Determination of the activation energy for crystal growth by differential thermal analysis

A method for determining the activation energy for crystal growth was calculated on the basis of the heat balance in the differential thermal analysis (DTA) measurements and the mechanism of nucleation and growth. The theoretical analysis showed that the term ln[C _pd(δT)/dt+KδT] should be a linear function of l/T, whereC _p is the heat capacity of sample and sample holder,K is the heat transfer coefficient,δT is the temperature difference between the sample and reference substance andt is the time. The energy term,E _D, obtained by multiplying the slope of the resulting straight line byR is indicative of the activation energy for crystal growth. It was shown thatE _D should be three times the activation energy for crystal growth when bulk nucleation is dominant, and equal to that for crystal growth only when surface nucleation predominates. The result of the analysis was tested by comparing the experimentally determinedE _D's with the activation energy for viscous flow, which was known to represent that for crystal growth. TheE _D for Li₂O·2SiO₂ glass with dominant bulk nucleation, approached three times the activation energy for viscous flow, as the heating rate in DTA decreased. TheE _D for 33.3Li₂O·66.7SiO₂·3TiO₂ glass with dominant surface nucleation approached the activation energy for viscous flow as the heating rate increased, suggesting the validity of the analysis.     

Influence of water content on the rates of crystal nucleation and growth in lithia-silica and soda-lime-silica glasses

Two sets of glasses were studied with compositions close to Li₂O·2SiO₂ and Na₂O·2CaO·3SiO₂, and with water contents ranging from 0.019 to 0.136 wt% and 0.007 to 0.040 wt%, respectively. The crystal nucleation and growth rates increased markedly with increase in water content, whereas the viscosities of the glasses decreased. For the lithia glasses, increases in nucleation rates at various temperatures closely corresponded to reductions in viscosity, indicating that the main effect of water was to lower the kinetic barrier to nucleation (G _D), rather than to alter the thermodynamic barrier to nucleation (W*). For the soda-lime glasses, G _D was also lowered by water content but additional effects due to differences in base compositions were observed. The kinetic barriers to growth were lowered by water content for both sets of glasses, increases in growth rates corresponding closely to reductions in the viscosities. It is suggested that the large effects of water on nucleation and growth may be due to an increase in the oxygen ion diffusion coefficient. In the soda-lime glasses addition of sodium fluoride produced similar effects to the addition of water. Liquidus temperature measurements, and the results of DTA, optical microscopy and electron microscopy are also reported.     

Determination of the activation energies for nucleation and growth of crystal nuclei in metallic glasses

A mathematical procedure is proposed in order to determine separately the activation energy for nucleation,E _n, and for growth,E _g, from isothermal crystallization experiments on metallic glasses. Differential scanning calorimetry (DSC) is used in the isothermal mode to estimate the crystalline fraction as a function of time. The model deals only with polymorphic and eutectic growth. Cu₆₀Zr₄₀ amorphous alloys produced with different quenching rates are taken as an example for demonstrating the ability of the proposed method. It is shown that the number of pre-nuclei can be related to the conditions of the initial quench.     

A differential method of determining the thermal properties of materials

A method for determining the thermal properties of materials is described, which enables one to distinguish small differences in the thermal properties of two specimens. Only two galvanometer readings need to be taken. The method belongs to the category of electrical measurements of nonelectrical quantities.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 20, No. 2, pp. 268–273, February, 1971.     

A simple differential thermal analysis technique for determining the pressure dependence of solid-liquid and solid-solid transition temperatures

A simple differential thermal analysis technique for determining solid-liquid and solid-solid transition temperatures as functions of pressure is described. The important feature of the technique is the use of a thin-walled ptfe tube both to contain the sample and to transmit pressure to it. The method has been tested at temperatures in the range 200–310 K at pressures of up to 350 MPa. Transition temperatures as functions of pressure are reported for benzene, carbon tetrachloride, and acetonitrile and compared with literature data.     

