The crystal nucleus is the growth center of the crystal.There are two ways to form crystal nucleus. If the probability of new crystal nucleus appearing in each region of the liquid phase is the same, it is called uniform nucleation.If in the liquid phase, the new phase preferentially nucleates in some regions, it is calledHeterogeneous nucleation。
To obtain the driving force necessary for the crystallization process, the actual crystallization temperature must be lower than the theoretical crystallization temperature (that is, the metal has supercooling phenomenon), so as to meet the thermodynamic conditions of crystallization.The greater the degree of supercooling, the greater the difference between the free energy of liquid and solid phases, that is, the greater the driving force of phase change, the faster the crystallization speed, so the metal must be supercooled during crystallization.
Structural conditions:
stayliquid metalThere will be some short-range ordered atomic clusters that disappear instantaneously, emerge one after another, and change indefinitely, as if some extremely small solid structures are constantly emerging in liquid metals.The changing short-range ordered atomic clusters are called structural fluctuations, or phase fluctuations.Only the relatively large phase fluctuations in the supercooled liquid can become embryos, but not all embryos can form nuclei, and the nucleation rules will be discussed later.[1]
Nucleation mode
There are two ways of nucleation, one is homogeneous nucleation, the other is heterogeneous nucleation.If it is attached to the particles of some impurities in the liquid metal, it is called heterogeneous nucleation or non spontaneous nucleation.If it does not depend on impurities and only depends on the liquid metal itself under certain undercooling conditions, the nucleation is called homogeneous nucleation or spontaneous nucleation.Two nucleation methods are introduced as follows:
Homogeneous nucleation
If the probability of new phase nucleation in each region of the liquid phase is the same, this nucleation mode is called homogeneous nucleation.
Satisfying this nucleation methodliquid metalIt is absolutely pure, without any impurities, and does not contact with the mold wall.It is just a process of nucleation directly from the crystal embryo depending on the energy change of liquid metal.Obviously, this is an ideal situation.[1]
In liquid metals, there are many regularly arranged "short range ordered" atomic groups.If above the melting point temperature, the growth of this regularly arranged atomic group will increase the free energy, so it is unstable.If it is below the melting point temperature, because the free energy of the solid phase is lower than the free energy of the liquid phase, at this time, the regularly arranged atomic groups in the liquid metal may stabilize and grow into crystal nuclei.[2]
Heterogeneous nucleation
In the liquid phase, the preferential nucleation of new phase in some regions is called heterogeneous nucleation.[1]
Figure 1[2]
Because pure metals inevitably contain some solid impurities and fine particles, these refractory impurities will be distributed in the metal liquid after the metal is melted.When a metal is crystallized, the crystal nucleus often first adheres to the surface of these impurities and forms.
In factliquid metalIt is impossible to be absolutely free of impurities, which always contain some solid impurities more or less.Therefore, the crystallization of actual metals is mostly heterogeneous nucleation.The process of heterogeneous nucleation follows the same rule as that of homogeneous nucleation.For the above two nucleation methods, heterogeneous nucleation is easier than homogeneous nucleation, and nucleation can be achieved under the condition of small undercooling.Heterogeneous nucleation and homogeneous nucleation and undercooling（
）It can be seen from Figure 1 that heterogeneous nucleation starts when the undercooling is small. When the nucleation rate of heterogeneous nucleation is already quite large, the homogeneous nucleation rate is insignificant.[2]
Energy change during nucleation
The crystallization of actual metal is mainly based onHeterogeneous nucleationThis nucleation method is relatively complicated.In order to facilitate the discussion, the uniform nucleation is first studied. The basic laws obtained from this study are not only instructive for the study of heterogeneous nucleation, but also the basis for the study of solid phase transition.
It was previously pointed out that not all embryos can be transformed into nuclei in supercooled liquids.In fact, only those embryos whose size is equal to or greater than a certain critical size can exist stably and grow spontaneously.This kind of embryo equal to or larger than the critical size is the nucleus.The reason why the nucleation of supercooled liquid requires a certain critical size of crystal nucleus needs to be analyzed from the change of energy during nucleation.
Under certain undercooling conditions, the free energy of the solid phase is lower than the free energy of the liquid phase. When there is a crystal embryo in this undercooled liquid, on the one hand, the free energy of the system will be reduced when the atoms change from liquid to solid, which is the driving force for crystallization;On the other hand, because the embryo forms a new surface and generates surface energy, the free energy of the system increases, which is the resistance of crystallization.If the volume of the embryo is V and the surface area is S, the difference between the free energy per unit volume of liquid and solid phases is
, surface energy per unit area is
. Then the total change of free energy of the system is:
Figure 2
It can be seen from the formula that the change of the volume free energy is proportional to the cube of the radius of the crystal embryo, and the change of the surface energy is proportional to the square of the radius.The total free energy is the algebraic sum of the volume free energy and the surface energy. Its change relationship with the radius of the crystal embryo is shown in Figure 2. It is formed by the superposition of the first term and the second term of the above equation.Since the first term is the volume free energy
While the second term, surface energy, decreases with
So when r increases, the volume free energy decreases faster than the surface energy.But at the beginning, the surface energy term is dominant. When r increases to some critical size, the reduction of the volume free energy will be dominant.So in
A maximum value appears on the relationship curve with r
, the corresponding r value is
。It can be seen from Figure 2 that when r<
With the increase of embryo size r, the free energy of the system increases. Obviously, this process cannot be carried out automatically.This kind of embryo can not become a stable nucleus, but forms and disappears instantaneously;When
When the size of the embryo increases, the free energy of the system decreases, and this process can be carried out automatically. The embryo can spontaneously grow into a stable nucleus, so it will no longer disappear;When
The embryo may disappear or grow into a stable nucleus, so the radius of
Relationship between nucleation and phase transition
The phase change begins with the nucleation of new phase.The new form was developed through the growth of the post formation nucleus, and finally ended in the elimination of the old form.The phase change process can be conveniently decomposed into four processes:
one
Realization of supersaturation state: caused by the change of temperature or pressure;
two
Nucleation generation of new phase: it can be divided into uniform nucleation in the old phase, or uneven nucleation due to the promotion of impurity surface or praseodymium position;
three
Grain growth from crystal nucleus: there are various growth modes, such as self shaped crystallization with free surface, irregular morphology formed due to grain boundary contact, regular domain structure like double crystal, etc;
four
The buffer process in which the tissue generated in the new phase changes to reach the normal state, and the process of changing from an unordered lattice to an ordered lattice.[3]
Nucleus growth
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stayliquid metalAfter the formation of the crystal nucleus, it will grow rapidly.The essence of crystal nucleus growth is the transfer of atoms from liquid to solid.That is, individual atoms hit the surface of the crystal nucleus one by one or simultaneously, and are connected with the crystal nucleus in the form of regular arrangement of atoms.The specific growth mode mainly depends on the temperature distribution in the liquid metal at the crystallization front.[2]
Nucleus formation and growth are carried out in batches.When the first batch of liquid metal is slightly larger thanCritical nucleus radiusThe crystallization process of liquid begins after the nucleation of.The crystallization process depends on the continuous generation of new nuclei, but more on the further growth of existing nuclei.For each single crystal (grain), after the stable nucleus appears, it immediately enters the growth stage.Macroscopically, the growth of crystal is a process in which the crystal interface gradually moves to the liquid phase;From a microscopic point of view, it is a process that depends on atoms diffusing from the liquid phase to the crystal surface one by one, and occupying appropriate positions one by one according to the requirements of the crystal lattice law, so as to combine with the crystal stably and firmly.
Conditions for crystal growth
It can be inferred from the above that the conditions for crystal growth are:
First, the liquid phase is required to continuously diffuse atoms to the crystal, which requires that the liquid phase has a sufficiently high temperature toliquid metalAtoms have sufficient diffusivity;
Second, it is required that the crystal surface can continuously and reliably accept these atoms.
However, the difficulty of accepting these atoms anywhere on the crystal surface is not the same. The location of accepting these atoms on the crystal surface is more or less related to the surface structure of the crystal, and should conform to the thermodynamic conditions of the crystallization process. This means that the reduction of the volume free energy of the crystal growth should be greater than the increase of the crystal surface energy. Therefore,Crystal growth must be carried out in supercooled liquid, but it requires much less supercooling than nucleation.
