DOCSLIB.ORG

Experimental Determination Op the Specific Heats of Sodium

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Experimental Determination Op the Specific Heats of Sodium EXPERIMENTAL DETERMINATION OP THE SPECIFIC HEATS OF SODIUM, COBALT, MANGANESE, AND COBALT-IRON BELOW 1°K. DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By ROGER EDGAR GAUMER, B. S. The Ohio State University 1959 Approved by Adviser Department of Hiysics and Astronomy ACKNOWLEDGEMENTS I wish to acknowledge my debt to Dr. C. V. Heer for his continued support and guidance throughout the course of these investigations. Dr. R. A. Erickson should be acknowledged for a variety of invaluable suggestions concerning experimental procedures. To my fellow graduate student, Mr. David Murray, I extend sincere thanks for all manner of help. Finally, I wish to express gratitude to my wife, Suzanne Morrison Gaumer, for unfailing moral support during these lean years. This work was supported in part by funds granted to The Ohio State University by the Research Foundation and by a contract between the Air Force Office of Scientific Research and The Ohio State University Research Foundation. ii TABLE OF CONTENTS ACKNOWLEDGMENTS..................... * » . LIST OF TABLES .............................. LIST OF ILLUSTRATIONS ....................... INTRODUCTION ................................ Chapter I. THEORY OF THE SPECIFIC HEAT OF SOLIDS . Lattice Specific Heat Electronic Specific Heats in Metals II. EXPERIMENTAL TECHNIQUES ............... Cooling Above 1°K. Cooling Below 1°K. Apparatus Thermometry Vapor Pressure Thermometry Sampe Preparation III. EXPERIMENTAL RESULTS.................. General Methods Thermometer Calibration Copper Sodium Cobalt Manganese Cobalt-Iron Alloy IV. INTERPRETATION OF R E S U L T S ............. Section 1t Copper and Sodium Section 2* Cobalt, Cobalt-Iron Alloy, and Manganese LIST OF REFERENCES LIST OP TABLES Table Page 1* Uanganese Deviation Curve D a t a ............ 61 2« Data Tablet Copper Heat Capacity •••••••• 64 3* Data Tablet Sodium Heat Capacity •••*«••• 66 4* Bata Tablet Cobalt Specific Heat • • 74 5* Data Tablet Manganese Specific H e a t .......... .. 77 6« Data Tablet Cobalt-Iron Alloy Heat Capacity • • • • 84 7« Specific Heats of Some Transition Metals•••••• 89 iv LIST OP ILLUSTRATIONS Figure Page 1. Einstein Theory of Lattice Specific Heat ............ 8 2. Debye Theory of Lattice Specific H e a t .............. 13 3. Born-Von Karman Theory of Lattice Specific Heat ...» 1? 4* magnetic Refrigerator ........................... 23 5« Magnetic Refrigerator Engine and Sample Area .......... 24 6. Superconducting Thermal Switch .................... 33 7* Thermal Switching R a t i o ......................... 36 8. Magnetic Calibration Curve ........................ 40 9. Carbon Resistor Calibration Curve ................. 43 10* Sodium Distillation Apparatus ..................... 46 11. Sodium Sample Assembly........................... 47 12. Cobalt Sample Assembly ........................... 49 13* Manganese Sample Ass e m b l y........................ 50 14* Cobalt-Iron Alloy Sample Assembly................. 52 15* Typical Heating C y c l e ........................... 56 16. Heat Capacity of C o p p e r ...................... 63 17. Specific Heat of Sodium M e t a l ..................... 71 18. Specific Heat of C o b a l t .......................... 73 19* C/T Versus T^ for Manganese...................... 81 20. Specific Heat of Manganese........................ 83 21* Cobalt-Iron Alloy Heat Capacity ................... 87 v INTRODUCTION Experimental Investigations of the specific heat of solids at low temperatures have constituted a sizable portion of cryogenic research during the last half century. The first liquefaction of helium occurred at Leiden, under Kammerlingh-Onnes, on July 10, 1908.^ Cryogenic research may well be said to date from this historic event. It is of interest to note that virtually all progress in the under­ standing of the mechanisms which contribute to the specific heat of solids also dates from the early part of this century. The specific heat of a solid at ordinary or "room” temperature is almost entirely due to the lattice vibrations. However, below 1°K. the specific heat of a solid is predominantly due to the energy of the electrons. As a consequence, experimental data concerning the specific heats of solids below 1°K. are of considerable value in increasing our understanding of the electronic and atomic domains. The present state of the theory of specific heats of solids will be reviewed in the first section of this dissertation. It will become clear that there exist several uncertainties in the present theory, despite the great advances made since 1910. It was with the hope of contributing information which would be of value in the construction of a completely satisfactory theory of specific heats that the inves­ tigations to be described here were begun. 1 2 The specific heat of sodium metal is of interest for several reasons. The structure of sodium is such that it would theoretically 2 approach very closely the free-electron model of Sommerfeld. Owing to the relatively simple electronic configuration of sodium, there has been extensive theoretical investigation of the hand structure, and experimental information would he useful in assessing the applic­ ability of the various theoretical treatments. Finally, previous measurements of the specific heat of sodium have indicated the poss­ ible presence of unexplained anomolies in the specific heat. Such anomolies, if verified, would require a modification of the present theory. For these reasons the specific heat of pure sodium metal has been measured. The results are given in Chapter III. Another area where there is need for experimental information on heat capacities is that of the transition metals. In these elements the electronic configuration is rather complex, and this complexity has led to the development of band theory. Measurements on these metals at low temperatures serve to give a direct indication of the filling of the d-bands. Another impetus for the study of these metals has been the observation of a specific-heat contribution at low temperatures that is attributed to a hyperfine coupling between the nucleus and the electronic magnetic moment of the atom. The existence of a specific-heat contribution attributable to hyperfine coupling was originally indicated by the nuclear orientation^ produced in cobalt crystals by a hyperfine interaction. The hyperfine-coupling specific heat in cobalt metal has been measured by Heer and Erickson^ between 0.6 and 3.0°K., and their results suggest a progressive increase in specific heat as the temperature is decreased to 0.01°K. For these reasons the specific heats of cobalt metal* manganese metal* and cm alloy of cobalt-iron have been measured in the temperature region 0.4-l»5°K * These results are also given in Chapter III. All of these investigations have been carried out in a magnetic refrigerator* the principles of which have been described pre- S 7 viously. * * Details of the particular refrigerator used have been a given by Stroud. The general oalorimetrio procedures and details of experimental modifications are given in Chapter II. Also to be dis­ cussed in Chapter II is the subject of thermometry, which is one of the more important areas of calorimetry below 1°K. Results of the measurements are given in Chapter III* and these results are discussed and analysed in Chapter XV. CHAPTER I THEORY OF THE SPECIFIC HEAT OF SOLIDS Solids may "be described as an assembly of parallepipeds which form a three-dimensional lattice. Each parallelepiped, or unit cell, contains an identical arrangement of atoms. Specific heat is thermodynamically defined as that quantity of heat necessary to raise the temperature of a unit mass of the sub­ stance by unity. Cp is the symbol for specific heat at constant pressure. In the temperature region 0.0-4.0°K.-, the difference between Cy and C^ is negligible for all practical purposes. In low- temperature work it is customary to use the symbol C without a subscript to indicate the specific heat} i.e., the quantity of heat necessary to increase the temperature of one mole of the substance by 1°K. As a consequence of the definition of specific heat, an application of the first law of thermodynamics yields the result that the specific heat of a substance refers to the rate of change of internal energy of the system with change in temperature. Thus, (1 .1 ) (1.2) 4 5 at low temperatures. It is then clear that the specific heat of a solid depends entirely upon the internal energy of the solid and so upon the manner in which temperature changes affect the internal energy* The internal energy of a solid may be divided into two main cate­ gories. One category is that of internal energy owing to vibrations of the atoms in their lattice, while the other type of internal energy is that associated with the electronic structure of the individual atoms. The lattice component is dominant at ordinary temperatures, while the electronic component becomes relatively sizable only at very low temperatures where the lattice vibrational energy is quite small* Lattice Specific Heat The theory of the lattice specific heat of solids has been the subject of extensive investigation in recent times. This section will endeavour to outline the development of the theory and to indicate the salient features of each development. In 1819 Dulong and Petit^ made the empirical observation that the product of specific heat and atomic weight was approximately constant at a value c v = 3 R ^ ^ ~°/c d-3) This empirical law found a justification in classical theory by assum­ ing that each atom in a crystal is associated with a definite lattice point and vibrates about its equilibrium point because of the forces 6 exerted by neighboring atoms. The vibrations of the atoms are assumed to be simple harmonic. The energy of a simple harmonic oscillator of frequency V ’is, in one dimension The average energy of the oscillator in thermal equilibrium may be shown to be £ (1.5) independent of frequency. The total internal energy of a system of N such oscillators in a three-dimensional solid will be (1.6) and the Dulong-Petit value follows.
Load more

Recommended publications
  • Density of States Information from Low Temperature Specific Heat
    JOURNAL OF RESE ARC H of th e National Bureau of Standards - A. Physics and Chemistry Val. 74A, No.3, May-June 1970 Density of States I nformation from Low Temperature Specific Heat Measurements* Paul A. Beck and Helmut Claus University of Illinois, Urbana (October 10, 1969) The c a lcul ati on of one -electron d ensit y of s tate va lues from the coeffi cient y of the te rm of the low te mperature specifi c heat lin ear in te mperature is compli cated by many- body effects. In parti c ul ar, the electron-p honon inte raction may enhance the measured y as muc h as tw ofo ld. The e nha nce me nt fa ctor can be eva luat ed in the case of supe rconducting metals and a ll oys. In the presence of magneti c mo­ ments, add it ional complicati ons arise. A magneti c contribution to the measured y was ide ntifi e d in the case of dilute all oys and a lso of concentrated a lJ oys wh e re parasiti c antife rromagnetis m is s upe rim­ posed on a n over-a ll fe rromagneti c orde r. No me thod has as ye t bee n de vised to e valu ate this magne ti c part of y. T he separati on of the te mpera ture- li near term of the s pec ifi c heat may itself be co mpli cated by the a ppearance of a s pecific heat a no ma ly due to magneti c cluste rs in s upe rpa ramagneti c or we ak ly ferromagneti c a ll oys.
    [Show full text]
  • THERMO POWER of Kr IMPLANTED MANGANIN- Cu THERMOCOUPLE T
    Solid State Physics ANNUAL REPORT 2005 THERMO POWER OF Kr IMPLANTED MANGANIN- Cu THERMOCOUPLE T. WilczyĔ ska, R. WiĞ niewski, K. Wieteska Institute of Atomic Energy Low electric thermo power of manganin (Cu- junctions were placed into small glass containers insu- Mn_Ni alloy) relative to the copper is an advantage of lated thermally from each other by polystyrene box. The manganin alloy. The aim of this investigation was to hot junction container had suitable electrical heater. check if electric thermo power remains low after im- Temperature of the junctions was measured with mer- plantation with Kr ions. The work described is part of cury micro thermometer or an additional constantan- wide projected concerned with studies on properties of copper thermocouple. manganin implanted with various heavy ions [1]. Our measurements revealed that implantation of The 10P m thick stripe samples of 1 × 75mm were manganin with Kr ions reduces its thermo power rela- implanted with Kr ions in Laboratory of Nuclear Reac- tive to copper by ~50%. Another result of our study is tion at Joint Institute for Nuclear Research, Dubna. A that thermo power of non implanted manganin relative moderation aluminum foil of 11P m thick and 3mm to Cu is a little lower than given in literature. width was used. According to modeling performed with To assess the origin of such significant decrease in TRIM code [2] implantation produced the enhanced thermo EMF after implantation the thermally forced deposition layer near the back side of sample (Fig. 1). electron diffusion in junctions, contact potential and After implantation the samples were annealed for 100h o phonon forced electron drag components of the Seebeck at 130 - 150 C.
    [Show full text]
  • Chapter 25 Resistance and Current
    Chapter 25 Resistance and Current Current in Wires • We define the Ampere (amp) to be one Coulomb of charge flow per second • A Coulomb is about 7 x 1018 electrons (or protons) of charge • For reference a “mole” is about 6.02 x 1023 units • Thus a “mole” of Copper 63.5 g/mole (z=29, A=63 (69.15% - 34 Neutrons, A=65 ( 30.85% - 36 Neutrons ) • Contains about 3 x 106 Coulombs BUT only outer electrons are free to move (4S1 state) – one electron per Cu atom in “valence band” • Density of Copper is about 8.9 g/cm3 • Density of free electrons in Cu ~ 1.4 x 104 Coul/cm3 • Or density of free electrons ~ 1023 e/cm3 A bit of History • chalkos (χαλκός) in Greek • Cyprium in Roman times as it was found in Cyprus • This was simplified to Cuprum in Latin and then • Copper in English • Copper mined in what is now Wisconsin 6000-3000 BCE • Copper plumbing found in Egyptian pyramid 3000 BCE • Small amount of Tin (Sn) helps in casting – Bronze (Cu-Sn) Ancient mine in Timna Valley – Negev Israel Current in wire • Lets assume a metal wire has n free charges/ vol • Assume the wire has cross sectional area A • Assume the charges (electrons) move at “drift speed” vd • Lets follow a section of charge q in length x • q = n*A*x (n*volume)e • Where e = electron charge • This volume move (drifts) at speed vd • This charge moves thru x in time • t = x/vd • The current is I= q/t = n*A*x*e/ (x/vd ) = nAvde , Wire gauges AWG – American Wire Gauge • Larger wire gauge numbers are smaller size wire • By definition 36 gauge = 0.005 inches diam • By definition 0000 gauge “4
    [Show full text]
  • Mixed Valence Driven Heavy-Fermion Behavior and Superconductivity in Kni2se2
    Mixed Valence Driven Heavy-Fermion Behavior and Superconductivity in KNi2Se2 James R. Neilson,1,2† Anna Llobet,3 Andreas V. Stier,2 Liang Wu,2 Jiajia Wen,2 Jing Tao,4 Yimei Zhu,4 Zlatko B. Tesanovic,2 N. P. Armitage,2 and Tyrel M. McQueen1,2* 1 Department of Chemistry, Johns Hopkins University, Baltimore MD. 2 Institute for Quantum Matter, and Department of Physics and Astronomy, Johns Hopkins University, Baltimore MD. 3 Lujan Neutron Scattering Center, Los Alamos Neutron Science Center, Los Alamos National Laboratory, Los Alamos, NM. 4 Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NY. †[email protected] *[email protected] Based on specific heat and magnetoresistance measurements, we report that a “heavy” electronic state exists below T ≈ 20 K in KNi2Se2, with an increased carrier mobility and enhanced effective electronic band mass, m* = 6mb to 18mb. This “heavy” state evolves into superconductivity at Tc = 0.80(1) K. These properties resemble that of a many-body heavy-fermion state, which derives from the hybridization between localized magnetic states and conduction electrons. Yet, no evidence for localized magnetism or magnetic order is found in KNi2Se2 from magnetization measurements or neutron diffraction. Instead, neutron pair-distribution-function analysis reveals the presence of local charge-density-wave distortions that disappear on cooling, an effect opposite to what is typically observed, suggesting that the low-temperature electronic state of KNi2Se2 arises from cooperative Coulomb interactions and proximity to, but avoidance of, charge order. Introduction Methods KNi Se was synthesized from the elements as a Many-body states, in which complex phenomena 2 2 polycrystalline, lustrous, purple-red powder, as previously arise from simple interactions, often exhibit rich phase described12; the same batch of sample was used for all diagrams and lack formal predictive theories.
    [Show full text]
  • Phonons – Thermal Properties
    Phonons – Thermal properties Till now everything was classical – no quantization, no uncertainty.... WHY DO WE NEED QUANTUM THEORY OF LATTICE VIBRATIONS? Classical – Dulong Petit law All energy values are allowed – classical equipartition theorem – energy per degree of freedom is 1/2kBT. Total energy independent of temperature! Detailed calculation gives C = 3NkB In reality C ~ aT +bT3 Figure 1: Heat capacity of gold Need quantum theory! Quantum theory of lattice vibrations: Hamiltonian for 1D linear chain Interaction energy is simple harmonic type ~ ½ kx2 Solve it for N coupled harmonic oscillators – 3N normal modes – each with a characteristic frequency where p is the polarization/branch. Energy of any given mode is is the zero-point energy th is called ‘excitation number’ of the particular mode of p branch with wavevector k PH-208 Phonons – Thermal properties Page 1 Phonons are quanta of ionic displacement field that describes classical sound wave. Analogy th with black body radiation - ni is the number of photons of the i mode of oscillations of the EM wave. Total energy of the system E = is the ‘Planck distribution’ of the occupation number. Planck distribution: Consider an ensemble of identical oscillators at temperature T in thermal equilibrium. Ratio of number of oscillators in (n+1)th state to the number of them in nth state is So, the average occupation number <n> is: Special case of Bose-Einstein distribution with =0, chemical potential is zero since we do not directly control the total number of phonons (unlike the number of helium atoms is a bath – BE distribution or electrons in a solid –FE distribution), it is determined by the temperature.
    [Show full text]
  • Thermodynamics of the Magnetic-Field-Induced "Normal
    Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2010 Thermodynamics of the Magnetic-Field- Induced "Normal" State in an Underdoped High T[subscript c] Superconductor Scott Chandler Riggs Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] THE FLORIDA STATE UNIVERSITY COLLEGE OF ARTS AND SCIENCES THERMODYNAMICS OF THE MAGNETIC-FIELD-INDUCED “NORMAL” STATE IN AN UNDERDOPED HIGH TC SUPERCONDUCTOR By SCOTT CHANDLER RIGGS A Dissertation submitted to the Department of Physics in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Summer Semester, 2010 The members of the committee approve the dissertation of Scott Chandler Riggs defended on March 27, 2010. Gregory Scott Boebinger Professor Directing Thesis David C. Larbalestier University Representative Jorge Piekarewicz Committee Member Nicholas Bonesteel Committee Member Luis Balicas Committee Member Approved: Mark Riley, Chair, Department of Physics Joseph Travis, Dean, College of Arts and Sciences The Graduate School has verified and approved the above-named committee members. ii ACKNOWLEDGMENTS I never thought this would be the most difficult section to write. From Tally, I’d have to start off by thanking Tim Murphy for letting me steal...er...borrow way too much from the instrumentation shop during the initial set-up of Greg’s lab. I still remember that night on the hybrid working with system ”D”. After that night it became clear that ”D” stands for Dumb. To Eric Palm, thank you for granting more power during our specific heat experiments. We still hold the record for most power consumed in a week! To Rob Smith, we should make a Portland experience every March.
    [Show full text]
  • Specific Heat
    8 Specific Heat more complicated, because not only standard repre- Electronic States of; Lattice Dynamics: Vibrational Modes; sentations but projective representations also occur. Periodicity and Lattices; Point Groups; Quantum Mechan- Finally, a basis for the full state space can be con- ics: Foundations; Quasicrystals; Scattering, Elastic structed as follows. The group of k is a subgroup of (General). the space group G. G can be decomposed according to PACS: 61.50.Ah; 02.30. À a G ¼ Gk þ g2Gk þ ? þ gsGk where the space group elements gi have homogeneous Further Reading parts Ri for which Rik ¼ ki. Then the basis is defined as C Cornwell JF (1997) Group Theory in Physics . San Diego: Aca- ij ¼ Tgi cj ½23 demic Press. Hahn Th. (ed.) (1992) Space-Group Symmetry. In: International The dimension of the representation is sd , where s is Tables for Crystallography. vol. A, Dordrecht: Kluwer. the number of points ki, and d the dimension of the Hahn T and Wondratschek H (1994) Symmetry of Crystals: In- point group representation D(Kk). The irreducible troduction to International Tables for Crystallography. vol. A . representation carried by the state space then is char- Sofia, Bulgaria: Heron Press. acterised by the so-called ‘‘star’’ of k (all vectors k ), Janssen T (1973) Crystallographic Groups. North-Holland: Am- i sterdam. and an irreducible representation of the point group Janssen T, Janner A, Looijenga-Vos A, and de Wolff PM (1999) Kk. This means that electronic states and phonons can Incommensurate and commensurate modulated structures. be characterized by k, v. Their transformation prop- In: Wilson AJC and Prince E, International Tables for erties under space group transformations follows from Crystallography, vol.
    [Show full text]
  • Accessories 143143
    Wire IntroductionAccessories 143143 Wire Abbreviations used in this section American wire gauge AWG Single lead wire SL Duo-Twist™ wire DT Quad-Twist™ wire QT Quad-Lead™ wire QL Specifications Phosphor bronze Copper Nichrome Manganin Melting range 1223 K to 1323 K 1356 K 1673 K 1293 K Coefficient of thermal expansion 1.78 × 10-5 20 × 10-6 — 19 × 10-6 Chemical composition (nominal) 94.8% copper, 5% tin, 0.2% — 80% nickel, 20% chromium 83% copper, 13% manganese, phosphorus 4% nickel Electrical resistivity 11 µΩ·cm 1.7 µΩ·cm 120 µΩ·cm 48 µΩ·cm (at 293 K) Thermal 0.1 K NA 9 NA 0.006 conductivity 0.4 K NA 30 NA 0.02 (W/(m·K)) 1 K 0.22 70 NA 0.06 4 K 1.6 300 0.25 0.5 10 K 4.6 700 0.7 2 20 K 10 1100 2.6 3.3 80 K 25 600 8 13 150 K 34 410 9.5 16 300 K 48 400 12 22 AWG Resistance (Ω/m) Diameter Fuse Fuse current Number Name Insulated Insulation type Insulation Insulation (mm) current vacuum (A) of leads diameter thermal breakdown 4.2 K 77 K 305 K air (A) (mm) rating (K) voltage (VDC) Phosphor 1 SL-32 0.241 Polyimide bronze 2 DT-32 0.241 Polyimide 32 3.34 3.45 4.02 0.203 4.2 3.1 493 400 QT-32 0.241 Polyimide 4 QL-32 0.241 Polyimide 1 SL-36 0.152 Formvar® 368 250 2 DT-36 0.152 Polyimide 493 400 36 8.56 8.83 10.3 0.127 2.6 1.4 QT-36 0.152 Formvar® 368 250 4 QL-36 0.152 Polyimide 493 400 Nichrome 32 33.2 33.4 34 0.203 2.5 1.8 1 NC-32 0.241 Polyimide 493 400 Copper 30 0.003 0.04 0.32 0.254 10.2 8.8 1 HD-30 0.635 Teflon® 473 250 34 0.0076 0.101 0.81 0.160 5.1 4.4 2 CT-34 0.254 Teflon® 473 100 Manganin 30 8.64 9.13 9.69 0.254 4.6 4.3 1 MW-30 0.295 Heavy Formvar® 400 32 13.5 14.3 15.1 0.203 3.8 3.5 1 MW-32 0.241 Heavy Formvar® 378 400 36 34.6 36.5 38.8 0.127 2.6 2.5 1 MW-36 0.152 Heavy Formvar® 250 Lake Shore Cryotronics, Inc.
