Precipitation strengthening
Encyclopedia
Precipitation hardening, also called age hardening, is a heat treatment
technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium
, magnesium
, nickel
and titanium
, and some stainless steel
s. It relies on changes in solid solubility
with temperature
to produce fine particles of an impurity phase
, which impede the movement of dislocation
s, or defects in a crystal
's lattice
. Since dislocations are often the dominant carriers of plasticity
, this serves to harden the material. The impurities play the same role as the particle substances in particle-reinforced composite materials. Just as the formation of ice in air can produce clouds, snow, or hail, depending upon the thermal history of a given portion of the atmosphere, precipitation
in solids can produce many different sizes of particles, which have radically different properties. Unlike ordinary tempering
, alloys must be kept at elevated temperature for hours to allow precipitation to take place. This time delay is called aging. Solution treatment and aging is sometimes abbreviated "STA" in metals specs and certs
.
Note that two different heat treatments involving precipitates can alter the strength of a material: solution heat treating and precipitation heat treating. Solid solution strengthening
involves formation of a single-phase solid solution via quenching and leaves a material softer. Precipitation heat treating involves the addition of impurity particles to increase a material's strength. Precipitation hardening via precipitation heat treatment is the main topic of discussion in this article.
, and involves careful balancing of the driving force for precipitation and the thermal activation energy available for both desirable and undesirable processes.
Nucleation
occurs at a relatively high temperature (often just below the solubility limit) so that the kinetic
barrier of surface energy
can be more easily overcome and the maximum number of precipitate particles can form. These particles are then allowed to grow at lower temperature in a process called aging. This is carried out under conditions of low solubility
so that thermodynamics
drive a greater total volume of precipitate formation.
Diffusion
's exponential dependence upon temperature makes precipitation strengthening, like all heat treatments, a fairly delicate process. Too little diffusion (under aging), and the particles will be too small to impede dislocations effectively; too much (over aging), and they will be too large and dispersed to interact with the majority of dislocations.
. While a large volume of precipitate particles is desirable, a small enough amount of the alloying element should be added that it remains easily soluble at some reasonable annealing
temperature.
Elements used for precipitation strengthening in typical aluminum and titanium alloys, make up about 10% of their composition. While binary alloys are more easily understood as an academic exercise, commercial alloys often use three components for precipitation strengthening, in compositions such as Al(Mg, Cu
) and Ti(Al, V
). A large number of other constituents may be unintentional, but benign, or may be added for other purposes such as grain refinement or corrosion
resistance. In some cases, such as many aluminum alloys, an increase in strength is achieved at the expense of corrosion resistance.
The addition of large amounts of nickel and chromium needed for corrosion resistance in stainless steels means that traditional hardening and tempering methods are not effective. However, precipitates of chromium, copper or other elements can strengthen the steel by similar amounts in comparison to hardening and tempering. The strength can be tailored by adjusting the annealing process, with lower initial temperatures resulting in higher strengths. The lower initial temperature increase driving force of nucleation. More driving force means more nucleation sites, and more sites, means more places for dislocations to be disrupted while the finished part is in use.
Many alloy systems allow the aging temperature to be adjusted. For instance, some aluminium alloys used to make rivets for aircraft construction are kept in dry ice
from their initial heat treatment until they are installed in the structure. After this type of rivet is deformed into its final shape, aging occurs at room temperature and increases its strength, locking the structure together. Higher aging temperatures would risk over-aging other parts of the structure, and require expensive post-assembly heat treatment. Too high of an aging temperature promotes the precipitate to grow too readily.
The presence of second phase particles often causes lattice distortions. These lattice distortions result when the precipitate particles differ in size and crystallographic structure from the host atoms. Smaller precipitate particles in a host lattice leads to a tensile stress, whereas larger precipitate particles leads to a compressive stress. Dislocation defects also create a stress field. Above the dislocation there is a compressive stress and below there is a tensile stress. Consequently, there is a negative interaction energy between a dislocation and a precipitate that each respectively cause a compressive and a tensile stress or vice versa. In other words, the dislocation will be attracted to the precipitate. In addition, there is a positive interaction energy between a dislocation and a precipitate that have the same type of stress field. This means that the dislocation will be repulsed by the precipitate.
