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Design of Resistivity Instrumentation for a He

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1. V This means that cool down measurements are very untrustworthy while for warm up measurements this is a very minimal contribution to measurement signal disturbance 2 2 5 Electromagnetic Noise The environment has many sources of magnetic fields electric fields and electromagnetic fields Radio frequency RF noise is naturally present in the environment and is easiest to reduce RF noise comes from space man made sources for telecommunication as well as from undesired radiation sources such as paired signal lines that have bends termina tions or discontinuities 16 These sources that are present in the environment present a source of noise in the lab by absorption into signal transmission lines that are not properly shielded RF noise can be effectively removed from the system by wrapping 4The rate of cooling is greatest below the Leidenfrost point because there is no insulating vapor blanket 17 2 2 MEASUREMENT NOISE CHAPTER 2 INSTRUMENTATION all of the signal lines used with a conductor that is grounded This grounded shield prevents signals entering the system by acting as a reflector and Faraday cage This blocks both RF signals and electrostatic fields A coaxial cable is a typical example of the implementation of this idea and is used in this resistivity measurement system Magnetic noise however is more difficult to block Slowly varying magnetic fields such as those from an AC power distribution the
2. 2 2 3 Nyquist Noise Nyquist noise discovered by Johnson in 1928 12 is noise that arises in a circuit due to charge carriers in thermal equilibrium which are in a state of permanent thermal agitation 13 Nyquist noise is voltage fluctuations that occur on average uniformly over the whole frequency spectrum called white noise 13 The equation is given by Vnus VAkgTRAf 2 5 3The spectral density of Nyquist noise is constant up to the angular frequency corresponding with the correlation time 101 571 see bibliography entry 13 15 2 2 MEASUREMENT NOISE CHAPTER 2 INSTRUMENTATION Where Vrms is the RMS noise of the voltage in the conductor in the frequency band width Af R is the resistance in ohms T is the temperature in Kelvin and kg is the Boltzmann constant 14 We are interested in making DC measurements and ideally the bandwidth is zero but no DC measurement is purely DC since there is always a time range of measurement which sets the bandwidth Therefore the noise that arises in the measurement from Nyquist noise is unavoidable at some level since the measurement is always carried out at finite temperature This means that the measurement leads and the material that is being measured are likely to contribute the most Nyquist noise 2 2 4 Thermoelectric Effects Thermoelectric generation effects occur when there is a temperature difference across two contacts in a circuit that are made of different co
3. RAB pDC4 TRAD BC4 e P e e 1 2 1 Where p is the resistivity of the material and d is the thickness There is practical further improvement to this measurement By reversing the current in each configuration and taking the average of each any DC offset present in the system can be canceled out Taking the averages for the resistances in their respective configurations HAB pc RBA DC Rhorz m 2 Rap oc RpA Bc 2 Rarer Gives us a more reliable value for those resistances Equation 2 1 becomes Rhorzl TRyertd e r e e l 2 2 A Hall effect measurement using the setup to be described can be done by applying current on A C and measuring the voltage change on D B as a uniform magnetic field is applied perpendicularly to the surface and then reversed in direction 11 d AVpg 2 METTRE 253 Where Ry is the Hall coefficient and B is the magnitude of the magnetic field lnot to be confused with the subscript B which represents the contact across which the voltage is being measured 12 2 2 MEASUREMENT NOISE CHAPTER 2 INSTRUMENTATION 2 2 Measurement Noise There were many different sources of noise that entered the system before it was im proved Noise levels prevent accurate measurements Noise can drown out important characteristics in data reduce resolution and prevent valuable measurements of very low resistance materials In the work carried out for this thesis sour
4. Earth or a vibrating ferromagnetic mate rial will penetrate Faraday cages A straight transmission pair will have a gap between the conductors and if a varying magnetic field is present the flux through that area will induce a voltage One solution to this problem is to surround the signal lines with a high permeability material to redirect the field lines away from the signal lines an example product being MuMetal 17 The magnetic field does not need to be zero inside this region there is an alternative solution Consider a transmission line that consists of two twisted wires as shown in Figure 2 3 a If we assume the source of the varying magnetic field to be sufficiently far so that the field is almost uniform around the twisted pair and the twists to be approximately the same spacing then for any direction of the magnetic field the flux in each twist will be equal and opposite to adjacent ones This will cause an EMF to be induced in equal yet opposite directions and therefore cancel out shown in Figure 2 3 b Cables using twisted pairs inside a braided metal sleeve that is grounded remove most of both RF and slowly varying magnetic fields This is implemented everywhere possible in the resistivity system that was designed for this thesis work 5Referring to power for buildings in north America 120Vgms at 60Hz 18 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION gt 4 a th gt gt
5. Magneto optical of acu 13 5 RSE es m 56 A Pressure Induced Noise 58 B GPIB Communication 62 C Program Interface 65 lv Glossary AC API BCS CDW DC EMF GPIB IC SIP MPMS RF RMS SC SQUID VDP Alternating Current Application Programming Interface J Bardeen L N Cooper and J R Schrieffer Theory of Superconductivitiy Charge Density Wave s Direct Current Electromotive force General Purpose Interface Bus specified by the IEEE 488 standard Integrated Circuit Single Inline Package Quantum Design Magnetic Property Measurement System Radio frequncy specifically electromagnetic waves in the radio spectrum Root Mean Squared Superconductivity Superconducting Quantum Interference Device Van der Pauw List of Figures 1 1 1 2 1 3 The phase diagram of Cu TiSez Shows as doping of copper increases CDW disappears in favor of SC states Note that there is a region of coexistence The inset is the crystal lattice of Cu TiSez Reproduced Crystal structure of 17 TiSez a Cross sectional view of the lattice layers showing relative positions Layers X and X are chalcogen atoms and M is the transition metal b Octahedral form of the 1T phase of the lattice where the chalcogen is Selenium and the metal is Titanium Reproduced Joint density of states in 2D momentum space of the two dimensional superconducting T 2 3K CDW Tcpw 65K material 2H Na TaSs in the CDW state The CDWs are situated on t
6. gt Eo Sample Thickness mm E 5 38 06 Sample2 Thickness 0 992 nm y Es A E 2 7E 06 TN Y lis Ni Average over dT 01 k y 3 997 20003000 4000 50006000 7000 8000 900010000 Elapsed Seconds IV Measure Sample 1 Port E e a 788 Measure Sample 2 Port 4 Hd U sie Record Charcoal Resistance M MeasPrssr s 428 w 338 M t Setti ly i58 Measurement Settin de de n 67 9 C Van der Pauw Resistivity 22 1 G Quick A 3 997 2000 3000 4000 5000 6000 7000 8000 900010000 ick Res Elapsed Seconds ct 296 m m 296 295 295 5 295 8294 m 234 294 3293 g 293 Sore Jk i a o E n 3 997 2000 3000 4000 5000 6000 7000 8000 9000 10000 m S Elapsed Seconds Ran Messuenen E m System Idle Figure C 1 A screen shot of the resistivity measurement system program main form Right Panel is the graphing area upper left panel is the experiment param eters and lower left is the type of measurement to perform problem A debugging form was programmed to discover where the source of problems may be located It shows see Figure C 2 the circuit diagram of the circuit constructed in the HP 34903A switch card showing the current state of each relay there within The cross settings buttons configure a Hall effect configuration but also can debug improper configuration of the contacts on the sample Checking the voltage reading when current is on vs off makes a very quick determination of whether a contact has broken or
7. in the old measurement system from liquid ni trogen temperatures b Results in the new resistivity measurement system from liquid He temperatures Inset shows a 20 order polynomial baseline fit showing a CDW transition of 166 K 50 6 Conclusions A resistivity measurement system was constructed and interfaced in a user friendly man ner to perform low noise resistivity measurements The noise on the voltage measure ments was reduced from 15 nVrys to 4 5 nVrys This noise reduction was crucial for the determination of the CDW transition for low doped Cu TiSez samples Sample 1 was determined to have a CDW transition at 162K by the resistivity mea surement and a transition temperature of 125K by the field dependent magnetization MPMS measurement see Figure 6 1 The determination of the CDW transition temperature by resistivity was done by a high order 8 20 order polynomial base line fit which revealed the discontinuity in the data and is assumed to be the CDW transition point The determination of the transition temperature through the resistivity measurement in the old resistivity mea surement system was not possible due to the noise washing out the features The values for the CDW transition are not similar but it is noted that the magnetization data was being compared to polycrystalline samples The SC transition temperature measure ment showed a wide transition which may have been due to doping inhomogeneity The 51
8. selected from a crystal growth carried out by Artorix de la Cruz de Ona at Brock University The dopings of the samples were not known In order to test the resistivity system that was constructed a set of DC magnetic suscep tibility measurements were done on these samples to characterize their superconducting transition temperatures These measurements were conducted in a Quantum Design Inc Magnetic Property Measurement System MPMS The MPMS measures the sus ceptibility by applying a field then physically transporting the sample through a set of counter wound coils which pick up the change in induction measured with a SQUID The magnetic susceptibility is then calculated based on the EMF measured and cor rected by a correlation table 34 The temperature range of the MPMS is 1 9K 400K 34 The sample was placed in a plastic capsule with some vacuum grease to prevent the sample from moving while being transported in the MPMS and oriented such that the a b plane was parallel to the H field Measurements were compared to results from E Moroson et al 5 to determine the doping concentration x A temperature dependent measurement was conducted at 0 5T field strength from 300 K to 1 8 K on sample 1 37 CHAPTER 4 MAGNETIC PROPERTIES OF CUx TISE shown in Figure 4 1 In Figure 4 1 a it can be seen that at high temperature the susceptibility is positive and then as temperature decreases drops at a certain temperature This temperatu
