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The far-infrared powder absorption spectra of bis-tetramethyltetraselenafulvalene salts [(TMTSF)₂X, X=(PF₆,… Homes, Christopher C. 1985

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T H E F A R - I N F R A R E D P O W D E R A B S O R P T I O N S P E C T R A O F B I S - T E T R A M E T H Y L T E T R A S E L E N A F U L V A L E N E S A L T S [ ( T M T S F ) 2 X , X = ( P F 6 , A s F 6 , S b F 6 , B F « , C I O * and R e 0 4 ) ] By C H R I S T O P H E R C. H O M E S B.Sc.(Hon.), McMaster University, 1983 A THESIS S U B M I T T E D IN PARTIAL F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F M A S T E R O F S C I E N C E in T H E F A C U L T Y O F G R A D U A T E STUDIES ( D E P A R T M E N T O F PHYSICS) We accept this thesis as conforming to the required standard. T H E UNIVERSITY O F BRITISH C O L U M B I A November 1985 © Christopher C . Homes, 1985 In presenting this thesis in partial fulfilment of the requirements for an ad-vanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of the Department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Physics The University of British Columbia 6224 Agriculture Road Vancouver, B . C . C A N A D A V 6 T 2A6 Date: November 27, 1985 ii A B S T R A C T The far-infrared powder absorption spectra from 20-250 c m - 1 have been ex-amined in a series of six protonated and deuterated ( T M T S F ^ X compounds, with X=PF 6 , AsF 6 and SbF 6 (octahedral anions) and X=BF 4 , C104 and Re0 4 (tetrahe-dral anions) as a function of temperature from 10K to 290K . The octahedral-anion spectra are all very similar, having 4 sharp resonances which have been attributed to three lattice modes and one internal mode. These assignments were made on the basis of isotope shifts upon deuteration, and wave number temperature depen-dence. The intensity of the lines is roughly proportional to the d.c. conductivity, and indicate a phase transition around 12K. The spectra of the tetrahedral-anion compounds are also similar. They show, however, extra structure below the anion-ordering temperature, TAOI including a strong feature at 30 c m - 1 . The 30-cm - 1 feature shows a magnetic field depedence and may be related to the superconduc-tivity. Simple one- and two-dimensional models are presented that indicate that this feature may be due to the activation of a transverse acoustic zone-boundary phonon, due to zone-folding, which accompanies the formation of a superlattice created by the anion-ordering transition. Extended measurements from 100-300 c m - 1 have been performed on proto-nated AsFe and SbFe compounds, allowing the identification of two internal modes. Extended measurements from 100-400 c m - 1 have been performed on protonated and deuterated B F 4 and Re0 4 compounds, which show internal modes of both the TMTSF and anion molecules, and a torsional mode of the TMTSF methyl groups. These assignments were made on the basis of isotope shifts upon deuteration an extensive published vibrational analysis of T M T S F . Iv T A B L E O F C O N T E N T S Abstract ii Table of Contents iv List of Tables vi List of Figures vii Acknowledgements xt C H A P T E R 1 I N T R O D U C T I O N 1 1.1 Quasi-one-dimensional Conductors 1 1.2 High Temperature Organic Superconductors 2 1.3 The ( T M T S F ) 2 X Charge Transfer Salts 5 1.4 Structure of ( T M T S F ) 2 X Salts 7 1.5 Electronic Band Structure of ( T M T S F ) 2 X 9 1.6 ( T M T S F ) 2 X Salts with Centrosymmetric Anions 15 1.7 ( T M T S F ) 2 X Salts with Non-centrosymmetric Anions 19 1.8 Far-infrared Optical Properties 21 1.9 Fluctuating Superconductivity 24 C H A P T E R 2 E X P E R I M E N T A L T E C H N I Q U E S 29 2.1 Sample Prepatation 29 2.2 Michelson Interferometer 30 2.3 Cryostat 32 2.4 Detectors 35 2.5 Powder Absorption Coefficient 2.6 Numerical Analysis V 35 36 CHAPTER 3 POWDER ABSORPTION MEASUREMENTS 39 3.1 Powder Absorption Spectra for Octahedral Anions 39 3.2 Powder Absorption Spectra for Tetrahedral Anions 59 3.3 Extended Measurements for (TMTSF) 2 X Compounds 72 CHAPTER 4 LATTICE DYNAMICS OF (TMTSF) 2 X: SIMPLE MODELS . . 87 4.1 Introduction 87 4.2 One-dimensional Model of (TMTSF) 2 X 87 4.3 Two-dimensional Model of (TMTSF) 2 X 92 4.4 An Estimate of the TMTSF Zone-boundary Acoustic Phonons 99 CHAPTER 5 CONCLUSIONS 102 5.1 Conclusions 102 5.2 Suggestions for Future Experiments 103 BIBLIOGRAPHY 104 APPENDLX A 109 L I S T O F T A B L E S I-I Properties of some (TMTSF) 2 X salts. IJI-I Calculated and measured isotope shifts of the ( T M T S F ^ X lattice modes. (C ordinates are shown in Fig. 3-12) ni-II Line shifts for different anions UI-III Low-energy internal vibrations of octahedral anions. III-IV Low-energy internal vibrations of tetrahedral anions. IJI-V Low-energy internal vibrations L I S T O F F I G U R E S 1-1 The dimerization of a linear-chain material (Peierls distortion) resulting in the formation of a charge-density wave 6 1-2 The structure of ( T M T S F ) 2 X 8 1-3 Perspective view of the ( T M T S F ) 2 X crystal structure showing the crystallo-graphic axes a, b and c 10 1-4 The high temperature band structure and Fermi contour in the first Brillouin zone for the reciprocal lattice for (TMTSF) 2 AsFe 11 1-5 Model band structures for the three most highly commensurate two-dimensional broken symmetries .13 1-6 The (a) d.c. resistivity and (b) resistivity at 35 GHz versus temperature for some typical samples of ( T M T S F ) 2 X 14 1-7 The phase diagram of (TMTSF) 2AsF6 under pressure 16 1-8 The single crystal reflectance of ( T M T S F ) 2 P F c for E || a at various tempera-tures (a) by Tanner et al. and (b) Eldridge et al 23 2-1 A schematic of the Beckman/RIIC FS-720 spectrophotometer, with the tail of the Janis dewar 31 2-2 A schematic of the detection and recording electronics used in the 10-350 c m - 1 region 33 2-3 A longitudnal cross-sectional view of the Janis Supervaritemp dewar (model 8 C N D T ) 34 3-1 The powder absorption coefficient ad (in abritrary units) of (TMTSF) 2PF6 powder in Nujol on a polyethylene backing showing the four resonances. . 41 3-2 The powder absorption coefficient ad (in arbitrary units) of (TMTSF) 2 AsFe powder in Nujol on a T P X backing showing the four resonances 42 3-3 The powder absorption coefficient ad (in arbitrary units) of (TMTSF)2AsF6 powder in Nujol on a T P X backing showing the four resonances 43 3-4 The temperature dependence of wave number of the four ( T M T S F ) 2 P F e lines seen in Fig. 3-1 44 3-5 The temperature dependence of wave number of the four (TMTSF)2AsF6 lines seen in Fig. 3-2 45 3-6 The temperature dependence of wave number of the four (TMTSF)2SbF6 lines in Fig. 3-3 46 3-7 The integrated intensity of the four lines of ( T M T S F ) 2 P F 6 seen in Fig. 3-1 versus temperature 47 3-8 The integrated intensity of the four lines of ( T M T S F ) 2 A s F 6 seen in Fig. 3-2 versus temperature 48 3-9 The integrated intensity of the four lines of ( T M T S F ) 2 S b F 6 seen in Fig. 3-3 versus temperature 49 3-10 The 6-K powder spectra of protonated and deuterated (TMTSF) 2PF6 powders, in Nujol on a polyethylene backing showing the four resonances 50 3-11 The internal coordinate system for the T M T S F molecule, and the two lowest-energy modes of T M T S F , with the calculated shift upon deuteration 54 3-12 The 8-K powder absorption coefficient ad (in arbitrary units) of ( T M T S F ) 2 P F 6 , ( T M T S F ) 2 A s F 6 and ( T M T S F ) 2 S b F 6 powders in Nujol on a T P X backing, ex-cept for P F c which had a polyethylene mount 55 3-13 The wave number of the internal mode versus anion mass 56 3-14 The powder absorption coefficient ad (in arbitrary units) of (TMTSF) 2BF4 powder in Nujol on a T P X backing 61 3-15 The powder absorption coefficient ad (in arbitrary units) of (TMTSF) 2 C104 powder in Nujol on a T P X backing 62 ix 3-16 The powder absorption coefficient ad (in arbitrary units) of (TMTSF)2Re04 powder in Nujol on a T P X backing 63 3-17 The low-temperature powder absorption coefficients of the three tetrahedral-anion compounds, rescaled and displaced for clarity. 64 3-18 The integrated intensity of the "30 c m - 1 * feature in the powder spectra of the BF4 and C10 4 compounds 65 3-19 The full width at half-maximum of the K30 c m - 1 " feature in the powder spec-trum of ( T M T S F ) 2 C 1 0 4 66 3-20 The 6-K powder absorption spectra ad (in arbitrary units) of protonated and deuterated ( T M T S F ) 2 B F 4 powders in Nujol on T P X mounts 68 3-21 The 6-K powder absorption spectra ad (in arbitrary units) of protonated and deuterated ( T M T S F ) 2 C 1 0 4 powders in Nujol on T P X mounts 69 3-22 The 8-K powder absorption spectra ad (in arbitrary units) of protonated and deuterated ( T M T S F ) 2 R e 0 4 powders in Nujol on T P X mounts 70 3-23 The 6-K powder absorption coefficient ad of (TMTSF) 2 AsFe powder form 25-275 c m - 1 , and ( T M T S F ) 2 S b F 6 powder from 25-325 c m - 1 , in Nujol on T P X mounts 74 3-24 The 6-K protonated and deuterated powder absorption spectra for quench cooled ( T M T S F ) 2 B F 4 powders in Nujol on T P X mounts 75 3-25 The 6-K protonated and deuterated powder absorption spectra for quench cooled ( T M T S F ) 2 R e 0 4 powders in Nujol on T P X mounts 76 3-26 A comparison of the powder absorption spectra ad (in arbitrary units) of pro-tonated ( T M T S F ) 2 B F 4 and ( T M T S F ) 2 R e 0 4 powders in Nujol on T P X mounts at 6 K in the 100-300 c m - 1 region 77 3-27 The 6-K powder absorption spectra ad (in arbitrary units) of protonated and deuterated ( T M T S F ) 2 R e 0 4 powders in Nujol on T P X mounts 78 3-28 The temperature dependence of the powder absorption coefficient ad (in arbi-trary units) of deuterated ( T M T S F ) 2 R e 0 4 powders in Nujol on T P X backing. 100-300 c m - 1 region 79 3-29 The low-energy normal modes of vibration of the octahedral anions 80 3-30 The correlation table for the molecular point group and the site and unit cell group for the octahedral anions 81 3-31 The low-energy normal modes of vibration of the tetrahedral anions 82 3-32 The symbolic designation of the internal coordinate system used in the normal coordinate calculation of the vibrational states of the TMTSF and TMTSF+ molecules 85 3-33 Atomic displacement vectors for the totally symmetric (ag) modes of neutral TMTSF 86 4-1 Linear system for (TMTSF) 2 X 88 4-2 The frequency dispersion curves for the one-dimensional model shown with the eigenmodes at the zone origin and at the zone boundary 91 4-3 Two-dimensional system for (TMTSF) 2 X 94 4-4 The frequency dispersion curves for the two-dimensional model for a wave vector along the path T -> M X T 96 4-5 The frequency dispersion curves for the two-dimensional model for a wave vector along the path r —• M Y -+ T 97 4-6 The eigenmodes for the two-dimensional model of the phonons at the zone origin and at the zone boundary 98 A C K N O W L E D G E M E N T S I would like to thank my supervisor, Dr. J.E. Eldridge for his help with the experiments and many useful suggestions. I would also like to thank Dr. G.S. Bates of the Department of Chemistry at U.B.C. for preparing the crystals, and Dr. Frances E. Bates for valuble discussion. I am grateful to Mary-Ann Potts, as well as the electronics shop, for setting up the data acquistion system. I would like to thank Kevin Kornelsen for his help in the lab. During this research, I have been supported by a Natural Sciences and Engi-neering Research Council (NSERC) Postgraduate Scholarship. This work was also supported by Grant No. A5653 from NSERC. CHAPTER 1: INTRODUCTION 1 C H A P T E R 1 I N T R O D U C T I O N 1.1 Quasi-one-dimensional Conductors Organic molecules display an amazing diversity of forms and have many different properties. One of the physical properties that organic molecules seldom display, however, is electrical conductivity and even more rarely, superconductivity. The first stable organic conductors were synthesized in the early 1960's. The organic molecule tetracyanoquinodimethane, or T C N Q , was prepared in 1960 by workers at E.I du Pont de Nemours & Company. Little energy is needed to introduce an extra electron into T C N Q and the negatively charged structure that results is chemically stable. T C N Q by itself, however, is not able to conduct electrons, and so in an electronically neutral system there is no tendancy for the electrons to move from one T C N Q molecule to another. If the T C N Q molecules (anions) can obtain a fraction of electronic charge from other atoms or molecules (cations), the material can become conductive and is called a charge transfer salt. In the cesium salt of T C N Q , ( C s + ) 2 ( T C N Q - * ) $ for example, each cesium atom gives up an average of two-thirds of an electron to each T C N Q molecule. Thus, two out of every three T C N Q molecules become negatively charged, and if an electric field is imposed, the extra electrons can move from the charged T C N Q molecules to the neutral ones. Another T C N Q charge transfer salt, tetrathiafulvalene-tetracyanoquinodimethane ( T T F - T C N Q ) , was synthesized in 1973 by Cowan and Ferraris, and by Heeger CHAPTER 1: INTRODUCTION 2 and Garito. In the solid form the T T F and T C N Q molecules stack in seperate columns, and electrons are donated from the T T F stack to the T C N Q stack. A fractional charge of 0.59 electron per molecule is transferred from one stack to another. Because of the electron transfer there can be a net motion of electrons along both stacks; hence the material is conductive. At room temperature T T F -T C N Q has a conductivity of ~ 2000 ( O c m ) - 1 , or about three orders of magnitude smaller than that of copper. The architecture of the T T F - T C N Q crystal gives rise to a striking electri-cal property: the material is highly conductive in one direction only. The most favourable direction is 500 times as conductive as the least favourable direction. This is because the T T F and T C N Q molecules are large planar molecules, with the valence ir— electrons located above and below the planar framework. They stack to-gether like pancakes so that the orbitals of the valence ir— electrons overlap, allowing the electrons to move freely up and down the stacks. The reason for the anisotropy is that the T T F and T C N Q molecules are stacked in parallel planes, with little over-lap between adjacent stacks. Compounds that display this anisotropic behavior are called quasi-one-dimensional solids or linear-chain materials. 