Precipitate particles also serve by locally changing the stiffness of a material. Dislocations are repulsed by regions of higher stiffness. Conversely, if the precipitate causes the material to be locally more compliant, then the dislocation will be attracted to that region.
Furthermore, a dislocation may cut through a precipitate particle. This interaction causes an increase in the surface area of the particle. The area created is
where, r is the radius of the particle and b is the magnitude of the burgers vector. The resulting increase in surface energy is
where
is the surface energy. The dislocation can also bow around
a precipitate particle.
Dislocations cutting through particles:
where
is material strength, 
is the second phase particle radius, 
is the surface energy, 
is the magnitude of the Burgers vector
, and
is the spacing between pinning points. This governing equation shows that the strength is proportional to 
, the radius of the precipitate particles. This means that it is easier for dislocations to cut through a material with smaller second phase particles (small r). As the size of the second phase particles increases, the particles impede dislocation movement and it becomes increasingly difficult for the particles to cut through the material. In other words, the strength of a material increases with increasing r.
Dislocations bowing around particle:
where
is the material strength, 
is the shear modulus, 
is the magnitude of the Burgers vector, 
is the distance between pinning points, and 
is the second phase particle radius. This governing equation shows that for dislocation bowing the strength is inversely proportional to the second phase particle radius r. Dislocation bowing, also called Orowan strengthening, is more likely to occur when there are large particles present in the material.
These governing equations show that the precipitation hardening mechanism depends on the size of the precipitate particles. At small r, cutting will dominate, while at large r, bowing will dominate.
Looking at the plot of both equations, it is clear that there is a critical radius at which max strengthening occurs. This critical radius is typically 5-30 nm.
Heat treatment
Heat treating is a group of industrial and metalworking processes used to alter the physical, and sometimes chemical, properties of a material. The most common application is metallurgical. Heat treatments are also used in the manufacture of many other materials, such as glass...
technique used to increase the yield strength of malleable materials, including most structural alloys of aluminium
Aluminium
Aluminium or aluminum is a silvery white member of the boron group of chemical elements. It has the symbol Al, and its atomic number is 13. It is not soluble in water under normal circumstances....
, magnesium
Magnesium
Magnesium is a chemical element with the symbol Mg, atomic number 12, and common oxidation number +2. It is an alkaline earth metal and the eighth most abundant element in the Earth's crust and ninth in the known universe as a whole...
, nickel
Nickel
Nickel is a chemical element with the chemical symbol Ni and atomic number 28. It is a silvery-white lustrous metal with a slight golden tinge. Nickel belongs to the transition metals and is hard and ductile...
and titanium
Titanium
Titanium is a chemical element with the symbol Ti and atomic number 22. It has a low density and is a strong, lustrous, corrosion-resistant transition metal with a silver color....
, and some stainless steel
Stainless steel
In metallurgy, stainless steel, also known as inox steel or inox from French "inoxydable", is defined as a steel alloy with a minimum of 10.5 or 11% chromium content by mass....
s. It relies on changes in solid solubility
Solubility
Solubility is the property of a solid, liquid, or gaseous chemical substance called solute to dissolve in a solid, liquid, or gaseous solvent to form a homogeneous solution of the solute in the solvent. The solubility of a substance fundamentally depends on the used solvent as well as on...
with temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...
to produce fine particles of an impurity phase
Phase (matter)
In the physical sciences, a phase is a region of space , throughout which all physical properties of a material are essentially uniform. Examples of physical properties include density, index of refraction, and chemical composition...
, which impede the movement of dislocation
Dislocation
In materials science, a dislocation is a crystallographic defect, or irregularity, within a crystal structure. The presence of dislocations strongly influences many of the properties of materials...
s, or defects in a crystal
Crystal
A crystal or crystalline solid is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating pattern extending in all three spatial dimensions. The scientific study of crystals and crystal formation is known as crystallography...
's lattice
Crystal structure
In mineralogy and crystallography, crystal structure is a unique arrangement of atoms or molecules in a crystalline liquid or solid. A crystal structure is composed of a pattern, a set of atoms arranged in a particular way, and a lattice exhibiting long-range order and symmetry...
