1. Ionic Conductors: Characterisation of Defect Structure Lectures 9-10 Fast ion conduction in solids II amorphous materials Dr. I. Abrahams Queen Mary University of London Lectures co-financed by the European Union in scope of the European Social Fund

2. Oxide Glasses Glasses are typically made up of polymeric frameworks which show no long-range order. In inorganic oxide based glasses the framework typically consists of corner sharing MO 4 tetrahedra or MO 3 trigonal planes. Three types of oxides are of interest in glass chemistry: (1) Network Formers Oxides that readily form glasses when quenched from high temperatures, e.g. SiO 2, P 2 O 5, B 2 O 3 etc. (2) Network Modifiers Oxides that that can be mixed with network formers to yield glasses. They are typically ionic and act by disrupting the network., e.g. Li 2 O, Na 2 O, CaO etc. (3) Network Intermediates These oxide do not form glasses on their own, but when mixed with glass formers may either act as network formers or network modifiers, e.g. Al 2 O 3, SnO 2, TiO 2 etc.

3. Lectures co-financed by the European Union in scope of the European Social Fund Glasses are typically formed by rapid cooling of melts and are thus governed by kinetics, through the control of the cooling rate. In theory, every inorganic material, within a certain compositional range, can be transformed into a glass, if extreme conditions of synthesis are available If the liquid cooling rate is sufficiently high, then instead of crystallisation, the undercooled liquid is transformed into a supercooled state. This state of the liquid is thermodynamically metastable, as it possess a higher internal energy than the corresponding crystalline state. Glass formation

4. Lectures co-financed by the European Union in scope of the European Social Fund The described behaviour would be changed if the supercooled liquid were cooled extremely slowly. In this case, the entropy of the supercooled liquid would follow the dashed line and would be zero at a positive temperature, T 0. A plot of entropy vs temperature leads to the conclusion that a glass, at 0K, would have a finite amount of entropy known as the zero-point entropy. This is regarded as frozen-in configurational entropy.

5. Lectures co-financed by the European Union in scope of the European Social Fund As a consequence, further cooling would result in a negative entropy of the glass at 0 K. Obviously, according to the third law of thermodynamics this hypothetical behaviour is impossible and is known as the Kauzmann paradox. This has been explained by considering that below T 0 vibrational entropy would still remain and this would be reduced to zero at 0 K in accordance with the third law. The major consequence of this is that glasses cannot be formed below T 0 (the Kauzmann temperature) and hence this temperature can be identified as the ideal glass transition temperature.

6. Lectures co-financed by the European Union in scope of the European Social Fund Thus glasses have a higher free energy than the corresponding crystal and are considered metastable.

7. Lectures co-financed by the European Union in scope of the European Social Fund When a glass is heated it exhibits characteristic thermal events, Tg the glass transition temperature, Tc the crystallisation temperature and Tm the melting temperature. Thermal Analysis of Glasses

8. Lectures co-financed by the European Union in scope of the European Social Fund DTA trace of 56Li 2 O:2ZrO 2 :40 P2O 5

9. Lectures co-financed by the European Union in scope of the European Social Fund Cation Conducting Glass Electrolytes When oxides such as Li 2 O or Ag 2 O are used as a network modifiers, the M + ions are potentially mobile and can hop between available sites in the glass. Advantages over crystalline electrolytes: While crystalline conductors show anisotropic conduction properties, in glasses conduction is isotropic. When used as real materials, crystalline electrolytes suffer from grain boundary resistances which reduce their overall conductivity. In monolithic glasses there are no grain boundaries. Crystalline solid electrolytes generally have well defined composition ranges. In glasses it is possible synthesize glasses with wide ranging compositions and hence tailor specific properties such as conductivity, air sensitivity and thermal stability.

10. Lectures co-financed by the European Union in scope of the European Social Fund Monolithic Glass Batteries Glass Electrodes Substitution of the network forming oxide by suitable transition metal oxides allows for the introduction of electronic conduction into the system. This means that glasses can be synthesized which show conductivities varying from pure ionic to pure electronic. This could allow for the construction of a monolithic glass battery with anode, cathode and electrolyte regions.

11. Lectures co-financed by the European Union in scope of the European Social Fund In such a system is that the network extends throughout the glass monolith and components are air stable. Advantages: Problems associated with electrode/electrolyte interface are diminished, while grain boundary resistances are removed altogether. Cheap construction Potentially miniaturisable therefore suitable for miniature power supplies e.g. on board and on chip power sources.