1.2 H i g h Temperature Organic Superconductors Some of the highly conducting inorganic linear-chain solids have been known for a long time. Tetracyanoplatinate, or T C P , was first synthesized in 1842 and the material poly(sulfurnitride), (SN)X, in 1910. However, the properties of T C P and (SN)X were not examined until the 1970's. There are two good historical reviews in the Scientific American 3 ' 8 . The search for new linear chain compounds was prompted by W.A. Little, who in 1964 proposed an alternative method for the formation of Cooper pairs 4. The theory of superconductivity in metals was formulated in 1957 by John Bardeen, Leon Cooper and J . Robert Schriffer5. Superconductivity results when the electrons CHAPTER 1: INTRODUCTION 3 in a metal form into bound pairs called Cooper pairs. As an electron moves through the lattice there is an electrostatic attraction between the electron and the positive ions around it. As the electron moves away, the positive ions remain displaced for a comparatively long time since the vibrational motion of the lattice is much slower than the motion of the electron. This lattice distortion creates a temporary region of positive charge to which another electron is attracted and a Cooper pair is formed. At high temperatures, the effect is destroyed by the random, thermal vibrations of the lattice, but it can emerge below a certain critical temperature (Tc) and cause the electrons that make up each Cooper pair to act as if they were connected by a weak spring. The electrons vibrate back and forth in response to the variations in charge density set up by their own motions in the atomic lattice. Electrical conduction in a superconductor is caused by the net motion of the centers of mass of the Cooper pairs, whereas electrical conduction in an ordinary metal is caused by the net motion of individual valence electrons. A quantum mechanical aspect of the Cooper pairs is that when the electrons enter the bound state, the total energy of the system is minimized if all of the Cooper pairs have the same momentum. If there is no current flowing through the material, the momentum of each Cooper pair is zero: the electrons in each pair are thereby constrained to move in opposite directions with respect to the lattice, and the velocity of each center of mass must be zero. When there is a current in the material, the electrons in each pair must move in such a way that all of the Cooper pairs have the same constant momentum. Every motion of one electron that threatens to break up the Cooper pair must be immediately compensated for by its partner so that equilibrium is always maintained. This itself does not explain why the resistance in a superconductor is zero. In an ordinary metal, electrical resistance is the result of the scattering of moving electrons by imperfections in the lattice and by the thermal vibrations of the lattice at any temperature above absolute zero. Each time an electron is scattered, the CHAPTER 1: INTRODUCTION 4 energy of the electronic system is reduced by a small amount, and there is a cor-responding increase in the vibrational energy of the lattice at a finite temperature. The resistivity of a perfectly regular metallic lattice would theoretically be zero at absolute zero because there is no vibrational energy available in the lattice for the scattering of electrons. In a superconductor, the electrical resistivity can be zero at finite temperature because once the Cooper pairs are put into motion by an electric field, they acquire a net momentum. The net momentum cannot decay through scattering: unlike the scattering of an ordinary electron which costs little energy, the scattering of the Cooper pair costs much more energy than the binding energy which holds the electrons together. Furthermore, in the highly organized superconducting state, changing the momentum of one Cooper pair requires a change in the momenta of all of the other Cooper pairs as well. The energy needed to redistribute the momenta is much larger than the vibrational energy available in the lattice at low temperature and hence the Cooper pairs do not encounter resistance as they move through the lattice. At higher temperatures, it is possible for the lattice to redistribute the momenta and break up the pairs, and the electrons are scattered as they are in an ordinary conductor; the resistance of the material jumps from zero to some finite value. Since the condensation of electrons into Cooper pairs depends on deformations of the atomic lattice, Tc is related to the "stiffness" of the lattice: its resistance to deformation by a passing electron. If the atoms in the lattice have small masses and the interatomic bonds are relatively "soft", the deformations are large compared with the deformations caused by thermal vibrations and Tc is high. More precisely, the critical temperature varies inversly with the square root of the mass of the anions in the lattice5 ^ - (Mon ) " * . (1-1) CHAPTER 1: INTRODUCTION 5 Little proposed a way that Cooper pairs might be produced without lattice distortions. He consided a large organic molocule consisting of two parts: a long chain of carbon atoms called the "spine" and a series of arms or side chains at-tatched to the spine. Each molecule would be a hydrocarbon with loosely bound valence electrons, such as an organic dye. An electron travelling along the spine of the carbon atoms would repel the outer electrons of the hydrocarbon molecules, thus creating a region of net positive charge on the parts of the side chains nearest to the spine. A second electron moving along the spine in the opposite direction,-would be attracted by the relatively dense positive charge and indirectly to the first electron thus forming a Cooper pair. The region of enhanced positive charge is created by the displacement of electrons rather than atoms in a lattice. Since the electron is about 100,000 times less massive than a typical ion, equation 1-1 gives us that Te for this material should be increased by a factor of ~ 300. Such a material would be superconducting at room temperature, and in principle the superconducting state could be stable up to 2000 K. It is known from theoreti-cal calculations that it is impossible to sustain the formation of Cooper pairs in a strictly one-dimensional conductor at any temperature above absolute zero. Thus the strictly one-dimensional superconductor cannot exist. In any real molecular sys-tem, however, the conductors are only approximately one-dimensional, and there will be some interaction between the chains that will allow a Cooper pair to jump from one stack to another. Hence the theoretical obstacle to superconductivity in one-dimension is not a practical one. While no one has succeeded in constructing the sort of organic molecule that Little envisoned, the idea has generated a strong interest in organic superconductors, and the possibilities of technological applica-tions for such materials have been discussed8. 1.3 T h e ( T M T S F ) 2 X Charge Transfer Salts The organic conductor T T F - T C N Q is a good electrical conductor at room CHAPTER 1: INTRODUCTION 6 temperature. As the temperature is lowered the conductivity increases in a metallic fashion until at about 60 K the uniform molecular spacing in the stacks gives way to a more energetically favourable structure in which the seperation of adjacent molecules in the stack changes. The result of this structural change is to alter the electronic density along the chain. The charge density undergoes a periodic concentration and rarefaction that is called a Peierls distortion or a charge-density wave ( C D W ) 6 . MOMENTUM Figure 1-1 The dimerization of a linear-chain material (Peierls distortion) resulting in the formation of a charge-density wave. The diagrams at the right depict the creation of a band gap due to band splitting*. The onset of a C D W causes the partially filled conduction-electron band to split into two bands, the lower one completely filled, the upper one completely empty. Conduction may occur only if electrons are promoted across the energy gap by thermal activation or photon-absorption. Thus, the material changes suddenly CHAPTER 1: INTRODUCTION 7 from a conductor to a semiconductor or an insulator. In T T F - T C N Q the C D W transition occurs at 53 K. While the valence electrons are no longer available for free conduction, an alternate mechanism for conduction is the sliding C D W 7 , which slides along the lattice stacks. The electrons "surf-ride'' on the C D W . It is this effect which is responsible for the enhanced conductivity in T T F - T C N Q at ~ 68 K 8 ' f t . As the temperature is lowered below 58 K for T T F - T C N Q , there is a decrease in the conductivity. This is attributed to the C D W becoming pinned to charged impurities, lattice defects and significant interchain coupling 1 0 . In other words the oppositely-charged CDW's on adjacent stacks are pinned to each other by Coulomb attraction, as well as to impurities and defects. This motivated the search for a new organic conductor which would have small molecules in the anion stacks that would not be susceptable to C D W formation, thus allowing sliding CDW's and suppressing pinning due to interchain coupling. In 1979 a fascinating new series of charge transfer salts were synthesized by K . Bechgaard et a i 1 1 . The bis-tetramethyltetraselenafulvalene-X compounds have the chemical form (TMTSF)2X, where X is any one of a number of relatively small inorganic radical anions e.g. hexafluorophosphate (PFe), hexafiuoroarsenate (AsFe), hexafluoroan-timonate (SbFe), tetrafluoroborate (BF4), perchlorate (CIO4), perrhenate (Re0 4), nitrate (NO3), etc., and are known as Bechgaard salts. 1.4 Structure of ( T M T S F ) 2 X Salts The crystal structure is shown in Fig. 1-2. It is triclinic with a P i (C,-) space group 1 3 . The anion positions are centers of inversion symmetry, but no other symmetry operations apply to the crystal lattice. The planar T M T S F molecules are slightly dimerized as they stack together in a zig-zag fashion to form a linear chain. The chain direction is the a-axis. The stacks are tightly arranged along the interchain or b-axis, forming a sheet in the ab-plane. The anions form a well CHAPTER 1: INTRODUCTION 8 T M T S F AsF 6 Figure 1-2 The structure of ( T M T S F ) 2 X . (a) The T M T S F molecule. The methyl groups strongly involved in the definition of the anion cavity are indicated by the solid shading 1 8 , (b) Molecular stacking in ( T M T S F ) 2 A s F 6 . This sh ows the side view of the chain and the set of crystallographic coordinates1 4, (c) View of (TMTSF) 2 AsF6 down the a-axis showing the anion lattice 1 4. Typical dimensions for the unit cell of ( T M T S F ) 2 A s F 6 are a = 7.277(2) A, 6 = 7.711(1) A, c = 13.651(2) A, a = 83.16(1)° , 0 = 86.00(2)°, 7 = 7 1 . 2 7 ( 2 ) ° 1 4 . CHAPTER 1: INTRODUCTION 9 defined lattice and sit in the cavities left by the T M T S F molecules. The c-axis lies along the anion lattice direction that is almost normal to the ab-plane. Other sets of axes that are routinely used are the orthogonal set (a, b ' and c') and the set of principal magnetic axes (a*, b* and c*). In the orthogonal set b' is orthogonal to a and in the ab plane, and c' completes the set. The principal magnetic axes are those crystal directions along which the magnetic susceptability is greatest. In fact a and a* are the same, but b* and c* are close to, but not the same as b and c respectivley. The T M T S F molecules stack almost perpendicular to the a-axis, deviating from perpendicularity by ~ 1.1°16. The stack units repeat by inversion with overlap displacements alternating along the a-axis. The value of the lattice parameters for the unit cell will vary depending on the anion subst i tut ion 1 8 - 1 9 . There are two T M T S F molecules per unit cell, and there is a transfer of one electron from two T M T S F molecules to one anion giving a half filled band if we take a to be two molecular distances. Conduction along the T M T S F stacks is by normal band conduction. Unlike most other charge tranfer salts the anion stacks do not have overlapping atomic orbitals and thus conduction electrons do not move up and down the anion stacks. The anions are important in controlling lattice parameters and play a major role in the bandfilling. 1.5 Electronic B a n d Structure of ( T M T S F ) 2 X The effect that charge-density waves can have on the band structure has been examined, but the actual band structure of the ( T M T S F ) 2 X compounds has not yet been discussed. A tight-binding calculation for a unified single-particle model has been developed by Grant at I B M 3 0 to calculate the band structure of these compounds. If one were to consider all of the valence electrons in this method, it would involve solving a secular equation for 76 bands. The calculations are simplified considerably if some simple assumptions are made about the ( T M T S F ) 2 X CHAPTER 1: INTRODUCTION 10 salts, the most important of which being that only the highest occupied molecular orbital (HOMO) will be relevent to transport in the solid. Immediately we have reduced the number of bands to just two. Rather than labor through Grant's developement of the problem, we will jump directly to his results. Figure 1-3 Perspective view of the ( T M T S F ) 2 X crystal structure showing the crys-tallographic axes a, b and c. The lables II —»14 refer to the interstack interactions, and S i and S2 to the chain interactions that Grant uses in his calculations2 0. The crystal structure Grant uses in his calculations is shown in Fig. 1-3. Along with the crystallographic axes, there are also the labels II —• 14, S i and S2. The labels correspond to interstack and chain interactions, with the chain interactions being treated as distinct due to the dimerization of the stack. The high temperature band structure and Fermi contour for (TMTSF)2AsF6 are shown in Fig. 1-4. The band structure shown here is representative of basically all the ( T M T S F ) 2 X compounds. The model is solved in two-dimensions because CHAPTER 1: INTRODUCTION the anisotropy is basically two-dimensional; the difference between the b- and c-axis being minor with respect to the a- and b-axis. 11 BOO 400 -(TM75F) 2 AsF6 > E -400 -800 -r x v Y (0, 0) (n/a. 0) (n/a. n/b) (0. n/b) r (0, 0) Figure 1-4 The high temperature band structure and Fermi contour in the first Brillouin zone of the reciprocal lattice for (TMTSF) 2 A s F 6 a o . If one were just to consider a one-dimensional conductor along the highly conducting a-axis, then this would correspond to the electronic band structure along the T —* X path. The location of the ep below the top of the band, and the absence of any gap indicates that the band is not closed and that conduction by valence electrons is possible. This is just the sort of band structure that one expects from a quasi-one-dimensional system. The formation of a charge-density wave at low temperatures can change the lattice parameters and alter the reciprocal space and the shape of the first Bril-louin zone thus changing the band structure of the system. Such a change in the CHAPTER 1: INTRODUCTION 12 lattice parameter is referred to as a broken symmetry. The band structures shown in Figs. l-5(a),(b) and (c) are for the most highly commensurate two-dimensional broken symmetries. Besides the formation of a C D W , lattice parameters may also be changed by an anion-ordering transition which alters the size of the unit cell. The anion-ordering transition arises only in those Bechgaard salts tlat have non-symmetric (i.e. tetrahedral, planar, etc.) anions. Diffuse X-ray studies show no 2kp scattering indicating that the transition is not due to a charge-density wave* 1 ' 3 3 . Single-crystal neutron-diffraction experiments establish that the salts with non-symmetyric anions undergo crystallographic phase transitions at low temperatures due to anion ordering 3 8 . These anions have different orientations in the anion cav-ity which are non-degenerate. The octahedral anions do not display anion-ordering transitions because they are symmetric; all the allowed anion orientations are the same. At high temperatures the non-symmetric anions are randomly oriented and the anion lattice shows no long-order due to the presence of a crystallographic inver-sion center 3 4. Below the anion-ordering temperature, T^o, the anions order along preferential directions. The anion sites do not interact directly, but rather through the cation/anion Se-X interaction for X=ReC>4, CIO4 and B F 4 3 8 the C H 3 - X inter-action for X=NC>3 1 9 . The strength of these interactions is thought to determine how the anions will order. In (TMTSF)2Re04 the anions order in an alternating sequence along the a-, b- and c-directions, whereas in (TMTSF)2C104 the anions order only along the b-direction. The formation of long-range order in the anion lat-tice along any one of these crystal directions creates a superlattice structure which changes the size of the unit cell. The anion-ordering transitions that have been observed in these compounds 3 8 show that these transitions are commensurate with the existing lattice parameters, and double the size of the unit cell in the direction which the anions order. The three cases that are considered are: (a) doubling of the lattice parameter along the chain direction only, corresponding to a modulation wave-vector of Q = (1/2,0); (b) doubling of the lattice parameters in both the chain CHAPTER 1: INTRODUCTION I S and transverse directions, resulting in a modulation wave-vector of Q = (1/2,1/2) and (c) a doubling of the lattice parameter in the transverse direction only, result-ing in a modulation wave-vector of Q = (0,1/2). In each case the figures show the change in the shape of the first Brillouin zone in the reciprocal lattice. A doubling of the lattice parameter along the stack direction occurs in the NO3 compound at ~ 41 K due to an anion-ordering transition 2 8, resulting in a 2a x 6 x c unit cell with a modulation wave vector of (ir/a,0,0)86, or a q = (1/2,0) broken symmetry in Grant's model. An anomaly in the conductivity is observed in the NO3 compound at 41 K, however, unlike other Bechgaard salts which undergo A O transitions and experience a decrease in the conductivity, the NO3 is a better conductor in the 2a x 6 x c superlattice. As the temperature is lowered below 7^40 the conductivity continues to increase in this compound until 12 K, where a metal-insulator (MI) transition occurs 1 1 . The differences in the crystal structures of ( T M T S F ) 2 N 0 3 at 41 K and 12 K are minor. It is thought that the change in the magnitude and the anisotropy of the cation/cation and cation/anion interactions at 12 K may be responsible for the MI transiton in this compound 1 8 . In the model a gap of 2 A opens near the Fermi energy resulting in either a semimetal or an indirect gap semiconductor, depending on the size of A . The Fermi contour is a line that joins all the points in the first Brillouin zone where the electron energy is equal to the Fermi energy. The creation of a gap is represented by a break in the Fermi contour, as shown in Fig. l-5(a). In Fig. l-5(a) the Fermi energy (shown by a line) is tangent to the valence band at X and to the conduction band at V resulting in a zero-gap semiconductor. Increasing the size of A shifts ep above the valence band leaving the conduction band empty and resulting in a semiconductor. In view of Grant's model and the behavior of the NO3 compound, it is possible that at 41 K a zero-gap seimconductor forms due to the Q = (1/2,0) broken symmetry. At 12 K, the size of the energy gap may increase resulting in a semiconductor and explaining sudden decrease in the conductivity. CHAPTER 1: INTRODUCTION 14 r r x v Y r Figure 1-5 Model band structures for the three most highly commensurate two-dimensional broken symmetries: (a) Q = (1/2,0); (b) Q = (1/2,1/2); (c) Q = (0,1/2) J 0 . CHAPTER 1: INTRODUCTION 15 A doubling of the lattice parameter along both the stack and transverse direc-tions occurs in (TMTSF) 2 BF4 at ~ 38 K and in ( T M T S F ) 2 R e 0 4 at ~ 180 K due to an anion-ordering transition resulting in a 2a x 26 x 2c unit cel l 3 8 . This gives a modulation wave-vector of (*r/a, n/b, J T / C ) 8 8 and corresponds to the Q = (1/2,1/2) broken symmetry in Grant's model. From Fig. l-5(b) a direct gap of 2A is created in the band structure. This can also be seen from the Fermi contour. This is the only symmetry that yields an insulator for every finite value of 2A, since sp is in the middle of the gap and thus the valence band is closed for any non-zero gap. A doubling of the lattice parameter along the transverse direction occurs in (TMTSF) 2 C104 at ~ 24 K due to an anion-ordering transition resulting in a ax26xc unit cell and a modulation wave-vector of (0 ,Tr /6 ,0) 3 8 ' 8 8 . This corresponds to the Q = (0,1/2) broken symmetry in the model. A gap 2A is introduced, but it is not near £F and the number of Fermi contours increases from two to four preserving the metallic ground state. This may explain why no anomaly in the conductivity of ( T M T S F ) 2 C 1 0 4 is observed. 