. Since dislocations are often the dominant carriers of plasticity
Plasticity (physics)
In physics and materials science, plasticity describes the deformation of a material undergoing non-reversible changes of shape in response to applied forces. For example, a solid piece of metal being bent or pounded into a new shape displays plasticity as permanent changes occur within the...
, this serves to harden the material. The impurities play the same role as the particle substances in particle-reinforced composite materials. Just as the formation of ice in air can produce clouds, snow, or hail, depending upon the thermal history of a given portion of the atmosphere, precipitation
Precipitation (chemistry)
Precipitation is the formation of a solid in a solution or inside anothersolid during a chemical reaction or by diffusion in a solid. When the reaction occurs in a liquid, the solid formed is called the precipitate, or when compacted by a centrifuge, a pellet. The liquid remaining above the solid...
in solids can produce many different sizes of particles, which have radically different properties. Unlike ordinary tempering
Tempering
Tempering is a heat treatment technique for metals, alloys and glass. In steels, tempering is done to "toughen" the metal by transforming brittle martensite or bainite into a combination of ferrite and cementite or sometimes Tempered martensite...
, alloys must be kept at elevated temperature for hours to allow precipitation to take place. This time delay is called aging. Solution treatment and aging is sometimes abbreviated "STA" in metals specs and certs
Product certification
Product certification or product qualification is the process of verifying that a certain product has passed performance tests and quality assurance tests or qualification requirements stipulated in contracts, regulations, or specifications...
.
Note that two different heat treatments involving precipitates can alter the strength of a material: solution heat treating and precipitation heat treating. Solid solution strengthening
Solid solution strengthening
Solid solution strengthening is a type of alloying that can be used to improve the strength of a pure metal. The technique works by adding atoms of one element to the crystalline lattice of another element . The alloying element diffuses into the matrix, forming a solid solution...
involves formation of a single-phase solid solution via quenching and leaves a material softer. Precipitation heat treating involves the addition of impurity particles to increase a material's strength. Precipitation hardening via precipitation heat treatment is the main topic of discussion in this article.
Kinetics versus thermodynamics
This technique exploits the phenomenon of supersaturationSupersaturation
The term supersaturation refers to a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances...
, and involves careful balancing of the driving force for precipitation and the thermal activation energy available for both desirable and undesirable processes.
Nucleation
Nucleation
Nucleation is the extremely localized budding of a distinct thermodynamic phase. Some examples of phases that may form by way of nucleation in liquids are gaseous bubbles, crystals or glassy regions. Creation of liquid droplets in saturated vapor is also characterized by nucleation...
occurs at a relatively high temperature (often just below the solubility limit) so that the kinetic
Chemical kinetics
Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition...
barrier of surface energy
Surface energy
Surface energy quantifies the disruption of intermolecular bonds that occur when a surface is created. In the physics of solids, surfaces must be intrinsically less energetically favorable than the bulk of a material, otherwise there would be a driving force for surfaces to be created, removing...
can be more easily overcome and the maximum number of precipitate particles can form. These particles are then allowed to grow at lower temperature in a process called aging. This is carried out under conditions of low solubility
Solubility equilibrium
Solubility equilibrium is a type of dynamic equilibrium. It exists when a chemical compound in the solid state is in chemical equilibrium with a solution of that compound. The solid may dissolve unchanged, with dissociation or with chemical reaction with another constituent of the solvent, such as...
so that thermodynamics
Thermodynamics
Thermodynamics is a physical science that studies the effects on material bodies, and on radiation in regions of space, of transfer of heat and of work done on or by the bodies or radiation...
drive a greater total volume of precipitate formation.
Diffusion
Diffusion
Molecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...
's exponential dependence upon temperature makes precipitation strengthening, like all heat treatments, a fairly delicate process. Too little diffusion (under aging), and the particles will be too small to impede dislocations effectively; too much (over aging), and they will be too large and dispersed to interact with the majority of dislocations.
Alloy design
Precipitation strengthening is possible if the line of solid solubility slopes strongly toward the center of a phase diagramPhase diagram
A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions at which thermodynamically distinct phases can occur at equilibrium...
. While a large volume of precipitate particles is desirable, a small enough amount of the alloying element should be added that it remains easily soluble at some reasonable annealing
Annealing (metallurgy)
Annealing, in metallurgy and materials science, is a heat treatment wherein a material is altered, causing changes in its properties such as strength and hardness. It is a process that produces conditions by heating to above the recrystallization temperature, maintaining a suitable temperature, and...
temperature.
Elements used for precipitation strengthening in typical aluminum and titanium alloys, make up about 10% of their composition. While binary alloys are more easily understood as an academic exercise, commercial alloys often use three components for precipitation strengthening, in compositions such as Al(Mg, Cu
Copper
Copper is a chemical element with the symbol Cu and atomic number 29. It is a ductile metal with very high thermal and electrical conductivity. Pure copper is soft and malleable; an exposed surface has a reddish-orange tarnish...
) and Ti(Al, V
Vanadium
Vanadium is a chemical element with the symbol V and atomic number 23. It is a hard, silvery gray, ductile and malleable transition metal. The formation of an oxide layer stabilizes the metal against oxidation. The element is found only in chemically combined form in nature...
). A large number of other constituents may be unintentional, but benign, or may be added for other purposes such as grain refinement or corrosion
Corrosion
Corrosion is the disintegration of an engineered material into its constituent atoms due to chemical reactions with its surroundings. In the most common use of the word, this means electrochemical oxidation of metals in reaction with an oxidant such as oxygen...
resistance. In some cases, such as many aluminum alloys, an increase in strength is achieved at the expense of corrosion resistance.
The addition of large amounts of nickel and chromium needed for corrosion resistance in stainless steels means that traditional hardening and tempering methods are not effective. However, precipitates of chromium, copper or other elements can strengthen the steel by similar amounts in comparison to hardening and tempering. The strength can be tailored by adjusting the annealing process, with lower initial temperatures resulting in higher strengths. The lower initial temperature increase driving force of nucleation. More driving force means more nucleation sites, and more sites, means more places for dislocations to be disrupted while the finished part is in use.
Many alloy systems allow the aging temperature to be adjusted. For instance, some aluminium alloys used to make rivets for aircraft construction are kept in dry ice
Dry ice
Dry ice, sometimes referred to as "Cardice" or as "card ice" , is the solid form of carbon dioxide. It is used primarily as a cooling agent. Its advantages include lower temperature than that of water ice and not leaving any residue...
from their initial heat treatment until they are installed in the structure. After this type of rivet is deformed into its final shape, aging occurs at room temperature and increases its strength, locking the structure together. Higher aging temperatures would risk over-aging other parts of the structure, and require expensive post-assembly heat treatment. Too high of an aging temperature promotes the precipitate to grow too readily.
Theory
The primary species of precipitation strengthening are second phase particles. These particles impede the movement of dislocations throughout the lattice. You can determine whether or not second phase particles will precipitate into solution from the solidus line on the phase diagram for the particles. Physically, this strengthening effect can be attributed both to size and modulus effects, and to interfacial or surface energy.The presence of second phase particles often causes lattice distortions. These lattice distortions result when the precipitate particles differ in size and crystallographic structure from the host atoms. Smaller precipitate particles in a host lattice leads to a tensile stress, whereas larger precipitate particles leads to a compressive stress. Dislocation defects also create a stress field. Above the dislocation there is a compressive stress and below there is a tensile stress. Consequently, there is a negative interaction energy between a dislocation and a precipitate that each respectively cause a compressive and a tensile stress or vice versa. In other words, the dislocation will be attracted to the precipitate. In addition, there is a positive interaction energy between a dislocation and a precipitate that have the same type of stress field. This means that the dislocation will be repulsed by the precipitate.
Precipitate particles also serve by locally changing the stiffness of a material. Dislocations are repulsed by regions of higher stiffness. Conversely, if the precipitate causes the material to be locally more compliant, then the dislocation will be attracted to that region.
Furthermore, a dislocation may cut through a precipitate particle. This interaction causes an increase in the surface area of the particle. The area created is
where, r is the radius of the particle and b is the magnitude of the burgers vector. The resulting increase in surface energy is
where
is the surface energy. The dislocation can also bow arounda precipitate particle.
Governing Equations
There are two equations to describe the two mechanisms for precipitation hardening:Dislocations cutting through particles:
where
is material strength, is the second phase particle radius, is the surface energy, is the magnitude of the Burgers vectorBurgers vector
The Burgers vector, named after Dutch physicist Jan Burgers, is a vector, often denoted b, that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice....