    [Show full text]
  • Phonon, Magnon and Electron Contributions to Low Temperature Specific Heat in Metallic State of La0·85Sr0·15Mno3 and Er0·8Y0·2Mno3 Manganites
    Bull. Mater. Sci., Vol. 36, No. 7, December 2013, pp. 1255–1260. c Indian Academy of Sciences. Phonon, magnon and electron contributions to low temperature specific heat in metallic state of La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3 manganites DINESH VARSHNEY1,∗, IRFAN MANSURI1,2 and E KHAN1 1Materials Science Laboratory, School of Physics, Devi Ahilya University, Khandwa Road Campus, Indore 452 001, India 2Deparment of Physics, Indore Institute of Science and Technology, Pithampur Road, Rau, Indore 453 331, India MS received 19 June 2012; revised 21 August 2012 Abstract. The reported specific heat C (T) data of the perovskite manganites, La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3, is theoretically investigated in the temperature domain 3 ≤ T ≤ 50 K. Calculations of C (T) have been made within the three-component scheme: one is the fermion and the others are boson (phonon and magnon) contributions. Lattice specific heat is well estimated from the Debye temperature for La0·85Sr0·15MnO3 and Er0·8Y0·2MnO3 manganites. Fermion component as the electronic specific heat coefficient is deduced using the band structure calculations. Later on, following double-exchange mechanism the role of magnon is assessed towards spe- cific heat and found that at much low temperature, specific heat shows almost T3/2 dependence on the temperature. The present investigation allows us to believe that electron correlations are essential to enhance the density of states over simple Fermi-liquid approximation in the metallic phase of both the manganite systems. The present numerical analysis of specific heat shows similar results as those revealed from experiments. Keywords. Oxide materials; crystal structure; specific heat; phonon.
    [Show full text]
  • Phys 446 Solid State Physics Lecture 7 (Ch. 4.1 – 4.3, 4.6.) Last Time
    Phys 446 Solid State Physics Electrons in metals: free electron model Lecture 7 • Simplest way to represent the electronic structure of metals (Ch. 4.1 – 4.3, 4.6.) • Although great simplification, works pretty well in many cases, describes many important properties of metals Last time: • In this model, the valence electrons of free atoms become conduction electrons in crystal and travel freely Finished with phonons, optical and thermal properties. • Neglect the interaction of conduction electrons with ions of the lattice and the interaction between the conduction electrons – a free electron gas Today: Start with electronic properties of metals. • Fundamental difference between the free electron gas and ordinary gas of molecules: Free electron model. 1) electrons are charged particles ⇒ to maintain the charge neutrality of Fermi energy. the whole crystal, we need to include positive ions. This is done within the jelly model : the positive charge of ions is smeared Density of states. out uniformly throughout the crystal - charge neutrality is maintained, no field on the electrons exerted Electronic heat capacity 2) Free electron gas must satisfy the Pauli exclusion principle, which Lecture 7 leads to important consequences. Free electron gas in one dimension What is Hamiltonian? Assume an electron of mass m is confined to a length L by infinite barriers Schrödinger equation for electron wave function ψn(x): En - the energy of electron orbital assume the potential lies at zero ⇒ H includes only the kinetic energy ⇒ Note: this is a one-electron equation – neglected electron-electron interactions General solution: Asin qnx+ Bcos qnx boundary conditions for the wave function: ⇒ B = 0; qn = πn/L ; n -integer Substitute, obtain the eigenvalues: Fermi energy First three energy levels and wave-functions of a free electron of mass m confined to a line of length L: We need to accommodate N valence electrons in these quantum states.
