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Study of lithium intercalation in titanium disulphide using time differential perturbed angular correlations Surono, Djoko 1991

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S T U D Y O F L I T H I U M I N T E R C A L A T I O N IN T I T A N I U M DISULPHIDE USING T I M E DIFFERENTIAL P E R T U R B E D A N G U L A R CORRELATIONS  by  DJOKO SURONO B.Sc, Universitas Indonesia, 1986 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF T H E REQUIREMENTS FOR T H E DEGREE OF MASTER OF SCIENCE in T H E FACULTY OF GRADUATE STUDIES Departement of Physics  We accept this thesis as conforming to the required standard  T H E UNIVERSITY OF BRITISH COLUMBIA July, 1991 ©DJOKO SURONO, 1991  In  presenting  degree at the  this  thesis  in  University of  partial  fulfilment  of  of  department  this thesis for or  by  his  or  requirements  British Columbia, I agree that the  freely available for reference and study. I further copying  the  representatives.  an advanced  Library shall make it  agree that permission for extensive  scholarly purposes may be her  for  It  is  granted  by the  understood  that  head of copying  my or  publication of this thesis for financial gain shall not be allowed without my written permission.  Department The University of British Columbia Vancouver, Canada  DE-6 (2/88)  Abstract Lithium intercalation into layered compound TiSj was studied using time-differential perturbed angular correlations (TDPAC). Fast electrochemical intercalation was performed to bring Li atoms into the host. The probe atoms Hf registered two nuclear quadrupole interactions corresponding to the empty host TiS^ with quadrupole frequency i/,i=461(5) MHz and a high packing density Li TiS?. ( x « l ) compound with quadrupole frequency i/,2=599(6) MHz. The contribution fractions of both interactions evolved as a function of charge transport, rip. The second intercalation becomes dominant at rip > 0.3. No evidence was found for intermediate x values. 1 8 1  x  ii  List of Contents Abstract  ii  List of figures  v  Acknowledgement  vii  1. The Intercalation Compound TiS  1  2  1.1. Introduction 1.2. Structure of TiS  1 2  2  1.3. Electrochemical intercalation  6  2. Theory of Time Differential Perturbed Angular Correlation  10  2.1. Introduction  10  2.2. The Perturbed Angular Correlation  14  2.3. Nuclear Quadrupole Interaction  14  2.4. Correction for Broadening Mechanisms  16  3. Experiment  18  3.1. Sample preparation  18  3.2. Design of the electrochemical cell  19  3.3. Time Differential Perturbed Angular Correlation Experiment  22  3.4. Data reduction method  27  4. Results  28  4.1. The electrochemical cell  28  4.2. Analysis of the TDPAC data  31  4.3. Data for empty  33  host  TiS  2  4.4. Data for intercalated compound Li TiS x  5. Discussion  2  '. .•  36 39  5.1. Introduction  39  iii  5.2. Cathode utilization  39  5.3. Nuclear Quadrupole Interaction in Li TiS2  40  5.3.1. The broad, non-specific interaction  40  5.3.2. The well resolved, specific Nuclear Quadrupole Interaction  41  6.Conclusion  45  Bibliography  47  x  iv  List of Figures 1. Figure 1.1: A-B-C arrangement of atoms  4  2. Figure 1.2: Structure of TiS  5  3. Figure 1.3: Diagram of an electrochemical process (discharge)  7  2  4. Figure 2.1: A successive dipole transition with I: 0 —• 1 —* 0 and the possible values of m and A m  11  5. Figure 2.2: Schematic of a quantum nuclear state connected by a 7-7 cascade  13  6. Figure 2.3: Splitting of the intermidiate state due to a symmetric efg  15  7. Figure 3.1: X-ray diffraction pattern of the TiS sample used  19  8. Figure 3.2: Diagram of the electrochemical cell  20  2  9. Figure 3.3: Gamma-ray spectra of 10. Figure 3.4: The decay scheme of  1 8 1  1 8 1  Hf  Hf  11. Figure 3.5: Schematic diagram of fast electronic circuit  .21 23 24  12. Figure 3.6: Slow electronic circuit diagram of a four detector system TDPAC  24  13. Figure •.,.<: A typical raw time spectrum of a TDPAC measurement for an annealed sample  26  14. Figure 4.1: Cell EMF v.s. charge transport np v  30  15. Figure 4.2: G 2(0 of 2  1 8 1  H f in TiS and their respective Fourier 2  transforms  32  16. Figure 4.3: Pertubation factors, G (<), of 22  1 8 1  H f in Li TiS x  2  35  17. Figure 4.4: The dependence of fit parameters on the charge transport, UF  38  18. Figure 5.1: Nuclear quadrupole frequencies and percent contribution of the first and second interactions 19. Figure 5.2: A model of Li —• TiS intercalation process 2  vi  42 43  Acknowledgement  I would like to thank Dr. Peter W. Martin for his supervision and encouragement, without which this work would not be possible. I am also indebted to Drs. Jeff Dahn, Peter Mulhern, Salah El Kateb and Mr. Dazong Li, for their suggestions and opinions in making the cell. Finally, I would like to thank the government of Republik Indonesia in which through the Overseas Fellowship Programe gave financial support during my study at UBC, and the World University Service of Canada, the administrator of the fellowship programme in Canada.  vii  Chapter 1 The Intercalation Compound TiS  2  1.1 Introduction In the past decade condensed matter physics has witnessed an ernormous upsurge of activity in the area of materials science. In particular, the class of materials known as intercalation compounds has received a great deal of attention [1]. In these systems guest atoms, or molecules, called the intercalant, can be inserted in a controlled fashion between layers of the host material. The resulting materials are of great interest for both theoretical and practical reasons. On the one hand, theorists are finding such layered compounds ideal testing grounds for theories of 2-dimensional physics. Moreover, by utilizing the staging phenomenon, whereby intercalant layers are separated by a definite number of host layers, the transformation from 2 to 3-dimensional behaviour can be studied. On the other hand, the ability to produce materials with specific, desired properties clearly offers many practical applications. Indeed, one such material, Li MoS , has alx  2  ready been exploited as a commercial electrical battery. Consequently a great deal of 1  experimental work has been brought to bear on the problem of characterizing these new materials, and the elucidation of the reaction mechanism by which they are produced. In this thesis we are concerned with an investigation of the layered transition metal dichalcogenide compound, T1S2, with Li atoms as the intercalant. A layered transition metal dichalcogenide compound refers to a chalcogen-metal-chalcogen sandwich structure. One writes MX , where M refers to the transition metal ( T i , V, Cr, Mn, Fe, 2  ^oly-Energy Ltd., 3985 Myrtle Rd., Burnaby, B C , Canada.  1  Chapter 1. The Intercalation Compound TiS  2  2  C o , etc.) and X refers to the chalcogen atom (S, Se). E a c h layer can be considered as a two-dimensional sheet of atoms. T h e X - M - X sandwiches are bound to each other by V a n der Waals forces. Due to the weak nature of the forces between the sandwiches, guest atoms can be inserted into the gap; when they are extracted, the host crystal returns to the original structure. T h e process is called intercalation. T h e technique used i n these studies is that of time differential perturbed angular correlations ( T D P A C ) . In T D P A C a radioactive probe nucleus, i n this case  1 8 1  H f , is  introduced into the system under study (TiS ) and the directional correlation of a suitable 2  71-72 cascade is measured w i t h a system of detectors.  A s w i l l be explained later i n  Chapter 2, such a measurement of the perturbed angular correlation allows one to monitor changes i n the electric field gradient (efg) w i t h i n the host crystal, which can then be related to the electronic structure.  We hope then to be able to answer the following  questions: • In the intercalation process for the production of Li TiS2 how many and what type x  of sites are occupied by Li atoms ? • A r e there variations i n the packing fraction p within a given layer, as has been found by Ramos et al. [2] for the Ag TaS x  2  system ?  • C a n T D P A C suggest a model for the intercalation dynamics ?  1.2  Structure of TiS  2  One usually uses the symbols A , B , C etc.  and their lowercase counterparts to  describe the arrangement of atoms i n a layered structure. T h e letters A , B , C refer to the sites i n the first, second and t h i r d layers of atoms respectively. A s depicted i n figure 1.1, type A specifies the sites of atoms i n a hexagonal structure, while types B and C are  Chapter 1. The Intercalation Compound TiS  2  3  the two possible octahedral sites above the first layer. The stacking of atoms in the next layer can always be positioned in A, B, or C sites. The number of layers can be very large and depends on the size of the crystalline grain. Different atoms are distinguished by letter type (upper case, lower case, Greek letters, etc.). An AbC structure, for example, is an arrangement of two different atoms which are represented by upper and lower case letters and positioned in A, B and C sites respectively. Transition metal dichalcogenide compounds have a hexagonal closed packed structure. In ABC notation the metal and chalcogenide atoms are represented using lower case and upper case letters respectively. There are two possible sites for the transition metal: trigonal prismatic and octahedral coordination sites. In both coordinations the metal atoms have six chalcogen nearest neighbours. These two different crystal symmetries lead to a different band structure and electronic properties [3]. A trigonal prismatic coordination is an arrangement in which the third layer of atoms lies directly above atoms in the first layer. The metal atom lies in the center of the prism (see fig. 1.1). It is written as A-b-A coordination. An octahedral coordination, on the other hand, is written as A-b-C. In this case the third layer atoms are rotated 180° about the z- axis. It is also called trigonal anti prismatic coordination. The terms 1H and IT are also used to denote trigonal prismatic and octahedral coordination respectively. The number 1 refers to the number of layers per unit cell and the letters T and H do not represent the position of the transition metal, but relate to the whole crystal structure of the compound. Titanium disulfide has a IT-CdJ structure . It is a layered A-b-C coordination of 2  2  S-Ti-S. The titanium atoms occupy octahedral sites and are surrounded by six sulphur atoms. The covalent bonds in TiS are relatively strong and stable, but the Van der 2  Waals force is sufficiently weak so that the intercalation process can be performed. The 2  This type of structure was apparently first known for Cdl^.  Chapter 1. The Intercalation Compound  STRUCTURE  TiS  4  2  STRUCTURE  ©  C atom in the third layer  (§) B atom in the second layer ®  A atom in the first layer  (100) projection of ABC structure Figure 1.1: A - B - C arrangement of atoms. reverse process, i.e. pulling guest atoms out from the crystal, is called de-intercalation.  3  The a lattice parameter does not change very much in the intercalation process [5,6]. This follows from the fact that the covalent bond in TiS  2  is very stable. On  the other hand, the c parameter varies with the content of Li in intercalated compound Li TiS . x  2  This phenomenon can only be explained if the Li atoms occupy sites within  the Van der Waals gap, with a consequent change in the width of the gap. Sometimes people refer the word intercalation for both processes.  3  Chapter 1. The Intercalation Compound TiS  5  2  o o o o o  OS  o o o o  oTi  O O O O O a  o  9 n  O  A  H  o  • vacant sites  !-C  ?  D D van der Walls gap  o o o o o I—•'(**>/•  o o o o o  I—< °> 112  (b) Detail structure of US, notice the vacant sites with octahedral symmetry and tetrahedral symmetry .  (a) S-TI-S sandwich  D  A  Figure 1.2: Structure of TiS . 2  There are two types of symmetry sites in the Van der Waals gap : octahedral and 4  tetragonal sites. The octahedral sites have the same nearest neighbors as the metal in the second layer (six sulphur atoms), i.e. they are similar to those occupied by Ti in the S-Ti-S sandwich. From fig. 1.2 one can see that the octahedral sites are positioned directly above Ti atoms, so that there is one octahedral site in the Van der Waals gap per TiS molecule. Tetrahedral sites are the vacant sites above the third layer S atoms. 2  There are four nearest neighbour sulphur atoms for each site and 2n sites per n TiS  2  molecules. The octahedral site has a larger radius than the tetrahedral site. For TiS , the 5  2  radii of octahedral and tetrahedral sites are 0.89 A and 0.64 A respectively [1]. It would 4  It can be considered as the fourth layer of S - T i - S - L i sandwich  The radius of a vacant site is the maximum radius of an atom which can be inserted in this site without changing the whole stucture (hard sphere ball model). 5  Chapter 1. The Intercalation Compound TiS  6  2  seem then that the tetrahedral site is too small for the Li  ion, which has radius of 0.7  +  A. Previous workers (see for example [6,7]) confirm that for 0 < x < 1 only octahedral sites are occupied by Li ions. +  For titanium disulphide Ti S , where y=l+5 (6 a small number), excess Ti atoms y  2  also occupy the vacant sites in" the Van der Waals gap [8], thus reducing the number of possible intercalation sites and the rate of intercalation . In contrast to the former 6  situation where expansion of the c-axis occurs with increasing number of intercalant atoms, in this case the c-parameter decreases with increasing excess of titanium atoms, even though in both cases guest atoms reside in the gap. Whittingham [9] suggested that the strong covalent bonding of Ti to the layers was responsible for this phenomenon. Excess Ti pins the sandwiches together, so that the gap becomes narrower and more rigid. Consequently it may reduce the rate of Li diffusion into the host in electrochemical intercalation.  1.3  Electrochemical intercalation Intercalation can be achieved using chemical (n-butyl lithiation) [9,10], electro-  chemical [6,7] or physical methods (temperature and pressure) [11]. In this work, only electrochemical intercalation was performed. The procedure involved charging and discharging a battery system constructed using host material as cathode and intercalant metal (Li sheet) as anode. A salt material serves as the electrolyte, transporting the metal intercalant into the host. The intercalation process is based on a simple electrochemical reaction, xT xT  z+  6  + xze~ + MN  2  *± xT  z+  *±  + xze~  T MN X  (1.1) (1.2)  2  In this work Thompson used the n-butyl lithiation method to intercalate TiS 2  Chapter 1. The Intercalation Compound TiS  7  2  LlAsF /P.C. 6  © Li ion Figure 1.3: Diagram of an electrochemical prosess (discharge). The Li metal and TiS compound are used as cathode and anode respectively. The electrolyte used is LiAsF& in Propylene Carbonate. 2  The number of guest atoms, T, intercalated into the host material, MN , is proportional 2  to the charge transport. As shown in the diagram (fig. 1.3), electrons travel from cathode to anode via an external circuit, while metal ions are transported through the electrolyte. There is no external voltage needed in the intercalation process; chemical potential difference serves as a driving force. The reverse process, de- intercalation, can be achieved by applying external voltage to the cell (charging the cell). The amount of charge transported is measured from the external current. The molar fraction, x, can simply be calculated if the mass, m, of the cathode material, the external current, I, and the period of time for the process, t, are all known.  Chapter 1. The Intercalation Compound TiS  8  2  Let N be the number of molecules, N=mA /M, where iVo is Avogadro number (A^o = /  0  6.02 x 10 ) and M is the molecular wieght of the cathode material. The total charge 23  transported is Q=Ixt. The number of guest atoms intercalated can be written as N = x  Q/(z x e~), where z is the valence of the guest atoms. The mole fraction x is equal to the ratio of the number of guest atoms transferred, N , and the number of the host x  molecules N; it can be written as x  N  ~ ~w QM x  zme~No zmF  v  '  where F is known as the Faraday constant and the equation is called Faraday's law. In the above calculation one has assumed that the guest atoms are distributed homogeneously throughout the entire crystalline host. The fraction x generally refers to the average molar composition. One may prefer using charge transport, np, to indicate the molar fraction in electrochemical intercalation. Charge transport np is defined as the number of electrons transported from anode to 7  cathode via an external circuit, divided by the number of molecules of cathode material. np — =  Q/eN xz  (1.4)  For 2=1 (such as Li), the molar fraction is equal to the charge transport, x = np. In TDPAC measurements one is interested in the amount of charge transferred from intercalated atoms to the host crystal, as this will contribute to the changes in the electric field gradient (efg) within the host. For this reason one defines a new parameter, the 7  The letter F in np indicates that this parameter is calculated from Faraday's law  Chapter 1. The Intercalation Compound TiS  2  9  charge transfer ni (L refers to metal intercalant Li, Ag, etc.), as the number of electrons transferred from the intercalated metal to the host per number of host molecules. For empty host material n£=0, and in general 0 < njr, < s, where s is the maximum uptake. The charge transfer parameter can not be determined theoretically. Its value depends on the quality of the sample used and cell performance. It indicates the local concentration of intercalated metal in the host, so that a sample (the material used as cathode of the cell) may have several values of UL in the case of non-homogeneous intercalation. In this case one may prefer using packing fraction p instead of the global molar fraction x. The packing fraction is defined as the number of intercalated atoms per molecule; it refers to the local concentration of intercalated metal in the host crystal, and could vary even within a given layer. In an ideal situation in which the intercalated atoms are distributed homogeneously and transfer their charge properly, all of the four parameters above have a simple relation, viz.  x = p = UF/Z = TIL/Z.  In the special case when the valence number of the  intercalated atom is z=l, all these quantities have the same value. In the following chapter the theory of TDPAC will be presented briefly. Details of the electrochemical intercalation experiment and a brief description of the TDPAC detector system used can be found in Chapter 3. Results of the experiment and their interpretation are presented in Chapters 4 and 5. In Chapter 6 we draw some conclusions and give some suggestions for future work to improve our understanding of layered compound systems.  Chapter 2  Theory of Time Differential Perturbed Angular Correlation  2.1  Introduction A brief description of the theory of angular correlations is presented here. A de-  tailed account can be found in the review article by Frauenfelder and Steffen [13]. It is well known that a randomly oriented radioactive material emits particles or 7-rays isotropically. The intensity of radiation depends on the strength (activity) of the source, the distance and nature of the medium between the source and the detector. Since there is no preferred direction, i.e. the z- axis is arbitrary, it does not depend on the angle the detector makes with the z-axis. If, however, the nuclear spin is somehow aligned preferentially with respect to the z-axis (for example by low temperature nuclear orientation, or by the application of an extremely intense electric or magnetic field), it can be shown that as a consequence of angular momentum conservation, the nuclear radiation will in general exhibit a definite angular distribution with respect to the quantization axis. Consider for an example an unstable nucleus in a state characterized by spin angular momentum numbers (Z,-,m,). It decays to a state (If,mj) and the emitted 7-ray has quantum numbers (L,M). For the angular momentum to be conserved, one has to have Ii = L-\-If and m,- = M-\-rrij. The magnetic quantum number M is defined as L = Mh, z  where L is the projection of X on an arbitrary quantization axis (z-axis). The probability z  distribution of the emitted 7-ray is characterized by a directional distribution function FM{6), where 0 is the angle between the z-axis and the emitted 7-ray. This function  10  Chapter 2. Theory of Time Differential Perturbed Angular Correlation  I  A m  0-  11  m  •  0  -1  1 0 -1  -1  ty  1  -[  *WMMMAr+)-  e  — —-  start  —j  z-axis  Figure 2.1: A successive dipole transition with I: 0 —» 1 —• 0 and the possible values of m and Am (a); schematic diagram of an angular correlation experiment (b). depends on the values of L and M , but not on the initial or final state spins. For the well known case of dipole radiation, for example, the probability distribution functions are given by: = Csin (0); 2  F  l ±1  = | { 1 + cos\6)}  where C is a constant. In the language of quantum mechanics we can say that preferential alignment of the nuclear spins is achieved when the magnetic substates of the initial state are not evenly populated. In the case of low temperature nuclear orientation this is achieved through the Boltzmann factor, exp(-fiBfkT),  by generating large magnetic fields (~ 10 - 50 T)  Chapter 2. Theory of Time Differential Perturbed Angular Correlation  12  at very low temperatures (~ mK). The need to produce large magnetic fields at such low temperatures is circumvented by TDPAC, whereby successive 7-rays in a suitable nuclear cascade are detected in coincidence. In this case the detection of the first 7-ray serves as a quantum state selector for the intermediate state, producing a preferential population of its magnetic substates, with the result that the second transition will (in general) exhibit a directional correlation with respect to the first. This can be demonstrated readily by the following example indicated infigure2.4, which shows successive dipole transitions for the 0 —• 1 —• 0 spin sequence. If the 71 transition is not detected, i.e. we just detect the singles corresponding to 72, we obtain the expected isotropic distribution for 72, viz. W(6)  =  £p i^(0) m  m  where p  =  Csin (6) + 2^{l + cos (0)}  =  constant (i.e. isotropic)  2  2  are the (equal) relative populations of the magnetic sublevels.  m  Suppose now we arbitrarily choose the direction of 71 as the z-axis, noting, however, that there is zero probability for emission of the Am=0 transition in this direction, since FQ ~ sin (#). The probability of detecting 71 and 72 in coincidence is now : 2  W(0)  = =  EPm^(0) m C{1 + cos (6)} 2  {with  P o  = 0) (2.5)  so that the correlation is no longer isotropic. Typically the situation is more complex than this example, but the principle is the same. For the more general situation depicted in figure (2.5) it can be shown that the  Chapter 2. Theory of Time Differential Perturbed Angular Correlation  Oi.m,)  13  Initial State  7i(UM,) Intermediate State  (l,m)  Final State  (li.m ) f  Figure 2.2: Schematic of a quantum nuclear states connected by a 7-7 cascade. angular correlation function for a randomly oriented ensemble of nuclei can be expressed as : W{6) =  1  £  A P (cos6) kk  k  (2.2)  where rjv is the life time of the intermediate state. Conservation of parity demands only even values for the index k, with a maximum value determined by angular momentum conservation : k The parameters A  kk  max  = Min(2I,2L 2L ). u  2  (2.3)  are real numbers called radiation parameters. They involve  the product of two parameters, A {l) and A (2), originating from the first and second k  k  transitions respectively, A  kk  = A (l) x A (2). k  k  (2.4)  One can calculate the values of A (i) theoretically if all quantum numbers and mixing rak  tios involved in the cascade are known. Conversely, A  kk  can be determined by measuring  W(9) in an angular correlation experiment so that information about nuclear properties can be extracted.  Chapter 2. Theory of Time Differential Perturbed Angular Correlation  2.2  14  The Perturbed Angular Correlation Expression (2.6) assumes that the nucleus is in afieldfree environment with a negli-  gibly short lifetime in the intermediate state. If the intermediate state has a life time, TJV, interactions can then occur between the multipole moments (e.g. magnetic dipole, electric quadrupole) of the state and the local electromagnetic environment (magnetic field, efg). Such interactions can induce transitions between the substates of the intermediate level, resulting in a redistribution of the populations and consequently a perturbation of the correlation function in eq.(2.5). The latter can be written as W(0,i) = l— E A G (t)P (cos6)  (2.9)  ,  7  l  kk  kk  k  where G (t) is the perturbation factor. kk  Measurement of the latter is the primary goal of TDPAC. The form of G (t) dekk  pends on the type of interaction causing the perturbation. Thus TDPAC is an environmental technique, since the determination of the pertubartion factor yields information about the probe's electromagnetic environment, which in turn relates to the electronic structure of the material. 2.3  Nuclear Quadrupole Interaction In this work we are concerned primarily with nuclear quadrupole interactions (NQI).  A static efg from surrounding atoms causes a splitting in the intermediate nuclear state. The situation is shown infig.(2.6)for the case of spin  1=5/2.  For an axially symmetric efg, the energy eigenvalues of the substates m are  Here eQ is the nuclear quadrupole moment and eq is the largest component of the efg tensor (V ). I and m are the quantum numbers of the intermediate state. zz  Chapter 2. Theory of Time Differential Perturbed Angular Correlation  15  m= ± 5 / 2  AE  Intermediate State  3  m= ± 3 / 2 m= ± 1/2  Figure 2.3: Splitting of the intermediate state due to a symmetric efg. The electric field gradient is a traceless tensor and can be written as 0  V  /  xx  V = \  0 ^  0  Vyy  0  0  0  V  where V  xx  + V  yy  + V  zz  = 0  /  Zi  For the non-symmetric case one can define the asymmetry parameter as T) =  Clearly, 0 < n < 1 for V > V zz  \{V  — Vyy)\  XX  (2.7)  > V . It equals zero (symmetric efg) only if V =V .  xx  yy  xx  yy  The energy difference between sublevels m can be calculated from equation (2.6) : 3(m - m ) -eQV = 4/(27 - 1) 2  AE . i m  m  n  Zi  (2.8)  One defines the angular frequency U>Q corresponding to the smallest energy difference by (2.9) and the quadrupole frequency by,  v = q  eQV  Zi  (2.10)  Chapter 2. Theory of Time Differential Perturbed Angular Correlation  16  For the case of axial symmetry, the smallest energy difference is equivalent to hu\, where v\ is the first harmonic of the interaction. For I = | one writes AE^ = hvi =  A£±  , i  3  — eQV , 40 Z2  then from eq.(2.14) we have (2.15) o However, in terms of the fundamental (angular) frequency, U>Q, where AE\ = hu)o, we have uo =  (2.16)  -j-giv  Similarly it can be shown that AE = 2hu> and AE = Z%u respectiveley. For the case 2  of  181  0  T a , the daughter product in the decay o f  3  181  0  Hf, terms in k>2 are negligible, and the  perturbation factor in this case is (1=5/2, T/=0, randomly oriented sample) : G (t) = 22  S +JZ S cos(u: t) 0  n  n  (2.17)  where w„ = nu> ("•=12,3). 0  )  For the case 7 / ^ 0 , the quadrupole frequencies no longer form a harmonic series. Now we must write w„ = /fo)wb  (2.18)  where the coefficients / ( 7 ; ) are calculable functions of n.  2.4  Correction for Broadening Mechanisms The expression in eq.(2.17) must be corrected for various broadening mechanisms  before the theory can be compared with experimental data. Details on the experimental procedure and data reduction methodology will be discussed in Chapter 3.  Chapter 2. Theory of Time Differential Perturbed Angular Correlation  17  Since the detectors subtend a finite solid angle, the radiation parameters Akk must be corrected accordingly [13]. We write Ar\l)  = Q {E )A (l) k  ll  (2.19)  k  and a similar expression for A| (2). The solid angle correction factors were calculated orr  using the routine  DEWF  [13].  As the fast coincidence circuit is limited by its finite resolving time  (FWHM=TR),  the perturbation factor must also be multiplied by a factor exp(—|a; cr ), where we have 2  2  assumed a Gaussian spread with standard deviation cr, with TR = 2V^v In2<7.  (2.20)  /  Finally, owing to imperfections in the crystal lattice, not all nuclei will experience the same efg, but will see some Gaussian distribution 6 in the quadrupole interaction. The correction factor in this case takes the form exp(—^ui 6 t ). 2  2 2  Chapter 3  Experiment  3.1  Sample preparation Production of titanium disulphide (Tz^) can be performed using several methods.  The most simple one is by placing stoichiometric ratios of titanium and sulphur in a quartz tube and then heating to 600-1000 °C. The tube has to be evacuated to avoid oxidation. Dahn [6] reported formation of several crystallite sizes depending on the baking temperatures. Single crystals of TiS can be produced using the iodine vapour 2  transport method. The titanium disulphide used in this work was prepared using the stoichiometric method. A small amount of high purity hafnium was added as a probe atom for the TDPAC measurements. Thefinalsample was determined to be li'/o.oo97Tto.9903<S'2.oooo5  a  golden brown metallic powder. The sample had to be ground to get a uniform crystallite size with an average diameter of 40 fim. An X-ray analysis was performed before the sample could be used as cathode material. The X-ray pattern of the sample was well matched with the standard X-ray diffraction pattern of TiS as shown infigure3.7. This constituted a preliminary check of the 2  sample before it could be used as cathode material for the Li/Li TiS x  2  electrochemical  cell. The isotope required for the angular correlation experiments was  1 8 1  Hf. A 10-12  mg sample of #/o.oo97T3 .9903'S'2.oooo was placed in a small quartz tube, about 4 mm in 0  18  Chapter 3. Experiment  19  APRIL 3/90"  DJOKO TIS2 ?? OJ  cn rOJ  II  OJ  co u  cn  3  LL.  10  20  30  40  50  60  70  Diffraction Angle (degree) Figure 3.1: X-ray diffraction pattern of the TiS sample used (red pen); the green pen is the calculated spectrum. 2  diameter, sealed and sent to Mc Master University to be neutron irradiated. The resulting activity of the sample was approximately 10 /LtCi. As the thermal neutron absorption cross section for hafnium is very high (12.2 b), it was expected that radiation damage to the sample would be negligible. However, the results of this work revealed drastic differences in TDPAC spectra (G22 vs. time) for samples with and without further treatment after being neutron irradiated. Further discussion on radiation damage and possible treatment can be found in Chapter 4.  3.2  Design of the electrochemical cell The design of cells used in this work is similar to that used by previous workers  [3,6]. However, some changes in the design of the cell were required to minimize the effect of 7-ray absorption so that the cell could be used in TDPAC measurements.  Chapter 3. Experiment  20  Screw Insulator  5 mm  1-2 mm j—1_  T  t  T  -I  i  L  Li*-  •» Stainless steel  • Separator Rubber 0—ring Spacer (Insulator)  (substrate)  L' Ha-3.0 cm-w  —7.5 cm  Figure 3.2: Diagram of the electrochemical cell. Basically the cell used here consisted of two stainless steel flanges as the main body. They are joined together by six insulated metal screws (see fig. 3.2), but separated from each other by an 0-ring to avoid direct contact. The intercalation process taking place inside the flanges was thus isolated from the atmosphere. The flanges also served as electrical contacts. Assembly of the cell was performed in a glove box under a clean (Argon) atmosphere. The central part of theflangeshad to be made as thin as possible to minimize 7-ray absorption. However, care had to be taken in designing the flanges since they still had to be strong enough to support the whole assembly and exert uniform pressure over the area of the sample. A schematic diagram of theflangescan be seen in fig. 3.2. The electrolyte used in this work was 1M Lithium Hexafluor Arsenate (LiAsF ) in 6  propylene carbonate (PC). It was supplied by Moly Energy Co. Water and propylene 1  1  Thanks to Dr. J.R.Dahn who supplied the electrolyte.  Chapter 3. Experiment  21  Figure 3.3: Garnma-ray spectra of Hf, £ ^ = 1 3 3 keV, £ = 4 8 2 keV and £ = 3 4 6 keV; the 7 is not involved in the cascade of interest (see fig. 3.4). (a) The sample was placed in a pyrex tube, (b) Hf spectra of Li/Li TiS2 cell. The Ta X-ray peak (Ex-ray = 57 keV) was absorbed by the stainless steelflanges(arrowed). 181  7 2  S  x  7 X  Chapter 3. Experiment  22  glycol content was less than 20 ppm. A Celgrad Microporus Film (product type #3501) was used as a separator. This material permits ionic contact between anode and cathode via the electrolyte, but on the other hand prevents direct electrical contact. A 0.25 mm thick lithium foil from Foote Mineral Company was used as the metal intercalant (anode). The cell was constructed as follows : (i) outside the glove box, the cathode was made by placing the TiS powder on a nickel sheet which had been etched in nitric acid and 2  rinsed using destilled water. A few drops of solvent (cyclohexane) were then added. By properly mixing the powder and the solvent, the powder sticks to the nickel sheet after the solvent evaporates; (ii) the anode was made by cutting the Li foil to about 1.5-2 cm in diameter; (iii) the whole cell was fabricated by adding a few drops of electrolyte to the cathode and then constructing a sandwich of cathode-separator-anode as depicted in fig.3.8. Steps (ii) and (iii) were performed in the glove box. It has been mentioned previously that the flanges of the cell should be as thin as possible to minimize 7-ray absorption, but still thick enough to provide mechanical robustness. Figure 3.9 shows that the effects of absorbtion by theflangeson the 7-rays of interest (133 keV and 482 keV) are negligible. In fact it can be seen that the stainlees steel confers a distinct advantage by preferentially absorbing the low energy Tantalum X-ray at 57 keV. This is presumably a result of resonant absorption by Ta atoms in the stainless steel. The elimination of such unwanted signals is of particular advantage in lowering the count rate in the time-to- amplitude converter, with a corresponding decrease in the random background.  3.3  Time Differential Perturbed Angular Correlation Experiment This work was performed win" the four detector system described by Martin et  al.  [14].  Each detector consi  ; a Nal crystal (4.41 cm diameter, 1.27 cm and  Chapter 3. Experiment  23  «'Hf  133 koV  10.8 na  -r-i  482 keV  346 keV  40 pa 136 keV «iTa  Figure 3.4: The decay scheme of  181  Hf.  5.08 cm thick for the start and stop detectors respectively) mounted on Philips 56 AVP photomultipliers. The axes of these detectors were set perpendicular to each other. There were four pairs of start-stop detectors: AB(7r), AC(|), D C ( X ) and DB(|). The configuration of the detectors can be seen infigure3.5. As mentioned earlier, the isotope used for the TDPAC measurements was Figure 3.4 shows the decay scheme of state of the daughter product,  1 8 1  181  181  Hf.  Hf. Following 0-decay to the 18 /xs isomeric  Ta, the electronic shells have plenty of time to establish  equilibrium before the ensuing 7-7 cascade of interest, in this case the 133 keV (start) and 482 keV (stop) transitions. Each detector produces a fast and a slow signal. The fast signals are required for precise timing measurements, while the slow signals are used in logic circuits to analyze the 7-rays i.e. to select by energy those 7-rays involved in the cascade and to determine (by a slow coincidence requirement) from which pair of detectors each event originated.  24  Chapter 3. Experiment  Tima  Figure 3.5: Schematic diagram of fast electronic circuit (based on Martin et al. [14]).  DET  OCT  A  B  [QUI  IDLM  DET  C  DET  D  [DLA| IDLAl  ITS ok I ITSCAI ITSCAI ITSCAI AB  MULTI CHANNEL ANALYSER  AC DC DB SLOW COINCIDENCE | TAC | —  LOS  1/4 2/4  3/4 4/4  PA : Pre-Amplifier DLA : Delay Line Generator TSCA : Timing Single Channel analyser : Stretcher S GDG : Gate and Delay Generator TAC : Time—to—Amplitude Converter LGS : Linear Gate and Stretcher  ROUTER  Figure 3.6: Slow electronic circuit diagram of a four detector system TDPAC (based on Martin et al. [14]).  Chapter 3.  25  Experiment  Each fast output signal is first sent to a discriminator in order to generate a standard logic signal. A constant fraction timing discriminator (CFTD figure 3.11) produces the needed signal with minimum walk. It accomplishes this by triggering at a constant fraction of maximum amplitude of the input signals, consequently producing more precise timing measurements. Start signals from detector A and D and stop signals from detectors B and C enter the time-to-amplitude converter (TAC) via an OR circuit. The voltage output of the TAC is proportional to the time delay between the arrival of the first and second 7-rays. This information is finally presented to the MCA after passing through a linear gate. The gating signal for the latter is generated by the slow logic (see figure (3.12). After being amplified and delayed, the slow signals are passed to single channel analysers (SCA's) which impose energy selection on the 7-rays involved in the cascade. If a true start-stop event occurs, the slow coincidence circuit then generates a signal and sends the information to a router and to the MCA. The router directs the MCA to register any event in designated quadrants of the MCA memory. The MCA used in this work was a Nuclear Data model ND76. It has 8192 channels which can be subdivided into two groups of 4096 channels. Each group contains four quadrants of 1024 channels. The first 300 channels were usually used to store the timeuncorrelated random background. The zero time and the system resolving time were determined using a prompt source, such as C o or Na, with the windows in the side 60  22  channels set for the 7-rays of interest. The resolution was found to be 2.2 ns (FWHM). Data were stored in the next 500-600 channels; beyond this point the data (i.e. event numbers) were comparable to the background level and not used. In order to get relatively good data we ran each, measurement for about two days of data collection time; this was repeated two or three times to get better statistics and to check reproducibility. The perturbation factor, G22, was calculated for each run, then  I  200  I  I  400  I  1 600  I  I  800  I  I  1000  Channel N u m b e r ( 1 . 0 6 9 7 n s / c h a n n e l )  Figure 3.7 : A typical raw time spectrum of a TDPAC measurement for an annealed sample. The region labelled R corresponds to the random background. The time zero, to, was determined from the prompt peak using Na as a source.  to  Chapter 3. Experiment  27  individual runs summed to obtain the weighted average. The summed data were then used in the fitting procedure. The total time needed for one sample ( or for one x value in Li TiS2) x  3.4  was about one week.  Data reduction method The raw data of the TDPAC measurements comprised four delayed coincidence  spectra (event number vs. time) originating from the AB, AC, DC and DB detectors. Figure 3.7 shows such a time spectrum from the AB detectors for the annealed sample (see Chapter 4). The time zero, to, was determined using Na as a prompt source. 22  The background level per channel was calculated from region R (see fig. 3.7) and then subtracted. The experimental  G 2 2 ( t )  function was determined from the following expression :  ~ ^ W ^t)Wcs^t) {[  ]2  AD  ~  1  }  .  ( 3  -  2 1 )  with the A22 parameter corrected for solid angle effects as described earlier. Here Wu(6,t) is the true coincidence number i.e. the event number minus background for detector IJ (IJ= AB, CD, AD, or CB). This method of data reduction using a multidetector system has several advantages : (i) higher data acquisition rates; (ii) compensation of errors in source centering (owing to the symmetric positioning of the detectors); (iii) to first order a cancellation in the detector efficiencies in expression (3.21) and removal of the exponential envelope in eq. (2.5). The Gii calculated using the above equation represents the total G22 i-e. a superposition of perturbation functions originating from several crystalline surroundings. The probe  1 8 1  H f atoms may reside in several sites, each with a particular local environment  corresponding to a specific NQI. Details of the data analysis and fitting procedure will be discussed in the next chapter.  Chapter 4  Results  4.1  The electrochemical cell Investigations on Li TiS2 x  compound which have been performed by many previous  workers (Whittingham [1], Dahn et al [4,15], Thompson [7], for examples) are mainly based on voltametry, V vs. x relation. In the following section a brief resume is given of their results and suggestions, with a view to understanding the results of this work. Thompson claimed to observe a Li-ordering due to the long range repulsive Coulomb interaction [7]. He suggested that the intercalated Li atoms transfer their valence electrons to the host. The corresponding L i ions are constrained to reside in certain octa+  hedral sites in the gap and form a two-dimensional ordered structure. The occupation of octahedral sites by Li atoms was also confirmed by Dahn [6] for x in the range of 0 < x < 1. On the other hand, his neutron scattering data definitely excluded three dimensional ordering, and was unable to confirm the existence of a two-dimensionally ordered structure. The structure of Li TiS2 x  depends on the molar fraction x. Neutron and X-ray  investigations [6,16] give a =3.407 A and co=5.696 A for empty host TiS . Both paramo  2  eters increase monotonically with x. The a lattice parameter seems to be more stable and rigid than the c parameter. It changes only by about 2% from x—Q to x=1.0, while c changes by 10%. This is consistent with the formation of a sub-layer in the Van der Waals gap, whereby the width of the gap increases with little change in the structure of  28  Chapter 4. Results  29  atoms parallel to the plane. The voltage of the cells used in this work varies with  in a manner similar to that  observed by other experimenters. The tenth continuous charge-discharge cycle of cell JK10 can be seen infigure4.13. The current used was 50 fiA, which corresponds to an intercalation rate of 12.3 hours. Figure 4.13.b represents the V-x relation of cell R7. The 1  intercalation was interrupted at points x=0.3, 0.5, 0.7 to allow TDPAC measurements; the interruptions were about 6 days for each point. All the TDPAC measurements in this work were performed using cells R5, R6 and R7. All cells exhibited similar performance to that shown infigure4.13.b. In figure 4.13.b, cell R7 was discharged at 1=500 //A (intercalation rate = 4.73 hours) to x=0.3; the voltage dropped to 1.91 Volt. The cell was then left in the open circuit condition to allow TDPAC measurements. The voltage recovered to 2.2 Volt in an hour and slowly increased continuously during the TDPAC measurements. After one week the cell voltage was found to be 2.3 Volt. Then the cell was discharged at 1=300 / i A to the next points of interest, x=0.5, 0.7 and 0.9. A similar procedure was followed for cell R5; cell R6 was used for the x=0.1 measurement only. Fast intercalation in thefirstdischarge (i.e. using relatively high current) was aimed to avoid solvent co- intercalation. As a result, the voltage was found to decrease faster 2  than that found by Thompson [7], for example. In the case of a fast discharge, Li ions +  are deposited on the surface of the cathode material thus preventing further deposition and solvent co-intercalation processes. It would appear that the diffusion rate of Li+ is slower than the rate of electrochemical reaction. The voltage of the cell recovers after the cell is disconnected. The deposited Li atoms diffuse into the host crystal so that the packing density of Li atoms in the surface The intercalation rate is the time required to change the mole fraction x by A x = l . Solvent co-intercalation is a spontaneous intercalation by the solvent molecules, see Dahn [6] for detail. 1  2  30  Chapter 4. Results  Si  (a)  284  * _  discharging  O  charging  "* -  -«.  I «s 50 fiA for both charging and discharging  time  (hours)  P.  (b)  o op.  a  ^ 5 0 0 JIA  l  0.0  i  i  0.2  1-300  1  i  0.4 n  1-200 pA  1-300  1  i  0.6  1  1  0.B  i  I  1.0  F (•-/T1S0  Figure 4.1: Cell E M F vs charge transport np. (a) The tenth continuous charge-discharge cycle of cell JK10. (b) Discontinuous first discharge of Cell R7, 1=500 fiA corresponds to an, intercalation rate 4.73 hours.  Chapter 4. Results  31  region reduced and the voltage increases to a value which depends on the molar fraction of Li in Li TiS x  2  compound as described in the references.  In future work, cell performance might be improved by using a large molecule electrolyte and adding carbon-black to the cathode material [17]. The large molecule electrolyte may prevent the co-intercalation process so that one does not need high current in the first discharge. A slow electrochemical process will allow intercalant metal to diffuse into the host properly and there will be no voltage jump in the open circuit cell. The carbon-black will serve as a good conducting mediator between crystalline grains to guarantee a homogeneous distribution of charge transfer into the entire host material. 4.2  Analysis of the T D P A C data The quantity of physical interest, the pertubation factor, G (t),  w  a  s  22  obtained from  the raw correlation time spectra by the method described in section 3.4. For a given np the measurement was repeated 2 or 3 times to check the consistency of G (t), 22  final  (?22(<)  a n  d the  was calculated from the weighted average of individual runs.  Each NQI is characterized by the following parameters : i/ , the quadrupole interg  action frequency; 77, the asymmetry parameter and 6, the width of the interaction. By performing a discrete Fourier transform (DFT) on the perturbation function data, it was then possible to identify each static quadrupole interaction by its associated characteristic triplet in the frequency power spectrum. From the magnitudes of these frequency components and their ratios, initial values could be assigned for v and 77 [12]. q  Fits to the G  22  data were then performed using the program Minuit [18], with G ? ^ = £ «.•<&(*)  (4.22)  t  where a,- are the fractional populations for each NQI  a,- = 1), and G  l 22  represent  static interactions of the form given in eq.(2.13). Since it was found (see section 4.3) that  Chapter 4. Results  32  Ga(t)  of TiSa  Fourier Transform  11  VAAA J J L VAAA  (b)  CO C ; fl> '  1  : WWWV £  3 V_AJ\_^  1  j  '  Time (ns)  100  '  100  ~"  Frequency (MHz)  300  Figure 4.2: G (t) of H f in TiS and their respective Fourier transforms : (a) sample without further treatment after being neutron irradiated; (b) the sample was annealed at 550 °C for 50 hours; (c) the sample was quenched in cool water after being annealed; (d) the annealed sample was placed in between two stainless steel flanges. Note that the frequencies v\ and v are not the quadrupole frequencies of the first and second interactions, but the first and second harmonics of the first interaction. 1 8 1  22  2  2  the samples clearly exhibited a preferential orientation, the S coefficients in eq. (2.13) n  were also allowed to vary in the fits. Thus, by minimizing x (chi squared) using the 2  Minuit routine, the following best fit parameters to and a,-.  G (0 were derived : v , S ,w ,r),8 22  q  n  0  Chapter 4. Results  4.3  33  Data for empty host TiS  2  Perturbation functions  G22W of empty host TiS  2  in several conditions are presented  in figure 4.14. The right side offigure4.14 shows their respective Fourier power transforms. The latter indicate the presence of a well-resolved, static NQI. The fits to G (i), 22  however, require also the presence of a second, broadened NQI, which does not appear in the Fourier transforms. The well-resolved interaction is characterized by J/,=456(4) MHz, n = 0.06(3) and 8 = 0.022(3) whereas the broadened interaction has a wide range of v , n and 8. It should be recalled that for each interaction three frequencies should q  be observed for spin | . Owing to damping effects, however (see Chapter 3), the highest component of a given triplet is not always observed above the background. The non-annealed sample produces poor results (see figure 4.14.a). The NQI in this case contributes only 16% to the total spectrum. Radiation damage may play an important role here, but the mechanism of the process is not fully understood. Figures 4.14.b and 4.14.C represent annealed samples with and without quenching. The (b) sample was annealed at 550 °C for 50 hours and then cooled naturally by simply turning the furnace off. Sudden cooling was performed for sample (c), by placing the sample in cool water (t=15 °C) directly after 50 hours in the furnace. The time spectra of both samples are slighly different, but their Fourier transforms are almost identical to each other. The NQI contributes approximately 56% in both cases. All three samples (a), (b) and (c) above are in the form of powders placed in pyrex tubes. For the purpose of electrochemical intercalation, each sample had to be placed in a sandwich comprising the substrate-sample-separator-Li foil, and the whole sandwich placed in between two stainlees steel flanges (see figure 3.2). An experiment performed to simulate the empty host sample in conditions similar to the Li TiS x  2  described above  gave results shown infigure4.14.d. This can not be done after an actual Li/Li TiS x  2  cell  Chapter 4. Results  34  Table 1: Thefittingparameters of the well-resolved NQI of TiiS^  Non annealed  Annealed  Quenched  Pressed  465(8)  452(4)  457(4)  454(4)  0.18(4)  0.06(3)  0.06(3)  0.08(3)  8  0.044(8)  0.021(3)  0.0.027(3)  0.022(3)  % Contribution to the spectrum  15(2) %  56(2) %  55(2) %  45(2) %  (MHz)  has been constructed, since the cell has to be discharged immediately to avoid the cointercalation process by solvent molecules, as described in the previous section. The pressed sample produced the same u as the other empty host samples, but 3  q  with different relative intensities for the individual frequency components. This phenomenon occurs because the pressed sample no longer represents a truly randomly oriented ensemble of microcrystallites, but shows a preferred orientation. This is reflected in the values of the S parameters; in the case of the annealed sample the S\ and S n  2  parameters are 0.481 and 0.224 respectively, whereas for the pressed sample 51=0.256 and 52=0.506. A list of the parameters of interest for the empty host samples can be seen in Table 1 for the well resolved static interaction. A discussion of the origin of the broad interaction is deferred to a later section. For simplicity the annealed TiS sample placed in between stainless steelflangesis called a pressed sample. 3  2  Chapter 4. Results  35  Perturbation Foctors. G»(t)  Fourier Transforms  \ywC^v^ °- — ^ 2  ^ A A ^ V * ^ 0.3  \—-A  \ ^ A n A - ^ W °-  4  -— —~ V A  Ay^V/W**^. 0.5  L A N A ^ * ^ 0.6 0.7  o -1 0  1  1  25  1  1  50  1  Time (ns)  \ 1  /V 1  0  1  100  1  1  1  200  r  300  Frequency (MHz)  Figure 4.3: Perturbation factors, G , of 2 2  transforms.  V  1 8 1  Hf in Li TiS x  2  and their respective Fourier  Chapter 4. Results  4.4  36  Data for intercalated compound Li TiS2 x  The perturbation functions G 2{i) for intercalated compound Li TiS2 and their 2  x  respective Fourier transforms can be seen in figure 4.15. In this case it was found that equation (4.22) required three interactions in order to obtain reasonable fits. Table 2 lists the parameters obtained from the fits for the NQI of interest. Table 2: Fitting parameters of Li TiS2 x  First Interaction Si (MHz)  np  0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0  .08(3) .09(3) .19(4) .12(4) .29(4) .23(3) .27(3) .22(3) .27(3) .00(3) .17(3)  .022(3) .024(4) .076(5) .082(6) .108(5) .094(5) .102(5) .092(5) .066(5) .066(5) .057(5)  454(4) 460(5) 460(5) 451(5) 451(5) 453(5) 477(5) 456(5) 480(5) 448(5) 451(5)  Second Interaction 82 (MHz)  %  45(2) 21(2) 15(2) 11(2) 12(2) 16(2) 15(2) 15(2) 14(2) 14(2) 11(2)  _  _  _  .14(4) .12(4) .15(4) .14(4) .09(3) .14(4) .14(4) .12(4) .18(4) .14(4)  .061(5) .054(5) .064(5) .050(5) .064(6) .054(5) .058(5) .040(4) .094(6) .069(6)  568(5) 568(5) 587(5) 608(6) 595(5) 606(6) 602(6) 599(5) 589(6) 597(5)  %  „  19(2) 44(3) 27(3) 36(3) 36(3) 43(3) 30(3) 38(3) 32(3) 40(3)  There are two well defined static interactions of narrow width : thefirstone is the empty host NQI, whose contribution decays rapidly in the range 0 < x < 0.2, thereafter remaining constant; the second interaction increases slowly in the region 0 < x < 0.2, becoming dominant for x > 0.2. The third interaction contributes approximately 40%60% to the spectrum. It is similar to the second interaction found in the empty host case i.e. characterized by a small asymmetry parameter 77, a large 6 and large scatter in v . This interaction was introduced in order to get satisfactory fits. As will be pointed q  Chapter 4. Results  37  out in the discussion of Chapter 5, although the presence of this interaction is a useful indicator of sample quality, it is not of great interest theoretically. Figure (4.16) summarizes the results of the TDPAC measurements on the Li TiS2 x  system. Here we depict the variation of the fit parameters with np for the two interactions of interest. The quadrupole frequency v is presented in figure 4.16.a. The first interaction q  produces a more or less constant frequency with average t^T = 461(5) MHz. The second interaction reveals itself at x « 0.1 with a 19% contribution and becomes dominant at x « 0.2 at the 44% level. Its frequency stays constant below x=0.2, then increases in the region 0.2 < x < 0.4, remaining constant beyond x=0.4 with 1727=599(6) MHz. The relative change in the populations of interactions 1 and 2 is presented in figure 4.16.b, treating the broad, non-specific third interaction as a background which can be subtracted. It can be seen that while the empty host population decreases at the expense of the second NQI, it does not decay to zero. Finally infigure4.16.C and 4.16.d we show the variation of 8 with np. In both interactions 8 is essentially constant, although 8\ falls off slightly in the region 0 < x < 0.3.  38  Chapter 4. Results  (a)  (b) o  N  •c cr o-| y  e e •  q1  II o,  4  —i—i  O.b " 0.2 ' 0.'4 ' 0.'6 ' 0.8 " 1.b n (e"/TiS ) F  Si  <  0.2  i  0.4  i  i  0.6  i  i  0.8  n ( e V T S Ia )  i  i  1.0  F  2  oI  (c)  (d)  o CM  o  CM. O  o  OJ  o  O.b ' 0.2 ' 0.'4 ' O.'e ' 0.B ' 1.0 n (e"/TiS ) F  2  0.b ' 0."2 ' 0.4 ' o.'e ' 0.8 ' i.b n (e"/TiS ) F  2  Figure 4.4: The dependence of fit parameters on the charge transport, np. Note: The dashed lines in (b) are aids to the eye. The error bars in (a), (c) and (d) lie inside the data points.  Chapter 5  Discussion  5.1  Introduction The work of Butz and his colleagues [19-22] has shown that TDPAC spectroscopy is  a powerful tool in elucidating the intercalation mechanism. Studies of Li TaS2, x  Ag TaS2 x  and Li ZrS2, for example, have shown that TDPAC can reveal the sequence of intermex  diate phases formed during intercalation and their intercalate packing density. Especially important was the finding that the nuclear quadrupole frequency was directly related to p, the local intercalate packing density of lithium atoms [21], so that even variations in p within the same layer can be detected. There is almost no possibility to detect this using X-ray or neutron scattering techniques. Thus the observation of sharp, discrete quadrupole frequencies and their variation in magnitude and intensity as a function of UF provides a key to the interpretation of the intercalation process.  5.2  Cathode utilization Cathode utilization represents the percentage of cathode material involved in the  electrochemical reaction. Poor electrical contact can occur between the cathode material and the substrate [6], as a result of which not all of the cathode material can be intercalated. A certain fraction of the host material remains unchanged. By definition cathode utilization of a cell must be less than or equal to 100%. In the following section  39  Chapter 5. Discussion  40  we discuss the cathode utilization in this work and how it can be determined. Cathode utilization of a cell is usually determined from its cycling performance (charge-discharge cycle). A cell having cathode utilization less than 100% gives shorter cycles than that of an ideal cell. Numerically it can be calculated using the equation: [/ = — x 100%. x  (5.23)  The molar fraction x is determined by measuring the voltage of the cell V(n^) and then inferring x from calibrated measurements of V(x) in the literature [1,7]. The charge transport np is determined from eq.(1.4) by measuring the time and current of the reaction. In our case, however, this method is not readily applicable, owing to the discontinuous nature of the discharge process, as mentioned in Chapter 4. Instead, the TDPAC data can be used to infer the cathode utilization factor directly from the fact that an empty host interaction persists even until np=1.0. Assuming a homogeneous distribution for the Hf probe, this signal must represent regions of the crystal structure unavailable to the intercalating Li atoms. The data in figure 4.4.b. indicate an empty host component, /EH = 27.9 ± 3.5%, yielding a cathode utilization factor in the region of 70-80%, comparable with that quoted by Thompson [7].  5.3 5.3.1  The Nuclear Quadrupole Interaction in Li TiS2 x  The broad, non-specific interaction In both the empty host TiSi and Li TiS2 x  samples the TDPAC spectra showed  evidence for a broad, non- specific interaction characterized by a wide range of v and 6. q  We speculate that there are two possible sources for this interaction. One possibility is that this signal originates from  1 8 1  H f probe atoms which have  not substituted for Ti atoms in regular lattice sites. Such atoms could, for example,  Chapter 5. Discussion  41  be trapped at crystalline grain boundaries, where a wide variation in the efg could be expected. The dramatic improvement of the time spectra following the annealing process (see figure 4.2) lends support to this conjecture. In the annealed sample the fractional population corresponding to this interaction is reduced by almost a factor of 2. The fact remains, however, that even after annealing a significant fraction of sites (w 40%) still exhibit these features.  