gll'j‘ J2” “T‘Z;\.1_ ‘ __ "a‘ I $45 | Q (1‘1:ng \ «at ’12.”, ' AM 344' '9 . A {‘3 . I '{fi} grfi‘ ‘f'k ’ “ "fit“: 3‘. 2;) . “(1."? ‘1. "4‘ x g - » ‘F’J“12:\d')"~ "”‘fi N ‘La'f‘io r Angus. -:"‘Lv M N 50101 ‘1 rwu: ‘ mMaggyWW LIaRARYW , Michigan State' University j This is to certify that the dissertation entitled Superconductivity and Metal—Insulator Transitions in Layered Solids: High T Oxides and Graphite Intercalation Compounds presented by Yi—Yun Huang has been accepted towards fulfillment of the requirements for Physics Ph°D' degreein «Z6: Major professor 0x. 531/??? I)ate MS U it an Affirmative Action/Equd Opportunity Institution 0-12771 PLACE IN RETURN BOX to remove this checkout from your recon]. TO AVOID FINES return on or before date due. DATE DUE DATE DUE DATE DUE MSU I8 An Affirmdivo ActioNEqual Opportunity lndltution .——————_ i, _ surnacounucrmrr AND mam msuuroa mnsmons IN um SOLIDS: HIGH Tc OXIDES AND GRAPHITE INTERCALATION COMPOUNDS BY Yiyun Huang A DISSERTATION Submitted to Michigan State University .in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Physics 1989 0‘ J bobqfi5 ABSTRACT SUPERCONDUCTIVITY AND METAL INSULATOR TRANSITIONS IN LAYERED SOLIDS : HIGH Tc OXIDES AND GRAPHITE INTERCALATION COMPOUNDS by Yiyun Huang Field and temperature dependent levitation properties of high temperature superconducting copper oxide compounds were studied over the ranges ISHSIOkG, 0568/8250J7kG/mm and 4.2KSTS3OOK-. A novel cryogenic levitometer was developed for these experiments.‘ For all of the specimens studied the levitation height shows a threshold temperature TL above which the specimen will not levitate, and a dramatic slope discon- tinuity at a temperature '1'J which is associated with the onset of the phase coherence between Josephson weakly linked grains. A linear relationship between I: and the inverse field gradient was theoretically derived and found to be in excellent agreement with experiment for both the Y and Bi based compounds. The magnetization properties revealed by the levitation experiments were also examined using a SQUID suscep- tometer. A least squares fit using these data yielded parameters which agree well with a Ginzberg-Landau model of the temperature dependence of the penetration depth. MT). We have also carried out systematic resistance measurements in order to study the kinetic and electronic properties of potassium- ammonia graphite intercalation compounds. The time dependence of c-axis resistance measurements reveals the kinetics of the ammoniation of K624 to form the ternary graphite intercalation compounds (GIC) K(NH3)xC24. Olo. This transition is attributed to a 2D Mott type transition in the intercalated.K-NB3 liquid monolayer. The electrical anisotropy of the ternary GIC ‘K(.NH3)XC24 at x-l» is found to be about 5x104 which is the highest yet reported for a stage-1 donor GIC. Other alkali metal ammonia intercalation GICs such as Rb(N83)xczl. and Cs(NHa)xC were also studied in order to explore ion size effects. An 2!» empirical relationship between the saturation resistance and ionic parameters has been found. ACKNOWS I wish to express my sincere gratitude to Professor Stuart A. Solin for his guidance, stimulating encouragement, and his invaluable support throughout all stages of my research. I have benefited a great deal from the numerous discussions we have had over the past five years. He has taught me how one could seize the key physics from the vast ex- perimental data and discover new phenomena. His intuition, rich experience and generous help have secured the completion of this work. I am also grateful to Professor S.D. Hahanti, Professor P.A. Schroeder, Professor K. Gelbke and Professor 3.6. Pope for their service on my guidance committee and to Professors G. Pollack and P. Pratt for helpful assistance. A I am indebted to Professor D.R. Stump and Dr. J. Heremans for their valuable suggestions during the early stages of my program when we were collaborators. Thanks are also due to X.V. Qian, Y.B. Fan, 5. Lee, T. Park and P. Zhou for their assistance and for interesting dis- cussions. I am appreciative of the friendship and useful help from H. Langer, T. Palazzolo. J. Buns, J. Zhao, Y.J. Qian. There are many others to whom I owe thanks. They are too numerous to mention one by one. But in particular, I would like to thank R. Kennan who has spent considerable time correcting and shaping my English. Finally, I am grateful for the financial support from the NSF, NASA, and the MSU cm. iv TABLE OF CONTENTS PART I: Levitation Studies of High Tc Superconductors .............. 1 Chapter I Overview ....................................... 2 Chapter 2 Variable Temperature and Variable Field Levitometer ........ ......... ......... .... 14 2.1 Introduction .. ............. ............. ....... 14 2.2 Apparatus Details ..... ........................ . 15 2.3 Operation of the Levitometer ....... ..... ....... 22 2.4 Concluding Remarks ............................. 28 Chapter 3 Levitation Studies of High Tc Superconductors .. 30 3.1» Introduction ....... .............. .. ............ 30 3.2 Experiments and Results ..... .... .......... ..... 30 3.3 Discussion and Analysis ................. ....... 46 3.4 Summary and Concluding Remarks . ............... . 62 List of References .............. ..... ............... . ...... 64 PART II: Resistivity Studies of Alkali-metal Ammonia . ........... 68 Intercalated Graphite Ternary Compounds Chapter 1 Overview ... ........... . ...... . ............ ..... 69 Chapter 2 Two-Dimensional Diffusion-Limited Kinetics ..... 86 2.1 Introduction ...... ......... .................... 86 2.2 C-axis Resistivity Measurements of K-Nfla-GIC ... 89 2.3 Two Dimensional Diffusion-Limited Kinetics ...... 99 V 2.4 conCIuSion ......OOOOOOOOOOOOOO0.000000000000000105 Chapter 3 Two Dimensional Hetal-Nonmetal Transition ......107 3.1 ’ Introduction ....................... ..... .......107 3.2 a-axis Resistivity Studies of K(N33)x624 ....... 109 3.3 Two Dimensional Metal-Insulator Transition in K(N33)IC24 ....... . ........... .. ............ 119 3.4 conCIuSion O...OO....0.0.000...000.00.00.0000000127 Chapter 4 Ion Size Effect of Alkali-Metal Ammonia Graphite Intercalation Compounds .... ..... .....129 4.1 Introduction ............................ ..... ..129 4.2 Experiments and Results ...... ..................129 4.3 Discussion ........... .......... ....... ...... ...134 List of References . ......... . ............... . ...... . ....... 138 APPENDICES 00.000.00.00. 00000 0.0.0.000.00.0..00.00.000.000...0.0.0.143 vi Table 1.1 2.1 2.2 3.1 3.2 1.1 1.2 4.1 LIST OF TABLES Page Part I Superconducting elements ........ ...................... ..... 3 The optimum coefficients ai yielded by the least squares fit of polynomials to the magnetic field strength .......... 23 A comparison of the results of levitation and SQUID measurements for Nbo 78(Al0 78Geo 22)0 22 ....... . 29 A list of the values of xj, Aj, and Hj for three states .... 35 The parameter a and l/fi used in the four different models .. S6 ' Part II Commonly used donor and acceptor intercalants ......... ..... 72 Temperature ranges used in the binary sample preparation ... 78 Parameters and properties of the stage-1 M(NHS)XC24 ........ 135 vii Figures 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.5 3.6 3.8 LIST OF FIGURES Part I (a) and (b) are schematic phase diagrams for type I and type II superconductors. (c) shows the flux penetration for three states . .. ...... ........... 6 The unit cell of YBaZCu307 ......... ............. . .......... 8 A schematic diagram showing a twin plane boundary .......... 10 The orthorhombic structures of the Bi-based or Tl-based high temperature superconductors ..... ............ 11 A schematic diagram of the levitometer ..................... 16 The magnetic field and field gradient distribution in the levitometer ..... ...................... 21 The Levitation height of Nb0.78(A10.7BGe0.22)0.22 ........ ... 26 The susceptibility of the Nb0078(A10.7BGe0.22)0.22 ......... 27 A schematic diagram of the pellet press . ................... 32 A schematic diagram showing the relevant axes for the levitation of a twinned single crystal ........... .. 33 The levitation height of a YBaZCu307_6 ..................... 37 A plot for YBaZCu307-6 of the square of the levitation temperature (Ti) versus the inverse field gradient ......... 38 The magnetization of YBaZCu307_6 deduced from the levitation height ................................. 40 The susceptibilities of an YBaZCu307_6 pellet as measured using a SQUID susceptometer .......... .......... 41 The corresponding magnetization of YBaZCu3O7_6 as measured by a SQUID susceptometer ......... .............. 42 The temperature dependent magnetization of the conventional superconductor Nb0.78(A10.78GeO.22)0.22 ...... . 43 viii 3.9 3.10 3.11 3.12 3.13 3.14 1.1 1.2 1.3 1.6 2.2 The levitation results for a sintered pellet of YBaZCu3O7 6° 45 The levitation results for a BiZSr CunOy pellet ....... ..... 47 2 The square of the levitation temperature versus the inverse of the gradient for a Bi-based high Tc superconductor . ..... 48 A schematic diagram of the field dependent magnetization for most type II superconductors ............. 52 The temperature dependent magnetization obtained from Eqs.3.3.10 and 3.3.11 in text . ............... 55 A least squares fit of the magnetization versus temperature data for YBazCu307_6 ........ ....... . .......... 58 A comparison of the levitation results for YBa Cu O in the form of a pressed pellet, 2 3 7-6 a sintered pellet and a single crystal . .................... 61 Part II The structure of hexagonal graphite . ........... . ........... 70 A schematic representation of the stage-1 to stage-4 graphite intercalation compounds .................. 74 The potassium to carbon composition ratio .................. 76 (a) single domain model. (b) DH domain model (c) migration of DH domain walls ........................... 80 A schematic diagram of an ammonia molecule ................. 83 in graphite and its planar rejection A schematic representation of the potassium ammonia seed cluster and computer generated K-NH3 in-plane structure x... 84 A sketch of the experimental set up for the resistivity experiments ....... . ............................ 91 The saturated ammonia vapor pressure versus temperature .... 93 The ratio of the saturated isothermal c-axis resistance of K(NH3)xc24 to the resistance of R024 as a function of ammonia pressure ................ .... 95 ix 2.4 2.5 2.6 3.3 3.5 3.6 3.7 3.8 4.1 4.2 4.3 A schematic representation of the graphite planes and ammonia intercalants in K(NH3)xC 97 24 .............. Time dependence of the c-axis resistance ratio ........ ..... 98 The composition dependence of the function [Ri(sat)/Ro-1] ..101 The onion skin like structure of the graphite fibers ....... 110 The schematic diagram showing the two-bulb method for preparation of the stage-2 graphite fiber'intercalation compounds ..................... 112 The (00L) x-ray scattering results for a stage-2 K024 fiber in a standard glass ampoule and in the specially prepared thin wall capillary tubing ............. 113 The (00L) x-ray diffraction pattern of a pristine graphite fiber, its intercalated stage-2 KC 24' and the stBSE'l K(N33)xc24 eeeeeeeeee e e e e e e eeeeeeeeeeeeeeee 114 The room temperature isothermal a-axis relative resistance versus the ammonia pressure . ..... ...... ........ 116 The composition dependence of the reflectance R(w) ......... 121 The Kramers-Kronig derived imaginary part of the dielectric function 62(0,w) ........................... 122 A plot of the Lorentzian oscillator strength versus the ammonia composition in K(NH3)XC24 .............. 124 The c-axis relative resistance (R/Ro)a for M(NH3)XC24, M-K, Rb, Cs ................................... 132 The a-axis relative resistance (R/Ro)C for the three alkali metal GIC's .......................... 133 A plot of the maximum relative c-axis resistance . 2 (R/Ro)max versus the ionic parameters xmax (dc/r ) ... ..... 136 PART I LEVITATION STUDIES OF HIGH TEMPERATURE SUPERCONDUCTORS CHAPTER ONE Overview Since the discovery of superconductivity in mercury in 1911, the spectacular physical properties of superconductors have attracted many physicists to explore this mysterious state and to search for new materials with even higher transition temperatures (or critical temperature) Tc. In 1933, Meissner and Ochsenfeld discovered that a magnetic field (provided that it is not too strong) cannot penetrate into the interior of a superconductor. that is to say superconductors exhibit perfect diamagnetisml. This effect is named the Meissner effect. Perfect electrical conductivity and perfect diamagnetism are two independent signatures of the superconductivity. Another striking feature of a superconductor is an energy gap of width 2A centered about the Fermi energy in the set of allowed one-electron levels. More than twenty metallic. elements have been found to become superconducting at very low temperature (see table 1.1). Meanwhile, a few thousands of alloys and compounds have also exhibited superconducting properties2 which have been extensively studied. Among this group of superconductors, the highest Tc has been found in the 70'33 to be 23K. In spite of the low transition temperature, many practical applications have been found in various fields. One of the H He 0 LI 8e 8 C N O F Ne Na Mg Al Sl P 3 Cl Ar K Ce Se Ti V Cr Mn Fe Co NI Cu Zn Ge a“. As Se 8r Kr Rb Sr Y Zr Nb Me To Ru Rh Pd Ag Cd In Sn Sb Te 1 Xe O 0 Cr 8e Lu H! Te W Re Os Ir Pt Au Hg Tl Pb Bl ‘ Po At Flu Fr Re . 7 ’ . Le Ce ! Pr l Nd] Pm Sm Eu Gd Tb Dy Ho Er Tm Yb [Ac ThIPelU—INQ‘ Pu Si Superconducting Superconducting under high pressure or in thin films Table 1.1 Superconducting elements. reference 4 After G. Gladstone et al. most important applications is in high magnetic fields. Superconducting coils which provide several Tesla magnetic fields have been widely used in cyclotron in nuclear and high energy physics experiments. Another important application is the detection of very small signals. The superconducting quantum interference device (SQUID) can detect a voltage 15 9 differences as small as 10' V, and a magnetic field as small as 10- G. To date, most superconducting devices are operated in liquid helium with increasing costs. Many applications are limited due to the low critical temperature Tc of conventional superconductors. Bednorz and Miiller recently introduced a new class of superconductors which are copper oxides with a layered perovskite-like crystal structures. Their work has generated a wave of intense excitement and activity which brought the transition temperature Tc from 20K to 125K in a year or 806.9. This revolution in high temperature superconducting materials may bring us ,to a new era of technology and open whole new applications of superconductivity such as high speed superconducting computers and large scale superconductive magnetic energy storage (SITES). The study of this new class of superconductors has become extremely attractive not only because of the potential technical applications, but also because these new materials may. exhibit a new mechanism for superconductivity. A full understanding of 'the mechanism may offer a new direction in looking for other types of superconductors with higher Tc. In general, superconductors can be classified in two types, namely type I and type II. For type I superconductors. they undergo a transition from the normal state to the Meissner state at a certain critical temperature Tc. In the ideal Meissner state (ignoring London- like flux penetration at the surface), all flux is expelled from the superconductor when it is exposed to a weak magnetic field. The magnetic induction field 3 inside the superconductor is zero. This is true until the external applied field reaches the so called critical field 3c' after which the sample goes into the normal state and 3 increases linearly with the applied field H as shown in figure 1.1a. Meanwhile, the magnetization increases linearly with H until EC, after which it jumps to zero. In contrast, type II superconductors exhibit a vortex state between the normal state and the Meissner state. In the ’vortex state, some flux penetrates into the material and forms vortices. Figure 1.1c shows the flux penetration for these three states. If we look at magnetization versus magnetic field, for an isotrOpic type II superconductor the linear relationship between the two quantities ends at the so called lower critical field BC where the superconductor 1 enters the vortex state from the Meissner state. The magnetization then decreases with the applied field until the field reaches the upper critical field Hc Above this field, the material becomes normal. The 2. schematic behavior of magnetization and magnetic induction for type II superconductors is plotted in figure 1.1b. The new class of layered oxides has been found to be type II superconductors. Unlike the conventional type II superconductors, the upper critical fields of these new materials are so high that they have not been directly measured to date. The ratio of ch to He can be as high as tens of thousands while 1 H B T 7} AM (o) normal I / Heissner / Si? He ”E a H B 1‘ A A" (5) normal vortex meisaner : ‘rd’ 1 J T H... Ht: ‘3 H.. “a 17 AAATATJLATAtILJLAltl normal state vortex Stltfi Heissner state Figure 1.1 (a) and (b) are schematic phase diagrams for type I and type II superconductors, respectively. relations between the external field H, the magnetic induction field B and the magnetization M for each state are also shown in the figure. flux penetration for the three states. (c) shows the it is only an order of ten for most conventional type II superconductors. I The high temperature materials include single-layered La _xMxCuO 2 4-6 (M=Ba, Sr, Ca, Na, ...) compoundss, double-layered RBaZCu307_‘S (RsY and a lanthanide element except Ce, Pm, or Tb) compounds7 and multi-layered Bi-Ca-Sr-Cu-Oeand Tl-Ca-Ba-Cu-Ogcompound's; In the crystal structure of each of the above specieS, one or more Cuo layers have been found by 2 10-12. As a independent X-ray and neutron diffraction studies representative, the orthorhombic structure of a yttrium-barium-copper oxide compound is shown in figure 1.2. The unit cell consists of two dimpled CuO 2 planes separated by a yttrium layer which contains no oxygen and inserted with two BaO and one Cuo layers (containing Cu-O chains). Strong anisotropy has been observed in the lower critical field and in the critical current density”. These measurements have suggested that the 'good' conducting directions are along the Cu-O planes. The CuO2 plane, which is referred as the ab plane, has become a major focus of many theoretical and experimental studies due to its important role in high temperature superconductivity. It is generally believed14 that the supercurrent is localized in the Cqu planes and that the spins which are associated with the holes on the copper site are responsible for antiferromagnetism in the normal state. 