Lecture 26: Crystallization PHYS 430/603 material Laszlo Takacs UMBC Department of Physics

Nucleation Heterogeneous nucleation: Nuclei form at pre-existing surfaces, so that little extra surface is created, the energy barrier is small. The most typical places for heterogeneous nucleation are the wall of the container and high- melting particles present in the melt. Temperature independent. Homogeneous nucleation: Nuclei form due to the random motion of atoms in the melt. Increases with lowering temperature, dominates far below the melting point. In order to achieve large undercooling, heterogeneous nucleation has to be avoided. The best is a small droplet with “no room” for a seed particle, levitated freely in a rf magnetic field. In industrial settings only a few degrees of undercooling take place, but ~15% of T m is possible in the laboratory. Nucleation and crystallization can be avoided with fast cooling between T m, where the formation of nuclei can start, to T 0, where diffusion becomes negligible.

The nucleation rate Crystallization - can be avoided, by fast enough cooling to avoid the nucleation line. This is how metallic glasses are made. Finish Start A deep eutectic point often makes the formation of a glassy phase possible. Ni-P is an interesting system because it can also be made amorphous by mechanical alloying and Ni-P coatings deposited by electrochemical methods can also be amorphous.

STM images of a crystalline Zr and a glassy Zr-Ni-Al-Cu alloy

Mechanical property comparison for a bulk metallic glass Notice the very competitive properties and the uniquely high elastic limit.

Stability and phase transformation - always of interest in the case of metastable materials. Crystallization of Fe(80)B(20) glass  Fe + Fe 4 B  Fe + Fe 3 B  Fe + Fe 2 B It takes place in several steps, with the formation of simpler (thus easier-to-nucleate) but still metastable intermediate phases. Magnetism - promising for soft magnetic material: no crystal structure, no magnetocrystalline anisotropy; stress sensitivity (anisotropy due to magnetostriction) can be minimized by varying the composition E.g.: (Fe 1-x Co x ) 75 Si 15 B 10 shows zero magnetostriction at about x = 0.9 Even if rapid quenching from the melt does not result in a glassy phase, the first phase to form is not the most stable one but the one that nucleates the most easily. Quite often metastable crystalline compounds form. An interesting case is quasicrystals, alloys that have no translational periodicity but possess five-fold rotational symmetry. Nucleation is also an important component of solid-solid phase transformations e.g. during recrystallization.

“Ordinary” crystallization at moderate cooling rates: The role of heat flow during solidification Heat flow is an important component of solidification. Heat has to be conducted away to lower the temperature to below the melting point. Solidification is an exothermic process, the latent heat has to be take away also. Heat balance of dx: heat flow into crystal - heat flow from liquid = latent heat Heat flows toward the (colder) solid: stable solidification front Heat flows toward the liquid (colder due to undercooling and latent heat): instability

Undercooling and the warming from solidification can lead to inverse temperature gradient even if the melt is solidifying in a cold container. The resulting instability leads to the formation of dendrites - a very common phenomenon, not a rare occurrence.

The mechanism behind crystal habit These Wulff diagrams show the direction dependence of the surface energy and the resultant external shape of the crystal. The lowest energy faces grow the fastest during crystallization. This is the reason behind crystal habit, the most obvious external feature of crystals. Historically, crystallography developed from the study of habit way before the existence of atoms had been proven.

The crystallization of alloys: 1. Fast diffusion in both S & L; system is always in equilibrium. 2. Fast diffusion in L, little in S; coring 3. Slow diffusion in L & S; constitutional supercooling, dendrites. Solidification results in concentration differences. Initial Sn concentration is 23 at.%. On cooling: 1.Pb-Sn(12%) crystallizes first. 2.The (uniform) Sn content of the liquid increases. The concentration of the solid also shifts, the (Pb) phase develops coring. 3.The liquid reaches the eutectic point, the solid is Pb-Sn(29%). 4.Simultaneous crystallization of Pb-Sn(29%) and Sn-Pb(1.4%) usually in a lamellar structure.

Zone melting Suppose we have a PbSn(23 at.%) rod, melt a short section at the left end and move the molten region (the heater) to the right. The Sn content of the left end will be only 12%; the Sn will move to the right. Repeating the process several times purifies the left end and concentrates the Sn (or any other impurity) on the right. This is one of the most important methods of material purification (electro- refining is another.)

Solidification in a mold Heat flow, cooling rate, variation of impurity concentration determines the micro- structure of cast metals: 1.Chill zone, fast cooling fast nucleation, many small grains. 2.Columnar growth in the direction of the heat flow. Only grains with low- energy face in the right direction grow. 3.Impurities are swept toward the middle, more random nucleation and the formation of equiaxed grains can take place. 4.Volume decrease results in a shrinkage pipe.

Nucleation in the solid state Most transformations in the solid state - such as precipitation - begin with nucleation also. Interface energy is the smallest for coherent boundaries, larger for semi- coherent boundaries, the largest for incoherent phase boundaries. A phase with low interface energy can form, even if it is not the phase with the lowest free energy. Other factors:Direction dependence of the interface energy. Volume change and related elastic energy.

Spinodal decomposition Consider the free energy of a two- component alloy system that shows phase separation in equilibrium. If it is cooled very quickly from the melt (quenched) solid solution may be obtained with a concentration outside the equilibrium solubility range. At a concentration where the G(C) curve is convex from below, e.g c 1, decomposing the solid solution to two regions with slightly different concentrations increases G, it will not happen. (Notice that the equilibrium state at c 1 is a two-phase state.) But at a concentration where the G(C) curve is concave from below, e.g c 3, decomposing the solid solution to two regions with slightly different concentrations decreases G. There is a driving force for phase separation by gradual change of concentration distribution. Usually a lamellar microstructure develops - Gunier-Preston zones.

For a regular solution with H AA = H BB, the Gibbs free energy as a function of concentration is: Spinodal decomposition is possible between the inflection points - the zeros of the second derivative: Decomposition is energetically favorable anywhere between the two end-points of the common tangent. But outside the spinodal range, it can only start with nucleation.

Nucleation versus spinodal decomposition