The ''α''-factor is a
dimensionless quantity
Dimensionless quantities, or quantities of dimension one, are quantities implicitly defined in a manner that prevents their aggregation into unit of measurement, units of measurement. ISBN 978-92-822-2272-0. Typically expressed as ratios that a ...
used to predict the solid–liquid
interface
Interface or interfacing may refer to:
Academic journals
* ''Interface'' (journal), by the Electrochemical Society
* '' Interface, Journal of Applied Linguistics'', now merged with ''ITL International Journal of Applied Linguistics''
* '' Inter ...
type of a material during
solidification
Freezing is a phase transition in which a liquid turns into a solid when its temperature is lowered below its freezing point.
For most substances, the melting and freezing points are the same temperature; however, certain substances possess dif ...
. It was introduced by physicist Kenneth A. Jackson in 1958. In his model, crystal growth with larger values of ''α'' is smooth, whereas crystals growing at smaller ''α'' (below the threshold value of 2) have rough surfaces.
Method
According to John E. Gruzleski in his book ''Microstructure Development During Metalcasting'' (1996):
:
where
is the
latent heat of fusion
In thermodynamics, the enthalpy of fusion of a substance, also known as (latent) heat of fusion, is the change in its enthalpy resulting from providing energy, typically heat, to a specific quantity of the substance to change its state from a s ...
;
is the
Boltzmann constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative thermal energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin (K) and the ...
;
is the
freezing temperature at equilibrium;
is the number of nearest neighbours an
atom
Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
has in the interface
plane; and
is the number of nearest neighbours in the bulk solid.
As
, where
is the
molar entropy of fusion
In thermodynamics, the entropy of fusion is the increase in entropy when melting a solid substance. This is almost always positive since the degree of disorder increases in the transition from an organized crystalline solid to the disorganized ...
of the material,
:
According to Martin Glicksman in his book ''Principles of Solidification: An Introduction to Modern Casting and Crystal Growth Concepts'' (2011):
:
where
is the
universal gas constant
The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant, expressed in units of energy per temperature, temperature ...
.
is similar to previous, always
< 1.
References
Materials science
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