Supporting information

Transcription

1 Electonic Supplementay Mateial (ESI) fo Physical Chemisty Chemical Physics. This jounal is the Owne Societies 18 Suppoting infomation Nonstoichiometic oxides as a continuous homologous seies: linea fee-enegy elationship in oxygen exchange Stanislav A. Chizhik a,b, Alexande P. Nemudy a, * a Institute of Solid State Chemisty and Mechanochemisty, SB RAS; 6318 Kutateladze 18, Novosibisk, Russia b Novosibisk State Univesity, 639 Piogova, Novosibisk, Russia Appendix 1 The equilibium exchange ate can be consideed in tems of the tansition state theoy as k i n i G i exp G RT (S.1) whee α i and n i ae activities and eaction odes of the ds eactants, k is the ate of tansfomation of the tansition state to the eaction poducts (usually popotional to kt/h), G and G ae standad Gibbs enegies fo the tansition state and fo the system of eactants in thei gound states. The fomulation given by eq S.1 assumes that a specific diection of the eaction is consideed the fowad o the evese (oxidation o eduction). The components in eq S.1 and thei values will indeed depend on the diection selected. At the same time, as the equilibium is consideed, the esulting value of is independent of the eaction diection by the definition. Additionally, as the equilibium state of an oxide having cetain oxygen non-stoichiomety δ (the state of a δ-homologue) is fully defined by the pai of paametes δ and T (o equivalently by po and T), the dependence (δ, T) (o (po, T)) does not depend on the selected eaction diection as well. It can be said moe detailed that values of the mass action facto n i i i and standad Gibbs enegies enteing eq S.1 ae unambiguous functions of (δ, T) o (po, T) due to constaints caused by equilibium, chage neutality and consevation of cystallogaphic positions atios in the oxide phase. G The equation S.1 could be the way to detemine Gibbs activation enegy G but it would equie knowledge of detailed mechanism of ds (that is the mass action poduct), which is unknown as a ule, and is athe a subject of study in most cases. A compomise could be the fomal inclusion of the mass action coefficients into the activation facto of the eaction like the following

2 G k exp G RT, (S.) with G to be Gibbs enegy of the ds eactants system at thei cuent activities. This notation is totally independent of the selected eaction diection. This allows fomulation of an appaent enegetic value qualitatively analogues to Gibbs activation enegy a i lni ln G G RT n RT k i The usage of such pseudo-activation enegy instead of tue Gibbs baie given by G G (S.3) bings an advantage of easy analysis of possible LFER without knowledge of G the detailed mechanism of ds. The tem appeaing in a due to k does not influence the desied LFER analysis as not contibuting a dependence on δ (the same is tue fo any othe possible constant coefficients of, which may appea due to featues of expeimental techniques). A dawback is that BEP coefficient β in eq obtained that way will contain additional contibution by the δ-paametic dependence of the mass action poduct in the equation S.1. This hindance is not an insupeable one though as this additional contibution can be analyzed by poviding and testing necessay hypotheses on the mechanism of ds. An example of a theoetic famewok necessay fo such analysis is suggested in [7]. Appendix Expeimental setup and theoetic backgound of the oxygen patial pessue elaxation technique Figue 1S. Expeimental installation fo obtaining of the phase diagams «3-δ log po -T» by means of the quasi equilibium oxygen elease (QEOR) method and kinetic data by means of oxygen patial pessue (OPPR) technique.

3 To accomplish the task of LFER analysis, we need to obtain two sets of data: equilibium data (chemical potentials of δ-homologues) and kinetic data (elaxation data at diffeent tempeatues on oxygen exchange fo oxide with a cetain stoichiomety). Ealie [13, 15], we have developed an installation (Fig. 1S), which allows fo continuous monitoing of ро in continuous-flow fixed-bed eacto with MIEC oxide sample duing the step-like change of oxygen patial pessue using YSZ oxygen senso. The installation allowed obtaining both data sets [13, 3] while opeating in diffeent conditions. The installation is based on the CSTR type eacto made of quatz tube filled with quatz insets in ode to minimize the fee volume V in which the oxide sample is placed. The section of the eacto tube including the gas line and the sample placement position is kept at egulated tempeatue. The gas switching/mixing equipment povides supplement of the eacto with the mixtue of an inet sweep gas (usually He) with oxygen at egulated patial pessue. Afte holding the sample in the gas flow with a constant initial oxygen patial pessue (fo a time necessay fo the oxide stoichiomety equilibation) step like dop/ise (usually dop) of the oxygen patial pessue is tiggeed by the gas switching equipment. The dop/ise povokes the oxygen elease/uptake fom/on the oxide and coesponding change of the stoichiomety until the new equilibium is eached with the lowe/highe oxygen pessue. The pocess of elaxation is egisteed with the oxygen senso installed in the gas line downsteam to measue the dependence of po on time at the outlet of the eacto. The evolution of po afte the pessue dop/ise is defined by the mass balance equation descibing the change of po in the eacto due to contibutions povided by input and output gas flow J in/out and intenal oxygen elease/uptake by the oxide dq dt W d po p Jin poin p Jout po p dq dt dt (S.4) W is is numbe of moles of gas in the fee eaction volume at given tempeatue V p RT, po in is the oxygen patial pessue in the input sweep gas flow, p is total gas pessue (1ba), Q is cuent numbe of oxygen moles in the oxide sample. The output sweep gas flow is defined by the oveall mass balance J J dq dt. The solutions to the equation S.4 ae used fo out in analysis of po (t) dependencies obtained in two typical egimes of the setup (details of the solutions ae descibed in [13, 14]). In the oxygen quasi-equilibium elease (QEOR) egime the input oxygen pessue is typically dopped fom 1 ba to zeo (oxygen flow is switched to He). Setting the gas flow to a sufficiently low level and using the sample with high specific suface

