, produced by evaporation of liquid sulfur at a total pressure determined by the source temperature, reaches the cell compartment with its higher temperature, the E M F (volts) 0.20 0.18 0.16 0.14 0.12 0.10 0.08 1 0.06 0.04 0.02 calculated with formula (JT-1 1) -200 -I00 Temp °C E (volts) 2.50 Pig. 17* Emf as function of temperature for the sodium-sulfur cell with saturated and non saturated sulfur vapor. * Saturated sulfur pressure curve * Sulfur source at 350°C 0 Sulfur source at 300°C ° Sulfur source at 250° C x Sulfur source at 200° C 200 250 300 -*~Temp. °C 350 400 VO f \ 3 53 total pressure remains the same, but the partial pressure of the molecular species S2, S^...Sy, Sg is changed. The pressure of a particular species, e.g. S2, is related to those of all other species by known equilibrium constants of reactions such as 3S2 2S 2S2 -> S^, etc., (98) and for a given total pressure, the pressures of the various species can be calculated. Figure 18 shows the partial pressure of S2 at different temperatures with the sulfur source at 200, 250, 500 and 350°C. By combining Figures 17 and 18, we can construct the emf of cells of type (2) as a function of pa at 2 different temperatures (Figure 19). The emf can be represented by E = EQ - BE = 3.32 - ( 1.03 x 10~3 + ^ In aNa p| ) T (5-18) The sulfur pressure dependence indicates that sulfur is incorporated at the glass surface as single ions S" , as is to be expected if Ua2S is formed. The intercept at T‘ = 0 is EQ = 3.32 volts, or ^agS + Hexc.g )=153 kcal/mole for this reaction. As H^a^s = -'93 kcal/mole, HexcS= -60 kcal/mole, some- 94 3 0 0 °C o> in CL 1 10-= 250 °C 200 °C 10j L - l - 200 *-Temp, Fig. 18. Partial pressures of sulfur as a function of the temperature of overheating for sulfur vapor 300 generated by heating sulfur at various temperatures (indicated at the ctirves). 2.90 2.80 Ps = 10mm 2.70 — 2.60 2.50 Ps = 0.01 mm 2.40 200 250 300 350 -----------►- T °C pig. 19» Pc- isobars of the sodium-sulfur cell with Do 400 450 experimental points deduced from the data of Pig.17* 96 what smaller than in the oxide case. It should he not too different from the unknown enthalpy of the reaction NaoS + SiOo^ UapS.SiOp. Further, we find _ _= 2 d ^ d d 1 exc.sulf -17 cal/deg.mole t ^ In The four lines in Figure 19 fit the relation of eq.(5-13). With, low sulfur pressures established with the aid of H^S and mixtures BLpS + cells of type (2) give the emf as shown in Figure 20. The reaction H2S = H2 + iS2 leads to PHn # PSP K (ai) = ---1----S (.5-19) p PH^S with(97) 5 log Kp(,T) = - 4- ,5T- * 10 + 2.35 (5-20) Using eqs. (5-19) and (5-2.0; we can calculate values of pg as f(T), both for pure H2S and for mixtures H2 + HgS. Then using eq.(5-13) we can calculate the expected values of E of our cells and compare these to the observed emf's. There is good agreement, for T>330°C, but discrepancies are found for pure H2S at TO30°C. As shown in Figure 20 these discrepancies are removed by assuming that the tank H2S used con tained an excess of sulfur equivalent to (pg )extra E( volts) 2 3 0 100 -R = Imm Hg from fig. 7 * Measured • Calculated for pure H.S * Calculated for H2 S +10 atm S2 H2 S + H2 2' ■r4 200 3 0 0 4 0 0 ■Temp. °C 5 0 0 6 0 0 i’ ig* 20* Emf measurements of the sodium electrode in B>>S and equimolar H2 + H2S mixture compared with values calculated for Ps produced by pure H2S and by H2S + 10“^ S2 . -3 98 = 10”^atm. This extra sulfur may have originated from persulfide ions present in the material used to gene rate the E^S. It may he concluded that Pyrex glass cells may he used to measure the sulfur activity in gases. In order to reduce errors connected with a large