9. showed 23 by taking the relaxation The isotope effect is the change in the SC transition temperature based on the mass of the isotope of superconducting material T x M 26 29 3 1 SUPERCONDUCTIVITY CHAPTER 3 THEORY time to be infinite in the Drude model of conductivity that E AJ 3 1 where A is defined as jg m Sy 3 2 C Ne 3 2 Here A is called the London penetration depth n is the density of superconducting electrons e is the charge of the carrier and m is the mass of the charge carrier Equation 3 1 shows that for steady current the electric field is zero This is what we expect for superconductivity In the same paper London showed H V x AJ 3 3 If we substitute 3 1 into 3 3 we obtain 3 4 A particular solution to 3 4 is for an infinite flat slab superconductor in the YZ plane where the superconductor exists everywhere x gt 0 and a magnetic field strength of H exists everywhere outside the sample The magnetic field inside the superconductor is then given 27 as gt H x Hye which makes it clear why A is described as the penetration depth since it describes the 30 3 1 SUPERCONDUCTIVITY CHAPTER 3 THEORY penetration of a magnetic field into the superconductor An important result follows for a flat slab of thickness d it can be shown that 25 when d gt X the susceptibility becomes H M gb 3 5 This perfect diamagnetism in superconduct
10. the resistivity data while the sudden increase introduced by the second order phase transition wouldn t be fitted sufficiently If we call the polynomial fit to the resistivity data above the SC transition of nt order Pt order and the data experiment then the base line fit is defined as Poin T Pexperiment T nth gilt 5 1 The base line fit given by equation 5 1 can show the sudden spike that marks the CDW phase transition Taking the second derivative of the data would also reveal the CDW transition temperature but the noise in the measurement prevented this method from clearly showing the feature in the second derivative shown in Figure 5 2 Plots of the base line fits for 7 10 order are shown in Figure 5 3 There is a clear common bump in all orders around 162K Assuming that other bumps that are not common between the orders are just continuous smooth portions of the data that are not fitted properly we can assume this is the sudden onset that we have been looking for which is the transition temperature to the CDW state However this value doesn t appear to correspond to the value obtained by magnetic susceptibility Discrepancy could be explained by the fact that E Morosan et al 5 used a different method of identifying the CDW transition temperature Notice that the noise is quite 45 CHAPTER 5 DC TRANSPORT PROPERTIES OF CU x TISE 0 45 0 40 0 33 d Resistivity dT yOhm cm K 0 30 50 10
11. with the data shown in Figure 5 1 a the doping of Sample 1 appears to be in the range of x 0 055 to about x 0 065 Temperatures utilizing the He system on the cryostat Rate of change of temperature with time 43 CHAPTER 5 DC TRANSPORT PROPERTIES OF CU x TISE a re w x 0 015 E ome o 0 049 00 c 0 025 9 m 0 01 F a 0 055 E f d a e gt 0 065 2 4 p H 0 080 gu H WU oum Hi 0110 0 2 dp 8 10 1E 3 4 0 45 0 40 Resistivity mOhm cm 50 100 150 200 250 Temperature K Figure 5 1 Temperature dependence of the resistivity in Cu TiSez a Results for dif ferent dopings on single crystal samples in the a b plane reproduced from 8 b Resistivity of Sample 1 measured in the new resistivity system Shows a CDW transition temperature of 162K The dotted line is a power law forced fit that emphasizes the CDW bump CHAPTER 5 DC TRANSPORT PROPERTIES OF CU x TISE The beginning of the bump signifies the onset of the CDW state However the start of this bump is very hard to observe for a weak CDW state Theory suggests that the onset of CDW must be quite sudden since the gap suddenly forms at the transition temperature No function is known to fit to the resistivity data A polynomial of infinite order theoretically would fit the curve exactly but for lower orders the polynomial will fit the smooth parts of
12. 0 150 200 250 Temperature K 0 25 Resistivity mOhm cm 0 20 d Resistivity dT nOhm cm T 0 15 50 100 150 200 250 Temperature K 50 100 150 200 250 Temperature K Figure 5 2 Resistivity of Sample 1 The top left inset shows the first derivative of the data The bottom right inset shows the second derivative of the data The CDW feature is not visible beyond the first derivative 46 CHAPTER 5 DC TRANSPORT PROPERTIES OF CU x TISE Pbl 7 nOhm cm 2 0 50 100 150 200 250 300 Pol 10 nOhm cm 2 l 0 50 100 150 200 250 300 Pb1 20 nOhm cm e 0 50 100 150 200 250 300 Temperature K Figure 5 3 Polynomial baseline fit on resistivity data for Sample 1 There is a clear common dip at 161K which could be the CDW transition a Seventh order b Tenth order c 20 order 47 CHAPTER 5 DC TRANSPORT PROPERTIES OF CU x TISE significant in the base line fit Veras values in the new measurement system on this sample were around 4 5 nV rms In the old system a measurement was taken on the same sample where the results didn t produce anything that could confidently be extrapolated for the CDW due to noise wash out shown in Figure 5 4 Pol 10 nohm cm E 3 E o E o ri B a 100 150 200 250 Temperature K 0 50 100 150 200 250 300 Temperature K Figure 5 4 Tenth order polynomial baseline fit on resistivity data measured on old resistivity system f
13. 0 mm along its length oriented horizontally in the figure 4 1mm along its width oriented vertically in the figure and 0 344mm in thickness 1 2 SAMPLE PREPARATION CHAPTER 1 INTRODUCTION Figure 1 5 Photograph of Sample 2 taken under a microscope The background was erased to show the boundaries of the crystal clearly Four gold wire silver paint contacts are on the perimeter of the sample Largest dimensions of the sample are 6 9 mm along its length oriented horizontally in the figure 3 0mm along its width oriented vertically in the figure and 0 700mm in thickness 2 Instrumentation A resistivity measurement system was greatly improved upon and further developed in order to conduct more accurate and reliable measurements The original set up consisted of nano volt meter nano current source actuator switch connected into the cryostat through various connection boxes where the instruments were controlled with GPIB IEEE488 through a macro for the MPMS MultiVu program The distribution box for connections into the cryostat was made by Infrared Labs An input line was used for setup conditions and data was recorded to a file which MultiVu reported This original resistivity instrumentation produced noisy results due to the system being unshielded and cluttered by redundant and insecure connections The software implementation was also crude and gave little information to the details of the measurement and no chance of diag
14. 60 120 A 0 0 02 0 04 0 06 0 08 0 10 xin Cu TiSe Figure 1 1 The phase diagram of Cu TiSez Shows as doping of copper increases CDW disappears in favor of SC states Note that there is a region of coexistence The inset is the crystal lattice of Cu TiSez Reproduced from 5 1 1 CRYSTAL STRUCTURE OF CU x TISE CHAPTER 1 INTRODUCTION 1 1 Crystal structure of Cu TiSe The undoped crystal structure of TiSez belongs to a group of materials called chalco genides with the generic formula MT M is a transition metal and T is a chalcogen anion S Se or Te They usually have one of two crystal structures designated either 1T or 2H phase 8 Chalcogenides are layered compounds where the layers are held together by van der Waals forces In the 1T phase the Ti atoms are in octahedral coordination with Se shown in Figure 1 2 b to produce a trigonal octahedral crystal shown in inset of Figure 1 1 The layers X and X are the chalcogens and M is the transition metal The layers X and X are two dimensional hexagonal lattices where the X layer is parallel and rotated 60 degrees relative to the X layer In the 2H phase the layers are stacked using notation from Figure 1 2 X MX XMX instead of X MX X MX producing a trigonal prismatic structure TiSes takes on the 1T phase It is between the layers the area held together by the van der Waals force that the copper dopant is intercalated causing expansion of the unit cell
15. 6K To 2 5K Doping Factor x 0 055 0 06 0 015 0 025 Table 6 2 Results for Sample 2 must be used to determine the true orientation The SC transition measurement may also have given an incorrect value for the doping since the transition temperature does not change linearly with doping 5 These measurements demonstrate that the reduction in noise of the new resistivity measurement system has made the determination of crucial material properties possible which would have been either inaccurate or impossible using the previous resistivity measurement system 54 Future Research Directions There are two directions for the future of this research In the instrumentation intro duction of a source of uniform magnetic field into the cryostat would make possible the measurements of the Hall effect using van der Pauw method This measurement would be able to detect the CDW transition that occurs in Cu x TiSes since it can measure the change in the dominant carrier type 8 An additional 32 pin plug could be installed on the cryostat to make possible more sample measurements simultaneously to conserve liquid helium It takes roughly 25L of liquid helium to produce one cool down to low temperatures The old resistivity measurement system would cost roughly of 500 per could be measured measurement With another 32 pin plug up to eight samples simultaneously making a measurement on a single sample cost only 60