A hybrid experimental-numerical procedure for determining creep crack growth rates

Creep crack growth in a nickel base superalloy at elevated temperatures was analyzed through a hybrid experimental-numerical (HEN) procedure. This HEN procedure consisted of simultaneous use of creep crack growth test displacement data from center cracked plate specimens of IN-100 at 732°C and a theoretical finite element model of the test specimen.A method for getting creep crack growth behavior solely from high resolution displacement measurements, in conjunction with a cracked specimen model which utilizes realistic constitutive relationships, has been developed. The constitutive law, in the form of the Bodner-Partom material model, was especially tailored to the nickel base superalloy studied which displays time-dependent nonlinear inelastic behavior at elevated temperatures. It has been demonstrated that the technique can be applied where crack extension is very small and could not otherwise be resolved by conventional experimental crack measuring techniques. This method provides realistic monotonically increasing crack growth values. The predictions agreed to within 10% of post-test measurements.     

A thermal elastic model for constrained crystal growth with facets

A model for computing thermal stress inside a crystal with facets is presented. Using a systematical perturbation analysis, a semi-analytical thermal-stress solution is obtained for constrained directional growth with small lateral heat flux. This solution can be applied to crystals grown by various growth techniques such as the Czochralski method. The semi-analytical nature of the solution leads to a much more efficient approach for computing thermal stress in crystals with facets, compared to a full 3D simulation. Examples are given for crystals pulled in a variety of seed orientations.     

Ultrasonic method for determining the thermal diffusivity of materials

A method is proposed for determining the thermal diffusivity of materials by recording the amplitude variation of resonance vibrations of a disk-shaped specimen of the investigated material subjected to heat flux.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 30, No. 6, pp. 965–971, June, 1976.     

A contact method of determining the thermal effusivity of solids

A contact method of measuring the thermal effusivity of solids, based on periodic heating of the surface of a standard plate, in contact with the solid being investigated, and measuring the temperature oscillations in the plate at various distances from the source, is described.     

A new method of determining the thermal activity of nonmetals

A method is described for determining the thermal activity of nonmetallic materials from the magnitude of the control current flowing in the measuring circuit. This method does not require the use of thermocouples and automatic potentiometric recorders.Notation ) thermal conductivity - a thermal diffusivity - U_h0 voltage drop at heater with bridge balanced     

The application of differential thermal analysis by high temperature microscopy to kinetic and structural studies on the crystallisation of glasses

The application of a recently developed micro differential thermal analyser (DTA) to studies on the crystallisation of glasses is described.The technique permits continuous visual observation of microdroplets of melts and glasses during thermal analysis over a wide range of heating and cooling rates.Nucleation and crystallisation processes can be studied in conjunction with techniques of X-ray diffraction and electron microscopy. Crystal growth rates can be measured. Semiquantitative values for the heats of crystallisation of glasses can be obtained and kinetic data relating to the rate at which glasses undergo volume crystallisation can be derived from an analysis of the thermograms.The scope of the technique in linking structural information with the thermal and kinetic data associated with transformations in glasses is illustrated with data from three lithium aluminosilicate glasses.     

Interpretation of the thermal curve in differential thermal analysis

On the basis of an analysis of the heat transfer between samples and the surrounding medium, principles are formulated for the correct interpretation of the thermal curves in DTA. The influence of the type of phase transformation and the test conditions on the form of the thermal curve is shown.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 3, pp. 480–486, March, 1979.     

Knudsen effect in determining the thermal conductivity of gases by the coaxial-cylinder method

The properties of the thermal conductivity of gases are investigated by the coaxial-cylinder method at low pressures. It is established that there is a temperature-jump effect, which must be taken into account, especially for light gases at P1 atm and room temperature.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 36, No. 3, pp. 472–479, March, 1979.     

A modified method of determining the thermal constants of nonmetallic materials

We describe a method and the experimental set-up for a comprehensive determination of thermal constants. The method is applied to reinforced composite materials.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 33, No. 6, pp. 1052–1057, December, 1977.     

Extended three-dimensional generalized differential quadrature method: The basic equations and thermal vibration analysis of functionally graded fiber orientation rectangular plates

The present article deals with free vibration of functionally graded fiber orientation rectangular plates considering temperature effect. Three different types of fiber orientation distributions through the thickness of the plate are proposed. The properties of the plate are assumed to be temperature-dependent. Equations of motions are derived based on a three-dimensional theory of elasticity. General differential quadrature method is used to discretize these equations. Effects of temperature, fiber orientation, and boundary conditions besides some geometric parameters are presented. Also, some interesting conclusions are obtained since temperature and functionality of a functionally graded plate have a significant effect on the natural frequency of the plate.