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Elastic Properti...
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Glass – An Intro...
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General Introduc...
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Glass Applicatio...
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Glass Technology...
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Glass Arts
Decor...
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Glass Art
Roman ...
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Next-generation ...
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Glass Definiti...
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Definition
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Basic Ultrasonic...
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Type of ultrason...
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2 methods of pre...
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Glass Formation
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Crystal vs Glass...
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Glass Structure
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Structure of Bin...
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Substance is wei...
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Preparing Commer...
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Special Glass
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Other Types of G...
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Colored Glass
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Colored Glass
Io...
SEM Photos XRD Pattern of
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TeO2 powder
TeO2 glass
ZnO Powder
TeO2-ZnO glass
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Wave Velocity
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Elastic studies of Glass Materials Studied by Ultrasonic Technique
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Elastic studies of Glass Materials Studied by Ultrasonic Technique

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Brief review about glass and its physical, elastic and other properties. It also covers the glass preparation techniques, characterization as well as elasticity.

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Elastic studies of Glass Materials Studied by Ultrasonic Technique

  1. 1. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Properties of Glass Materials Studied by Ultrasonic Technique Sidek Ab Aziz Universiti Putra Malaysia
  2. 2. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Ultrasonic Waves • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism
  3. 3. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass – An Introduction What is a glass? Glass - hard, brittle solid material that is normally lustrous and transparent in appearance and shows great durability under exposure to the natural elements. The latin term glesum, probably originated from a Germanic word for a transparent, lustrous substance. The term glass developed in the late Roman Empire. Natural heat-producing processes like volcanoes and lightning strikes are responsible for creating various forms of natural glass. Obsidian - super-heated sand or rock that rapidly cooled. Moldavite formed by meteorite impact (Besednice, Bohemia)
  4. 4. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion General Introduction • These three properties— lustre, transparency, and durability — make glass a favoured material for such household objects as windowpanes, bottles, and lightbulbs. Clear glass for Incandescent light bulb Thermal Insulation Glass
  5. 5. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Application Special properties of glass make it suitable for folllowing applications – flat glass – Tempered glass – Annealed glass – Laminated glass – container glass – optics and optoelectronics material – laboratory equipment – thermal insulator (glass wool) – reinforcement fiber (glass- reinforced plastic, glass fiber reinforced concrete) – and art.
  6. 6. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Technology Glass building Energy saving mirror
  7. 7. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Arts Decoration Glass- Venetian millefiori. Chinese ring Glass beads are made with silica (usually from sand). Cross section of Korean broken beads
  8. 8. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Art Roman Cage Cup from the 4th century A.D. Roman glass A 16th-century stained glass window. A vase being created at the Reijmyre glassworks, Sweden Stained glass
  9. 9. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Next-generation large-scale panels Glass substrates for LCDs To form various functional films on glass substrates. ASAHI Glass, Japan
  10. 10. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Specific Potential Application of Glassy Materials CD memory device Optical switching device Non-linear optical devices Electrochemical devices Laser host Infra-Red Fiber Optics Optical waveguides
  11. 11. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General – Definition • Ultrasonic Waves • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism
  12. 12. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion . Glass Definition ♦ Glass is an inorganic product of fusion that has cooled to a rigid condition without crystallization (American Society for Testing Materials ,1945) True for most commercial materials (e.g., soda-lime-silica) but ignores organic, metallic, H-bonded materials, ignores alternate processing routes (sol gel, CVD, electron or neutron -bombardment, etc.) ♦ Glass is an X-ray amorphous material which exhibits a glass transition. (Wong and Angell, 1976) Not all amorphous solids are glasses; wood, cement, a-Si, thin film oxides, etc. are amorphous but do not exhibit the glass transition. ♦Glass is an undercooled liquid." Problems: glasses have 'solid' properties (e.g., elastic material) No flow at room temperature ♦ Glass as any isotropic material, whether inorganic or organic, which lacks three dimensional atomic periodicity and has a viscosity greater than about 1014 poise (Mackenzie, 1960)
  13. 13. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Zachariasen’s model According to Zachariasen, in order for a given oxide AmOn to form a glassy solid, it must meet the following criteria: (1) the oxygen should be linked to no more than two atoms of A, (2) the coordination number of the oxygen about A should be small, on the order of 3 or 4, (3) the cation polyhedra must share corners only, and (4) at least three corners must be shared. In 1932, physicist W.H. Zachariasen defined glass is an extended, three- dimensional network of atoms that form a solid which lacks the long-range periodicity (or repeated, orderly arrangement) typical of crystalline materials.
  14. 14. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Definition • These criteria are useful guidelines for the forming of conventional oxide glasses, but unsuitable for nonoxide glasses. • Chalcogenide glasses – for instance, are chains of random lengths and random orientation formed by the bonding of the chalcogen elements sulfur, selenium, or tellurium. – Ions of these elements have a 2- coordination requirement, and the chains are cross-linked by 3- or 4-coordinated elements such as arsenic, antimony, or germanium. ♦ Glass is a solid that possesses no long range atomic order and, upon heating, gradually softens to the molten state. Non-crystalline structure Glass transformation behavior
  15. 15. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Basic Ultrasonics • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism
  16. 16. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Basic Ultrasonics • “Ultrasonic" refers to sound that above the frequencies of audible sound, (beyond 20 kHz) • Ultrasonic can be produced by transducers – piezoelectric effect – magnetostrictive effect • Piezoelectricity is the ability of some crystals (quartz) and certain ceramics materials to generate an electric potential in response to applied mechanical stress. • Magnetostrictive transducers use magnetic strength to produce high intensity ultrasonic sound in the 20-40 kHz range for the ultrasonic cleaning and also other mechanical applications
  17. 17. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Ultrasonic wave are able to propagate in medium by method such as: • Reflection • Refraction • Propagation • Transmission • Dispersion • etc Advantages of ultrasonic wave • ability to form coherent wave in which amplitude, frequency, • direction of propagation can be controlled Advantages of ultrasonic wave
  18. 18. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Type of ultrasonic wave 2 type of ultrasonic wave traveling in solid such as glass:  longitudinal wave  shear wave Longitudinal wave also known as compressional waves •the oscillation of the particle is forward and backward, compressing, and depressing. Shear wave also known as transverse wave •the oscillation of particle in medium is at right angles to the direction of propagation. •Shear wave can only propagate through solid and cannot propagate in liquid and gas. N N U U
  19. 19. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Ultrasonic Waves • Physical Properties of Glass – Glass Preparation – Density and Molar Volume • Elastic Properties – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism
  20. 20. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion 2 methods of preparing glass samples Glass Preparation Conventional Method  Cooling from the liquid state/ Melt quenching technique  Condensation from the vapor  Pressure quenching  Solution hydrolysis Unconventional Method Unconventional melting Solution methods Deposition methods Solid-state transformations
  21. 21. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Formation Normally, glass is formed upon the cooling of a molten liquid in such a manner that the ordering of atoms into a crystalline formation is prevented. Instead of the abrupt change in structure that takes place in a crystalline material such as metal as it is cooled below its melting point in the cooling of a glass-forming liquid there is a continuous stiffening of the fluid until the atoms are virtually frozen into a more or less random arrangement similar to the arrangement that they had in the fluid state.
  22. 22. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Crystal vs Glass Glasses •lack of long-range order results in larger volumes (lower density), higher energies; atoms could rearrange to form denser structures if given enough thermal energy and time. •thermodynamically metastable phase Crystals ordered atomic structures mean smaller volumes (high density) & lower energies •thermodynamically stable phase
  23. 23. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Structure Glass • amorphous • isotropic macroscopic physical properties • no grain structure when viewed under an optical microscope. Glass structure relates to various physical properties such as density, thermal expansion, viscosity, surface tension and also miscellaneous mechanical (including elastic), chemical and electrical properties of glass.
