1. Ionic Conductors: Characterisation of Defect Structure Lectures 11-12 Structure-Conductivity Relationships Dr. I. Abrahams Queen Mary University of London Lectures co-financed by the European Union in scope of the European Social Fund

2. Polymorphism Gibbs’ definition of a phase “A substance that is uniform throughout not only in chemical composition, but also in physical state”. In crystalline solids more than one structure may exist for a particular compound of a defined composition. This is known as polymorphism. Wurtzite: hexagonal close packed S 2- ions with Zn 2+ in half the tetrahedral sites Sphalerite: cubic close packed S 2- ions with Zn 2+ in half the tetrahedral sites Eg. ZnS

3. Lectures co-financed by the European Union in scope of the European Social Fund Phase Transitions In solids where polymorphism exists, structural changes may occur due with time, pressure or temperature. These phase transitions can have important consequences for the properties of materials based on these compounds. Phase transitions can range from major changes in structure: e.g. ring and chain formation in metaphosphates To more subtle transitions such as the ferroelectric transition in BaTiO 3 In solid electrolytes, there are usually high numbers of vacancies/interstitials and therefore there is often the possibility that order  disorder transitions can lead to polymorphism.

4. Lectures co-financed by the European Union in scope of the European Social Fund The Phase Rule P + F = C + 2 P = Number of phases. As defined above C = Number of components. The minimum number of chemical species needed to define the composition. F = degrees of freedom and relate to variation in temperature and pressure. If we work at constant pressure there is one less degree of freedom (condensed phase rule). P + F = C + 1

5. Lectures co-financed by the European Union in scope of the European Social Fund

6. Classification of Phase Transitions Every polymorph has an associated free energy (G) where: G = H - TS = U + PV - TS At a phase transition between two polymorphs the difference in free energy  G = 0.

7. Lectures co-financed by the European Union in scope of the European Social Fund First order transitions show a discontinuity in the first derivates of free energy, i.e. discontinuities in S, V (H). Second order phase transitions are those that show a discontinuity in the second derivatives of free energy: heat capacity, thermal expansion, compressibility. Heat capacity can be measured by calorimetry. In techniques such as differential thermal analysis. First order transitions are seen as endothermic or exothermic peaks, while second order transitions are often seen as changes in the baseline.

8. Lectures co-financed by the European Union in scope of the European Social Fund Monitoring Phase Transitions Phase transitions are commonly monitored by a number of techniques, e.g. Differential Thermal Analysis (DTA) Differential Scanning Calorimetry (DSC) Dilatometry Densitometry X-ray Diffraction Neutron Diffraction In fact, any technique which measures the physical properties of a material can in principle used to study phase transitions. For conducting solids, conductivity is dependent on structure and therefore a.c. impedance spectroscopy can be extremely sensitive to structural changes.

9. Lectures co-financed by the European Union in scope of the European Social Fund Impedance Spectroscopy A.C. impedance spectroscopy is the technique of choice for measuring conductivity behaviour in ion conducting solids. In a.c. impedance spectroscopy the response to an alternating voltage through measurement of impedance (complex resistance) is observed. Typically, this involves the application of a range of single-frequency voltages and measurement of impedance in the frequency domain. Measurements are normally carried out over a broad frequency range. On application of an applied alternating voltage, an alternating current is produced which is shifted in phase from the voltage by angle . This phase difference is attributed to the delay in the electrical response of the sample to the applied voltage.

10. Lectures co-financed by the European Union in scope of the European Social Fund where  (t) = V 0 sin (  t) which is the monochromatic signal at frequency of  / 2  applied to the system, and i(t) = I m sin(  t + θ) is the resulting steady state current measured. θ is the phase difference between the voltage and the current. The impedance Z is given by:

11. Lectures co-financed by the European Union in scope of the European Social Fund Since the voltage and current alternate periodically as determined by the applied frequency, they can be described by complex quantities including real and imaginary components. Assuming a linear response to the applied voltage (as occurs at low applied voltages) then the waveforms can be considered to be sinusoidal and can be described by vector quantities.

