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Far-infrared reflectivity measurements including thin films of ice and a mosaic of TTF-TCNQ crystals Kornelsen, Kevin E. 1986

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F A R - I N F R A R E D R E F L E C T I V I T Y M E A S U R E M E N T S I N C L U D I N G T H I N F I L M S O F I C E A N D A M O S A I C O F T T F - T C N Q C R Y S T A L S By K E V I N E . K O R N E L S E N B.Sc, University of Alberta, 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 February 1986 © Kevin E . Kornelsen, 1986 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: February 5, 1985 ii A B S T R A C T The main objective of this thesis project involved the design and construction of a reflectance module to be used with a far infrared Fourier spectrometer. This module would be used for specular reflectivity measurements with small samples at temperatures between liquid helium and room temperature. Early tests of this reflectance module were used to investigate some of the interesting changes in the far infrared spectrum which result from ice condensation on the sample surface. With the condensing substrate at temperatures between 130 and 200K the condensation is in a crystalline phase and can drastically reduce the intensity of the reflected radiation. The effects are most significant in the spectral range between 150 and 300cm - 1 . Substrate temperatures lower than 130K lead to condensation of ice in a vitreous phase which does not have such a large effect on the far infrared spectrum. Modifications were made to the reflectance module design to eliminate the unpredictable effects of ice condensation and a final set of tests were performed measuring the reflectance of a mosaic of T T F - T C N Q crystals. The resulting data shows much of the fine structure which has been observed in other measurements using bolometric techniques. T A B L E O F C O N T E N T S Abstract « Table of Con tents , iii List of Figures v Acknowledgements vii C H A P T E R 1 I N T R O D U C T I O N 1 1.1 Fourier Transform Spectroscopy 1 1.2 Reflectivity Measurements 9 1.2(a) Ellipsometry 13 1.2(b) Asymetric Interferometry 14 1.2(c) Specular Reflectance Measurements 16 1.3 Reflectivity of One-Dimensional Crystals 16 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 23 2.1 Interferometer 23 2.2 Reflectance Module 25 2.3 Vacuum System 31 2.4 Cryostat 33 C H A P T E R 3 T H I N FILMS O F C O N D E N S E D ICE 38 3.1 Phases of Condensed Ice 38 3.2 Far Infrared Measurements 41 3.3 Reflectance Module Results 3.3(a) Interference Effects in the Ice Layer Iv 42 45 C H A P T E R 4 T T F - T C N Q M O S A I C R E F L E C T I V I T Y 54 4.1 Mosaic Mounting Technique 54 4.2 T T F - T C N Q Thermometer 56 4.3 Experimental Results 59 4.3(a) Low Temperature Measurement 59 4.3(b) Temperature Dependent Results 66 4.4 Conclusions 66 B I B L I O G R A P H Y 69 L I S T O F F I G U R E S 1-1 Michelson Morley experiment 3 1-2 Michelson's interferometric spectrometer 4 1-3 Basic Michelson interferometer 8 1-4 Reflectivity as a function of angle of incidence 15 1-5 Molecules used in construction of quasi-one-dimensional compounds 17 1- 6 Reflectance of a mosaic of crystals before and after gold evaporation 20 2- 1 Ray diagram for a Beckman IR-720M interferometer 24 2-2 Reflectance module ray diagram 27 2-3 Heli-Tran refrigerator mounted in reflectance module lid 29 2-4 Reflectivity of Csl 30 2-5 Vacuum pumping system 32 2-6 LT-3-110 Heli-Tran refrigeration system 35 2- 7 Overall view of cryogenic system 36 3- 1 Table of ice phases 40 3-2 Absorption spectra of ice .• 42 3-3 Measured vitreous and crystalline ice spectra 44 3-4 Thin film of absorbing film on an absorbing substrate 46 3-5 Crystalline ice spectra as a function of time 48 3-6 160 c m - 1 ice thin film interference effects 50 3-7 210 c m - 1 thin film interference effects 51 vi 3- 8 229 c m - 1 thin film interference effects 52 4- 1 Sample mosaic mounting ring 55 4-2 T T F - T C N Q thermometer resistance as a function of temperature 58 4-3 High resolution far infrared T T F - T C N Q reflectivity 60 4-4 Reflectivity of a T T F - T C N Q mosaic as a function of temperature 61 4-5 Measured T T F - T C N Q reflectivity at 25K 62 4-6 Reflectivity of the mosaic before and after gold plating 63 4-7 Reflectivity of the gold plated mosaic at room temperature and at 80K . . . 65 4-8 Measured T T F - T C N Q reflectivity as a function of temperature 67 4-9 35K T T F - T C N Q mosaic reflectivity 68 A C K N O W L E D G E M E N T S I wish to thank Dr. J.E. Eldridge for his patience and for many helpful sug-gestions. The knowledge and assistance of the people in the machine shop, s.t.s., and the electronics shop has been indispensible in the completion of this project. Thanks also go to Chris Homes for the many late nights which he spent breaking in the new computer and for other assistance in the lab. Funding for this work came from NSERC Grant No. A5653. 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 Fourier Transform Spectroscopy The term optical spectroscopy is used to describe any measurement of light intensity reflected, absorbed or transmitted by a sample as a function of incident photon energy. Spectroscopy using light from the infrared or far infrared regions of the optical spectrum can be used for investigation of electronic states and low-lying molecular or lattice vibrations in solids. Most of these types of far infrared measurements are made with interferometric spectrometers. These instruments are also known as a Fourier transform spectrometers because of the need to spectrally analyse the interferometer's output to derive the frequency spectrum. The most widely used instrument for far-infrared spectroscopy is based on the interferometer used in the famous Michelson-Morley experiment. Albert Michelson built this apparatus in 1880 to investigate the long held belief that light waves could only propogate in some mysterious medium called ether. Although the properties of this substance were not at all clear, it was thought that light waves would be carried along much like vibrations on a tightly stretched wire or waves on the surface of water. If these analogies were correct, it would follow that movement of the earth through the ether could speed up or slow down the speed at which light would appear to travel. The Michelson-Morley experiment would be used to detect any CHAPTER 1: INTRODUCTION 2 difference in speed between the light rays travelling across the ether flow and the ones travelling with or against the flow. A schematic of a Michelson interferometer is shown in figure 1.1. Light from a source is incident on a beam splitter which is partially reflecting and partially transmitting. The reflected and transmitted beams travel down the two perpendic-ular arms, reflect from mirrors and then recombine back at the beam splitter. For an interferometer using light from the visible frequency range, path differences be-tween the two arms lead to a series of bright and dark interference fringes spatially distributed in the output beam. When the earth moves through the ether, the light going across the ether flow should return to the beam splitter a little bit sooner than the light going with the flow one way and against it the other. Therefore rotating the interferometer would change the relative phases of the recombining light beams and could lead to observable changes in the interference pattern. Michelson built his apparatus very carefully, using only the finest optical com-ponants and mounting the mirrors on a stone slab which was floating in a trough of mercury to provide vibration isolation and to allow smooth rotation. After spend-ing a few years taking measurements and improving his experimental technique, he concluded that to the best of his observational ability light travels with the same velocity in all directions. This was an important experimental result but Michelson also realized that the principle of the interferometer could have other applications as well. He was especially interested in its use as a high resolution spectrometer, one of his goals being to establish an accurate and reproducable standard for length measurement based on the wavelength of light and another being an investigation of some of the close doublet lines in atomic emission spectra. To use an interferometer as a spectrometer, the mirror in one of the arms is carefully moved to change the path length travelled by half of the light in the recombining beam. The effect of this movement is most easily understood if one CHAPTER 1: INTRODUCTION T Figure 1-1 The Michelson-Morley experiment, (a) Schematic (v indicates the expected ether flow), (b) Apparatus. considers the case of a monochromatic light source. The light intensity at one point in the spatial interference pattern then alternates between a maximum and a minimum every time the mirror moves one-quarter wavelength. By counting the number of modulations and measuring the mirror displacement, it is possible to establish the wavelength of the light very accurately. Michelson's most accurate measurements on atomic singlet lines could determine the wavelengths to within a relative accuracy of 1 part in twenty-million. Michelson also found that the interference pattern produced by these singlet light sources would deteriorate if the moving mirror was positioned at a large path difference. This is because the light is not perfectly monochromatic. The sources actually emit a series of finite wave trains of duration At which originate in elec-tronic transitions of individual atoms. The finite lengths in the time domain lead CHAPTER 1: INTRODUCTION 4 to linewidths in the frequency domain given by At> « When the path difference in the interferometer becomes large, the points of constructive interference for the different frequencies appear at different positions in the output beam and the inter-ference pattern becomes blurred. An alternate (but ultimately equivalent) view of this deterioration considers coherence of the light in the time domain. Since there is no correlation between the light emitted in different atomic transitions, when the light takes a time comparable to At in travelling the extra path length in the variable arm of the interferometer there can be no coherent interference pattern. Figure 1-2 Michelson's interferometric spectrometer.1 (a) Source. (b),(c),(d) Spec-troscope, (d) Slit, (e) Beamspitter. (f) Moving Mirror, (g) Stationary Mirror, (h) Telescope. CHAPTER 1: INTRODUCTION 5 In the more complicated spectra which Michelson investigated, the source lamp emitted a band of light covering a certain frequency range. In this case, movement of the mirror modulates each frequency in the source spectrum at a rate proportional to the wavelength of the light. The intensity at a point in the inter-ference pattern therefore varies as a sum of sine waves, each with an amplitude proportional to a corresponding intensity in the source spectrum and all starting in phase when the mirrors are adjusted for zero path difference. By performing a harmonic analysis of the light intensity as a function of mirror position (the inter-ferogram), it is possible to determine the frequency spectrum of the light source1''. Two difficulties had to be overcome in order to perform this experiment suc-cessfully. The first problem is that the quantity observed at the output of the interferometer is an interference pattern, not the light intensity. However, Michel-son noted that these two quantities are not unrelated. With the adjustable mirror set for zero path difference, the points of constructive interference for all the differ-ent source frequencies very nearly coincide and the interference pattern looks very sharp. This is also the point at which the peaks in the interference pattern have maximum intensity. As the mirror moves away from this position, the different wavelenths are modulated