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Solid State Physics

Solid State Physics

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  • Slide 10/28:
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  • Slide 14/28: Best encapsulans: - B 2 O 3 - LiCl, KCl, CaCl2, NaCl
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  • advantages growth from free surface (stress free) crystal can be observed during the growth process forced convection easy to impose large crystals can be obtained high crystalline perfection can be achieved good radial homogeneity Drawbacks delicate start (seeding, necking) and sophisticated further control delicate mechanics (the crystal has to be rotated; rotation of the crucible is desirable) cannot grow materials with high vapor pressure batch process (axial segregation, limited productivity)
  • Slide 17/28:
  • Slide 18/28: advantages Charge is purified by repeated passage of the zone (zone refining). Crystals may be grown in sealed ampules or without containers (floating zone). Steady-state growth possible. Zone leveling is possible; can lead to superior axial homogeneity. Process requires little attention (maintenance). Simple: no need to control the shape of the crystal. Radial temperature gradients are high. Drawbacks Confined growth (except in floating zone). Hard to observe the seeding process and the growing crystal. Forced convection is hard to impose (except in floating zone). In floating zone, materials with high vapor pressure can not be grown.
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  • Slide 25/28: Tellurium dioxide can be found in nature in two forms: tellurite (orthorombic) and paratellurite (tetragonal). Paratellurite is by far more interesting for its acoustic and optical properties. Paratellurite (α-TeO 2 ) has a distorted rutile (TiO2) structure with asymmetric covalent Te-O bonds. The short bonds (1.88 Å) are indicated by dashed green lines and long bonds (2.12 Å) by full violet lines. One of the C 2 symmetry axis is shown. Crystals are colorless and highly transparent in the range of 350 nm - 5 μm. The density of grown crystals is 6.04 g/cm 3 , measured lattice constants: a = 4.8088 Å and c = 7.6038 Å. Crystals are grown from melt (melting point at 733 °C) Note the relatively low melting point which in principle should make the crystal growth not very complicated which is not true in TeO2 case (melt hydrodynamic instability, high anisotropy of expansion coefficient).
  • Slide 26/28: Powdered tellurium dioxide used as raw material for crystal growth is typically obtained by “wet” methods consisting of successive chemical reactions, washings, filterings and dryings. Nitric and hydrochloric acids and ammonium hydroxide are used in this process which gives at the end powders of typical 99.999% purity. Crystals may be grown by Czochrlaski or Bridgman in Pt crucibles (short comment on each method peculiarities). In principle Bridgman grown crystals should be more stressed than Czochralski ones but annealing at about 550°C helps in removing the residual stresses. ================================== HNO3 nitric acid NO2 nitrogen dioxide HCl hydrochloric acid NH4OH ammonia (Ammonium Hydroxide) NH4Cl ammonium chloride Te(OH)4 tellurium hydroxide Te2O3(OH)NO3 tellurium nitrate TeCl4 tellurium chloride TeO2 tellurium dioxide =======================================
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  • Slide 28/28: Besides the natural repellence of foreign ions in TeO2 lattice mentioned before, there are other facts which contribute to a certain optimism concerning the radiopurity of grown TeO2 crystals. If we consider as radioactive contamination risk those elements: belonging to main radioactive series having natural radioactive isotopes having ionic radius close to Te4+ and neutron activation radioactive isotopes A peculiar attention has to be devoted to Pt because as it stays in direct contact with the melt during the growth process Note that most of radioactive isotopes have ionic characteristics incompatible with substitutional incorporation in TeO 2 crystal lattice. It is expected therefore a larger than usual purification effect through crystal growth
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Solid state physics d r joshi Solid state physics d r joshi Presentation Transcript

  • Introduction to SOLID STATE PHYSICS A Random Walk Dr. Dattu Joshi Applied Physics Department Faculty of Tech. & Engg. The M S University of Baroda Vadodara-390 001 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • INTRODUCTION
    • AIM OF SOLID STATE PHYSICS
    • WHAT IS SOLID STATE PHYSICS?
    • CONTENTS
    • APPLICATIONS AND
    • RESEARCH
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Aim of Solid State Physics
    • Solid state physics (SSP) explains the properties of solid materials as found on earth.
    • The properties are expected to follow from Schrödinger’s eqn. for a collection of atomic nuclei and electrons interacting with electrostatic forces.
    • The fundamental laws governing the behaviour of solids are known and well tested.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystalline Solids
    • We will deal with crystalline solids, that is solids with an atomic structure based on a regular repeated pattern.
    • Many important solids are crystalline.
    • More progress has been made in understanding the behaviour of crystalline solids than that of non-crystalline materials since the calculation are easier in crystalline materials.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • EP364 SOLID STATE PHYSICS INTRODUCTION What is solid state physics ?
    • Solid state physics, also known as condensed matter physics , is the study of the behaviour of atoms when they are placed in close proximity to one another.
    • In fact, condensed matter physics is a much better name, since many of the concepts relevant to solids are also applied to liquids, for example.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • What is the point?
    • Understanding the electrical properties of solids is right at the heart of modern society and technology .
    • The entire computer and electronics industry relies on tuning of a special class of material, the semiconductor , which lies right at the metal-insulator boundary .
    • Solid state physics provide a background to understand what goes on in semiconductors.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Electrical resistivity of three states of solid matter
    • How can this be? After all, they each contain a system of atoms and especially electrons of similar density. And the plot thickens: graphite is a metal , diamond is an insulator and buckminster-fullerene is a superconductor .
    • They are all just carbon!
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
    • Among our aims - understand why one is a metal and one an insulator , and then the physical origin of the marked features.
    • Also think about thermal properties etc. etc.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Solid State Physics
    • Crystal Structure
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Solid State Physics
    • Crystal Diffraction and the Reciprocal Lattice
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Solid State Physics
    • Imperfections in Crystals
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Solid State Physics
    • Crystal Bonding
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Solid State Physics
    • Magnetic Materials
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
    • Elastic constants and Elastic Waves
    • Lattice Vibrations and Phonons
    • Thermal Properties of Solids
    • Free Electron Theory of Metals
    • Transport Properties
    • Band Theory of Solids
    • Semiconductors
    • Superconductivity
    • Dielectrics
    • Optical Phenomena in insulators etc.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • CRYSTAL STRUCTURE
    • Elementary Crystallography
      • Solid materials (crystalline, polycrystalline, amorphous)
      • Crystallography
      • Crystal Lattice
      • Crystal Structure
      • Types of Lattices
      • Unit Cell
      • Directions-Planes-Miller Indices in Cubic Unit Cell
    • Typical Crystal Structures (3 D – 14 Bravais Lattices and the Seven Crystal System)
    • Elements of Symmetry
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • X-RAY CRYSTALLOGRAPHY
    • X-ray
    • Diffraction
      • Bragg equation
    • X-ray diffraction methods
      • Laue Method
      • Rotating Crystal Method
      • Powder Method
    • Neutron & electron diffraction
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • CRYSTAL STRUCTURE Elementary Crystallography Typical Crystal Structures Elements Of Symmetry 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Objectives
    • By the end of this section you should:
    • be able to identify a unit cell in a symmetrical pattern
    • know that there are 7 possible unit cell shapes
    • be able to define cubic, tetragonal, orthorhombic and hexagonal unit cell shapes
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure matter 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Gases
    • Gases have atoms or molecules that do not bond to one another in a range of pressure, temperature and volume.
    • These molecules haven’t any particular order and move freely within a container.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Liquids and Liquid Crystals
    • Similar to gases, liquids haven’t any atomic/molecular order and they assume the shape of the containers.
    • Applying low levels of thermal energy can easily break the existing weak bonds.