  24. 24. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Structure Two-dimensional representation of (a) an oxide crystal and (b) a glass of the same chemical composition (A2O3) due to Zachariasen (1932) Schematic two-dimensional representation of the microscopic structure of binary oxide glass; (a) composed of basic glass former and glass former; (b) showing the effect of network modifying cations on the network of the glass former.
  25. 25. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Structure of Binary Borate Glass Some structural groupings in borate glasses as indicated from nuclear magnetic resonance experiments (Bray 1985). Small solid circles represent boron atoms, open circles oxygen atoms and an open circle with negative sign indicates non- bridging oxygen.
  26. 26. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Ultrasonic Waves • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism Quartz sand (silica) as main raw material for commercial glass production.
  27. 27. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Substance is weight First Furnace 400 C for 30 min Second Furnace 750-800 C for 60 min Pour melt into mould Placed molten and mould in First Furnace and annealed at 400 C Removed the mould after the melt was hard enough Cut and polished sample GLASS PREPARATION PROCESS
  28. 28. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Preparing Commercialized Glass • Pure silica (SiO2) melts at a viscosity of 10 Pa s (100 P)— of over 2300 °C (4200 °F). • Sodium carbonate (Na2CO3) lowers the melting point to about 1500 °C (2700 °F) in soda-lime glass • Soda makes the glass water soluble, which is usually undesirable, so lime (calcium oxide (CaO), some magnesium oxide (MgO) and aluminium oxide are added to provide for a better chemical durability. • The resulting glass contains about 70 to 74 percent silica by weight and is called a soda-lime glass.Soda-lime glasses account for about 90 percent of manufactured glass. Lead glass, such as lead crystal or flint glass, is more 'brilliant' because the increased refractive index causes noticeably more "sparkles", while boron may be added to change the thermal and electrical properties, as in Pyrex. Marlinda Daud, Pusat Minerologi Ipoh
  29. 29. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Special Glass • Adding barium also increases the refractive index. • Thorium oxide gives high refractive index and low dispersion, (for high-quality lenses) but due to its radioactivity has been replaced by lanthanum oxide in modern eye glasses. • Large amounts of iron are used in glass that absorbs infrared energy, such as heat absorbing filters for movie projectors, • cerium(IV) oxide for absorbs UV wavelengths (biologically damaging ionizing radiation). Finally, fining agents such as sodium sulfate, sodium chloride, or antimony oxide are added to reduce the bubble content in the glass.
  30. 30. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Other Types of Glass Besides common silica- based glasses, many other inorganic and organic materials may also form glasses, including – plastics (e.g., acrylic glass) – phosphates, – borates, – chalcogenides, – fluorides, – germanates (glasses based on GeO2), •tellurites (glasses based on TeO2), • antimonates (glasses based on Sb2O3), • arsenates (glasses based on As2O3), • titanates (glasses based on TiO2), • tantalates (glasses based on Ta2O5), • nitrates, carbonates and many other substances.
  31. 31. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Colored Glass • Color in glass may be obtained by addition of electrically charged ions and by precipitation of finely dispersed particles (such as in photochromic glasses).[ • Ordinary soda-lime glass appears colorless • iron(II) oxide (FeO) impurities of up to 0.1 wt%produce a green tint • Further FeO and Cr2O3 additions may be used for the production of green bottles. • Sulfur, together with carbon and iron salts, is used to form iron polysulfides and produce amber glass ranging from yellowish to almost black. • Manganese dioxide can be added in small amounts to remove the green tint given by iron(II) oxide.
  32. 32. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Colored Glass Ion Silicate-based Glass Phosphate-based Glass Fe+2 deep blue-green slight greenish blue Fe+3 yellowish-brown slightly brownish The color of a glass may depend upon the nature of the glass as well as the coloration ion. For example, iron ions have the following color influences:
  33. 33. SEM Photos XRD Pattern of Starting Materials TeO2 powder TeO2 glass ZnO Powder TeO2-ZnO glass 0 200 400 600 800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200 3400 10 20 30 40 50 2 theta Intensity(a.u) 0 5000 10000 15000 20000 25000 30000 35000 40000 45000 50000 10 20 30 40 50 2 Theta Intensity(a.u) 0 5000 10000 15000 20000 25000 30000 35000 10 20 30 40 50 2 Theta Intensity(a.u) TeO2-ZnO-AlF3 glassAlF3 (97.0%) Powder
  34. 34. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion XRD patterns 100 600 1100 1600 2100 10 20 30 40 50 2 theta Intensity(a.u) TZ7 TZ6 TZ5 TZ4 TZ3 TZ2 TZ1 TZ0 • no discrete or continuous sharp peaks • but broad halo at around 2 260 - 300 , which reflects the characteristic of amorphous materials. • absence of long range atomic arrangement and the periodicity of the 3D network in the quenched material 400 600 800 1000 1200 1400 1600 1800 10 20 30 40 50 2 theta Intensity(a.u) S5 S4 S3 S2 S1 TeO2)1-x (ZnO)x (x = 0.1 to 0.4 in 0.05) (TeO2)90(AlF3)10-x(ZnO)x (x = 1 to 9) binary ternary
  35. 35. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Glass Forming Region
  36. 36. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Density & Molar Volume ρ M V = Molar volumes ac aca a s ww w ρρ       − = Density Measurement (Archimedes Method)
  37. 37. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Density & Molar Volume Variation of density and molar volume with mol% Bi2 O3 in Bi2 O3–B2 O3 glass systems. The increase of the density of the glasses accompanying the addition of Bi2 O3 is probably attributable to a change in cross-link density and coordination numbers of Bi3+ ions. 26 26.5 27 27.5 28 28.5 29 0.55 0.6 0.65 0.7 0.75 0.8 0.85 Mole fraction of TeO2 Molarvolume(cm3 mol-1 ) 4650 4700 4750 4800 4850 4900 4950 5000 Density(kgm-3 ) Density and molar volume of TeO2.B2O3 glasses 28 28.5 29 29.5 30 30.5 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Pecahan Mol Ag2 O Isipadumolar(cm3 ) 4800 4900 5000 5100 5200 5300 Ketumpatan(kg/m3 ) Density and molar volume of [(TeO2)x (B2O3)1-x)]1-y [Ag2O]y
  38. 38. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Density and Molar Volume 3500 4500 5500 6500 7500 0 20 40 60 80 Bismuth Oxide (mol%) Density(kgm-3) Dependence of density on the composition of bismuth oxide glass systems as measured by El-Adawy and Moustafa (1999) (5 - 45 mol%), Wright et al (1977) (20 – 42.5 mol%) and present works (40 – 70 mol%).
  39. 39. Density & Molar Volume 4700 4800 4900 5000 5100 5200 5300 5400 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 Mole fraction of ZnO Density(kg/m3 ) 22 24 26 28 30 32 34 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 Mole fraction of ZnO Molarvolume(10-6 m3 mol-1 ) •The increase in density indicates zinc ions enter the glassy network •The decreases in the molar volume was due to the decrease in the bond length or inter-atomic spacing between the atoms • The stretching force constant (216 N/m – 217.5 N/m) of the bonds increase resulting in a more compact and dense glass. • Atomic Radius (Shelby, 2005). •R(Zn2+ )(0.074 nm) << R(Te2+ ) (0.097 nm) •there is no anomalous structural change (non-linear behaviour)
  40. 40. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Ultrasonic Waves • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Theory – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism A modern greenhouse in Wisley Garden, England, made from float glass.
  41. 41. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Properties of Materials Application of external forces to a solid body produces complex internal forces which cause – motion of the body, – in the form of linear translation, rotation and deformation. The body is in a condition of stress and any changes in the shape or volume are then referred to as strain Elastic body - after removal of the external force, the material returns to its original unstressed condition. To study of elasticity we consider infinitesimal elastic deformations, where stress is linearly proportional to strain, as stated in Hooke's law.
  42. 42. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Properties of Materials Elastic constants connect stress and strain Elastic constant can be determined by propagating ultrasonic elastic waves travel through a medium. The velocity of these waves and density of the sample can be used to determine the values of these elastic constants. The concept of elastic continuum is applied to explain quantitatively the elastic behavior of a solid body, under external stresses (temperature and hydrostatic pressure) Materials are assumed to behave like a homogeneous continuous medium. This approximation valid for elastic waves of wavelengths λ longer than 10-6 cm, i.e. frequencies below 1012 Hz, and ultrasonic waves fulfill this criterion.
  43. 43. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Theory of Elasticity Theory of elasticity and the anharmonicity of solids, both crystal and noncrystalline (glass) systems The propagation of elastic waves in crystals, including the thermodynamic definition of elastic constants The concept of anharmonicity is also outlined. The effect of hydrostatic pressure and temperature on the elastic
  44. 44. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elasticity and Hooke's Law • For sufficiently small deformations of the solid body, each component of stress is linearly related to each component of strain by Hooke's law σij=Cijkl ( i,j, k,l= 1,2,3)ϵ 6 components of stress 6 components of strain σij=Cijklϵ ( i,j, k,l= 1,2,3)
  45. 45. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Thermodynamic Definition of Elastic Constants Elastic constants can be also defined thermodynamically i.e. with respect to thermodynamic parameters (Brugger, 1964). 4 main thermodynamic potentials can be involved, U - internal energy F - Helmholtz free energy H - enthalpy and G - Gibbs free energy Each of these to be a function of entropy S, temperature T, thermodynamic tension components tij and reduced Lagrangian strain components ηij/ρo where ρo, represents the density of the unstrained solid. ijijdηt ρ 1 TdsU       +=  d ijijdηt ρ 1 SdTF       +−=  d ijijdt ρ 1 TdsH η      −=  d ijijdt ρ 1 SdTG η      −−=  d 0', ijkl s ... U C =         ∂∂ ∂ = η ηη ρ Sklij n o 0', ijkl T ... F C =         ∂∂ ∂ = η ηη ρ Tklij n o 0', ijkl S ... H S =         ∂∂ ∂ −= tSklij n o tt ρ 0', ijkl T ... G S =         ∂∂ ∂ −= tTklij n o tt ρ
  46. 46. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Constant ......... 6 1 2 1 )( 5 5 o +      +       = mnkljijklmn klijlijk iC CU ηηη ηηηρ Energy density of the solid may then be written as 0' ijkl s ... U C =         ∂∂ ∂ = η ηη ρ klij n o 0' 3 ijklmn s C = ∂∂∂ ∂ = η ηηη ρ mnklij o U Second Order Elastic Constant Third Order Elastic Constant Since the form of this expansion is similar to the expansion of potential energy in terms of interatomic displacement, It is possible to relate the elastic stiffness constants to the interatomic forces in a solid.
  47. 47. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Propagation of Elastic Waves In Solid One way to determine the elastic properties of any solid is through a dynamic test in which elastic waves are propagated in the solid. Assumption • Propagated waves behave adiabatically: • Entropy is conserved; • Wavelengths are much greater than the interatomic spacing • Small displacement of the atoms To ensure that the deformation is elastic and Hooke's law is obeyed. j iji o xt u ∂ ∂ = ∂ ∂ σ ρ 2 2                 ∂ + ∂ ∂ ∂ ∂ = ∂ ∂ i j j i ijkl k i o dx u x u C xt u 2 1 2 2 ρ kj i ijkl i o xx u C t u ∂∂ ∂ = ∂ ∂ 2 2 2 ρ ( ) 02 =−∂ oljkolijklilo UNNUCvρ Christoffel's equation For a specific combination of N and U, the equation of motion will provide only three solutions of wave velocities, one of which resembles a longitudinal and two shear waves. N - Propagation Direction U - Polarization direction
  48. 48. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Contants – Wave Velocity Mode No Propagation Direction N Polarization direction U (ρv2 ) 1 [100] [100] C11 (L) 2 [100] In [100] plane C11 3 [110] [110] (C11+C12+2C44)/2 4 [110] [001] C44 (G) 5 [110] [1 0] C’=(C11-C12)/2 6 [111] [111] (C11+2C12+4C44)/3 7 [111] In [111]plane (C11+C44-C12)/3 1 Ultrasonic wave velocity and elastic stiffness constant relationships for a cubic crystal
  49. 49. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic constants of the glasses Longitudinal modulus Shear modulus Bulk modulus Poisson’s ratio Young’s modulus Debye Temperature 2 lVL ρ= 2 sVG ρ=       −= 22 3 4 sl VVK ρ ( ) ( )22 22 2 2 sl sl VV VV − − =σ ( ) 22 222 43 sl sls VV VVV E − − = ρ mDt V M Np k h 3 1 4 9       =≈ π ρ θθ 3 1 33 12 −         += lS m VV V
  50. 50. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Ultrasonic System Schematic representation of (a) simple pulse ultrasonic system. (b) Envelope of pulse echo train and (c) detail of each echo as seen on oscilloscope display
  51. 51. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Ultrasonic Pulse Echo Overlap System Pulse echo overlap system Pulse echo overlap waveforms Block diagram of the experimental set up – ultrasonic wave velocity and attenuation measurement (Mepco Engineering College, INDIA)
  52. 52. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Ultrasonic System Ultrasonic – MBS 8000 Ultrasonic Data Acq. System
  53. 53. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Interatomic Potential Energy In a simple lattice dynamical model, the restoring forces between atoms and hence their potential energy are generally considered to be a function of the atomic displacement from equilibrium positions. In the harmonic and anharmonic lattice vibration models for a solid TOEC play an important role in accounting for the anharmonic and nonlinear properties of solids in the long wavelength acoustic modes.
  54. 54. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Wave Velocity Compositional dependence of the velocity of longitudinal and shear acoustic waves in Bi2 O3–B2 O3 glass systems. Both increase at first with increasing Bi2 O3 mol% up to a maximum at 25 mol% Bi2 O3 and then decrease as the Bi2 O3 mol% increases further. 1000 1500 2000 2500 3000 3500 4000 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Pecahan mol of Ag2O Halajuultrasonik(m/s) Compositional dependence of the velocity of longitudinal and shear acoustic waves in [(TeO2)x (B2O3)1-x)]1-y [Ag2O]y glass 1500 2000 2500 3000 3500 4000 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 Mole fraction of ZnO Velocity(m/s) Longitudinal Longitudinal Shear Shear Compositional dependence of the velocity of longitudinal and shear acoustic waves in [(ZnO)(TeO2) glass
  55. 55. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Lead Magnesium Chloride Phosphate Glass
  56. 56. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Modulus Dependence of longitudinal modulus on the composition of Bi2 O3–B2 O3 glass systems. One reason for this difference may come from the volume effect, in that C44 expresses the resistance of the body to deformation where no change in volume is involved, while C11 expresses the resistance where compressions and expansions are involved. 10 20 30 40 50 60 70 0.05 0.10 0.15 0.20 0.25 0.30 0.35 Pecahan mol Ag2O Moduluskenyal(GPa) L E K G Compositional dependence of the longitudinal and shear modulus of [(TeO2)x (B2O3)1-x)]1-y [Ag2O]y glass
  57. 57. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion 15 20 25 30 35 40 45 50 55 60 0 0,05 0,1 0,15 0,2 0,25 0,3 0,35 0,4 Mole fractionof ZnO ElasticModuli(GPa) Longitudinal Modulus, L Young’s Modulus, E Bulk Modulus, K Shear Modulus, G