at different rates—this means that the intensity of the peaks goes down and the interference pattern starts to look blurred. In this way both the intensity and the interference pattern visibility are measures of the de-gree of constructive or destructive interference among the recombining light waves. Michelson developed a system for measuring visibility curves. By making compar-isons with photographed interference patterns of known quality he could estimate the sharpness of an interference pattern to within 10 or 15%. Michelson's other difficulty lay in harmonically analysing the interferogram. The theory of Fourier transformation could be used to mathematically calculate the frequency components for some simple spectra but for an experimentally measured interferogram, this kind of computation would be almost impossible. The solution CHAPTER 1: INTRODUCTION 6 was to build an analog computer which could perform these transformations. The harmonic analyser which Michelson constructed could take a measured curve with up to 80 points , perform the harmonic analysis and plot the derived frequency spectrum 1 . Using this machine to analyse his visibility curves, Michelson was able to establish the existance of several doublet structures which were beyond the resolution of the best dispersion spectrometers of his day. The principles which Michelson recognized in using the interferometer for spectroscopy in the 1890's are the same ones used today. However, two factors led to the technique not becoming widely used until the 1960's. The first is that estimating the visibility of an interference pattern could not be done very accurately and to measure an entire interferogram with 80 points would be a difficult task. The years Michelson spent trying to measure the effects of ether drift on the speed of light must have helped to develop his patience to an unusual degree. In the later years of Michelson's lifetime, the interferograms could have been measured using light from the infrared part of the spectrum. For these longer wavelengths the mirrors could be alligned with enough accuracy to eliminate the spatial interference fringes and to allow direct measurement of the intensity as a function of mirror position. Light detectors sensitive at these frequencies were being developed by Heinrich Rubens at this time s . However, there were still difficulties in the spectral analysis of the interferogram. Michelson realized that a spectral computer 3 or 4 times as large as the one he was using would be needed to allow proper analysis of a spectum more complicated than the simple doublet structures which he usually looked at. He never built such a machine and the techniques of interferometric spectroscopy were not fully exploited until the advent of digital computers many years later. Today it is recognized that the interferometer has two advantages over a grat-ing spectrometer. They are most often called the Fellgett and Jacquinot advantages. CHAPTER 1: INTRODUCTION 7 The Fellgett (or multiplex) advantage is a consequence of the fact that all frequen-cies of the spectrum are incident on the detector all the time . This means that the detector for an interferometer will have a larger signal to noise ratio than a grating instrument which divides the spectrum into many small elements in order to measure each one individually. Jacquinot's advantage relates to the interferometer's efficiency in measuring high resolution spectra. Increasing the resolution of a conventional grating spec-trometer is achieved by decreasing the slit width but this also decreases the light intensity at the detector. This means that high resolution spectra require mea-surement of more points with each one requiring a longer integration time. For an interferometer however, the resolution depends on the total distance through which the mirror moves. This distance can be increased to several meters to obtain high resolution spectra. There is a certain point at which the size of the source aperture will also limit the interferometer's resolution. Calculations comparing an interfer-ometer in this limit and a grating spectrometer with a similar source area, focal length for the collimator, and resolution show that the interferometer will be able to give a signal several hundred times larger than the dispersion instrument. This means that while both types of spectrometers will have to measure more points to obtain higher resolution, the interferometer does not have the disadvantage of a decreased signal level at the detector. Figure 1-3 shows a Michelson interferometer in the configuration often seen in the commercially produced instruments made in the 1960's and 70's. The main improvements over the original design lie in the electronic signal detection and mo-torized mirror movement. They automatically measure the light intensity in steps as the mirror moves through a range on both sides of the zero-path-difference. These machines can only be used in the infrared or far-infrared regions of the spectrum because higher frequency measurements would require much more accuracy in the mirror movement and allignment. By the late 1970's technological improvements CHAPTER 1: INTRODUCTION 8 and faster computers made it possible to use fast scanning mirrors in interferome-ters to allow measurements in the spectral range all the way from the far infrared up to the ultra-violet. The higher frequencies become accessible because the fast scan-ning mirror modulates the shorter light wavelengths at a frequency easily handled by electronic filtering (usually several hundred hertz). Fignre 1-3 Basic Michelson interferometer.4 (A) Source. (B) Chopper. (C) Col-limator. (D) Beamsplitter. (E) Moveable mirror. (F) Compensator. (G) Fixed mirror (H) Focusing mirror. (I) Spectral filters. (J) Detector Today one of the main disadvantages in using a Fourier transform spectrom-eter still lies in the need for computational machinery to convert the measured interferograms into a useful spectrum. When using one of the older stepping inter-ferometers, the entire interferogram is recorded before the spectral analysis begins. For runs which can take several hours this can be a major disadvantage since there G CHAPTER 1: INTRODUCTION 9 is no opportunity to check the results at an intermediate stage. The newer ma-chines which use fast scanning mirrors largely circumvent this problem. A large computer records an interferogram, does the spectral analysis and averages each new spectrum with the previous ones while the data is being collected. It can be programmed to discard noisy interferograms and to stop the measurement as soon as the desired level of accuracy is reached. The average spectrum is displayed and upgraded while the measurement is in progress. The disadvantage of this type of system is the high cost of a computer capable of meeting all the requirements for high speed analysis. 1.2 Reflectivity Measurements Optical reflectivity measurements are important because they can be used to determine any of the response functions commonly used in electromagnetic theory. The complex reflectivity of a material is defined as the ratio of the incident and A A reflected electric field amplitudes, E\ and E^: A ?=5 = v / £ e , > ' . (1-1) Here R is the proportion of incident power reflected and <pr is the phase difference between the incident and reflected fields. Knowing both R and <pr allows one to calculate the optical constants n and k, the dielectric constants e1 and e", and the conductivity a. In most reflectivity measurements it is possible to measure the power reflected but not the phase change. In this case a Kramers-Kronig relation can be used to calculate >pr in terms of the measured reflectance. These equations can be applied to the real and imaginary parts of any causal response function (they can also be applied to n and k or e1 and e") but they require knowledge of the measured CHAPTER 1: INTRODUCTION 10 quantity at all frequencies between 0 and co. The Kramers-Kronig relation used for calculating the phase from the reflectivity is: , , u f+0° \nR(u')J , JT Jo U'—U)' For practical purposes the values of R(u>) far away from the frequency region of interest will be of little importance because of the rapid increase in the denominator of the integrand. If the values of R and <pr are known, it is a straightforward calculation to derive the optical constants n and k. The refractive index n is used to describe the propogation of an electric field through a dielectric medium using the equation6: E = Eoe< —> (1-3) where h = n-ik (1-4) and EQ is the electric field amplitude at the dielectric surface, E is the field a distance x into the material, u is the angular frequency of the light and c is the speed of light in a vacuum. Writing equation 1-3 in the form —iunx —ukz E = Eoe~^~e~^ (1-5) we see that c/n is the effective speed of the electric field propogation through the material and k is proportional to the dielectric absorption coefficient, a: et uk ^ = _ = 2 T T F * . (1-6) The quantity V introduced here is the wavenumber of the light and is usually mea-sured in c m - 1 . For light normally incident on a reflecting surface surrounded by air CHAPTER 1: INTRODUCTION 11 or vacuum, the optical constants can be calculated from the reflectivity using the equations6: n = •= (1 - 7) 1 + R-2VRco3<pr 1 + R-2VRcos<pr ' The complex dielectric function is another quantity which is commonly used to describe the response of a material to an electromagnetic field. The real part (e*) is a measure of the polarizability of the material while the imaginary part (c") is proportional to the electrical conductivity. The dielectric function is related to the optical constants by the equation8: h = n - i k = v V - **e". (1-9) Equating real and imaginary parts gives e* and e" in terms of n and k (which are already known in terms of R and <pr from equations 1-7 and 1-8). Putting the frequency dependence explicitly in terms of the wavenumber one obtains: e'(V) = n(uf - k(uf (1 - 10) c"(F) = 2n(V)k(u). (1-11) The electrical conductivity of the material can be related to the dielectric function or the optical constants using the equation: <x(u) = v 1 = - ^ r - . (1 - 12) v ' 30 60 i • / A value of V measured in c m - 1 gives the conductivity in units of 0 - 1 c m - 1 . CHAPTER 1: INTRODUCTION 12 Measuring the reflectivity is not the only way to determine the optical prop-erties of a material. A measurement of the absorptivity a could be used instead to give a value for the imaginary part of the optical constant through equation 1-6. A Kramers-Kronig analysis would then be applied to the real and imaginary parts of n to give: Once again the or dependence in the the denominator of equation 1-13 ensures that measurements in regions far from the frequency of interest will be less important, allowing extrapolations to be made without introducing large errors. Two factors must be considered when deciding whether to use absorptivity or reflectivity measurements on a particular sample. First, for any absorption mea-surement the incident, reflected, and transmitted light intensities must all be known. Therefore more information is required than for measuring the reflectivity where only the incident and reflected signals have to be recorded. A second consideration involves the specific characteristics of the sample being studied. If a sample is a poor reflector, an absorption measurement might be best because the reflected sig-nal is very small and hard to measure. On the other hand, good reflectors are also strong absorbers of light so measurement of a transmitted signal can be impossible. Sometimes samples with high reflectivity can be made very thin to increase the transmitted signal. However, with many materials it is difficult to make such a thin layer with uniform thickness and with all the same properties as the 3-dimensional solid. If one is willing to look at a highly reflective sample on a more qualitative basis, another alternative may be to study the spectrum of light transmitted by a fine powder. Quantitative measurements are impossible because sample thickness, particle size and particle orientation are all factors which are hard to control and (1 - 13) CHAPTER 1: INTRODUCTION I S which will vary throughout the sample. The results of such measurements cannot be used to obtain values of the optical constants. For strongly reflective samples it is often more convenient to measure the reflectivity. For this type of a measurement using far-infrared light one needs a fairly large sample with a flat clean surface. The dimensions of the sample must be large compared to the wavelength of the light to avoid unwanted diffraction effects and to allow focusing of the light from the source onto the sample. The surface must also be of good quality because often only a small fraction of the light penetrates past the first few atomic layers of the material. There are three different ways in which a Michelson interferometer could be used for reflectivity measurements. The most commonly used method measures the power reflectance R and uses the Kramers-Kronig relation of equation 1-2 to calculate the phase. This method can be used to look at small or weakly reflecting samples if one uses mirrors to focus the light onto the sample. If larger reflect-ing surfaces are available, it may be possible to use the techniques of asymetric interferometry or ellipsometry. 