    Liquid crystals have mobile molecules, but a type of long range order can exist; the molecules have a permanent dipole. Applying an electric field rotates the dipole and establishes order within the collection of molecule s. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara + - + - + - + - + - + - + -
  • Crystal Structure Crytals
    • Solids consist of atoms or molecules executing thermal motion about an equilibrium position fixed at a point in space.
    • Solids can take the form of crystalline, polycrstalline, or amorphous materials.
    • Solids (at a given temperature, pressure, and volume) have stronger bonds between molecules and atoms than liquids.
    • Solids require more energy to break the bonds.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure ELEMENTARY CRYSTALLOGRAPHY 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara SOLID MATERIALS CRYSTALLINE POLYCRYSTALLINE AMORPHOUS (Non-crystalline) Single Crystal
  • Crystal Structure Types of Solids
    • Single crsytal, polycrystalline, and amorphous, are the three general types of solids.
    • Each type is characterized by the size of ordered region within the material.
    • An ordered region is a spatial volume in which atoms or molecules have a regular geometric arrangement or periodicity.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Crystalline Solid
    • Crystalline Solid is the solid form of a substance in which the atoms or molecules are arranged in a definite, repeating pattern in three dimension.
    • Single crystals, ideally have a high degree of order , or regular geometric periodicity, throughout the entire volume of the material .
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Crystalline Solid Single Crystal Single Pyrite Crystal Amorphous Solid
    • Single crystal has an atomic structure that repeats periodically across its whole volume. Even at infinite length scales, each atom is related to every other equivalent atom in the structure by translational symmetry
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Polycrystalline Solid Polycrystalline Pyrite form (Grain)
    • Polycrystal is a material made up of an aggregate of many small single crystals (also called crystallites or grains).
    • Polycrystalline material have a high degree of order over many atomic or molecular dimensions.
    • These ordered regions, or single crytal regions, vary in size and orientati on wrt one another.
    • These regions are called as grains ( domain) and are separated from one another by grain boundaries. The atomic order can vary from one domain to the next .
    • The grains are usually 100 nm - 100 microns in diameter . Polycrystals with grains that are <100 nm in diameter are called nanocrystalline
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Amorphous Solid
    • Amorphous (Non-crystalline) Solid is composed of randomly orientated atoms , ions, or molecules that do not form defined patterns or lattice structures.
    • Amorphous materials have order only within a few atomic or molecular dimensions.
    • Amorphous materials do not have any long-range order, but they have varying degrees of short-range order.
    • Examples to a morphous materials include a morphous silicon, plastics, and glasses.
    • Amorphous silicon can be used in solar cells and thin film transistors.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Departure From Perfect Crystal
    • Strictly speaking, one cannot prepare a perfect crystal. For example, even the surface of a crystal is a kind of imperfection because the periodicity is interrupted there.
    • Another example concerns the thermal vibrations of the atoms around their equilibrium positions for any temperature T>0 °K.
    • As a third example, actual crystal always contains some foreign atoms, i.e., impurities. These impurities spoils the perfect crystal structure.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Distinction Between Crystalline and Amorphous Solids
    • Crystalline Solids
    • Have a regular arrangement of particles
    • Have different physical properties (thermal conductivity, electrical conductivity, refractive index etc.) in different directions i.e. Anisotropic
    • Melting point is very sharp
    • Amorphous Solids
    • Have completely random particle arrangement
    • Have physical properties same in all directions, i.e. isotropic
    • Do not have sharp melting point e.g. as the temperature of glass is gradually raised, it softens and starts flowing without any sharp change from solid state to liquid state
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
    • The cooling curve for crystalline substance has breaks, see curve 1 in the fig., the middle of which corresponds to the process of crystallization. In the process of crystallization some energy is liberated which compensates the loss of heat and hence temperature remains constant.
    • Crystalline Solid
    • Amorphous Solid
    • The cooling curve for amorphous substance is smooth, see curve 2 in the fig.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure CRYSTALLOGRAPHY What is crystallography? The branch of science that deals with the geometric description of crystals and their internal arrangement. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Science of Crystallography
    • The study of the geometric form and other physical properties of crystalline solids by using X-rays, electron beams and neutron beams etc., constitute the science of crystallography.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara The
  • Crystal Structure
    • Crystallography is essential for solid state physics
    • Symmetry of a crystal can have a profound influence on its properties.
    • Any crystal structure should be specified completely, concisely and unambiguously.
    • Structures should be classified into different types according to the symmetries they possess.
    Crystallography 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure
    • A basic knowledge of crystallography is essential for solid state physicists;
      • to specify any crystal structure and
      • to classify the solids into different types according to the symmetries they possess.
    • Symmetry of a crystal can have a profound influence on its properties.
    • We will concern in this course with solids with simple structures.
    ELEMENTARY CRYSTALLOGRAPHY 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure CRYSTAL LATTICE What is crystal ( space ) lattice? In crystallography, only the geometrical properties of the crystal are of interest, therefore one replaces each atom by a geometrical point located at the equilibrium position of that atom. Platinum Platinum surface Crystal lattice and structure of Platinum ( scanning tunneling microscope ) 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure
    • An infinite array of points in space,
    • Each point has identical surroundings to all others.
    • Arrays are arranged exactly in a periodic manner.
    Crystal Lattice 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara α a b C B E D O A y x
  • Crystal Structure Crystal Structure
    • Crystal structure can be obtained by attaching atoms, groups of atoms or molecules which are called basis (motif) to the lattice sides of the lattice point.
    Crystal Structure = Crystal Lattice + Basis 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • A two-dimensional Bravais lattice with different choices for the basis 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure E H b) Crystal lattice obtained by identifying all the atoms in (a) a) Situation of atoms at the corners of regular hexagons Basis
    • A group of atoms which describe crystal structure
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara O A C B F b G D x y a α a b C B E D O A y x
  • Crystal Structure Crystal structure
    • Don't mix up atoms with lattice points
    • Lattice points are infinitesimal points in space
    • Lattice points do not necessarily lie at the centre of atoms
    Crystal Structure = Crystal Lattice + Basis 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Crystal Lattice Bravais Lattice (BL) Non-Bravais Lattice (non-BL)
    • All atoms are of the same kind
    • All lattice points are equivalent
    • Atoms can be of different kind
    • Some lattice points are not
    • equivalent
    • A combination of two or more BL
  • Crystal Structure Types Of Crystal Lattices 1) Bravais lattice is an infinite array of discrete points with an arrangement and orientation that appears exactly the same, from whichever of the points the array is viewed. Lattice is invariant under a translation. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Nb film
  • Crystal Structure Types Of Crystal Lattices
    • The red side has a neighbour to its immediate left, the blue one instead has a neighbour to its right.
    • Red (and blue) sides are equivalent and have the same appearance
    • Red and blue sides are not equivalent. Same appearance can be obtained rotating blue side 180 º.
    2) Non-Bravais Lattice Not only the arrangement but also the orientation must appear exactly the same from every point in a bravais lattice. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Honeycomb
  • Crystal Structure Translational Lattice Vectors – 2 D A space lattice is a set of points such that a translation from any point in the lattice by a vector; R n = n 1 a + n 2 b locates an exactly equivalent point, i.e. a point with the same environment as P . This is translational symmetry . The vectors a , b are known as lattice vectors and (n 1 , n 2 ) is a pair of integers whose values depend on the lattice point. P Point D(n1, n2) = ( 0 ,2) Point F (n1, n2) = (0,-1) 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure
    • The two vectors a and b form a set of lattice vectors for the lattice.
    • The choice of lattice vectors is not unique . Thus one could equally well take the vectors a and b’ as a lattice vectors.
    Lattice Vectors – 2 D 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Lattice Vectors – 3D An ideal three dimensional crystal is described by 3 fundamental translation vectors a, b and c . If there is a lattice point represented by the position vector r , there is then also a lattice point represented by the position vector where u , v and w are arbitrary integers .   r’ = r + u a + v b + w c      (1) 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Five Bravais Lattices in 2D 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 2D-Crystal Unit Cell Unit Cell in 2D
    • The smallest component of the crystal (group of atoms, ions or molecules), which when stacked together with pure translational repetition reproduces the whole crystal.
    S S 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara a b S S S S S S S S S S S S S
  • Crystal Structure 2D-Crystal Unit Cell in 2D
    • The smallest component of the crystal (group of atoms, ions or molecules), which when stacked together with pure translational repetition reproduces the whole crystal.
    The choice of unit cell is not unique . a b 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara S S S S
  • Crystal Structure 2D Unit Cell example -(NaCl) We define lattice points ; these are points with identical environments 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Choice of origin is arbitrary - lattice points need not be atoms - but unit cell size should always be the same . 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure This is also a unit cell - it doesn’t matter if you start from Na or Cl 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure - or if you don’t start from an atom 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure This is NOT a unit cell even though they are all the same - empty space is not allowed ! 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure In 2D, this IS a unit cell In 3D, it is NOT 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Why can't the blue triangle be a unit cell? 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Unit Cell in 3D 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Unit Cell in 3D 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Three common Unit Cell in 3D 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Body centered cubic(bcc) Conventional ≠ Primitive cell Simple cubic(sc) Conventional = Primitive cell 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara UNIT CELL Primitive Conventional & Non-primitive
    • Single lattice point per cell
    • Smallest area in 2D, or
    • Smallest volume in 3D
    • More than one lattice point per cell
    • Integral multibles of the area of
    • primitive cell
  • Crystal Structure The Conventional Unit Cell
    • A unit cell just fills space when translated through a subset of Bravais lattice vectors.
    • The conventional unit cell is chosen to be larger than the primitive cell , but with the full symmetry of the Bravais lattice .
    • The size of the conventional cell is given by the lattice constant a.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Primitive and conventional cells of FCC 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Primitive and conventional cells of BCC Primitive Translation Vectors: 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Simple cubic (sc): primitive cell=conventional cell Fractional coordinates of lattice points: 000, 100, 010, 001, 110,101, 011, 111 Primitive and conventional cells Body centered cubic (bcc): conventional  primitive cell Fractional coordinates of lattice points in conventional cell : 000,100, 010, 001, 110,101, 011, 111, ½ ½ ½ 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Body centered cubic (bcc): primitive (rombohedron)  conventional cell Face centered cubic (fcc): conventional  primitive cell Fractional coordinates : 000,100, 010, 001, 110,101, 011,111, ½ ½ 0, ½ 0 ½, 0 ½ ½ ,½1 ½ , 1 ½ ½ , ½ ½ 1 Primitive and conventional cells 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Fractional coordinates : 000, 100, 101, 110, 110,101, 011, 211, 200
  • Crystal Structure Hexagonal close packed cell (hcp): conventional  primitive cell Fractional coordinates : 100, 010, 110, 101,011, 111,000, 001 Primitive and conventional cells -hcp 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara points of primitive cell 120 o
  • Crystal Structure
    • The unit cell and, consequently, the entire lattice, is uniquely determined by the six lattice constants : a, b, c, α, β and γ .
    • Only 1/8 of each lattice point in a unit cell can actually be assigned to that cell.
    • Each unit cell in the figure can be associated with 8 x 1/8 = 1 lattice point.
    Unit Cell 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure
    • A primitive unit cell is made of primitive translation vectors a 1 ,a 2 , and a 3 such that there is no cell of smaller volume that can be used as a building block for crystal structures.
    • A primitive unit cell will fill space by repetition of suitable crystal translation vectors. This defined by the parallelpiped a 1 , a 2 and a 3 . The volume of a primitive unit cell can be found by
    • V = a 1 .(a 2 x a 3 ) (vector products)
    Cubic cell volume = a 3 Primitive Unit Cell and vectors 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure
    • The primitive unit cell must have only one lattice point .
    • There can be different choice s for lattice vectors , but the volumes of these primitive cells are all the same.
    P = Primitive Unit Cell NP = Non-Primitive Unit Cell Primitive Unit Cell 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Wigner-Seitz Method
    • A simply way to find the primitive
    • cell which is called Wigner-Seitz
    • cell can be done as follows;
    • Choose a lattice point.
    • Draw lines to connect these lattice point to its neighbours.
    • At the mid-point and normal to these lines draw new lines.
    • The volume enclosed is called as a
    • Wigner-Seitz cell.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Wigner-Seitz Cell - 3D 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Lattice Sites in Cubic Unit Cell 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Crystal Directions Fig. Shows [111] direction
    • We choose one lattice point on the line as an origin, say the point O. Choice of origin is completely arbitrary, since every lattice point is identical.
    • Then we choose the lattice vector joining O to any point on the line, say point T. This vector can be written as;
    • R = n 1 a + n 2 b + n 3 c
    • To distinguish a lattice direction from a lattice point , the triple is enclosed in square brackets [ ...] is used.[n 1 n 2 n 3 ]
    • [ n 1 n 2 n 3 ] is the smallest integer of the same relative ratios .
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure X = ½ , Y = ½ , Z = 1 [½ ½ 1] [1 1 2] Examples 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara 210 X = 1 , Y = ½ , Z = 0 [1 ½ 0] [2 1 0]
  • Crystal Structure Negative directions
    • When we write the direction [n 1 n 2 n 3 ] depend on the origin, negative directions can be written as
    • R = n 1 a + n 2 b + n 3 c
    • Direction must be
    • smallest integers.
    Y direction 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara (origin) O - Y direction X direction - X direction Z direction - Z direction
  • Crystal Structure X = -1 , Y = -1 , Z = 0 [110] Examples of crystal directions X = 1 , Y = 0 , Z = 0 [1 0 0] 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Examples X =-1 , Y = 1 , Z = -1/6 [-1 1 -1/6] [6 6 1] We can move vector to the origin. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Crystal Planes
    • Within a crystal lattice it is possible to identify sets of equally spaced parallel planes. These are called lattice planes .
    • In the figure density of lattice points on each plane of a set is the same and all lattice points are contained on each set of planes .
    The set of planes in 2D lattice. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara b a b a
  • Crystal Structure Miller Indices Miller Indices are a symbolic vector representation for the orientation of an atomic plane in a crystal lattice and are defined as the reciprocals of the fractional intercepts which the plane makes with the crystallographic axes. To determine Miller indices of a plane, take the following steps; 1) Determine the intercepts of the plane along each of the three crystallographic directions 2) Take the reciprocals of the intercepts 3) If fractions result, multiply each by the denominator of the smallest fraction 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Example-1 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Axis X Y Z Intercept points 1 ∞ ∞ Reciprocals 1/1 1/ ∞ 1/ ∞ Smallest Ratio 1 0 0 Miller İndices (100) (1,0,0)
  • Crystal Structure Example-2 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Axis X Y Z Intercept points 1 1 ∞ Reciprocals 1/1 1/ 1 1/ ∞ Smallest Ratio 1 1 0 Miller İndices (110) (1,0,0) (0,1,0)
  • Crystal Structure Example-3 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Axis X Y Z Intercept points 1 1 1 Reciprocals 1/1 1/ 1 1/ 1 Smallest Ratio 1 1 1 Miller İndices (111) (1,0,0) (0,1,0) (0,0,1)
  • Crystal Structure Example-4 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Axis X Y Z Intercept points 1/2 1 ∞ Reciprocals 1/( ½ ) 1/ 1 1/ ∞ Smallest Ratio 2 1 0 Miller İndices (210) (1/2, 0, 0) (0,1,0)
  • Crystal Structure Example-5 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Axis a b c Intercept points 1 ∞ ½ Reciprocals 1/1 1/ ∞ 1/( ½ ) Smallest Ratio 1 0 2 Miller İndices (102)
  • Crystal Structure Example-6 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Miller Indices Indices of the plane (Miller): (2,3,3) Indices of the direction: [2,3,3] 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Reciprocal numbers are: Plane intercepts axes at (100) (200) (110) (111) (100) 3 2 2 [2,3,3]
  • Crystal Structure 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Example-7 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Indices of a Family or Form
    • Sometimes when the unit cell has rotational symmetry, several nonparallel planes may be equivalent by virtue of this symmetry, in which case it is convenient to lump all these planes in the same Miller Indices, but with curly brackets.