    [Show full text]
  • Heavy Fermion Physics
    Heavy Fermion Physics Hua Chen Course: Solid State II, Instructor: Elbio Dagotto, Semester: Spring 2008 Department of Physics and Astronomy, the University of Tennessee at Knoxville, 37996¤ This article is intended to be a very brief review on the most basic facts and concepts of heavy fermion physics. A general overview is given as an introduction. In the following part, the mechanism leading to the formation of heavy fermions is explained briefly, and its connection to Kondo e®ect is emphasized. Then we talk about heavy fermion theories in more detail, where the concepts like Kondo lattice, slave boson are introduced. Then there are two separate parts on Kondo insulators and heavy fermion superconductivity respectively. Keywords: heavy fermion, Kondo e®ect, Kondo insulator, superconductivity I. INTRODUCTION higher than usual, which is the origin of the name heavy fermion (Fig 1). Heavy fermion martials are those metallic compounds which have enormously large e®ective electron masses be- The ¯rst material of this kind in history is CeAl3 low certain temperatures. It is well known that, at tem- alloy, which was discovered by Andres, Graebner and peratures much below the Debye temperature and Fermi Ott [2] in 1975. Since then, bunch of other heavy fermion temperature, the heat capacity of metals can be written materials have been discovered and studied, which in- as the sum of electron and phonon contributions: clude CeCu2Si2, CeCu6, UBe13, UPt3, UCd11,U2Zn17, NpBe , etc. Among them, there are superconductors, 3 13 C = γT + AT (1) antiferromagnets and insulators. However, one common property of these compounds is that one of the con- and the electron term is linear in T and dominant at stituents of each is a rare-earth or actinide atom with low temperatures.
    [Show full text]
  • Manganina 43 Resistance Heating Wire and Resistance Wire Datasheet
    MANGANINA 43 RESISTANCE HEATING WIRE AND RESISTANCE WIRE DATASHEET Manganina 43 is a copper-manganese-nickel alloy (CuMnNi alloy) for use at room temperature. The alloy is characterized by very low thermal electromotive force (emf) compared to copper. Manganina 43 is typically used for the manufacturing of resistance standards, precision wire wound resistors, potentiometers, shunts and other electrical and electronic components. The alloy's low emf vs. copper makes it ideal for use in electrical circuits, especially D.C., where a spurious thermal emf could cause malfunctioning of electronic equipment. Due to the low operating temperature, the temperature coefficient of resistance is controlled to be low over a range of 15 to 35°C (59 to 95°F) CHEMICAL COMPOSITION Ni % Mn % Cu % Nominal composition 4.0 11.0 Bal. MECHANICAL PROPERTIES Wire size Yield Strength Tensile Strength Elongation Hardness Ø Rp0.2 Rm A mm (in) MPa (ksi) MPa (ksi) % Hv 1.00 (0.04) 180 (26) 390 (57) 30 110 PHYSICAL PROPERTIES Density g/cm3 (lb/in3) 8.4 (0.303) Electrical resistivity at 20°C Ω mm2/m (Ω circ. mil/ft) 0.43 (259) Temperature coefficient of resistance (15 - 35 °C) (x 10-6/K) 0 ± 15 COEFFICIENT OF THERMAL EXPANSION Temperature °C (°F) Thermal Expansion x 10-6/K (10-6 /°F) 20 - 100 (68-212) 18 (10) THERMAL CONDUCTIVITY Datasheet updated 2/4/2021 1:31:17 PM (supersedes all previous editions) 1 MANGANINA 43 Temperature °C (°F) 20 (68) W m-1 K-1 (Btu h-1ft-1°F-1) 22 (12.7) SPECIFIC HEAT CAPACITY Temperature °C (°F) 20 (68) kJ kg-1 K-1 (Btu lb-1 °F-1) 0.410 (0.10) Melting point °C (°F) 1020 (1868) Max continuous operating temperature in air °C Room temperature Magnetic properties The material is non-magnetic Disclaimer: Recommendations are for guidance only, and the suitability of a material for a specific application can be confirmed only when we know the actual service conditions.
    [Show full text]