1.2 ( a ) Ellipsometry Ellipsometry measures the intensity of the light reflected from a sample using polarized light and a variable angle of incidence. The optical constants which would give angular reflectances similar to the measured values are then estimated using a computer. Figure 1-4 shows the expected reflectivity at angles of incidence between 0 and 90 degrees for samples of silver and T T F - T C N Q (one of the one-dimensional or-ganic crystals which v/ill be introduced later) using far infrared light with wavenum-ber 200 c m - 1 . The reflectivities shown in figure 1-4 were calculated in terms of the optical constants n and k using Maxwell's equations and illustrate the large differ-ence between the light polarized parallel to the plane of reflection (Rp) and that CHAPTER 1: INTRODUCTION 14 polarized perpendicular to this plane (Rt). The values of n and k used in the calculations were determined experimentally for the T T F - T C N Q 7 and from the Hagen-Rubens relation for the silver8. This equation can be used to calculate the optical constants for any metal in the infrared or far infrared frequency regions: € = (n - tk) =1 = 1 + _ . (1 - 14) For silver the measured static conductivity is <TQ = 6x 10 7 f t - 1 m - 1 = 5.5x 101 7sec - 1. The two plots of figure 1-4 illustrate undesirable characteristics which are common to all angular reflectivity measurements involving good conductors. The first is that the s-polarized reflectance is high and nearly constant for all angles of incidence. A second disadvantage is that the biggest feature in the p-polarized curve is seen at an angle of incidence between 70 and 90 degrees. A large sample surface and a well collimated light beam are required to accurately map Rp(9) at these oblique angles of incidence. This last constraint makes the method unpractical in the far-infrared where weak light sources often make it necessary to focus the light onto the sample. The focusing will generally lead to angular deviations of between 5 and 10 degrees in the incident light rays. 1.2(b) Asymetric Interferometry Reflectivity measurements can also be performed using an asymetric interfer-ometer. This technique also requires measurement of two spectra- first an instru-mental background and then a sample spectrum with the interferometer's stationary mirror replaced by the reflecting sample. Using these two spectra one can calculate both R and <pr directly and the optical constants can be calculated from equations 1-7 and 1-8 without resorting to any Kramers-Kronig analysis4. The disadvantage of this method is the need for a large reflecting surface to give a good signal. For example, in our interferometer the sample would be put in the position of a 3 inch diameter plane mirror. CHAPTER 1: INTRODUCTION 15 Figure 1-4 Reflectance for s and p-polarizations at an air-sample interface, (a) Silver, (b) T T F - T C N Q . CHAPTER 1: INTRODUCTION 16 1.2(c) Specular Reflectance Measurements A third technique measures only the power of the light reflected from the sample surface. In these measurements the light beam is reflected from either the sample or a mirror before going into the detector. A ratio of the two resulting spectra gives the power reflectance R and the phase <pr is then calculated using the Kramers-Kronig relation given in equation 1-2. R(OJ) must be measured over a large spectral range in order to calculate the Kramers-Kronig integral accurately and extrapolations are used to cover the regions where the reflectivity cannot be measured. Although the equations used to calculate the optical constants from the reflectivity are derived for light at normal incidence, figure 1-4 illustrates the fact that the reflectivity does not change very quickly at small angles of incidence. Therefore equations 1-5 and 1-6 can be used for reflectivity measurements taken with any angle of incidence less than 20 degrees. The main advantage in measuring the specular reflectance is the ability to focus the light beam onto the sample, making it possible to use small or weakly reflecting samples. 1.3 Reflectivity of One—Dimensional Crystals Many new materials have been made in the last 20 years which are classified as quasi-one-dimensional. These are three-dimensional substances which display a large electrical conductivity along one axis but are electrically insulating in other di-rections. In some cases the anisotropy can lead to differences as large as 105 for the conductivity measured along different directions in the material. This type of prop-erty is often observed in crystals which have large flat molecules arranged in stacks (these are sometimes compared to stacks of poker chips). Electrons conduct between molecules in a stack but the large distance between molecules in different stacks pre-vents conduction in any other direction. The molecules used in synthesizing such a crystal are usually arrangements of atoms commonly found in organic compounds such as carbon, hydrogen, sulfer, nitrogen or selenium. The first molecule of this CHAPTER 1: INTRODUCTION type was made in 1960 and was given the name 7,7,8,8-tetracyano-p-quinodimethane (often abbreviated as TCNQ). Some of the commonly used molecules are shown in figure 1-5. Figure 1-5 (a) Some molecules used in construction of quasi-one-dimensional coumpounds. (b) A typical stacking arraingement.® Part of the impetus behind the development of these types of materials has been the hope of finding a high-temperature superconductor. The BCS theory predicts a superconducting state in normal metals at low temperature because of relatively weak attractive forces that bind the conducting electrons together in Cooper pairs. The attractive force is caused by a slight increase in concentration of positive ions left behind in the trail of an electron moving through the lattice. W.A. Little proposed the idea of a one-dimensional superconductor in 19649. He CHAPTER 1: INTRODUCTION 18 pointed out the possibility that the electrons bound to the molecules in quasi-one-dimensional material would be repelled by a conduction electron moving along the stack. This would lead to polarization and creation of a region of positive charge which could attract another conduction electron, once again leading to formation of Cooper pairs. Normal metals display superconductivity only at very low temper-ature because thermal vibration of the lattice can easily overwhelm the ability of a conduction electron to influence the motion of the positive ions. The mechanism which Little proposed for a one-dimensional material might allow superconductivity at higher temperatures because it should be relatively easy to rearrange the distri-bution of bound electrons on a molecule. It was speculated that this would enable the creation of a superconducting state at temperatures as high as 2000 K. Superconductivity in a quasi-one-dimensional compound was first observed by Denis Jerome and colleagues using a (ThfTSF^PFz compound in 197910. This crystal becomes a superconductor when held at a temperature of 0.9 K and under a pressure of 12,000 atmospheres. More recently, some compounds based on other oganic molecules have been synthesized which superconduct at ambient pressure and at temperatures up to 7 K. The difficulties encountered in obtaining these results have reduced the expectations for high temperature superconductivity considerably. In fact, measurements on the existing superconducting compounds point to a mech-anism involving normal BCS superconductivity rather the one-dimensional version which Little proposed. Although the superconductivity of one-dimensional conductors has not de-veloped as originally hoped, the compounds have exhibited some other interesting properties. For example, many of the one-dimensional conductors undergo a metal-semiconductor transition at temperatures below 200 K. This phase transition was first predicted by R. Peierls in 195311. He showed that it would be energetically favourable for any one-dimensional conductor to have non-uniform inter-molecular spacing at low temperature. This distortion is accompanied by a transition from CHAPTER 1: INTRODUCTION 19 metallic to semiconducting properties. When decreasing the temperature of such a material, the conductivity increases in a metallic fashion until the transition takes place. After this the conductivity decreases due to the creation of a semiconductor band gap. In order to obtain a highly conducting one-dimensional material at low temperatures, this transition must be supressed—possibly by putting the crystal under pressure as in the first observations of superconductivity. The Peierls distortion can have a direct effect on the optical spectrum of a one-dimensional material. Symmetry properties of the ordered lattice often make certain lattice vibrations inactive in the far-infrared spectrum. However a Peierls transition introduces disorder to the crystal structure and can lead to the appearance of new resonances in the optical spectrum. A Peierls distortion can also produce charge-density-waves. When the distortion is free to move through the lattice, electrons can be pushed along in front of a space in the lattice much like surfers on a wave. This can give the material an enhanced direct current conductivity. Physical characteristics of the one-dimensional conductors often make optical measurements difficult. Because these materials are good conductors, they are also good reflectors and poor transmitters of radiation. This means that reflectivity measurements are most often performed since they allow measurement of a relatively large signal. Unfortunately single crystals are usually too small to provide a good reflecting surface in the far infrared. The largest ones are usually less than 1 mm wide and 10 mm long—dimensions comparable to the wavelenth of the far-infrared radiation. Focusing the light onto such a small surface is difficult. In order to make a sufficiently large reflecting surface it is necessary to lay down a mosaic of crystals, resulting in an uneven surface which diffracts some of the light. The diffraction effects can be compensated for by measuring the spectrum of each sample twice— first with the clean mosaic and then with the same surface plated with gold. Figure 1-6 shows a result from H.K. Ng's thesis illustrating the effect of this diffraction. Although the metallized sample will reflect almost all of the incident radiation, CHAPTER 1: INTRODUCTION 2 0 figure 1-6 shows that nearly 40% of the light is diffracted and does not reach the detector. 