12. Lectures co-financed by the European Union in scope of the European Social Fund There is no single theory of ion transport in glasses to explain high ionic conductivity. The three most important models are: (1) The strong electrolyte model (Anderson-Stuart) This is based on the assumption that effective carrier density N i is independent of ion concentration and temperature and thus  i the mobility, of these species is a quantity that depends on both parameters, (ion concentration and temperature). (2) The weak-electrolyte model According to this model  i is independent of ion concentration and is weakly dependent on temperature, while N i depends on both parameters. (3) The defect model This is based on the same principles as those identified in crystalline ion conductors. Ionic Conduction in Glasses

13. Lectures co-financed by the European Union in scope of the European Social Fund According to the strong electrolyte model a cation hops from an occupied site near a non-bridging oxygen (NBO) to a vacant site which is close to another NBO. In doing this, the conducting ion has to overcome the energy barrier generated by the bridging oxygen (BO). At first the mobile ion needs to remove itself from association with NBO (binding energy, E b,). The energy that is associated with long range motion, is strain energy, E S. Thus, the total activation energy for this process is given as a sum of these energies. (a) strong-electrolyte model and (b) weak- electrolyte model

14. Lectures co-financed by the European Union in scope of the European Social Fund After necessary approximations this equation can be written as Where, z o and r o are the charge and radius of the O 2- ion, respectively,  is a non-periodic lattice parameter determined by the distance between neighbouring sites, r is the cation radius r D is the bottleneck radius in the glass, G is the elastic modulus and  is a covalency parameter. The weak electrolyte model assumes the existence of two sites and that the conduction process is dominated by the ions, which are thermally brought to higher energy sites.

15. Lectures co-financed by the European Union in scope of the European Social Fund Because there is no long range order, the structure of glasses are not easily accessible using standard characterisation techniques such as X-ray diffraction. Other techniques such as NMR, IR, EXAFS and neutron scattering, can be employed to probe the local structure. Most of these techniques are also suitable for crystalline materials where diffraction methods can give a clear picture of the structure. Therefore it is possible to compare results from the glasses with crystalline compounds of similar composition in order to yield the structure of the glass. The preferred coordination environments of ions in oxides will be the same whether in glass or crystalline forms. Structural Characterisation of Glasses

16. Lectures co-financed by the European Union in scope of the European Social Fund Glass Structure Glass forming oxides typically adopt tetrahedral or trigonal planar coordination environments. These can be classified according to the Q n nomenclature. Where n represents the number of bridging oxygens.

17. Lectures co-financed by the European Union in scope of the European Social Fund NMR is a nucleus specific technique that can yield important information on local structure. Atomic nuclei are made up of protons and neutrons (except 1 H). The nuclear spin results from the coupling of these nucleons and is characterised by the spin quantum number I I can have integral, half integral or zero values. Nuclei with an odd mass number have half-integral spins e.g. 1 H I = 1/2, 7 Li I = 3/2 Nuclei with an even mass number and even charge number have zero spin e.g. 12 C and 16 O I = 0 Nuclei with an even mass number, but with an odd charge number have integral spins, e.g. 14 N and 6 Li I =1 Solid State NMR

18. Lectures co-financed by the European Union in scope of the European Social Fund The motion of charged particles has an associated magnetic field. If a nucleus possesses angular momentum then there is an associated magnetic moment . Let us represent the magnetic moment by a vector No Applied field Random orientation Applied field Parallel or antiparallel to applied field direction

19. Lectures co-financed by the European Union in scope of the European Social Fund m I = -1/2 m I = 1/2 Energy In an applied field the energy of the nucleus is dependent on the magnetic quantum number m I This interaction of the magnetic moment with the applied static magnetic field is known as the Zeeman interaction.

20. Lectures co-financed by the European Union in scope of the European Social Fund In order to obtain an NMR spectrum we need to excite nuclei. This is achieved using a radio frequency pulse. Energy rf The resulting NMR spectrum shows an absorption of the rf frequency. The resonance frequency is proportional to the strength of the applied field.

21. Lectures co-financed by the European Union in scope of the European Social Fund Chemical shift One of the most important features of NMR is the chemical shift. This is caused by nuclei with differing degrees of shielding. This means that they absorb at different applied field strengths. Thus the circulating electrons shield the nucleus from the full extent of the applied field. Electrons surrounding each nucleus interact with the magnetic field causing a circulation of the electronic charge around the nucleus. This results in a secondary magnetic field at the nucleus that is opposed to the applied field.

22. Lectures co-financed by the European Union in scope of the European Social Fund Electron withdrawal causes a de-shielding effect, while electron donation causes a shielding effect. The degree of shielding is dictated by the chemical environment, i.e. the neighbouring atoms/ions and the nature of the bonding. The resulting chemical shift of the resonance is therefore characteristic of particular chemical environments. Chemical shifts are recorded with respect to a standard reference Chemical shift (  ppm) = (observed resonance frequency – resonance frequency of standard) ____________________________________________________ operating frequency

23. Lectures co-financed by the European Union in scope of the European Social Fund Dipolar interactions between spins can occur. In the case of interaction between like spins, for a single nucleus the spectrum would consist of two lines with peak separation given by: Where  is the gyromagnetic ratio for a particular nucleus  is the angle between the internuclear vector and the magnetic field r is the distance between nuclei. A similar equation can be written for interactions between unlike spins.