12. Lectures co-financed by the European Union in scope of the European Social Fund In order to simplify the handling of the impedance of an a.c. circuit with multiple components, Heaviside in 1886 adapted these complex exponential functions to the study of electrical circuits. In the complex form impedance may be described as: where: Thus when  = 0, Z’ = R e and when  =  /2 where: R e is the frequency independent resistance and C is the capacitance. Measurement of the impedance magnitude |Z| and phase  allows for the calculation of the real and imaginary parts of impedance, Z' and Z''

13. Lectures co-financed by the European Union in scope of the European Social Fund In the standard two probe measurement, a sintered pellet of the sample is coated with gold or platinum electrodes. The impedance is then measured as a function of frequency and plotted as Z’’ vs Z’. The spectrum will have contributions to impedance from the sample grains and their grain boundaries. Since the electrodes are blocking, there is a build up of charge at the electrode electrolyte interface and this is seen as a capacitative spike. R 1 = intra grain resistance R 2 = Total resistance R 3 = inter grain (boundary) resistance  = 1/R x (thickness/area)

14. Lectures co-financed by the European Union in scope of the European Social Fund Structure-conductivity relationships in the BIMEVOXes The BIMEVOXes represent a good example to illustrate structure- conductivity relationships. They are solid solutions based on substitution of V 5+ (and/or Bi 3+ ) by iso- and alio- valent cations in Bi 4 V 2 O 11- . They show high oxide ion conductivities at relatively low temperatures. These solid solutions have a general formula Bi 2 M l + x V 1-x O 5.5-(5- l )x/2-  e.g. Bi 2 Co x V 1-x O 5.5-(3x/2)-  (BICOVOX)  300 = 10 -4 S cm –1 Bi 4 V 2 O 11-  and the BIMEVOXes show complex polymorphism.

15. Lectures co-financed by the European Union in scope of the European Social Fund Structure of Bi 4 V 2 O 11-  The idealised structure of Bi 4 V 2 O 11-  consists of alternating layers of [Bi 2 O 2 ] n 2n+ and [VO 3.5 0.5 ] n 2n-

16. Lectures co-financed by the European Union in scope of the European Social Fund Polymorphism in Bi 4 V 2 O 11-  In Bi 4 V 2 O 11-  three principal polymorphs have been identified: 720 K 840 K 1160 K       liquid The phase transitions are associated with vacancy ordering in the oxide sublattice. The crystallographic relationships of the various polymorphs have been characterised with respect to a mean orthorhombic cell: a m  5.53, b m  5.61 c m  15.28 Å

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18. Oxide Ion Conductivity in Bi 4 V 2 O 11-  High oxide ion conductivity observed in Bi 4 V 2 O 11-  in the order of 10 -3 S cm -1 in the  -phase stability region.

19. Lectures co-financed by the European Union in scope of the European Social Fund Close examination of the Arrhenius plot of Bi 4 V 2 O 11-  reveals a possible phase transition at around 650  C. This transition appears to be very subtle and is not evident in DTA thermograms. Conventional X-ray diffraction also shows no obvious structural change. High resolution neutron diffraction appears to confirm the existence of an orthorhombic distortion of the tetragonal  -phase. a = 3.978(3), b = 3.983(3), c = 15.47(1) Å

20. Lectures co-financed by the European Union in scope of the European Social Fund  -Bi 4 V 2 O 11-  at 650  C  -BIMGVOX at 25  C  -Bi 4 V 2 O 11-  a new polymorph

21. Lectures co-financed by the European Union in scope of the European Social Fund  -Phase BIMEVOXes In the divalent cation substituted BIMEVOXes,  -phase stabilisation generally occurs in the range x  0.10 to 0.13. X-ray diffraction shows no evidence for structural change from ambient temperatures to melting above 800  C Arrhenius plots of conductivity do however show two linear regions of different activation energy. Arrhenius plot of total conductivity for BINIVOX14

22. Lectures co-financed by the European Union in scope of the European Social Fund   ’ Transition Using neutron diffraction, the  ’   phase transition is clearly evident. The  ’-phase shows an incommensurate superlattice due to ordering of oxide vacancies in the vanadate layer. At higher temperatures this superlattice disappears leaving the fully disordered  -phase.

23. Lectures co-financed by the European Union in scope of the European Social Fund Kinetics of Phase Transitions Aging effects on annealing can be measured through isothermal measurements of conductivity e.g. in BIZNVOX19.

24. Lectures co-financed by the European Union in scope of the European Social Fund The conductivity decay profiles in BIZNVOX0.19 were modelled using a combination of a stretched exponential and simple exponential functions: t (  C)  1 (h)  2 (h) 21722.71600 2748.3889 3332.5113 Two processes are evident: (1) Ordering of oxygen vacancies (2) Change in oxygen stoichiometry