This suggest that another mechanism must be  present which is basically unaffected by the annealing process.  Such an effect could  be produced by co-intercalation of the PC solvent. This occurs when lithium ions are intercalated into the host along with a PC solvation cloud. In fact the term intercalation here is a misnomer, in the sense that the changes in the host lattice are quite drastic and irreversible. Instead we refer to this process as PC insertion [6]. It is believed that solvent insertion can be avoided by using less polar solvents [17]. Because of its high sensitivity, TDPAC will be an excellent vehicle to check this hypothesis, and this will be on the agenda for future experiments. Thus TDPAC may be able to play a significant role in quality control analysis for the testing of new materials in electrochemical cells. 5.3.2  The well resolved, specific Nuclear Quadrupole Interaction Figure 4.4.b indicates that 27.9% of the cathode material is not involved in the  electrochemical reaction and remains unchanged. Since the intercalation of available sites should be complete by np=l, any residual empty host contribution at this value of rip must represent those regions of the material inaccessible to intercalating Li atoms. Hence, in order to obtain the true growth and decay of the NQI for the crystalline material involved in the intercalation process, the residual empty host signal at large np should be regarded as the zero level and consequently the contributions represented in fig. 4.4 (b) should be rescaled. This gives rise to the relative contributions depicted in fig. 5.1, which shows the growth and decay of the NQI frequencies in sites available for intercalation.  42  Chapter 5. Discussion  o to  'q2  N X o in  o-\  the first interaction  u c m CD  =5 _  the second interaction  ^ in "q1  o OH  .2o Z5 T • —  c m O O  f o.o  0.2  0.4  0.6  Charge transport n  0.8  1.0  F  Figure 5.1: Nuclear quadrupole frequencies and percent contribution of the first (solid circles) and second (open circles) interactions vs. np after subtraction of residual empty host background. This represents the behaviour in regions of the crystal accessible to intercalating Li atoms. Note: the error bars of the frequency curves are contained in the data points.  43  Chapter 5. Discussion  o o o  o Intercalation o process o begins p<1/3  o  o  o C-axIs  o  o  o  o  o rapidly o 0sp£1/3  expands  o C-axIs. expansion  o  o  o  o  o  o  o  o  o  o  o Is complete.  o  o  o  o  o  have o sites been occupied. p-1  All octahedral  Figure 5.2: A model of Li —> TiS intercalation process. The circles and horizontal lines represent Li atoms and TiS sandwiches respectively. 2  2  The molar fraction behaviour is very similar to that obtained for Li ZrS x  2  by Lerf and  Butz [23], where the empty signal disappears after np « 0.3. On the other hand, in our case the NQI frequency for the lithiated regions, u , is higher, as opposed to lower, than q2  the empty host signal, u \, and u q  q2  shows a gradual increase in the region 0 < np < 0.3  before attaining the constant value of w 600 MHz. In the interval 0 < nF < 0.3, where the c-axis expands rapidly [6,24], the behaviour of v  q2  indicates that the local  packing density of Li atoms, p, slowly increases to a maximum, steady value. This may still be consistent with the finding of Thompson [7], who suggested that ordering can occur in a two-dimensional superlattice in the Li TiS x  2  for x = 1, | , j , | , | , • • •• Owing  possibly to the high initial lithium current densities, the lower Li packing densities are not resolved in the TDPAC measurements, consequently initial values are smeared out and only the limiting value p=l is observed. This implies that the NQI is extremely localized, determined almost solely by the charge transfer to surrounding sulphur atoms.  Chapter 5. Discussion  44  Figure 5.18 demonstrates a model for the intercalation process. As the c-axis expands, p increases to its maximum value of 1, thereafter remaining constant. Unfortunately it is not feasible to make a realistic calculation of the efg in such a complex system as Li TiS2, x  since little is known about the electronic wave functions  and band structure, particulary for the Hf-doped compound. From other measurements [7] we know that in the range 0 < x < 1 only octahedral sites are occupied. The NQI parameters obtained from the fits are consistent with such an assignment.  Chapter 6  Conclusion  In the high current electrointercalation of Li in TiS two nuclear quadrupole in2  teractions, consistent with octahedral symmetry, are observed in the region of charge transport 0 < np < 1. The first interaction originates from empty host material (p=0). It is characterized by a constant quadrupole frequency with average P^"=461(5) MHz. The quadrupole frequency of the lithiated TiS  2  (Li TiS2) shows a gradual increase in x  the low np region, 0 < np < 0.3, and then attains a constant value of 7^2=599(6) MHz for 0.3 < np < 1. The second interaction corresponds to a compound which rapidly reaches a high packing density of Li (p=l). TDPAC provides a sensitive tool for assessing material quality in electrochemical cells. The cathode utilization factor is readily determined from the size of the residual empty host signal; microcrystalline imperfections are revealed as NQI frequencies with large 5. In addition TDPAC demonstrates the necessity for annealing the sample following neutron irradiation. Quenching of the samples appears to make little difference to the results. Further work which may be performed should include : • Improvement of battery performance so that a slow intercalation process can be performed. This may involve — Using other electrolytes so that co-intercalation processes can be avoided.  45  Chapter 6.  Conclusion  46  — Adding conductive material to the sample to improve electrical conduction between substrate and crystalline grains and between crystalline grains themselves. This might improve cathode utilization. • TDPAC measurements in the low np region. The region 0 < x < 0.4 seems to be very sensitive to variations in np. • Temperature dependence of the intercalation process. The above mentioned work should greatly improve our understanding of metal intercalation into layered compounds.  Bibliography  [1] M . S. Whittingham, Prog. Solid State Chem., 12 (1978), 41. [2] C. Ramos, A. Lerf, S. Saibene and T. Butz, Solid State Ionics, 31, (1988), 177. [3] Peter J. Mulhern, Lithium Intercalation in Crystalline Li MoS , partment of Physics, Univ. of B. C , (1986). x  2  PhD. Thesis, De-  [4] J. R. Dahn, D. C. Dahn and R. R. Hearing, Solid State Comm., 42, 3, (1982), 179. [5] M . Inoue, H. P. Hughes and A. D. Yoffe, Advance in Physics, 38, 5, (1989), 565. [6] J. R. Dahn, Lithium Intercalation in Titanium Disulphide, MSc. Thesis, Dept. of Physics, Univ. of British Columbia, Canada, (1980). [7] A. H. Thompson, Phys. Rev. Let., 40, 23, (1978), 1511. [8] A. H. Thompson and F. R. Gamble, Mat. Res. Bui., 10, (1975), 915. [9] M . S. Whittingham and F. R. Gamble Jr., Mat. Res. Bui., 10, (1975), 363. [10] M . B. Dines, Mat. Res. Bui., 10, (1975), 287. [11] W. R. McKinnon, Solid State Comm., 40, (1981), 343. [12] H. Frauenfelder and R. M. Steffen, in Alpha-, Beta-, and Gamma-, Spectroscopy, ed. K. Siegbahn, North Holland Publishing Co., Amsterdam, (1965). [13] M . E. Rose, Phys. Rev., 91, (1953), 610. [14] P. W. Martin and S. El-Kateb, J. Chem. Phys., 76, (1982), 3819. [15] J. R. Dahn and W. R. McKinnon, J. Phys., 17, (1984), 4231. [16] T. Hibma, Physica, 99B, (1980), 136. [17] J. R. Dahn, private communication. [18] F. James and M . Roos, Comp. Phy. Com., 10, (1975), 343. [19] T. Butz and A. Hubler, Mat. Res. Bui., 16, (1981), 541.  47  [20] T. Butz, A. Vasquez, H. Saitovitch, G. M. Kalvius, and A. Lerf, Hyp. Int., 4, (1978), 978. [21] T. Butz, A. Lerf, Ber. Bunsenges. Phys. Chem., 90, (1986), 638. [22] A. Lerf and T. Butz, Angew. Chem. Int. Ed. Engl., 26, (1987),110. [23] A. Lerf and T. Butz in Reactivity of Solids edited by P. Barret and L. C. Dufour, Elsevier Science Publiser B. V., Amsterdam, (1985), p 493. [24] Whittingham, F. R. Gamble and C. R. Simon, Mat. Res. Bui., 10, (1978), 363.  48  

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