24. Lectures co-financed by the European Union in scope of the European Social Fund This interaction occurs between a nucleus and all of its neighbours. In addition in a randomly orientated polycrystalline solid this interaction is averaged over all values of . This leads to severe broadening of spectra compared to solution state NMR. The peculiar line shape of solid state spectra is due to directionally dependent differences in shielding. This is known as chemical shift anisotropy.

25. Lectures co-financed by the European Union in scope of the European Social Fund Isotropic Chemical Shift  iso = (  11 +  22 +  33 )/3 Chemical Shift Anisotropy  =  33 - (  11 +  22 )/2 Asymmetry  = (  22 -  11 )/(  33 -  iso ) The solid state line shape can be described by the chemical shift tensor which has three principal components which are ordered according to the Haeberlen convention |  33 -  iso | > |  11 -  iso | > |  22 -  iso |

26. Lectures co-financed by the European Union in scope of the European Social Fund In order to narrow the line width and minimise the effects of chemical shift anisotropy, the sample can be spun in the magnet. If the spinning sample is orientated at the so called magic angle of 54  44’ to the applied field then the term (1- 3cos 2  ) = 0 and the spectrum simplifies. In order to reduce the spectrum to a single line, the sample must be spun at frequency greater than or equal to the spread of frequency corresponding to the anisotropy. At lower spinning speeds the spectrum appears as a central isotropic peak flanked by spinning sidebands.

27. Lectures co-financed by the European Union in scope of the European Social Fund 31 P NMR spectra of lithium aluminium titanium phosphate (LATP) glasses Q 1 Ti/Al Q2Q2 Q 1 Li

28. Lectures co-financed by the European Union in scope of the European Social Fund Derived NMR parameters for 31 P spectrum of LTP glass. QnQn  iso ppm  ppm  Area (%) -3.21360.012.8 -10.41191.041.5 -19-1580.645.7

29. Lectures co-financed by the European Union in scope of the European Social Fund The area of each peak (and its associated spinning sidebands) is proportional to the number of phosphate atoms in a particular environment. This means that the spectrum contains quantitative information. By taking the ratios of the different phosphate species present and with a knowledge of the composition of the glass it is possible to calculate how much oxygen is not associated with the phosphate network and therefore bonded exclusively to Ti. Since the number of Q 1 Ti species is known we can also calculate the number of phosphate groups that are linked to Ti (i.e. coordination number). Hence it is possible from this simple 1-dimensional spectrum to derive a structural formula for LTP glass.

30. Lectures co-financed by the European Union in scope of the European Social Fund Li + 10 Ti 4+ 0.17 (TiOO 4/2 ) 2- 0.83 (PO 2 O 2/2 ) - 6.98 (PO 3 O 1/2 ) 2- 1.03 5-CN Ti Q 1 PQ 2 P NetworkIons Structure of LTP glass

31. Lectures co-financed by the European Union in scope of the European Social Fund 27 Al NMR spectra of LATP glasses [Al(OP) 4 ] [Al(OP) 6 ] [Al(OP) 5 ]

32. Lectures co-financed by the European Union in scope of the European Social Fund Compositional Variation of Al species in LATP glasses

33. Lectures co-financed by the European Union in scope of the European Social Fund Electrode Glasses Electrode glasses, show mixed ionic/electronic conduction. e.g. in lithium manganese phosphate the Mn 2+ ion is strongly paramagnetic causing severe line broadening in NMR. However at low concentrations it is possible to obtain spectra. LMnP (60-x)Li 2 O : (10-x)MnO : 40P 2 O 5

34. Lectures co-financed by the European Union in scope of the European Social Fund At x = 5, both Q 1 and Q 2 groups are visible in the 31 P spectrum At x = 10, both sites are still visible. However the relative intensity of the Q 1 resonance is greatly reduced. This suggests that Mn 2+ is preferentially located near Q 1 sites.

35. Lectures co-financed by the European Union in scope of the European Social Fund Trends in isotropic chemical shift (  iso ) Trends in (  iso ) with composition can yield important structural information. For example in the glass system (0.55-x)Na 2 O: xSrO:0.45P 2 O 5 (0  x  0.55) The glass network is a mixture of Q 1 and Q 2 phosphate groups R. Pires, I. Abrahams, T.G. Nunes and G.E. Hawkes, J. Non-Cryst. Solids. 337, 2004, 1.