200 300 400 Wavenumber (cnrr1) 500 600 Figure 1-6 Reflectance of a mosaic of crystals and the same mosaic plated with gold". Reflectivity measurements using mosaics of one-dimensional crystals have been performed by H.K. N g 1 3 ' 1 8 , C.S. Jacobsen14>15,and W.A. Challener1 6'1 7. All three used a conventional Michelson interferometer to measure the specular re-flectance of far-infrared light. Using other types of spectrometers in higher fre-quency ranges allowed Kramers-Kronig analysis and derivation of the optical con-stants and the conductivity. These experimentors all used almost identical experimental techniques. A liquid helium cooled cryostat held both the sample mosaic and a detector (the bolometers used to detect the radiation are semiconducting devices and must be CHAPTER 1: INTRODUCTION 21 cooled to reduce the number of electrons thermally excited across the band gap). A heater on the sample mount allowed the temperature to be controlled at any temperature between the minimum of 2 K and a maximum of around 60 or 100 K. The upper limit depended on the temperature at which heat conduction from the sample to the detector caused the bolometer to warm up and lose sensitivity. Far-infrared light was directed to the sample through a light pipe. Before reaching the sample, the light passed through a polarizer located inside the cryostat which had to be correctly orientated before the cryostat was cooled down. This meant that at least two runs were required in order to measure the reflectivity using both the possible polarizations. The sample holder was rotatable to allow interchange of the sample mosaic and a reference mirror. The spectrum recorded using reflection from the mirror was used to account for any change in the instrumental background while the sample was removed for the gold plating process. There are several possible sources of uncertainty in these experiments. One consideration is the fact that the light pipe does not direct all the radiation onto the sample. Jacobsen found that 30% of the light arriving at his detector came from sur-faces other than his sample. Only through careful measurement of the background spectra was he able to determine that this factor would not introduce a significant error. Some of the early experiments did not take into account the scattering of light by the mosaic of crystals. Figure 1-6 shows that this is a neccessary part of the procedure. Accounting for the effects of thermal cycling on the sample can also be a difficult task. Ng observed that some of his freshly prepared crystals had a dark colour and a shiney surface but after cooling to liquid helium temperatures a few times, the surface started to look a bit dull and small cracks could be ob-served when looking at the sample through a microscope13. These physical defects could be reduced by minimizing the amount of cryopumping done by the crystals. However, thermal cycling can still have unavoidable effects on many of the more sensitive sample characteristics including phonon vibrations, charge density waves, CHAPTER 1: INTRODUCTION 22 and superconductivity. For good quality results it is important to keep thermal cycling to a minimum. T h e apparatus which we will be using for reflectivity measurements will have three advantages over the ones mentioned above. T h e first is that by focusing the light beam onto the sample rather than using a light pipe, we will make sure that all of the light going to the detector is actually reflected from the sample. This will reduce the magnitude of the error which must be corrected using the mea-sured background. Secondly, the sample and detector will be mounted in separate cryostats. This will give us access to a larger range of sample temperatures, going all the way from room temperature down to liquid helium temperatures. O u r third advantage will be the ability to change the polarization of the light beam without warming up the sample, allowing us to keep thermal cycling of the sample to a minimum. CHAPTER S: EXPERIMENTAL TECHNIQUE 2S 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 2.1 Interferometer The Fourier spectrometer used in this project was manufactured by Beckman Research and Industrial Instruments Company and has the model number IR-720M. A ray diagram for the instrument is shown in figure 2-1. The only modification made for measuring reflectance spectra was in the replacement of the sample chamber shown with a reflectance module. The source of radiation provided with the spectrometer is a high pressure mercury arc lamp. In these lamps the heated mercury vapour plasma provides most of the light at frequencies below 200 c m - 1 while higher frequencies are emitted from the hot quartz envelope in the form of blackbody radiation with effective temperature of 800-900 K. An aperture in front of the source can be chosen to have a diameter of 3, 5 or 10 mm. A chopper modulates the light going to the interferometer at a frequency of 15 Hz so that any dc background signal measured by the detector can be rejected. Light from the source is reflected from a surface-aluminized off-axis parabolic mirror(l) which directs a parallel beam of light toward the mylar beam splitter(2). The light reflected by the beam splitter goes to a moving mirror(3) which is driven by a synchronous motor. A gearbox allows the mirror to travel at speeds between 0.5 and 500 micrometers per second with a maximum displacement of 10 cm to either CHAPTER 2: EXPERIMENTAL TECHNIQUE 25 side of the position of zero optical path difference. This gives a maximum resolution of 0.1 c m - 1 . Light transmitted by the beam splitter reflects from the stationary mirror. Both the stationary mirror and the beam splitter are on adjustable mounts to allow optical allignment of the beam. A second off-axis parabolic mirror(5) is used to focus the recombined light beam into the sample chamber. Here, filters are used to remove high frequency radiation before the beam goes through a focusing lens(8) and into the far infrared detector. The Golay cell used as a detector is a room temperature device with a signal to noise ratio within a factor of 3 or 4 of the theoretical limit for a detector at 300 K. The signal from the detector is integrated using a standard R C circuit with a time constant which can be adjusted to match the rate at which data points are being recorded. A Moire grating mounted on the moving mirror assembly provides an accu-rate measure of the moving mirror displacement. The electronics controlling the instrument are set up to send the measured light intensity to the computer memory each time the mirror moves a distance of 4, 8, 16, 32 or 64 micrometers. High wavenumber limits in the resulting spectra are related to the mirror displacements (Ax) by the equation: u m a x = J L . (2 - 1) Step sizes ranging from 4 to 64 micrometers result in upper spectral limits between 1250 c m - 1 and 78.125 c m " 1 . 2.2 Reflectance M o d n l e One part of this project consisted of building a reflectance module which could be used in place of the standard interferometer sample chamber. This ap-paratus would ultimately be used to measure the far infrared reflectivity of some one-dimensional organic conductors. The measurements would require use of a CHAPTER 2: EXPERIMENTAL TECHNIQUE 26 polarized light beam, accurate exchange of sample and reference surfaces, and sam-ple temperatures controlled between liquid helium and room temperatures. Limits due to the small sample sizes make it most convenient to measure the specularly reflected power R. Figure 2-2 shows a schematic diagram of the reflectance module which was designed for this purpose. It has walls of 1.25 cm thick aluminum glued together with degassed epoxy to make a vacuum tight box with outside dimensions of 24.0 cm x 24.4 cm x 17.7 cm and an internal volume of 7100 cm 3 (7.1 liters). A plexiglass window in the front wall allows visual observation of the sample while experiments are in progress. The top and bottom plates and the plexiglass window are all removeable to allow allignment of the optical components. These surfaces along with the connections between the reflectance module and the interferometer and the golay detector are sealed with elastomer o-rings. Two ports in the back wall of the box are used for a vacuum gauge and an air inlet valve. Most of the optical components in the reflectance module are taken from an older apparatus which was made by RIIC. The two torroidal mirrors M2 and M3 have radii of curvature 9.5 cm in the vertical cross section and 10.2 cm horizontally. These give the light directed toward the sample an average angle of incidence of 15 degrees. Mirror M2 is positioned to focus an image of the iris at the sample, allowing accurate control of the size and shape of the spot of light on the sample surface. Work in the far-infrared requires use of special windows and filters. As in any Fourier transform interferometer, filters are needed to remove all radiation above the maximum wavenumber in the spectrum given by equation 2-1. We have used a thin sheet of black polyethylene to take out the frequencies above 1000 c m - 1 while a set of filters from the original sample chamber give cutoff frequencies of 250, 260, 600 or 700 c m - 1 . These filters are Fresnel lense-shaped and are designed to replace the thick convex polyethylene lens(8) used to focus light into the detector light pipe CHAPTER t: EXPERIMENTAL TECHNIQUE 27 Figure 2-2 Reflectance module ray diagram. An image of the iris is focused on the sample. CHAPTER S: EXPERIMENTAL TECHNIQUE as shown in figure 2-1. For spectra with maximum wavenumber below 250 c m - 1 an additional filter is placed in the beam before reflection from mirror M4. Plastic windows which transmit far infrared radiation are used to separate the high vacuum region around the cryogenic sample from the rest of the interferometer. We have used a type of plastic called T P X because this material has a refractive index which is the same in both the far infrared and visible parts of the spectrum. This allows one to allign the far infrared beam using the visible light coming from the source. The window is wedged at an angle of 2 degrees to prevent channelling of the spectra. A polarizer can be placed in a holder at the port between the reflectance mod-ule and the interferometer. The position on the outside of the purge window allows adjustment of the polarization without breaking the high vacuum region surround-ing the cold sample. Reflections from mirrors M l and M2 have a depolarizing effect of less than 5%. A copper reference mirror and the reflecting sample are mounted on opposite sides of a cryostat cold finger. Rotation of the cryostat through an angle of 180 degrees exchanges the two surfaces. The design of the adapter for mounting the cryostat in the reflectance box lid is shown in figure 2-3. Rotation is possible without breaking the vacuum or disturbing the sample temperature. A superstructure fitting over the cryostat gives the mount extra stability. Sample and reference surfaces can be given the same orientation with very good accuracy by shining the beam from a Helium Neon laser between the two torroidal mirrors (M2 and M3) onto the reflecting surface and observing the position of the reflected beam which is sent back between the mirrors. The vertical orientation must be set before cooling the sample and can only be adjusted by bending the sample mount. This is easily done by hand. Rotating the sample about the vertical axis adjusts the horizontal displacement of the reflected beam and can be done at any temperature. CHAPTER £.