16. CHAPTER 6 CONCLUSIONS 4x10 H 5000 Oe 3x10 2x10 1x10 Susceptibility emu Oe mol Ti 5 1x10 0 50 100 150 200 250 300 Temperature K Figure 6 1 Temperature dependence of the magnetic susceptibility in Cu TiSes for a field strength of 0 5T for Sample 1 Absolute value was shifted down due to diamagnetic contribution from the capsule and grease used to hold the sample Shows the CDW transition temperature at 120 K and identifies the CDW transition temperature as identified by the resistivity measure ments at 162 K There is a small feature around 162 K see inset for expanded view which might identify as the CDW transition temperature if the measurement was conducted with more resolution in that region 52 CHAPTER 6 CONCLUSIONS base line fit method might have also skewed the results since the dip may not have corresponded to a discontinuity in the resistivity but may have been the result of mea surement fluctuations or fluctuations in the polynomial fit Other bumps in the base line fit may have corresponded to other CDW transitions due to regions of different doping in the sample Comparing the estimations for the doping Sample 1 was determined to be between x 0 055 to x 0 065 with resistivity between x 0 06 and x 0 08 by the small field magnetization measurement detecting the SC transition and between x 0 03 and x 0 05 for the high field magnetization measurement Again it appears that the hig
17. COCOCOQO Figure 2 3 a Two insulated conductors twisted together to form a twisted pair signal line The arrows indicate an example for the direction of the current b shows how the twists create spaces of opposite vector areas such that the in duction in one twist is canceled out by the next for a magnetic field spatially uniform in that region Reproduced from 18 2 3 Design and Method The instrument design consisted of three basic components The sample was mounted on a holder inside the Infrared Labs HDL 10 He cryostat The connections led to a 32 pin connector that in turn led to the distribution box where the instruments were connected The information from the instruments was then read through IEEE 488 known as GPIB communication to the computer where the data was collected in the resistivity program 19 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION 2 3 1 The Cryostat The cryostat is where the sample resides and which provides an environment that can potentially reach temperatures of 0 4 degrees Kelvin The sample holder is mounted on either the bolometer stage or sample stage see Figure 2 4 Spare connections inside the cryostat were utilized for resistivity connections by installing 6 pin IC SIP plugs Once the sample holder is mounted and plugged in the cryostat is sealed and evacuated to pressures on the order of 1 1076 Torr Thermal radiation shielding is maintained by filling the shield vessel nitrogen
18. Design of Resistivity Instrumentation for a He Cryostat and its Application to the Charge Density Wave Superconductor Cu TiSe by Jason Iwachow B Sc University of Waterloo 2011 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE The Faculty of Mathematics and Sciences Department of Physics 0 BROCK UNIVERSITY January 21 2014 2014 Jason Iwachow Abstract Fermi patches in quasi two dimensional charge density waves CDW have not described the connection to superconductivity SC according to theory adequately at this point in time The connection between CDW and SC in the quasi two dimensional material Cu TiSez is an interesting one which might reveal mechanisms in unconventional super conductors A previous Brock graduate student grew crystals of Cu TiSez The precise doping of the samples was not known In order to determine the doping parameter x in Cu TiSes a sensitive resistivity measurement system was necessary A new resistivity measurement system was designed and implemented utilizing an Infrared Labs HDL 10 He cryostat By comparing with data from the literature doping of two samples was investigated using the new measurement system and a Quantum Design Magnetic Prop erty Measurement System MPMS Methods for determining the doping revealed that the old resistivity system would not be able to determine the CDW transition temper ature of highly doped sam
19. Experimentaland Theoretical Study of the Relation between Magnetic Field and Current in a Superconductor Proceedings of the Royal Society A 216 1127 547 568 1953 25 M Tinkham Introduction to Superconductivity Second Edition McGraw Hill Inc 1996 26 Charles P Poole Jr Handbook of Superconductivity Academic Press 2000 E 27 Harold T Stokes Solid State Physics Allyn and Bacon Inc 1987 Y 71 Bibliography Bibliography 28 29 30 31 32 33 34 ee 35 36 37 James F Annett Superconductivity Superfluids and Condensates Oxford Univer sity Press 2004 L N Bulaevskii Inhomogeneous state and the anisotropy of the upper layer critical field in layered superconductors with josephson layer interaction Sov Phys JETP 38 634 1974 Elisabeth J Nicol Pair Breaking in Superconductivity McMaster University 1991 P Flude Cooper Pair Breaking Mod Phys Lett B 24 26 2601 2624 2010 Neil W Ashcroft N David Mermin Solid State Physics Brookes Cole 1976 W Kohn Image of the Fermi Surface in the Vibration Spectrum of a Metal Phys Rev Lett 2 393 1959 Mike McElfresh Fundamental of Magnetism and Magnetic Measurements Featuring Quantum Designs Magnetic Property Measurement System Quantum Design Inc 1994 Li G et al Anomalous Metallic State of Cu0 07TiSe2 An Optical Spectroscopy Study Phys Rev Lett 99 167002 2007 R C Morris Co
20. H Na TaS in the CDW state The CDWs are situated on the high density patches in three directions Q4 Q and Qs Reproduced from 6 1 2 SAMPLE PREPARATION CHAPTER 1 INTRODUCTION checking the plane which is easiest to cleave This will be parallel to the a b plane 1 2 Sample Preparation Batches of single Cu TiSes crystals were grown by Artorix de la Cruz de Ona at Brock University using the iodine vapour transport method as described by Wu et al 8 Large crystals were selected to be able to conduct measurements easily and for future optical spectroscopy research that yields stronger signals for larger reflective sample surfaces Two large single crystal samples were selected to be measured Sample 1 was the largest out of these and is shown in Figure 1 4 Sample 2 is elongated and shows the silver paint contacts to be quite close to each other on either end of the sample as seen in Figure 1 5 Both Figures 1 4 and 1 5 show the silver paint contacts for resistivity measurement whose dimensions can be seen to be a significant fraction of the distance between contacts The consequences of this will be discussed later in section 2 2 1 1 2 SAMPLE PREPARATION CHAPTER 1 INTRODUCTION Figure 1 4 Photograph of Sample 1 taken under a microscope The background was erased to show the boundaries of the crystal clearly Four gold wire silver paint contacts are on the perimeter of the sample Largest dimensions of the sample are 6
21. L J van der Pauw A Method of Measuring The Resistivity and Hall Effect on Lamellae of Arbitrary Shape Philips Res Repts 20 220 224 1958 12 J B Johnson Thermal Agitation of Electricity in Conductors Phys Rev 32 97 1928 13 esi No lle Pottier Nonequilibrium Statistical Physics Linear Irreversible Processes Oxford University Press New York 2010 14 H Nyquist Thermal Agitation of Electric Charge in Conductors Phys Rev 32 110 1928 15 Cd Supriyo Data Lessons from Nanoelectronics A New Prospective on Transport World Scientific 2012 16 Constantine A Balanis Antenna Theory Second Edition Wiley Sheel Print N Pack Noida India 2009 70 Bibliography Bibliography 17 Magnetic Shield Corp Fabrication with MuMetal Brochure 2012 18 Jason Iwachow 1 F Noise in Josephson Junctions Undergraduate Thesis Univer sity of Waterloo January 17 2011 19 HDL 10 Cryostat IR Labs 1995 20 David J Griffiths Introduction to Electrodynamics Third Edition Pearson Addi son Wesley Prentice Hall Inc 1999 21 pen Charles Kittel Introduction to Solid State Physics Eighth Edition Wiley 2005 22 feet HP 34420A Nano Volt Micro Ohm Meter User s Guide Hewlett Packard Printed in the USA 1994 23 F London H London The Electromagnetic Equations of the Supraconductor Proceedings of the Royal Society A 149 866 71 1935 24 A B Pippard An
22. MPMS cali bration measurements should be done on the thermal grease to check if its calibration was distorted over time or if the grease changed To detect the transition temperature more accurately X ray diffraction measurements for a single crystal to determine precisely its orientation would improve the results of Limited to the space available on the sample and bolometer stages 95 7 1 MAGNETO OPTICAL CHAPTER 7 FUTURE RESEARCH DIRECTIONS any measurement CDW is a quasi two dimensional phenomena in Cux TiSe therefore any measurement of values which are directionally dependent would be affected Optical measurements on Cuy TiSez could also be performed in the same cryostat Optical con ductivity shows two peaks in the frequency spectrum one for a resonance that follows a Drude Lorentz model and another peak that characterizes the single particle excitations at the energy of the gap 35 3 The CDW transition temperature would be easier to detect by checking for their characteristic peaks 7 1 Magneto optical During this thesis work an interesting phenomena presented itself R C Morris dis covered 36 that in the superconducting material NbSez the 2D CDW state can be suppressed by applying a field parallel to the c direction while at the same time SC is enhanced New evidence from D W Shen et al 6 shows that 2D CDW materials may have multiple 1D CDW vectors It would be interesting to investigate the pair break
23. P resistivity measurement plugs see Figure 2 4 voltage pins were shorted and pressure dependent measurements were taken reading the shorted plugs Voltage spikes were observed when pressure was increased or decreased Figure A 3 A possible explanation for this phenomenon is that the current carrying wires are in the same bundle with the voltage signal wires inside the cryostat Pressure or temperature will cause a slight expansion or compression of these wires relative to each other which could induce an electromotive force EMF This agrees with the spikes in Figure A 3 59 APPENDIX A PRESSURE INDUCED NOISE 36 34 gt o T 32 o Oo S E 30 28 0 10 20 30 40 Time 10 s Figure A 2 Room temperature 295 K voltage measurement on a steel disk in the current resistivity measurement system At 1150s into the measurement the vacuum pump was turned on since the EMF would be opposite in sign for expansion compression as well as for the fact that the spike for removing vacuum is larger than in evacuating since the pressure change is faster when removing the vacuum line to vent to atmospheric pressure The voltage on the steel disk Figure A 2 doesn t drop back to the value before evacuating as in the shorted case possibly due to capacitive effects in the instrument setup This source of noise can be largely eliminated by evacuating first and maintaining low pressure while measuring as well as utilizing the quasi st
