Crystal growth

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Crystallization
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Schematic of a small part of a growing crystal. The crystal is of (blue) cubic particles on a simple cubic lattice. The top layer is incomplete, only ten of the sixteen lattice positions are occupied by particles. A particle in the fluid (shown with red edges) is joining the crystal, growing the crystal by one particle. It is joining the lattice at the point where its energy will be a minimum, which is in the corner of the incomplete top layer (on top of the particle shown with yellow edges). Its energy will be a minimum because in that position it has three neighbors (one below, one to its left and one above right) which it will interact with. All other positions on an incomplete crystal layer have only one or two neighbours. Schematic of crystal growth of simple cubic lattice, showing additional molecule adding in corner.png
Schematic of a small part of a growing crystal. The crystal is of (blue) cubic particles on a simple cubic lattice. The top layer is incomplete, only ten of the sixteen lattice positions are occupied by particles. A particle in the fluid (shown with red edges) is joining the crystal, growing the crystal by one particle. It is joining the lattice at the point where its energy will be a minimum, which is in the corner of the incomplete top layer (on top of the particle shown with yellow edges). Its energy will be a minimum because in that position it has three neighbors (one below, one to its left and one above right) which it will interact with. All other positions on an incomplete crystal layer have only one or two neighbours.

A crystal is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. Crystal growth is a major stage of a crystallization process, and consists of the addition of new atoms, ions, or polymer strings into the characteristic arrangement of the crystalline lattice. [1] [2] The growth typically follows an initial stage of either homogeneous or heterogeneous (surface catalyzed) nucleation, unless a "seed" crystal, purposely added to start the growth, was already present.

Contents

The action of crystal growth yields a crystalline solid whose atoms or molecules are close packed, with fixed positions in space relative to each other. The crystalline state of matter is characterized by a distinct structural rigidity and very high resistance to deformation (i.e. changes of shape and/or volume). Most crystalline solids have high values both of Young's modulus and of the shear modulus of elasticity. This contrasts with most liquids or fluids, which have a low shear modulus, and typically exhibit the capacity for macroscopic viscous flow.

Overview

After successful formation of a stable nucleus, a growth stage ensues in which free particles (atoms or molecules) adsorb onto the nucleus and propagate its crystalline structure outwards from the nucleating site. This process is significantly faster than nucleation. The reason for such rapid growth is that real crystals contain dislocations and other defects, which act as a catalyst for the addition of particles to the existing crystalline structure. By contrast, perfect crystals (lacking defects) would grow exceedingly slowly. [3] On the other hand, impurities can act as crystal growth inhibitors and can also modify crystal habit. [4]

Nucleation

Silver crystal growing on a ceramic substrate. Silver surface crystal growth SEM.png
Silver crystal growing on a ceramic substrate.

Nucleation can be either homogeneous, without the influence of foreign particles, or heterogeneous, with the influence of foreign particles. Generally, heterogeneous nucleation takes place more quickly since the foreign particles act as a scaffold for the crystal to grow on, thus eliminating the necessity of creating a new surface and the incipient surface energy requirements.

Heterogeneous nucleation can take place by several methods. Some of the most typical are small inclusions, or cuts, in the container the crystal is being grown on. This includes scratches on the sides and bottom of glassware. A common practice in crystal growing is to add a foreign substance, such as a string or a rock, to the solution, thereby providing nucleation sites for facilitating crystal growth and reducing the time to fully crystallize.

The number of nucleating sites can also be controlled in this manner. If a brand-new piece of glassware or a plastic container is used, crystals may not form because the container surface is too smooth to allow heterogeneous nucleation. On the other hand, a badly scratched container will result in many lines of small crystals. To achieve a moderate number of medium-sized crystals, a container which has a few scratches works best. Likewise, adding small previously made crystals, or seed crystals, to a crystal growing project will provide nucleating sites to the solution. The addition of only one seed crystal should result in a larger single crystal.

Mechanisms of growth

An example of the cubic crystals typical of the rock-salt structure. ImgSalt.jpg
An example of the cubic crystals typical of the rock-salt structure.
Time-lapse of growth of a citric acid crystal. The video covers an area of 2.0 by 1.5 mm and was captured over 7.2 min.