- EXPERIMENTAL TECHNIQUE 29 H e l i - T r a n R e f r i g e r a t o r C o o l i n g L i q u i d Return Flow _ E l e c t r i c a l Feedthrough for -^ Heater and Thermometers <-Double 0-ring Se a l A l l o w i n g R o t a t i o n - B To D i f f u s i o n Pump Vacuum S h r o u d ^ R a d i a t i o n S h i e l d Thermometers Far I n f r a r e d Beam Sample and Reference Surfaces Figure 2-3 Heli-Tran refrigerator mounted in reflectance module lid. Sample and reference surfaces are on opposite sides of the low temperature cold finger. (This diagram also shows the vacuum shroud which will be discussed in the next section) CHAPTER t: EXPERIMENTAL TECHNIQUE Using this mounting technique for a sample Csl crystal gave a spectrum similar to that observed by Beairsto and Eldridge19. The measured reflectivity shown in figure 2-4 has a peak at 62 c m - 1 close to the 92% value seen previously. One has to be careful when using this method in spectral regions where the sample has a low absorption coefficient because light can travel through the sample to bo reflected from the backside of the copper mirror rather than the surface of the sample. This is not a problem with Csl in the region around the strong reflectivity peak since here the absorption coefficient is of the order of 103 c m - 1 . However, in other spectral regions the 2 mm thick crystal which we used could transmit a significant amount of light. In this case it might help to coat the backside of the mirror with infrared absorbing paint although one would still have to account for the light internally reflected from the back surface of the Csl sample. 1. 0 i 1 1 1 1 1 1 1 1 Figure 2-4 Reflectivity of Csl. CHAPTER S: EXPERIMENTAL TECHNIQUE 31 2-3 Vacuum System There are two evacuated regions in this apparatus—the main body of the interferometer and the high vacuum region around the cryostat. The interferometer is evacuated to remove the water vapour present in the air which absorbs infrared light while a region around the cryostat must be under high vacuum to prevent heat conduction and vapour condensation onto the cold surfaces. Figure 2-5 is a diagram of the pumping system used in these experiments. The interferometer volume is pumped using a standard rotary pump which has a speed of 140 liters per minute. A double bellows arrangement in the pumping line is used for vibration isolation and an oil mist filter prevents migration of oil vapour into the interferometer chamber where it could contaminate the mirror surfaces. This pump must maintain a pressure less than 100 microns (1 micron= 10~3mm of Hg = 10 - 3 torr) in order to remove the effects of water vapour absorption in the spectrum. A thermocouple gauge in the pumping line is used to measure the pressure which is normally less than 100 microns after about 15 minutes of pumping. Outgassing of the chamber walls is the most significant factor limiting both the pumpdown speed and the ultimate pressure. It was found that after several days of pumping a pressure as low as 3 microns could be obtained. After reaching this limit the pump was turned off and the pressure remained below 100 microns for more than 24 hours, indicating that the leakage rate is very low. The high vacuum region around the cryostat is pumped by a diffusion pump with a liquid nitrogen cold trap. A flexible stainless steel tube connecting this pump to the vacuum chamber is the factor limiting the pumping speed. For conditions in the molecular flow regime the speed will be 6 I/sec (for the 5 cm diameter tube, this should be the speed whenever the pressure is less than 10 - 3 torr). Our original design as shown in figure 2-5 used this pump to evacuate the entire reflectance module which was isolated from the rest of the interferometer with the T P X purge window. It was thought that the pumping speed of 6//sec would be sufficient to Mef lectance Module Thermocouple Gauge Interferometer F l e x i b l e S t a i n l e s s _ S t e e l Pumping L.ine Thermocoup le Gauge Rotary Pump Figure 2-5 Pumping system (not drawn to scale). CHAPTER S: EXPERIMENTAL TECHNIQUE pump the volume of 7.1 liters. Measuring the pressure with an ionization gauge mounted in the back wall of the module, we found an ultimate pressure of 8 x 10 - 5 torr with the sample at room temperature while a sample at liquid nitrogen temperatures would cryopump to bring the pressure down to 3 x 10~6 torr. At these pressures, significant amounts of ice would condense onto the surface of a cold sample after only a few hours at low temperature. Details of the effects of water condensation on the far infrared spectrum will be discussed in chapter 3. To eliminate this problem a vacuum shroud was built to go around the sample as shown in figure 2-4. This reduced the volume of the high vacuum region from 7.1 liters to 0.6 liters. The original purge window was removed to allow the bulk of the reflectance module to be pumped along with the interferometer and the ionization gauge in the back wall was replaced with a thermocouple gauge. A T P X window in the vacuum shroud allows passage of radiation to and from the sample. The ultimate pressure measured at the vacuum shroud was 1.2 x 10 - 5 torr with the sample at room temperature while cooling the sample to liquid nitrogen temperatures lowered the pressure to 5x 10 - 7 ton*. This modification to the system proved to be successful in reducing the ice condensation on the sample to a negligible level. 2-4 Cryostat The cryostat used to hold the sample in these experiments was an Air Prod-ucts LT-3-110 Heli-tran liquid transfer refrigeration system as shown in figure 2-6. This apparatus can be used with either liquid nitrogen or helium as the coolant giving minimum sample temperatures potentially as low as 77.3 K and 4.2 K. Cold sample temperatures are maintained by a steady flow of liquid cryogen from a pres-surized supply dewer to the cryostat through a high efficiency transfer line. A portion of the liquid is used for cooling a heat shield in the transfer line while the remainder goes to the cold stage heat exchanger. The temperature of the sample is CHAPTER S: EXPERIMENTAL TECHNIQUE 84 maintained by balancing the flow ofcryogen to the sample with the electrical power input to a heater in the heat exchanger. Flow of the liquid can be adjusted using either a needle valve at the end of the transfer siphon in the cryostat or a valve on the flowmeter in the return line. Liquid helium temperatures can be maintained using 1 liter of helium per hour while the liquid nitrogen consumption is only 0.2 liters per hour at the minimum temperature. By pumping on the return line it should be possible to maintain temperatures as low as 2 K when using liquid helium although this technique was not used in these experiments. The power input to the heater is controlled by a Scientific Instruments Series 5500 microprocessor-based temperature-controller/thermometer which is sold with the Air Products cryostat. A silicon diode thermometer is factory-mounted in the cryostat cold finger for use with this instrument. The temperature measured by this thermometer can be controlled to within 0.4 K for temperatures between 4 and 300 K. The largest temperature deviations are caused by fluctuations in the flow rate of liquid cryogen to the cryostat. In our first experiments, the silicon diode thermometer measured minimum temperatures of 78.9 K and 6.2 K when cooling with liquid nitrogen and helium respectively. The fact that these temperatures were not the expected values of 77.3 K and 4.2 K was partially due to inadequate thermal conductivity of the radiation shield which is cooled by gas leaving the cold stage of the cryostat. The cylindrical radiation shield which comes with the cryostat has a diameter of 36.2 mm and is made of 0.6 mm thick nickel plated OFHC copper. Two holes 16 mm wide and 9.5 mm high were cut to allow passage of the far infrared light beam to the sample and reference surfaces (see figure 2-3). A silicon diode thermometer varnished to the botton of this shield measured a temperature of 180 K when operating with liquid nitrogen and 130 K when using helium. Mounting the thermometer at various heights on the shield showed a significant thermal gradient along its length. A new CHAPTER I: EXPERIMENTAL TECHNIQUE 35 Figure 2 - 6 LT-3-110 Heli-tran refrigeration system10. High F f f i c i n n c y Transphcr- Siphon 0> CHAPTER g: EXPERIMENTAL TECHNIQUE radiation shield was made (again using OFHC copper) but with walls 2.5 times thicker than those of the original shield. The higher thermal conductivity which resulted lowered the temperature at the bottom of the shield to 85 K and 40 K when cooling with nitrogen and helium respectively. The lower temperature of this shield made it possible to put activated charcoal on the shield to help adsorb water vapour in the sample chamber and lowered the minimum sample temperatures to 77.9 K and 5.9 K. The remaining difference between the thermometer readings and the liquid temperatures may be due to room temperature radiation passing through the holes in the radiation shield. CHAPTER 3: THIN FILMS OF CONDENSED ICE C H A P T E R 3 T H I N F I L M S O F C O N D E N S E D I C E An ice layer condensed onto a cold sample surface absorbs light strongly in the spectral region between 100 and 300 c m - 1 . Specific characteristics of the absorption depend on the phase of the condensed ice which is determined by both the temper-ature of the condensing substrate and the rate of condensation. In our experiment the ice condensation was observed only because water vapour was outgassing from the walls of the reflectance module chamber. It was found that when maintain-ing the whole reflectance module at high vacuum, an ice layer causing significant absorption accumulated after having the reflecting surface at low temperature for only a few hours. A vacuum shroud was made to fit closely around the cryostat cold finger and reduce the outgassing surface area. This improvement lowered the effects of ice condensation to a negligible level. 3.1 Phases of Condensed Ice Water vapour which is condensed onto a cold substrate can form in one of three phases depending on the temperature of the base. Figure 3-1 shows a table from the book by Hobbs called Ice Physics'1. It summarizes the results from some of the experiments which have been used in determining the structure of water vapour deposited onto substrates held at various temperatures. X—ray diffraction, electron diffraction, and calorimetry have all been used extensively. Three different phases are generally observed. At low temperatures the deposit has a vitreous CHAPTER S: THIN FILMS OF CONDENSED ICE or amorphous structure. At intermediate temperatures the phase is cubic and at higher temperatures the structure is hexagonal. For substrate temperatures lower than the minimum shown in the table, condensation continues in the amorphous phase while temperatures higher than 215 K are not included because rapid sample evaporation takes place above 200 K. The large scatter in the observed transition temperatures can be related to differences in the rate of deposition, sample purity, and difficulties in determining the actual temperature of the deposit. When warming a sample of ice condensed in the vitreous phase, a transition to the cubic formation is observed. Measurements of this transition temperature also vary significantly. In early experiments using electron difraction, Konig saw the transition occuring at 135 K while Blackman and Lisgarten found it to be at 155 K. With continued heating Konig observed another transition to the hexagonal phase at 185 K before sample evaporation at 205 K. Blackman and Lisgarten saw no change from the cubic structure before sample evaporation at 170 K. Although this evaporation temperature is much lower than that observed by Konig, it is in agreement with other measurements on the evaporation rate of ice in a vacuum. The deviations between the results of Konig and those of Blackman and Lis-garten have been attributed to differences in their experimental techniques. Konig's samples were produced by cooling a substrate in a vacuum chamber in which water vapour was provided through evaporation from the