4 aea povide the conditions at which oxygen elease fom the oxide in the sample is able to estoe po in the eacto s fee volume to a value close to po eq (Q) coesponding to equilibium with the oxide with cuent oxygen stoichiomety. In this egime, the oxygen elease ate dq dt is defined by oxygen emoval fom the eacto by the sweep gas flow. Thus, integation of the equation gives the appoximation to Q eq (t) dependence coesponding to the egisteed po (t) t p po t po t Q q t Q W ln J dt e p po in p po t (S.5) Recalculation of Q values to the oxygen non-stoichiomety paamete 3-δ finally gives the equilibium dependencies fo ln(po ) 3-δ T phase diagams. In the second egime, the oxygen patial pessue elaxation (OPPR), the oxygen patial pessue is dopped fom the initial value coesponding to definite initial 3-δ i composition to the final value poviding decease of the stoichiomety by definite small Δδ<<1 [13]. At this egime, high level of the sweep gas flow is used and the sample has lowe suface aea which povide that oxide appeas in the non-equilibium conditions in the sweep gas flow. The oxygen elease ate dq dt is defined then by the oxygen exchange eaction with the oxide going in the conditions of small deviation fom the equilibium. The solution to the equation (S.4) can be obtained in the quasi-stationay appoximation as po po po f i f po Aexp k t (S.6) whee po i and po f ae the initial and final oxygen patial pessues, A is the amplitude of the pessue elaxation signal and k is the elaxation ate constant defined by 1 V Q p po k Sk J po in f (S.7) ΔQ is the total change of oxygen content in oxide afte the elaxation, ΔpO = po i - po f is the oxygen patial pessue step in the elaxation [14], V and S ae total volume and suface aea of the oxide sample, k δ is the oxygen suface exchange constant. The equilibium exchange ate is then obtained accoding to the equation 3.

5 Appendix 3 oxide O Eq. 1 has the consequence; it allows to conside the equilibium dependencies as infomation on electonic stuctue of oxide and to estimate the density of states (DOS) nea the Femi level [15]: g oxide [ e ] O e 8 F 1 (4) In paticula, fo the SCF peovskite, whee the dependence of the oxygen nonstoichiomety (δ) fom the patial oxygen pessue po (Fig. 1a) may be appoximated by the atio ln po, the DOS is: 8 g( F ) RT (5) Since the slope changes duing the tansition fom P 1 to P phase, it can be assumed that these phases have metal-like electonic stuctue with diffeent density of states nea the Femi level. Table 1S. Paametes β (the (slope of equilibium dependence of 3-δ vs. log po ) fo SCF phases P 1 and P. T, o C Paamete β fo P 1 phase Paamete β fo P phase 8 -,47 1,4E-4 -,147 4,8E ,758 1,9E-4 -,36 6,6E ,678 1,3E-4 -,381 5,6E-5 9 -,57 7,E-4 -,69 6,9E-5

6 Fig. 3S. Density of states nea the Femi level and log po vs. oxygen nonstoichiomety fo P 1 and P phases of SCF Fig. 4S. Density of states nea the Femi level and log po vs. oxygen nonstoichiomety fo SF calculated using igid band model Appendix 4. SCo.8 Fe. O 3-δ SFeO 3-δ a b

7 c d Fig. 6S. Dependencies of patial enthalpy (hh ) (a, b) and entopy (s-s ) (c, d) on oxygen nonstoichiomety fo SCF and SF peovskites calculated fom the equilibium data obtained using QEOR method. e coelation of patial enthalpy and entopy fo SCF e