24. SAMPLE HOLDER FOR FSP Ca nant OPTICAL MEASUREMENTS j SS Y X He3 HOUSING SAMPLE STAGE CHARCOAL PUMP 12 DEGREES Figure 2 4 The schematic of the Infrared Labs HDL 10 He cryostat Modified from 19 Sample holder was mounted on the bolometer stage 21 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION condensed He Temperature is not maintained at any point other than at the boiling points of N and Het Temperature dependent data is taken by letting the system warm up at its own pace With the system evacuated and the thermal shield vessel depleted typical warm up times from 4 K to 300 K are on the order of 72 hours 2 3 2 Sample holder The sample holder was constructed to make mounting of samples easily interchangeable Figure 2 5 shows one empty sample holder Samples are either glued with GC varnish epoxy or double sided tape into positions A and C Gold wire is soldered to the copper wires around those positions and the other end is made into a contact on the sample using silver paint Copper wires around the sample positions are placed so that orientation of the contacts is unambiguous In the center at position B there is a Lakeshore DT 670 silicon diode temperature sensor mounted to measure temperature for temperatures between 1 4 K 500 K There are three temperature sensors built into the cryostat Two sensors at the sample stage a B sensor for high temperature and an A sensor for low temperature
25. Temperature dependence of the gap function Reproduced from 25 The energy of the zero temperature gap in BCS theory can be determined by the equation 28 2A 0 3 52kgT 3 6 where kg is the Boltzmann constant The principle which the magnetic field breaks the pair or sufficiently high current to generate a field to break the pairs is when the landau splitting causes high enough energy to reach the gap energy orbital vortex pair breaking 29 or Zeeman splitting when the field is strong enough to split the energies sufficiently to exceed the gap energy pauli pair breaking 30 31 So when measuring the SC transition temperature it is important to use low fields and currents to prevent the Cooper pairs from breaking The Meissner effect is utilized to find the superconducting transition temperature by susceptibility measurements 32 3 2 CHARGE DENSITY WAVES CHAPTER 3 THEORY 3 2 Charge Density Waves The concept of the charge density wave CDW was first theorized by Rudolf Peierls in 1930 2 A CDW is a periodic distortion of a quasi one dimensional lattice producing a static wave distortion in the charge density along the lattice 3 The mechanism that produces this distortion is an electron hole condensate similar to the electron electron Cooper pair of BCS theory Coincidentally the Ginzburg Landau theory in the long wavelength limit can be used to describe CDW 3 One way to show how CDW comes about is to consider
26. ancel Figure C 3 A screenshot of the resistivity measurement system program machine set tings screen Instruments may be swapped out or replaced while the pro gram can still operate 68 Bibliography 1 J Bardeen L N Cooper and J R Schrieffer Theory of Superconductivity Phys Rev 108 1175 1957 2 H Fr lich On the Theory of Superconductivity One Dimensional Case Proceed ings of the Royal Society A 223 1154 296 305 1954 3 George Gr ner Charge Density Waves In Solids Perseus Publishing Cambridge Massachusetts 1994 4 J A Wilson F J Di Salvo and S Mahajan Charge Density Waves in Metallic Layered Transition Metal Dichalcogenides Phys Rev L 32 882 April 1974 5 E Morosan et al Superconductivity in CurTiSe2 Nature Physics Vol 2 pg 544 Aug 2006 6 D W Shen B P Xie J F Zhao Et al Novel Mechanism of a Charge Density Wave in a Transition Metal Dichalcogenide Phys Rev L 99 216404 2007 69 Bibliography Bibliography 7 T Yokoyaet al Fermi Surface Sheet Dependent Superconductivity in 2H NbSe Science 294 2518 2001 S G Wu H X Et al Transport properties of single crystaline Cuz TiSe2 Phys Rev B 76 024513 2007 9 S S Jaswal Lattice dynamics of TiSez Phys Rev B 20 5297 1979 10 L J van der Pauw A Method of Measuring Specific Resistivity and Hall Effect of Discs of Arbitrary Shape Philips Res Repts 13 1 9 1958 11
27. atic temperature measurement process described in section 2 2 4 whereby any slow variation of the voltage will be canceled out 60 APPENDIX A PRESSURE INDUCED NOISE 10 Voltage 10 V 0 2000 4000 6000 8000 10000 Time s Figure A 3 Room temperature 295 K voltage measurement for a shorted contact on the sample plug inside the cryostat Vacuum was introduced at 3740s where a voltage spike is introduced Atmospheric pressure was observed at 7460s which shows a voltage spike of opposite direction 61 B GPIB Communication General Purpose Interface Bus GPIB is a common abbreviation for National Instru ments standard IEEE 488 Most scientific measurement equipment uses IEEE 488 or RS 232 standards The advantages of GPIB are that it is common rugged and can connect up to 15 instruments to a single card in a daisy chain or star configuration see Figure B 1 The configuration for the resistivity measurement setup is shown in Figure 2 6 which used a 24 pin GPIB cable for communication There are eight data pins 1 4 and 13 16 three are handshake pins 6 8 and five management lines 9 11 15 and 17 see Figure B3 The communication is based on talkers listeners Only one device can talk at a time and data is transfered byte per byte The computer is a talker listener in this setup In a network ring only one instrument can be the talker while the rest are listeners When the computer requests information from a
28. ces of electromag netic noise that were present in the system were suppressed using standard engineering practices Noise is typically measured in root mean squared RMS values of voltage and power The root mean squared value can be calculated for a set of data x in the following way Erme ma S Gk Zz 2 4 Where z is the base line signal value The noise that is of importance to the measurement of resistivity is the noise associated with the voltage measurement 2 2 1 Contact Problems The van der Pauw method assumes that the contacts are very small compared to the sample size and they occur at the circumference of the material When measuring a sample which is less than about 0 5mm in its largest dimension the contact size becomes a problem The estimation of error 11 in resistivity Ap deviating from the true value p for a length along the circumference Figure 2 2 a a strip length l of contact from the circumference Figure 2 2 b or a contact a distance away from the circumference 13 2 2 MEASUREMENT NOISE CHAPTER 2 INSTRUMENTATION Figure 2 2 c for a circular sample of diameter 9 causes an error on the order of Ap i p 9ln 2 Figure 2 2 Errors with the van der Pauw method associated with different imperfect contact types Reproduced from 11 This error becomes quite large when the distance between contacts approaches the size of the contact The other problem that arises for small sampl
29. ction in one twist is canceled out by the next for a magnetic field spatially uniform in that region Reproduced from 18 19 vu List of Figures List of Figures 2 4 The schematic of the Infrared Labs HDL 10 He cryostat Modified from 19 Sample holder was mounted on the bolometer stage 21 2 5 The sample holder that is used inside the cryostat Samples are mounted with glue onto the copper plate at positions A and C Sample one is at A and sample two is at C At position B there is a Lakeshore DT 670 silicon diode temperature sensor mounted with indium solder Used as the B sensor in the temperture controller see main text at sections 2 3 2 anu 2 9 9 s fea s s ARCU acu e ab bot e e OR Dod ees ote eon 23 2 6 The block diagram of the resistivity setup Voltage sources specified are power supply equipment that were made at Brock University s Electronics Shop The HP 34970A data acquisition switch unit utilized an HP 34903A 20 channel actuator general purpose switch card with a custom backplate that housed the plugs cdi REGE UNS RS X DAC E da 25 3 1 Temperature dependence of the gap function Reproduced from 25 32 3 2 Wavevector dependent Lindhard response function for a one two and three dimensional free electron gas at zero temperature Reproduced from 3 3 a The charge density on a one dimensional lattice and below it the dispersion relation of a free electron model of a metal b I
30. e are power supply equipment that were made at Brock University s Electronics Shop They manually control power to the bolometer stage charcoal pump sample stage charcoal pump and cold plate heater An HP 34401A Multimeter is used to measure the resistance of the charcoal pumps giving a rough estimation of its temperature A switch on the distribution box controls which stage it is measuring 24 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION Computer Keithley 6221 DC and AC Current Source HP 34420A Nano Volt Meter Lakeshore DRC 91CA emperature Controlle HP 34401A Multimeter HP 34970A Data Aquisition Switch Uni Voltage Source Voltage Source Voltage Source Distribution Box Figure 2 6 The block diagram of the resistivity setup Voltage sources specified are power supply equipment that were made at Brock University s Electronics Shop The HP 34970A data acquisition switch unit utilized an HP 34903A 20 channel actuator general purpose switch card with a custom backplate that housed the plugs 25 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION Step Instruction 1 Read Sample Temperature 2 Set Horizontal Configuration Pause 3 Set Current Pause then Read Voltage 4 5 Set Vertical Configuration Pause Set Current Pause then Read Voltage Table 2 1 Basic program steps for a resistivity measurement Setting configuration occurs at the data swi
31. es is when the sample is elongated such that contacts A B and C D are very close while each pair are far from each other This causes the horizontal configuration to have high noise since the electric field that extends to C D is weak thus the voltage measured is very low and then other sources of noise which are independent of signal amplitude start to dominate while the vertical configuration will yield a higher voltage If the sample is sufficiently long then 2When Lap gt Lag the van der Pauw derivation is no longer valid for finite contact size 14 2 2 MEASUREMENT NOISE CHAPTER 2 INSTRUMENTATION the resistivity can be approximated to that of a two contact measurement with four leads 2 2 2 Instrument Noise In reality instruments for measurement never meet the ideal case which is discussed in theory In the case of a voltmeter it ideally has infinite impedance and measures the voltage exactly without noise However in order to do a measurement of voltage some current must be drawn and thus presents a finite impedance Even more problematic measurement devices involve their own circuitry that introduces its own sources of noise in particular thermal agitation noise in transistors T his sets a lower bound on the noise level that can be achieved Noise levels are usually given by the manufacturer in the specifications however in this thesis work they were measured to confirm them and identify other sources of noise
32. for SC when BCS predicts an isotropic gap 7 The connection between SC and CDW is of valuable interest in seeking the answers to the problems associated with understanding unconventional superconductors Measurements on the previous resistivity measurement system were too noisy to de termine the CDW transition temperature in crystals of Cu TiSez2 In order to make investigations of the properties of Cu TiSes it was necessary to construct a resistivity measurement system which could accurately measure the resistivity to detect the tran sition in and out of the CDW state as well as the SC transition This system has been realized and utilized to determine the doping concentration x in Cu TiSez which was not possible before Noisy measurement systems require stronger applied currents which affect the values that are of interest The previous system based on Infrared Lab s HDL 10 He Cryostat that was intended for optical measurements was adapted haphazardly by previous graduate students with little attention to noise protection in the system Additional measurement capabilities which were lacking on the previous design were also incorporated Measurement of multiple samples was implemented which conserves liquid helium and time The Hall effect measurement capability was also introduced with the new design and could be used to probe the charge of the carriers thus probe for a CDW transition 5 CHAPTER 1 INTRODUCTION 240 200 1
33. h field magnetization measurement is not within the range for other measurements due to comparing single crystals to polycrystalline samples and doping inhomogeneity in the samples The true range is thus assigned to be between x 0 06 and x 0 065 using results of the resistivity and SC transition measurements In Sample 2 the high resistivity data shows low doping at a doping parameter be tween x 0 025 and x 0 015 while the SC transition showed that the doping may be between x 0 055 and x 0 06 Resistivity measurements on Sample 2 showed high noise in the previous measurement system which was eliminated using the new measurement system These doping concentrations do not agree with one another It appears that the resistivity measurement shows that Sample 2 should have inhomogeneous doping since the phase diagram of Cux TiSes showed that no SC transition exists for dopings below x 0 045 see figure 1 1 while the resistivity data shows a higher slope and lower dop ing This skewed result may have also been a result of not measuring exactly on the a b plane Cleaving only gave a rough estimate of the crystal orientation X ray diffraction 93 CHAPTER 6 CONCLUSIONS Sample 1 High Field Susceptibility Low Field Susceptibility Resistivity Tone 125K 162K Te 3 6K Doping Factor x 0 03 0 04 0 06 0 10 0 055 0 065 Table 6 1 Results for Sample 1 Sample 2 Low Field Susceptibility Resistivity Tcpw 16
34. hat CDW would cause a discontinuity in the phonon disper sion where a notch is formed around 2k 33 This is shown in Figure 3 4 In CDW there is a gap function that describes the energy needed to destroy the pairs analogous to the BCS gap function This gap function forms suddenly producing a second order phase transition In superconductivity the Cooper pair has a net charge 34 3 2 CHARGE DENSITY WAVES CHAPTER 3 THEORY a vel ke 0 kp 7 20 Figure 3 3 a The charge density on a one dimensional lattice and below it the disper sion relation of a free electron model of a metal b In the CDW state the lattice and charge density has a static periodic distortion Below it shows that a gap of size A opens in the dispersion relation Reproduced from 3 35 3 2 CHARGE DENSITY WAVES CHAPTER 3 THEORY 3D N 2D 1D ia 0 2kg q Figure 3 4 Acoustic phonon dispersion relation of one two and three dimensional metals Reproduced from 3 thus contributes to conduction However it is important to note that the electron hole pair bosonic quasi particle amplitudon is charge neutral and has an interaction with impurities and lattice imperfections which causes it not to contribute to DC conduction The introduction of the gap however causes resistivity to increase The onset of this defines the CDW transition 3 36 4 Magnetic Properties of Cu TiSe Several samples of Cu TiSe were
35. he high density patches in three directions Q1 Qz and Qs Reproduced from IDs cer sede ee oet vi List of Figures List of Figures 1 4 Photograph of Sample 1 taken under a microscope The background was erased to show the boundaries of the crystal clearly Four gold wire silver paint contacts are on the perimeter of the sample Largest dimen sions of the sample are 6 0 mm along its length oriented horizontally in the figure 4 1mm along its width oriented vertically in the figure and 0 344mm in thickness xod AA A ed bh 8 1 5 Photograph of Sample 2 taken under a microscope The background was erased to show the boundaries of the crystal clearly Four gold wire silver paint contacts are on the perimeter of the sample Largest dimen sions of the sample are 6 9 mm along its length oriented horizontally in the figure 3 0mm along its width oriented vertically in the figure and 0 700mm in thickness ss 9 2 1 Top view of an arbitrary shape of uniform thickness with point contacts labeled A B C and D which can be used with the van der Pauw method 11 2 2 Errors with the van der Pauw method associated with different imperfect contact types Reproduced from 11 cue Yer doe Paba XR 14 2 3 a Two insulated conductors twisted together to form a twisted pair signal line The arrows indicate an example for the direction of the current b shows how the twists create spaces of opposite vector areas such that the indu
36. in Figure A 1 The jumps occur at 300 K when liquid N was filled and at 77 K when liquid Hef began to transfer into the vessel The amplitudes were too large to be taken into account by simple thermoelectric effects Further investigation to determine the cause has found that this is a pressure dependent effect that causes the voltage to change Using the new resistivity system a steel disk with spot welded contacts was utilized as the sample to locate the source of noise Base noise levels were on the order of 4 5 nVrys At room temperature the voltage across two contacts was recorded as a function of time The vacuum pump connected to the cryostat cavity was turned on causing a large voltage shift Figure A 2 This can be safely assumed to be independent of the wiring and instruments from the Spot welded contacts were utilized to prevent contact breaking on the sample 58 APPENDIX A PRESSURE INDUCED NOISE 16 14 12 10 Resistivity 10 Ohm M 0 50 100 150 200 250 300 Temperature K Figure A 1 Cool down data in the previous resistivity measurement system using the same HDL 10 He cryostat on Sample 1 Notice the jumps at 300 K when liquid Ng is filled and 77 K when liquid Het begins to transfer into the main vessel outside to the 32 pin plug on the cryostat This effect was not a property of the material being measured To further determine the source of this noise the sample holder was removed the IC SI
37. in the a and c direction This expansion is linear until it becomes constant for dopant concentration x gt 0 11 5 The structure shows clear quasi two dimensionality and this results in a quasi two dimensional CDW The CDW in two dimensions occurs by nesting on flat portions called Fermi patches at the Fermi energy in the first Brillouin zone 5 As an example Figure 1 3 shows the 2D Fermi patches in the joint density of states of 2H Na TaS another superconducting CDW material The van der Waals forces are weak compared to the bonding in the crystal which makes determination of the orientation of the crystal for this material relatively easy by the rough method of 1 1 CRYSTAL STRUCTURE OF CUx TISE CHAPTER 1 INTRODUCTION VAN DER WAALS GAP CHALCOGEN X X CHALCOGEN ABOVE PLANE METAL X CHALCOGEN BELOW PLANE M METAL IN PLANE IQP VIEW Figure 1 2 Crystal structure of 17 TiSez a Cross sectional view of the lattice layers showing relative positions Layers X and X are chalcogen atoms and M is the transition metal b Octahedral form of the 1T phase of the lattice where the chalcogen is Selenium and the metal is Titanium Reproduced from 9 1 1 CRYSTAL STRUCTURE OF CUx TISE CHAPTER 1 INTRODUCTION C 4 0 arb units 1 6 1 2 0 8 0 4 0 4e b Figure 1 3 Joint density of states in 2D momentum space of the two dimensional su perconducting T 2 3K CDW Tcpw 65K material 2
38. ing a range of doping in a single crystal due to different doping concentrations in different regions of the crystal causing a range of transition temperatures E Morosan et al 5 performed measurements on polycrystalline samples which may behave differently than a single crystal since all crystal orientations are taken into account with polycrystalline samples while Samples 1 and 2 were measured with the H field parallel to the a b plane Notice in Figures 4 2 a and 4 3 a that the transition temperature increases with doping from x 0 55 to x 0 08 However above doping of x 0 08 there seems to be a turning point which causes doping of x 0 10 to go to a lower SC transition temperature It is not clear from this measurement whether the doping is above or below the peak SC transition temperature concentration The result can however be compared to other measurement techniques to find the doping to look for consistency 40 CHAPTER 4 MAGNETIC PROPERTIES OF CUx TISE Q emn o o gt a a o gt AA gt Magnetization emu Oe mol Ti A III CA e o do a Temperature K o Nr Magnetization emu Oe mol Ti H 10 Oe 1 2 3 4 5 6 Temperature K Figure 4 2 Temperature dependence of the magnetic susceptibility in Cu TiSez for low field strength around the SC transition a Polycrystalline data from E Morosan et al 5 at 5 Oe b Sample 1 a single crystal magnetization for a field st
39. ing mechanism for the electron hole pair of the CDW by trying to suppress one of the CDW vectors while having the rest unaffected This could be achieved by applying a magnetic field parallel to the a b plane if the pair breaking mechanism was the orbital pair breaking Polarized reflectance spectroscopy measurements would reveal which an gle of polarized light would produce the typical CDW optical conductivity peaks and therefore would probe for individual CDW vector suppression Instrumentation for this kind of measurement is being constructed as part of Jason Iwachow s Ph D thesis The 56 7 1 MAGNETO OPTICAL CHAPTER 7 FUTURE RESEARCH DIRECTIONS instrument under design is an adapter for the cryostat such that high field neodymium magnets are held in a rotating device in the cold chamber such that it will rotate in the a b plane of the sample while reflectance measurements can be taken parallel to the c direction The rotator has been constructed and is shown in Figure 7 1 Figure 7 1 Photograph of the part of the magneto optic measurement device that will rotate two large neodymium magnets around the sample inside the cryostat Designed by Jason Iwachow 57 A Pressure Induced Noise It was observed that cool down data in the resistivity system yielded characteristic jumps when changing the cooling fluid An example of what occurs is shown for resistivity taken in the previous resistivity measurement system with Sample 1
40. m of the auxiliary field H fields caused by a current and the magnetization by B uol H M When the magnetization is a linear response in the auxiliary field we have M xH where y is the magnetic susceptibility Diamagnetism arises from orbital motion of the electrons and is present in all materials and in general is very weak Diamagnetism has a field that opposes the H field and therefore has negative susceptibility Paramagnetism arises from the spin of the electrons attempting to align to the H field and can only do so when there are unpaired electrons and is related to the density of states 21 3 1 Superconductivity Superconductivity is a state of matter for which the material has perfect conductivity and exhibits perfect diamagnetism The original phenomenological explanation of zero resistance and the Meissner effect by the London brothers 23 was expanded by Pip pard to the nonlocal generalized case 24 Ginzburg and Landau in 1950 introduced the theory of superconductivity based on characterizing the superconducting electrons by a pseudo wavefunction order parameter 25 With this spatial variations of the density of superconducting electrons could be calculated Finally the microscopic theory of super conductivity was put forth by Bardeen Cooper and Schrieffer in 1957 1 BCS theory predicted the isotope effect and predicted that electron pairs mediated by phonons were responsible for superconductivity 1 London
41. mperature controller which contains the data for the voltage temperature curves It has two inputs one for sensor A the low temperature sensor and one for B the 23 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION high temperature sensor The distribution box has a switch to control which A and B sensor to read from either bolometer or sample stage The B sensor mounted within the cryostat the Lakeshore DT 470 silicon diode sensor is only accurate to 6 K The A sensor the Lakeshore GR200A germanium sensor is accurate below this temperature to about 0 3 K With the DT 670 sensor used as the B sensor the switch from A to B sensor occurs at 1 4 K An HP 34420A nano volt meter and Keithley 6221 DC and AC current source are connected with a 4 pin mini XLR cable utilizing the noise reduction methods described earlier to the HP 34970A data acquisition switch unit with an HP 34903A 20 channel actuator general purpose switch card The HP 34903A card in the switch unit allows for the voltage V V and current source I I contacts to be arranged in any permutation to the contacts A B C and D on sample A or B This allows for not only resistivity measurements but also Hall effect measurements From the switch unit two 4 pin mini XLR cables each representing the four contacts from one sample are connected to the distribution box The three voltage sources in Figure 2 6 are connected to the distribution box by BNC coaxial cables Thes
42. n instrument it passes the control to be a talker while the computer becomes the listener and receives the data one byte at a time 37 The programming interface used was NI 488 2 NET assembly from National 62 APPENDIX B GPIB COMMUNICATION lt SE Device D Es eee Device A E LEE AA Device C Device B Device C a Linear Configuration b Star Configuration Figure B 1 Configurations that GPIB can take on a Linear configuration also known as daisy chain configuration b Star configuration Reproduced from 37 12 1 Dao 000000000000 24 13 Figure B 2 GPIB female connector with pins numbered Instruments This assembly takes care of the detailed communication protocol in an easy to use API IEEE 488 instruments have standard commands as well as vender specific commands Standard commands must be recognized by every IEEE 488 device Some of the important commands used in debugging are listed in Table B 1 Devices require a unique device number ID a number between 0 and 30 where the primary address used 63 APPENDIX B GPIB COMMUNICATION Instruction Description IDN Returns Device Description RST Resets the device STB Reads the status byte CLS Clear the status Table B 1 Standard commands recognized by all IEEE 488 devices by the computer in this case is zero Other instruments can change their ID either by swi
43. n the CDW state the lattice and charge density has a static periodic distortion Below it shows that a gap of size A opens in the dispersion relation Reproduced vill List of Figures List of Figures 3 4 Acoustic phonon dispersion relation of one two and three dimensional metals Reproduced from 3 Eb sik qo ee e BO PCR 36 4 1 Temperature dependence of the magnetic susceptibility in Cu TiSesz for a field strength of 0 5T a Results from E Moroson et al 5 b Results from Sample 1 Absolute value was shifted down due to diamagnetic contribution from the capsule and grease used to hold the sample Shows the CDW transition temperature at 120 K 39 4 2 Temperature dependence of the magnetic susceptibility in Cu TiSes for low field strength around the SC transition a Polycrystalline data from E Morosan et al 5 at 5 Oe b Sample 1 a single crystal magnetization for a field strength of 10 Oe SC is observed with an onset at 3 6K 41 4 3 Temperature dependence of the magnetic susceptibility in Cu TiSes for low field strength around the SC transition a Polycrystalline data from E Morosan et al 5 at 5 Oe b Sample 2 a single crystal magnetization for a field strength of 10 Oe SC observed with an onset at 2 5K 42 5 1 Temperature dependence of the resistivity in Cu TiSez a Results for different dopings on single crystal samples in the a b plane reproduced from 8 b Re
44. nductors specifically with different Seebeck Coefficients Thermoelectric voltages are generated when there is an electro chemical potential in the circuit and are created by a thermal gradient 13 The voltage generated is defined as Enf SAT 2 6 where S is the Seebeck coefficient and AT is the difference in temperature between the contacts 15 In order to cancel these effects for equilibrium conditions resistance is measured by applying current in both directions and averaging the results However these effects can have an impact on the measurement while temperature is changing The time dependent version of the Seebeck equation equation 2 6 for a delay 7 in 16 2 2 MEASUREMENT NOISE CHAPTER 2 INSTRUMENTATION measuring positive and negative current is given by T dT dT Sup Wc AT 2 V sf it SAT 2 7 In the Infrared Labs HDL 10 He cryostat henceforth to be referred to as the cryo stat the largest Seebeck coefficient difference of any signal carrying wires is 40 yV K Constantan and Copper at room temperature If we estimate that the rate of cooling is 0 2 K s and modestly estimate the Leidenfrost point for liquid nitrogen is 277K in the cryostat we obtain a value of a time dependent thermoelectric voltage of about 16mV This is highly significant for materials being measured with very low currents or very low resistivities However for warm up times that take days this value is on the order of 107
45. nnection between Charge Density Waves and Superconductivity in NbSez Phys Rev Lett 34 1164 1975 NI 488 2 User Manual National Instruments February 2005 72
46. nosing problems Noise levels were on the order of 15 nVams Contributions to this noise were from the instruments Nyquist noise magnetic and RF sources The new system implementation has reduced noise in the system by a factor of 3 10 2 1 PRINCIPLE CHAPTER 2 INSTRUMENTATION 2 1 Principle Instrumentation was designed to implement multiple sample resistivity or Hall effect measurements by the van der Pauw method In 1958 L J van der Pauw showed that resistivity or the Hall coefficient of an arbitrary shape can be measured by a four contact measurement if the sample is thin and of uniform thickness contacts are small contacts are on the circumference and the sample contain no holes 10 Consider the arbitrary shaped sample of small uniform thickness in Figure 2 1 D Figure 2 1 Top view of an arbitrary shape of uniform thickness with point contacts labeled A B C and D which can be used with the van der Pauw method If we apply a current to A positive and B negative 4p and measure the voltage at D positive and C negative Voc then we can define the resistance _ Voce RAB De LAB We can call this resistance measurement the horizontal configuration Similarly for current on B C and voltage reading on A D gives Rap gc similarly called the vertical 11 2 1 PRINCIPLE CHAPTER 2 INSTRUMENTATION configuration then the resistivity of the sample can be shown 10 to be 7
47. not Each instrument has its own vender specific instruction set To keep the program versatile it was programmed with net interfaces so that different instruments could be used with minimal programming Only a few lines of code is necessary to construct a 66 APPENDIX C PROGRAM INTERFACE TI ck ij x Actuator Switch Temperature Controler Set Sample Port 1 Initialize Set Sample Port 2 Set VDP Config Vert Set YDP Config Cross amp Set VDP Config Cross B CurrentOn Set Current B ma vl Read Voltage Read Resistance MALE A Co o o D Figure C 2 A screen shot of the resistivity measurement system program diagnostics screen The tab that is selected shows a diagram of the circuit inside the HP 34903A switch card as well and multiple commands to diagnose the source of a problem new set of commands that the program can use to perform measurements Changing the instruction set involves just selecting a different instrument from the drop down list see Figure C 3 Data is saved as a text file with the first row as the column names separated by commas This format is easily accepted into Microsoft Excel Igor Pro or Origin for further data analysis 67 APPENDIX C PROGRAM INTERFACE Machine Settings 3 Voltmeter HP 344204 Current Source ETE Switch Actuator HP 34970 y Temperature Controller Lakeshore DRC SICA y Multimeter HP 3ssota y Ok Apply C