15-17 Optical studies have demonstrated that various kinds of flat defects exist in the high temperature oxide superconductors YBaZCu307_6 Figure 1.2 The unit cell of YBaZCu307. The 3 axis is along the direction which is perpendicular to the copper oxide . plane, 3 is parallel to the plane and along the copper oxide chain and d is perpendicular to both 3 a. and c. (hereafter denoted by 123). Bi-Ca-Sr-Cu-O and Tl-Ca-Ba-Cu-O. The three 18 most commonly seen defects are twin planes in the 123 compounds 17 strip domains in Bi based copper oxide superconductors , and stacking faults in both Bi based and T1 based copper oxide superconductorsls. The twin planes are a direct consequence of the very slight difference between the lengths of a and b axes in the 123 materials and are 18. In figure 1.3, 2 and b referred to as antiphase domain boundaries are interchanged in the two adjacent striations. Light microscopy studies15 have shown that small grains (typical size 5pm or less) are unidirectional grains i.e. the twin planes in these grains are aligned in one direction. On the other hand, large grains have a multi- directional domain structure and contain different twin plane orientations. Although twin planes are not found in Bi (or T1) based copper oxide compounds, stacking faults are almost inevitable. These compounds form a hierarchy of structures which differ in the number of Cqu planes and number of perovskite layers n (see figure 1.4). The generic chemical formula can be written as Bimcan-lsrzcunOZn-rm-i-y or T1 Ca Ba Cu O . The critical temperature T increases as the m n-1 2 n 2n+m+y c . number of Cqu planes n increases and the Cu-O distance decreases. The low binding energy of this structure leads to stacking errors in the number of perovskite layers between the two metallic layers as has been shown by using transmission electron microscopyls. The lattice constants of Bi-Ca-Sr-Cu-O compounds have been found to exhibit ratios Figure 1.3 10 D3) 5") A schematic diagram showing a twin plane boundary. 3 and b are interchanged in the two adjacent striations. Note that the orientation are orthogonal in (a) and (b). The boundaries between the striations are referred to as twin planes. They are along the (110) direction. From reference 18. 11 l I 3A. 2021 — . ' . AA Bi(<23K) . , T1(<80K) 1 “. “=1 2122 — ' Bi(80K) 3 , T1(105K) 4 “=2 2223 Bi(110K) g gu T1(125K) . e T1 or Bi "’3 2324 0 Ba or Sr ? 9 .Ca 11:4 A: perovskite layer IB:rnetaflh:layer Figure 1.4 The orthorhombic structures of the Ei-based or T1- based high temperature copper oxide superconductors. Tc (in brackets) increases as the number of perovskite layers, n. increases. 12 which are similar to those of some mineral materials. The structure is called an aurivillius phase where a, b, and c can be expressed in terms of a characteristic length ap as follows: a-fiap, b-Sfiap, and c-eap. o . For the Bi high Tc compound 31) is equal to 3.811. Capponi et al. have shown, using lattice fringe images, that the lengths along the b-axis are incommensurate”. The periodicity in the b direction varied from 4\/-2-ap to 6J2ap instead of being exactly 5.5211,. This is shown in the images taken along the c-direction where two scriations have different repeat distances in the b-direction. These mass density modulations along the b-axis are referred to as stripe domainsl7. An understanding of the perturbative role of flat defects and the link strength between and within grains may reveal properties that have important consequences in the design and fabrication of practical superconducting devices. An example is field induced orientation. Solin et al. 19-21 have reported the first preparation of oriented bulk polycrystalline specimens aligned at T < Tc. They have shown that twin planes have a marked effect on the macroscopic magnetic properties of YBaZCu307_6. They also demonstrated the alignments along the [110] axes 22-23 with an applied weak magnetic field at T < Tc while others obtained alignment of the c-axes with a strong field at T > Tc. Vierira et al.24 have reported a simple levitation experiment soon after the discovery of the 90K superconductors. They have immersed a 13 permanent magnet in a liquid nitrogen dewar. Superconducting particles were then dropped from the top of a glass tube which was inserted between the two magnet poles. They have found that larger particles (>50pm) experienced a greater force and actually levitated while small particles (20pm or less) collected at the bottom of the sample tube. All of these particles were known to be superconductors from independent SQUID measurements of the magnetization. It was found that if the small particles were then pressed into a single pellet, the pellet also levitated. Their results served as an another example of the impact of the grain morphology and their orientation on the properties of high temperature superconductors. The simple explanation of their results is that small particles are single grained and have a unidirectional twin plane domain structure. They therefore can adopt a unique alignment with the magnetic field which minimizes the flux expulsion and thus the magnetic force. However,‘ large particles are multigrained and have no unique alignment direction. Therefore, they experienced a larger magnetic force and levitated. Their experiments were performed at fixed field and fixed temperature. In addition, their samples were immersed in the liquid nitrogen, the buoyant force of which could not be ignored. In this part of my dissertation, I will present the results of variable field and variable temperature levitation studies which explore the levitation/orientation phenomenon quantitatively and thus elucidate the influence of intergranular weak links in high temperature superconductors. 14 CHAPTER THO Variable Temperature and Variable Field Levitometer 2.1 Introduction Since the discovery of the Meissner effect, levitation experiments have been widely used to demonstrate superconductivityzs, and to develop the possible applications, particularly levitated trains“. Many other potential applications including frictionless bearings”, levitated coil 'for multipole fusionza, and pressure gauges which operate by diamagnetic suspension. in the Brownian-motion29 have been envisioned. The basic principle of magnetic levitation is to balance the magnetic force and the weight oF the} superconductor. Therefore, the levitometer can also be used as a magnhtic"‘balance. Conversely, one can find the magnetic force from the known gravitational force, and hence determine the related magnetization and susceptibility. Following the reports of the 90K high temperature superconductors, the levitation experiment was immediately repeated by many groups all over the world. The common configuration of their experiments consisted of a permanent magnet and a high temperature superconducting pellet. The superconducting pellet is immersed in a small cup of liquid nitrogen. After the pellet is cooled and enters the superconducting state, one carefully puts a small permanent magnet onto the pellet and 15 the magnet will levitate on the top of the superconduting pellet. This simple setup gives a clear view of the Meissner effect in the high temperature superconductors. But it cannot give any quantitative measure of the levitation. Meanwhile, Vieira et al.“ introduced the idea of separating superconducting particles and non-superconducting particles as noted above. Again, their levitometer only works at fixed magnetic field with a permanent magnet and only at liquid nitrogen temperature. Unlike the other levitation devices. the variable temperature and variable field levitometer we designed provides the capability of accomplishing quantitative studies of the magnetization and direct visual access to themagnetic field induced alignment of individual particles. In this chapter, I shall first give a detailed description of our levitometer and then discuss the application of the device. 2.2 Apparatus details Figure 2.1 is a schematic diagram of our levitometer. In order to achieve magnetic levitation, a non-uniform magnetic field is essential. A cryogenic levitation chamber is also required to provide a low temperature environment for the sample entering the superconduting state. Finally, a cathetometer and other accessories are used to make quantitative measurements of the levitation height. Figure 2.1 shows these important components. We use an Alpha Scientific model 4800 electromagnet to obtain the desired magnetic field. This is a 4" magnet which is small enough to l6 'Slldlng Seal Sliding Tubing Pressure Valve ’1 e'ul ,’ ‘U «...... r, " 1'1 0. .a of W a .' ‘ l quuld He ‘m ..- """3 8'3“." Actlvated/H "'- ' " Charcoal t quuld He Dewar Figure 2.1 .A schematic diagram of the temperature and field variable levitometer. l7 mount on a platform or a table. The two poles are facing each other in the horizontal direction. The minimum air gap between the two pole caps is determined by the diameter of the levitation chamber and associated cryogenic equipment (see discussion below). The magnetic field strength can be as high as ZOkG when the air gap is set as 0.6'. This is the upper limit of the magnetic field strength in our levitometer. Clearly, one can increase the maximum operating magnetic field by decreasing the air gap between the pole caps and later I shall discuss this in detail. Between the pole caps is the cryogenic levitation chamber. We have modified the magnet frame from 90° upright to 45° mounting in order to allow the levitation chamber to pass through the magnet. Tapered pole caps have been chosen to provide an increasing field gradient which is the driving force of levitation. For best results, we have machined the caps until the diameter of the pole end is slightly larger than the air gap. Further sharpening the pole caps will decrease the field strength and hencexthe'. field gradient. This is because decreasing the area of the pole caps'is*2quivalent to increasing the distance between the poles. The cryogenic levitation chamber is made of double walled glass tubing with a vacuum jacket to stop heat flow. To reduce heat radiation, the glass wall is coated with silver leaving a 5mm wide un- coated strip to allow for visual access. The lower end of the cryogenic levitation chamber is immersed in a liquid helium dewar underneath the magnet. Cold helium vapor flows through the levitation chamber for cooling. The cooling rate can be controlled by the pressure relief valve shown in the figure 2.1. By completely closing the valve, the pressure of helium vapor will build up in only a few minutes. The 18 liquid helium level can be raised as high as the sample region. The sample temperature drops to 4.2K immediately under this maximal cooling condition. Leaving the pressure valve slightly opened, one can reduce the liquid helium boiling rate and provide much longer running time using only limited liquid helium. On the other hand, a certain helium pressure is required for cooling. Insufficient cooling will cause a temperature gradient along the inner tubing. The pressure valve is used to optimize both aspects. Under our experimental conditions, two liters of liquid helium can last for six hours. Since helium can easily diffuse through glass tubing when the temperature is above liquid nitrogen temperature (77K), activated charcoal is placed in the vacuum jacket to absorb helium and maintain good vacuum insulation of our levitation chamber. This helps maintain the levitometer in good working conditiom'andzteffectively increase the length of the period that one has before reyevacuation of the vacuum jacket is required. The samp-Le‘,-is'-;confined in another glass tube which is co-axial with the double wall tubing. The bottom of the inner tubing is sealed to prevent the sample from ‘being exposed to helium vapor flow directly. But a small hole on the side of the inner tubing ensures helium 'gas exchange and heat convection. This helps cool more effectively and allows a more uniform temperature over the whole sample levitation region. For most of our experiments. the maximum temperature difference is about one or two degrees. Also a copper tube. used as a heat bath. is tightly fitted to the outside of the inner tubing. A slot along the copper tubing was machined to allow visual access to the inner tubing. GE varnish was used to fill the gap between the copper tubing and the l9 inner glass tubing to ensure good thermal contact. Three Gallium- Arsenide diode temperature sensors are attached on the bottom. the middle and the top of the copper tubing to monitor temperature. The reason we choose a GaAs sensor is because the Lil curve of the GaAs diode varies little under the influence of a magnetic field. A heater wound at the bottom of the copper tubing provides accurate temperature variation/control. The temperature range of our levitometer is from 4.2K to room temperature or even higher. The heater is double wound to eliminate the solenoid effect that will affect the magnetic field distribution. The dimensions of the temperature sensors, c0pper temperature sink. and inner glass tubing limit the minimum size of the. chamber and the air gap between pole caps. We have used rectangular tubing to reduce the air gap from 0.8' to 0.5". This leads to a considerable“. increase in the field gradient. The maximum value is as high as Bké/cm. Ice is very'harmful since it will not only freeze the sample at some height. but also destroy superconductivity. Therefore, the levitometer must be a frost free system. This is accomplished by putting all components together with o-ring seals and using homemade feedthroughs for sensor and heater wires. With a sliding seal at the upper portion of the inner tubing, one is able to move the inner tubing up and down without bringing in moisture. Because of hysteresis in type II superconductorsSo, the initial position of the inner tubing is important. It corresponds to different initial conditions of the measurement. By varying the initial 20 condition. one can study no: only levitation but also suspension. Our levitometer serves both purposes. To make quantitative studies. we should first find the field strength and field gradient. Magnetic fields were mapped in detail by using a Hall probe. Figure 2.2 shows a typical field distribution as a function of position for a magnet current of 25 amps. The open circles in the figure are the actual measured values. Similar curves are measured for other magnet currents such as 10A. 15A. 20A, 30A, etc. The position of the probe is recorded by a HEERBRUGG model XII-325 cathotometer with an accuracy tSOpm. The levitation height is also read by this cathotometer. A polynomial least squares fit has been used to approximate the position dependence of the field strength Kym). The solid line in figure 2.2 is a fit using a sixth order polynomial 6 Hy(z)= Zaizi. (2.2.1) i-O By taking the derivative of this funCticn, one can find the field gradient as a funCtion of position. To obtain an accurate field gradient from fitting and differentiation, one should choose an appropriate order polynomial fit. We found that lower order polynomials do not fit the field strength well. On the other hand. a polynomial with additional terms does not significantly alter the quality of the fit. Rather it introduces many oscillations in the field strength curve which suggest incorrect field gradient. A sixth order polynomial turns out to be a good choice. The dashed line in figure 2.2 is the field gradient given by differentiation of equation (2.2.1). It has the form of H,(KG) 21 20.0 b fi .. I \ — 0.6 .. 1 \ . . 