electron diffraction camera film. This procedure made control of sample purity impossible because the camera film introduced other chemicals in addition to the water vapour. Another impurity in the vitreous ice samples would be the ice in the crystalline phase condensed while cooling the substrate to low temperature. Conditions in the Blackman and Lisgarten experiment were more carefully controlled. Their condensing substrate was put in a separate vacuum chamber and was held at constant temperature while pure water vapour was introduced from an external source. Blackman and Lisgarten attempted to explain Konig's results by CHAPTER S: THIN FILMS OF CONDENSED ICE 4 0 c Experimental method -180 -160 Temperature ranges f C ) •140 -120 -100 -80 - 6 0 Reference X-ray diffraction vitreous or amorphous semi-crystalline hexagonal Burton and Oliver (1935) Calorimetric X-ray diffraction amorphous crystalline Staronka (1939) small crystals intermediate range not investigated hexagonal Vegard and Hillesund (19421 Electron diffraction small crystals cubic hexagonal Konig (1942) Calorimetric amorphous crystalline Pryde and Jones (1952) Calorimetric amorphous crystalline Ghormley (1956a) Electron diffraction crystal growth poor cubic hexagonal Honjo etal. (1956) X-ray diffraction Mixture of cubic and hexagonal hexagonal Sh a Her oss and Carpenter (1957) Electron diffraction amorphous or small crystals cubic hexagonal and cubic hexagonal Blackman and Lisgarten (1957) X-ray diffraction vitreous and cubic hexagonal Dowell and Rinfret (I960) Electron microscope and electron diffraction cubic hexagonal Fernandez-Moran (1960) X-ray diffraction vitreous cubic j hexagonal Beaumont el al. (19611 Calorimetric vitreous (glass transition at - 134°C) 1 cubic hexagonal McMillan and Los (1965) Electron microscope and electron diffraction amorphous ! cubic j hexagonal Vertsner and Zhdanov (1969) X-ray diffraction (diffuse rings) cubic hexagonal Defrain and Linh (1966) Electron microscope and electron diffraction minute cubic crystals cubic hexagonal and cubic hexagonal Kumai (1968) Figure 3-1 Table summarizing experimental results on the structure of ice con-densed onto a base at low temperature. CHAPTER 9: THIN FILMS OF CONDENSED ICE 41 reproducing his experimental technique as closely as possible. They confirmed that crystalline impurities were present in the vitreous samples condensed by cooling the substrate in the presence of the water vapour. These impurities could lead to the transition to the crystalline phase occuring at a temperature anywhere between 125 K and 160 K depending on the amount of crystalline phase condensed while cooling. An evaporation temperature as high as 205 K could also be seen but only when certain condensing substrates were used. Another phenomenon which Blackman and Lisgarten observed was the de-pendance of the phase on the rate of condensation. Most of their samples were condensed in a few minutes. Speeding up the process to just a few seconds raised the minimum temperature for crystalline ice formation from 135 K to 145 K. Slow-ing down the condensation rate seems to have a similar effect. The far infrared measurements of Arrandeau mentioned in Bertie's 1967 paper3' used ice condensed over a period of between 3 and 8 hours. While Arrandeau assumed that his sample would be in the vitreous form, Bertie's interpretation of the recorded data indicates that there must be some contamination with the crystalline phase. 3-2 Far Infrared Measurements Bertie has measured the infrared and far infrared spectra of H2O and D2O ice in the cubic, hexagonal and vitreous phases3 3'3 8. In this experiment the phase of the ice was determined independently using X-ray diffraction. These measurements „. show that most of the absorption in the spectral region above 1000 c m - 1 is due to internal vibrational modes of the water molecules while the absorption at lower wavenumbers is almost exclusively due to translational vibrations in the crystal lattice. It was found that the far infrared spectra of ice in the cubic and hexagonal phases are indistinguishable and show a sharp absorption peak at 229 c m - 1 along with a broader maximum at 164 c m - 1 . Vitreous ice has an absorption spectrum with no sharp features but a broad maximum in the absorptance centered at 230 CHAPTER 8: THIN FILMS OF CONDENSED ICE 42 c m - 1 . The absorption spectra from both the crystalline and the vitreous phases are shown in figure 3-2. 3*3 Reflectance Module Results A high vacuum region around the cold sample in our reflectance module was maintained to reduce thermal conduction to the cryogenic surface and to lower the rate of vapour condensation. It was found that even at pressures low enough to provide good thermal isolation, water vapour could condense onto the cold surface at an unacceptable rate. The buildup of ice introduces many uncertainties since the resulting far infrared absorption depends on both the phase of the condensed ice and the thickness of the ice layer. The ice layer thickness increases with time at CHAPTER S: THIN FILMS OF CONDENSED ICE 43 a rate depending on the water vapour pressure in the chamber, the flux rates for water vapour on the sample and reference surfaces, and the sticking coefficients for the water molecules incident on the two surfaces. All these factors are unknown. The main source of water vapour in our reflectance module is the water that is adsorbed onto the walls at atmospheric pressure which is then slowly released when a vacuum is applied. The plexiglass window covering most of the front wall of the chamber is probably providing most of the water vapour in this way although the unpolished aluminum walls of the chamber also adsorb more water vapour than some other possible materials like stainless steel. Measuring the reflectance of the copper reference surface maintained at 80 K gave the spectra shown in figure 3-3(a) after times of 9, 16 and 21 hours. IoO7) is the spectrum measured immediately after cooling the mirror while l(u) is the spectrum recorded some time later. The pressure in the reflectance module during this run was 4 x 10 - 6 torr. The layer of adsorbed ice gives a broad spectrum much like the absorption spectrum which Bertie observed for vitreous ice samples although the peak appears at a slightly lower frequency. Ice condensing onto the copper mirror held at 165 K resulted in the spectra shown in figure 3-3(b). These spectra were measured after only 1 and 1.5 hours at low temperature in the reflectance module which was evacuated to a pressure of 2 x 10 - 4 torr. The sharp peak at 210 c m - 1 and the broader maximum at 154 c m - 1 are in some ways similar to the peaks in the absorption spectrum which Bertie observed at 229 c m - 1 and 164 c m - 1 . We would not expect exact correlation between our spectra and Bertie's absorption spectrum because in our experiment we observed both the light intensity transmitted through the ice layer to be reflected from the copper substrate and that reflected directly from the front ice surface. It will be shown in the next section that the interference effects between these two beams of light played an important roll in the spectra which we observed and that CHAPTER 3: THIN FILMS OF CONDENSED ICE 44 CD Wave Number (cm"1) Figure 3-3 (a) Vitreous ice spectra (measured after 9, 16, and 21 hours at 80 K). (b) Crystalline ice spectrum (after 1 and 1.5 hours at 165 K). CHAPTER 9: THIN FILMS OF CONDENSED ICE the optical constants which Bertie has measured actually agree with our data quite well. A phase transition from the vitreous to the crystalline phase was observed when warming the ice condensed at low temperature. The change occurred at a temperature between 145 K and 165 K and was observed as a sharp decrease in the far infrared signal. This decrease in light intensity and spectra measured before and after the transition indicate that there are large differences between the optical properties of ice in the crystalline and vitreous phases. Such differences could be expected since Bertie has shown that the far infrared optical constants of ice are de-termined mainly by the translational modes of vibration in the crystal lattice. With continued heating, the crystalline ice remained on the mirror until a temperature of 200 K was reached. At this point a rise in both the far infrared signal and the reflectance module pressure indicated the start of evaporation. This temperature is within the range of evaporation temperatures which have been observed in the past and may be higher than some either because the sample was not condensed from pure water vapour or because of the particular substrate used. The vacuum shroud shown in figure 2-4 reduced the ice condensation to a negligible level. The improvement was due to a reduction in outgassing surface area. There was no observable decrease in the far infrared signal after either 8 hours with the copper mirror at 165 K or 24 hours at 80 K. 3.3(a) Interference Effects in the Ice Layer Maxwell's equations are often used to calculate the reflected and transmitted signals for light incident on a thin film of dielectric such as that shown in figure 3-4. In our case the results can be applied to a thin film of ice condensed onto a copper mirror. The general equations for reflections from such thin films are derived in CHAPTER S: THIN FILMS OF CONDENSED ICE 46 many books (for example Born and Wolf34) and predict a reflected electric field amplitude given by: ?12 + r23C— Here f i 2 and f23 are the reflected electric field amplitudes at the two interfaces and the factor e~,/3 accounts for the attenuation and phase lag of radiation reflected from the second interface. For radiation with normal incidence, the reflectivities f i2 and f23 are calculated in terms of the optical constants using equations of the form: f u - ^ i ^ (3-2) ni + n 2 ' and P is given by p=4jrh2d = A,(n-ik)d ( 3 _ 3 ) CHAPTER S: THIN FILMS OF CONDENSED ICE In our case, the thickness of the ice layer (d) is increasing as long as the copper reflecting surface is held at low temperature. If the absorption coefficient of the ice (fc) is not too large, equation 3-1 predicts that interference effects will lead to several maxima and minima in the reflected signal before it approaches the value fi2 at large d. Some of the effects of interference on the ice film reflectance spectrum are illustrated in figure 3-5. This data was measured a few hours after that shown in figure 3-3(b). At frequencies between 125 and 229 c m - 1 the ice layer thickness required for maximum destructive interference has already been passed and the signal is now increasing again. Above 229 c m - 1 the intensity is still decreasing as the ice layer thickens. At 229 c m - 1 the signal has stabilized at a value close to that measured by Bertie for the reflectivity of an ice—air interface. At this frequency the absorption coefficient of the ice is so strong that any light transmitted into the ice layer is absorbed. A computer program was written to compare our measurements with predic-tions calculated using equations 3-1 to 3-3. Equations 3-2 and 3-3 were slightly mod-ified to allow calculations at arbitrary angles of incidence although the correction was not very important when using our experimental value of 15 degrees. The solid lines in figure 3-6(a), (b) and (c) show the results of such calculations at 160, 210, and 229 cm - 1respectively. Optical constants for copper were calculated using the Hagen-Rubens relation (equation 1-14 with CQ = 6.6x 1 0 7 f t _ 1 m _ 1 = 6x 10 1 7sec _ 1) while those for the ice were taken from Bertie's published data for crystalline ice 3 8 . All three graphs assume an ice layer thickness which is increasing at a constant rate of 1.62\imjhour. The calculations at 160 and 210 c m - 1 clearly show a sharp minimum in intensity due to destructive interference while the ice layer is increasing in thickness. At 229 c m - 1 however, the