The interface between a crystal and its vapor can be molecularly sharp at temperatures well below the melting point. An ideal crystalline surface grows by the spreading of single layers, or equivalently, by the lateral advance of the growth steps bounding the layers. For perceptible growth rates, this mechanism requires a finite driving force (or degree of supercooling) in order to lower the nucleation barrier sufficiently for nucleation to occur by means of thermal fluctuations. [5] In the theory of crystal growth from the melt, Burton and Cabrera have distinguished between two major mechanisms: [6] [7] [8]

Non-uniform lateral growth

The surface advances by the lateral motion of steps which are one interplanar spacing in height (or some integral multiple thereof). An element of surface undergoes no change and does not advance normal to itself except during the passage of a step, and then it advances by the step height. It is useful to consider the step as the transition between two adjacent regions of a surface which are parallel to each other and thus identical in configuration—displaced from each other by an integral number of lattice planes. Note here the distinct possibility of a step in a diffuse surface, even though the step height would be much smaller than the thickness of the diffuse surface.

Uniform normal growth

The surface advances normal to itself without the necessity of a stepwise growth mechanism. This means that in the presence of a sufficient thermodynamic driving force, every element of surface is capable of a continuous change contributing to the advancement of the interface. For a sharp or discontinuous surface, this continuous change may be more or less uniform over large areas for each successive new layer. For a more diffuse surface, a continuous growth mechanism may require changes over several successive layers simultaneously.

Non-uniform lateral growth is a geometrical motion of steps—as opposed to motion of the entire surface normal to itself. Alternatively, uniform normal growth is based on the time sequence of an element of surface. In this mode, there is no motion or change except when a step passes via a continual change. The prediction of which mechanism will be operative under any set of given conditions is fundamental to the understanding of crystal growth. Two criteria have been used to make this prediction:

Whether or not the surface is diffuse: a diffuse surface is one in which the change from one phase to another is continuous, occurring over several atomic planes. This is in contrast to a sharp surface for which the major change in property (e.g. density or composition) is discontinuous, and is generally confined to a depth of one interplanar distance. [9] [10]

Whether or not the surface is singular: a singular surface is one in which the surface tension as a function of orientation has a pointed minimum. Growth of singular surfaces is known to requires steps, whereas it is generally held that non-singular surfaces can continuously advance normal to themselves. [11]

Driving force

Consider next the necessary requirements for the appearance of lateral growth. It is evident that the lateral growth mechanism will be found when any area in the surface can reach a metastable equilibrium in the presence of a driving force. It will then tend to remain in such an equilibrium configuration until the passage of a step. Afterward, the configuration will be identical except that each part of the step will have advanced by the step height. If the surface cannot reach equilibrium in the presence of a driving force, then it will continue to advance without waiting for the lateral motion of steps.

Thus, Cahn concluded that the distinguishing feature is the ability of the surface to reach an equilibrium state in the presence of the driving force. He also concluded that for every surface or interface in a crystalline medium, there exists a critical driving force, which, if exceeded, will enable the surface or interface to advance normal to itself, and, if not exceeded, will require the lateral growth mechanism.

Thus, for sufficiently large driving forces, the interface can move uniformly without the benefit of either a heterogeneous nucleation or screw dislocation mechanism. What constitutes a sufficiently large driving force depends upon the diffuseness of the interface, so that for extremely diffuse interfaces, this critical driving force will be so small that any measurable driving force will exceed it. Alternatively, for sharp interfaces, the critical driving force will be very large, and most growth will occur by the lateral step mechanism.

Note that in a typical solidification or crystallization process, the thermodynamic driving force is dictated by the degree of supercooling.

Morphology

Silver sulfide whiskers growing out of surface-mount resistors. SilverSulfideWhiskers1.jpg
Silver sulfide whiskers growing out of surface-mount resistors.

It is generally believed that the mechanical and other properties of the crystal are also pertinent to the subject matter, and that crystal morphology provides the missing link between growth kinetics and physical properties. The necessary thermodynamic apparatus was provided by Josiah Willard Gibbs' study of heterogeneous equilibrium. He provided a clear definition of surface energy, by which the concept of surface tension is made applicable to solids as well as liquids. He also appreciated that an anisotropic surface free energy implied a non-spherical equilibrium shape, which should be thermodynamically defined as the shape which minimizes the total surface free energy. [12]

It may be instructional to note that whisker growth provides the link between the mechanical phenomenon of high strength in whiskers and the various growth mechanisms which are responsible for their fibrous morphologies. (Prior to the discovery of carbon nanotubes, single-crystal whiskers had the highest tensile strength of any materials known). Some mechanisms produce defect-free whiskers, while others may have single screw dislocations along the main axis of growth—producing high strength whiskers.

The mechanism behind whisker growth is not well understood, but seems to be encouraged by compressive mechanical stresses including mechanically induced stresses, stresses induced by diffusion of different elements, and thermally induced stresses. Metal whiskers differ from metallic dendrites in several respects. Dendrites are fern-shaped like the branches of a tree, and grow across the surface of the metal. In contrast, whiskers are fibrous and project at a right angle to the surface of growth, or substrate.

Diffusion-control

NASA animation of dendrite formation in microgravity. Dendrite formation.gif
NASA animation of dendrite formation in microgravity.
Pyrolusite (manganese(IV) oxides) dendrites on a limestone bedding plane from Solnhofen, Germany. Scale in mm. Dendrites01.jpg
Pyrolusite (manganese(IV) oxides) dendrites on a limestone bedding plane from Solnhofen, Germany. Scale in mm.

Very commonly when the supersaturation (or degree of supercooling) is high, and sometimes even when it is not high, growth kinetics may be diffusion-controlled. Under such conditions, the polyhedral crystal form will be unstable, it will sprout protrusions at its corners and edges where the degree of supersaturation is at its highest level. The tips of these protrusions will clearly be the points of highest supersaturation. It is generally believed that the protrusion will become longer (and thinner at the tip) until the effect of interfacial free energy in raising the chemical potential slows the tip growth and maintains a constant value for the tip thickness. [13]

In the subsequent tip-thickening process, there should be a corresponding instability of shape. Minor bumps or "bulges" should be exaggerated—and develop into rapidly growing side branches. In such an unstable (or metastable) situation, minor degrees of anisotropy should be sufficient to determine directions of significant branching and growth. The most appealing aspect of this argument, of course, is that it yields the primary morphological features of dendritic growth.

See also

Simulation

Related Research Articles

In physical chemistry, supersaturation occurs with a solution when the concentration of a solute exceeds the concentration specified by the value of solubility at equilibrium. Most commonly the term is applied to a solution of a solid in a liquid, but it can also be applied to liquids and gases dissolved in a liquid. A supersaturated solution is in a metastable state; it may return to equilibrium by separation of the excess of solute from the solution, by dilution of the solution by adding solvent, or by increasing the solubility of the solute in the solvent.

<span class="mw-page-title-main">Freezing</span> Phase transition in which a liquid turns into a solid due to a decrease in thermal energy

Freezing is a phase transition where a liquid turns into a solid when its temperature is lowered below its freezing point. In accordance with the internationally established definition, freezing means the solidification phase change of a liquid or the liquid content of a substance, usually due to cooling.

<span class="mw-page-title-main">Supercooling</span> Lowering the temperature of a liquid below its freezing point without it becoming a solid

Supercooling, also known as undercooling, is the process of lowering the temperature of a liquid below its freezing point without it becoming a solid. It is achieved in the absence of a seed crystal or nucleus around which a crystal structure can form. The supercooling of water can be achieved without any special techniques other than chemical demineralization, down to −48.3 °C (−54.9 °F). Supercooled water can occur naturally, for example in the atmosphere, animals or plants.

<span class="mw-page-title-main">Epitaxy</span> Crystal growth process relative to the substrate

Epitaxy refers to a type of crystal growth or material deposition in which new crystalline layers are formed with one or more well-defined orientations with respect to the crystalline seed layer. The deposited crystalline film is called an epitaxial film or epitaxial layer. The relative orientation(s) of the epitaxial layer to the seed layer is defined in terms of the orientation of the crystal lattice of each material. For most epitaxial growths, the new layer is usually crystalline and each crystallographic domain of the overlayer must have a well-defined orientation relative to the substrate crystal structure. Epitaxy can involve single-crystal structures, although grain-to-grain epitaxy has been observed in granular films. For most technological applications, single domain epitaxy, which is the growth of an overlayer crystal with one well-defined orientation with respect to the substrate crystal, is preferred. Epitaxy can also play an important role while growing superlattice structures.