, and
is the spacing between pinning points. This governing equation shows that the strength is proportional to , the radius of the precipitate particles. This means that it is easier for dislocations to cut through a material with smaller second phase particles (small r). As the size of the second phase particles increases, the particles impede dislocation movement and it becomes increasingly difficult for the particles to cut through the material. In other words, the strength of a material increases with increasing r.Dislocations bowing around particle:
where
is the material strength, is the shear modulus, is the magnitude of the Burgers vector, is the distance between pinning points, and is the second phase particle radius. This governing equation shows that for dislocation bowing the strength is inversely proportional to the second phase particle radius r. Dislocation bowing, also called Orowan strengthening, is more likely to occur when there are large particles present in the material.These governing equations show that the precipitation hardening mechanism depends on the size of the precipitate particles. At small r, cutting will dominate, while at large r, bowing will dominate.
Looking at the plot of both equations, it is clear that there is a critical radius at which max strengthening occurs. This critical radius is typically 5-30 nm.
Some precipitation hardening materials
- 2000-series aluminum alloys (important examples: 2024 and 2019, also Y alloyY alloyY alloy is a nickel-containing aluminium alloy. It was developed by the National Physical Laboratory during World War I, in attempt to find an aluminium alloy that would retain its strength at high temperatures....
and HiduminiumHiduminiumThe Hiduminium or R.R. alloys are a series of high-strength, high-temperature aluminium alloys, developed for aircraft use by Rolls-Royce before World War II. They were manufactured and later developed by High Duty Alloys Ltd....
) - 6000-series aluminum alloys (important example: 6061 for bicycle frames and aeronautical structures)
- 7000-series aluminum alloys (important examples: 7075 and 7475)
- 17-4PH stainless steel (UNSUnified numbering systemThe unified numbering system is an alloy designation system widely accepted in North America. It consists of a prefix letter and five digits designating a material composition. A prefix of S indicates stainless steel alloys, C for copper, brass, or bronze alloys, T for tool steels, etc...
S17400) - Maraging steelMaraging steelMaraging steels are steels which are known for possessing superior strength and toughness without losing malleability, although they cannot hold a good cutting edge. Aging refers to the extended heat-treatment process...
- InconelInconelInconel is a registered trademark of Special Metals Corporation that refers to a family of austenitic nickel-chromium-based superalloys. Inconel alloys are typically used in high temperature applications. It is often referred to in English as "Inco"...
718 - Alloy X-750
- René 41René 41René 41 is a nickel-based high temperature alloy developed by General Electric which retains high strength in the 1200/1800°F temperature range...
- WaspaloyWaspaloyWaspaloy is a registered trademark of United Technologies Corp that refers to an age hardening austenitic nickel-based superalloy. Waspaloy alloy is typically used in high temperature applications, particularly in gas turbines.-Nominal composition:...
See also
- Alfred WilmAlfred WilmAlfred Wilm , was a German metallurgist, who invented the alloy Al-3.5–5.5%Cu-Mg-Mn, now known as duraluminium, which is used extensively in aircraft....
- Strength of MaterialsStrength of materialsIn materials science, the strength of a material is its ability to withstand an applied stress without failure. The applied stress may be tensile, compressive, or shear. Strength of materials is a subject which deals with loads, deformations and the forces acting on a material. A load applied to a...
- Strengthening mechanisms of materialsStrengthening mechanisms of materialsMethods have been devised to modify the yield strength, ductility, and toughness of both crystalline and amorphous materials. These strengthening mechanisms give engineers the ability to tailor the mechanical properties of materials to suit a variety of different applications. For example, the...
- MetallurgyMetallurgyMetallurgy is a domain of materials science that studies the physical and chemical behavior of metallic elements, their intermetallic compounds, and their mixtures, which are called alloys. It is also the technology of metals: the way in which science is applied to their practical use...
- SuperalloySuperalloyA superalloy, or high-performance alloy, is an alloy that exhibits excellent mechanical strength and creep resistance at high temperatures, good surface stability, and corrosion and oxidation resistance. Superalloys typically have a matrix with an austenitic face-centered cubic crystal structure. ...