1.6 ( T M T S F ) 2 X Salts wi th Centrosymmetric Anions The Bechgaard salts display a variety of interesting low temperature states. Despite having the same stoichiometry, the compounds having centrosymmetric an-ions have different physical properties than those with non-centrosymmetric anions. The salts with the centrosymmetric anions (PF6, AsF6, SbF6 and TaFe) dis-play electrical conductivities as large as 105 ( f i c m ) - 1 along the a-axis at ~ 20 K. Some plots of d.c. resistivity versus temperature for some ( T M T S F ) 2 X compounds are shown in Fig. l-6(a) 1 1 . The resistivity at 35 Ghz is also shown in Fig. l -€(b) 1 1 for comparison. The superconductivity occurs in the centrosymmetric compounds under pressure. The first organic material discovered to exhibit superconductivity was ( T M T S F ) 2 P F 6 1 3 , which becomes a bulk superconductor at Te ~ 1 K with the CHAPTER 1: INTRODUCTION application of > 6.5 kbar of pressure (Te is used to indicate the critical temper-ature at which the material becomes superconducting in three-dimensions). Evi-dence for type II superconductivity includes both zero resistance1* and a partial Meissner effect3 5'3 6. Increasing the pressure decreases T c 3 7 . Superconductivity has also been observed at ~ 11 kbar in (TMTSF) 2 AsF 6 3 8 , (TMTSF) 2 SbF 6 3 9 and (TMTSF) 2 TaF 6 3 9 . 3 10 30 100 300 TEMPERATURE IK 1 Figure 1-6 The (a) d.c. resistivity and (b) resistivity at 35 GHz versus temperature for some typical samples of of (TMTSF) 2X. Note the logarithmic temperature and resistivity scales11. CHAPTER 1: INTRODUCTION 17 The one-dimensional behavior of the superconducting state in these com-pounds has been shown using a Schottky electron-tunneling technique 8 0 ' 8 1 . All of these salts undergo metal-insulator (MI) transitions at ~ 12 K at am-bient pressure. The absence of a 2k$ superlattice below the MI transition rules out a charge-density wave for the formation of an energy gap at the Fermi surface* 1 ' 3 3. The disappearance of the ESR signal 8 3 , the anisotropic lattice magnetic suscep-tibility below the transition 8 8, and a spin-flop transition at 4.5 k G 8 4 using the static magnetic susceptability measurements indicate the occurence of an Over--hauser antiferromagnetic transition to a spin-density-wave (SDW) state, making these materials itinerant antiferromagnets. The nuclear spin-lattice relaxation rate of enriched 1 3 C nuclei in (TMTSF)2PF6 indicate that the spin-density-wave state interacts weakly with the carbon sites in the crystal 8 5 . This transition marks a di-mensionality crossover from two- or three-dimensional behavior at low temperatures to one-dimensional behavior at higher temperatures85. The SDW state is interest-ing because a Peierls instability is more common among low-dimensional metals. The anisotropy of the susceptibility is consistent with expectations of a simple an-tiferromagnet with the easy, intermediate and hard axes close to the b*, a and c* directions 8 8. In the SDW state the periodicity of the spin structure along the chain direction is given by the Fermi wave-vector, leading to a doubling of the unit cell, i.e. there are now four T M T S F molecules in the unit cel l 8 8 . The band structure calculations by Grant indicate that the SDW antiferromagnetic state may possess the Q = (1/2,1/2) broken symmetry, which results in an insulator. Confirmation of a doubling of the transverse lattice constants in the cent rosy mmetric compounds must await a polarized neutron study 8 6 . A phase diagram for the (TMTSF)2AsF6 salt is shown in Fig. 1-7. This diagram may be generalized for all of the compounds with centrosymmetric anions. For a constant pressure (~ 10 kbar), it is possible to enter the insulating SDW state for some critical temperature, and then to enter CHAPTER 1: INTRODUCTION 18 P/Kbor Figure 1-7 The phase diagram of (TMTSF)2AsF6 under pressure (P < 8 kbar open dots, P > 8 kbar open triangles). TE is the critical temperature (for some pressure P) for either a SDW or SC transition. The inset shows the re-entrance of the superconductivity at ~ 10 kbar from the insulating SDW state 8 7. the superconducting state. This striking feature is referred to as the re-entrant superconductivity. The d.c. conductivity in ( T M T S F ^ P F e is highly anisotropic (a : b : c ~ 105 : 400 : 1) and increases beyond 105 ( f l c m ) - 1 upon cooling to ~ TMI, and then decreases rapidly with the onset of the SDW state 8 8. These values of <T\\ are about ten times larger than the maximum conductivity observable in other charge transfer compounds at low temperatures. Given the electron density of 102 2 charges c m - 3 , a mobility of » 2 x 103 c m 2 V - 1 s - 1 is derived at 1.3 K (for ay = 5 x 105 ( f lcm) - 1 ) leading to an approximate mean-free path of 700 inter-molecular spacings along the a-axis. The conductivity of (TMTSF)2PF6 in the SDW state increases at frequencies above ~ 1 G H z 8 9 , and is attributed to the CHAPTER 1: INTRODUCTION 19 SDW response to the a.c. field40. The SC state (type II) in ( T M T S F ) 2 P F 6 and (TMTSF)2AsF6 is destroyed by a small magnetic field. The critical fields are also highly anisotropoic, with = 200 G along the c-axis and H*2 = 2 k G along the b-axis for ( T M T S F ) 2 P F 6 , and = 1.4 k G along the c-axis, and Hjj = 20 kG along the b-axis for ( T M T S F ) 2 A s F 6 . 4 1 . Some of the properties of the ( T M T S F ) 2 X salts are shown in Table I-I. 1.7 ( T M T S F ) 2 X Salts wi th Non-centrosymmetric Anio ns The non-centrosymmetric anions include B F 4 , Re04, CIO4, F S O 3 and N O 3 . Superconductivity is observed in (TMTSF) 2ReC>4 at ~ 1.3 K under ~ 9 kbar of pressure4*. Efforts to eliminate the need for pressure led to the substitution of very small anions in order to decrease the interstack distance. When this was done with the CIO4 anion in 1980, the resulting salt became superconducting at ~ 1.2 K at ambient pressure 4 8 , 4 4 . Thus (TMTSF) 2 C104 was the first ambient pressure organic superconductor! The superconductivity in (TMTSF)2C1C>4 was confirmed by the observation of Meissner signals4 6 and specific heat measurements using an a.c. calorimetric technique4 6, indicating a type II character. The molar specific heat displays a very large anomaly around 1.2 K. Above T2 = 1.2 K 2 the specific heat obeys the classical relation C/T = 1+/3T2, where p = 11.4 m J m o l - 1 K " 4 and 7 = 10.5 m J m o r 1 K ~ 2 . The C/T versus T plot of the electronic contribution allows a very accurate determination of the critical temperature, namely Tc = 1.22 K. These salts are different than those with centrosymmetric anions in that they undergo metal-insulator transitions4 7, but at much higher temperatures. Neutron-diffraction 8 8 and X-ray diffuse scattering' 1 '" studies have shown that this transi-tion is due to an ordering of the anion lattice, thus forming a superlattice structure. The compounds ( T M T S F ) 2 B F 4 and ( T M T S F ) 2 R e 0 4 have MI transitions at 38 K and 180 K respectively, and below these temperatures the anions alternate in orien-tation along all three lattice directions, thus the unit cell changes from a x b x c to CHAPTER 1: INTRODUCTION Table I - I ° - 6 c Properties of some ( T M T S F ) 2 X salts Anion Anion TMI Transition T C Pc Symmetry (°K) (°K) (kbar) P F 6 Octahedral 12 SDW 1.4 8.5 A s F 6 Octahedral 12 SDW 1.4 9.5 SbF 6 Octahedral 17 SDW 0.38 10.5 T a F 6 Octahedral 11 SDW 1.3 11 B F 4 Tetrahedral 39 A O _ — C10 4 Tetrahedral 24 A O 1.2 atm 3.5 SDW - -R e 0 4 Tetrahedral 180 A O 2 5 F S O 3 Asymmetric 87 A O 2 5 N 0 3 Planar 40 A O _ — 12 ? - -T \ n The temperature of the SDW or A O transition. SDW Spin-density wave transition. A O Anion-ordering transiton. T c Temperature at which the salt becomes a superconductor. P c Minimum pressure for superconductivity to occur. • Ref. 22 6 Ref. 23 c Ref. 36 2a x 26 x 2c. This corresponds to a modulation wave-vector (nja^Jb^/c), corre-sponding to the Q = (1/2,1/2) broken symmetry in the electronic band structure model. It is apparent that the gap created by the A O transition is responsible for a semiconducting state. While (TMTSF) 2 C104 has an anion-ordering transition at 24 K, the anions only alternate along the b-axis, thus the unit cell changes from CHAPTER 1: INTRODUCTION 21 a x 6 x c t o a x 2 6 x c 2 8 . With a modulation wave-vector of (6, ?r/6,0), this cor-responds to the Q = (0,1/2) broken symmetry in the electronic band structure model. The fact that (TMTSF) 2C10 4 remains metallic below the AO transition agrees with the model. If (TMTSF) 2C10 4 is cooled rapidly below 50 K (~ 25 K/min - quenched), the anion disorder is frozen in and a magnetic SDW state is observed below ~ 3.5 K 4 7 , 4 8 , with no SC transition. This effect is reversible, and when the sample is cooled slowly below 50 K, (~ 1 K/min - relaxed), then the usual anion ordering transition is observed at 24 K and an SC state at ~ 1.4 K. The SC state in (TMTSF) 2C10 4 is very sensitive to the magnetic field. The critical magnetic fields for a type U superconductor, extrapolated to T = 0 K, are highly anisotropic, with W*2 ~ 150 G and H* 2 ~ 10 k G 4 1 ' 6 0 . Some of the properties of the non-centrosymmetric salts are included in Table I-I. 1.8 Far-Infrared Optica l Properties The far-infrared region of the optical spectrum, 10-1000 c m - 1 (1-120 meV), is important because many of the physical properties displayed by quasi-one-dimensional conductors, such as spin-density waves, charge-density waves, semiconducting and superconducting transitions, low-lying lattice modes and free-carrier absorption all have activation energies in this region. The far-infrared optical properties of the (TMTSF) 2X compounds have been studied by a number of groups, including Challener et ai., Eldridge ef ai., Tanner et ai. and Timusk et ai. Single-crystal reflectance measurements have been performed on C 1 0 4 6 1 ' " ' 6 8 ' 5 4 , P F 6 B 4 , 5 B , S b F 6 6 6 , 6 7 and A s F 6 6 7 ' 6 8 compounds, however, there is disagreement between the results obtained for the all of the compounds. The difficulty arises from the small crystal sizes which necessitates the use of crystal mosaics below 1000 c m - 1 when measuring the reflectivity. The problem with this method is that it is almost impossible to align the crystals properly. The use of CHAPTER 1: INTRODUCTION 22 a mosaic also introduces diffraction effects into the reflectance spectra, making it difficult to obtain absolute values of reflectance; especially when R is very close to 100% as it is for these compounds. A completely different method of obtaining R was used by Eldridge, Bates and Bates. It involves a bolometric technique whereby that part of the incident radia-tion which is absorbed by a single crystal at liquid-helium temperatures, heats the crystal by a small amount. If the crystal is semiconducting then this temperature rise produces a drop in the electrical resistance which can be measured and is pro-portional to 1 — R since everything not reflected is absorbed and none is transmitted. (The absorption coefficient of these crystals is veiy high). This "simple-bolometric" technique has been used to measure R for T T F - T C N Q 5 9 - 6 0 . The ( T M T S F ) 2 X salts at low temperature, even though they may be semiconducting, have conductivities too high for a good bolometer, so that "composite-bolometers" have been made instead. A small germanium bolometer is glued to the rear face of the single crystal and the temperature rise measured in this way. Once again the signal is propor-tional to 1 — Rt which is exactly what one wishes when R is so close to unity. The results for ( T M T S F ) 2 P F c obtained by this method 6 4 and the mosaic reflectance method 6 5 are shown in Figure 1-8. The incident radiation may be polarized for either E || a or EJ_a to give information about the electronic properties along the parallel and transverse axes. By sampling the reflectivity of a crystal over a very large interval (from P ~ 0 to p —» co), then a Kramers-Kronig 6 1 ' 6 3 analysis may be used to determine the optical properties of the material, such as the electrical conductivity. The single-crystal reflectance spectra of (TMTSF) 2 PF6 for E || a, shown in Fig. l -8(a) 6 6 and (b) 6 4 , illustrates the different experimental results for this com-pound. The electrical conductivity is calculated using a Kramers-Kronig analysis of the reflectivity spectra in Figs. l-8(a) and (b), and is shown in Figs. l -8(c) 6 5 and (d) 6 4 respectively. The calculated conductivities are quite different, and more study CHAPTER 1: INTRODUCTION Figure 1-8 The single-crystal reflectance of (TMTSF) 2 PF 6 for E || a at various temperatures (a) by Tanner et ai . 6 6 and (b) Eldridge et ai . 6 4 The conductivity cal-culated from the reflectivity in (a) is shown in (c)6B, and the conductivity calculated from (b) is shown in (d) 6 4. The experimental results are not in agreement. CHAPTER 1: INTRODUCTION 24 is needed to resolve this issue. One thing the conductivities do emphasize is the low far-infrared conductivity above the SDW transition (~ 300 (ft cm) - 1) compared to the large d.c. conductivity (> 104 (ft cm) - 1 ) 1 1 . Below the SDW transition at ~ 6 K, the far-infrared conductivity agrees with the d.c. conductivity. The measurements done in this thesis are with powders rather than single crystals, and we are concerned with the 20-250 c m - 1 region. The main disadvantage of powder samples is that they are not oriented along any one direction, thus the information they give is for all polarizations rather than just one. The powder spectra of (TMTSF) 2 PF 6 and (TMTSF) 2Re0 4 has been measured by Bozio and Pecile et ai. in the mid-infrared region68. Meneghetti et ai. have made an extensive vibrational analysis of TMTSF, and its radical cation, TMTSF" 1 " 6 4 . No powder measurements have been made below 250 c m - 1 . The results from the powder measurements that have been made for (TMTSF) 2X, X=PF 6 , AsF 6 , SbF 6, BF 4 , C104 and Re0 4 will be compared with the vibrational studies. 