reflected signal drops almost directly to the 26% value determined by the reflectivity of the ice-air interface. This is in agree-ment with the data shown in figure 3-5 which shows the reflectivity at 229 c m - 1 CHAPTER 3: THIN FILMS OF CONDENSED ICE l C r y s t a l l i n e Ice SneerTJIP Wave Number (cm-1) Figure 3-5 Crystalline ice spectra measured after 3.5, 4, and 4.5 hours at 165 K. remaining constant with time. The absorption coefficient which Bertie measured at this frequency is a = 3772 c m - 1 . The crosses in figures 3-6(a, b, and c) indicate the reflectance at 160, 210, and 229 c m - 1 measured over an 8.5 hour time period during which the copper mirror was held at 165 K. Reflectances were taken from spectra which were measured every half hour with each interferogram taking 5 minutes to record and giving spectra with 6 c m - 1 resolution. A comparison of two room temperature spectra measured before cooling showed deviations of less than 1% in the wave number region from 50 c m - 1 to 350 c m - 1 . During the 8.5 hours over which this experiment was performed, CHAPTER S: THIN FILMS OF CONDENSED ICE 49 the reflectance module pressure was constant at 2 x 1 0 - 4 torr but the background signal increased by a wave number independent factor of 5%. It was assumed that the signal was increasing linearly with time and the measured reflectivities were adjusted accordingly. When drawing curves such as those shown in figure 3-6 at different frequencies it became apparant that the measured signal initially changed in a way consistent with a deposition rate of approximately 1.62 ^m/hour. However, after 3 or 4 hours the ice layer thickness was no longer increasing at this rate. Since the measured reflectance module pressure was constant, a lowered sticking coefficient for water vapour striking the cold surface would be the most likely explanation. This factor could decrease because of warming of the ice surface temperature with increasing thickness. Such a temperature change could be expected since the ice layer is both a good thermal insulator and a strong absorber of thermal radiation (the emissivity is very close to 1). The intensities measured over a period of time and shown in figure 3-6 match the curves predicted using Bertie's optical constants very well. However, figure 3-6(c) shows our measured 229 c m - 1 reflectivity approaching 23% rather than the predicted value of 26%. One possible cause for this difference could be impurity in the condensed ice. The limited resolution of our spectra could also affect the measured intensity since the the optical constants are changing very rapidly in the frequency region around 229 c m - 1 . Looking at the complete spectra as shown in figure 3-5, one would expect the mixing of frequencies in the range around 229 c m - 1 could lead to a slight decrease in our measured intensity at 229 c m - 1 . Another possible consideration is non-uniformity in the ice layer thickness. From the data shown in figure 3-6 it is clear that this effect is not causing the discrepency between the measured and predicted curves. Interference effects were not important in the spectra of ice films condensed in the vitreous phase. Observations of the transition between the vitreous and CHAPTER S: THIN FILMS OF CONDENSED ICE Figure 3-6 (a) Reflectivity of a copper mirror at 165 K coated with a thin film of condensed ice. The solid curves are calculated and assume a deposition rate of 1.62 r ^ - while the crosses show the measured data. The values of n and k indicated hour were used in the calculation and are taken from measurements by Bertie88. CHAPTER 3: THIN FILMS OF CONDENSED ICE CHAPTER S: THIN FILMS OF CONDENSED ICE CHAPTER S: THIN FILMS OF CONDENSED ICE crystalline phases when warming confirmed the fact that the two types of ice have very different far-infrared optical properties. Looking back to figure 3-3(a), the continuing decrease in signal after condensing ice for 24 hours would imply that the vitreous ice has a relatively low absorption coefficient (remember that the crystalline phase absorbed almost all of the 229 c m - 1 radiation transmitted into the ice after only a few hours at low temperature). The absence of interference effects would also indicate a relatively low reflectivity at the vitreous ice-air interface. CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY C H A P T E R 4 T T F - T C N Q M O S A I C R E F L E C T I V I T Y As a final test of this reflectivity measurement technique some experiments were performed on the reflectivity of polarized far-infrared radiation from a mosaic of T T F - T C N Q crystals. This material has been studied quite extensively in the past and the far infrared spectrum is well known. Our measurements will be compared with the spectra recorded in these earlier experiments. 4.1 Mosaic Mount ing Technique The sample mount used for the mosaic measurements is shown in figure 4-1(a). It consists of a nylon ring with 14 mm inside diameter into which two copper bars are inserted. The gap between these bars is 3.2 mm and is spanned by the crystals in the mosaic. This sample mounting ring is held against the back of the copper mirror as shown in figure 4-1(b). As in earlier experiments the entire cryostat will be rotated through 180 degrees to exchange sample and reference surfaces. Special materials were chosen for construction of this sample mount. Impor-tant considerations included thermal contact between the sample and the cryostat cold finger and the thermal contraction of the sample when cooling. Thermal con-ductivity was maximized by using O F H C copper for the two bars on which the crystals are sitting. The ends of these bars are held firmly against the back of the copper reference mirror and should be in thermal equilibruim with the cold finger. CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 55 Figure 4-1 (a) Sample mounting ring, (b) Cross section showing the orientation of the sample and reference reflecting surfaces. The T T F - T C N Q crystals are held in place with a small amount of silicon heat sink grease. The second consideration was thermal contraction of the reflecting crystals. Measurements by Blessing and Coppens' 5 show that the length of a T T F - T C N Q crystal will decrease by 2.3% along the crystallographic b-axis (which is parallel to the long crystal dimension) when cooled from room temperature to 40 K. To minimize strain on the crystals the gap between the two copper bars should decrease by a similar amount. Contraction of this sample mount is determined by the thermal CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 56 properties of the mounting ring. Teflon and Nylon are both materials with thermal expansion coefficients in the required range. Our ring was machined from Nylon-101 which contracts by a factor of 2% when cooled to 40 K. The reflecting mosaic was made up of 15 T T F - T C N Q crystals with average widths of 0.5 mm and lengths of approximately 5 mm. These were placed side by side with the crystallographic b-axis perpendicular to the mounting bars to provide a reflecting surface 3 mm x 7 mm. During the first cooling cycle to liquid helium temperatures it was found that the heat sink grease holds the crystals securely to the mounting bars at all temperatures. However, when the sample mosaic was warmed up, it was found that 3 of the crystals had broken at both ends and fallen from the mosaic while many (but not all) of the others were cracked in the middle. Most of the thicker and stronger crystals survived cooling without damage. In the reflectivity measurements which were later performed using this mosaic, the 3 missing crystals were replaced with new ones and the crystals which were only cracked were left in place. This mosaic was cooled to liquid helium temperatures 3 times with no further visible damage occuring. 4-2 T T F - T C N Q Thermometer The temperature of the sample was determined by measuring the resistance of another T T F - T C N Q crystal mounted next to the reflecting mosaic. This crystal was also held in place with silicon heat sink grease and was electrically insulated from the copper mounting bars with a thin layer of G E 7031 varnish. The two electrical leads to the crystal were # 32 brass wire. Both leads were wrapped around the copper bars several times and varnished in place before being attached to the ends of the crystal with silver conducting paint. This thermometer should be in thermal equilibrium with the copper mounting bars and it should have an electrical resistivity directly related to the actual sample temperature. The thermometer CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 57 crystal was not broken or damaged during any of the four cycles cooling to liquid helium temperatures. The T T F - T C N Q thermometer was calibrated with the two thermometers provided with the Heli-Tran cryostat. One of these was mounted above the sample in the cold finger and the other was located at the bottom of the sample mount. Thermal radiation onto the sample was reduced by covering the holes in the ra-diation shield with aluminized mylar tape. Even though the thermal conductivity between the lower thermometer and the sample mount was not very good, the two calibrated thermometers would eventually stabilize at the same temperature. At this point the resistance of the T T F - T C N Q crystal was recorded. Resistance of the crystal was measured using a standard digital multimeter. The ohmmeter acts as a constant current source with the current level set internally according to the resistance range setting. By measuring the crystal resistance using various current levels it was possible to see that power dissipation in the crystal produced no significant heating. Figure 4-3 shows the resulting resistance versus temperature curve with the circles and crosses indicating the resistances measured while cooling and warming respectively. Near room-temperature the T T F - T C N Q crystal behaves in a metallic fashion with resistance decreasing as the temperature is lowered. At about 60 K a Pieirls distortion changes the material into a semicon-ductor and the resistance begins to increase dramatically. For temperatures below 50 K the resistance behaves as R = keT (4 - 1) where A is the semiconducting activation energy (half the band gap) and k is a temperature independant constant. Previous experiments with T T F - T C N Q have measured A « 225 K in agreement with the data in figure 4-2. The minimum cold finger temperature which could be obtained when calibrating the thermometer was 9.5 K although for all temperatures below 11.5 K crystal resistance was larger than CHAPTER I TTF-TCNQ MOSAIC REFLECTIVITY o nj o o T h e r m o m e t e r C a l i b r a t i o n C u r v e ~i 1 1 r 1 Figure 4-2 Thermometer resistance as a function of temperature. CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 59 the 20 Mf2 maximum resistance which could be measured using our meter. When the holes in the radiation shield were uncovered to perform reflectivity measure-ments the minimum sample temperature went up to 14.5 K. The four lowest temperature measurements in figure 4-2 are clearly displaced from the straight line predicted by equation 4-1. The most likely explanation is that thermometer was not in thermal equilibrium with the sample mount when these points were recorded. 4-3 Experimental Results The reflectivity of the T T F - T C N Q crystal mosaic was measured in the fre-quency range from 50 to 250 c m - 1 using light polarized along the crystallographic b-axis. Some of the features which have been observed in measurements by Bates and Eldridge 3 6 3 7 and by Tanner and Cummings38 are shown in figures 4-3 and 4-4. Tanner's experiments involved reflection of far-infrared radiation from a mo-saic of crystals while Eldridge used a single T T F - T C N Q crystal as the light sensing element in a liquid helium cooled bolometer. Clearly, the two methods of measure-ment have given results which disagree in the frequency region above 300 c m - 1 . These differences have an effect on the conductivity which can be calculated from the reflectivity using Kramers-Kronig relations. It is hoped that in the future the apparatus used here will also be used to determine the correct nature of the re-flectivity in this region. However, the measurements reported here are limited to a lower wavenumber region because of the transmission properties of the TPX purge window. 