36. Lectures co-financed by the European Union in scope of the European Social Fund The trend observed  iso, appears to indicate a preferential substitution of Na + ions by Sr 2+ associated with the Q 1 phosphate species and subsequent substitution of the Q 2 associated cations. This suggests that the distribution of cations is non-random. At the critical composition (x  0.20) Sr 2+ is predominantly associated with Q 1 phosphate groups, while Na + is predominantly associated with Q 2.

37. Lectures co-financed by the European Union in scope of the European Social Fund EXAFS Extended X-ray Absorption Fine Structure (EXAFS) is a useful technique for examining the local environment around an atom. It is element specific and so is useful for distinguishing different species in mixed systems. It is useful in both crystalline and amorphous solids. The EXAFS phenomenon is weak and requires a high intensity X-ray beam as obtained at a synchrotron source. If a sample is irradiated with X-rays of a small range of energies then when the energy of an X-ray matches the binding energy of a core electron in a specific element, absorption occurs and the electron is either promoted to a higher energy level or ejected. By measuring the X-ray absorption coefficient  as a function of photon energy an X-ray absorption spectrum is obtained. resulting transmitted (or reflected) intensity an X-ray absorption spectrum is obtained. where I m is the measured intensity (transmitted) and I 0 is the incident intensity.

38. Lectures co-financed by the European Union in scope of the European Social Fund The region just before and after the edge is known as the X-ray Absorption Near Edge Structure. While the EXAFS is present as small post edge oscillations.

39. Lectures co-financed by the European Union in scope of the European Social Fund The XANES region can be analysed for information on the oxidation state of metals. Structural information is obtained from the EXAFS part of the spectrum which is typically in the rage 400 to 1000 eV above the absorption edge. The energy in this range is much higher than the binding energy of the electron and so the excited electron has a high kinetic energy and is ejected. On leaving the atom the electron wave undergoes interference with electrons in neighbouring atoms. The resulting constructive and destructive interference gives rise to oscillations in the absorption cross section  seen in the EXFAS region of the XAS spectrum. The outgoing electron wave will be backscattered by its neighbours. Therefore the pattern is a complex mixture of scattered and backscattered waves.

40. Lectures co-financed by the European Union in scope of the European Social Fund The energy data (E) in eV are usually transformed to wave vector to wave vector k for analysis. where E 0 is the absorption edge energy, m e is the mass of an electron and  is h/2 . The amplitude of each EXAFS wave depends on the number of surrounding atoms and their backscattering power (i.e. their atomic number) and the distance between the excited atom and the backscattering atom. One can define the total EXAFS spectrum  (k) as the sum of individual EXAFS contributions in a multi-component system.

41. Lectures co-financed by the European Union in scope of the European Social Fund  i (k) can be defined as: Where N s is the number of backscattering atoms at distance R as from the absorbing atom, A s is the backscattering strength of the backscattering atom, S 0 is a passive electron reduction factor in the interaction,  2 is the Debye-Waller factor,  is the mean free path of the electron and  as is the phase shift of the wave. Analysis of the EXAFS spectrum yields N s, R as and  2 as There are a number of theoretical approaches to modelling EXAFS data. We will not discuss these here.

42. Lectures co-financed by the European Union in scope of the European Social Fund NaCaP 3 O 9 glass Na spectrum R 1 = 2.317(7) Å2  2 = 0.034(2) Å 2 N 1 = 6 R 2 = 3.16(8) Å2  2 = 0.07(2) Å 2 N 2 = 6

43. Lectures co-financed by the European Union in scope of the European Social Fund Diffraction by glasses In diffraction experiments amorphous materials show no Bragg peaks, but they do exhibit scattering that can be analysed. For analysis of glass diffraction data we transform the data to Q space where:  = Bragg angle, = wavelength and d = d-spacing.

44. Lectures co-financed by the European Union in scope of the European Social Fund In order to get good radial distribution function data. the range of Q should be large. Typically neutron data allows Q ranges up to ca. 50 Å -1 while in X-ray data the maximum useable Q value is close to 20 Å -1 For laboratory X-ray data, Cu tubes have maximum Q value around 8 Å -1. Ag tubes increase the Q-max to ca. 20 Å -1 Synchrotron radiation is commonly used for X-ray experiments. The total interference function F(Q) is given by Where c represents the fraction of a chemical species, is the mean scattering length and S is the partial structure factor. The total pair correlation function G(r) is obtained by Fourier transfor of F(Q), while individual pair correlations g i,j (r) are obtained by Fourier transform of the partial structure factors.

45. Lectures co-financed by the European Union in scope of the European Social Fund Neutron diffraction correlation functions for lithium borate glasses Swenson et al. Phys Rev. B. 52 (1995) 9310 For more detail see Lecture 15 January lectures.