1.9 Fluctuating Superconductivity The idea of fluctuating superconductivity (FSC) in quasi-one-dimensional compounds, such as the (TMTSF) 2X salts, was first advanced by Jerome et ai., and refined by Schultz66. The one-dimensional superconductor can be considered an array of stacks of organic molecules whose average dimensions amount to a few Angstrom. By introducing a weak interchain coupling t±, where tj. <S t||, there is a finite probability that an electron will jump from one stack to another, i.e. transverse electron motion is possible. In the presence of such coupling fluctuations long-range three-dimensional order is possible at finite temperature. To investigate the behavior of these fluctuations more carefully, the Ginzburg-Landau theory is employed. In this phenomenalogical description, the free energy of the system is expanded in terms of an order parameter (the gap energy), which is allowed to vary slowly and is treated as a classical variable. By demanding that the free energy CHAPTER 1: INTRODUCTION 25 be minimized over all configurations by the use of a self-consistent field approxi-mation, the properties of the system may be obtained. One of the consequences of the Ginzburg-Landau theory is that because the free energy contains high order terms that are usually ignored in simpler models (such as mean-field approxima-tion), the correlation lengths in the stack and transverse directions (£|| and £ ± ) are allowed to fluctuate. The SC transition temperature also exhibits fluctuations in this model. Fluctuating superconductivity is normally discussed in the temperature regime T$ < T < T\ where below T$ three-dimensional behavior dominates and be-low T\ one-dimensional properties characterize the system. The bulk superconduct-ing transition temperature Tc < T$. F S C effects may be possible at temperatures up to 40 K. There is also a pairing of electrons in F S C . Normal electrons form virtual Cooper pairs above the Fermi surface in time Ty. They decay back to the normal state in time TS . Because of the formation of virtual Cooper pairs, there is a decrease in the density of states at the Fermi level given by [Ar(ffp) — NQ]/NO = TNITS- This reduction, but not complete removal of the density of states is called a pseudo-gap. Since FSC is thought to occur below Ti, this would imply a large pseudo-gap. There is some evidence to support the premise of a fluctuating superconduc-tivity in the ( T M T S F ) 2 X salts. The longitudnal conductivity exceeds 104 ( f l cm)" 1 at 4.2 K for ( T M T S F ) 2 P F 6 , ( T M T S F ) 2 A s F c , etc. under pressure11 and for the CIO4 compound at ambient pressure4 8. These conductivities are larger than any other organic material by an order of magnitude. This is considered to be evi-dence for a new form of electrical transport (FSC). In addition, the temperature dependence of the electrical resistivity is still large below 4.2 K, in a tempera-ture domain where the resistivity of all three-dimensional metallic conductors with single-particle transport is limited by residual impurit ies 1 6 ' 8 6 ' 6 6 . The large mag-netoresistance in the ( T M T S F ) 2 X salts may be explained by the destruction of fluctuating Cooper pairs. The extreme sensitivity of the conductivity to radiation-induced defects is difficult to explain in terms of single-particle transport, but if the CHAPTER 1: INTRODUCTION 2 6 defects are magnetic then they can destroy the fluctuating Cooper pairs by acting as orbital pair-breakers 1 6 ' 8 6 , 6 6 . The large drop in the thermal conductivity below ~ 50 K can be restored by a magnetic field applied parallel to the a-axis. Carriers that are involved in F S C do not contribute to the thermal conductivity, but if the fluctuating Cooper pairs are destroyed by the magnetic field, then carriers are freed and the thermal conductivity will be restored, in agreement with experiment 8 6 ' 6 5 ' 6 7 . The conductivity at 4.2 K may be explained for single-particle transport only if the mean-free path of the. carriers is ~ 700 intermolecular spacings along the a-axis. This would require samples of high purity, which is unlikely 6 6 . Electron quantum tunnelling is by far the most sensitive probe of the density of states. The transition probability of single electrons, which obey Fermi statistics, to tunnel between two metal electrodes seperated by a thin insulating barrier, is proportional to the density of final states. Measurement of tunnelling resistance can thus be used to determine changes in the density of states of quasiparticles in a one-dimensional conductor above Tct which indicate the development of the pseudo-gap below 3*1. Sr.ch measurments have been sucessfully made with (TMTSF)2PF6 using the Schottky barrier geometry, namely studying the tunnel resistance of quasipar-ticles between a single crystal and an evaporated N/GaSb semiconductor through the intrinsic potential existing at the interface. The zero-tunnel resistance mea-surements shows a psuedo-gap in the conductivity at ~ 6.3 meV (~ 50 c m - 1 ) . This gap is much too large to be associated with the 1 K SC gap, and in addi-tion is measured at temperatures well above 1 K . It cannot be associated with the magnetic SDW, because a magnetic field tends to destroy the measured gap in the tunnelling experiment rather than stabalize it. Also, if a SDW pseudo-gap exists at ~ 30 K, the resistivity should begin to increase with decreasing temperature CHAPTER 1: INTRODUCTION 27 as the SDW state becomes more stable, something that is not seen in the experi-ments. These results would, however, be consistent with the theory of fluctuating superconductivity 2 9 - 8 0 ' 8 6 ' 6 6 . Not all experimental data is in agreement with the theory of a F S C . Green et ai. think the in general the interchain coupling is much stronger than the weak interchain coupling used by Schultz in the Ginzburg-Landau formalism 4 1 . The mea-sured anisotropy of the SC critical magnetic field in ( T M T S F ) 2 C 1 0 4 is 28:15:1 for H2 2 :H£ 2 :H£ 2 . The Ginzburg-Landau theory predicts 200:20:1 if the same mechanism is involved in limiting H c in all three directions. The critical field is much smaller than expected, and therefore it must be limited by something other than orbital pair-breaking, such as the Pauli limiting effect due to spin pair-breaking. The Pauli critical magnetic field is directly related to TC and the size of the SC energy gap. The measured H * 2 is in good agreement with the 1 K transition temperature. The large gap measured in the tunnelling experiment, however, implies a Pauli limit which is 20 times larger than the measured H * 2 and therefore the tunnel gap must not be related to the superconductivity. The thermopower drops torward zero, with decreasing temperature, but then becomes negative at 7.5 K 6 7 . The change in sign of the thermopower cannot be explained by superconducting fluctuations, and demonstrates that a different trans-port mechanism is giving rise to the temperature dependence. If the scattering rate at the Fermi surface is anisotropic, then the large mag-netoresistance can be explained by the single-particle transport model. The d.c. conductivity is principally due to carriers in regions of the Fermi surface with long lifetimes, but in a magnetic field these carriers are swept into other regions with a high scattering rate and the conductivity is reduced. An increased scattering rate caused by radiation induced defects is also sufficient to explain the reduced conductivity for a single-particle transport system 6 8 . CHAPTER 1: INTRODUCTION The pseudo-gap measured in the infrared data for (TMTSF) 2 PF 6 B B , is at ~ 200 c m - 1 (25 meV), and not at ~ 50 c m - 1 . It is much too large to be associated with the gap measured in the tunnelling experiment (3-4 meV). The pseudo-gap in the infrared data also exists up to 300 K, well above the temperaures at which superconducting fluctuations are thought to be important. Furthermore, Green ar-gues that off stoichiometric films of GaSb are superconducting with TC as high as 8 K 6 9 . It is possible that such Ga or Sb superconducting phases could be formed on the (TMTSF)2PF6 surface during the tunnel junction preparation. The tran-sition temperature TC also decreases as the pressure is increased37. The simplest explanation is that the pressure decreases the distance between the stacks allowing the initial onset of superconductivity, however in this view increasing the pressure should then increase TE even more. The fact that just the opposite happens seems to contradict FSC. The issue of whether FSC is viable or not has not yet been resolved, and will continue to be a source of debate. CHAPTER S: EXPERIMENTAL TECHNIQUES 29 C H A P T E R 2 E X P E R I M E N T A L T E C H N I Q U E S 2.1 Sample Preparation Samples of protonated ( T M T S F - i i 2)2X and deuterated (TMTSF-d^hX, for X = P F 6 , AsFe, SbF6, B F 4 , CIO4 and Re0*4, were prepared by electrocrystallization using a modified H-cel l 7 0 by Gordon Bates of the Chemistry Department at the University of British Columbia. The reaction was typically carried out under a nitrogen atmosphere in anhydrous dichloromethane (5 x 10 - 2 M in electrolyte, 4 x 10~3 M in T M T S F at the anode) at a constant current of 2.2 or 4.0 /iA. The electrolysis was discontinued at ~ 50% conversion. The R 4 N X electrolytes were purified by recrystallization prior to use. Initially, the T M T S F was prepared in our laboratory. However, comercially available71 material is now routinely used. The TMTSF-di2 was prepared from deuterated 3-methanesulphonyl-2-butanone (from 2,3-butandione-de) using a modification of the literature procedures7'. Deuterium incorporation levels in the intermediate products were esitmated by proton magnetic resonance and/or high resolution mass spectrometry. The deuterium content of 4,5-dimethyl-1, 3-diselenole-2-selone, the immeadiate precursor to T M T S F - d n (~ 90%) is assumed to be that of the 2-selone precursor. The crystals were ground up in Nujol mineral oil with a mortar and pestle and the resulting mull was transferred to a wedged piece of T P X . Photomicrographs of the powder samples were made with a high power microscope at 400 x. The small CHAPTER S: EXPERIMENTAL TECHNIQUES SO particles in the powder had a typical diameter of < 1/x and the larger particles had a typical diameter of < 3/i. 2.2 Michelson Interferometer T h e far infrared measurements were made on a modified B e c k m a n / R U C F S -720 Fourier spectrophotometer. T h e polarizing Martin-Puplett m o d e 7 8 was used for measurements in the 20-125 c m - 1 region. This method employs a beam-splitter oriented at 4 5 ° to the roof-top mirrors and two fixed tungsten wire beam-splitters (with a wire thickness of 10 fim and a separation of 25 fim), one before and one after the beam-splitter. T h e main advantage of this type of interferometer is its excellent high constant transmission characteristics below about 150 c m - 1 , unlike a mylar beam splitter which has a sinusoidal response. For measurements in the 100-350 c m - 1 range a 25G (6.25 jum) mylar beam splitter was used. For measurements in the 100-750 c m - 1 range a polycarbonate beam splitter was used. A Beckman/RIIC IR-7L d.c. mecury arc lamp was used as a source. T h e optical system is shown in F i g . 2-1. T h e interferometer has a stepping mirror which is driven by a Superior Elec-tronic S L O - S Y N M O 6 1 - F C 0 8 synchronous/stepping motor which is controlled by a modified Beckman/RIIC F S - M C l step control. At each discrete position the pream-plified signal from the bolometer was sent to another Princeton Applied Research 116 Preamplifier and then to a P . A . R . 124A Lock-In Amplifier. T h e reference sig-nal of 70 Hz was provided by a phototransistor and diode on the chopper assembly. T h e signal output was then sent to a true integrator and integrated for a selected time interval (typically one second) after a chosen delay. T h e delay time allows the mirror vibrations to damp out improving the signal to noise ratio. This feature is only used in cases where the signal is extremely small, and the detector is very sensitive to vibrations. T h e integrated value is given to a 12 bit A D C , and the binary number is sent serially via RS-232C line to a PDP-11 /23 P L U S computer CHAPTER t: EXPERIMENTAL TECHNIQUES Figure 2 - 1 A shcematic of the Beckman/RUC FS-720 spectrophotometer, with the tail of the Janis dewar. In the 100-750 c m - 1 range the cold filters and the bolometer are are replaced by a Golay detector. CHAPTER t: EXPERIMENTAL TECHNIQUES 32 where it is written by a data acquistion program onto a RL02 removable hard disk. The sample-and-hold from the integrator is sent to a Heath SR 206 Dual pen chart recorder so that the interferogram is drawn out as it is measured. The detection and recording electronics are shown in Fig. 2-2. A cryotrapped Varian VHS 4 diffusion pump evacuates the'spectrometer chamber directly under the beam-splitter at a rate of ~ 400 litres per second for air. The Welch 1376-B80 300 l/xmn backing pump is mechanically isolated by a dual bellows to prevent it from vibrating the spectrometer. Pressures of ~ 10~6 Torr may be attained in the spectrometer chamber with this configuration. The spectrometer table is also acoustically isolated from the floor. 2 .3 Cryostat The samples were mounted in a Janis Supervaritemp Optical Research Dewar (model 8 C N D T ) 7 4 . The tail of the dewar sits at the focus of the spectrometer. A cross-section of the dewar and sample arrangement is shown in Fig. 2-3. Up to two samples may be mounted in the dewar. at one time. The usual procedure was to place the sample, and a wedged piece of T P X (with a thin coat of Nujol mineral oil) used as a background, in these positions. Temperatures from 4.2 K up to room temperature were achieved by vaporizing helium with a heater located beneath the sample. The temperature of the sample was measured using a silicon diode embeded in the sample holder. A second silicon diode is located on the vaporizer. A P.A.R. 152 Temperature Controller monitors the voltage of the diode on the vaporizer and compares it to a reference voltage (determined by the user), and then adjusts the heater current to minimize the difference between them. The reference voltage is used to hold the temperature controller at a fixed temperature. Above 20 K temperatures are accurate to ± 1 K, while below 20 K the sensitivity of the diodes improves and accuracies better than ± 0 . 1 K are typical. CHAPTER 2: EXPERIMENTAL TECHNIQUES cn CM V . CM o —1 a c r a a . UJ > CD I-I Z _ l c r M O a o _ i o c I Z Q . I -Q . 4 X Z UJ < o t - t o o cn o a cn §3 X c r i (— o a UJ t-z z co < < H l L c r i « * u . cn L U c o o ca 2 1 CO cn m a til c r •< c r Z a m Figure 2-2 A schematic of the detection and recording electronics used in the 10-350 c m - 1 region. In higher regions the bolometer circuit is replaced by a Golay detector. The rest of the configuration remains unchanged. CHAPTER 2: EXPERIMENTAL TECHNIQUES Nylon Plug Sample Chamber F.I.A. Optical Path Windows Heater Figure 2-3 A longitudnal cross-sectional view of the Janis Supervaritemp dewar (model 8 C D N T ) 7 4 . The original drawing has been modified to show the changes made in it so that the Nitrogen shield and the sample mount sit in the optical path of the interferometer. CHAPTER 2: EXPERIMENTAL TECHNIQUES 35 Activated charcoal getter was placed inside the dewar vacuum chamber in order to absorb any Helium gas which goes through the mylar windows above 100 K. 2.4 Detectors An Infrared Labs 7 6 composite bolometer of Gallium-doped Germanium on a metalized saphire sheet was used for the experiments in the 10-350 c m - 1 region. At its operating temperature of 4.2 K it had a responsivity of 8.75 x 103 V / W and. a noise equivalent power of 4.8 x 10~13 W/Hz~ J at 80 Hz. For those experiments conducted in the 100-750 c m - 1 region a Pye Unicam7 8 type IR50 Golay infrared detector was used. 2.5 The Powder Absorption Coefficient The powder absorption coefficient (a) is defined by D « e~ad (2-1) where D is the transmitted power and d is the thickness of the powder sample. Because we are measuring the transmitted power through the powder sample, D is equal to the intensity through the sample (/,) divided by the intensity of the background (h), or It/h = D. In this way an absorption line would appear as a dip in the spectrum, however, we represent the absorptions as peaks, so that we consider Jfc//,, thus ]n{D~l) = ad. (2-2a) -(8-Since the thickness (d) of the sample is constant, then this term may be neglected, thus equation 2-2a may be written (2 - 26) CHAPTER I: EXPERIMENTAL TECHNIQUES 38 All of the spectra discussed in this thesis are the powder absorption spectra ad, unless specifically stated otherwise. 