value of E0, it is advisable to use cells Pt, OgCgVPyrex/ C» 82(g) rather than cells (2). Chapter YI Conduction in CdS CdS, pure or doped with foreign donors is a low resistivity electronic conductor when prepared under a high Cd vapor pressure, but becomes an insulator or a high resistivity semi-conductor after preparation in sulfur vapor(99). It is of interest to see if ionic conduction becomes appreciable under the latter condi tions. The use of cells to discriminate between ionic and electronic conduction has been discussed in detail by Wagner(100,101). One of these methods is to use the material in question as a solid electrolyte in an electro-chemical concentration cell, for our case, it is done by maintaining a different sulfur' partial pressure at each side of the crystal as shown: The potential developed in the cell is (6-2) with AGr = RT In (6-3) 100- In this equation n is the number of farads of charge transported for each mole of molecular sulfur* If we assume the reaction to be S2 + 4e“ = 2S“ (,6-4) then n = 4 in this case, t^ is the transport number for ions defined by = {6_5) 1 total ^i + ^1. Thus if the current is carried exclusively by ions, i.e. (Tel« ^ and t^ = 1, the emf measured will be equal to T5Q1 P S 2 ( I I ) Ei = If ln 1 42 PS2(I) . On the other hand, if the charge is carried mainly by electrons,., then - will short out E •, and then Em = 0. 7 ■ el i m If the crystal is a mixed conductor, intermediate values corresponding to eq.(6-2) with 0<t-<1 are found. VI. I Experimental Two single crystals of GdS were used. One was a single crystal of pure, undoped CdS. The other was a crystal doped with 2 x 10 ^cm J gallium. The doping was achieved by burying the CdS crystal under a powder mixture of CdS + 10“^ Ga(NO^)^ and heating it in H^S at 8O0°C for 30 hours. The crystal changed its color from yellow to orange red. 101 Figure 21 shows half of the cell used in this inves tigation. The other half was identical. Dried nitrogen gas was used as an inert carrier gas. The gas was loaded with S2 or Cd vapor by passing it over sulfur or cadmium sources present at the two sides of the cell, heated at temperatures appropriate to give the required vapor pressures. The source temperatures were established with the aid of resistance heaters provided with temperature controllers. In this manner it was possible to establish different sulfur or cad mium vapor pressures at the two sides of the crystal. Chromel-alumel thermocouples were used to mea sure the temperature distribution in the apparatus. Graphite paste and wire were used as contacts and leads; voltages were measured with the aid of a high- impedence Keithley 61 OB voltmeter. VI. II Results and Discussion Instead of establishing different sulfur of cadmium pressures, we can also use cadmium at one, sulfur at the other side, such as Cd(gj / CdS-crystal / S2(g) (6-7J The cell emf now is given by eq.(6-2) with AG. = AG:q^s> the free enthalpy of the reaction N+S, T . C . T1C1 N^+S, Sulfur Z' CdS Crystal Cadmium or Quartz Furnace Fig. 21. Apparatus used in GdS conduction experiments. 102 Cd(g) + S2(g) = CdS(s) ; aG° 103 (6-8) with(102) A^CdS " 7 7 m r = lo g KcdS _ _ 13, 970 + 20.486. (6-9) CdS The emf we measured is approximately zero for both pure CdS and Ga-doped CdS crystals as solid electro lyte. A small emf occasionally measured was found to be due to the thermoelectric power produced by the diffe rence in temperature at the two electrodes. It is seen in Figure 22 that E measured is proportional to T', the difference of temperature across the sample. This straight line relationship is expected for an electro nic conductor as discussed in