Generally speaking,liquid metalThe diffusion and migration of atoms are not very difficult. Therefore, the main factors determining the growth mode and growth rate of crystals are the interface structure of the crystal nucleus, the temperature distribution near the interface, and the release and dissipation conditions of latent heat.The combination of the two determines the shape of the crystal after growth.Since the crystal morphology is related to the structure after crystallization, attention should be paid to the crystal morphology and its influencing factors.
Crystal growth mechanism
Due to the different microstructure of the interface, its ability to accept atoms migrated from the liquid phase is also different, so there will be different mechanisms when the crystal grows.
1. Two dimensional nucleation growth mechanism
Figure 3
When the solid-liquid interface is smooth, it is difficult to form a stable state if a single liquid atom diffuses and migrates to the interface. This is because the increase in surface free energy it brings is far greater than the decrease in volume free energy.In this case, the growth of the crystal can only rely on the so-called two-dimensional nucleation mode, that is, relying on the structural fluctuations and energy fluctuations in the liquid phase, so that a certain size of atomic clusters almost simultaneously fall to the smooth interface, forming a flat atomic cluster with an atomic thickness and a certain width, as shown in Figure 3.
According to thermodynamic analysis, the reduction of the volume free energy brought by this atomic group must be greater than the increase of its surface energy, so that it can form a stable state on the smooth interface.Looks like a wetting angle
Is the same as the non-uniform shape ofCritical nucleus radiusThe nucleus is a two-dimensional nucleus.
After the two-dimensional crystal nucleus is formed, steps appear around it, and the liquid atoms migrated backward fill these steps one by one, so that the increased surface energy is small, until the entire interface is covered with a layer of atoms, it becomes a smooth interface again, and then a new two-dimensional crystal nucleus is required to form, otherwise the growth will be interrupted.When a crystal grows up in this way, its growth speed is very slow (the linear speed of crystal growth in unit time is called growth speed, which is expressed in G
)。
2. Screw dislocation growth mechanism
In general, the growth rate of crystals with smooth interfaces is much faster than that of two-dimensional nuclei. This is because it is always difficult to avoid the formation of various defects when the crystals grow up. The interface steps caused by these defects make it easy for atoms to stack upward, so the growth rate is faster than that of two-dimensional nuclei.The screw dislocation is exposed on the crystal surface, that is, steps are formed on the crystal surface. In this way, the liquid atoms are piled up to these steps one by one, and the newly added surface energy is very small, which can be completely compensated by the reduction of the volume free energy.
Each row of atoms is paved, and the step moves forward a distance between atoms. Therefore, the linear velocity of the step moving forward along the crystal surface is equal everywhere.However, because the starting point of the step is not moving, the angular velocity of the step moving relative to the starting point is not equal everywhere.The closer to the starting point, the greater the angular velocity;The farther away from the starting point, the smaller the angular velocity.Thus, with the spreading of atoms, the steps first bend, and then spiral around the starting point. The steps will never disappear, so the process continues.Every time the step sweeps across the interface, the crystal will thicken an atomic spacing. However, because of the fast cyclotron speed of the center, the center will inevitably protrude to form a screw like crystal. The spirally rising crystal face is called "growth curl line".
3. Vertical growth mechanism
On the smooth interface, the ability to accept liquid atoms varies with the location.At the step, the liquid atoms are firmly bonded with the crystal, so the step plays a very important role in the growth of the crystal.However, the steps on the smooth interface can not be generated spontaneously, and can only be generated by two-dimensional nuclei.
This fact means that: on the one hand, the discontinuity of growth on the smooth interface (when the crystal has grown a layer, a new step can be generated only by re forming a two-dimensional crystal nucleus);On the other hand, it shows that crystal defects (such as screw dislocation) play an important role in the smooth interface growth, and these defects provide endless steps.But on the rough interface, almost half of the atomic positions that should be arranged according to the crystal rules are vacant, and the atoms diffused from the liquid phase can easily fill these positions and connect with the crystal.Since the ability of these positions to receive atoms is equivalent, all positions on the rough interface are growth positions, so the liquid phase atoms can be added to the interface continuously and vertically, and the properties of the interface will never change, so that the interface will move rapidly toward the liquid phase.The crystal defects do not play an obvious role in the growth process of the rough interface.
This growth is called vertical growth.It grows very fast, and most metal crystals grow in this way.