1 \ 1 15.0 A ‘\ . I \ - - ‘ — 0.41:. . ‘ . :1: \ ’x 10.0 — \ .... g b - . \ q X P \ . E; b \ \ . \ "‘GL23E; £51) '- q \—v ' \s - . . ‘~ ‘~ -4- L 1 L j J L 1 l J l l L J ft: 1 .1- l. l i ‘ 0'0 725 750 775 800 325 0'0 z(mm) Figure 2.2 The magnetic field and field gradient distribution in the levitometer. measured at a magnet current of I=25A. and are accurate to 506. The field strength data are 22 5 “Ian Ziaizi'l (2.2.2) 8: i=1 The optimum values of the ai's from the fitting procedure are listed in table 2.1. One can also use a differential Hall probe to measure the field gradient. A differential Hall probe is constructed from two regular Hall probes with fixed separation (e.g. 1mm). The difference between the response of the two probes divided by the separation gives the field gradient. One must be very careful to ensure that the two probes are parallel to each other and the separation must be small. Up to now, I have described in detail the components of our unique levitometer. I shall now discuss the operation of this device. 2.3 Operation of the levitometer As noted earlier, the initial condition is very important in the levitation measurement. One should thus initiate levitation under consistent conditions. To accomplish this, the following experimental scheme was used. Starting from room temperature, the inner tubing was pulled to well above the electromagnet. The sample is at zero field or at the earth's magnetic field, and in this state the flux in the sample is essentially zero. Then, the pressure valve is closed. Helium vapor pressure quickly builds up and sample temperature is lowered to 5K in just a few minutes. After the sample is cooled, the electromagnet is turned on and the magnet current is increased to the desired value. When the field is 23 a0 al. a2 a3 a4 35 5.6 6.97.1.71 4.05 -1.94 5.66 9.49 9.06 xlO""'"x*lOI§'[x‘lO" x10" x104 :10" x10"11 Table 2.1 The optimum coefficients at yielded by the least squres fit of the polynomials to the magnetic field strength. _ 24 below the sample's lower critical field, there is no flux inside of the sample since it is in the Meissner state and is completely diamagnetic. When the field strength is stronger than the lower critical field, some flux penetrates the sample. The stronger the field is, the more the flux penetration. Some flux will be trapped in the sample when one tries to reduce magnetic field. Therefore, the key point in this scheme is to monotonically increase the magnetic field. Since the sample is well above the magnet pole pieces, the magnetic field is very weak. The sample is still seated at the bottom of the inner tubing. At this time, the inner tubing is slowly lowered with continuous vibration. The sample then enters the stronger field and higher field gradient. At some point, the levitation force would be strong enough to lift the sample. After that, the sample would stay at the same height while the operator keeps lowering the tubing until the bottom of the tubing passes through the pole caps. The height of the sample was recorded as the first data point. The pressure valve is then opened slightly at this time to select the desiredzcooling'ratea Now one is ready to measure the temperature dependeni‘c'e”of"the levitation height and hence the magnetization. The heater is activated and the sample temperature is increased step by step. The levitation height is then recorded at each fixed temperature by using the cathotometer described in the previous section. The magnetization can be found from the levitation height by using the equations below. Since the magnetic force balances the gravitational force when the sample is at rest, we have F IIF mag .' ng (2.3.1) gra 25 6H (2) 1 1 Also, F - _H(z) V (2.3.2) mag. 2 ———-az where H(z) is the magnetization when the sample is at the height 219. Thus, u(2)- 293 (2.3.3) [6Hy(z)/6z]. Note that the magnetization of the sample depends on its density and not on its volume. As temperature increases, the magnetization will decrease. To keep the product of magnetization and field gradient constant, the sample will drop closer to the edge of pole caps where the field gradient is higher. Therefore, we did make measurements with ever increasing field strength as we intended. The susceptibility as a function of temperature can also be found using X(T.H(z))- ”(T'Z) (2.3.4) H(z) To test our levitometer, we have measured the temperature dependent levitation height of a conventional superconductor. Figure 2.3 shows the measured results for a Nb sample. Each curve o.7a‘Alo.7aGeo.zz’o.22 corresponds to a selected magnet current and certain field strength and gradient distribution. The levitation height decreases as the sample temperature increases just as we expected. Also, a higher magnet current produces a stronger magnetic field and field gradient. As a consequence, the magnetization will decrease as illustrated in figure 1.1b. The product of the magnetization and field gradient determines the absolute levitation height. Using equations (2.3.1)-(2.3.4), one can find the susceptibility and compare these results with SQUID (Superconducting Quantum Interference Device) measurements which are Z(mm) 26 620 [- 800 5“ o I=ZOA C I: On 0 U I=15A 780 '— m o 1310‘ .. 0 0° : 0 0 0g _ (3 . 760 :- OD : 00°00 - O 740 :— 3300 I 00% m . 3.0 D 720 L- 8 " 1 1 1 n l 1 L L1 1 1 L 1 l I 1 1 1 1 I L 1 L 1 5 6 7 8 9 10 T00 Figure 2.3 The levitation height of Nbo,73(Alo.7BGeo,22)o,22 measured as a function of temperature and magnet current. The conventional superconductor was used here to verify the reliability of levitometer. Note that the data are taken at very low temperature and the temperature uncertainty is 10.5K. The levitation height Z is accurate to 1mm. 27 0.0 .lfl' ". I#+# e 1. 1 m|e|1vlea1leeI-|e1y 4‘1. 11gz3< C, a 3E all " 33$ OVOJOII .("'I l;- f‘fif QB flag? $3??? I o in fir.‘ O H x a x ‘4 Edipg Egg; {0 ”m ° ° H-6.5kG “E ‘L x H-4.5kG o i 0 ° H-3.0kc E: ‘3 H-2.5kG E "1.0 .- 0 + H-ZDkr ‘3’ ' 2 3121:: > h ‘ '1“ H-1.21°;c; 3“" H-1.0kG ° H=3000 4 1 1 1 l L 1 1 i 15.0 200 ' 5.0 10.0 T(K) Figure 2.4 The susceptibility of the Nbo,7g(Alo.736eo,zz) sample measured using a SQUID susceptometer. The temperature uncertainty is +1K. The susceptibility measured by the SQUID susceptometer is accurate to one-thousandth of its value. 26 shown in figure 2.4. Since the field strength changes in each levitation curve while field is fixed in the SQUID measurements, we can not directly compare these two sets of data. Instead, the results of the two methods are compared in table 2.2. They agree well with each other. 2.4 Concluding Remarks We have developed a unique variable field and variable temperature levitometer which can accomplish the measurements of magnetization and susceptibility. Although the levitometer is not as accurate as a commercial SQUID susceptometer, .it provides magnified direct visual access of the orientation of superconducting particles in a magnetic field. Magnetic force and field induced alignment of individual particlesfwranging in size from 10 pm to 3mm can be measured simultaneouslyii:Thixlevitometer is thus complementary to a commercial susceptometer. 29 Field T SQUID Levitometer M /d(emu) M /d(emu) 1.01:6 6.2K 6.32 8.6 $0.9 1.21:6 6.7K - 7.80 7.3i0.7 1.61:0 7.6K 5.1 4.91-0.59 Table 2.2 A comparison of the results of levitation and SQUID measurements for Nb0.78(Alo.786‘0.22)0.22' 30 CHAPTER IRREE Levitation Studies of High Tc Superconductors 3.1 Introduction High temperature COpper oxide superconductors were first prepared by solid state diffusion techniques. This was followed by sintering in an oxygen environment at about 900°C for several hoursé'7. Hh'ller et al. have pointed out that the sintering process used to prepare these oxide systems yielded granular materialss. These materials can be described as systems which are formed from many anisotropic grains. The granularity of these materials strongly affects a number of their magnetic properties. In this chapter, I will discuss levitation studies on these granular high temperature superconductors. 3.2 Experiments and Results The yttrium-barium-copper oxide superconductor samples used in our experiments were synthesized using a solid state diffusion method7. Yttrium oxide (Y203), cupric Oxide (CuO), and Barium carbonate (BaCu03) powders were first dried at 100°C and then were mixed with a ratio of approximately 2:4:7. In order to enhance solid state reaction, the powders were well mixed and tightly packed into a crucible. After 31 firing at 800°C for 12 hours under flowing oxygen, the black color single phase YBaZCu307_6 was formed. The greenish nonsuperconducting phase could always be eliminated by repeated firing. Bulk YBaZCuBOF5 samples were ground into powders in a ball mill and passed through selected sieves. Powders with a dimension of less than 20pm were selected and pressed into a pellet using a UABASH Hydraulic Press. Figure 3.1a shows that homemade die parts used in this press. Two hardened steel pistons of identical diameter (A and B) were fit into another hardened steel cylinder C. The surfaces of piston A and piston B were polished using a HRIRG Surface Grinder. The longer piston A was first placed into cylinder C and then the sample powders were added. The shorter piston B was inserted in C on top of the sample. By turning B, powders were uniformly spread between the two of faces of A and B. Thiswouldset the powder into an evenly packed layer and yield a pressedwpellet which-.wasuniform. The whole assembly was then placed in the center of the VABASH'p'ress'and pressed to the desired pressure (Figure 3.1b)w.-...V1'o remove the-isample pellet, piston B was pressed into C from the bottomsi‘de of A as shown in figure 3.1c. A set of die with sizes from 3/8' to 1.5' allowed us to obtain pellets with desired diameters. The amount of powder we used determined the thickness of the pellet. The actual levitation experiments were performed using our variable temperature and variable field levitometer described in chapter two. Figure 3.2 is a schematic diagram showing the magnetic configuration of a twinned single grain disc. The axes 2 and 3 refer to the ab planes while 1 refers to the c axis.- 0 and 10 are the conventional Euler 32 (b) (C) Figure 3.1 A schematic diagram of the pellet press. (a) shows ‘ the die parts used in making the pellet. (b) and (c) show the direction of the force applied to the die in the two steps of the pellet preparation. Figure 3.2 A schematic diagram showing the relevant axes for the levitation of a twinned single crystal. The axes 2 and 3 refer to the ab plane while 1 refes to the c-axis. 9 and ¢ are the conventional Euler angles. Lines across the sample represent twin planes. 34 angles. Lines across the sample represent twin planes. The most general case is that the susceptibility in each direction is different. In other words, the sample is completely anisotropic. We also assume that the demagnetization factors are also fully anisotropic. The magnetic energy of the levitated grain can then expressed as follovsalz 3 u-II 3.3 dV - v EE:LA.H2. j-x,y,z (3.2.1) " ° — J 0] 2 V 2 . J'l X. Aj- J (3.2.2) 1+N. ij Here 6 is the magnetization of the sample while Hoj’ Nj, and Xj are, respectively, the jth components of the applied field, demagnetization factor and the susceptibility. Table 3.1 lists the values of xj, Aj, and the net field strength Hj for the three typical states of a type II materials. The superconducting. state corresponds to complete isotropic flux exclusion and the;'su7sceptibility..is -l/l+II in all three directions. The normal state is also isotropic with approximately zero susceptibility and the field in the sample is equal to the applied field. The displacement derivative of magnetic energy gives the magnetic forces while the angular derivatives yield the magnetic torques. These relations are expressed in (3.2.3)-(3.2.5) for the components which are relevant to our levitometer. Fz-- au (3.2.3) 62 19-- 30 (3.3.4) 39 35 ESTIAKPIB 2!} Ah, Ii! 1 _'"_J_ Meissner ~1/411' Nj-MT "oi/(1" 477) HI 1-1j “1 ‘_- C] ... c] .4. ""'FII Vortex 477'” 477110i ] 477 c] )flOl‘INIl (J (J f1€,i' Table 3.1 state . (x, y, or z). A list of the values of xj. AJ Meissner state, ., and Hj for the the vortex state and the normal j denotes one of the Cartesian coordinates See text, equation 3.2.2. 36 r¢- - 60 (3.2.5) ‘55" The 2 component of the magnetic force balances the gravitational force in levitation while the torques will orient the sample in the magnetic field. Figure 3.3 shows the levitation height as a function of temperature for a YBaZCu307_6 pellet. This data was taken by strictly following the procedure described in chapter two. Each curve corresponds to one magnet current. The higher current yields greater field gradient at the same height and thus greater magnetic force. As a result, the pellet is levitated higher. The center of the pole faces is at z°=697nun. He know from chapter two that the levitation height will decrease as the temperature increases. This is because more flux will penetrate the sample at higher temperature. Figure 3.3 clearly shows this feature. We have defined a so called levitation temperature (TL) which is the highest temperature that can be obtained before levitation ceases. This temperature increases as the magnet current increases. A plot of the square of levitation temperature versus the inverse field gradient at the height the levitation ceased (ZL) is shown in figure 3.4 which clearly exhibits a linear relationship between these two quantities. A linear least squares regression fit has been used to determine the slope and intercept on the T: axis. It is found that the straight line can be expressed T 2=6537-l424[ 1 ] (3.2.5) L aH/az 760 750 730 720 710 Figure 3.3 37 H 0:301 9, AT I=25A 1:201 I=15A I=10A T(K) The levitation height as a function of temperature of a YBaZCu3O7Jg pressed pellet. Each curve corresponds to a fixed magnet current. AT, AZ are typical error bars of the measurements. 38 5 4 _ A 3 *- ‘ 9‘) . O . 2:1 . # “5:: 2 :- / ,7; - TL’=6537-1424[1/(aH/BZ)] 5-4 _ 4.2 - .. 1° 1 -- T,=a1K l O lLlllLLLllJllLlLLLllllJlLJJL 1.0 1.5 2.0 2.5 3.0 3.5 4.0 [1/(6H/BZ)(kG/mm)] Figure 3.4 A plot for YBaZCu307_6 of the square of the levitation temperature (T?) vs. the inverse field gradient where levitation ceased. 39 A detailed discussion of this linear form will be given in the next section. Anorher interesting feature shown in figure 3.3 is the kink around 20K for all five currents. To verify that these kinks do not result from a nonuniform magnetic field, magnetization verses temperature is plotted in figure 3.5 using our knowledge of the field gradient at height 2 and formula (2.3.3). Clearly, the kinks remains in the plot. Moreover the kink-like feature has been observed in more than ten specimens which have been examined. This suggests a discontinuity in the derivative of the magnetization, which is related to a transition at 20K as will be discussed below. A more accurate measurement of the temperature dependence of the magnetization was carried out on the same pellet using an SHE SQUID. The results are plotted in figures 3.6 and 3.7. Data were also acquired by zero field cooling and field heating. Figure 3.7 is a plot of the magnetic moment versus temperature at five different field strengths. The temperature dependence of the magnetization can be obtained by multiplying the ordinate of this plot by the density of the sample. The kinks observed in our levitation experiments were once again present around 20K (Fig. 3.7). In addition, the magnetic moment is essentially independent of magnetic field above that temperature. This field independent magnetization is not observed in conventional superconductors as evidenced by figure 3.8 which shows the results of (Al G 0.73 80.22) the same measurement on Nb0 At temperature below 78 O.22° the kink, themagnetization strongly depends on the field strength. In general, the slope decreases as the field increases with the exception 0.00 —_M/d(emu- cma/ gram) ~ : s: .o 9 31 ‘0” 8 H‘. as. tn 1.50 Figure 3.5 40 2" or Q _— o I=30A . X I=25A ; o I=20A — D I=15A : + I=10A l:.'c1 " a j, Llllnll"llllllilJLlllllllllllll 0 20 40 60 80 100 120 T(K) The magnetization of YBaZCu307_6 deduced from levitation height measured using our levitometer. d is the density of the sample. The relative errors of the magnetization are less than 0.1. The temperature uncertainty is 11K. 41 0.00 ’21 6‘ ~ 9W g 3 + g 'c) : O o 0 0 O D D + X “-0.25 F— M U D D E. N _ i E . 0 H=6.5kG 34.50 x H=5.0kG {0 o H=3.0kG as U H=2.0kG + H=1.0kG g 0'75 x H=SOOG E ’i' H=Z5OG 0 x H=150G v1.00 E X -1.25 ' JW _1.50.1L1LLJIALILLLIIILLIIIJLIILII O 20 4O 60 60 100 T(K) Figure 3.6 The susceptibilities of YBEZCU307;8'33 measured using a SQUID susceptometer. The same pressed pellet was used as that used in the levitation The error bars are smaller than the symbols used in the figure. experiments. 120 O O 2‘ 82 IUIIIIIUWVIUIITTUU'I .0 .q 0| -—M/d(emu . cma/ gram) s 1.25 1.50 Figure 3.7 42 8 n: TIT. U “3‘ III I; r O H=6.5kG H=5.0kG H=3.0kG H=2.0KG H= 1 .OKG +DOXO )( 21x E,“ [ILLL 14 LLLLLILLLLLLJLILI 20 40 60 30 100 T(K) The corresponding magnetization of YBaZCu3OT.5 as measured by a SQUID susceptometer. The error bars are smaller than the symbols used in the figure. 43 p . y! p E M s o "'2 _ 9 Lo Cl) . a g a _ . 9 o H=6.5kG :3 X.H=4.5kG E o H=3.0kG c", _ u H=2.5kG Q + H=2.0kG 2 11 H=1.6kG 1‘ H=1.4kG -3 3 H=1.2kG 33': H=1.0kG _1 . L . n1 1 . . . 15 20 T(K) Figure 3.8 The magnetization of the conventional superconductor Nbo.73(Alo.7gGeo.22)o,22. d is the density Of the sample. The temperature uncertainty is 11K. while the magnetization is accurate to one-thousandth of its value. 44 of the 11:6 field. The susceptibility of the YBaZCu3O7_5 pellet is plotted in figure 3.6. At very low fields (2506, 1506 in the figure), the susceptibility is independent of field indicating a Meissner state with complete flux exclusion. From figure 3.6, we have found that the ransition temperature Tc of our sample is about 89K and the lower critical field Hc1 is about 3006. The levitation experiments were performed with the sample in the vortex state, i.e. the field is above the lower critical field Hc 1 and below the upper critical field ch. The same levitation experiments were repeated using a sintered pellet which is fired at 950°C for four hours . Similar results are obtained and are plotted in figure 3.9. From the kinks shown again at 20K, we can conclude that the slope discontinuity occurs at the same temperature for both sintered pellets and unsintered ones. Comparing the scale in figure 3.9 and figure 3.3, it is evident that there is a dramatic slope difference in the slope discontinuity before and after the sintering process. Since the sintering process enlarges the grain size in a pellet, this experiment gives us a clue to the grain size effect of the transition at 20K. This will be discussed in detail in the next section. Another family of high temperature superconductors is the Bi or T1 based copper oxides. They have a similar orthorhombic structure to that shown in figure 1.4. This class of materials can achieve even higher Tc than the 123 materials. It is interesting to study the difference between these two classes of materials. The temperature dependent lev1tation height of a BiZSrZCam-lCunOy 45 620 X fl 0 I=30A %°X 800 740 720 b )- _ t .. . t _ L. b D D h— I 1- .. .. b. - .. .. .‘ ... b L. .. .. .. o. Figure 3.9 The levitation results for a sintered pellet of YBaZCu307_6. The temperature uncertainty is 11K and the levitation height uncertainty is $0.1m. 46 pressed pellet has been measured using the same methods as for the 123 material. A plot of the levitation height versus temperature for the Bi material is shown in figure 3.10. The overall behavior is the same as for the 123 compounds. The levitation height decreases as temperature increases until levitation ceased at a temperature TL. The sample levitates higher at higher magnet current. The data for the Bi material also exhibits a pronounced kink but at about 15K which is significantly lower than the corresponding temperature for the YBa2Cu307- 6 pellets. The square of the levitation temperature T2 L verse field gradient at the threshold levitation height zL is plotted in figure 3.11. Like the Yttrium-Barium-copper oxide pellet, a linear behavior is also observed within experimental error. In this case a linear regression fit yields the expression 1‘2 L-79l7-2646xl: 1 ] ' 'h p 1’ (3.2.7). 33/32 The experimental error'arisesirom uncertainties in the polynomial fit to find the field gradient, from the~.'error in the determination of the levitation height, and also from a small temperature gradient which introduces 11K error in the measurement of specimen temperature (see chapter two). 3.3 Discussions and Analysis In order to interpret the linear behavior shown in figures 3.4 and 3.11, the critical fields were first considered. One of the most unusual features of the new oxide superconductors is their extremely 47 760 U _ 9 75° __" a: o I=3OA - :1 <>I=20A : DC) D I==154i 740 — U ’3‘ - u° g . '3 DJ . 730 — 720 - 710 h 1 I 1 l 1 1 1 1 l l 1 1 1 I 1 l 1 v 0 20 4O 6O 80 T(K) Figure 3.10 The levitaion results for a BiZSrZCunOY pressed pellet. uncertainties are 11K and :0.1mm respectively. The temperature and the levitation height 48 A 3 0‘) 0 g .. N —1',,'=7917-2a4s[1/(aH/52)] a: 2 ‘ ' , a; T. E" -593: 1 ITTIIUUUIjTUUIII'jl—TITI fl lllllLJlLlL 1.0 1.5 2.0 2.5 3.0 3.5 4.0 [1/(6H/62)(kG/mm)] OJIILILLLLLIL14141 Figure 3.11 The square of the levitation temperature versus the inverse of the field gradient for Bl28r2Can,1CunOy. 49 high upper critical fields ch. As noted in chapter one, there are no '5‘ direct measurements of ch available to date. It is generally believed that the ch is as high as a few hundred kilogauss. Meanwhile, the lower critical field He is quite low as suggested by our SQUID 1 measurement of Eli - 3006 (figure 3.6). If one examines the magnetization with respect to the applied field such as shown in figure 1.1b. magnetization decreases to zero gradually over the large range of Bel-862' Therefore, it is reasonable to assume that the magnetization remains constant when the applied field is in the range Hli'l0. (3.3.6) 4n 6H°y(z(T))/az Equation (3.3.4) becomes - E_;H:ff(0)x[1-( T )2]+A= 293 (3.3.7) 4n TCA 8H0y(z(T))/82 where TcA is the actual transition temperature. Thus 2 2 8npgT: 8H0 (z) -1 T -T (1-A')- x V (3.3.3) L M m —6—z—z=zL cl where A'=Ax4n/H:if(0) and g . 1/2 TCA TC/(l-A ) (3.3.9) From Eq.3.3.9 and the values of TC and TcA determined from levitation 52 f ~47rM Figure 3.12 A schematic diagram of the field dependent magnetization for most type II superconductors 53 and SQUID measurements we find that A=20.7(_}__G)=1.656 and 4H 10( 1 G)=0.7BG respectively for the 123 and Bi compounds. 41'] We now consider the origin of the kinks shown in figures 3.3, 3.7, and 3.10. The "double transition" like behavior shown in these figures is similar to the one previously observed in weakly coupled granular 33 . . . . superconductors . The first tran51tion at around 90K 15 the conventional normal state to superconducting state transition which is associated with the individual grains becoming superconductors. The second transition at around 20K for YBaZCu3 7-6 and 15K for the Bi compounds is associated with the onset of phase coherence of Josephson weakly linked grains. This transition temperature is denoted as TJ. Vhen the specimen temperature is below Tc’ but above T flux is expelled J by individual grains, but is able to penetrate through the boundaries between these grains. When the temperature is lower than TJ, supercurrents bridge the intergranular Josephson weak links. Flux is then expelled by the whole sample. To quantitatively examine this transition, we first consider the London-like flux penetration in an ideal plate-like grain of thickness a. The magnetization for applied fields parallel to the plate can be expressed in terms of the penetration depth A as tanh(a//\)] (3.3.10) M(T)=M [1- ° a/A where the penetration depth A is a function of temperature. Figure 3.13 shows the typical behavior of this function for several different a/A 54 values labeled for each curve. As a/A increases, the curve steepens and the transition sharpens eventually yielding a step function as a/A goes to infinity. The penetration depth A increases as temperature increase-s. There are several models toIdeal with this relationship. These models can generally be written in the form 2131(0)[1-(3_)"‘]‘1/“3 TSTC (3.3.11) '1' C where 11(0) is the penetration length at zero kelvin. The parameters 0: and 5 take different values for different models. Table 3.2 lists the values which are used in the Casimir-Gorter, Ginsberg-Landau, ordered 3D KY and disordered 3D XY models. By substituting Eq.3.3.ll into Fq.3.3.10, the magnetization can be expressed as a function of grain size a, and temperature T. M(T)=M(a,/\(T,a,fl)) - (3.3.12) A five parameter (a/A, ”0' Tc’ (1, and ,6) least squares fit was used to fit the measured magnetization above the phase coherence transition temperature TJ. The error is fit: Ek=ld(Tk)-M (Tk) (3.3.13) where H(Tk) is measured value at the temperature Tk and Hfltflk) is calculated value from the fit function (3.3.7). The mean square error function is defined as £11134 Zea (3.3.14) where N is the number of the observed points. Obviously, the larger N $5 01) rfiiir I F: J8 fiTITII a/x-2 -0 6 L- a/x-a C a/Aa5 -416‘ b a/K=10 a/X=1 _1.0 11LIL111L1111L11L1IL111 Figure 3.13 20 40 60 30 100 T(K) The temperature dependence of the magnetization obtained from Eqs. 3.3.10 and 3.3.11 using Ho-l, Tc-90K, a-l, and l/fi-O.5. Note that the transition sharpens as the ratio of the grain size to the penetration length a/Ao increases. 56 MODEL 01 1/fi Casimir Gorter 4 0.5 Ginzberg-Landau 1 0.5 ordered 30 XY ’ 1 1 /3 Diana...) 30 XY 1 0.7 11.... 3.2 .1... pm...“ . ... 1/3 .... ... ... f... an“... models in the expression of the temperature dependence of the penetration depth. 57 is, the better the fit one will achieve. Recalling that in the temperature range T 2, which can be interpreted in terms of the growth of DH domains. However, in neither of the above cited experiments was a quantitative analysis of the kinetic effects provided. Clearly , a quantitative study of stage kinetics is not only warranted, but also would best be conducted using those GIC's which do not suffer from the severe complications associated with multidegenerate (HD) in-plane 2D domain structures. The ammoniation of RC2“ to form ternary potassium-ammonia graphite compounds involves a kinetic process of staging transformation from the stage-2 binary compound to the stage-l ternary compoundao-AI. Moreover, this system does not suffer from the many complications associated with a HD 2D domain structure. Therefore, it provides a suitable arena with which to study the staging kinetics which are governed by a simple mechanism from the initial state to the nearly saturated region of ammoniation. Nevertheless, one would expect that the ammoniation of RC“ would be dominated by either diffusion of the guest species to the domain surface (diffusion limited) or by the rate of incorporation of guest species at the domain surface (reaction limited or nucleation 89 limited). In this chapter I shall describe the former process we have observed and quantitatively verify the first definitive example of variable composition diffusion-limited intercalation of GIC's for a large range of the ammonia composition, 0 o "UIO qxsv’sabvg-oahfiw,h_~n- ~~-“ N- ~w¢~\ s = a o c: . S 8 2:, (b) l- ~ g m .. I __ . < ‘o.- q ID v " o O >- ° 3 : ”..“t‘og. c0 2: (3 m A N l" .. o (c) :3 ES 53 - c: . g 3 1. c - .. 53 c: \ Me... .A_“.-_-’ ‘je. ~.-... .... . . fl) 1, L, L L " L 1 2 3 4 5 0-1 q(A ) Figure 3.4 The (00L) x-ray diffraction pattern of (a) a pristine graphite fiber, (b) the same fiber as in (a) after intercalation with potassium to form the binary stage-2 GIC KC24, and (c) the same fiber after ammoniation to form the ternary GIC K(N33’a.3°24‘ 115 forms on top of the ceramic. This ammonia solvates some potassium from the potassium intercalated GIC and forms a potassium-ammonia liquid on the ceramic. This liquid foam became a good conductor and shorted the four leads when a sufficient amount of potassium was solvated. Therefore, the fiber had to be suspended in the ammonia vapor. To do this, the four platinum wires were bent like hooks arranged in a straight line. The stage-2 KC 4 fiber was then seated on the four books 2 in the glove box and affixed on the platinum hooks by silver paint (inset of figure 2.1). The sample cell was then sealed to the Pyrex 0- tube described in the previous chapter. The entire procedure must be done in the glove box as usual, since the stage-2 RC GIC is very 24 reactive with. oxygen and water vapor. Since the fiber is very small relative to HOPG, surface oxidation is much more deleterious in the former. To prevent the fiber from oxidizing, pure potassium was poured onto a piece of aluminum foil in the glove box. The potassium acts as a purifier/getter since it is more active than KC Thus we could keep 24' the fiber 'fresh' by transferring it from the glass tubing to the measurement cell in a few minutes. The Pyrex U-tube and the stainless steel cell were all baked dry before use. This could significantly reduces the outgasing and prevent the sample from oxidizing throughout the entire experiment (two days). In situ electrical measurements were first carried out using a DC four probe technique. Figure 3.5 shows the room temperature isothermal a-axis relative resistance (R(P)/R0) as a function of the ammonia pressure. R(P) is the a-axis resistance at ammonia pressure P and Ro is (R 112,), 0 10014301 7 116 "' qu. _ f D o-oxis 1— M-A 1 11111111 I lllllel 1 11111111 1 [1111111 I Ill"! 10"4 10"3 10'”2 10" 10° 10' P~H3(oim.) Figure 3.5 The room temperature isotherm a-axis relative resistance (R(P)/R0)a versus the ammonia pressure. The instruments’error bars are smaller than the symbols used in the figure. 117 the a-axis resistance of the pure stage-2 RC“ before exposure to the ammonia atmosphere. Comparing this to a similar plot of c-axis relative resistance eg. figure 2.3, we note that the first step increase in resistance at 0.0045atm does not appear in the a—axis relative resistance curve. This is to say that the a-axis resistance remains unchanged even after some ammonia intercalates into the interior of the sample. This result can be understood by treating the graphite layer and the intercalate layer as conductors in parallel for a—axis conduction. Vhen a small amount of ammonia intercalates the interior of the sample, the basal spacing along the c—direction expands. But the charge back transfer from the carbon layer to the intercalate layer is negligiblez. Also, the charge transfer from the potassium intercalate layer to the graphite layer yields a carbon layer conductance in the a- direction which is much larger than the conductance of the potassium intercalate layer. Therefore, at very low ammonia concentrations the c- axis conduction change is notable while that in the a-axis direction is negligible. A more significant observation from this data is the precipitous drop in relative resistance (R/Ro1a at about 2.5atm. From the 0 measurements by York et al.4 , we know that the ammonia composition x in R(N'HS)XC2 is about 4 at this pressure. The stage-2 to stage 1 phase 4 transition has taken place before this composition has been reached. Thus, the observed resistance drop is at fixed stage. To our knowledge, there is no other GIC reported to date that displays such a decrease in a-axis resistance with increasing intercalation at constant stage. To 118 verify this unusual behavior, more than twenty specimens have been examined. All of them showed this drop at about the same pressure, although the magnitude of this drOp varied from sample to sample. An AC LOCK-IN four probe technique was also used to eliminate all possible noise and circuit induced measurement errors. The resistance drop at x-4 has been found in all our measurements. A similar experiment was repeated on a pristine fiber and the drop was not observed. Since it is well known that ammonia hardly intercalates into pristine graphite, the observed drop in resistance of R(NH3)x024 can be attributed to ammoniation. Another important phenomenon obtained from figure 3.5 is the conduction anisotropy of the stage-1 R(NH3)xC24. Figure 3.5 shows that the maximum a-axis resistance increases by only a factor of 4, while figure 2.3 shows that the c-axis resistance increases by a factor of 200 which is accomplished by both expansion of the basal spacing in the c- direction and the staging phase transition. It is obvious that the anisotropy has been magnified after ammonia intercalates into Kc24' Using the known conductivities of the stage-2 KC 2 binary GIC and the 24 relative resistances shown in figures 2.3 and 3.5, one can show that (a )b (a )b 4 (ca/ac)t-[ ____]/ [_ =2.5x10 at x84 (3.2.1) (R/Ro )13 (R/Ro )c where t represents ternary compounds and b represents binary compounds. This is the highest anisotrOpy yet reported for a stage-1 donor GIC32 and provides strong evidence for the 2D character of the conduction process in R(NH3)x024. 119 3.3 Two Dimensional Hetal-Insulator transition in R(NH3)xC24 In order to interpret the observed unusual eleccrical features of R(NH3)IC vis-a-vis the structure and properties we refer again to the 24’ bulk potassium-ammonia solution. It is known that the solvated potassium ion and ammonia form a six fold coordinated octahedral structure. Six ammonia molecules surround the potassium ion or the detached electron from top, bottom, left, right, front and back respectively. The rest of the ammonia molecules are free. The electron appear to be localized as evidenced by a narrow optical absorption band at 0.8ev. This band has been attributed50 to a ls-Zp transition of the solvated electron in the spherical potential of a 63 diameter solvent bubble. Vhen the concentration of potassium is high enough so that the wavefunctions of the solvated electrons overlap each other, the solution undergoes the metal-insulator transition. The conductance of the solution was found to increase by three orders of magnitudeso. X-ray and neutron scattering have shown that the structure of the intercalate layer of R(NH3)xC is a 2D potassium ammonia solution. 24 Instead of being solvated in the six fold ammonia cluster, potassium atoms are surrounded by four ammonia molecules and form a square planar 16'17'21. This is because the basal spacing of the four fold structure carbon layer limits the height of the cluster. Therefore, the top and the bottom ammonia present in the bulk octahedral cluster are not seen in the clusters of the 2D potassium-ammonia liquid. The structural 120 analog between the intercalate layer of the 2D I(--NH3 liquid and the 3D bulk K-NH3 promotes the association of the a-axis resistance drop with a 2D metal-nonmetal transition. To further verify this transition, the optical absorption bands were examined. Figure 3.6 shows the x-dependence of the reflectance R(w) . Light beams were incident on an intercalated HOPG sample in a near-normal direction to the carbon planes. The obtained c-face reflectance spectra were subsequently transformed by the Kramers-Kronig relation356'57. 4’“ U 3 n(w)-1+PJ 1“ . k‘” 1 (3.3.1) -0 it 00-10 ' (3.3.2) . '1'” c 1 ' k(w)--PI dw . n(w 1’1 -°° n w'-w where P is a principle value integral. The a-plane complex dielectric functions 52(0,w) were then calculated through the relation e-(n+ik)2 (3.3.3) The results are shown in figure 3.7 (solid lines). The composition x-O compound. Its complex dielectric corresponds to the pure stage-2 KC24 function has been measured by other groups2 and agrees well with the data shown here. ez(o,w) can be decomposed into a free carrier absorption and an interband absorption. The free carrier absorption obeys an nag/ma law and vanishes very quickly when the light frequency exceeds the plasma frequency cup. The increase in 62(0,w) is due to interband absorption which can be further decomposed into a narrow band at 1.85ev and a broader contribution which resembles a typical threshold 121 ID ‘~ LL! 0 2 <1 p. 0 DJ ‘ ...l U. Lu cr flu (8V) Figure 3.6 The composition dependence, x, of the reflectance R(w) of p0tassium-ammonia-GIC's. Figure 3.7 8 6 4 2 O 4.. 2 ‘0 6 4 2 O 4- X= L49 ‘ 2_ ..J ‘1 1 1 1 1 00 l 2 3 4 5 6 1°11» (eV) The Rramers-Rronig derived imaginary part of the dielectric functions 62(0,w) (solid lines). The functions are subsequently decomposed into the Lorentzian oscillator (dashed line) and a broader contribution (dash dot line). (see text) 123 for the graphite n-rr* transition”. Clearly, the narrow band is most pronounced when the ammonia composition x equals 4.1. The full width at half maximum (FWHH) is 0.4ev for this composition. As more and more ammonia intercalates into the interior of the specimen, the oscillator strength (the narrow band peak at 1.85ev) increases at first and then exhibits a sharp drop when x exceeds 4.1. This behavior is plotted in figure 3.8 for clarity. When the concentration of intercalated ammonia is low and thus x<<4. the inserted NH leads to gallery expansion and 3 participates in the cluster formation. Therefore, the concentration of the spacer ammonia ("free' ammonia) is zero. Also the back-charge transfer 6f=0. When the ammonia composition x in ternary K111335024 is close to 4, some newly intercalated ammonia will enter the spacer‘s position since almost all potassium present in the sample is bound with ammonia in a four fold cluster. When x>4, all the newly entered ammonia are spacers which promote salvation and thus give rise to an increases in 6f. These spacer ammonia molecules will back transfer charge from the carbon layer to intercalate layer since they trap electrons in a hydrogen cage formed by a spacer and a cluster NH This is consistent 3. with figure 3.8. When x increases from zero to 4, more and more K-ammonia four fold clusters are formed but the back transferred electrons are localized so that the ls-Zp bound state oscillator strength increases as does the resistivity. Further increases in ammonia composition leads to the increase of spacer ammonia concentration and charge back transfer to the metal ammonia layer. The concentration of this back transferred charge can become so dense that the in-plane wavefunctions of the charge Oscillator Strength (Arbitrary Units) 124 Figure 3.8 K(NH3)X 024 .A plot of the Lorentzian oscillator strength versus 'the ammonia comp031tion x in R(NH3)xC24. 125 overlap and form band-like extended states. As a result, the metal ammonia layer becomes a conductor and the a-axis resistivity decreases. These back transferred charges become delocalized and the oscillator strength decreases as x increases from 4.1 to 4.3. This is the so- called metal-insulator transition. Under this transition, localized charges have become delocalized charges. ‘The size of the potassium-ammonia clusters in graphite intercalation compounds is small compared to the size of the bulk six fold cluster since the former is confined between carbon layers while the latter is in free space. The Heisenberg uncertainty principle in quantum mechanics dictates Ax-Ap>h. The smaller the cavity size Ax, the larger momentum Ap and hence the larger the band energy. Therefore, we have seen an upshift of the band from 0.8ev for the 3D bulk metal- ammonia solution to 1.85ev for 2D K-NH3 solution. We suggest that this metal-nonmetal transition is a Mott transitionss. A criteria for a three dimensional Hott transition is * ni/3a -0.26 (3.3.4) where nc is the critical electron volume density. Now a* can be 0 expressed in terms of the Bohr radius ao-O.529A, the static dielectric * constant e, and the effective mass m 'A' 'A' ' a =[e/(m /mo)]ao (3.3.5) where no is the mass of a free electron. Using dimensionality arguments, we find that the 2D Hott condition is 126 1/2 *_ . nc a A2D constant (3.3.6) where nc is the critical electron areal density. A self-consistent value for nc and xc can be determined with the aid of a 2D Clausius Hossotti equation which was calculated for an ellipsoidal cavity in a dielectric. (E-l) -2nNa (3.3.7) (6+1) 0 Here N is the molecular number density in a 3.28A thick 21 ammonia layer. The area of twenty-four carbon atoms is calculated to be 02 62.86A . Thus, -3 N-[x/(62.86X3.2s)13 (3.3.8) Using e-25 and )0-0.817gm/cm3 for liquid NH3 at -77°C59, the static 3 o polarizability a is found to be 7.36A from equation 3.3.7. Combing equation 3.3.5 -—— 3.3.8, nc can be expressed as a function of the effective mass, and composition. Ve write * nc-fl(m /(m xc) (3.3.9) OAZD)' A linear model is expressed in Eq.3.3.10 below and is used to relate the back charge transfer to the spacer ammonia concentration. x<4 0 6f- {7(x-4) :34 (3.3.10) . . . 21,20 where 7-1s a constant and is equal to 0.2/0.38 in this case . Thus, nC-f2(xc)- . (3.3.11) 0.38X62.86 127 Setting the two functions fl and f2 equal to each other, a cubic equation will be obtained with only one solution which has physical meaning. A reasonable estimate of A2]) is obtained by comparing the 2D and 3D Fermi wavevectors which depend on electron density. _ 2 1/3 1/2 _ ' AZD {(3n ) /(2n) }A3D 0.31 (3.3.12) From equation (3.3.6)-(3.3.12), we find that 1: 4.09 1000, 146 j - ||, 1 relative to the ab planes. As a result. in the range Hal < H << H22 the vortex state susceptibility can be approximated as . _ 1 X3 ( l/4n) Hcl(T)/H~ (2) . ' 2 2 If we employ the relation Hgl(T) - Hgl(0)[l - T /Tc] then Eqs. (1) and (2) can be combined to relate the maximal levitation temperature to the inverse field gradient and 12 - 12(1 - .8122. ll/(aH (allaznl (3) L c eff y H (0 cl where HszW) is an effective lower critical field which results from the orientational distribution of the grains. A plot of T: vs. inverse gradient for YBa Cu O is shown in Fig. 2 and presents clear 2 3 7-x verification of the linear relation defined in Eq. (3). From the slope of this line, we find Tc - 88 t 4 K in agreement with susceptibility measurements on this specimen and Hszw) - 90 t 15 G which, as expected, is less than, but of the same order as, HQ (0) - 270 e 50 s'[3.4]. The kink in the magnetization and levitation data at 20K is, we believe. due to the onset of intergranular phase coherence which results in a field-dependent magnetization for T < 20K. Several models are avaiIa'ble to exp‘l‘ii'n s‘u”ch intergranular effects [5,6] including one which treats the onset of intergranular phase coherence as a 3D KY problem [6], but further work is necessary to identify the correct model. Note. however. that independent of the particular model which is applicable, the temperature at which the levitation kink occurs provides a quantitative measure of the intergranular coupling strength, an important parameter. Preliminary levitation results [7] on an admued BiZSrZCan.1CunOx compound with n - 2,3 show that these materials exhibit the same type of levitation behavior as evidenced by the Y compounds. The dramatic slope discontinuities in levitation and magnetization data which we observe in pressed pellets are also clearly observable with single crystals ”which, by inference contain weak-links, too. 147 References 1. L. Krusin-Elbaum. A.P. Halozemoff and Y. Yeshurun, in "High- Temperature Superconductors.‘ 203, H.B. Brodsky, R.C. Dynes, g, Kitazawa, and H.L. Tuller, (eds.), Haterials Research Soc., Pittsburgh, (1988), p. 221. S. Vieira, P. Zhou, S.A. Solin. N. Garcia, H. Hortal and A. Aguilo, "Interfacial Effects and Superconductivity in High Tc Haterials", Phys. Rev. gag, (1989), 334. S.A. Solin. N. Garcia, S. Vieira. and H. Hortal, ”Field Induced Orientation of Small Superconducting YBa Cu 0 Particles', Phys. 2 3 7—x Rev. Letters 99. (1988), 744. Y. Yeshurun, A.P. Halpozemoff, L. Krusin-Elbaum, T. Worthington and F. Holtzberg, “Giant Flux Creep in High Tc Superconductors: Implication for Heasurements of Upper and Lower Critical Fields.“ in Intl. Conf. on Critical Currents in High Temperature Superconductors, Snowmass Village, Colorado, August 1988 (unpublished). H.A. Dubson, S.T. Herbert, J.J. Calabrese, D.C. Harris, B.R. Patton. and J.C. Garland. "Non-Ohmic Dissipative Regime in the SuperconduCting Transition of Polycrystalline Y Ba Cu 0" Phys. 1 2 3 Rev. Lett. 99. (1988), 1061. C. Lebeau. et al., "Inductive Transitions and the Heissner Effect in High TC Supercondutors." in Proc. of the European Workshop on High T Superconductors and Potential Applications, Genovaq Zitaly, July 1-3, 1987. p. 357. YuY. Huang, S.A. Solin and W.P. Pratt, "Levitation Studies of BiZSrZCan_10unOy, n - 1,2 and 3," in Intl. Conf. on Critical Currents in High Temperature Supercondutors. Snowmass Village, Colorado. August, 1988 (unpublished). 148 760+ Figures ; Ol-SOA 1- &000 ° I'ZOA : 9. 11“, O I-lSA 740 — . °e ' l-IOA A 1- D II E 1- ..X 00%0 a . “be.” x ° 0° 0 ‘N" " ‘be 1“ °°o°° g e 730 — o D O. :0 O % h ‘9 . ’5 90° - 1s 9 o ”09" l- 4. ° 0 Don .txx‘ o 720 P- ,. , k ...X l’ r 710 ...1...111...1...1 O 20 4O 60 80 T(K) Fig. 1 Zero-field-cooled (ZFC) Levitation height of YBa2Cu307 1 vs. temperature and magnet current. The center of the magnet is at a height 20 - 697mm. 5\ TL'(K31103) N vTI—rvjwrvuvu' 0AA411L14114441111111111L11A l 1.5 2 2.5 3 3,5 4 [1/(5H/62)(kG/mm)] Fig. 2 Haximum levitation temperature vs. inverse gradient for YBaZCu307_x. The solid line is a linear least-squares fit to the data using Eq. 3 of the text and yields the values Tc - 88 3 4K and Hcl(0) - 90 r 150. 149 © Printed in Great Britain. Solid State Communications, Vol.6l,No.8, pp.469-473, I987. 0038-l098/87 53.00 + Two-Dimensional Diffusion-Limited Kinetics in a Ternary Graphite Intercalation Compound Y. Y. Huang, 0. R. Stump, and S.A. Solin Department of Physics and Astronomy, Michigan State University. East Lansing, MI 38824 and J. Heremans General Motors Research Laboratories. Warren, MI 38090 (Received 27 October by J. Tauc) The kinetics of the graphite intercalation compound (GIC) R(NH31xC,u, studied by monitoring the time dependence of the c-axis resistance. ammoniation of KC 4 to form the ternary 0 5 x 5 4.38. has been Our 2 results are in quantitative agreement with a two-dimensional (20) diffu- sion model which yields diffusion constants ~10.8 2 cm /sec. In contrast to binary GIC's which exhibit intercalation kinetics that may be limited by the growth of planar multidegenerate domains, the K-NH3 ternary system provides a clear example of 20 diffusion-limited intercalation. Kinetic effects in layered systems. and in particular graphite intercalation compounds (GIC's). have been the subject of intense recent experimental”3 and theoretical”.7 interest. To date the focus has been on kinetic processes which are dominated by the growth and coales- cence of intercalate domains of which two types have been considered: namely, multidegenerate (HD) in-plane two-dimensional (20) islands8 and the so-called Daumas-Herold (DH)9 30 stacked columns of planar domains whose 20 structure is unspecified. There is evidencee'1o that MD 20 domains are prevalent in binary GIC's and that their formation constitutes a theoretically complex step U1 the kinetics of both ln-plane ordering and staging. (A stage n GIC contains a regular c-axis stacking sequence in which nearest pairs of guest layers are separated by n graphite host layers.) Moreover, the traditional”’12 and still popular13 approach to kinetic studies of 010': ignores the com- plexities of H0 domains and quantitatively addresses only that small part of the kinetic process which exhibits a (supposedly) diffusion- limited t1’2 variation of intercalatant concentration with time. ll The kinetics of in-plane diffusion1 and in-plane ordering1 (at constant stage and con- stant composition) and of stagingz'3 (variable composition) in binary GIC's have been recently probed by real-time in-situ neutron and x-ray diffraction studies. However, very similar experiments on staging kinetics in potassium- graphite yielded conflicting qualitative 2. 3 conclusions. Clearly. a quantitative study 469 of staging kinetics which accounts for both the t1/2 and saturation regions of the intercalation process is warranted. Furthermore, this study would best be conducted using GIC's which do not suffer from the severe complications15 as- sociated with HD 20 domain structures. Until now, such studies were apparently precluded by the lack of suitable specimens. We have recently shown that unlike binary GIC‘s, the alkali-ammonia ternary GIC K(NH3)XC2H. 0‘3 x g 4.38, forms an intercalate that is a simple 20 metal-ammonia liquid, the structure of which ' is the planar analog of the structure of the famous18 bulk 30 metal- ammonia solutions. While the substrate potential is of course "felt" by the K—NH3 liquid, its structure is dominated by intercalate-intercalate interactions rather than by intercalate-substrate interactions which generate H0 2D domains in binary GIC's. Modern X-ray techniques are not sufficiently sensitive for direct detection of DH domains' and electron microscopic methods are incompatible with a high-pressure ammonia environment. Nevertheless, one would expect that ammonia intercalation in the alkali-ammonia GIC's would be governed by the formation of 30 DH domains the growth rate of which could be kinetically constrained by diffusion of guest species to the domain surface (diffusion-limited) or by the rate of incorporation of guest species at the domain surface (reaction/nucleation-limited). In this letter we show that the former process obtains and we quantitatively verify the first definitive example of variable composition diffusion-limited intercalation of 3 CIC from induction to near-saturation. .00 Pergamon Journals Ltd. 150 £70 DIFFUSION-LIMITED $INETICS [H A TEENARY GRAPHITE INTERCALAIION COMPOUND Vol. 5|, No. 8 Samples of binary stage-2 KC of typical 2!: dimension 5.2 x 3.5 x 0.5 mm were prepared from highly oriented pyrolytic graphite (HOPG) for a u-probe DC resistance measurement. After x-ray characterization. the encapsulated samples were placed in a high-purity glove box (02 level < 0.5 ppm), removed from their glass mmpoules and affixed with four platinum wires using flexible silver paint that was protested and found to be impervious to attack by ammonia. Two leads. each with a separate silver paint dot. made contact to the two c-faces of the sample. one opposing pair for current and one for voltage. The anisotropy of the resistivity ensures that the equipotentia; lines are parallel to the graphite planes as desired. The sample as- sembly. which consisted of a vacuum feedthrough to which the four platinum leads were soldered. was sealed to one end of a ?yrex U-tube. the other end of which was filled with purified liquid ammonia and isolated by a Teflon isola- tion valve (TIV). 3y accurately controlling the temperature of the ammonia reserVOir (:O.SK) in the range TTK to 300K the vapor pressure could be controlled to better than :32 over the range 10.9 atm. to 10 atm. All neasurements reported here were carried out with the sample held at room temperature. To assess the intercalation process with u very high sensitivity (-1 part in 10 ). we monitored the time dependence of the c-axis resistance of K(21H3)xczu as a function of am- monia pressure (or x) using a sequential pressure up-quenching technique as follows. with the TIV closed and the sample space evacuated to a pressure Po (corresponding to a Kczu c-axis resistance of R0) the temperature of the ammonia reservoir was adjusted for a pres- sure ?1. At time t - 0. the TIV was opened and the c-axis resistance of the sample R1(t) was monitored until the measured resistance appeared to be time independent and equal to 31(sat) (points 3-5. 7-10, and :2-12: in Fig. i) or until sufficient near-saturation data was acquired to analytically determine (see below) the satura- tion resistance R1(sat). Then the TIV was closed, the reservoir pressure was raised to P2. the TIV was opened and R2(t) and R2(sat) were determined in the same way. This process was repeated until a pressure Pn -10 atm was reached. The measur-ent apparatus was desimed so that a negligible time was required to achieve pressure equilibriin following an open- ing of the TIV. The room temperature resistance isotherm of the c-axis saturation resistance of K(NH3)xC2u relative to the resistance of “2:: is shown in Fig. 1. The data of Fig. 1 mimic previous studies20 of the dependence of the composition (or x value) of K(NH3)XC2u on ammonia pressure and exhibit step-like plateaus, with onset pressures of 40-3 atm. and -0.5 atm., '9 O 12 - e'. a 11 - O 93 I “L - a 10 10' Fig. 1 Relative increase in e-axis resis- tivity, RixsatVRo of KTNH3 xtzu as function of ammonia vapor pressure 3. t r (PMs. no is he esistance of the KC," specimen before ammoniation. Inset: The composition dependence of the function {Ri’fsatHZ-lo ~11. The data points in this figure are numeri- cally labeled for reference in the text. respectively. From previous x-ray studies20 it is known that the step at ~10.3 atm. corresponds to the incorporation of ammonia into the ex- panded galleries of KC” while the step at ~O.5 atm. corresponds to an n-Z-to-n-I staging phase transition in which the potassium and ammonia redistribute to fill every gallery. The exact pressures at which the plateaus in Fig. 1 occur are sample dependent. Therefore, we were unable to successfully acquire data in the mid-region of the step itself. Moreover. the ammoniation 20 of “an is not reversible and on depressuriza- tion a residue compound forms with Rresidue/RO - 102. To explore the kinetics of the ammoniation of K62“. we have monitored the time dependence of the resistance ratio g(t) - R1(t)/R1_‘(sat) for several of the intervals between the labeled points of Fig. 1. The results for i - 6 and H are shown in Fig. 2. He will now show that the form of g(t) is well described by a model of 20 diffusion-limited intercalation kinetics. Consider a rectangular parallelepiped sample with c-faces of dimensions a and b and height c << a.b. We assume that the specimen is bathed in vapor at pressure l"1 and that this vapor can intercalate only through the edge faces by the process of 20 diffusion. Let "(i-ihiht't) be the areal number density (hereinafter called the density) of ammonia in the specimen at position 3 at time t following an increase in ammonia pressure from Pi-l to P1 1551 V01. 61, No. 8 DIFFUSION-LINITED KINETICS IN A TERNAR! GRAPHITE INTERCALAIION COMPOUND and assume that nu_n.1(r.t) obeys the diffu- sion equation: an (F.t) (i-1)*i at ' D V2"(i-1)*i The boundary condition which expresses the fact that the density is constant at the edge faces r‘ - ss/Z or ry - :p/z is (F,:). (1) O n(1_‘).i(r,t) - n1(sat) (2) where n1(sat) is the saturation density cor- responding to the pressure P1. The initial condition for lr‘l < a/2 or lryl < b/2 is n(1-1)’1(r.0) - 0. (3) He may neglect the initial density.pf ammonia since n1_,(sat)/nt(sat) is small, of the order of 0.01 for the transitions at i - 6 and 11. a. (£_‘)‘t(r, t) as the change in the density of ammonia compared to n‘.‘(sat). Equivalently, we may regard n He have determined the solution to the boundary value problem represented by equations (1)-(3) to be * x 0t 0t n(1_,),1(r.t) - n1(sat) [1 ' 0(3. :5) ° 0 [%. :51]. where 2 u (-1)” -1q “5.” ' '; X 2W1 9 003015). (5) w-O and 0" (2w 0 1):. (6) 20 A comparison of our previous measurements of x vs. PNH3 for R(NHB)‘CZu with the data of Pig. 1 yields a plot of 108 [(R1(sat)/Ro) - 1] vs. log x as shown in the inset of Fig. 1. Here the composition x is proportional to the ammonia areal number density, n and is given by x - Zln/nc where he is the areal density of carbon atoms in the specific pristine graphite specimen from which the intercalation compound was 47! 0.07 < x ( n.3, the latter of which spans the staging phase transition. Straight line fits to the data of Fig. 1 inset indicate that for a uniform intermediate density. say ni(sat). in the range between data points 5 and 6 or between 10 and 11, the intermediate saturation resis- tance Ri(sat) is of the form ni(sat) p a;(:.:) - R1_1(sat) £1 . (r - "(fi:?§3E7) ]. (7) Here f - R1(sat)/Rl_1(sat) and p is the slope of the curve of log (Riisat)/Ro - 1) vs. log x. From Fig. 2 we estimate that p - 0.77 between data points 5 and 10. and p - 1.31 between data points 10 and 1h. The observed nonlinear de- pendence of Ri(sat) on x is presumed to result from both weight gain and basal spacing expansion. Now Eq. (7) gives the relation between the intermediate saturation resistance Ri(sat) and the uniform saturation density ni(sat). But when the pressure is changed from P to P i-1 1' the actual density, n(1_1).1(3.t) given by Eq. (u) is not uniform but evolves both spatially (u) 1 1 a1(€1 nl_, - I (sat) ab {1 ¢ (f-1) [n prepared. Thus nc - Hen/(12 ab) where "c is the mass of graphite in our specimen, A is Avagadro's number, and 12 is the atomic weight of carbon. [The very small change in the in- plane lattice parameter of the carbon layers22 as ammonia is introduced into the galleries is negligible.) Notice from the inset of Fig. 1 that the saturation resistance varies as a power of composition over the ranges 0 < x < 0.07 and Nevertheless. in an increment- ally small neighborhood of area d2; at F the density can be treated as spatially uniform. Moreover, the conductance per unit area cor- responding to the case of uniform density is 1 9 simply EB—RITEEET where R1(sat) is given by Eq. .9 (7). (t_')‘1(r,t). the conductance per unit area is locally given and temporally. For the nonuniform density n w. by the same formula with n(1_1).1(r,t) replacing ni(sat). Then the conductance of the entire sample is obtained by integrating the local conductances per unit area over F; that is. 1 d2? , p . (a) (i-1)*i(r’t)] } The solution for R1(t) given in Eq. (8) involves three dimensionless parameters; namely, f, D. and i - a/b. __ For i - 1.h7 corresponding to the measured_ dimensions of our specimen, we have performed least squares fits to the data of Fig. 2a) and b) using Eq. (8) with p - 0.77 and 1.N1, respec- tively and with f and 0 treated as adjustable parameters. The results of these fits are shown 152 ' I 100 200 300 400 500 500 n.(mn.-1(San (a) 1.20 1.1!) L00 ' ‘ ' ' ' ' ' ' 0.0 10.0 20.0 30.0 40.0 50.0 00.0 t(hrs) Time dependence of the ratio g(t) - R1(t)/R1_1(sat) (solid circles). Panels (a) and (b) pressures P6 . 3.5 - 10"3 atm. and P Fig. 2 correspond to 11 - 0.25 atm., respectively. The dashed (solid) line is a least souares fit using Eq. (8) with (without) a dwell time and yields the following fitting parametears: panel (a), solid line: 0 - 3.2:9-10‘9cm2/sec. r - 1.37. ‘0 - 0; -9cm2/sec. f - Panel (b). solid -9cm2/sec. f - "3.21, dashed line: D cmzlsec. f - “6.39. dashed line: D - 8.69-10 1.90. td - 2.08 hr. line: 0 - 8.20-10 to O; 5.55-10'9 29.8 hr. td - - as solid lines in Fig. 2 which evidences good agreement between theory and experiment. It is particularly gratifying that the values of D we obtain, 8.fl9-10-9cm2/sec and 8.20-10-9cm2/sec for Figs. 2a and b, respectively, are typical of gas diffusion in solids.23 There are small deviations between theory and experiment in the small time region. especially in Fig. 2a where the diffusion theory rises faster than the data. Therefore, we also attempted to fit the data by introducing one additional parameter. a dwell time td.d" For the data of Fig. 2a, the intro- duction of a dwell time (dashed lines of Fig. 2) improved the fit with td optimized at 2.08 hours and D and f at 8.69 x 10-9cm2/seo and 1.90, respectively. However; the same procedure when DIFFUSION-LIMITED KINETICS IN A TERRA” GRAPHITE MWION COMPOUND Vol. 61, No. 8 applied to Fig. 2b yielded an unphysical ne - tive dwell time td - -29.8 hours with 0 - 6. 5 x 10.9 cmzlsec and f - 36.39. Moreover, the introduction of a dwell time in Fig. 2b had a negligible effect on the fitting parameters 0 and f. Therefore, we Justifiably infer that td - O for Fig. 2b. We suggest that the dwell time may be associated with surface adsorption. It has been known for some time25 that intercalation in GIC's cannot occur unless the basal surfaces of the specimen are exposed even though access to the specimen interior is through its edges. This has been attributedz6 to surface adsorption which produces a localized charge density wave distortion that weakens the interlayer bonding and promotes access to the gallery through the edges. Note that the diffusion constant as- sociated with the staging transition. a structurally disruptive process. is slightly smaller than that for absorption at constant stage. For intercalation accompanied by stag- ing, the dwell imposed by surface absorption is apparently insignificant as in Fig 2b. We allowed the saturation resistance ratio f to be a free paraeter in fitting the diffu- sion theory to the experimental results. The saturation resistance ratios obtained from the fits of the time dependence of R1(t) are ap- proximately f - 1.9 for i - 6 and f - R3 for i - 11. The corresponding measured values shown in Fig. 2 are 1.33 and 39. respectively. Part of the difference between theory and experiment may be attributed to some undersaturation in the experimental measurements. In addition. the time dependence of the diffusion theory does differ somewhat from the observed time depend- ence in the case of i - 6. even when a time delay is naively included: this is reflected in an artificially large fitted value of f. A more detailed knowledge of the physical mechanism responsible for the time delay might make pos- sible an even more accurate description of the diffusion process. The numerical solutions of Eq. (8) were found to be very insensitive to l. The quality of the fits obtained for the data of Fig. 2 was also very insensitive to the value of the parameter p in Eq. 8 as was the diffusion con- stantant deduced from Fig. 2a) which changed by only +91 when p was changed *301 from .77 to 1. However, the diffusion constant deduced from Fig. 2b) was more sensitive to the parameter p and changed by +731 when p was increased by +u1$ from 1 to 1.u1. Note that it is the quality of fit and not the exact value of D which is impor- tant here. Therefore, the essential physics of our results still obtain: in GIC's. which are not structurally dominated by H0 20 domains, the intercalation process itself is apparently governed by the formation of 30 DR islands whose growth rate. in the case of potassium-ammonia- graphite, is kinetically limited by 20 diffusion of the intercalant to the specimen interior. We acknowledge useful discussions with G. Pollack, Y.B. Fan. and X.H. Qian. This work was supported by NASA under grant NAG‘3‘595 and in part by the NSF under grant DHR 85-17223. 153 Vol. 6|, 80. 8 DIFFUSION-LMTED KINETICS I! A IBM GRAPHITE INTENTION C(RiPOUND 473 References 1. 11. Home and R. Clarke. Phys. Rev. Lett. 1!. ii. label. A. Magerl. A.J. Dianoux, and J.J. 2. 629 (1985). Rush. Phys. Rev. Lett. 22, I9 (1983). 2. R.E. Hisenheimer and H. Zabel, Phys. Rev. 15. 1.21. Lifshitz, Zh. Eksp. Teor. Fiz 02, 135:; 821, 131113 (1983). (1962) [Sov. Phys. JETP E. 939 (1962)]. 3. R. NISDUSIBI. Y- Uno, and H. 50°03‘38“. 16. X.'d. Qian. B.R. Stump. B.R. York, and S.A. Phys. Rev. 821. 6572 (1983). Solin. Phys. Rev. Lett. 22. 1271 (1985). 9. fl. Hinuki and c. Horie. 31m- Hot. 3. N9 17. x.w. Qian. 0.3. Stump. and S.A. Solin, (1985). Phys. Rev.. in press. 5. P. Rawrylak and K.R. Subasswamy, Phys. Rev. 18. J.C. Thompson. Electrons in Liquid Ammonia Lett. 51. 2098 (198"). (Clarendon. Oxford. 1976). 5- C. KIPOZN‘IOU. PHYS- ROV- Lett. 23. 1'37‘ 19. 0.F. Shutz and H. Zabel, Bull. Am. Phys. (198k). Soc. 11. 596 (1986). 7. S.A. Safran. Phys. Rev. Lett. 16. 1581 20. B.R. York and S.A. Solin, Phys. Rev. 3a. (1981). 8206 (1985). 8. H.J. Ninokur and R. Clarke, Phys. Rev. 21. B.R. York, S.K. Hark. 3.0. Hahanti, and Lett. 2, 8111 (1985). S.A. Solin. Solid State Comm. 2, S95 9. N. Daumas and A. Herold. C.R. Acad. Sci.. (1982). Ser. 0 g6_8.. 273 (1969). 22. 11.5. Dresselhaus and G. Dresselhaus. Adv. 10. ii. Homma and R. Clarke, Phys. Rev. 83;. Phys. 33. 139 (1981). 5865 (1985). 23. H.B. Jacobs. Diffusion Processes (Springer, 11. J.C. Rooley and J.L. Smee. Carbon 2. waiork,1967 . 135 (196M). 2!. The dwell time is introduced by applying 12. R.E. Dowell and 0.3. Badorrek, Carbon 1_'6_. the transformation t e t o td to Eq. (8). 2I1 (1978). 25. J.C. Hooley, Carbon 11. 225 (1973). 13. F. Beguin and R. Setton. Syn. Met. 1. 263 26. 0. Young. Carbon 2.1-73 (1977). (1983). 154 Solid State Communications, Vol.6ls.No.lo, pp.443-Mo6, 1987. Printed in Great Britain. 0038-1098/87 $3.00 + .00 Pergamon Journals Ltd. A 20 METAL-NOIHITAL TRAIBITIOI POTASSIUH-AHHDIIA LIQUID HONOLAYERS II GRAPHITE H.H. Huang, 2.3. Fan and S.A. Solin Department of Physics and Astronomy Center for Fundamental Materials Research Michigan State University East Lansing MI “882l J.H. Zhang and P.C. Eklund Department of Physics and Astronomy University of Kentucky Lexington KY “0506 J. Heremans and 0.0. Tibbetts General Motors Research Laboratories Warren MI “8090 Received 5 April 1987 by J. Tauc ABSTRACT The x-dependence of the a- and c-axis relative resistances and of the near-normal reflectance of the metal-ammonia ternary graphite intercalation compound K(NH ) C 11.38. 3 I: has been studied in the range 0 S x S For x 2 h the a-axis rglgtive resistance and the reflectance both exhibit unusual features which we associate with a two-dimensional Mott type metal-nonmetal transition in the intercalated K-NH monolayers. Bulk three dimensional (30) metal ammonia (HA) solutions constitute one of the most interesting topologically disordered condensed matter systems because they exhibit a composition dependent metal-nonmetal transition (MNHT). At low concentration (5 7 mole percent metal) the metal ion and its detached electron are both solvated by an enveloping cluster of NH molecules. The solvated electron is lotalized an$ exhibits a narrow optical absorption band. A HNHT occurs when sufficient metal is present in solution to cause the wavefunctions of the solvated electrons to overlap and form delocalized bands which sustain conduction. Although the possibility of studying the effect of dimensionality on the properties of HA solutions is intriguing, no such studies have been reported to date. It has been known for several decades that HA monolayers could be periodically inserted between the host layers of graphite. However. interest in HA graphite intercalation compounds (GIC's) remained dormant until recent x-ray studies showed that the HA monolayers in the stage—1 compound K(NH )u C2” were the two dimensional (20) strgctgegl analogue of the corresponding 30 HA solution. (In a stage n GIC. nearest pairs of guest layers are separated by n graphite host layers.) This result stimulated several other measurements of thg system K(Hy3)xc u' 0 S x S “.38 inclu ing NHR. kinetics and2 neutron scattering studies. These studies provided information on the 443 3 liquid configuration. correlations and motions of the NH molecules in the 20 liquid and showed that am oniation of KC results.in a back-transfer of electron charge. 6f per K ion, from the C layers to the MA liquid. Such information was prerequisite to a careful analysis of the x- dependent electronic properties of that novel liquid. Accordingly, we report here electrical and optical studies of the K-NH monolayers in graphite. Our results indica e that these monolayers exhibit localized electronic states and a HNHT which may be considered the 20 of their-Bulk HA counterpart. The ternary GIC's K(NH ) C u were synthesized by exposing KC 11 at roam ltetgperature to pure NH vapor. The gelationship between x and pressur PNH has been carefully measured . Details of thgse measurements and of our synthesis procedures are given elsewhere. The compounds studied here were prepared from either highly oriented pyrolytic graphite (HOPG) or from individua methane-derived fibers heat treated to 30000 . The latter. being of much smaller dimension. exhibit a faster kinetic response. They also chemically decompose after several days following maximum ammoniation. In situ electrical measurements were carried out using both AC and DC H-probe techniques. Intercalated HOPG samples were used for the c-axis resistance and optical studies while fibers were used for the a-axis 155 1.46 POTASSIUM-Alma!“ LIQUID MWOLAYERS IN GRAPHITE measurements because of their ideal aspect ratio. Near-normal incidence in situ c-face reflectance spefifra R(u) were Kramers-Kronig (KK) transformed to obtain the a-plane complex dielectric function t(0.u). The c-axis resistance and optical spectra were measured in chemical equilibrium. Because of the decomposition alluded to above. a-axis resistance data were taken "on the fly" over a period of two days. Nevertheless. the enhanced kinetic response exhibited by the fibers ensures that our "on the fly" data represent an equilibrium result. Room temperature isotherms of the c and a- axis relative resistances (R/R )c and (R/R ). respectively of K(NH ) C h are sRown in Fig. I. Here R is the apppoprfate resistance of KC 11' The cugze for (3/3 ) exhi its three plateius separated by steps at 2-10 atm and 1.2-10 atm. In the first plateau a negligible amount of NH enters defect sites in the occupied galleries o} KC u' In the second a significant amount of NH en‘ers but the compound retains its stage-3 structure. For P“ 3 1.2-10 atm. the system H undergoes a stage-% to stage-1 transition and NH becomes the domina" constituent while the K inaplane density falls by a factor of 2 as the number of galleries which contain K doubles. The (ll/Ila)a isotherm in Fig. 1 exhibits an X 3.5. ° c-dxis 10° Relative Resistance (fl/Rd” II 10“ lo" IO" 10° 10' thfl'n.) O—NUbOI I Fig. 1. The T - 300K c-exis ( ) and a axis ([1) relative resistance ratios of K(NH3)xC u as a function of NH vapor pressure or x. Ifisets in the upper panael (log1 (R/R )) indicate the structure and cargpositQOn in the region of the corresponding plateau while the lower panel ((R/R ) ) inset depicts parallel conduction in the ‘carbon and metal- ammonia layers. The solid lines are a guide to the eye. 0.03 O.IO.5I 2 34438 Vol. 64, No. 6 extended plateau that is terminated by a step at 1 atm which is upshifted in pressure from the onset of the staging transition. But_§R/Ro) shows no sign of the step at 2-10 -atm i (ll/R0) . More significant is the precipitous drop i°n (am )a at x - 1:. Hhile the mamitude of this drop Pa sample dependent. it has been observed in more than twenty specimens which we have examined. To our knowledge. no other GIC displays such a decrease in Ra with increasing intercalation at fixed stage. In Fig. 2 we display the x-dependence of the reflectance Mn) and the KK-derived values of t (0.1.1). Our x - o resulfi is in excellent agre ent with previous work . The (2(0.u) K(NH3)XC24 6 52 4 2 O 6 63 4 J l l l 3 5 2 «(M O 6 62 4 1 1 1 3 5 2 n(CV) O 6.. 6: 4'- 2’ 1 O 1 #1 1 1.’L . O I 2 3 4 5 6 ,’ w(8V) 3' I Fig. 2. The T - 300K optical reflectance (solid lines. insets) and Kramers-Kronig- derived imaginary part of the d i e l e c t r i c function t (0.1») (solid lines. main panels) of K( H )xczu for several values of x. The dashed curve 3(------ -) is obtained from the solid cwve by subtracting the dotted (. . . . . .) Lorentzian curve (see text). 156 Vol. 64. No. 6 dscr ase near the plasma frequency. w . as - u In due to free carrier absorption. fellowed b a rise caused by interband absorption. This interband absorption has been decomposed into a narrow band at 1.85 eV (FHHH - 0.3 eV) plus a broader contribution which resembles a typical threshold for graphitic n-w transitions . The motivation for this decomposition comes from the x - u.1 c (0.») data in which the band is most pronounced. For the compositions x - 1.9 and h.3 the same energy and FHHH were used and the strength was adjusted to the maximum value which still ayoided introducing a notch at 1.85 eV in the e-s threshold. The x-dependence of the oscillator strength of the band reveals (Fig. 3.) an increase up to x - “.1 followed by a sharp drop at higher x values. The results shown in Figs. 1-3 are closely related to the x-dependent structure of the K- NH liquid and to 6f. The liquid strug§ure is dominated by planar K(NH )u clusters ' (inset Fig. 3) while we associate df with spacer molecules. These spacers may provide the stuructural configurations (eg. a hydrogen cage formed by a spacer and a cluster NH ) which trap electrons. For x < 3 the inserts NH causes gallery expansion but only particigates in cluster formation; thus. 6f - 0. When x 5 U some added NH 's enter as spacers and back? transfer commen es while for x > u. NH enters only as spasers which further increas’e 6f. A linear model : 6f - 0. x < u; 6f - Y(x-fl). x z 8 (Y - const.) has been found to be compatible with x-ray intensity measurements of K(NH,)xC u' when NH is ingested at - 2°10 atm. Ehe resultant galiery expansion causes a reduction in the electronic wavefunction c-axis overlap which results in the step-like increase in POTASSIUM-AMMONIA LIQUID HONOLAYERS IN GRAPHITE g 6— K(NH3)sz4 >. a 5- :3 £3 4w- £5 £3" E 2" .9 3 '— C I. L, l .L (J I 2 3 4 X Fig. 3 Dependence of the oscillator strength of the 1.85 eV absorption band (see Fig. 2) of K(NH ) can on x. The solid lines are a guide to EH5 eye. Inset - the computer generated planar structure of the K-NH liquid monolayers (from ref. ’4). the solid circles ( ). open circles () and hatched circles ( bound NH spacer molecules. molecules. and unbound NH 3 3 ) represent respectively K ions. 1.45 (R/R ) . At and above 0.12 atm. the onset of the Stdiing transition. the wavefunction overlap is even more drastically reduced as complete filling/expansion of all of the galleries is achieved. As a result. (R/Ro) rises by about two orders of magnitude and lsvels off when significant 3H3 uptake ceases to occur with increased PNH . This leveling commences at - 0.8 atm. well below the pressures of -1 atm at which 6f becomes significant and 6 atm at which the staging transition is complete. We attribute this lag to the inhomogeneous c-axis distribution of NH which forms an intercalation front that migrate; from the surfaces and edges of the specimen towards the interior during the stage transformation. Thus the c-axis resistance of the outer galleries. which are ammoniated well before the staging transition is complete. rises drastically and dominates the "series" resistance of the bulk specimen. For a-axis conduction. the HA layers and the C layers conduct in parallel as indicated in Fig. 1. Expansion of the galleries should not directly effect this conduction process so there is no change in (R/Ro) until charge back- transfer is initiated at x g a. This back- transfer causes a drop in the a-plane C layer conduction which is not compensated for by increased HA layer conduction because the charge which is received is localized. But as x increases further. the trapped electrons become sufficiently dense for their in-plane wavefunctions to overlap and form band-like extended states. The HA layers then conduct and (Fl/R0)a drops. Additional increases in P3“ result in minimal weight gain8 and minima; change in in-plane conduction. The 1.85 eV band in the data of Fig. 2 is direct evidence for localized electronic states in the MA layers. Similar bands (FHHH ~ 0. eV) have been Observed at lower energy (0.5 ) in 30 MA solutions and have been attributed to a solvated electron is-Zp transition between states which form in a - 6A diameter solvent bubble. It is clear from the work‘gf Jortner' and from studies of other solvents “ that the salvation band energy increases with decreasing cavity size. The cavities formed in the K-NH layers would be smaller than those in the bul fluid and thus give rise to an upshifted band. The drop in the oscillator strength of that band at x - h is consistent with the drop in (R/RO) once it is recognized that the band strength i proportional to the concentration of localized electrons. These localized electrons are lost to the newly formed conduction band arising from the HNHT. The low energy optical data were also subjected to a Drude analysis to determine a carrier relaxation time and m from which 6f could be obtained. Details 0 this analysis will appear elsewhere. or significance here is the fact that u is found to be essentially constant at 3.3 : 0.9ev as the strength of the 1.85 eV band decreases by a factor of -3. The cosresponding drop in (R/Ro) is ~101. Since a - °dc’ one would expect a ~51 increase in u 13. 6o - e0.15ev. The anticipated change i thereTore only slightly larger than the estimated experimental error in w . We have described the HNMT 13 our specimens 1557 446 POTASSIUM-AMMONIA LIQUID HONOLAYEHS IN GRAPHITE as a Mott transition‘“. This description is Justified as follows. It can be shown from dimensional and\or energy arguments that the Hott condition for the or ipal electron areal density, n . in .20 is he a - A - const. where a - [e/(m /mo)Ja . Here t E? the static dielectric constant. a Is the effective mass. m is the free electron mass. and a - 0.529A. Agthough the quantity in square br ckets is difficult to calculate for RA GIC's we can still determine a set of self-consistent values for n (or x ). He obtain c from a 2D Clausius Hossotfl (CM) relation (t - 1)/(t o 1) - Zde which was calculated for ansellipsoidal cavity iii a (ii e lllc tg'i c . ile rle N - [x/(62.86- .28)]A is the numberzdensity of a 3.28A thick NH3 layer where 62.86A is the area of 2 C atoms. The static polarizability d - 7.36A is computed from the 3D CM equation using c "Q? and p - 0.817 gm/cm3 for liquid NH3 at - 77 C . By combining the Mott condition with the 2D CH equation we obtain n - f1(m /(m A, ). xc). But the linear model yi lds n S‘ng/ 2?§5)-(x - u) - f (x ) where Y - O.2/O.3§ ' . Setting f - f as oobtain a cubic equation the threl soldiions of which are the self-consitent values of x . Only one of these solutions is physdgally significant and it is bounded: for 0 S m /(m A2 ) S 0. '1 S x S “.117. By comparing the 2D 4%a 8D Fermi wavechtors which depend on electron density 0 tain reasonable estimate of A -[(3:2§17§/(2'fi/§H - .31. Now a delocalized electron in an HA ”yer must be heavier than a free electron as evidenced by the fact that m In is between 1.5 and n.0a for 3D.HA solutions. If we reasonably limit (m /m ) ' to 10. the applicable range of x is 11.09 Sax" § n.39 for 1 s m /m :10. This r ge of x o erlaps closely the region in which (R/R and the 1.85ev band intensity drop prech‘tously. Thus. the HA layers should indeed conduct for x 3 h. This conclusion does not depend on A2 the value of which merely rescales m /m . Finally we can compute the Fermi temperagure T - (h anc)/(m k3) which for m Imo - 10 and T - 360K gives (T/Tf)min - 2.9“. Therefore. our measurements are at "high temperature" and L << L where LT is the (Thouless),gffect ve scale size fog1quantum interference and L is our sample size. Thus. quantum interference effects are negligible and the HNHT in the K-NH layers is of the Mott type. 3 He are grateful to S.D. Hahanti, H.F. Thorpe. J.L. Dye and X.H. Qian for useful discussions. This work was supported by the NSF under grant DMR 85-11559 (SAS). by NASA under grant NAG 3579 (SAS) and by the DOE under grant DE-EFOS-BHERHSTSI (PCE). References 1. J.C. Thompson. Electrons in Liquid Ammonia (Clarendon. Oxford. 1976). 2. J. Jortner, J. Chem. Phys. 39. 839 (1959). 3. H. Rudorff and E. Schultze, Angew. Chem. H. X.H. Oian. D.R. Stump. B.R. York and S.A. Solin. Phys. Rev. ;ett. fig. 12T1(l985): Phys. Rev. 211. 5756 (1986). S. H.A. Resing, B.R. York. S.A. Solin and R.M. Fronko, Proc. of the 17th C a r b o n Conference. Lexington. 1985. p. 190. 6. Y.Y. Huang. D.R. Stump. S.A. Solin and J. Heremans. Solid State Comm.. in press. 7. 1.8. Fan. S.A. Solin. D. Neumann, H. label and J.J. Rush. Phys. Rev.. submitted. 8. B.R. York and S. A. Solin. Phys. Rev. 831. 8206 (1985). 9. 0.0. Tibbetts. Appl. Phys. Lett. fig. 666 (1983). 10. D.H. Hoffman. R.E. Heinz. G.L. Doll and P.C. Eklund. Phys. Rev. B 32. 1278 (1985). 11 H. Zanini and J. Fischer. Hat. Sci. Eng. 21. 169 (1977). 12. See ref. 1 p.269. 13. J.M. Zhang. P.C. Eklund and S.A. Solin. to be publisned. 1“. T.V. Ramakrishnan, in "The Hetallic and Nonmetallic States of Matter" ed. by P.P. Edwarcs and C.N.R. Rao. (Taylor and Francis. London. 198$).p.23. 15. J.A. Stratton, Electromagnetic Theory. (McGraw-Hill. New York. 1991). p. 21“. 16. "cnc Handbook". nut" ed..C.D. Hodgman Ed.. (Chemical Rubber Publishing Co. Cleveland. 1962). pp 529 and 2062. Vol. 66, No. a 1581 Synthetic Metals. 23 (1988) 223—228 223 Two DIMENSIONAL HETAL-INSULATOR TRANSITIONS IN ALKALI-AHMONIA nanny GRAPHITE INTERCALATION conrounos S.A. SOLIN' and 2.x. HUANG Department of Physics and Astronomy and Center for Fundamental Materials Research. Michigan State University. East Lansing. Michigan (USA) ABSTRACT The composition dependence of the c-axis and a-axis resistance of the alkali-ammonia ternary graphite intercalation compounds M(NH3)XC2u. M - K. Rb. Cs and O S x S xmax has been measured at room temperature for xm" values of 11.33. m. and L92 corresponding respectively to. K Rb. and Cs. The c-axis resistances relative to that of M02“ exhibit features which we associate with the onset of a stage-2 to stage-1 structural phase transition whereas the a-axis relative resistances exhibit features which we associate with a metal-insulator transition in the metal-ammonia intercalate layers. For some vales of x the alkali-ammonia ternary OIC.s exhibit electrical anisotropies which are among the highest yet reported for stage-1 donor GIC's. INTRODUCTION Bulk metal-ammonia (MA) solutions have been the subject of intense study over the past several decades [1] primarily as a result of the composition dependent three dimensional (3D) metal-insulator transition (MIT) which they exhibit when an alkali metal is added to the insulating ammonia fluid. In a chemical synthesis effort unrelated to the conducting properties of bulk MA solutions. Rudorff and coworkers [2] showed that an alkali metal and ammonia could be cointercalated into powdered graphite to form binary monolayers in the host galleries. Following a three decade period of underwhelming interest in ternary MA GIC's. renewed interest in those materials developed when York and Solin[3] pointed out that MA monolayers in graphite might be the 2D analogues of the bulk HA solutions and thus may exhibit a host of interesting physical properties. 0 Invited paper. 0379-6779/88/3350 © Elsevier Sequoia/Printed in The Netherlands 159 224 During the past half decade the research efforts on ternary MA GIC's have been focussed on the potassium compounds K(NH3)xC3u' O s x s 3.38 and many composition dependent measurements have been made on those materials. These measurements include x-ray studies. [3] elastic. inelastic and quasi elastic neutron diffraction studies, [“3 nuclear magnetic resonance studies. [5] optical reflectivity and absorption studies. [6] absorptuMIisotherm measurements [3] and measurements of the a-axis and c-axis resistance. [6] Naturally sucn studies have generated a wealth of knowledge about the K-NH3 ternary GIC's. Most significah:-1. we now know that: 1. The HA monolayers in K(NH3)XC2u. x z 2, are the ED structural analogue of the 30 MA solution. These intercalated layers possess a 20 fluid structure in which the K ions are u-fold coordinated to NH3 molecules whose C3 axes are tilted by approximately 90 with respect to the graphite c-axis so that the nitrogen lone pair electrons point towards the potassium cation. To satisfy the stoichiometry for x > u, ”spacer" ammonia molecules which are dynamically uncoupled from a K ion are also present in the fluid. 2. The HA monolayers in potassium-ammonia-graphite are the £3,225,322}: analogue of the corresponding 30 MA solutions and exhibit a composition dependent MIT. For the potssium compound. this transition obeys a 2D Mott condition [6] for the critical concentration namely. nCVZah -o.31 1.1) where “é is the critical areal electron density at which the MIT takes place and an is an effective-Bohr radius for the system. To date only the potassium-ammonia ternary GIC has been probed for a MIT and attendant properties. In this paper we report the first corresponding studies of the electrical behavior of the Rb and Cs alkali-ammonia ternary GIC's. These studies also yield evidence for a MIT in the Rb and Cs compounds the electrical behavior of which is similar to that of the potassium compound. Moreover. we will show that there is a systematic relationship beteween the c-axis resistance at maximal ammonia concentration and the physical properties. e.g. the ionic radius. of the alkali species in H(NH3)XC2u. EXPERIMENTAL METHODS The intercalation procedures employed by Rudorff [2] invariably caused drastic exfoliation of the host material. To avoid this undesirable morphological effect. York and Solin [3] developed sequential intercalation methods in which binary alkali GIC.s prepared from highly oriented pyrolytic gaphite (HOPG) could be ammoniated and partially reversibly deammoniated without 160 225 exfoliation. To prepare and study the in situ electrical properties of M(NH3)XC2u. stage-2 ”can was exposed to purified ammonia vapor the pressure of which was controlled by adjusting the temperature of an ammonia resev0ir that was attached to the sample tube through a valved off side arm. The absorption isotherm which relate composition. x. to ammonia pressure, P has been NH3 thoroughly studied for K(NH3)XC2n but only the saturation composition COPP9390“51“8 to the V390? Pressure of ammonia at room temperature. ~ 10 atm, has been determined for the Rb and Cs compounds. The results of these COMPOSitiO" measurements together with x-ray derived basal spacings and other physical Parameters which are relevant to further discussions in this paper are summarized for the alkali-ammonia ternary GIC's in TABLE 1. Further details 3f the sequential sample intercalation method are given elsewhere. TABLE 1 Parameters and properties of the stage-1 alkali-ammonia ternary graphite intercalation compounds. H(NH3)xC2u for x - xmax corresponding to an ammonia pressure of - 10 atm alkali x [7] basal spacing C7] ionic radius [7] saturation relative ion max d (A) (A) resistance (R/R ) c 0 c K 1:. 33:0.05 '6.620:o.oos 1. 