Chapter II. Similar results were obtained with cells of type (6-1;. These results indicate that t^ = u. Recent measurements of the self diffusion of cadmium and sulfur in CdS(103) make it possible to check this result. The conductivity of an ionic species j with charge z-q, = n.z.qv., 1 J J J tJ and the coefficient of self diffusion involving this " f t species, Di are related through the Einstein J J z.qD * relation v^ = ■ Thus if is known, can be calculated. It was found that at high Pq^» -^cd^ ^S * AE mv 0.6 0.5 0,4 0.3 0.2 0 6 8 AT °C 10 12 Pig. 22. Emf measured against at of the two electrodes. o 4 * - 105 * x * at low , only involves a charged species, Thus at all pQ(j we need only consider For pure CdS, DCd = x 10~^ P§d3 exp^ ”1,2^ ev/kT ) (6-10) and the species involved is the singly ionized inter stitial Cd£ . From this we find at T' = 700°C and pCd “ 1 atm> h*d = 7.29 x 10“10,6 cm2/sec = 1.82. x 10“^ cm2/sec and * ziqD 1.87 x 1019 i4- 1.87 x 10 3 2/ nJ_ Toar = E¥0T C3T om /volt-seo- Inserting these values into G". = n.z.qv. , with the J J J J relation of n. = N'tjl, where K' is the value of J # of sites/c.c. of the compound involved, in this case 22 we have N' = 2 x 10 /cm 0 , so —6 / ^Cdf = ^ x /cm-ohm. On the other hand <Te = 2nvj , q ve (6-11) b p with vg = 300 cm /v-sec; n v " = < 1 / + K S ^ 1 / 3 P c / 3 t 6 - 1 2 ) b , . . 106 i i cq . Kgy = 9*15' x 105y exp( -1.75 ev/kl ) (6-13) Therefore, at pC(^ = 1atm, CT = 13.2 /cm-ohm, this leads to t = g" 1 s S. f cre +o~i ^ = 1 x 10“ , which is indeed«1. In doped crystals under high sulfur pressure we ii have to deal with as the major ionic species. For this case we may use the diffusion coefficient of In-doped CdS, thus DCd = x 1°2 [Ga^expC -1.39ev/kl ) (6-14) • H * decreases at higher pcd values; for the sake of simplicity we neglect this decrease so that we over- * X * estimate Dcd • Thus, for (G-a) = 10~y site fraction and T = 700°C, we have = 1.14 x 10-7 cm2/sec> * }Cd and ,-3 0*7 = 1.49 x 10 ^ /cm-ohm at p ^ = 1 atm. 1Q — ^ On the other hand n0 varies between 2 x 10 * cm ^ 1 f t « — and 1 x 10 cm” (104). Taking an average of 5 x 10' ,18 cm , we get 107 0~Q = 240 /cm-ohm. Thus, for this case we have t = ^ i ore = 6.2 x 10 , which is again«1. Therefore, under all our conditions the ionic conductivity is negligible as observed. Chapter VII Conclusion This thesis deals with various applications of electrochemical cells having solids as the electrolytes# Electrolytic cells based on stabilized zirconia as a solid electrolyte may be used to remove oxygen from streaming or stationary gas. Minimum oxygen pres sures that can be accurately measured are limited by the onset of electronic conduction in the zirconia at low oxygen pressures. Typical values for the minimum oxygen pressure, reached when using commercial zir conia tubes, were 10~5® atm at 530°G and 3 x 10“^ atm at 800°C. Electrlytic cells Na/ Pyrex /lTa,Sn, in which Pyrex was used as a solid electrolyte, may be used to measure the sodium activities. Values of the sodium activity down to 1 x 10-5 moie fractions were achieved by electromotive force measurements on that cell. Pyrex cells W,Na/ Pyrex/ Pt,02 and W,Na/ Pyrex/ C,S2 may be used as an oxygen of sulfur sensor respec tively. 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Creator Yuan, Daniel Ta-Nien (author)

Core Title The Application Of Electrochemistry Of Solids

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Advisor Kroger, Ferdinand A. (committee chair), Smit, Jan (committee member), Whelan, James M. (committee member)

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Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA