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Thermoelastic stresses in ribbons and tubes grown from the melt by the Stepanov method

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Abstract

Ribbons and tubes grown from the melt by the Stepanov technique have a wide range of technical applications. Sapphire ribbons are used as substrates in microelectronics and sapphire tubes are used as gas-discharge balloons in laser engineering, fine chemical technology and high-vacuum equipment. Practice has shown that misorientation angles of small-angle boundaries in sapphire crystals should not exceed several degrees because an increase in the misorientation angles between blocks drastically lowers the strength and worsens the dielectric properties of these crystals. One of the main mechanisms of formation of the block structure of melt-grown crystals, including shaped sapphire crystals, is dislocation polygonization that begins when the dislocation density exceeds a certain critical value. In turn, dislocations are formed under deformations due to thermal stresses. Calculations of thermal fields in crystals and the corresponding thermoelastic stress fields can be used as an input to improve and optimize the growth process. The dependence of thermoelastic stresses in ribbons and tubes on the technological parameters has been calculated.

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Abbreviations

α1 :

Thermal diffusivity of the melt

α2 :

Thermal diffusivity of the crystal

k 1 :

Thermal conductivity of the melt

k 2 :

Thermal conductivity of the crystal

V 1 :

Velocity vector of the melt

V 2 :

Velocity vector of the growing crystal

V 0 :

Crystal pulling rate

ΔH f :

Latent heat of fusion

ρ1 :

Density of the melt

ρ2 :

Density of the crystal

in :

Interface normal vector

τ :

Crystal-melt interface normal vector

t :

Interface tangential vector

s :

Sided crystal-melt tangential vector

T m :

Melting temperature

T e :

Ambient temperature

T 01 :

Temperature at the bottom of the meniscus

T 02 :

Crystal temperature at the top of the meniscus

τ :

Normal vector at lateral surfaces of the crystal and meniscus

σ:

Stefan-Boltzmann constant

ε1 :

Emissivity of the meniscus lateral surface

ε2 :

Emissivity of the crystal lateral surface

g :

Acceleration due to gravity

ΣLG :

Melt-gas surface tension

a :

Die half dimension

φ0 :

Angle of growth

αt :

Thermal expansion coefficient

h 1 :

Heat transfer coefficient of the melt

h 2 :

Heat transfer coefficient of the crystal

C αs:

Heat capacity

E :

Young's modulus

ν:

Poisson's coefficient

μ:

Melt kinematic viscosity

P :

Pressure in the melt

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Authors and Affiliations

  1. Institute of Solid State Physics, Russian Academy of Sciences, 142432, Chernogolovka, Moscow district, Russia

    A. V. Zhdanov, L. P. Nikolaeva & S. N. Rossolenko

Authors
  1. A. V. Zhdanov
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  2. L. P. Nikolaeva
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  3. S. N. Rossolenko
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Zhdanov, A.V., Nikolaeva, L.P. & Rossolenko, S.N. Thermoelastic stresses in ribbons and tubes grown from the melt by the Stepanov method. JOURNAL OF MATERIALS SCIENCE 30, 75–84 (1995). https://doi.org/10.1007/BF00352134

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  • DOI: https://doi.org/10.1007/BF00352134

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