33 220125 Rb ".10:0.0S 6.6“0:0.005 1.u6 75:5 Cs 3.65:0.05 6.671:0.00S 1.67 zuzs For the c-axis resistance measurements. HOPG specimens were employed whereas benzene derived fibers which had been heat treated to 3000°C were used for the a-axis measurements. Conducting epoxy contacts which were pretested and found to be impervious to attack by high pressure ammonia were used for the HOPG measurements while mechanical contacts were used for the»fiber measurements. All of the electrical transport studies reported here were carried out using a _ four-probe configuration with both AC and DC detection. RESULTS AND DISCUSSION The dependences of the c-axis relative resistances (R/Ro)c on ammonia pressure (or equivalently on composition. x) for the three alkali-ammonia GIC's studied are shown in Fig. 1. Here R is the corresponding resistance of the O stage-2 binary alkali 51¢. 161 226 ‘0) ' “WW-cu . ' ° 103 ' CNWfiu . . . , .9 ° ' ’ g . .e e e a I 5 . 10' . 109 ‘ r 1 . 41 ° -. A 1.1“ , J . 16" to“ to" 10" 10° «:1 flung-nun Fig. 1. C-axis Relative Resistance of H(NH )XC as a Function of Ammonia p 3 2H ressure. Each of the c-axis relative resistance curves of Fig. 1 exhibit a step-like rise at an ammonia pressure of about 0.3 atm. This step is preceeded and followed by plateau regions in which the resistance is essentially independent of pressure. Given our understanding of the potassium-ammonia GIC's we associate this step with a stage-2 to stage-1 structural phase transition in which ammonia enters all available galleries and becomes the dominant guest species. This ingestion of ammonia causes a drastic expansion of the gallery height and the resultant reduction in the overlap of electron wave function along the c-axis direction gives rise to the observed increase in (R/Ro)c. The curve for K(NH ) C - 3 x 2“ ~ “.5X10 3 atm. which is associated with the uptake of small ammounts of ammonia also exhibits a step-like rise at a lower pressure of into the stage-2 galleries which are already occupied by potassium. Notice from Fig. 1 that there is a systematic decrease in the maximum value of the (R/Ro)c with increasing ionic radius. This point is further illustrated in TABLE 1 where we have catalogued the maximum c-axis resistance with other parameters of the alkali ion. We have noticed that there is an imperical relationship between the saturation resistance and the ionic parameters: xdc lni(R/R ) i - B . -—- + A (2) O c max r2 where R is a constant and all of the other parameters in Eq. (2) have been previously defined. From Fig. 2 which shows a straight line semilog plot of Eq. (2) using the appropriate parameters from TABLE 1 we find a value of A - 0.580 and B - 0.296. 162 227 10 V ‘VTv'v'v ((Rlno)c)m“ YVV'VII ‘ 1 A 1 1 L l 1 A e91011121314151e17 xmmguli 10 Fig. 2. The Experimental (.) and Theoretical (-) Variation (see text) of the C-axis Relative Resistance of M(NH3)XC2u as a Function of Composititni and Zen Parameters. Although we cannot derive Eq. (2) a priori. we can understand it on a qualitative basis. The c-axis wave function overlap integral which influences conduction can be expected to decrease exponentially with increasing separation of the carbon layers. thus the resistance ratio should increase exponentially with dc as observed. Moreover. the ammonia content controls the amount of to the M-NH 2H 3 layers so the resistance should increase with xmax and decrease with the area of the alkali ion. r3. because this area sterically limits the value of x charge which is backtransferred from the carbon layers of MC max' In Fig. 3 we show the a-axis relative resistances (R/Ro)a for the three alkali-ammonia GIC's as a function of ammonia pressure. As in the potassium 4.0 1- e manna“ 1... _ ' ”chu . ‘ CNWIQe 30° '- .3 C h e C I 2 .° x. 2.0 P . a 0 e I . . . . O. O . to . ' . 1 . . . .-. .L A. .A.~. I . O u_' so" to“ ‘ 10" to" 10' Push“) Fig. 3. a-axis Relative Resistance of H(NH )XC as a Function of Ammonia ii Pressure. 3 2 case which has been previously studied the Rb and Cs compounds exhibit a marked rise in (R/Ro)a followed by a slight decrease with increasing ammonia pressure. 163 228 This decrease in resistance or increase in a-axis conduction with intercalant weight gain at constant stage is unique to the alkali-ammonia ternary Grcv is associated with a 20 MIT in the HA monolayers. s and As ammonia is inserted with increasing pressure. a value of fiw1 is reached at which additional ammoniation results in the back transfer of charge from the carbon layers to the MA layers. Initially this charge is localized uithe an layers and the reduced carrier density in the C layers which conduct in parallel causes the rise in a-axis relative resistance. However. when sufficient charge backtransfer occurs to produce wave function overlap in the a-plane. a MIT occurs in the MA layers and their parallel contribution to the conduction causes the a-axis relative resistance to drop. Note that this drop is not a manifestation of the staging phase transition since it does not occur at me ammonia pressure at which the c-axis relative resistance shows a sharp rise. It is known from optical [6] and NNR measurements [5] that the potassimm- ammonia GIC's are donor compounds and the same can be reasonably assumed for the Rb and Cs species with ammonia. From a knowledge of the electrical anisotropies of the Mczu binary GIC's and the data of Figs. 1 and 3. one can deduce that the MA ternary GIC's exhibit some of the highest anisotopies yet reported for stage- 1 donor compounds. For example. at an ammonia pressure of about 1 atm the potassium compound has an anisotropy of 1.6X105 which is a factor of a thousand higher than that of a typical stage-1 donor GIC. The extreme anisotropy of the MA GIC's provides additional confirmation of the 2D nature of the conduction process in those novel materials. ACKNOHLEDGEHENTS We are grateful to J. Heremans for technical advice and for useful conversations. We also thank A.H. Moore and 0.6. Tibbets for providing the HOPG and fiber material. respectively. This work was supported by NASA under grant INAG 3-595 and by the NSF under grant DMR 8517223. REFERENCES 1. J.C. Thompson. Electrons in Liquid Ammonia (Clarendon. Oxford. 1976). 2. N. Rudorff and E. Schultze, Agnew. Chem. 93. 305 (195“). -3. B.R. York and S.A. Solin. Phys. Rev. Bil. 8206 (1985). u. D. Neumann, H. Zabel, Y.B. Fan. S.A. Solin and J. Rush. to be published. 5. H.A. Resing, B.R. York. S.A. Solin and R.M. Fronko, Proc. of the 17th Carbon Conference. Lexington. 1985. p. 190. 6. LI. Huang. v.3. Fan. S.A. Solin. J.H. Zhang. P.C. Eklund. J. Hermans and 6.0. Tibbets. Solid State Comm.. Submitted. 7. S.A. Solin. Y.B. Fan and X.U.Qian. Synth. Met. 12, 181 (1985). 164 Intercalation in Layered Materials (plenum. New York, 1987) EVIDENCE FOR A Z-DIMENSIONAL METAL‘INSULATOR TRANSITION IN POTASSIUM- AMMONIA GRAPHITE Y.!. Huang. X.H. Qian'. and S.A. Solin Department of Physics and Astronomy Michigan State University East Lansing. MI “882n-1116 J. Heremans and 0.6. Tibbets Physics Department General Motors Corporation Warren, MI "8090-9055 We have studied the ammonia pressure dependence and composition dependence of the a-axis electrical resistivity of the potassium-ammonia ternary graphite intercalation compounds K(NH,) Czwo C) < x < “.33. Our results show evidence of the ZD analog of the well-studied bulk 3D metal- insulator transition [1] in bulk K-NH, solutions. In order to probe the electrical properties of the intercalate layer in K(NH,) C,.. we measured the in-plane a-axis resistivity as a function of ammonia pressure [2]. For convenience. we used a benzene-derived onion skin-like graphite fiber [3] rather than HOPG. Thus. the fiber axis is approximately coaxial with the cylindrical graphite planes. From the (001) x-ray diffraction patterns of a single fiber (see Fig. 1) we determined the basal spacing of the pristine fiber (da - 3.3SA). of stage-2 KC,~ potassium binary GIC (d - 8.7uA) and of the stage-1 ternary GIC K(NH,)u 3G,. (dn’- 6.6UA). ‘The e results indicate that the graphite fiber has tn; same Gibbs phase diagram [h] as HOPG. A four-probe measurement technique was developed for monitoring the pressure dependence of the a-axis relative resistance (R/R ) of K(NH,) C,.. using a pressure up-quenching technique. [Here R(Ro) is the a-axis resistance of the amoniated (KC,.) compound.] The resuIt is plotted in Fig. 2. Note that the relative resistance ratio remains a constant below one atmosphere and then starts to increase in the stage-2 to stage-1 phase transition region at -0.5 atm. [S]. The increasing resistivity in a stage- 2 to stage-1 phase transition is a common feature of binary GIC's [5]. But when NH, is added to KC“. some delocalized electrons in the carbon layer are back-transferred to the intercalate layer [6] so that the conductivity' of the carbon layers decreases. However. R/R starts to decrease dramatically at about 3-14 atm. at which pressure x Is greater than four [6]. This phenomenon may be a consequence of a 20 metal-insulator transition. Nhen x - u. there are enough NH, molecules to completely solvate potassium and form a N-fold coordinated K-NH, clusters [7]. Higher NH, concentration leads to a sufficient amount of electron back-transfer 165 23 O o 3...” e . 0" O o “fie-303$Of. ...QO..I. . a“ “0’. 00:. 9”.” 5e. .0. 0; e. in '0.” 5.3.0 '0” I “no. ‘ 00’... . .0... o‘.".. eg .00. ..~.Oe.. INTENSITY (ARB UNITS) .0 ‘- 0.0.0.0 00.00.0'u00000~ e' Fig. 1. The (009,) x—ray diffraction patterns of (a) a sine“ PNSUM cylindrical onion skin-like graphite fiber, (b) the same fiber as in (a) after intercalation with potassium to form the binary GIC KC... and (c) the game no” as in (b) after ammoniation to form the ternary GIC K(NH.) C... The diffraction patterns were recorded at room temperature using 0 radiation. The background continuum is diffuse scattering from the glass envelope and from air in the beam path. 166 R/Ro (:1 -5 IN) (S! -l> (II 10 10 10 ‘IO 10 10 im.) PNH3(a Fig. 2. The room temperature relative resistance a-axis ratio R/R of potassium-ammonia-graphite as a function of ammonia pressure. Here R0 and R correspond respectively to the resistance of KC,. and K(NH,)‘C,.. from the graphite layers to the intercalate layers to induce a hopping-type metal-insulator transition [8]. When there is sufficient salvation to cause in-plane overlap of the electron wave function. the intercalate layer starts to conduct in parallel with the carbon layers and the a-axis resistance drape as is observed in Fig. 2. The study of the composition dependence of the dielectric constant of K(NH, ) xC,~ also provides evidence of a metal- insulator transition at x - l. ACKNOWLEDGEMENTS He thank Y.B. Fan for useful discussions. This work was supported by the National Aeronautics and Space Administration under grant NAG-3-595 and in part by the U.S. National Science Foundation under grant 85-17223. 'Exxon Fellow REFERENCES 1. J.C. Thompson. Electrons in Liquid Ammonia (Clarendon. Oxford. 1976). 2. Y.Y. Huang. S.A. Solin. J. Heremans. and G.G. Tibbets, to be published. 3. J. Tsukamoto. K. Matsumura. T. Takahashi. and K. Sakoda. Synthetic Metals 13. 255‘263 (1986). h. 1.8. Fan-and S.A. Solin. Proceedings of the Materials Research Society Meeting. Boston. (1985). 5. M.S. Dresselhaus and G. Dresselhaus. Adv. Phys. 39. 139 (1981). 6. B.R. York and S.A. Solin. Phys. Rev. 831. 8206 (1985). 7. XJI. Qian. D. R. Stump. B. R. York. and S.A. Solin. Phys. Rev. Lett. 5n, 8 9 1271 (1985). . See reference 1 and references therein. . J.M. Zhang. P.C. Ekiund. 1.3. Fan. and S.A. Solin. to be published. 167 Graphite Intercalation Compounds (Materials Research Society. Pittsburgh. OPTICAL AND ELECTRICAL MEASUREMENTS OE POTASSIUM-'AI‘WNIA-GRAPHITE: EVIDENCE FOR A METAL-NON NETAL TRANSITION LY. HUANG. LB. FAN. S.A. SOLIN'. J. HEREMANS. G.G. TIBBETTS". J.M. ZHANG and P.C. EKLUND'" 'Department of Physics and Astronomy. Michigan State University. E. Lansing. MI 1188213-1116 "General Motors Research Laboratoriesi Physics Department. warren. MI usogo "'Department of Physics and Astronomy. University of Kentucky. Lexington, KY 110506 The potassium-ammonia ternary graphite intercalation compound. K(NH3 xczu' O S x s ”.38. has been shown to have intriguing preperties such as a staging phase transition [1.2] and a simple unmodulated ZD metal-ammonia liquid structure of the intercalate layer [3]. These properties induce more extensive studies of metal-ammonia GIC's. Here we will report the results-of electrical resistance measurements of potassium-ammonia graphite in both the c-axis and a-axis directions. He also report optical reflectivity measure- ments carried out with the incident light approximately normal to the basal planes. 1 The samples that we used in the c-axis measurements were prepared from highly oriented pyrolytic graphite (HOPG). Pure binary stage-2 KC was exposed to ammonia vapor the pressure of which was controlled by cotrozlf‘ling the temperature of an attached ammonia reservoir. A four-probe method was employed in the resistance experiment. By stepwise increasing the ammonia pressure. we obtained the c-axis relative resistance ratio R/Ro of K(NH3)xC2u versus ammonia pressure as shown in Fig. 1a. Here. RC, is the resistance of the binary Kczu compound at various ammonia pressures. Clearly. the c-axis relative resis- compound and R is the saturation resistance of the ammoniated tance ratio exihibits two step-like plateaus at ammonia pressures of 3 approximately 5 x 10- atm. and 0.5 atm. The first plateau with a resistivity . increase of 10% is due to the ammonia weight gain of KC at a constant stage- 2 composition. The sample expanded macroscopically aiuammonia entered the potassium-occupied galleries between the carbon layers. and this expansion is the source of the small c-axis resistance increase. In contrast. the second plateau with a 100-fold relative resistance ratio increase is associated with a stage-2 to stage-1 phase transition which has been studied by (001.) x-ray diffraction. Besides the expanding gallery. the charge back-transfer from the carbon layers to the intercalate layers through this transition [1] also contributes to the large c-axis relative resistance ratio increase. He also measured the a-axis relative resistance ratio of potassium- ,ammonia graphite using individual graphite fibers with a cylindrical onion skin morphology and four-probe AC and DC techniques. The results of this 168 measurement are plotted in Fig. 1b. Compared with c-axis_measurement. the in- plane relative resistance ratio also increases at the staging phasg transition. but by only a factor of approximately 3.’ Moreover. it shows a significant decrease at an amonia pressure corresponding to a composition of x ~ 11 while the c-axis ratio is essentially flat in that composition range. In analogy with the famous metal-insulator transitions in the bulk 30 metal- ammonia solutions [11], we suggest that the drop in the a-axis relative resistance ratio is associated with a metal-nonmetal transition in the ZD potassium-ammonia liquid layer. Optical reflectivity measurements also provide evidence for this metal- insulator transition. In Fig. 2 are shown compositionedependent plots of the imaginary part of the complex dielectric constant of K(NH3)XC2n (derived from the optical reflectivity using a Kramers-Kronig analysis) as a function of incident photon energy. The sharp peaks at ~2e1l in the x - 11.1 and x - 11.3 spectra have never before been observed for any GIC. the typical optical response of which is shown for KC in the inset of Fig. 2. These peaks can be accounted for phenomenologigglly by adding a Lorentzian oscillator con- tribution at 1.85 eV to e, as shown schematically in Fig. 2. He associate this Lorentzian oscillator ~with an optical transition of the localized sol- vated electron in the potassium-ammonia layer. again in analogy with bulk potassium-ammonia solutions [11]. Note. however. that the oscillator strength of the 1.85 e11 excitation decreases with increasing ammoniation in the com- position range ): > 11.0. This decrease results from the wave function overlap and delocalization of the electron charge that is back-transferred to the K- N113 layers. The reduction in the bound/localized state density and concommitant charge delocalization in the intercalant layer also generates the observed decrease in the a-axis relative resistance ratio. ACIOIOHLEDQEMENTS He would like to thank LN. Qian for useful discussions. This work was supported by NASA under grant NAG-3695 (SAS).in part by the NSF under grant DMR 85-17223 (SAS) and by the DOE under grant DE-FGO‘J-BAERII5151 (PCE). REFERENCES 1. B.R. York and S.A. Solin. Phys. Rev. Bil. 8206 (1985). 2. B.R. York. S.K. Hark. S.D. Hahanti, and S.A. Solin. Solid State Comm. 29. 595 (1982). ' 3. X.H. Qian. D.R. Stump. B.R. York. and S.A. Solin. Phys. Rev. Lett. fig. 1271 (1985). t. J.C. Thompsbn. Electrons in Liquid Ammonia (Clarendon. Oxford. 1976). 169 «F E (a) . . . 10’ g- . 0010(0) .5 : -----(o-L1 a: ------- Lorentzian (L) g ... r a _ (E,=1.85 eV. m4 W) m b 5 m. E . . O O I . m E m g 10' r (u g e h . ° . V 62 '0 F e e e e e . G b . . --....l i . i.....l . . .-....l k. --.-..l . --.... 1o“ 10" 1o" 10" 10° 10 ‘ P~"31ath Fig. 1. Relative resistance ratio R/R of K(NH )XC u as a function of ammgnia vapo; pr ssure (P ). (a)c- NH 8 axis ratio (b) in-plane éa-axis) ratio. Fig. 2. The imaginary part of the complex dielectric constant of K(NH ) C2 vs. incident phonon freqéenxcy or x - 11.1 and x - 11.3. The corresponding plot for the pure stage-2 Kczu is shown in the inset.