48. nths of perpetual work xiii 1 Introduction Superconductivity SC had been theorized to come about by electron electron inter actions in 1957 by Bardeen Cooper and Schrieffer BCS 1 A similar phenomena the charge density wave CDW was postulated to exist by Fr lich in 1954 based on electron hole interactions 2 These two phenomena are quite similar in principle but the CDW leads to an insulating condensate because the pair is charge neutral while in SC the pair has a charge of 2e The theory behind CDW requires that the system is quasi one dimensional in order for the electron hole pairs to cause the Lindhard response function to diverge around k a process called nesting 3 In 1974 it was discovered that anomalous properties of TaSez and TaS2 which are quasi 2D systems are due to CDW s 4 Cu TiSez is also a quasi two dimensional material which exhibits the CDW state 5 Cu TiSez also exhibits a superconducting phase that has a varying Tc based on the doping parameter x which seems to take over the CDW state D W Shen et al 6 discuss the possibility that flat portions at the Fermi energy in two dimensions in the first Brillouin zone can allow for such nesting called Fermi patches to occur for three directions in the a b plane 6 However theory still fails to explain why CDW s appear CHAPTER 1 INTRODUCTION to compete with SC states the phase diagram of the material or why an anisotropic gap can occur
49. of Figures 6 1 Temperature dependence of the magnetic susceptibility in Cu TiSez for a field strength of 0 5T for Sample 1 Absolute value was shifted down due to diamagnetic contribution from the capsule and grease used to hold the sample Shows the CDW transition temperature at 120 K and identifies the CDW transition temperature as identified by the resistivity measurements at 162 K There is a small feature around 162 K see inset for expanded view which might identify as the CDW transition temperature if the measurement was conducted with more resolution in that region ps den et O E O O gee ee ad 52 7 1 Photograph of the part of the magneto optic measurement device that will rotate two large neodymium magnets around the sample inside the cryostat Designed by Jason Iwachow 0 00004 57 A 1 Cool down data in the previous resistivity measurement system using the same HDL 10 He cryostat on Sample 1 Notice the jumps at 300 K when liquid Ng is filled and 77 K when liquid He begins to transfer into the MA Vesse la m att a ane eg EQ ee BAe E an ode ri Sm 59 A 2 Room temperature 295 K voltage measurement on a steel disk in the current resistivity measurement system At 1150s into the measurement the vacuum pump was turned on 2 a eee eee 60 xi List of Figures List of Figures A 3 Room temperature 295 K voltage measurement for a shorted contact on the sample plug inside the cryostat Vacuum wa
50. or Sample 1 Notice the peak to peak noise is magnitudes of order higher up to 10 higher Note that the peak is still faintly visibly in the inset tenth order poloynomial base line fit at 161k however other features on this graph could easily be mistaken for the same transition In Sample 2 the noise reduction of the new system can be dramatically observed Sample 2 is an elongated sample with an aspect ratio of roughly 1 3 with the largest dimension being roughly 7mm As discussed in section 2 2 1 noise on elongated samples can be quite high Sample 2 was measured in the old system from 77 K 300 K while in the new system it was measured between 4 K 300 K The results are shown in Figure 48 CHAPTER 5 DC TRANSPORT PROPERTIES OF CU x TISE 5 5 When comparing the results of the new measurement in 5 5 b to 5 1 a we approximate the doping to be between x 0 025 and x 0 015 The CDW bump appears to be centered around 125 K The CDW transition occurs at 166 K as determined by a polynomial baseline fit 49 CHAPTER 5 DC TRANSPORT PROPERTIES OF CU x TISE a 1 f o 6 E 5 o BE 4 2 D 3 g 0 1 0 50 100 150 200 250 300 Temperature K 2 12 5 1 0 E e g 0 8 5 M E E g 2 i E 0 6 3 n o d ac N 100 150 200 250 0 4 Temperature 50 100 150 200 250 Temperature K Figure 5 5 Temperature dependence of resistivity in Sample 2 Cu TiSes in the two different systems a Results
51. ors is called the Meissner effect The Meiss ner effect means that there is no magnetic field in the material which is implied by London s equations The transition of the magnetization is sudden when entering the superconducting state There is however a critical field at which superconductivity is lost 25 and which is approximated by H T He 0 1 T T where T is the critical temperature Abrikosov investigated a different limit of Ginzburg Landau the ory and predicted that a mixed state might appear where the superconducting bulk would contain an array of flux tubes with superconducting vortices around them and cause a continuous transition in the magnetization instead 25 This is called a type II superconductor and the susceptibility is perfectly diamagnetic until it enters this mixed state at a critical field called H It remains in the mixed state until a second critical field called H above which it reverts to the normal state BCS Theory predicts that superconductivity is created by Cooper pairs pairs of weakly attractive electrons mediated by phonons BCS predicts the temperature depen dent gap energy A T which is the energy to break a Cooper pair 1 The temperature dependent gap function is shown in Figure 3 1 He investigated what would happen if the Ginzburg Landau parameter amp were large instead of small 25 3l 3 1 SUPERCONDUCTIVITY CHAPTER 3 THEORY A T AO ES T Figure 3 1
52. ples or doping for elongated samples due to electronic noise Doping in one sample was found to be between x 0 06 and x 0 065 Values of doping in the second sample had a discrepancy but could be explained by incorrect sample CHAPTER 0 ABSTRACT orientation Contents Abstract i Glossary v Acknowledgements xiii 1 Introduction 1 1 1 Crystal structure of Cu Vides 2252 X36 9E eR So Be a e 4 1 2 Sample Preparation e acd at abus e auae dice eie dde pias east 7 2 Instrumentation 10 A ME NN RR A A See ee A Doe eet tA 11 2 2 Measurement Noise s 13 2 2 1 Contact Problems 13 2 2 2 Instrument Noise 15 252 95 Nyguist NOISE ate ike y Ge ike xeu cigs HRS ede E arp A rte 15 2 2 4 Thermoelectric Effects o 16 ill Contents Contents 2 2 5 Electromagnetic Noise y sha ee GS SO Ge Se ee ES 17 2 3 Design and Method qeu Ds E A aie Se eta e c sat wh eph 19 2 hes ByOSLOL ae exo ate Go eed de E wx teu 20 23 27 Sample holders d a to Ius da te Bra een VPE een GPS AI av 22 23 3 Measuring COCHE 1E Ds seg D Sek QA e hh Ge dp d xad 23 2 3 4 Computer Data Acquisition 2 4 9 woe 84 bad Ae DAY as 26 3 Theory 28 3 17 Superconductivity o a ers Me AA Gre ene Bre de eye amp Bg ee Re 29 3 2 Charge Density Waves so doa ac dace deese E eA RIS Eois 33 4 Magnetic Properties of Cu TiSe 37 5 DC Transport Properties of Cu TiSe 43 6 Conclusions 51 7 Future Research Directions 55 7 1
53. re is the transition temperature into the CDW state which causes the susceptibility to decrease once the gap in the dispersion relation is formed This is because the electronic density of states drops and the contribution from Pauli paramagnetism is reduced and the core diamagnetism begins to dominate 5 The magnetization then rises with Curie Weiss like behavior as temperature is further lowered until it drops to pure diamagnetism below the SC transition temperature Figure 4 1 b shows the measurement on Sample 1 There appears to be a shift in the data to negative susceptibilities This may have been a diamagnetic shift due to an improper correlation table loaded in the MPMS to account for the grease However the importance for determining the doping is in the temperature dependent features and the absolute offset is not important The data is quite noisy but it can be approximated that the CDW transition temperature is around 120 K Comparing Figure 4 1a to 4 1 b we can estimate the doping to be between x 0 03 and x 0 04 In small fields we can observe the SC transition at low temperatures to characterize the doping of the sample E Morosan et al measured 5 the critical fields for polycrys talline Cuo os TiSez at 3 5 K to be Hea z 18 Oe and He 3000 Oe The zero temperature values are H 0 12 T and He 1 33 T In Sample 1 a field of 10 Oe was applied parallel to the a b plane to observe the SC transition The results shown in Fig
54. red to the thermal change in that time frame so noise is low which also implies that the temperatures are approximately equal to each other when measuring each van der Pauw configuration An averaging function is included in the program which averages the values over whatever temperature range is specified Since there are many different instruments and connections the program was made to include diagnos tic tools to identify sources of troubles Details of the program interface are included in Appendix C 27 3 Theory Before discussing the theories describing CDW and SC materials a brief review of mag netism is necessary to understand certain aspects of their properties Remember that the total magnetic dipole moment is defined as m la where I is the current and d is the vector area 20 A material may exhibit a magnetic field of its own without electrical current when there are tiny dipole sources through out the material If m is the sum of all these magnetic dipoles throughout the material we define magnetization as M gt 3 Where X is a volume mass or moles For convenience we will use the same units as the magnetic measurement system uses see chapter on magnetic properties Magnetization cu where is measured in lemu 10 A m The auxiliary field is measured in Oersted Oe 1000 A 10e 4r m 28 3 1 SUPERCONDUCTIVITY CHAPTER 3 THEORY The total magnetic field in space is the su
55. rength of 10 Oe SC is observed with an onset at 3 6K 41 CHAPTER 4 MAGNETIC PROPERTIES OF CUx TISE to Magnetization emu Oe mol Ti Temperature K 0 00 F 0 02 o E p O 004 3 E 0 06 2 S 0 08 o z o S 0 10 H 10 Oe 0 12 2 3 4 5 6 Temperature K Figure 4 3 Temperature dependence of the magnetic susceptibility in Cu TiSez for low field strength around the SC transition a Polycrystalline data from E Morosan et al 5 at 5 Oe b Sample 2 a single crystal magnetization for a field strength of 10 Oe SC observed with an onset at 2 5K 42 5 DC Transport Properties of Resistivity measurements were conducted in the a b plane on the same samples of Cu TiSe as in the magnetic properties chapter using the resistivity measurement system constructed The CDW transition temperature and SC transition temperature was extracted Measurements show a broad maximum which agrees with other groups 8 5 Low temperature measurements did not have the slow rate to obtain ideal low noise measurements due to unforeseen technical difficulties Time constraints did not allow the measurements to be repeated Typical contact resistance was between 3Q and 12Q The results for Sample 1 are shown in Figure 5 1 b with a power law forced fit to emphasize the CDW bump In Figure 5 1 a the CDW state produces an increase in resistivity manifesting in a broad peak centered around 90 K By comparison