  58. 58. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Properties Mole fraction, x 0.3 0.4 0.45 0.5 0.6 Elastic stiffness (GPa) C11 C44 C12 48.9 18.0 12.9 48.8 18.0 12.7 47.5 17.4 12.7 47.3 17.5 12.3 47.3 17.2 13.0 Young's modulus, E (GPa) 43.5 43.5 42.2 42.2 41.8 Bulk modulus, B (GPa) 24.9 24.7 24.3 24.0 24.4 Poisson's ratio, σ 0.208 0.207 0.211 0.207 0.215 Fractal dimension 2.90 2.92 2.87 2.92 2.82 Molar volume, V (cm3 /mole) 34.2 33.8 34.2 33.9 33.3 Number of atoms per volume (x1028 atoms/m3 ) 9.67 8.90 8.37 8.00 7.24 Debye Temperature (K) 291 275 263 255 238 The room temperature elastic properties of (PbO)x(P2O5)1-x glasses Mole fraction, y 0.04 0.06 0.07 0.1 Elastic stiffness (GPa) longitudinal, c11 shear, c44 c12 50.4 17.1 16.3 44.3 16.0 12.3 43.0 15.9 11.2 35.7 14.8 6.03 Young's modulus, E (GPa) 42.4 39.0 38.4 33.9 Bulk modulus, B (GPa) 27.6 23.0 21.8 15.9 Poisson's ratio, σ 0.244 0.217 0.206 0.145 Fractal dimension 2.47 2.79 2.92 3.73 Molar volume, V (cm3 /mole) 33.5 33.5 33.3 33.4 Number of atoms per volume (x1028 atoms/m3 ) 9.60 9.65 9.72 9.78 Debye Temperature (K) 276 266 264 251 Room temperature elastic properties of (PbCl2)y(PbO.2P2O5)1-y glasses
  59. 59. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Elastic Properties
  60. 60. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Ultrasonic Waves • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Theory – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism
  61. 61. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Temperature Dependence Low temperature dewar system Sample holder
  62. 62. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Temperature Variations of the SOEC The dependence of elastic constants upon temperature is another consequence of anharmonicity of the interatomic potential energy in solids. The normal behaviour of the thermal variations of the SOEC of most crystals,, is characterized by two general features; •a linear increase with decreasing temperature and •a zero slope in the region where the temperature approaches zero Kelvin. The linear dependence of elastic constants on temperature, especially above the Debye temperature θD ,is due to the anharmonic nature of the lattice vibrations. The linearity of this dependence may break down in the vicinity of a phase transition. Typical curve of second order elastic constant versus temperature ))/(1( DoJI TLFCC θ−= { }∫ −= T DD D dxxxTTF / 0 34 1)exp()/(3)/( θ θθ 3 2 v o T IJ JI dT df f C dT dC α −      =
  63. 63. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Temperature Dependence Variation of velocity and elastic moduli with temperature of Lead Bismuth Tellurite (BTP) Glasses
  64. 64. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Temperature Dependence At sufficiently low temperatures it is expected that in most crystalline solids the slope of dCIJ/dT would decrease i.e. dCIJ/dT →0 as T →0 which is a direct consequence of the third law of thermodynamics. However in certain materials like glasses, this particular feature is not always observed; instead of showing a zero slope of dCIJ/dT, the elastic constant increases to a maximum value at low temperature (~1K). This behaviour has been ascribed to interactions with two-level systems (Anderson et al. 1972, Phillips 1972).
  65. 65. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Temperature Dependence At very low temperatures where only ground states have to be considered, the groups of atoms are still able to tunnel through a barrier. This gives rise to an energy splitting of the ground state for this two- level system given by 2 0 2 ∆+∆=E )exp(00 λω −=∆  2 /2 mVd=λ where The parameter Δ designates the asymmetry of two-level potential, Δo represents the tunneling energy and λ is a tunnelling parameter describing the overlap of the wavefunctions of two states in a quantum mechanical theory (Phillips 1981). The parameter ωo is the frequency of oscillation in an individual well. Schematic representation of a double well potential, sometimes known as the two level system, characterized by a barrier V, asymmetry energy LI and distance d.