    Thus indices { h,k,l } represent all the planes equivalent to the plane (hkl) through rotational symmetry. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Find out which one is wrong?
  • Crystal Structure
    • There are only seven different shapes of unit cell which can be stacked together to completely fill all space (in 3 dimensions) without overlapping. This gives the seven crystal systems, in which all crystal structures can be classified.
    • Cubic Crystal System (SC, BCC,FCC)
    • Hexagonal Crystal System (S)
    • Triclinic Crystal System (S)
    • Monoclinic Crystal System (S, Base-C)
    • Orthorhombic Crystal System (S, Base-C, BC, FC)
    • Tetragonal Crystal System (S, BC)
    • Trigonal (Rhombohedral) Crystal System (S)
    3D – 14 BRAVAIS LATTICES AND THE SEVEN CRYSTAL SYSTEM TYPICAL CRYSTAL STRUCTURES 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Coordinatıon Number
    • Coordinatıon Number (CN) : The Bravais lattice points closest to a given point are the nearest neighbours .
    • Because the Bravais lattice is periodic, all points have the same number of nearest neighbours or coordination number. It is a property of the lattice .
    • A simple cubic has coordination number 6; a body-centered cubic lattice, 8; and a face-centered cubic lattice,12.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Atomic Packing Factor
    • Atomic Packing Factor (APF) is defined as the volume of atoms within the unit cell divided by the volume of the unit cell.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 1-CUBIC CRYSTAL SYSTEM
    • Simple Cubic has one lattice point so its primitive cell.
    • In the unit cell on the left, the atoms at the corners are cut because only a portion (in this case 1/8) belongs to that cell. The rest of the atom belongs to neighboring cells .
    • Coordinatination number of simple cubic is 6.
    a- Simple Cubic (SC) 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara a b c
  • Crystal Structure a- Simple Cubic (SC) 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Atomic Packing Factor of SC 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure b-Body Centered Cubic (BCC)
    • BCC has two lattice points so BCC is a non-primitive cell.
    • BCC has eight nearest neighbors. Each atom is in contact with its neighbors only along the body-diagonal directions.
    • Many metals (Fe,Li,Na..etc) , including the alkalis and several transition elements choose the BCC structure.
    a b c 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Atomic Packing Factor of BCC 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara 2 (0 . 433a)
  • Crystal Structure c- Face Centered Cubic (FCC)
    • There are atoms at the corners of the unit cell and at the center of each face.
    • Face centered cubic has 4 atoms so its non primitive cell.
    • Many of common metals (Cu,Ni,Pb..etc) crystallize in FCC structure.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 4 (0 . 353a) Atomic Packing Factor of FCC 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara FCC 0 . 74
  • Crystal Structure Atoms Shared Between: Each atom counts: corner 8 cells 1/8 face centre 2 cells 1/2 body centre 1 cell 1 edge centre 2 cells 1/ 2 lattice type cell contents P 1 [=8 x 1/8] I 2 [=(8 x 1/8) + (1 x 1)] F 4 [=(8 x 1/8) + (6 x 1/2)] C 2 [=(8 x 1/8) + (2 x 1/2)] Unit cell contents Counting the number of atoms within the unit cell 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Example; Atomic Packing Factor 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 2 - HEXAGONAL SYSTEM
    • A crystal system in which three equal coplanar axes intersect at an angle of 12 0 , and a perpendicular to the others, is of a different length.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 2 - HEXAGONAL SYSTEM Atoms are all same. 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 3 - TRICLINIC 4 - MONOCLINIC CRYSTAL SYSTEM
    • Triclinic minerals are the least symmetrical. Their three axes are all different lengths and none of them are perpendicular to each other. These minerals are the most difficult to recognize .
    Triclinic ( Simple )  ß  90 o a  b  c Monoclinic ( Simple )  =  = 90 o , ß  90 o a  b  c Monoclinic (Base C entered )  =  = 90 o , ß  90 o a  b  c, 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 5 - ORTHORHOMBIC SYSTEM Orthorhombic ( Simple )  = ß =  = 90 o a  b  c Orthorhombic (B ase-centred)  = ß =  = 90 o a  b  c Orthorhombic (BC)  = ß =  = 90 o a  b  c Orthorhombic (FC)  = ß =  = 90 o a  b  c 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 6 – TETRAGONAL SYSTEM Tetragonal (P)  = ß =  = 90 o a = b  c Tetragonal (BC)  = ß =  = 90 o a = b  c 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 7 - Rhombohedral (R) o r Trigonal Rhombohedral (R) o r Trigonal (S) a = b = c,  = ß =  90 o 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure THE MOST IMPORTANT CRYSTAL STRUCTURES
    • Sodium Chloride Structure Na + Cl -
    • Cesium Chloride Structure C s + Cl -
    • Hexagonal Closed-Packed Structure
    • Diamond Structure
    • Zinc Blende
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 1 – Sodium Chloride Structure
    • Sodium chloride also crystallizes in a cubic lattice, but with a different unit cell.
    • Sodium chloride structure consists of equal numbers of sodium and chlorine ions placed at alternate points of a simple cubic lattice.
    • E ach ion has six of the other kind of ions as its nearest neighbours .
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Sodium Chloride Structure
    • If we take the NaCl unit cell and remove all the red Cl ions, we are left with only the blue Na. If we compare this with the fcc / ccp unit cell, it is clear that they are identical.     Thus, the Na is in a fcc sublattice.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Sodium Chloride Structure
    • This structure can be considered as a face-centered-cubic Bravais lattice with a basis consisting of a sodium ion at 0 and a chlorine ion at the center of the conventional cell,
    • LiF,NaBr,KCl,LiI,etc
    • The lattice constants are in the order of 4-7 angstroms.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 2-Cesium Chloride Structure Cs + Cl -
    • Cesium chloride crystallizes in a cubic lattice.  The unit cell may be depicted as shown. (Cs+  is teal, Cl- is gold).
    • Cesium chloride consists of equal numbers of cesium and chlorine ions, placed at the points of a body-centered cubic lattice so that each ion has eight of the other kind as its nearest neighbors . 
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Cesium Chloride Structure Cs + Cl -
    • The translational symmetry of this structure is that of the simple cubic Bravais lattice, and is described as a simple cubic lattice with a basis consisting of a cesium ion at the origin 0 and a chlorine ion at the cube center
    • CsBr,CsI crystallize in this structure.The lattice constants are in the order of 4 angstroms.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 8 ce l l Cesium Chloride Cs + Cl - 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 3–Hexagonal Close-Packed Str.
    • This is another structure that is common, particularly in metals. In addition to the two layers of atoms which form the base and the upper face of the h e xagon, there is also an intervening layer of atoms arranged such that each of these atoms rest over a depression between three atoms in the base.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Bravais Lattice : Hexagonal Lattice He, Be, Mg, Hf, Re (Group II elements) ABABAB Type of Stacking  Hexagonal Close-packed Structure a=b a=120, c=1.633a,  basis : (0,0,0) (2/3a ,1/3a,1/2c) 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure
    • Sequence ABABAB..
    • hexagonal close pack
    Sequence ABCABCAB.. -face c entered cubic close pack Close pack Sequence AAAA… - simple cubic Sequence ABAB… - body centered cubic Packing 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara A A A A A A A A A A A A A A A A A A B B B B B B B B B B B C C C C C C C C C C B A A A A A A A A A B B B
  • Crystal Structure 4 - Diamond Structure
    • The diamond lattice is consist of two interpenetrating face centered bravais lattices.
    • There are eight atom in the structure of diamond.
    • Each atom bonds covalently to 4 others equally spread about atom in 3d.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 4 - Diamond Structure
    • The coordination number of diamond structure is 4.
    • The diamond lattice is not a Bravais lattice.
    • Si, Ge and C crystallizes in diamond structure.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 5- Zinc Blende
    • Zincblende has equal numbers of zinc and sulfur ions distributed on a diamond lattice so that each has four of the opposite kind as nearest neighbors. This structure is an example of a lattice with a basis, which must so described both because of the geometrical position of the ions and because two types of ions occur.
    • AgI,GaAs,GaSb,InAs,
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 5- Zinc Blende 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure 5- Zinc Blende Zinc Blende is the name given to the mineral ZnS. It has a cubic close packed (face centred) array of S and the Zn(II) sit in tetrahedral (1/2 occupied) sites in the lattice . 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure
    • Each of the unit cells of the 14 Bravais lattices has one or more types of symmetry properties, such as inversion, reflection or rotation ,etc .
    ELEMENTS OF SYMMETRY 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara SYMMETRY INVERSION REFLECTION ROTATION
  • Crystal Structure Lattice goes into itself through Symmetry without translation 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Operation Element Inversion Point Reflection Plane Rotation Axis Rotoinversion Axes
  • Crystal Structure Inversion Center
    • A center of symmetry: A point at the center of the molecule.
    • (x,y,z) --> (-x,-y,-z)
    • Center of inversion can only be in a molecule. It is not necessary to have an atom in the center (benzene, ethane). Tetrahedral, triangles, pentagons don't have a center of inversion symmetry. All Bravais lattices are inversion symmetric.
    Mo(CO)6 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Reflection Plane
    • A plane in a cell such that, when a mirror reflection in this plane is performed, the cell remains invariant.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Examples
    • Triclinic has no reflection plane.
    • Monoclinic has one plane midway between and parallel to the bases, and so forth.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure We can not find a lattice that goes into itself under other rotations
    • A single molecule can have any degree of rotational symmetry, but an infinite periodic lattice – can not.
    Rotation Symmetry 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Rotation Axis
    • This is an axis such that, if the cell is rotated around it through some angles, the cell remains invariant.
    • The axis is called n-fold if the angle of rotation is 2 π/n.
    120 ° 180 ° 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara 90 °
  • Crystal Structure Axis of Rotation 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Axis of Rotation 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Can not be combined with translational periodicity! 5-fold symmetry 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Symmetry Elements for Cubic System Axis of Symmetry present in cubic system 3-Tetrads 4-triads 6-diads Total-13 axes of symmetry Total =13+9+1 = 23 elements of symmetry Centre of symmetry
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara The characteristic symmetry elements in each of the seven groups are listed below The characteristic symmetry elements in each of the seven groups are listed below Cubic Three triads Hexagonal One hexad (// z) Tetragonal One tetrad (// z) Trigonal One triad (// [111]) Orthorhombic Three perpendicular diads (// x, y and z) Monoclinic One diad (// y) Triclinic -
  • 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara Concept Map
  • Crystal Structure Group discussion
    • Kepler wondered why snowflakes have 6 corners, never 5 or 7.By considering the packing of polygons in 2 dimensions, demonstrate why pentagons and heptagons shouldn’t occur.
    Empty space not allowed 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • Crystal Structure Examples
    • Triclinic has no axis of rotation.
    • Monoclinic has 2-fold axis (θ= 2π/2 =π) normal to the base.
    03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara 90 °
  • Crystal Structure 03/11/2011 Intro to Solid State by Dr Dattu Joshi, MSU, Vadodara
  • IMPERFECTIONS IN CRYSTALS
  • Lattice Defect or Imperfection
    • An important feature of crystals is their regular atomic arrangement but no crystal is perfectly regular.
    • Any deviation from this perfect atomic periodicity is called an imperfection or lattice defect .
    • A lattice defect is a state in which the atomic arrangement in the small region (of a size of only a few lattice constants) of a crystal has departed from regularity.
  • Electrical properties gets affected
    • The electrical resistance of the crystal is greatly affected.
    • These defects scatter the conduction electrons in a metal and thus increase its electrical resistance.
    • Especially in case of alloys this increase in electrical resistance is several tens of percentage.
  • Elastic properties get affected
    • The strength of crystals:
    • Certain kinds of defects exist very rarely but they decrease the strength of the crystal by a factor of several hundreds or thousands
    • Such properties that are greatly affected by the defects are called defect or structure sensitive properties.
  • CLASSIFICATION OF IMPERFECTIONS There are three types of imperfections exist in general. (A) Crystal Imperfections or atomic imperfections) (B) Electronic Imperfections (C) Transient Imperfections
  • (A) Crystal Imperfections (or atomic imperfections) :
    • Concerned with this types of imperfections. To list them they are:
    •  
    • (1) Thermal vibrations,
    • (2) Point defects,
    • (i) Vacancies,
    • (ii) Interstitials,
    • (iii) Isolated impurities.
    • Line defects; the dislocation: Edge and Screw dislocations,
    • (4) Surface defects,
    • (i) External surfaces of solids
    • (ii) Internal surfaces; grain boundaries and other internal boundaries.
  • (B) Electronic Imperfections:
    • They are the defects in electronic structure e.g.,
    • (i) conduction electron
    • (ii) hole,
    • which are excited thermally from filled bands or impurity levels.
    • These defects are responsible for important electrical and magnetic properties,
  •  
  • (C) Transient Imperfections :
    • These defects are introduced into the crystal from external sources and are, for example
    • (i) Photons are bombarded on crystals
    • (ii) Beam of charged particles like electrons, protons, and mesons etc.
    • (iii) Beam of neutral particles e.g., neutrons and neutral atoms.
    • Are bombarded on crystals.
  • Different types of point defects in crystals
  • Vacancy
  •  
  • Point defects in ionic crystals
  •  
  •  
  •  
  • CRYSTALLOGRAPHIC IMPERFECTIONS:  
    • To discuss the defects that arise due to the departure from perfect periodicity of an atomic array in a crystal
    • — the so called lattice defects.
    • They can then be classified according as the periodic regularity is interrupted in zero, one, two and three dimensions.
  • (1) Point Defects:
    • A lattice defect which spreads out very little in (zero dimension) is called a point defect.
    • They are of following types:
    • (i) Interstitial atoms
    • (ii) Vacancy –also known as Schottky defects
    • Impurity atom
    • Interstitial + Vacancy = Frenkel defects
  • (i) Interstitial atom:
    • This is an extra atom inserted into the voids (called interstice of the lattice) between the regularly occupied sites.
    • Thus such an atom does not occupy regular lattice sites.
    • This extra atom may be an impurity atom or an atom of the same types as on the regular lattice sites.
  • (ii) Vacancies :
    • These are the lattice sites from which the atoms are missing.
    • Such a vacancy is also called Schottky defect.
    • But if a vacancy is created by transferring an atom from a regular lattice site to an interstitial position then it is called Frenkel defect.
    • In this case, therefore, - two imperfections are created—vacancy as well as an interstitial atom.
  • Point defects in elemental solids
  • Frenkel defects in ionic crystals
  • Cation and Anion vacancy
  •  
  • (iii) Impurity atom :
    • This is a defect in which a foreign atom occupies a regular lattice site.
    • Point defects
    • The simplest point defects are as follows:
    • Vacancy – missing atom at a certain crystal lattice position;
    • Interstitial impurity atom – extra impurity atom in an interstitial position;
    • Self-interstitial atom – extra atom in an interstitial position;
    • Substitution impurity atom – impurity atom, substituting an atom in crystal lattice;
    • Frenkel defect – extra self-interstitial atom, responsible for the vacancy nearby.
  • Line defects
    • Linear crystal defects are edge and screw dislocations.
    • Edge dislocation is an extra half plane of atoms “inserted” into the crystal lattice.
    • Due to the edge dislocations metals possess high plasticity characteristics: ductility and malleability.
  •  
  •  
  • Screw Dislocation
    • Screw dislocation forms when one part of crystal lattice is shifted (through shear) relative to the other crystal part. It is called screw as atomic planes form a spiral surface around the dislocation line.
    • For quantitative characterization of a difference between a crystal distorted by a dislocation and the perfect crystal the Burgers vector is used.
    • The dislocation density is a total length of dislocations in a unit crystal volume.
    • The dislocation density of annealed metals is about 10 10 - 10 12 m − ².
    • After work hardening the dislocation density increases up to 10 15 -10 16 m - ².
    • Further increase of dislocation density causes cracks formation and fracture .
  •  
  • (2) Line Defects:
    • When a lattice defect is confined to a small region in one dimension, it is called a line defect. In this type of defect, called dislocation, part of the lattice undergoes a shearing strain equal to one lattice vector (called a Burgers vector).
    • They are of two types :
    • (1) Edge dislocation : This type of dislocation is created by a missing half plane of atoms.
    • (ii) Screw dislocation : It can be thought of as created by cutting the crystal part way and shearing down one part relative to other by one atomic spacing.
  • Planar defects
    • Planar defect is an imperfection in the form of a plane between uniform parts of the material. The most important planar defect is a grain boundary .
  •  
    • Formation of a boundary between two grains may be imagined as a result of rotation of crystal lattice of one of them about a specific axis. Depending on the rotation axis direction, two ideal types of a grain boundary are possible:
    • Tilt boundary – rotation axis is parallel to the boundary plane;
    • Twist boundary - rotation axis is perpendicular to the boundary plane:
    • An actual boundary is a “mixture” of these two ideal types.
    • Grain boundaries are called large-angle boundaries if misorientation of two neighboring grains exceeds 10°-15°.
    • Grain boundaries are called small-angle boundaries if misorientation of two neighboring grains is 5° or less.
    • Tilt boundary – rotation axis is parallel to the boundary plane;
    • Twist boundary - rotation axis is perpendicular to the boundary plane:
    • An actual boundary is a “mixture” of these two ideal types.
    • Grains, divided by small-angle boundaries are also called subgrains .
    • Grain boundaries accumulate crystal lattice defects (vacancies, dislocations) and other imperfections, therefore they effect on the metallurgical processes, occurring in alloys and their properties.
    • Since the mechanism of metal deformation is a motion of crystal dislocations through the lattice, grain boundaries, enriched with dislocations, play an important role in the deformation process.
    • Diffusion along grain boundaries is much faster, than throughout the grains.
    • Segregation of impurities in form of precipitating phases in the boundary regions causes a form of corrosion , associated with chemical attack of grain boundaries. This corrosion is called Intergranular corrosion .
  • (3) Plane Defects:
    • When a lattice defect is confined to a small region only in two dimensions; it is called a plane defect.
    • When line defects cluster together in a plane, they can form a plane which is described as follows :
    • (i) Lineage Boundary :
    • It is boundary between two adjacent perfect regions in the same crystal that are slightly tilted with respect to each other.
    • (ii) Grain boundary:
    • A crystal is made up of a large number of small grains or crystallites which are single crystals, (i.e., all molecules in a crystallite are oriented in the same direction). Generally, these crystallites in. the crystal of a solid remain oriented indiscriminately in random directions unless special precautions are taken during the crystal growth. Such crystals are called polycrystalline. Grain boundary is the boundary between two crystals in a polycrystalline solid.
  • (iii) Stacking fault :
    • It is possible for ‘mistakes’ to occur in the stacking sequence of hexagonal close packed layers. The plane separating the two incorrectly juxtaposed layers is called stacking fault.
  • We take the blue atoms as the base plane for what we are going to built on it, we will call it the &quot;A - plane&quot;. The next layer will have the center of the atoms right over the depressions of the A - plane; it could be either the B - or C - configuration. Here the pink layer is in the &quot;B&quot; position
  • If you pick the B - configuration (and whatever you pick at this stage, we can always call it the B - configuration), the third layer can either be directly over the A - plane and then is also an A - plane (shown for one atom), or in the C - configuration. If you chose &quot;C&quot;, you get the face centered cubic lattice (fcc) If you chose &quot;A&quot;; you obtain the hexagonal close packed lattice ( hcp ), The stacking sequences of the two close-packed lattices therefore are fcc: ABCABCABCA... hcp: ABABABA...
  • Trends of Research In Crystal Growth
  • Why to Grow and study crystals?
    • Various device fabrication requires crystal and various properties are exploited for that
    • Following Table gives some of the Uses of crystals
    • Some devices in the table marked with an asterisk use crystals with controlled additions of impurities.
    • In the complex structures, the necessary impurities can either be incorporated in a series of growth processes or can be added after growth by diffusion or by ion implantation.
  • Properties exploited Device Crystal 1 Uniformity alone X-ray prisms Neutron collimators Lithium fluoride 2 Uniformity giving reproducible mechanical properties and abrasion resistance Turbine blades Gramophone styli Bearings Tape-recorder heads Wire drawing dies Metals Sapphire Ruby Ferrites Diamond 3 Uniformity eliminating scattering of electromagnetic waves Lenses, prisms and optical windows Lasers* Microwave filters Alkali and alkaline earth halides Yttrium aluminum garnet Yttrium iron garnet 4 Uniformity reducing charged carrier scattering Transistors*, Diodes* Thyristors * Photocells Silicon, germanium and gallium arsenide Cadmium suiphide 5 Uniformity reducing scattering of sound waves Resonant filters Delay lines Quartz Lithium niobate Zinc oxide 6 Uniformity allowing exploitation of tensor properties Nicol prism Ultrasonic transducers Gramophone pick-ups Fluorite Rochelle salt Lithium sulphate
  • CRYSTAL GROWTH METHODS
    • MELT GROWTH METHODS
    • SOLUTION GROWTH METHODS
    • VAPOR PHASE GROWTH METHOD
    • MODIFICATION OF CRYSTAL GROWTH METHODS
  • MELT GROWTH METHODS
      • Horizontal Boat Growth Methods
        • Horizontal Gradient Freezing (HGF) method
        • Horizontal Bridgman (HB) method
        • Horizontal Zone Melting (HZM) method
      • Vertical Boat Growth Methods
        • Vertical Bridgman (VB) method
        • Vertical Gradient Freezing (VGF) method
        • Vertical Zone Melting (VZM) method
      • Pulling Methods
        • Czochralski (CZ) method
        • Liquid Encapsulated Czochralski (LEC) method
        • Kyropolous and Liquid Encapsulated Kyropolous (LEK) methods
      • Floating Zone (FZ) Method
      • Other Methods
        • Shaped Crystal Growth Method
        • Heat Exchange Method (HEM)
  • SOLUTION GROWTH METHODS
      • Simple Solution Growth Method
      • Traveling Heater Method (THM)
      • Solute Solution Diffusion (SSD) Method
      • Solvent Evaporation (SE) Method
      • Temperature Difference Method under Controlled Vapor Pressure (TDM-CVP)
      • Hydrothermal Synthesis Method
  • VAPOR PHASE GROWTH METHOD
      • Direct Synthesis (DS) Method
      • Physical Vapor Transport (PVT) Method
        • Open tube method
        • Closed tube method
      • Chemical Vapor Transport (CVT) Method
      • Solid Phase Reaction (Solid State Recrystallization)
  • MODIFICATION OF CRYSTAL GROWTH METHODS
      • In-Situ Synthesis
      • Vapor Pressure Control
      • Magnetic Field Application
      • Accelerated Crucible Rotation Technique (ACRT)
  • Survey of the methods of crystal growth In some cases huge quantities of crystals are grown annually e.g. silicon, quartz, germanium, Rubby, and di-hydrogen phosphates of potassium and ammonium Growth from Approximate % growth Melt 80 Vapour 7 Low Temperature solution 5 High Temperature Solution 5 Solid 3 Hydrothermal 2
  • Classification of Growth Techniques
  • Growth from the pure melt
  • Growth from the pure melt
  • Growth from Solution
  • Growth from Solution
  • Single Crystals for Research Purposes Crystal Doping Agent Uses  -Al 2 O 3, TiO 2 , CaF 2 Transition elements Paramagnetic studies CaWO 4 , etc. Rare Earths and Actinides Masers; Lasers ZnS, CdS, Organic Crystals Cr, Mn, Cu, Ag, Tl, etc. Fluorescence Photoconductivity Photoelectricity Ge, Si, InSb, GaAs, SiC, PbTe, Bi 2 Te 3 Donor or acceptor impurities Semiconductivity, Thermoelectric, Galvanomagnetic effects Fe 3 O 4 , MFe 2 O 4 , BaFe 12 O 19 , Y 3 Fe 5 O 12 Paramagnetic substituents Magnetic studies BeO, MgO,  -Al 2 O 3, UO 2 Pure Reactor material Al 2 SiO 5 , aluminosilicates, ZrSiO 4 , C, BN, WC, ThO 2 ZrO 2 , Si 3 N 4 , etc. Pure Refractories, abrasives, Structural materials Alkali halides,  -SiO 2 , CaF 2 , SrTiO 3 Pure Optical materials
  • Methods of Crystal Assessments Method Destructive or Non-destructive Information given 1 Chemical analysis Spectrographic analysis D Composition 2 X-ray analysis N Structure (Some information on composition) 3 X-ray fluorescence spectroscopy N Composition 4 Electron diffraction N Structure, surface detail 5 Electron microscopy N Surface detail 6 Electron beam X-ray spectroscopy N Composition 7 Optical spectroscopy, IR  UV N Structure and composition 8 Electron spin resonance N Purity (structure) 9 Optical examination N Imperfections, Surface detail 10 Etching, decorating N/D Perfection 11 Measurement of specialized physical properties (electrical or magnetic) N Perfection, purity
  • Requirements for growth control
    • As a particle settles on growing crystal surface a finite time is necessary for the particle to move to an available and proper site.
    • Growth rates must therefore be slow enough to allow this surface diffusion to be effective.
    • The most rapid growth is thus allowed at the melting point of a material, and the growth of crystals of the same material at lower temperatures (by solution techniques) must be correspondingly slower.
    From theory and practice
  • Typical example of growing corundum (  -Al 2 O 3 ) crystals by different techniques
    • Growth rates for corundum
    Method Temperature Linear growth rate Hydrothermal 650°C 0.1 mm/day Fluxed-melt 1200°C 1 mm/day Flame fusion 2100°C 450 mm/day
    • The result may appear as
    • Included material (‘ghosting’)
    • Variations in dislocation densities
    • Lattice irregularities
    • Inhomogeneity of composition
    Any fluctuation, irregularity or temporary halt in the growth process is reflected in the crystal obtained
    • fast (~mm/hr) growth rate is limited by heat transfer, not by mass transfer
    • allows for a large variety of techniques
        • Verneuil
        • Bridgman-Stockbarger
        • Czochralski-Kyropoulos
        • zone melting and floating zone
    characteristics growth from the melt
  • Verneuil 1902, Auguste Verneuil characteristics : no crucible contamination highly pure starting material (>99.9995%) strict control of flame temperature precise positioning of melted region vibration growth
  • The Verneuil method. :
    • A fine dry powder of the material to be grown is shaken through the wire mesh and falls through the oxy-hydrogen flame in which it melts.
    • A film of liquid is formed on top of the seed crystal.
    • This freezes progressively as the crystal is slowly lowered (a few mm/hr).
    • To maintain symmetry the seed is rotated (usually at about 10 r.p.m.)
    • The art of the method is to balance the rate of powder feed and the rate of lowering to maintain a constant growth rate and diameter.
    • The method is used extensively for the production of ruby crystals
  • temperature T melt Bridgman-Stockbarger characteristics : charge and seed are placed into the crucible no material is added or removed (conservative process) axial temperature gradient along the crucible
  •  
    • As the crucible is lowered, solid forms first at the pointed tip of the crucible.
    • If this tip is correctly shaped, usually only one crystal will be formed initially, and single crystal growth will generally continue if the conditions have been correctly chosen.
    • The latent heat of solidification, which is evolved as the crystal grows, is removed by conduction through the crystal and the crucible.
    • The principal characteristic of this method is that at least some part of the solid—liquid interface is in contact with the crucible.
  • Bridgman-Stockbarger
    • The shape of the crystal is defined by the container
    • No radial temperature gradients are needed to control the crystal shape.
    • Low thermal stresses result in low level of stress-induced dislocations.
    • Crystals may be grown in sealed ampules (easy control of stoichiometry)
    • Relatively low level of natural convection
    • Easy control and maintenance
    Advantages
    • Confined growth (crucible may induce stresses during cooling)
    • Difficult to observe seeding and growing processes
    • Changes in natural convection as the melt is depleted
    • Delicate crucible and seed preparation, sealing, etc.
    Drawbacks
  • Bridgman-Stockbarger reduced nucleation reduced thermal stresses reduced evaporation prevents contact between crucible and melt B 2 O 3 LiCl, KCl, CaCl2, NaCl
    • melts with volatile constituents:
        • III-V compounds (GaAs, lnP, GaSb)
        • II-VI compounds (CdTe)
    • ternary compounds:
        • Ga 1-x ln x As, Ga 1-x ln x Sb, Hg 1-x Cd x Te
    applications improvement example (liquid encapsulation) crucible encapsulant melt crystal low vapor pressure melting temperature lower than the crystal density lower than the density of the melt no reaction with the melt or crucible encapsulant characteristics
  • Czochralski-Kyropoulos A seed crystal mounted on a rod is dipped into the molten material. The seed crystal's rod is pulled upwards and rotated at the same time. By precisely controlling the temperature gradients, rate of pulling and speed of rotation, a single-crystal cylindrical ingot is extracted from the melt. The process may be peformed in controlled atmosphere and in inert chamber. Jan Czochralski (1885 - 1953) characteristics : charge and seed are separated at start no material is added or removed (conservative process) charge is held at temperature slightly above melting point crystal grows as atoms from the melt adhere to the seed seed grown crystal molten raw material heating elements seed grown crystal molten raw material Kyropoulos Czochralski 1918 1926
  • Pulling direction of seed on rod Heater Crucible Inert atmosphere under pressure prevents material loss and unwanted reactions Layer of molten oxide like B 2 O 3 prevents preferential volatilization of one component - precise stoichiometry control Melt just above mp Growing crystal Crystal seed Counterclockwise rotation of melt and crystal being pulled from melt, helps unifomity of temperature and homogeneity of crystal growth CZOCHRALSKI
    • Molten material is held in a crucible at a temperature just above its melting point.
    • Heat is abstracted through a water-cooled seed and crystallization occurs on the seed which grows down into the melt.
    • Temperature control of the furnace largely determines the diameter of the growing crystal, and some adjustment of the seed position relative to the crucible may be necessary if a large volume change occurs on solidification.
    • In practice the crystals are removed from the furnace for annealing, although this may be done in situ.
    Kyropoulous apparatus
    • The technique is mainly used for the production of large alkali halide crystals for optical use.
    • Growth rates of about 1 cm/hr are obtainable with gradients of the order of 50°C/cm.
    • Although optically of acceptable quality, the crystals contain numerous low-angle boundaries.
    • For high- purity materials, crucible contamination is a serious problem.
  • Czochralski-Kyropoulos
    • Growth from free surface (stress free)
    • Crystal can be observed during the growth process
    • Forced convection easy to impose
    • Large crystals can be obtained
    • High crystalline perfection can be achieved
    • Good radial homogeneity
    Advantages
    • Delicate start (seeding, necking) and sophisticated further control
    • Delicate mechanics (the crystal has to be rotated; Rotation of the crucible is desirable)
    • Cannot grow materials with high vapor pressure
    • batch process (axial segregation, limited productivity)
    Drawbacks
  • zone melting ultra-pure silicon characteristics : only a small part of the charge is molten material is added to molten region (nonconservative process) molten zone is advanced by moving the charge or the gradient axial temperature gradient is imposed along the crucible
  • zone melting
    • Charge is purified by repeated passage of the zone (zone refining).
    • Crystals may be grown in sealed ampules or without containers (floating zone).
    • Steady-state growth possible.
    • Zone leveling is possible; can lead to superior axial homogeneity.
    • Process requires little attention (maintenance).
    • Simple: no need to control the shape of the crystal.
    • Radial temperature gradients are high.
    advantages
    • Confined growth (except in floating zone).
    • Hard to observe the seeding process and the growing crystal.
    • Forced convection is hard to impose (except in floating zone).
    • In floating zone, materials with high vapor pressure can not be grown.
    drawbacks
  • other methods (1) melt non congruently decompose before melting have very high melting point undergo solid state phase transformation between melting point and room temperature growth from solutions key requirement high purity solvent insoluble in the crystal oxides with very high melting points PbO, PbF 2 , B 2 O 3 , KF very slow, borderline purity, platinum crucibles, stoichiometry hard to control carried on at much lower temperature than melting point typical solvents: main advantage: limitations: molten salt (flux) growth a liquid reaction medium that dissolves the reactants and products, but do not participate in the reaction flux:
  • other methods (2) high quality layers of III-V compounds (Ga 1-x ln x As, GaAs x P 1-x ) GaAs and GaSb from Ga solution liquid phase epitaxy advantage lower temperatures than melt growth limitation very slow, small crystals or thin layers aqueous solution at high temperature and pressure typical example: quartz industry SiO 2 is grown by hydrothermal growth at 2000 bars and 400 °C because of α-β quartz transition at 583°C hydrothermal growth
  • crystal purity (1) Solubility of possible impurity is different in crystal than melt, the ratio between respective concentrations is defined as segregation coefficient (k 0 ) impurity equilibrium concentration in crystal impurity equilibrium concentration in melt As the crystal is pulled impurity concentration will change in the melt (becomes larger if segregation coefficient is <1). Impurity concentration in crystal after solidifying a weight fraction M/M 0 is:
  • Simple laboratory techniques you can also try
    • Crystal growing is an art, and there are as many variations to the basic crystal growing recipes as there are crystallographers.
    • The recipes given below are ones which I have either tried or I have read about and sound reasonable.
    • The techniques chosen will largely depend on the chemical properties of the compound of interest:
      • Is the compound air sensitive,
      • moisture sensitive?
      • Is it hygroscopic? etc. etc.
  • Slow Evaporation.
    • The simplest way to grow crystals and works best for compounds which are not sensitive to ambient conditions in the laboratory.
    • Prepare a solution of the compound in a suitable solvent.
    • The solution should be saturated or nearly saturated.
    • Transfer the solution to a CLEAN crystal growing dish and cover.
    • The covering for the container should not be air tight.
    • Aluminium foil with some holes poked in it works well, or a flat piece of glass with microscope slides used as a spacer also will do the trick.
    • Place the container in a quiet out of the way place and let it evaporate.
    • This method works best where there is enough material to saturate at least a few milliliters of solvent.
    • This is good for solute-solvent systems which are less than moderately soluble and the solvent's boiling point is less than 100°C.
    • Prepare a saturated solution of the compound where the solvent is heated to just it's boiling point or a just below it.
    • Transfer the solution to a CLEAN large test tube and stopper.
    • Transfer the test tube to a Dewar flask in which hot water (heated to a temperature of a couple of degrees below the solvent boiling point).
    • The water level should exceed the solvent level in the test tube, but should not exceed the height of the test tube.
    • Stopper the Dewar flask with a cork stopper and let the vessel sit for a week.
    • A more elaborate version of this involves a thermostated oven rather than a Dewar flask.
    Slow Cooling.
  • Variations on Slow Evaporation and Slow Cooling
    • If the above two techniques do yield suitable crystals from single solvent systems, one may expand these techniques to binary or tertiary solvent systems.
    • The basic rationale for this is by varying the solvent composition one may inhibit growth of certain crystal faces and promote the growth of other faces, yielding crystals of suitable morphology and size.
    • If you choose this route for growing crystals, it is absolutely necessary to record the solvent composition you use!
    • If crystal growing is an art, growing crystals from binary or tertiary solvent mixtures is that much more imprecise.
    • Remember reproducibility is paramount in science.
  • crystal purity (2) As a consequence, floating zone method will give crystals with lower concentration of impurities having k<1 than Czochralski growth The effective segregation coefficient (k e ): multiple pass may be run in order to achieve the required impurity concentration there is no contamination from crucible
  • crystals for DBD DBD application constraints ββ emitters of experimental interest impurity allowed (g/g): T = 10 18 – 10 24 yr usual T i < 10 12 yr close to detection limit of the most sensitive techniques used for quantitative elemental analysis (NAA, ICP-MS)
  • TeO 2 crystal (1) relatively low melting point distorted rutile (TiO 2 ) structure anisotropy of expansion coefficient TeO 2 (paratellurite) a = 4.8088 Å c = 7.6038 Å short:: 1.88 Å long:: 2.12 Å
  • TeO 2 crystal (2) raw material preparation Te TeO 2 99.999% TeO 2 +HCl->TeCl 4 +H 2 O TeO 2 2Te+9HNO 3 -> Te 2 O 3 (OH)NO 3 +8NO 2 +4H 2 O Te 2 O 3 (OH)NO 3 ->2 TeO 2 +HNO 3 TeCl 4 +4NH 4 OH->Te(OH) 4 +4NH 4 Cl Te(OH) 4 ->TeO 2 +H 2 O HNO 3 TeO 2 HCl TeCl 4 TeCl 4 NH 4 OH TeO 2 TeO 2 washing filtering washing drying
  • TeO 2 crystal (3) TeO 2 crystal is particularly repellent to impurities most of radioactive isotopes have ionic characteristics incompatible with substitutional incorporation in TeO 2 crystal growth seed grown Xtal molten TeO 2 heating Czochralski molten TeO 2 Bridgman seed grown Xtal Bridgman grown crystals are more stressed than Czochralski ones annealing at about 550°C helps in removing the residual stresses
  • TeO 2 crystal (4) Te possible substitutional ions in TeO 2 238 U (T=4.5·10 9 yr) 184 W (T=3·10 17 yr)
  • TeO 2 crystal (5) radiopurity main radioactive series crucible material activation products natural radioactivity
  • conclusion shares of 20 000 tons, world crystals production in 1999 ECAL-CMS: (  80 tons PWO)/2000-2006 CUORE: (  1 ton TeO 2 )/?