In physics and chemistry, flash freezing is the process whereby objects are frozen in just a few hours by subjecting them to cryogenic temperatures, or through direct contact with liquid nitrogen at −196 °C (−320.8 °F). It is commonly used in the food industry.

<span class="mw-page-title-main">Pulsed laser deposition</span>

Pulsed laser deposition (PLD) is a physical vapor deposition (PVD) technique where a high-power pulsed laser beam is focused inside a vacuum chamber to strike a target of the material that is to be deposited. This material is vaporized from the target which deposits it as a thin film on a substrate. This process can occur in ultra high vacuum or in the presence of a background gas, such as oxygen which is commonly used when depositing oxides to fully oxygenate the deposited films.

<span class="mw-page-title-main">Dislocation</span> Linear crystallographic defect or irregularity

In materials science, a dislocation or Taylor's dislocation is a linear crystallographic defect or irregularity within a crystal structure that contains an abrupt change in the arrangement of atoms. The movement of dislocations allow atoms to slide over each other at low stress levels and is known as glide or slip. The crystalline order is restored on either side of a glide dislocation but the atoms on one side have moved by one position. The crystalline order is not fully restored with a partial dislocation. A dislocation defines the boundary between slipped and unslipped regions of material and as a result, must either form a complete loop, intersect other dislocations or defects, or extend to the edges of the crystal. A dislocation can be characterised by the distance and direction of movement it causes to atoms which is defined by the Burgers vector. Plastic deformation of a material occurs by the creation and movement of many dislocations. The number and arrangement of dislocations influences many of the properties of materials.

<span class="mw-page-title-main">Nanoparticle</span> Particle with size less than 100 nm

A nanoparticle or ultrafine particle is a particle of matter 1 to 100 nanometres (nm) in diameter. The term is sometimes used for larger particles, up to 500 nm, or fibers and tubes that are less than 100 nm in only two directions. At the lowest range, metal particles smaller than 1 nm are usually called atom clusters instead.

<span class="mw-page-title-main">Crystallization</span> Process by which a solid with a highly organized atomic or molecular structure forms

Crystallization is the process by which solid forms, where the atoms or molecules are highly organized into a structure known as a crystal. Some ways by which crystals form are precipitating from a solution, freezing, or more rarely deposition directly from a gas. Attributes of the resulting crystal depend largely on factors such as temperature, air pressure, and in the case of liquid crystals, time of fluid evaporation.

<span class="mw-page-title-main">Dendrite (crystal)</span> Crystal that develops with a typical multi-branching form

A crystal dendrite is a crystal that develops with a typical multi-branching form, resembling a fractal. The name comes from the Ancient Greek word δένδρον (déndron), which means "tree", since the crystal's structure resembles that of a tree. These crystals can be synthesised by using a supercooled pure liquid, however they are also quite common in nature. The most common crystals in nature exhibit dendritic growth are snowflakes and frost on windows, but many minerals and metals can also be found in dendritic structures.

<span class="mw-page-title-main">Nucleation</span> Initial step in the phase transition or molecular self-assembly of a substance

In thermodynamics, nucleation is the first step in the formation of either a new thermodynamic phase or structure via self-assembly or self-organization within a substance or mixture. Nucleation is typically defined to be the process that determines how long an observer has to wait before the new phase or self-organized structure appears. For example, if a volume of water is cooled below 0 °C, it will tend to freeze into ice, but volumes of water cooled only a few degrees below 0 °C often stay completely free of ice for long periods (supercooling). At these conditions, nucleation of ice is either slow or does not occur at all. However, at lower temperatures nucleation is fast, and ice crystals appear after little or no delay.

The Wegener–Bergeron–Findeisen process, is a process of ice crystal growth that occurs in mixed phase clouds in regions where the ambient vapor pressure falls between the saturation vapor pressure over water and the lower saturation vapor pressure over ice. This is a subsaturated environment for liquid water but a supersaturated environment for ice resulting in rapid evaporation of liquid water and rapid ice crystal growth through vapor deposition. If the number density of ice is small compared to liquid water, the ice crystals can grow large enough to fall out of the cloud, melting into rain drops if lower level temperatures are warm enough.

Critical radius is the minimum particle size from which an aggregate is thermodynamically stable. In other words, it is the lowest radius formed by atoms or molecules clustering together before a new phase inclusion is viable and begins to grow. Formation of such stable nuclei is called nucleation.

<span class="mw-page-title-main">Dendrite (metal)</span>

A dendrite in metallurgy is a characteristic tree-like structure of crystals growing as molten metal solidifies, the shape produced by faster growth along energetically favourable crystallographic directions. This dendritic growth has large consequences in regard to material properties.

<span class="mw-page-title-main">John W. Cahn</span> American scientist (1928–2016)

John Werner Cahn was an American scientist and recipient of the 1998 National Medal of Science. Born in Cologne, Weimar Germany, he was a professor in the department of metallurgy at the Massachusetts Institute of Technology (MIT) from 1964 to 1978. From 1977, he held a position at the National Institute of Standards and Technology. Cahn had a profound influence on the course of materials research during his career. One of the foremost authorities on thermodynamics, Cahn applied the basic laws of thermodynamics to describe and predict a wide range of physical phenomena.

Stranski–Krastanov growth is one of the three primary modes by which thin films grow epitaxially at a crystal surface or interface. Also known as 'layer-plus-island growth', the SK mode follows a two step process: initially, complete films of adsorbates, up to several monolayers thick, grow in a layer-by-layer fashion on a crystal substrate. Beyond a critical layer thickness, which depends on strain and the chemical potential of the deposited film, growth continues through the nucleation and coalescence of adsorbate 'islands'. This growth mechanism was first noted by Ivan Stranski and Lyubomir Krastanov in 1938. It wasn't until 1958 however, in a seminal work by Ernst Bauer published in Zeitschrift für Kristallographie, that the SK, Volmer–Weber, and Frank–van der Merwe mechanisms were systematically classified as the primary thin-film growth processes. Since then, SK growth has been the subject of intense investigation, not only to better understand the complex thermodynamics and kinetics at the core of thin-film formation, but also as a route to fabricating novel nanostructures for application in the microelectronics industry.

<span class="mw-page-title-main">Vapor–liquid–solid method</span> Mechanism to grow nano wires

The vapor–liquid–solid method (VLS) is a mechanism for the growth of one-dimensional structures, such as nanowires, from chemical vapor deposition. The growth of a crystal through direct adsorption of a gas phase on to a solid surface is generally very slow. The VLS mechanism circumvents this by introducing a catalytic liquid alloy phase which can rapidly adsorb a vapor to supersaturation levels, and from which crystal growth can subsequently occur from nucleated seeds at the liquid–solid interface. The physical characteristics of nanowires grown in this manner depend, in a controllable way, upon the size and physical properties of the liquid alloy.

<span class="mw-page-title-main">Colloidal crystal</span> Ordered array of colloidal particles

A colloidal crystal is an ordered array of colloidal particles and fine grained materials analogous to a standard crystal whose repeating subunits are atoms or molecules. A natural example of this phenomenon can be found in the gem opal, where spheres of silica assume a close-packed locally periodic structure under moderate compression. Bulk properties of a colloidal crystal depend on composition, particle size, packing arrangement, and degree of regularity. Applications include photonics, materials processing, and the study of self-assembly and phase transitions.

The strength of metal oxide adhesion effectively determines the wetting of the metal-oxide interface. The strength of this adhesion is important, for instance, in production of light bulbs and fiber-matrix composites that depend on the optimization of wetting to create metal-ceramic interfaces. The strength of adhesion also determines the extent of dispersion on catalytically active metal. Metal oxide adhesion is important for applications such as complementary metal oxide semiconductor devices. These devices make possible the high packing densities of modern integrated circuits.

Hoffman nucleation theory is a theory developed by John D. Hoffman and coworkers in the 1970s and 80s that attempts to describe the crystallization of a polymer in terms of the kinetics and thermodynamics of polymer surface nucleation. The theory introduces a model where a surface of completely crystalline polymer is created and introduces surface energy parameters to describe the process. Hoffman nucleation theory is more of a starting point for polymer crystallization theory and is better known for its fundamental roles in the Hoffman–Weeks lamellar thickening and Lauritzen–Hoffman growth theory.

References

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