CBE4010 Introduction to Materials Science for Chemical Engineers Chapter 9 Principles of Solidification

Study the principles of solidification as they apply to pure metals.

Examine the mechanisms by which solidification occurs.

Examine how techniques such as welding, brazing, and soldering are used for joining metals.

9.1 Technological Significance

9.2 Nucleation

9.3 Applications of Controlled Nucleation

9.4 Growth Mechanisms

9.5 Solidification Time and Dendrite Size

9.6 Cooling Curves

9.7 Cast Structure

9.8 Solidification Defects

9.9 Casting Processes for Manufacturing Components

9.10 Continuous Casting and Ingot Casting

9.11 Directional Solidification (DS), Single Crystal Growth, and

Epitaxial Growth

9.12 Solidification of Polymers and Inorganic Glasses

9.13 Joining of Metallic Materials

Solidification - an extremely important technology used to control the properties of many melt-derived products as well as a tool for the manufacturing of modern engineered materials.

Primary processing - Processes involving casting of molten metals into ingots or semi-finished useful shapes such as slabs.

Secondary processing - Processes such as rolling, extrusion, etc. used to process ingots or slabs and other semi-finished shapes, i.e., sheets, wires, rods, plates, etc..

Section 9.1 Technological Significance

Nucleation - The physical process by which a new phase is produced in a material.

Critical radius (r*) - The minimum size that must be formed by atoms clustering together in the liquid before the solid particle is stable and begins to grow.

Undercooling - The temperature to which the liquid metal must cool below the equilibrium freezing temperature before nucleation occurs.

Homogeneous nucleation - Formation of a critically sized solid from the liquid by the clustering together of a large number of atoms at a high undercooling (without an external interface).

Section 9.2 Nucleation

Heterogeneous nucleation - Formation of a critically sized solid from the liquid on an impurity surface.

Calculate the size of the critical radius and the number of atoms in the critical nucleus when solid copper forms by homogeneous nucleation. Comment on the size of the nucleus and assumptions we made while deriving the equation for radius of nucleus.

Example 9.1 Calculation of Critical Radius for the Solidification of Copper

Grain size strengthening: Grain refinement or inoculation - The addition of heterogeneous nuclei (grain refiners, inoculants) in a controlled manner to increase the number of grains in a casting.

ex) a combination of 0.03% titanium and 0.01%boron is added to many liquid-aluminum alloys. Tiny particles of an Al3Ti or TiB2 form and serve as sites of heterogeneous nucleation.

Second-phase strengthening, Dispersion strengthening - Increase in strength of a metallic material by generating resistance to dislocation motion by the introduction of small clusters of a second material.

Solid-state phase transformation - A change in phase that occurs in the solid state.

Glasses: Rapid solidification processing - Producing unique material structures by promoting unusually high cooling rates during solidification.

ex) metallic glass: cooling rates of 106 ºC/s or higher

colored glass, photochromic glass: nano-sized crystallites of different materials

are deliberately nucleated. The crystals are small and ,hence, do not make the

glass opaque.

Glass–ceramics: free from porosity, mechanically stronger, and often much more resistant to thermal shock. nucleating agent: titania(TiO2), zirconia(ZrO2). Up to 99.9% crystallinity can be obtained. If the grain size is kept small(50-100nm), glass-ceramics can often be made transparent.

9.3 Applications of Controlled Nucleation

Once the solid nuclei of a phase forms, growth begins to occur as more atoms become attached to the solid surface. The nature of the growth of the solid nuclei depends on how heat is removed from the molten material.-the specific heat of the liquid and the latent heat of fusion.

Planar growth –The growth of a smooth solid-liquid interface during solidification, when no undercooling of the liquid is present. If the liquid is well inoculated, undercooling is almost zero and growth would be mainly via the

planar front solidification mechanism. The latent heat of fusion is removed by

conduction from the solid-liquid interface.

9.4 Growth Mechanisms

Dendritic Growth – When the liquid is not inoculated and the nucleation is poor, the liquid has to be undercooled before the solid forms. The treelike structure of the solid that grows when an undercooled liquid solidifies.

Dendritic growth continues until the undercooled liquid warms to freezing temperature.

The difference between planar and dendritic growth arises because of the different sinks for the latent heat of fusion. The container or mold must absorb the heat in planar growth, but the undercooled liquid absorbs the heat in dendritic growth.

Dendrites in 9% nickel steel

1. Fern Forst: A

cross sectional

SEM picture of a

TiO2 thin film

deposited by the

metalorganic CVD

technique in the

extrime diffusion

limited region.

2. Dendrite

formation on the

facture surface of

a single crystal

turbine blade

made from a

high-performance

nickel-based

alloy.

SOLID/LIQUID INTERFACE CURVATURE

Thermodynamic Equilibrium Temperature

(1) First, consider the solid/liquid interface on the molecular scale. Basically, growth rate of a

crystal depends upon the net difference between the rates of attachment and detachment of

molecules at the interface.

(2) At equilibrium, at planar interface, there is a balance between attachment and

detachment of molecules at the interface which gives the normal thermodynamic melting

point, Tm.

(3) However, on a convex surface, which is defined as positive curvature, molecules binding

with fewer nearest neighbors compared with a planar interface are more easily detached,

and, thus, the thermodynamic equilibrium temperature is lowered. Conversely, the melting

point of a concave surface is increased.

Schematic Diagram of the Molecular Structure of S/L Interface

Gibbs-Thomson Equation

The amount of the “capillary” effect is given by the well-known Gibbs-Thomson

relationship:

where Tm is the melting point of pure substance at the planer interface;

Te is the equilibrium temperature at the curved surface;

γ is the solid/liquid surface tension;

L is the latent heat of fusion per unit volume;

κ is the total curvature of surface.

Therefore, the capillary effect lowers the melting point, and thereby reduces the

driving force for heat transfer from the interface which is convex to the melt. This

stabilizes the solidification front.

Chill zone - A region of small, randomly oriented grains that forms at the surface of a casting as a result of heterogeneous nucleation.

Columnar zone - A region of elongated grains having a preferred orientation that forms as a result of competitive growth during the solidification of a casting.

Equiaxed zone - A region of randomly oriented grains in the center of a casting produced as a result of widespread nucleation.

9.7 Cast Structure

Directional solidification (DS) - A solidification technique in which cooling in a given direction leads to preferential growth of grains in the opposite direction, leading to an anisotropic-oriented microstructure.

blades and vanes in turbine engines manufactured by castings:

titanium, cobalt or nickel based super alloys.

Better creep and fracture resistance - DS or SC technique.

9.11 Directional Solidification (DS), Single Crystal Growth, and Epitaxial Growth

.

Figure 9-11 Controlling grain structure in turbine blades: (a) conventional equiaxed grains, (b) directionally solidified columnar grains, and (C) single crystal.

Single Crystal Growth

Polycrystalline materials cannot be used effectively in many electronic and optical applications. Grain boundaries and other defects interfere with the mechanisms that provide useful electrical or optical functions. Therefore, high purity single crystals must be used.

Czochralski method, Bridgman method, Floating-zone method

Jan Czochralski ca 1907

Figure 19-22 (a) Czochralski growth technique for growing single crystals of silicon. (b) Overall steps encountered in the processing of semiconductors.

Overall semiconductor processing

1. Raw Material Processing - Material Purification

Single Crystal Growth

Substrate( wafer ) Manufacturing

2. Device Fabrication – Doping ( Dopant Diffusion )

Photolithography ( Patterning ) - Photoresist, Etching

Thin Films technology- CVD, Epitaxy, etc..

3. Testing and Packaging

Raw Material Processing

A Bi12(NbZn)O20 crystal grown by Czochralski method

50mm dia silicon crystal growing By the floating-zone method

Figure 19-22 (c) Production of an FET (Field effect transistor) semiconductor device:

(i) A p-type silicon substrate is oxidized.

(ii) Photolithography, ultraviolet radiation passing through a photomask, exposes a portion of the photoresist layer.

(iii) The exposed photoresist is dissolved.

(iv) The exposed silica is removed by etching.

(v) An n-type dopant is introduced to produce the source and drain.

(vi) The silicon is again oxidized.

(vii) Photolithography is repeated to introduce other components, including electrical leads, for the device.

Device fabrication

Etching(식각)-chemical etching/plasma etching Wet etching(liquid etchant)/dry etching(reactive gas) Selective Etching(by reactive gas)/nonselective etching(by sputtering ) Isotropic etching/anisotropic etching

Epitaxial growth - Growth of a material via epitaxy.

Homoepitaxy - Growth of a highly oriented material onto a crystal of the same material.

Heteroepitaxy - Growth of a highly oriented material onto a different substrate material.

Simulation of Rotating Pedestal CVD reactor

Zone melting(Zone Refining) is a method of separation by melting in which a molten zone traverses a long ingot of impure metal or chemical. In its common use for purification, the molten region melts impure solid at its forward edge and leaves a wake of purer material solidified behind it as it moves through the ingot. The impurities concentrate in the melt, and are moved to one end of the ingot. Zone refining was developed by Bill Pfann in Bell Telephone Laboratories as a method to prepare high purity materials for manufacturing transistors. Its early use was on germanium for this purpose, but it can be extended to virtually any solute-solvent system having an appreciable concentration difference between solid and liquid phases at equilibrium.