56. s and one in the bolometer stage an A sensor for low temperature Two sensors are used to accurately measure the full range of temperatures in the experiment see section 2 3 3 In the sample holder shown in Figure 2 5 the temperature sensor at position B is used as the B sensor for the temperature controller The bolometer stage has no sensor for Tf the shield is not depleted thermal equilibrium will be maintained at the boiling point of liquid nitrogen 22 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION f Figure 2 5 The sample holder that is used inside the cryostat Samples are mounted with glue onto the copper plate at positions A and C Sample one is at A and sample two is at C At position B there is a Lakeshore DT 670 silicon diode temperature sensor mounted with indium solder Used as the B sensor in the temperture controller see main text at sections 2 3 2 and 2 3 3 the temperature range 6 K 500 K Mounting the temperature sensor directly on the sample holder has the additional benefit of reducing error associate with reading the temperature in thermal non equilibrium for a temperature gradient between the sample and the sensor 2 3 3 Measuring Circuit The block diagram of the measuring instrument circuit is shown in Figure 2 6 The 32 pin connector from the cryostat goes into the distribution box which breaks out to all the instruments The temperature is measured through the Lakeshore DRC 91CA te
57. s introduced at 3740s where a voltage spike is introduced Atmospheric pressure was observed at 7460s which shows a voltage spike of opposite direction 61 B 1 Configurations that GPIB can take on a Linear configuration also known as daisy chain configuration b Star configuration Reproduced from 37 63 B 2 GPIB female connector with pins numbered 63 C 1 A screen shot of the resistivity measurement system program main form Right Panel is the graphing area upper left panel is the experiment pa rameters and lower left is the type of measurement to perform 66 C 2 A screen shot of the resistivity measurement system program diagnostics screen The tab that is selected shows a diagram of the circuit inside the HP 34903A switch card as well and multiple commands to diagnose the source of a problem ue ext ure exutus ud ew be S th 67 C 3 A screenshot of the resistivity measurement system program machine set tings screen Instruments may be swapped out or replaced while the program can still operate ake newts rade spp en VC eeu e 68 xli Acknowledgements Dr Maureen Reedyk For her stress free guidance throughout my studies Xiao Peng and Yang Pan For introducing me to the instruments in the lab when I was new to Brock University Jason Manson For his help in theoretical concepts and with experimental debugging And to my wife Megan For her constant support and understanding during those mo
58. sistivity of Sample 1 measured in the new resistivity sys tem Shows a CDW transition temperature of 162K The dotted line is a power law forced fit that emphasizes the CDW bump 44 ix List of Figures List of Figures 5 2 Resistivity of Sample 1 The top left inset shows the first derivative of the data The bottom right inset shows the second derivative of the data The CDW feature is not visible beyond the first derivative 46 5 3 Polynomial baseline fit on resistivity data for Sample 1 There is a clear common dip at 161K which could be the CDW transition a Seventh order b Tenth order c 20 order sia ox kale Aw 9s 4T 5 4 Tenth order polynomial baseline fit on resistivity data measured on old resistivity system for Sample 1 Notice the peak to peak noise is mag nitudes of order higher up to 10 higher Note that the peak is still faintly visibly in the inset tenth order poloynomial base line fit at 161k however other features on this graph could easily be mistaken for the same transition 8 28s E e SENILIS LR LEN E AC ae EON en a 48 5 5 Temperature dependence of resistivity in Sample 2 Cu TiSes in the two different systems a Results in the old measurement system from liquid nitrogen temperatures b Results in the new resistivity measurement system from liquid Het temperatures Inset shows a 20 order polynomial baseline fit showing a CDW transition of 166 K 50 List of Figures List
59. tch unit 2 3 4 Computer Data Acquisition The data from the instruments is read by the computer using IEEE 488 also known as GPIB communication The details of the communication are discussed in Appendix B Measurements are taken when both cooling and warming however only the warm up measurements are used for reasons discussed in section 2 2 on noise The rate at which data is read is limited by the speed of the instruments The HP 34420A nano volt meter has a built in function which integrates the measurement over a certain number of power supply cycles 22 At 10 cycles which was used for all measurements taken a response time of 0 5 seconds is given In order to assure that the relays in the HP 34903A 20 channel actuator general purpose switch card were at rest the measurement loop was paused for 0 5s after each configuration change in the unit The measurement loop measures the resistivity in the basic steps outlined in table 2 1 More time delay is introduced than shown by taking an average of several measure ments for each configuration and due to the fact that this cycle is repeated for the second sample at position C On average for a single sample measurement it takes 6 seconds for a single van der Pauw measurement to be taken As discussed before this time is TRelays or switches tend to bounce when switched over thus causing noise in the signal 26 2 3 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION small compa
60. tches on the back of the device or programmatically on the front panel 64 C Program Interface In order to handle the measurement and debugging in an efficient manner a program was made with an extensive easy to use user interface It was programmed in C utilizing the NI 488 2 NET assembly provided by National Instruments The main form includes a dynamic graphing area where multiple graphs can be displayed simultaneously Parameters of the experiment including the mass of the samples how many samples to measure applied current what environment parameters to measure and averaging interval are input on a side panel This readily records directly the resistivity of the material All data collected are saved in the specified dat file which can be selected with the save file dialog A screen shot of the program displaying some data is shown in Figure C 1 The graphing function allows up to five graphs to be displayed at once Zooming and auto scaling are included in the program which makes it convenient to look at old data from other experiments When sample contacts break during an experiment or if some connection is broken sometimes it is unknown to the operator and can be difficult to locate the source of the 65 APPENDIX C PROGRAM INTERFACE E Resistivity Measurement Program ni xi File Settings Diagnostics Help M Data Settings Data File shorted inside cryostat nov 18th dat EBEN 2 u 7 38 06 0 993 mm
61. the Lindhard theory of screening in one dimension It arises by considering a Schrodinger equation with a potential due to the lattice atoms and other electrons with charge screening in a free electron gas 32 In the case that the screen ing charge density is linear in the potential the dielectric constant becomes Lindhard response function 3 4 fifa xd 27 Ey 7 on where f is the fermi function at wavevector k and x is the dielectric susceptibility If this is integrated for three or two dimensional fermi surfaces of a free electron gas energy hk E 5 2m where m is the free electron mass the result isn t very interesting However integration in one dimension around the Fermi energy leads to a divergence around q 2k 3 The three situations are depicted in Figure 3 2 3linearized near the Fermi energy as Ey Ep hvg k kp 33 3 2 CHARGE DENSITY WAVES CHAPTER 3 THEORY 0 X q X q Figure 3 2 Wavevector dependent Lindhard response function for a one two and three dimensional free electron gas at zero temperature Reproduced from 3 This shows that there is a lowering of energy for an electron at kp and hole at kp This electron hole pair produces a gap thus reducing the energy in the electronic dispersion relation near tks This new state causes a static periodic distortion of the lattice and charge as shown in Figure 3 3 In 1959 Kohn proposed t
62. ure 4 2 show a SC transition temperature of about 3 6K This suggests by comparison to data 38 CHAPTER 4 MAGNETIC PROPERTIES OF CUx TISE i y DD ADA QA AAAA TS ye eee 0 06 1x10 F s m 0 50 100 150 200 250 300 Suceptibility emu Oe mol Ti Temperature K c H 5000 Oe Susceptibility emu Oe mol Ti 0 50 100 150 200 250 300 Temperature K Figure 4 1 Temperature dependence of the magnetic susceptibility in Cu TiSez for a field strength of 0 5T a Results from E Moroson et al 5 b Results from Sample 1 Absolute value was shifted down due to diamagnetic contribution from the capsule and grease used to hold the sample Shows the CDW transition temperature at 120 K 39 CHAPTER 4 MAGNETIC PROPERTIES OF CUx TISE from Figure 4 2 a that the doping is between x 0 06 and x 0 1 A second sample Sample 2 was also characterized for the SC transition with the field of 10 Oe parallel to the a b plane of the sample The results are shown in Figure 4 3 The SC transition temperature appears at about 2 5K which would suggest a doping between x 0 055 and x 0 06 The comparison of the results for the SC transition from E Morosan et al 5 to measured data on Samples 1 and 2 is not ideal to characterize the doping The SC transition curves in Figures 4 2 b and 4 3 b do not seem to have the same slope as the data of E Morosan et al 5 This may be the result of hav
63. vessel that is thermally connected with the shield with liquid nitrogen Cooling is achieved by filling the main vessel helium vessel which is thermally connected with the cold plate with liquid nitrogen first This is then replaced with liquid He Liquid Nitrogen precooling reduces liquid helium boil off during the transfer Evacuating the vessel pumping can lower the temperature to 2K below which then the He one shot refrigerator is utilized to go to as low as 0 4 degrees Kelvin He refrigeration is achieved by the following steps The He tank is connected through a valve to a charcoal pump The He tank valve is opened allowing absorption of He in the charcoal pump at the He boiling point A thermal switch is opened to thermally isolate the pump from the cold plate and sample and the He tank valve is closed trapping the He gas Heat is applied to the charcoal pump to raise its temperature The power is turned off at around 40K and the thermal switch to the stage where the sample holder is mounted is closed allowing the He vapour to condense in a vessel thermally connected to the stage on which the sample holder is mounted cooling it to as low as 0 4K when the charcoal pump is cooled to allow it to pump on the 20 23 DESIGN AND METHOD CHAPTER 2 INSTRUMENTATION PREAMPLIFIER BOX COLD PLATE RADIATION SHIELD DEWAR CASE RESISTIVITY LIGHT PIPES MEASUREMENT PLUGS QUARTZ WINDOWS

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