  66. 66. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Debye Temperature 3 1 3 3 3 2 3 1 3 1 1 111 4 9 −         Ω       +            = ∫ ππ θ d vvvk h V Ne D The Debye temperature θD is useful in describing the thermal behaviour of solids and it plays an important role in the theory of lattice vibrations. θD measure of the separation of the low temperature quantum mechanical region, where the vibrational modes begin to be "frozen out", from the high temperature region where all modes begin to be excited according to classical theory. θD can be obtained directly from heat capacity measurements, and it can be also derived from a set of the elastic constants. 3 1 33 21 3 1 −               += SL VV Vm VL (= (C11/ρ) 1/2 ) and VS= (=C44/ρ) 1/2 m e D V k h V N             = 3 1 1 4 9 π θ
  67. 67. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Ultrasonic Waves • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Theory – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism
  68. 68. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Pressure Dependence To compare between the measured values of (ρW2 )'p=0 and the pressure derivatives of the effective SOEC (ρV2 )', the following relations has to be employed, dP WVd W dP d W dP dW W dP V d oo o oooo )/()/( 2)( 22 22 2 ρ ρρ ρρ ρ ++=       −+= kmiimk T o IJ IJ SNN dP df f C dP dC 2 2 β Here Co IJ represents the SOEC at ambient condition, df/dP is the gradient of measured frequency in the pulse echo overlap experiment (see section 3.5) versus pressure, fo is the overlap frequency and βT and Skmii are the isothermal volume compressibility and the elastic compliances respectively. Hydrostatic pressure cell and sample holder
  69. 69. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Mode Grüneisen Parameters The mode Grüneisen parameter is an important tool for investigation of anharmonic effect in solid. One way to derive the Grünisen parameter is by considering the entropy of the system in the quasiharmonic form (Barron 1995) T TV SS i i i ),(ω ∑= 1 ln ln 1 ln )( − ∂ ∂ − ∂ ∂ −= ∑ TV TC ii i i ωω Vd d i i ln lnω γ −= 1 1 )( − − ∂ ∂ ∂ ∂ −= ∂ ∂ ∑ TTVT TC V S i V i T i i i V ωωω VT th C V V S ∂ ∂ =γ V T VP S V CVCV βαβα // == α is the coefficient of volume thermal expansion, V is the volume, and is isothermal and adiabatic compressibility respectively and Cv and Cp are specific heats at constant volume and constant pressure respectively dP vd Tl 1ln1 3 1 β γ += dP vd Ts 1ln1 3 1 β γ += ( ) 3 21 s el γγ γ + =
  70. 70. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Relation between SOEC and TOEC Even though we have not measured a set of individual TOEC, the TOEC can be obtained from the pressure derivatives of the second order elastic constants )2( )22( 1211 16614444121144 CC CCCCC P C + ++++ = ∂ ∂ )2(2 )233( 1211 1231111211 ' CC CCCC P C + −++ = ∂ ∂ )2(3 )26( 1211 123112111 CC CCC P B + ++ = ∂ ∂
  71. 71. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion
  72. 72. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Outline • Glass in General • Ultrasonic Waves • Physical Properties of Glass – Preparation – Density and Molar Volume • Elastic Properties – Theory – Compositional Dependence – Temperature Dependence – Hydrostatic Pressure Dependence • Conclusion Glass prism
  73. 73. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Conclusion • The general discussion on basic glass and its preparation, as well as the fundamental of elastic properties have been discussed • Experimental shows the physical and elastic properties of glasses were found slightly affected by the changes in the glass composition. • The densities of most glasses increases as the glass modifier content was added to substitute the glass former content while their molar volume increases or decreases due to the composition. •The experimental setup has been discussed for evaluating the ultrasonic and elastic properties of materials at low temperatures and high pressure. •There are possibility in evaluating the elastic properties of any glass based materials at elevated temperatures and pressure in order to obtain their elastic behaviour.
  74. 74. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Acknowledgement Glass Research Group • Dr Halimah Ahmad Kamari • Prof Madya Dr Zainal Abidin Talib • Prof Madya Dr Wan Daud Wan Yusof • Dr Khamirul Amin Matori • Prof Dr Abdul Halim Shaari • Our postgraduate students Special thanks to MOSTI and UPM for financial support.
  75. 75. Glass in General | Ultrasonic Waves | Physical Properties | Preparation | Elastic Properties | Conclusion Thank you for your attention drsidekaziz@gmail.com

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