2.6 Numerica l Analysis The great advantage of the interferometer is that many different wave num-bers may be examined at the same time. This is referred to as the Felgett advantage or "multiplex". To change the interferogram I(x) to its wave number representa-tion J(P) means using a complex Fourier transform (CFT). The C F T I(p) of I(x) is defined as J(p) = (°° I(x)e2*iPxdP (2 - 3a) J — C O or /(P) = C(P) + S(P) (2 - 36) where C(P) = j I(x) cos(2iriPx)dP J — OO S(i>) = t / I(x) sin(27rti>z)aV J—CO (2 - 3c) (2 - 3d) are refered to as the cosine and sine transforms respectively. We do not deal directly with the real and imaginary parts of the CFT, but rather with the power spectrum (PS) and the phase error (<p) which are defined PS(D) = \\I(P) \=\[C2(P) + S2(P)Y ( 2 - 4 ) ^ P ) = - a r c t a n ( ^ ) (2-5) For a symmetric interferogram, J(x) = /(—x), the sine transform is zero, giving the l 2 result that PS(P) = h \ C(u) \ and the phase error is zero everywhere. In a real CHAPTER 2: EXPERIMENTAL TECHNIQUES S7 system, because of component drift and other technical problems, the interferogram will probably not be sampled at the zero path-difference. This effectively adds a phase shift <f>(p) to the transform this yields /(p) - / ( P ) e - W (2 - 6) C(p) = Mcos(^ (P)) ( 2 - 7 ) S(P) = ^ s i n ( * ( P ) ) ( 2 - 8 ) thus PS(P) = \ | J(P) | (2 - 9) <p(P) = -<P(P). (2 - 10) Thus, the phase error introduced by not sampling symmetrically is eliminated from the PS by taking the two-sided interferogram and performing a complex Fourier transform. For single-sided interferogram analysis and the averaging of different power spectra, it is necessary to include this phase. This involves symmetrizing the in-terferogram. Initially, the first ten and the last ten points of the interferogram are fitted to a straight line using a linear least-squares routine. This line is then subtracted from the interferogram to give it a true zero-level and remove any slope caused by temperature drift. The problem remains that it has not been centered through the zero path-difference. By making use of the known fact that the phase error <p(p) of a practical interferometer operating in the far infrared is a smooth function and does not vary rapidly with P, we can calculate <p(P) from a short CHAPTER S: EXPERIMENTAL TECHNIQUES 88 double-sided interferogram. The original center is taken to be the central maxi-mum of the interferogram. When a symmetric interferogram is off-center by an amount e (t < mirror increment), then the phase error is linear with slope m 7 7 <p{p) = 2neP = mP (2 - 11a) or (2-116) The C F T can now be calculated with respect to this new point. The power spec-trum will remain unchanged since it has no dependence on <p(P). The phase error, which was previously an arbitrary function <f>[P), is now calculated explicitly. Thus, knowing the exact value for the phase error allows us to analyze one-sided interfer-ograms (where the power spectrum does depend on the phase error) and to average spectra. The apodizing window function that is used for all computations in these experiments is a modification of the one used by Happ and Genzel 7 8 W{x) = 0.5 + 0.5 x cos (2 - 12) where x is the step size in the interferogram, and X is the distance from the zero path difference to the edge of the interferogram. The integrated intensities were calculated by first fitting a linear background to the absorption peak of the powder absorption coefficient, and then summing the area under the curve for a given interval. Usually several backgrounds were chosen. The line widths were measured by fitting a Lorentzian with a linear back-ground to the peak using a non-linear least-squares fitting program 7 9 . CHAPTER S: POWDER ABSORPTION MEASUREMENTS C H A P T E R 3 P O W D E R A B S O R P T I O N M E A S U R E M E N T S 3.1 Powder Absorpt ion Spectra of Octahedral Anions The powder absorption spectra of three compounds with octahedral anions (PF6, AsF6 and SbFe) were measured as a function of temperature from 200 K down to 6 K in the 20-125 c m - 1 region. The powder absorption spectra of ( T M T S F ) 2 P F 6 , ( T M T S F ) 2 A s F 6 and of ( T M T S F ) 2 S b F 6 are shown in Fig. 3-1, Fig. 3-2 and Fig. 3-3 respectively. The spectra are at various temperatures above and below the MI transition, TMI ~ 12 K for the PF6 and AsF6 compounds, and TMI ~ 17 K for the SbF6 compound, and between 20 c m - 1 and 90 c m - 1 . There is no striking evidence of the MI transition in the spectra of any of the octahedral-anion compounds. The powder spectra of ( T M T S F ) 2 P F 6 at 6 K agrees with the results in the mid-infrared by Bozio and Pecile et a i . 6 8 . Because of the high conductivity of these compounds 6 4 measured for E || a which results in negligible power transmission for this polarization, the resonant modes that are observed in these powders are predominantly polarized with E ± a . In each of the octahedral-anion spectra taken at the lowest temperature, there are four sharp resonances. As the temperature is raised the lines shift and are thermally broadened 8 0. These modes agree with those seen in the single-crystal reflectivity in ( T M T S F ) 2 P F 6 for E_La by Eldridge and Bates 6 4 . The modes in ( T M T S F ) 2 S b F 6 also agree with those seen in the E ± a single-crystal reflectivity by Ng, Timusk and CHAPTER 3: POWDER ABSORPTION MEASUREMENTS Bechgaard 6 7 and Eldridge and Bates 6 6 . The modes in ( T M T S F ) 2 A s F 6 , however, were not seen by Ng, Timusk and Bechgaard in their E±a single-crystal reflectivity measurements68, but have been seen by Eldridge and Bates using a composite-bolometer technique6 8. The wave number as a function of temperature for each of the four resonances in ( T M T S F ) 2 P F 6 , ( T M T S F ) 2 A s F 6 and ( T M T S F ) 2 S b F 6 are shown in Fig. 3-4, Fig. 3-5 and Fig. 3-6 respectively. In each of the figures, three of the lines have a strong dependence on the temperature indicating an intermolecular (or "external" or "lattice") mode, and the remaining line shows no dependence on the temperature and is thus an intramolecular (or "internal") mode. Extrapolating to T = 0 K, ( T M T S F ) 2 P F 6 has three lattice modes at 50 ± 0.4 c m - 1 , 69 ± 0.4 c m - 1 and 71 ± 0.4 c m - 1 and one internal mode at 61 ± 0 . 4 c m - 1 . Similarly, ( T M T S F ) 2 A s F 6 has three lattice modes at 48 ± 0.4 c m - 1 , 60.4 ± 0.4 c m - 1 , and 67.5 ± 0.4 c m - 1 and one internal mode at 56.5 ± 0.4 c m - 1 , and (TMTSF) 2SbF6 has three lattice modes at 47 ± 0.4 c m - 1 , 60 ± 0.4 c m - 1 and 66 ± 0.4 c m - 1 , and one internal mode at 54.5 ± 0 . 4 c m " 1 . The integrated intensities for each of the four resonances in ( T M T S F ) 2 PF6 , ( T M T S F ) 4 A s F 6 and ( T M T S F ) 2 S b F 6 are shown in Fig. 3-7, Fig. 3-8 and Fig. 3-9 respectively. The intensity of the lines increases down to ~ 12 K in the PF6 and the AsF6 compounds, and ~ 17 K in the SbF6 compound; at which point a MI transition occurs. Below T\u the intensity decreases. The fact that the intensities of these lines are seen to follow the d.c. conductivity indicates that there is electron-phonon coupling. This coupling to free-carriers is similar to that previously observed for a lattice mode in T T F - T C N Q 8 1 . The spectra for the protonated and deuterated ( T M T S F ) 2 P F 6 at 6 K, along with the percentage shifts in the peaks, are shown in Fig. 3-10. The lattice modes can be translational, librational, or a mixture of both. The octahedral compounds CHAPTER S: POWDER ABSORPTION MEASUREMENTS 41 i — n 1 1 1 1 1 T W A V E N U M B E R ( c m " 1 ) Figure 3-1 Powder absorption coefficient ad (in arbitrary units) of ( T M T S F ^ P F g powder in Nujol on a polyethylene backing showing the four resonances. The dashed line at 80 c m - 1 replaces an incompletely cancelled polyethylene absorption line. The curves have the same scale and are displaced for clarity. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 42 Figure 3-2 Powder absorption coefficient ad (in arbitrary units) of (TMTFS)2AsF6 powder in Nujol on a T P X backing showing the four resonances. The curves have the same scale and are displaced for clarity. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 48 Figure 3-3 Powder absorption coefficient ad (in arbitrary units) of (TMTSF)2SbF6 powder in Nujol on a T P X backing showing the four resonances. The curves have the same scale and are displaced for clarity. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 44 i T TEMPERATURE (K) Figure 3-4 The temperature dependence of wave number of the four (TMTSF)2PF6 lines seen in Figure 3-1. Three lattice modes are indicated by the strong temperatue dependence. An internal mode is seen at 61 c m - 1 (T = 0 K) . CHAPTER S: POWDER ABSORPTION MEASUREMENTS 45 Figure 3-5 Temperature dependence of wave number of the four (TMTSF)2AsF6 lines seen in Figure 3-2. Three lattice modes are indicated by the strong tempera-ture dependence. An internal mode is seen at 56.5 c m - 1 (T = 0 K) . CHAPTER S: POV/DER ABSORPTION MEASUREMENTS 46 0 100 200 300 TEMPERATURE (K) Figure 3-6 Temperature dependence of wave number of the four (TMTSF)2SbF6 lines in Figure 3-3. Three lattice modes are indicated by the strong temperature dependence. An internal mode is seen at 54.5 c m - 1 (T = 0 K ) . CHAPTER S: POWDER ABSORPTION MEASUREMENTS 47 TEMPERATURE (K) Figure 3-7 The integrated intensity of the four lines of ( T M T S F ) 2 P F 6 seen in Fig. 3-1 versus temperature. The units are arbitrary, but each of the lines has the same scale. Note the turnover below the phase transition at ~ 12 K, indicating the onset of the insulating SDW state. CBAPTER 3: POWDER ABSORPTION MEASUREMENTS 48 >-C/J UJ 0 1 0 6 7 c m ' 0 2 - ( T M T S F ) 2 A s F 6 _ 6 0 . 5 c m - 1 5 6 . 5 c m - 1 4 8 c m - 1 0 1 0 0 2 0 0 T E M P E R A T U R E ( K ) 3 0 0 Figure 3-8 The integrated intensity of the four lines of (TMTSF)2AsF6 seen in Fig. 3-2 versus temperature. The units are arbitrary, but each of the lines has the same scale. Note the turnover below the phase transition at ~ 12 K, indicating the onset of the insulating SDW state. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 49 1 0 1 > - 0 £ Q 2 0 3 2 1 I -0 0 6 0 c m - 1 ( T M T S F ) 2 S b F 6 5 4 . 5 c m - 1 -4 7 c m - 1 1 0 0 2 0 0 T E M P E R A T U R E ( K ) 3 0 0 Figure 3-9 The integrated intensity of the four lines of ( T M T S F ) 2 S b F 6 seen in Fig. 3-3 versus temperature. The units are arbitrary, but each of the lines has the same scale. Note the turnover below the phase transition at ~ 17 K, indicating the onset of the insulating SDW state. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 50 6 K (TMTSF) h 12 -f(TMTSF)d 12 (TMTSF) 2 P F 6 30 50 70 90 WAVE NUMBER (cm - 1) Figure 3-10 The 6-K powder spectra of protonated and deuterated (TMTSF) 2 PF6 powders, in Nujol on a polyethylene backing showing the four resonances. The percentage decrease in wave number is indicated. The curves have been rescaled and vertically displaced for clarity. CHAPTER 8: POWDER ABSORPTION MEASUREMENTS 51 Table in-r Caculated and measured isotope shifts of the ( T M T S F ^ X lattice modes. (Coordinates are shown in F i g . 3-12) T y p e Molecules involved (calc) vp/vd (meas) Translational 2 ( T M T S F ) 1 (PF 6 ) 1.002 Translational T M T S F alone 1.013 1.010 Libration R x 2 ( T M T S F ) 1 (PF 6 ) 1.001 Libration R x T M T S F alone 1.044 Libration R t f 2 ( T M T S F ) 1 (PF 6 ) 1.002 Libration R y T M T S F alone 1.052 Libration R 2 2 ( T M T S F ) 1 (PF 6 ) 1.002 Libration Rz T M T S F alone 1.024 1.026 ? 2 ( T M T S F ) l ( P F c ) 0.998 a Ref. 82 are different from the tetrahedral ones in that the librational modes of the an-ions are not allowed by symmetry to couple with the infrared active lattice modes involving the T M T S F . For the tetrahedral compounds infrared active modes can involve librations of the anions. Table IU—I shows the calculated shifts expected upon deuteration for the various pure (unmixed) lattice modes. T h e shifts for the translational modes were calculated starting from (3 - la) and assuming that upon deuteration the change in the force constants is small, then CHAPTER 3: POWDER ABSORPTION MEASUREMENTS 52 where the reduced mass is defined as 1 1 1 for the two T M T S F molecules and one PFe molecule. This is different from the usual expression for the reduced mass in the k = 0 optical mode, because, in this case, both T M T S F molecules move together. The system was therefore treated as if it contained only two masses; one of mass m and another of mass 2M (the anion mass is m, the T M T S F mass is M, and the terms "prof and "deut" represent the protonated and deuterated compounds respectively). The shift for the librational modes is calculated in the following manner where the moments of inertia are defined as J.. ~ ronton ~*~ nTTMTSF for two T M T S F molecules and one PFe molecule. Again, the system is being treated as if it contained only two masses (an anion of mass m and a cation of mass 2M) and hence only two moments of inertia. The justification for this type of approach is motivated by the experimental results. If the system is treated for three masses the calculated shifts upon deuteration are too large; however, if the system is treated as it consists of only two masses (m and 2Af) then the agreement with observations is much closer. Here /,-,- represents the moment of inertia along the principal axes (t = x, y or z) in the anion molecule and in the T M T S F molecule. Because the anion PFe is centrosymmetric, and we have chosen the origin at the center and the principal axes along the P - F bonds, then all of the moments are the same. The moment of inertia in the T M T S F molecule is calculated in the form ( 3 - 2 ) ( 3 - 3 ) ( 3 - 4 ) CHAPTER S: POWDER ABSORPTION MEASUREMENTS 58 of an inertial tensor using the bond lengths and angles from the structure paper for ( T M T S F ) 2 P F 6 1 6 . The internal coordinate system for the T M T S F molecule is shown in Fig. 3-11. The origin is chosen at the center of the C - C bond joining the two fulvalene rings. The measured values of vvjv& are also shown in Table IJJ-I next to the ratio it most closely matches. This suggests that in (TMTSF) 2PF6 the line at 50 c m - 1 is a translational mode involving just the T M T S F molecule, and that the line at 69 c m - 1 is a librational mode along the z-axis involving just the T M T S F molecule. The lattice mode at 71 c m - 1 experiences a very small shift upon deuteration. Because of the associated error of ± 0 . 2 % , it is impossible to assign it to a translational or a librational mode directly, however, from group theory we would expect the librations to include just the T M T S F molecules. This suggests that the 71 c m - 1 feature is a translational mode involving both the T M T S F and PF6 molecules. The mode at 61 c m - 1 experiences a shift of 4.5% upon deuteration. From Table III—I, this shift is comparable to that of a librational R x mode for just the T M T S F molecules (4.4%), or a librational R y mode for just the T M T S F molecules (5.5%). It is evident from the temperature dependence of the modes in Fig. 3-4 that the 61 c m - 1 line is an internal mode, and not a libration. The proximity of the 4.5% shift to the librational R x and Ry modes, however, indicates that the internal mode probably has a torsion or a bending about either the x- or the y-axis. The two possible low-energy internal modes together with the calculated iso-tope shifts are shown in Fig. 3-11. The shift for the in-plane bending about the x-axis, the P54(6 2 «) mode, is calculated8* ( 3 - 5 ) This calculation is performed with only half a molecule since the origin acts as the pivot point. Thus D is the distance from the origin to the center of mass, M is the CHAPTER S: POWDER ABSORPTION MEASUREMENTS 54 L O W - E N E R G Y I N T E R N A L M O D E S ty ^ v T - ( c a l c ) = 1 . 0 5 5 a Figure 3-11 The internal coordinate system for the T M T S F molecule, and the two lowest-energy modes of T M T S F 6 4 , w i th the calculated shift upon deuteration (see equations 3-5 and 3-6). CHAPTER S: POWDER ABSORPTION MEASUREMENTS 55 ~ i 1 1 1 r LATTICE (TMTSF) UJ o u _ LU O O O h-Q-LT O (/) CD < LU O o i r INTERNAL LATTICE \ (TMTSF)^ N (TMTSF)2X / LATTICE (BOTH IONS) PF 6 (145 amu) _ AsF6(l89amu) SbF6(236amu) 30 50 70 90 WAVE NUMBER (cm"1) Figure 3-12 The 8-K powder absorption coefficient ad (in arbitrary units) of ( T M T S F ) 2 P F 6 , ( T M T S F ) 2 A s F 6 and ( T M T S F ) 2 S b F 6 powders in Nujol on a T P X backing, except for PF6, which had a polyethylene mount. The curves are rescaled and vertically displaced for clarity. The nature of the resonances is indicated and the dashed lines follow the features through the compounds. The molecular weight is included for reference. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 56 o N co m (,.WD) d3aiAinN 3AVM Figure 3-13 The wave number of the internal mode versus anion mass. The dependence shows a weakening of the lattice component of the force constant as the lattice expands. The accuracy of the internal mode wave number in the tetrahedral-anion compounds is poor due to the uncertainty in assignment, which resulted from the splittings and limited temperature range. The solid line is drawn as a guide to the eye. CHAPTER 3: POWDER ABSORPTION MEASUREMENTS mass of half of the molecule and IX = Ixx/2. The shift for the out-of-plane bending about the y-axis, the 1*72 (&3«) mode, is calculated 8 3 ^-V(/,-MX>2)P ( 3 _ 6 ) where IY = Iyy/2. The calculated shifts are 1.041 for the in-plane mode, and 1.055 for the out-of-plane mode. The measured shift is 4.5 ± 0.2%. As in the case of T T F - T C N Q 8 1 it is not really possible to distinguish between these two modes on the basis of the observed 4.5% shift, but since the deuteration was not complete, and the polarized spectra in the T T F - T C N Q indicated the 6 3 , mode, it is probable that we are also observing the &*72(&3«) mode. The translational and librational modes are very likely mixed 8 3 . The irre-ducible representation for the translational modes (Vt) is given b y 8 8 Tt = (3Ag + 3 A „ ) ( T M T S F ) + 3 A „ ( P F 6 ) (3 - 8) where A B and Ag belong to the C, representation which is isomorphous with the P i space group. The representation Tt includes the three acoustic modes, giving three Raman active and three infrared active modes. The representation the rotational vibrations (r r) is given b y 8 8 T r = (3A„ + 3Aj)(TMTSF) + 3A S (PF 6 ) (3 - 9) where the 3A B modes only involve the T M T S F molecules, giving three infrared and six Raman modes. Thus one expects a total of six infrared-active modes, and since T M T S F is not at an inversion center there will be mixing of the translational and librational motions. By following the relative intensities of the lines for different anion substitu-tions, the shifts of the resonances can be traced. This is not obvious from the CHAPTER S: POWDER ABSORPTION MEASUREMENTS 58 integrated intensities in Figs. 3-7, 3-8 and 3-9. The 8-K powder spectra of the P F c AsF6 and SbF& compounds are compared in Fig. 3-12. this composite makes it easy to follow the shifts of the modes, starting with the lightest anion, PF6 (145 amu) and proceeding to AsF« (189 amu) and SbFe (236 amu). The line shifts are shown in Table ni-JJ. Table JH- I I Line shifts for different octahedral anions. P F 6 A s F 6 SbF 6 Type of resonance (cm" 1) (cm" 1) (cm" 1) ± 0 . 4 ± 0 . 4 ± 0 . 4 Translation 50.0 48.0 47.0 Internal 61.0 56.5 54.5 Libration R z 69.0 67.0 66.0 Translation 71.0 60.5 60.0 The spectra in Figs. 3-1, 3-2 and 3-3 are all very similar to each other displaying four resonances, fairly close in number. Two of the lattice modes shift very little in going from one compound to another, indicating the negligible role of the anion (one is a translational mode involving just the T M T S F molecule, the other is a librational Rz mode involving just the T M T S F molecule). The third lattice mode, which involves both ions, shifts considerably between the PF6 and A s F c but very little between the AsF6 and SbF6- In the latter case it is probably interacting with adjacent modes. The internal mode shifts slightly from one compound to another, as the force constants are modified slightly by the changing size of the unit cell. Figure 3-13 shows the wave number of the i^j2(Hu) interval mode as a function of anion mass. The fact that a smooth line can be drawn through the points indicates that the complicated dependence of the internal mode on the out-of-plane restoring forces and the methyl interaction with the anion is mostly reduced to some unknown function of the anion mass. CHAPTER 8: POWDER ABSORPTION MEASUREMENTS 59 This sort of behavior is seen in the 1/3 mode of the ReO^ anion in the alkali halide salts 8 4 . The 1/3 mode shifts upwards as the lattice constant is decreased. 3.2 Powder Absorpt ion Spectra of Tetrahedral Anions The powder absorption spectra of three compounds with tetrahedral anions (BF4, CIO4 and Re04) were measured as a function of temperature from 200 K down to 6 K in the 20-90 c m - 1 region. The spectra of these compounds are very different from those of the octahedral-anion compounds. For the tetrahedral compounds the. infrared active modes can involve librations of the anions which can couple to the T M T S F infrared active lattice modes. The disorder or low site symmetry of the anions removes the degeneracy of some of the anion modes, i.e. we may see splitting of these bands. Other anion modes which are normally infrared inactive may be activated by the disorder. The powder absorption spectra of ( T M T S F ) 2 B F 4 , (TMTSF) 2 C104 and of ( T M T S F ) 2 R e 0 4 are shown in Fig. 3-14, Fig. 3-15 and Fig. 3-16 respectively, at temperatures above and below the MI transition. In Figs. 3-14 and 3-16, the curves are not vertically displaced, and have the same ordinate origin and scale. Above the MI transition there is continuous and strong free-carrier absorption, increasing with wave number as expected. Below the MI transition, TAO = 38 K for ( T M T S F ) 2 B F 4 and TAo = 180 K for ( T M T S F ) 2 R e 0 4 , the absorption decreases due to the to the formation of a semiconducting gap at the Fermi surface. The powder absorption spectra of protonated and deuterated (TMTSF) 2 BF4 , ( T M T S F ) 2 C 1 0 4 and ( T M T S F ) 2 R e 0 4 at ~ 6 K in the 20-90 c m " 1 region are shown in Fig. 3-17, Fig. 3-18 and Fig. 3-19 respectively. The percentage shifts of the lines have been included. In (TMTSF) 2 BF4 vibrational resonances begin to appear at 70 c m - 1 and 80 c m - 1 , but the peaks are broadened by thermal motion and anion disorder. At 6 K, the peaks have split up into multiplets, and there is a lot of additional structure at CHAPTER S: POWDER ABSORPTION MEASUREMENTS 33 c m - 1 and between 40 c m - 1 and 60 c m - 1 , as shown in Fig. 3-14. The spectra of (TMTSF)2BF4 is very complex below the MI transition, and without more detailed temperature dependent measurements the assignments cannot be certain. Tentative assignments based on the isotope shifts shown in Fig. 3-17 and the calculations in Table JJI-I indicate that the mode at ~ 40 c m - 1 is a lattice mode involving both the T M T S F molecule and the anion molecule, and the modes at ~ 50 c m - 1 and ~ 80 c m - 1 are translational and librational lattice modes respectivley. The internal i > 7 2 ( & 3 « ) mode is at ~ 70 c m - 1 . The positions are approximate because we cannot be certain which of the multiplet peaks corresponds to the true resonance. The feature at 32 c m - 1 does not shift. Below TAO in (TMTSF)2ReC>4 broad vibrational resonances appear. At 10 K there are four lines that dominate the spectra between 35 c m - 1 and 60 c m - 1 , similar to the sort of spectra displayed in the compounds with octahedral anions. There is also additional structure seen at 28 c m - 1 , 70 c m - 1 and 80 c m - 1 , as shown in Fig. 3-16. While the Re04 compound does not have the same multiplet structure as seen in the B F 4 compound, it does have some shoulders on the peaks as well as some extra structure between 60 c m - 1 and 90 c m - 1 . Tentative assignments based on the isotope shifts shown in Fig. 3-19 and the calculations in Table ITJ-I indicate that the resonance at 40 c m - 1 is a translational mode involving just the T M T S F molecule, the resonance at 49 c m - 1 is a lattice mode involving both the T M T S F molecule and the anion molecule and the line at 54 c m - 1 is a librational mode involving just the T M T S F . The internal mode is very difficult to locate and seems to be split into peaks at ~ 42 c m - 1 and ~ 51 c m - 1 , however both of these peaks have isotopic shifts that are characteristic of the i7 2 (&3ti) internal mode, and there is an uncertainty of ~ 5 c m - 1 in its position. The spectra for (TMTSF)2C1C>4, shown in Fig. 3-15, is slightly different in behavior than the B F 4 and Re04 compounds. A MI transition due to anion ordering occurs at TAO = 24 K in this compound, but the Fermi surface is not destroyed and CHAPTER S: POWDER ABSORPTION MEASUREMENTS 61 Figure 3-14 Powder absorption coefficient ad (in arbitrary units) of (TMTSF)2BF4 powder in Nujol on on a T P X backing. The curves are not displaced and have the same scale and origin. The anion-ordering temperature is indicated. A dashed line extrapolates the room temperature spectrum above 65 c m - 1 due to large noise resulting from the strong absorption. Cooling through TAO was at < 1 K/min. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 62 Figure 3-15 Powder absorption coefficient ad (arbitrary units) of (TMTSF)2C104 powder in Nujol on a TPX backing. The curves are displaced for clarity. The anion-ordering temperature is indicated. Cooling through T\o was at < 1 K/min. CHAPTER 3: POWDER ABSORPTION MEASUREMENTS 68 Figure 3-16 Powder absorption coefficient ad (arbitrary units) of (TMTSF)2ReC>4 powder in Nujol on a T P X backing. The curves have not been displaced and have the same scale and origin. The anion-ordering temperature is indicated. Cooling through TAO was at < 1 K/min. CHAPTER S: POWDER ABSORPTION ME A S VREMEN TS 64 i I I I ' I I L_ 30 50 70 90 WAVE NUMBER (cm - 1) Figure 3-17 The 6-K powder absorption spectra ad of protonated and deuterated (TMTSF)2BF4 powders in Nujol on T P X mounts. The percentage decrease in wave number is indicated. The curves have been rescaled and offset for clarity. The deuterated spectra is of poorer quality because fewer crystals were used. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 65 Fignre 3-18 The 6-K powder absorption spectra ord of protonated and deuterated (TMTSF)2C1C>4 powders in Nujol on T P X mounts. The percentage decrease in wave number is indicated. The curves have been rescaled and offset for clarity. The deuterated spectra is of poorer quality because fewer crystals were used. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 66 L J O L i -L i -U J O o g Q -(T O CO m < LJ o $ o Q_ ( T M T S F ) 2 R e 0 4 ( T M T S F ) h 12 3.8% 2.1% 3.8% ( T M T S F ) d 12 30 50 70 90 WAVE NUMBER (cm"1) Figure 3-19 The 8-K powder absorption spectra ad of protonated and deuterated (TMTSF)2Re04 powders in Nujol on T P X mounts. The percentage decrease in wave number is indicated. The curves have been rescaled and offset for clarity. The deuterated spectra is of poorer qulaity because fewer crystals were used. CHAPTER S: POWDER ABSORPTION MEASUREMENTS no semiconducting gap appears. This means that the free-carrier absorption will not change very much. The curves in in Fig. 3-15 have therefore been displaced for clarity. Above T^o only very broad features may be seen. At 7xo» however, four broad features are seen between 65 c m - 1 and 85 c m - 1 , and at 8 K an additional sharp feature at 31 c m - 1 . Tentataive assignments based upon the isotope shifts shown in Fig. 3-18 and the calculations in Table JH-I indicate that the internal f72(&3«) mode is found at ~ 67 c m - 1 , while the lines at 71 c m - 1 , 76 c m - 1 and 79 c m - 1 are lattice modes. The poor resolution in the deuterated (TMTSF)2C1C>4 spectra makes it really impossible to say which of the lattice modes is which. This portion of the spectrum (the three external modes and one internal mode) is just what we see in the octahedral anions. The multiplets seen in ( T M T S F ) 2 B F 4 and the shoulders in ( T M T S F ) 2 R e 0 4 below the anion-ordering transition are not as evident in ( T M T S F ) 2 C 1 0 4 . In the B F 4 and R e 0 4 compounds the A O transition changes the unit cell from a x 6 x c to 2a x 26 x 2c s s . The resulting superlattice is responsible for mapping many of the infrared inactive zone-boundary phonons back to the zone origin where some become infrared active. This would explain the extra structure which suddenly appears below T^o- In the C10 4 compound, the A O transition changes the unit cell from a x b x c to a x 26 x c. This superlattice does not map as many of the zone-boundary phonons back to the zone origin, consequently the extra structure seen in B F 4 and R e 0 4 is not as strong in the C10 4 compound. All of the samples were cooled slowly through the anion-ordering transition at a rate of < 1 K/min to ensure a relaxed state. The effect of rapid cooling into a quenched state was to broaden the lines seen in the spectra. This broadening is due to the anion disorder being frozen into the lattice. One of the interesting features in the spectra of these compounds appears at 31 c m - 1 . This feature is seen very strongly in the E || b ' single crystal reflectivity spec-trum of ( T M T S F ) 2 C 1 0 4 5 4 . It appears in both polarizations and was first seen by CHAPTER S: POWDER ABSORPTION MEASUREMENTS 68 O I I I I I I I I I I °- 30 50 70 90 WAVE NUMBER (cm"1) Figure 3-20 The low-temperature powder absorption coefficients of the three tetrahedral-anion compounds, rescaled and displaced for clarity. A dashed line joins the common "30 c m - 1 " features. Notice also the large wavenumber shift of the four normal lines between the CIO4 and the ReO* compounds. CHAPTER S: POWDER A BSORP TION ME A S UREMEN TS 69 LU O LU o r o ix l i -"30 cm - 1 " FEATURE f B R 4 ceo 4 Y J I I I I ' I L 0 50 100 TEMPERATURE (K) Figure 3-21 The integrated intensity of the "30 c m - 1 " feature in the powder spectra of the B F 4 and CIO4 compounds. The intensity is constant well beyond TAO- The data were taken up to a temperature beyond which the feature was too broad to measure. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 70 20 E o Q £ 10 LU 0 i 1 1 1 1 r i r "30 cm"1" FEATURE ' 0 T / / (TMTSF)2 Ce04 i i i i i i i i i — 50 100 TEMPERATURE (K) Figure 3-22 The full width at half-maximum of the "30 c m - 1 " feature in the powder spectrum of ( T M T S F ^ C I O * . The line was fitted to a Lorentzian on a sloping background. Above the line is broadened quickly and was not a true Lorentzian. The error bars indicate this. The dashed line is drawn as a guide to the eye. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 71 Ng, Timusk and Bechgaard 6 7 and by Challener, Richards and Green 6 8 . Ng, Timusk and Bechgaard found that for E || a, the feature at 2 K was reduced by the applica-tion of a magnetic field of 7 k G . The tunneling experiments on ( T M T S F ) 2 C 1 0 4 8 8 indicated a pseudogap of 3-4 meV (24-32 c m - 1 ) . Because the peak at 31 c m - 1 (3.8 meV) falls into this range, and because of its magnetic field dependence, this fea-ture was interpreted as evidence of ambient pressure fluctuating superconductivity in the material by Jerome. Challenar, Richards and Green 6 3 found no magnetic field dependence in the same feature, but it appears clear, both from their exper-imental procedure and from the structure seen in their spectra around 75 c m - 1 , that they were measuring the E ± a features, as seen in our spectra. Challenar et al. suggested that the feature was a coupled electron-phonon mode and suggested a comparision with other tetrahedral-anion compounds. The results for the three tetrahedral-anion spectra are shown together in Fig. 3-20. A "30 c m " 1 " feature is common to all three. Furthermore, if one plots the integrated intensity versus temperature, as seen in Fig. 3-21, one finds that it is constant up to a temperature beyond which it is too broad to measure. The width of the feature is constant below the anion-ordering temperature, but rises sharply above it and continues to grow with rising temperature, as shown in Fig. 3-22. This behavior may be explained in the following manner. The superlattice formed by the anion ordering leads to a zone-folding in which infrared inactive zone-boundary phonons are folded back to the origin and some become infrared active. This is the cause of the shoulders in the ( T M T S F ) 2 R e 0 4 and the multiplets in ( T M T S F ) 2 B F 4 spectra. The "30 c m - 1 " feature would appear to be a zone-boundary transverse acoustic phonon activated in this manner. It must couple very strongly with the electrons to have such a large oscillator strength. Above the anion-ordering transition, absorption would occur due to defect-induced one-phonon processes86 along the entire phonon branch, proportional to the density of states. This would explain the sudden increase in width above the transition CHAPTER S: POWDER ABSORPTION MEASUREMENTS temperature and the apparent downward shift in wave number. As the temperature and disorder increase, longer-wavelength phonons will contribute. The integrated intensity should be constant above and below 7AO> since the absorption mechanism is unchanged, only the way in which the momentum is conserved being different. Since the feature occurs near the same wave number for each compound, the zone-boundary transverse acoustic phonon would involve only the T M T S F molecules. The topic is treated in detail in Chapter 4, where simple dynamical models of the ( T M T S F ) j X salts are investigated. The results of Chapter 4 indeed show a low-lying zone-boundary transverse acoustic phonon which involves just the T M T S F molecules in the region of interest. If this is the case, however, then we might expect at least a 1.3% decrease in frequency upon deuteration (see Table III—I). Looking at the "30 c m - 1 " feature, one sees that it shows no downward shift at all, and the perchlorate feature actually shifted up by 0.5 ± 0.2%. On the other hand, two of the regular perchlorate lattice modes also had frequency shifts of 0% and an increase of 0.6 ± 0.2% respectively. Thus it would appear that a change in force constant is offsetting the mass increase. This is due to a decrease in the bond lengths in the deuterated methyl groups, which contracts the lattice. This is a common occurence in deuterated crystals. The f72(&3«) internal mode for the tetrahedral anions is plotted with those of the octahedral anions in Fig. 3-13. While there is some uncertainly as to the positions of the internal modes in the tetrahedral-anion compounds, the figure shows that the different anions are changing the lattice parameters and the restoring forces on the T M T S F molecule. 