4-3 (a) Low Temperature Measurement. Figure 4-5 shows the far infrared reflectivity of the T T F - T C N Q mosaic at 25 K measured using the present technique. A liquid helium cooled bolometer was used CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 60 (a) fb) 1 1 r 200 400 600 800 1000 WAVE NUMBER (cm-1) 80 100 120 WAVENUMBER (cm-1) 180 Figure 4-3 (a) Far-infrared T T F - T C N Q reflectivity measured using a bolometric technique27, (b) High resolution spectrum38. The original drawing (figure 7 in reference 26) has been inverted and scaled with the data of figure 4-3(a) to give the actual reflectivity. as the far-infrared detector. Calculation of the reflectivity required four separate spectral measurements: R(T) = {SAtt(300K)/BG2{300K))' (4-2) Si(T) is the signal reflected from the mosaic at temperature Tt DG\(T) is the back-ground signal reflected from the copper mirror, S A u ( Z O O K ) is the signal reflected CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 61 Photon energy (eV) 0 0.02 0.04 0 06 0.08 1.0 03 a> o c o T> 0.8 v "ai CE 0.7 0.6 0 200 400 600 Frequency (cm1) Figure 4-4 Reflectivity of a mosaic of T T F - T C N Q crystals as a function of temperature88. from the mosaic after evaporating a layer of gold onto the surface, and BG2{300K) is the background spectrum during this second measurement. Care was taken to ensure that the optical system was not disturbed while removing the mosaic for gold evaporation. Many of the prominent features in the measurement shown in figure 4-3 and the 25 K data in figure 4-4 are also evident in the new data shown in figure 4-5. Comparison with figure 4-3(b) is especially useful. There are similar dips in the reflectivity near 86, 92, 102 and 120 c m - 1 and peaks near 123, 135, 150, 160 and 175 c m - 1 . However, in the frequency region below 80 c m - 1 the data in figure 4-5 bears very little resemblance to the earlier measurement. There is a similar minimum around 54 c m - 1 but there are two points at which the reflectivity becomes larger than 1.0 which are clearly inaccurate. The overall level of the reflectivity in figure En b • 25K • 34K o 6 0 K o I60K • 300K CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 1 1— 1 1 1 1 1 • I I i 1 I 1 1 1 ° 50 100 150 200 Wavenumber (cm-1) Figure 4-5 Measurement of the T T F - T C N Q mosaic reflectivity at 25K. 4-5 is also lower than that shown in figures 4-3 and 4-4. Both Eldridge and Tanner recorded reflectivities above 80% over this entire wavenumber region while here we see a reflectivity as low as 72%. Most of the error in this measurement was probably caused by inaccurate can-cellation of the mosaic diffraction effects. Figure 4-6 shows the reflectivity spectrum of the mosaic at room-temperature before and after gold plating. The minimum at 70 c m - 1 seems to correspond with one of the low wavenumber maxima in the final spectrum shown in figure 4-5. Incomplete cancellation of such diffraction peaks may CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY be caused by some rearrangement of the mosaic reflecting surface at low temper-ature. Clearly, such changes in the reflecting surface could also effect the overall intensity of the reflected light. 0 5 0 1 0 0 1 5 0 2 0 0 Wavenumber (cm ) Figure 4-6 Room-temperature reflectivity of the mosaic before and after gold plating. Two separate effects could be leading to this temperature dependance of the mosaic scattering. The first is thermal contraction of the cryostat. Cooling the sample to liquid helium temperatures moves the position of the sample mosaic up about 0.5 mm. This means that the far infrared beam reflects from a different part CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 64 of the sample mosaic when the temperature is lowered. By direct visual observa-tion it was possible to ensure that the infrared light beam was focused within the sample mosaic boundaries at all temperatures. For a mosaic without large defects the changes in the spectrum due to this movement should be negligable because the displacement is parallel to the long crystal axis. However, since our mosaic included many crystals which were cracked in the middle it is possible that the mosaic movement may have introduced a significant error in these measurements. The second possible temperature dependent effect is rearrangement of the mosaic due to thermal contractions of the crystals themselves. It is thought that these movements caused some sudden jumps in the reflected signal intensity which were observed when the sample temperature was rapidly raised or lowered. The discontinuities could be as large as 10% of the signal strength. These jumps were not seen if the temperature was changed slowly. As mentioned earlier, after cooling the sample to liquid helium temperatures 3 times there was no visible damage to the mosaic. It was hoped that these sources of error could be eliminated by measuring the reflectivity of the gold plated mosaic as a function of temperature. This procedure could not be used because the gold layer made each crystal into a bimetallic strip which bent when the temperature was changed. Bending of the gold plated crystals could be observed visually and led to a 30% decrease in measured far infrared signal when the gold plated mosaic temperature was lowered from room temperature to 80 K. The effects which these distortions have on the mosaic reflectivity spectrum are illustrated in figure 4-7. This plot shows the reflectivity of the gold plated mosaic at 80 K and at room temperature. Diffraction effects are a little bit different in the low temperature spectrum and the attenuation of the signal increases slightly at lower wave numbers. It is possible that the differences seen in the low temperature gold plated mosaic spectrum illustrate the spectral changes which could occur to a lesser extent when the temperature of the uncoated T T F - T C N Q mosaic changes. CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 65 Because the entire mosaic was heated during the gold evaporation process, it is possible that the reflecting surface was already slightly distorted when cooled to room temperature. Any change in the spectrum due to this effect was probably small compared to the change in the spectrum due to rearrangement of the clean crystal mosaic when it was cooled from room temperature to liquid helium temperatures. All the measured T T F - T C N Q reflectivities were ratioed with the gold plated mosaic reflectivity measured at room temperature. Figure 4-7 Reflectivity of the gold plated mosaic at room temperature and at 80K. CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY One way to reduce the errors in the measurement of the mosaic reflectivity would be to minimize the possibility of temperature-dependent distortions in the original crystal mosaic. Improvements could be made by replacing those weaker crystals which were broken in the middle with thicker ones capable of withstanding the stresses introduced when cooling. Using only uncracked crystals would also reduce any error which could be introduced by thermal contraction of the cryostat. 4-3(b) Temperature Dependent Results Spectra recorded at sample temperatures of 295, 160 and 60 K are shown in figure 4-8. These measurements can be compared with those of Tanner and Cummings which were reproduced in figure 4-5. There are significant differences which could be caused by the factors outlined in the last section. One can still see some similarities between the two sets of data. The room temperature reflectivities have comparable magnitudes and in both cases the reflectivity begins by increasing as the temperature is lowered. This increase is expected since the crystals are behaving metallically in this temperature region. The large peaks at 40 and 60 c m - 1 in the 60 K spectrum are also seen at 35 and 25 K and are most likely caused by incomplete cancellation of the diffraction characteristics of the sample mosaic at low temperature as already mentioned. The 35 K spectrum is shown in figure 4-9. Most of the features which were seen in the 25 K data are still present here. As expected, the minimum at 100 c m - 1 lost some of its strength with the increase in temperature. 4-4 Conclusions These preliminary measurements show that this technique for measuring the reflectivity of crystal mosaics will be sensitive enough to detect much of the fine structure which is present in the far infrared spectra of the highly reflecting organic conductors. However, the absolute reflectivities which have been derived in these CHAPTER 4: TTF-TCNQ MOSAIC REFLECTIVITY 1 1 1 1 1 measurements are clearly not reliable. At this point it is not known if better sample mounting techniques will allow more accurate measurements to be obtained. The next mosaic should be made using thicker crystals which are strong enough to withstand the effects of cooling without cracking. Another improvement would be to construct the mosaic using fewer crystals with wider reflecting surfaces to help minimize the effects of light scattering and diffraction. BIBLIOGRAPHY B I B L I O G R A P H Y [1] A . A . Michelson, a Light Waves and Their Uses." Univ. Chicago Press, Chicago, 1912. [2] A . A . Michelson, Phil Mag. Ser. 5, 3 1 , 338 (1891). [3] H . Rubens and R.W. Wood, Phil Mag., 2 1 , 249 (1911) [4] R.J. Bell, u Introductory Fourier Transform Spectroscopy." Academic Press, New York, 1972. [5] K . J . Button (editor) " Infrared and Millimeter Waves." Vol 8, (Chpt. 1), Academic Press, New York, 1983. [6] J.R. Reitz, F.J . Milford, and R.W. Christy, " Foundations of Electromagnetic Theory." Addison-Wesley Pub. Co., London, 1979. [7] J .E. Eldridge, Phys. Ref. B, 3 1 , 5465 (1981). [8] C. Kittel, a Introduction to Solid State Physics." Whiley and Sons, New York, 1976. [9] W . A . Little, Phys. Ref. A, 1 3 4 , 1416 (1964). [10] K. Bechgaard and D . Jerome, Sci. Am., 2 4 7 , 50 (July 1982). [11] R.E . Peierls, * Quantum Theory of Solids." Oxford University Press, London, 1955. [12] H . K . Ng, Ph.D. Thesis (unpublished), McMaster University (1984). [13] H . K . Ng, T . Timusk, and K . Bechgaard, J . Phys. Colloq. C3 (Les Arcs), 4 4 , 867 (1983). [14] C S . Jacobsen, Ph.D. Thesis (unpublished), Technical University of Denmark (1975). [15] D.B. Tanner, C S . Jacobsen, A . F . Garito, and A . J . Heeger, Phys. Ref. B, 1 3 , 3381 (1976). BIBLIOGRAPHY W . A . Challener, Ph.D. Thesis (unpublished), University of California at Berke-ley (1983). W . A . Challener, D . L . Richards, and R . L . Green, Solid State Comm., 51, 765 (1984). B e c k m a n - R H C IR-720M Far Infrared Spectrometer Instruction Manual (1975). J . A . B . Beairsto and J . E . Eldridge, Canadian Journal of Physics, 51, 2550, 1973. A i r Products H e l i - T r a n Model LT-3-110 Liquid Transfer Refrigeration System Technical Manual (1984). P . V . Hobbs, ° Ice Physics." Clarendon Press, Oxford, 1974. J . E . Bertie and E . Whalley, J . Chem. Phys., 46, 1271,(1967). J . E . Bertie, H . J . Labbe, and E . Whalley, J . Chem. Phys., 50, 4501 (1969). M . Born and E . Wolf, " Principles of Optics ." Permagon Press, London, 1970. R . H . Blessing and P. Coppens, Solid State Commun., 15, 215 (1974). F . E . Bates and J . E . Eldridge, C a n . J . Phys., 59, 339 (1981). J . E . Eldridge, Phys. Ref. B, 31, 5465 (1985). D . B . Tanner and K . D . Cummings, Phys. Rev. Lett., 47, 597 (1981). 

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