3.3 Extended Measurements for ( T M T S F ) 2 X Compounds Extended powder transmission measurements in the 100-300 c m - 1 range were performed on ( T M T S F ) 2 A s F 6 and ( T M T S F ) 2 S b F 6 at 6 K and are shown in Fig. 3-23. Powder transmission measurements in the 100-400 c m - 1 region have CHA P TER 3: POWDER A BSORP TJON ME A S UREMEN TS 73 been performed on quench cooled protonated and deuterated (TMTSF)2BF4 and ( T M T S F ) 2 R e 0 4 at 6 K and are shown in Fig. 3-24 and Fig. 3-25 respectively. These measurements were performed with a Golay detector and hence the resolution is only 8 c m - 1 ; the rest of the figures are the result of experiments performed with a bolometer on annealed samples giving a resolution of 2 c m - 1 . Figure 3-26 shows a comparison of the powder absorption spectra of protonated (TMTSF)2BF 4 and ( T M T S F ) 2 R e 0 4 in the 100-350 c m - 1 region at 6 K. Figure 3-27 shows the powder absorption spectra of protonated and deuterated (TMTSF)2Re0 4 in the 100-350. c m - 1 region at 6 K and Fig. 3-28 shows the temperature dependence of the powder absorption spectra of (TMTSF) 2 Re0 4 in the 100-350 c m - 1 region from 205 K down to 6 K . There is little structure visible in either the AsF6 or the SbF6 compound, except for a weak mode at 250 c m - 1 and a strong feature at 290 c m - 1 which is seen only in the SbF6 compound. These measurements agree with the single-crystal measurements E J _ a 5 7 . The feature seen at 250 c m - 1 has been observed in the T M T S F + powder spectra 6 4, where it was assigned to a ^ 35(61,) or a i>53(&2«) mode. It is characteristic for these internal modes to shift in the presence of anions, thus it is difficult to assign this resonance to either a ^ 35(61.) or a 1/53(62,) mode. The v$[f2g) SbF6 mode was measured at 294 c m - 1 , but it is usually infrared inactive. Unlike the internal modes of the T M T S F molecule, we do not expect a large change in the internal modes of the anions, thus it is unlikely that a different anion mode is being observed. The 1/5 mode may be activated by disorder effects or coupling with electrons. Figure 3-29 shows the low-energy modes of the octahedral anions, and Table ni-III below it shows the frequencies of these modes for the PFg , AsFg and SbFg octahedral anions. For the octahedral anions, a correlation table may be constructed to show how the molecular point group changes when the anion is placed into a solid geometry, as is shown in Fig. 3-30. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 74 Figure 3-23 The 6-K powder absorption coefficient ad of (TMTSF)2AsF6 powder from 25-275 cm" 1 , and ( T M T S F ) 2 S b F 6 powder from 25-325 c m - 1 , in Nujol on T P X mounts. The curves have been rescaled and offset for clarity. Figure 3-24 The 6-K protonated and deuterated powder absorption spectra for quench cooled (TMTSF)2BF4 powders in Nujol on T P X mounts. The positions of the peaks and the percentage shifts upon deuteration are indicated. The curves have been shifted and rescaled for clarity. Cooling through TAO was > 10 K/min. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 76 Figure 3-25 The 6-K protonated and deuterated powder absorption spectra for quench cooled ( T M T S F ^ R e O * powders in Nujol on T P X mounts. The positions of the peaks and the percentage shifts upon deuteration are indicated. The curves have been shifted and rescaled for clarity. Cooling through TAO was > 10 K/min. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 77 1N3I0IJJ300 NOIldHOSaV U3QMOd Figure 3-26 A comparison of the powder absorption spectra ad (in arbitrary units) of protonated and deuterated ( T M T S F ) 2 B F 4 and ( T M T S F ) 2 R e 0 4 powders in Nujol on T P X mounts at 6 K in the 100-300 c m - 1 region. The peaks have been labelled. The curves have been offset and rescaled for clarity. Cooling through the respective T^o's was < 1 K/min . CHAPTER S: POWDER ABSORPTION MEASUREMENTS 78 Figure 3-27 The 6-K powder absorption spectra of protonated and deuterated (TMTSF)2Re04 powders in Nujol on T P X mounts. The positions of the peaks and the percentage shifts upon deuteration are indicated. The curves have been rescaled and offset for clarity. Cooling through TAO was at < 1 K/min . CHAPTER S: POWDER ABSORPTION MEASUREMENTS 79 I 1 I I I I 1 I 1N3I0IJJ30D NOIlddOSaV U3CIMOd Figure 3-28 The powder absorption coefficient ad of deuterated (TMTSF)2ReO*4 powder-in Nujol on a T P X backing. The anion-ordering transition temperature is shown, and the peaks are labelled. The curves have the same scale, but have been displaced for clarity. Cooling through. TAO was at < 1 K/min. CHAPTER S: POWDER ABSORPTION MEASUREMENTS u<Fiu> "s(F2g> »e(FzJ Figure 3-29 The low-energy normal modes of vibration of the octahedral anions 8 6 . There are a total of six normal modes for the octahedral anions. Table n i - H P Low-energy internal vibrations of octahedral anions Anion MM Mhg) MM (cm" 1) (cm" 1) (cm" 1) PF 6 - 555 465 402 or 329 AsFe 392 372 363 SbFe 350 294 208 a Ref. 86: K . Nakamoto, Infrared and Raman Spectra of Inorganic and Coordi-nation Compounds, 3rd ed., John Wiley <k Sons, New York (1963). Above the MI transition in the ReO^ compound some features are observable at ~ 260 c m - 1 and ~ 320 c m - 1 . As the temperature is lowered, these features sharpen and grow into three lines in the 250-270 c m - 1 region, four lines in the 320-340 c m - 1 region, and new features at 152 c m - 1 , 185 c m - 1 , 218 c m - 1 and 294 c m - 1 (the feature at 294 c m - 1 is very strong, but appears only in the deuterated spectra). Features at 365 c m - 1 and 425 c m - 1 are also observed. The spectra in this work have a higher resolution than those of Bozio et a i . 6 3 , and also extend to lower CHAPTER S: POWDER ABSORPTION MEASUREMENTS 81 CORRELATION TA3LE Molecular point group 0. S i t e and Unit c e l l group 2g fiu<Wz) A (Raman only) Au (IR active) Figure 3-30 The correlation table for the molecular point group and the site and unit cell group of the octahedral anions. This table determines which modes will become infrared active. energies. In addition, we also have spectra of the deuterated compounds which aid in the determination of vibrational modes. Similar features are seen in the B F 4 compound at 157 c m - 1 , three lines in the 250-270 c m - 1 region, a very strong feature at 280 c m - 1 (which occurs only in the deuterated spectra), and two features at 370 c m - 1 and 420 c m - 1 . The four sharp lines at 318 c m - 1 , 324 c m - 1 , 329 c m - 1 and 339 c m - 1 in the Re04 compound are not observed to shift upon deuteration, nor are they observed in the BF4 compound. The v4(/2) mode of the ReO^ anion is measured at 331 c m - 1 . Figure 3-31 shows some of the low-frequency vibrations of the tetrahedral anions, and Table ni-rV below it gives the frequencies of these modes for the B F 4 , C107 and ReO^ tetrahedral anions. CHAPTER S: POWDER ABSORPTION MEASUREMENTS 82 Figure 3-31 The low-energy normal modes of vibration of the tetrahedral anions 8 6 . There are a total of four normal modes for the tetrahedral anions. Table n i - I V a Low-energy internal vibrations of tetrahedral anions Anion i/2(e) Mf2) (cm" 1) (cm" 1) B F 4 360 533 ClO^ 459 625 ReO^ 331 331 a Ref. 86: K. Nakamoto, Infrared and Raman Spectra of Inorganic and Coordi-nation Compounds, 3rd ed., John Wiley & Sons, New York (1963). The extended measurements on the ( T M T S F ) 2 X compounds have been placed in Table III-V, along with the results of a calculation of the low-energy in-plane in-ternal modes of the TMTSF" 1 " molecule6 4, and the experimental results of powder measurements on T M T S F + 6 4 , ( T M T S F ) 2 P F 6 6 8 and ( T M T S F ) 2 R e 0 4 6 8 . These re-sults are preliminary, and no definite assignments have been made. There are some arguments, however, for suspecting certain modes. In the powder measurements Table JTH-V Low-Energy Internal Vibrations TMTSF + TMTSF+ TMTSF2PF«, (TMTSF) 2Re0 4 (TMTSF-h, 2) 2 (TMTSF-di 2) 2 (TMTSF-hi 2) 2 (TMTSF-d 1 2) 2 calculated" observed6 SbF,, AaFfl Re0 4 Re0 4 BF 4 B F 4 (8K) (15K) (6K)'1 (6K)'' {6K)d 1/9(0,,) 453 452 436 425, 440 420 420 420 i/,oK) 312 317 365 365 365 350-380 1*3(62.) 309 300 V3b(hj 300 298 300 i/„(o ?) 279 285 261.271 270 265 264 K3e(c>i.) 265 273 254«, 250'' 260 255 255 245 va[ba,) 183 185 i/12(a„) 137 155 152 157 1/54(62.) 55 55-60'' Anion 1/4(72) 329(Re04) 329 329 318(Re04) 318 318 Methyl group? 294 280 Out-of-plane 218 g mode? Anion us{f2g) 290(SbF«)<''e *0 1 o 1 So (33 Cn O So "O o I 2 * Ref. 64: M . Meneghetti et ai., J. Chem. Phys., 80, 6210 (1984). * Solution spectra ag modes. e Ref. 63: R. Bozio and C. Pecile, Solid State Commun., 41, 905 (1981). ' This work. e Seen in Ng, Eldridge single-crystal measurements also. underlined = seen to be activated at low temperatures. 0 0 c# CHAPTER S: POWDER ABSORPTION MEASUREMENTS 84 on T M T S F + made by Meneghetti et a i . 6 4 , all of the low-energy ag modes were observed, thus, an effort was made to identify these modes in our spectra as well. One feature which is particularly interesting is the strong resonance at 280 c m - 1 and 294 c m - 1 in the deuterated B F 4 and Re04 compounds. Neither of these features appears in the protonated spectra of these compounds, indicating that this mode may be a low-energy torsional mode involving the methyl groups of the T M T S F molecule. For such a mode, / p / / j ~ 2/1, where / is the moment of inertia along the torsional axis, which is the C - C bond going into the methyl group. This being the case, we would expect a 41% shift, which would place this feature at ~ 420 c m - 1 in the protonated spectra. The spectra in Fig. 3-24 and 3-25 are very noisy in this region, and it is impossible to locate this feature. This calculation is probably not too accurate anyway, since we have ingnored the interaction of the anions with the methyl groups. (When we discussed the anion-ordering transitions of the B F 4 and Re04 anions, the anion-cation interaction, and hence the anion-methyl interaction, was very strong). The four lines clustered around ~ 330 c m - 1 in the the Re04 compound are probably associated with the t>4(/2) mode, and possibly the 1^2(c) mode. As Table Etl-IV shows, the V2(t) and ^ ( / i ) modes are degenerate at 331 c m - 1 for a free ReO^ ion, however, in the solid the degenercy may be removed and a splitting of this line may occur. The 1/4(72) line may also experience splitting due to isotope effects. The 1/4 mode involves the rhenium atom as well as the oxygen atoms, and since the natural abundance of 1 8 7 R e : 1 8 5 R e is 63%:37%, then it is possible that this mode may be split. We expect the 1/4 feature to be stronger in the infrared than the U2 mode, since the v2 mode is activated by the disorder or low site symmetry of the lattice. The lines at 318 c m - 1 and 329 c m - 1 are very strong and are probably ( 3 - 9 ) CHAPTER 3: POWDER ABSORPTION MEASUREMENTS the f 4 ( / 2 ) mode. The splitting may be caused by isotope effects, or the folding of zone-boundary internal modes back to the origin (the same mechanism thought to be responsible for the activation of the the low-energy "30 c m - 1 " feature in this compound). The weaker lines at 324 c m - 1 and 339 c m - 1 may be the v2(c) mode being activated, or could be associated with the splitting of the f 4 ( / 2 ) mode. Figure 3-32 The symbolic designation of the internal coordinate system used in the normal coordinate calculation of the vibrational states of the T M T S F and T M T S F + molecules6 4. Note that all the coordinates are in the t/z-plane. The calculations performed by Meneghetti et a l . 6 4 for the internal modes of the T M T S F and T M T S F + molecules do not predict the shifts upon deuteration for the modes; however, they do provide information about the potential energy associated with each coordinate involved in a particular vibration. The symbolic CHAPTER S: POWDER ABSORPTION MEASUREMENTS 86 designation of the internal coordinate system used in the normal coordinate calcu-lation of the vibrational states of T M T S F a n d T M T S F + molecules is shown by Fig. 3-32. The feature at 365 c m - 1 is seen in both the B F 4 and Re04 spectra, and does not appear to shift upon deuteration, however, there is a lot of noise in the B F 4 spectra in this region. A possible candidate might be the vio{ag) mode, which has aisj(53) and 7AT7*(32); that is 53% of the potential energy of the vibration is associated with the si coordinate, and 32% is assiciated with the 7* coordinate. This means that the methyl groups will be active in this mode, as is indicated by Fig. 3-33 which shows the modes for four low-energy ag vibrations. ^ . ' \ / N . ' " V 12 Fignre 3-33 Atomic displacement vectors for the totally symmetric (ag) modes of neutral T M T S F . Note that all of these modes involve the methyl groups. Since there is apparently no shift upon deuteration, and this mode indicates that there should be one, this mode may be a candidate for an out-of-plane mode. A more detailed examination of this region will have to be made before any positive assignments can be made. CEA P TER 4: LA TTICE D YNAMICS OF (TMTSFh X: SIMPLE MODELS 87 C H A P T E R 4 L A T T I C E D Y N A M I C S O F ( T M T S F ) 2 X : S I M P L E M O D E L S 4.1 Introduction Having measured some of the infrared-active low-frequency lattice and in-ternal modes, it would be meaningful to construct simplified models to understand better the dynamical behavior of these complex compounds. In particular we suspect that the "30 c m - 1 " feature may be a low-lying zone-boundary transverse acoustic phonon which is being activated by zone-folding due to the formation of a superlattice in the tetrahedral-anion salts. Simple models can determine which eigenfrequencies and eigenmodes correspond to the low-lying acoustic mode, and give information about its behavior. Using sound velocity mea-surements the force constants may be calculated. This allows us to calculate the frequency of the acoustic mode at the zone boundary. 4.2 One-dimensional M o d e l of ( T M T S F ) 2 X We begin with the simplest conceptual picture of the ( T M T S F ) 2 X system, that is a one-dimensional lattice with a three-point basis. The construction of the system and of the cell in reciprocal space is shown in Fig. 4-1. The anion of mass m alternates along the chain with two T M T S F molecules of mass M. The force constant springs K joining the masses are all equal. The unit cell is of size a. One-GEAFTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 88 dimensional Model of (TMTSF) 2X (a) Brava is l a t t i c e with a three po int bas i s m M M a •< K K K oTMTSF mass M • Anion mass m -^sp r i ng constant K (b) Rec iproca l L a t t i c e F i r s t B r i l l o u i n zone Figure 4-1 Linear system for (TMTSF) 2X. (a) The unit cell for the lattice. The anions are represented by the mass m, and the TMTSF molecules by the mass M. Here a is the lattice constant. The force constant springs K are all equal in this particular model, (b) The reciprocal lattice for a one-dimensional model. CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 89 Consider the equation of motion for a mass M at a point R in the lattice 8 7 M ^ = X>"* (R ' -R) -*R' ( 4 - 1 ) R' where U R is the displacement of M about R, R' locates the nearest neighbours. The two indices j and j' locate the force constants in the unit cell. In other words, for each postion j in the unit cell the index j' points to each of the other points in the unit cell and labels the force constant springs joining them. Because the masses in the unit cell may not be equal, ; also indexes the mass, my. Looking for harmonic solutions to this equation of the form *(q,0~« ( q" a~w f ) ( 4 - 2 ) where q is the wave vector, then equation 4-1 becomes " 2 » V * R = £ K " (*' - R ) • » * ' ( 4 - 3 ) R' To generate solutions which are defined in reciprocal space (since we expect the solutions to involve the periodicity of the lattice), equation 4-3 must be changed from the direct lattice representation to one in reciprocal space. Using Fourier transforms, we define the following relations r/(q)e''« R = u R , (4 - 4) K y / ( q ) = X> y / (R' - R)e*'q ( R ' - R ) . R' (4-5) CEA P TER 4: LA TTICE D YNAMICS OF (TMTSF)2 X: SIMPLE MODELS 9 0 substituting equations 4-4 and 4-5 into equation 4-3 gives the result 3' ( 4 - 6 ) For our simple one-dimensional system by assuming the non-trivial solution (non-zero displacements), then the summations must be zero and equation 4-6 becomes ^ { K ^ - ^ m ^ y ^ O . ( 4 - 7 ) Here a indicates the lattice direction. By evaluating "KJJ (q) in equation 4-5 and substituting the results into equation 4-7, we can determine the system of coupled Unear differential equations. The secular equation is 2K - u / 2 m i -Ke* al z -Ke-wl* -Ke-wl* 2K - w 2 m 2 -Ke^ _Jf c «q«/3 _# c -»q<»/3 2K - < J 2 m 3 = 0. (4-8) Evaluating the determinant results in w €(mim2T7i3) — u/*(mim2 + rri2mz + m^mi) +3K2u7(mi + m 2 + m 3) - 2Kz(l - cos(ga)) = 0. (4 - 9 ) From the model, mi = m (m is the anion mass) and m2 = = M ( M is the mass of the T M T S F molecule). Only those phonons at the zone origin and at the zone boundary are of real interest. Hence, we want to find solutions for q = 0 and q = § in equation 4-9 " l ( 0 ) = \/lr ( 4 ~ 1 0 a ) ,n. \2K "2(0) = W — V m r (4 - 106) CHAPTER 4: LATTICE DYNAMICS OF (TMTSFJ2X: SIMPLE MODELS 91 i — i — ~ i — i — i — i — i — i — T a WAVE VECTOR k Figure 4 - 2 T h e frequency dispersion curves for the one-dimensional model shown with the eignemodes at the zone origin and at the zone boundary. T h e reduced mass, m r , is defined a s m , = 1/m + 1 /2M. Note that the zone-boundary acoustic phonon involves just the T M T S F molecules. CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 02 Where the reduced mass m r = 1/m + 1/2M. For q = |, the zone boundary of the first brillouin zone in reciprocal space U 2 ( - ) = J——{2M -f 3 m - V 4 M 2 + 9m2 - AmM (4 - 116) a and (2M + 3m + N A M 2 + 9m2 - 4mM (4-11c) The band structure for this model calculated for the values m=l, M=2, and K—At and shown along with the eigenmodes at the zone origin and at the zone boundary in Fig. 4-2. The zone-boundary acoustic phonon involves just the TMTSF molecules. This will be examined in more detail in the two-dimensional model. 4.3 Two-dimensional model of (TMTSF) 2 X One can argue from a physical point of view that since the ab plane does not differ greatly from the ac plane the two-dimensional analysis reveals almost as much as a three-dimensional analysis would. The configuration of the unit cell that we have chosen is shown in Fig. 4-3, along with the unit cell in reciprocal space and the first Brillouin zone, This model represents the ab plane, so we can now identify a stack direction (a-axis) and a transverse direction (b-axis). The calculation has been set up to allow each of the masses in the unit cell to be different. The TMTSF molecules are represented by mi and m2, although | mi |=| m 2 |. The TMTSF molecules are aranged in stacks, and are seperated by a distance a along the a or y direction. Each stack or chain is seperated from the next by a distance of 2a. The anions of mass mz are placed between the stacks at regular intervals, a distance a away from the chain along the b or x direction. The anions repeat with spacing CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS OS 2a along the x and y directions, interacting with every other T M T S F molecule in the stack, in this way forming their own sublattice. The T M T S F molecules are connected by a force constant spring K\} and the anions are joined to alternate T M T S F molecules by force constant springs K2. The unit cell is of size 2o x 2a. Once again we must find the set of coupled equations, this involves solving equation 4-7, only there are now two lattice directions a and 0 so that with this new degree of freedom the 3 x 3 determinant will become a 6 x 6 determinant for the two-dimensional model. 2K2 - u/2mi 0 -2K2 cos (qxa) 0 0 0 —u2m2 0 0 0 0 —2K2con{qxa) 0 2K2 - u7mi 0 0 0 0 0 0 2Ki - w'mi —2Ki cos(gva) 0 0 0 0 —2K\ ccs(fya) 2Ki — urm2 0 0 0 0 0 —w2m3 = 0. (4 - 12) Notice that in this particular model we have completely decoupled the x and y systems, thus the 6 x 6 matrix can be reduced to two 3 x 3 matrices. The first determinant corresponds to a = x and (3 = z, and the second determinant to a = y and f3 = y. If we define the reduced mass as m,- + my (4 - 13) Solving for the first determinant gives the eigenmodes with a qx dependence wi(q) = A*l3 ]K\ 4if 2 Jsin 2(g Ia) mim3 (4 - 14a) a^(q) = J f 2 + \K\ 4Klsm2(qxa) A»i3 V ^13 rnxm2 (4 - 146) CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 94 T w o - d i m e n s i o n a l M o d e l o f ( T M T S F ) 2 X ( a ) B r a v a i s l a t t i c e w i t h a t h r e e p o i n t b a s i s © T M T S F m a s s m ± © T M T S F m a s s m 2 • A n i o n m a s s m 3 s p r i n g c o n s t a n t K - ^ s p r i n g c o n s t a n t K. 1 ( b ) R e c i p r o c a l L a t t i c e O O A O T Q Y rt o o J L a o \ o F i r s t B r i l l o u i n z o n e Figure 4 -3 Two-dimensional system for ( T M T S F ^ X . (a) The anions of mass mz are joined to alternate T M T S F molecules of mass | mi |=| m2 \ by force constant springs K2. The T M T S F molecules are joined by force constant springs K\. The unit cell is of size 2a x 2a. The coordinate system for the direct lattice is shown, (b) The reciprocal lattice for the two-dimensional system and the first brillouin zone. The coordinate system for the reciprocal lattice is shown. CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 05 Recall that for a cubic lattice in real space, the reciprocal lattice will also be cubic with its axes oriented in the same directions as the axes in the direct lattice. Thus, these branches represent the modes which propogate along the x-direction, trans-verse to the stacks. Solving the second determinant gives the eigenfrequencies with These branches represent the modes which are polarized along stacks. Note that one of the effects of decoupling the x and y systems is to give eigenmodes which are completely polarized along the x- or y-direction in the direct lattice. The transverse and longitudinal modes usually refer to the motion of the ions with respect to the direction of the wave vector. Because this model represents two uncoupled one-dimensional models, we would have no transverse modes in the true sense. Instead, we simply denote the direction of the ions as either being in the transverse (x) direction or longitudinal (y) direction. If we consider that the frequency dispersion curves are those for a a wave vector in the qy direction, then this is equivalent to a model with more degrees of freedom where true transverse modes would exist; using this simple trick we can consider the phonons in our simple model as being truly transverse or longitudinal. The frequency dispersion curves are calculated using the estimates mi = m2 = lj mz = \Y K\ = 1 and K2 = \T based on the mass ratios and the relative coupling strengths, along the paths r —» M X —• T and r — • M —• Y — • T i n reciprocal space and are shown in Fig. 4-4 and Fig. 4-5 respectively. The frequency dispersion curves at M shows a transverse acoustic phonon and a longitudinal acoustic phonon present, along with the longitudinal and transverse a qy dependence (4 - 14c) CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 9 6 Figure 4-4 The frequency dispersion curves for the two-dimensional model for the path r —• M —• X —• T. The branches have been labelled according to which solu-tion they correspond to. Along the path M—»X the longitudinal acoustic mode goes to zero, while the transverse acoustic mode remains constant, as does the transverse optic mode. The transverse modes depend only on qxi and the longitudinal modes only depend on qy] thus if either one of these variables is constant (as is the case along M—»X and X—• T), then the corresponding mode will not change along the path. CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 97 Figure 4-5 The frequency dispersion curves for the two-dimensional model for the path r —• M —• Y —• T. The branches have been labelled according to which solu-tion they correspond to. Along the path M—*Y the transverse acoustic mode goes to zero, while the longitudinal acoustic mode remains constant, as does the longi-tudinal optic mode. The transverse modes depend only on qxt and the longitudnal modes only depend on qy; thus if either one of these variables is constant (as is the case along M—+Y and Y—• T), then the corresponding mode will not change along the path. CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 98 r(o,o) LO r(o,o) TO Y(o£) © LO • x(J ,o) © TO © © • Y(0,£) $ x(£,o) e© • L A © • T A © Figure 4-6 The eigenmodes of the optical phonons at V (the zone origin), the transverse optic and transverse acoustic phonons at X, and the longitudinal optic and longitudinal acoustic phonons at Y (the faces of the first Brillouin zone). The eigenmodes at the origin are the only ones that may be observed optically, unless zone folding occurs. Note that the zone-boundary longitudinal optic, longitudinal acoustic and and transverse acoustic involve just the T M T S F molecules. CHAPTER 4- LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 99 optic modes. Along the V —>X path the longitudinal acoustic phonon disappears, and along the T —*Y path the transverse acoustic phonon disappears. The eigen-modes for the phonons at T (the zone origin) and X and Y (the zone faces) are shown in Fig. 4-6. The zone origin is chosen because these are the modes that may be activated using optical techniques. The zone faces show the eigenmodes of the acoustic phonons which are not active at the zone origin. At the zone boundary only the longitudinal optic, longitudinal acoustic, and transverse acoustic phonons involve just the T M T S F molecules, however the longi-tudinal acoustic and longitudinal optic phonons are degenerate and are not really distinct. Thus, both the one- and the two-dimensional models have shown that the low frequency zone-boundary acoustic phonon involves just the T M T S F molecules. 4.4 A n Estimate of the T M T S F Aconstic Phonon An estimate of the zone-boundary phonon can be obtained based on sound ve-locity measurements along the a-axis. This corresponds to the longitudinal acoustic mode at the origin. From the previous section, we know that the frequency u>3(q), which for convenience will be labeled a;£,4(q), is given by (4 - 15) For this mode, mj — m2, equation 4-15 may be rewritten (4 - 16) The velocity of sound, v,> at the zone origin is defined as d(jja (4 - 17) CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 100 Substituting equation 4-16 into 4-17 and evaluating in the limit as qy —• 0, since direct substitution yields an indeterminant value, gives the expression cm/s (4 - 18) or (4 - 19) Note that we are working with cgs units. The velocity of sound has been measured in ( T M T S F ) 2 F S 0 3 8 8 by Lacoe et aJ. and found to be vFSOs _ 3 g x 1 Q 5 c m / 8 (±25%) and in ( T M T S F ) 2 P F 6 8 9 by Chaikin et ai. v?F« = 3.1 x 105 cm/s (±5%) along the a-axis. The large error in the F S O 3 crystal is due to problems with the sample dimensions. The mass of the TMTSF molecule is 448.05 amu, thus the reduced mass is / * i 2 = 3.7189 x 10 - 2 2 g. The distance between the anions is taken to be 7.266 A 1 6 , which is twice the lattice spacing in our model, that is 2a, thus a = 3.633 x 10 - 8 cm. Using these values and the velocity of sound for the PF6 compound and substituting into equation 4-19 gives the value for the spring force constant Ki K\ = 5.371 ± 0.537 x 104 gm/s2. At the zone boundary, equation 4-16 becomes (4 - 20) CHAPTER 4: LATTICE DYNAMICS OF (TMTSF)2X: SIMPLE MODELS 101 Thus the angular frequency of the phonon at the zone boundary is ULA(~) = 1-202 ± 0.06 x 1013 rad/s. a This, however, is the angular frequency. Recalling that / = ^p, then ILA{-) = 1-912 ± 0.095 x 101 2 Hz. a Finally, the conversion factor to wave numbers is 1 c m - 1 = 3.0 x 101 0 Hz (some other useful relations are given in Appendix A). The longitudinal acoustic phonon is calculated to have a frequency of HA{~) = 63.73 ± 3.19 c m - 1 . a It is not unusual for the frequency of the transverse acoustic phonon to be half that of the longitudinal phonon 0 0 . For the choice of masses and spring force constants (which are reasonable in view of the fact that no accurate data for the intermolecular restoring forces is available) in this simple model, we get the result that at the zone boundary the transverse acoustic phonon is half the frequency of the longitudnal acoustic phonon. Thus, it would not be unrealistic to expect the transverse acoustic phonon to have a frequency of PTA[~) ~ 30 c m - 1 , o These simple models show that 30 c m - 1 is a reasonable estimate of the zone-boundary transverse acoustic phonon, and that such a mode would likely involve just the T M T S F molecule. CHAPTER 5: CONCLUSIONS 102 C H A P T E R 5 C O N C L U S I O N S 5.1 Conclusions The compounds with centrosymmetric and non-centrosymmetric anions (an-ions with octahedral and tetrahedral symmetry) show behavior which is both differ-ent and similar. The presence of four sharp resonances, three external modes and one internal mode, is common to all of the ( T M T S F ^ X salts examined. They are very sharp, however, in the compounds with octahedral anions. Those compounds with tetrahedral anions undergo anion-ordering transitions which results in the for-mation of a superlattice. Thus, zone-boundary phonons which are infrared inactive are mapped back to the origin where they may become infrared active. The four resonances are broad due to disorder effects, and are accompanied by multiplets and shoulders in the compounds with 2o x 26 x 2c superlattice (BF4 and Re04), but are well defined in the CIO4 compound with the superlattice along just one transverse direction a x 26 x c. In addition to these features, there is a prominent feature at ~ 30 c m - 1 in all of the tetrahedral-anion compounds. From its behavior as a function of temperature, and the fact that it appears in all three of these compounds, it is likely that this feature is a zone-boundary transverse acoustic phonon that has a similar frequency in all of the compounds. Calculations using simple models sup-port this conclusion. This feature is very strong, due probably to electron-phonon coupling and it may be related to the superconductivity. CHAPTER 5: CONCLUSIONS 103 Extended measurements only yield information on internal modes that are common to all of the ( T M T S F ^ X salts examined. The tetrahedral anion salts, however, show evidence of zone folding in this region. Anion internal modes are identified, as well as a T M T S F methyl torsional mode. 5.2 Suggestions for Future Experiments The "30 c m - 1 " feature represents some very elegant physics, although it is questionable whether or not it is associated with FSC. It is interesting to note, that all of the compounds in which it has been observed so far have anion-ordering transitions along the b-axis, which appears to be necessary for superconductiv-ity. (TMTSF)2N03, however, has an anion-ordering transition along the a-axis, resulting in a 2a x 6 x c anion superlattice and has been found not to exhibit sup-erconductivity under pressure1 4. If the "30 c m - 1 " feature is a transverse acoustic phonon, then because it is completely polarized in the transverse direction, it should not be activated by a superlattice formed along the stack direction. That is, at Y in the reciprocal lattice, and along the T —*Y direction, this mode is not infrared active. 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[90] H.A. Mook and C R . Watson, Jr., Phys. Rev. Lett., 36, 801 (1976). APPENDIX A 109 A P P E N D I X A 1 c m " 1 = 124 MeV = 3 x 101 0 Hz = 1.9 x IO 1 1 rad/s = 1.44 °K = 10.7 k G = 2.1 x I O - 1 ( f l c m ) - 1 1 amu = 1.66043 x I O - 2 4 g 

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