Essential Foundational Knowledge in Materials Science

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The theoretical foundations of materials science include:

Mechanics: Materials Mechanics

Thermodynamics: Materials Thermodynamics

Physics: Materials Physics

Chemistry: Materials Chemistry

Dynamics (Theoretical Mechanics): Materials Dynamics

Electrochemistry: Materials Electrochemistry

Surface Science, Interfaces, and Surfaces: Materials Surface Science, Materials Interfaces, and Surfaces

Understanding material science helps us to do better engineering. Below are the details.


Atoms are regularly arranged in a three-dimensional space with a fixed melting point and anisotropy.

Intermediate Phase

When two groups of elements A and B form an alloy, in addition to forming solid solutions based on A or B, a new phase with a crystal structure different from both A and B groups may also be formed. These phases are usually called intermediate phases as they are typically located in the middle on a binary phase diagram.

Metastable Phase

Metastable phase refers to a phase that cannot exist stably thermodynamically but temporarily stabilizes during rapid cooling or heating due to thermodynamic barriers or kinetic factors preventing its transformation into a stable phase.

Coordination Number

The number of nearest and equidistant atoms surrounding any atom in a crystal structure.


After heating a metal that has undergone cold deformation to a certain temperature, undistorted new grains are formed in the original deformed structure. This process, known as recrystallization, leads to significant changes in properties, reverting them to the state before deformation.


Under non-equilibrium solidification conditions, alloys with certain sub-eutectic or super-eutectic compositions may exhibit a eutectic microstructure. This eutectic structure formed from non-eutectic components is termed pseudo-eutectic.

Cross Slip

When a screw dislocation encounters resistance on its original slip plane, it may move to another intersecting slip plane to continue slipping. This process is called cross slip.


After solution treatment of aluminum alloys, precipitation of GP zones, θ”, θ’, and θ occurs during heating and holding. Overaging happens when extended holding leads to the precipitation of θ’, resulting in a decrease in hardness and strength, which is referred to as overaging.

Strain Hardening

After cold plastic deformation of a metal, its strength and hardness increase while ductility and toughness decrease. This phenomenon is known as strain hardening.

Solid Solution Strengthening

The phenomenon of increased strength in a metal alloy is due to the addition of alloying elements (impurities) that form a solid solution with the metal matrix.

Dispersion Strengthening

Materials composed of two or more phases, where one phase consists of fine particles dispersed throughout the material, often exhibit increased strength, known as dispersion strengthening.

Incomplete Dislocation

A dislocation for which the Burgers vector is not an integer multiple of the lattice vector is referred to as an incomplete dislocation.

Extended Dislocation

Usually refers to the decomposition of a full dislocation into two incomplete dislocations separated by a stacking fault.

Screw Dislocation

A dislocation where atoms near the dislocation line are arranged in a helical pattern is called a screw dislocation.

Peritectic Transformation

In a binary phase diagram, peritectic transformation refers to the isothermal transformation of a solid phase and the remaining liquid phase to form another solid phase.

Eutectic Transformation

The transformation is where a liquid phase separates into two different solid phases.

Eutectoid Transformation

The transformation is where one solid phase decomposes to form two different solid phases.

Uphill Diffusion

The process of solute atoms diffusing from a low concentration to a high concentration region indicates that the driving force for diffusion is a chemical potential gradient rather than a concentration gradient.

Interstitial Diffusion

A mechanism of atomic diffusion where small-sized atoms move through interstitial sites in the crystal lattice, hopping from one interstitial position to an adjacent one.

Composition Undercooling

The actual temperature at the liquid interface is lower than the solidification temperature determined by solute distribution.

First-Order Phase Transition

A phase transition is where the chemical potentials of the new and old phases are equal, but the first-order partial derivatives of the chemical potential are not equal.

Second-Order Phase Transition

In terms of thermodynamics, a phase transition where the free energy (enthalpy) of the two phases is equal, the first-order derivatives of the free energy (enthalpy) are equal, but the second-order derivatives are not equal. Examples include magnetic transitions, order-disorder transitions, and normal-superconducting transitions.

Coherent Phase Boundary

If all atoms on the interface between two phases have a one-to-one matching relationship, occupying lattice points in both crystal lattices simultaneously, it is called a coherent phase boundary.

Precipitation Hardening

The process where supersaturated solid solutions decompose into two phases with the same structure but different compositions at a certain temperature.

Tempering Embrittlement

During the tempering process of quenched steel, plasticity and toughness usually increase with the tempering temperature. However, within a specific tempering temperature range, a phenomenon known as tempering embrittlement occurs, leading to a decrease in toughness. There are two types: first and second-class tempering embrittlement, each with different temperature ranges, influencing factors, and characteristics.

Recrystallization Annealing

Recrystallization annealing refers to the process of heating a metal that has undergone cold deformation to a temperature above the recrystallization temperature, holding it for a certain time, and then slowly cooling it to room temperature.

Tempered Martensite

The structure formed by tempering quenched steel at a temperature between 400-600°C, consisting of equiaxed ferrite and fine particles (worm-like) of carbide.

Ordered Solid Solution

When one component dissolves in another, and the atoms of each component occupy separate Bravais lattice points, forming a solid solution with an ordered arrangement of atoms, it is called an ordered solid solution.

Heterogeneous Nucleation

The nucleation of a new phase at heterogeneities present in the parent phase, such as impurities or foreign surfaces in the liquid phase.

Martensitic Transformation

The phase transformation process in which steel, when heated to the austenite phase and then rapidly quenched, undergoes a significant increase in hardness, forming a needle-like structure known as martensite.

Bainitic Transformation

The transformation in steel that occurs below the pearlite transformation temperature but above the martensite transformation temperature (550°C-230°C), known as bainitic transformation.

Age Hardening of Aluminum Alloys

The phenomenon of significant increases in strength and hardness of aluminum alloys over time after quenching, also known as age hardening.

Thermoelastic Martensitic Transformation

When the shape change during martensitic transformation is coordinated by elastic deformation, it is referred to as thermoelastic martensitic transformation.

Kirkendall Effect

Reflects the diffusion mechanism of substituting atoms. In a diffusion couple consisting of two pure components, during diffusion, the interface moves toward the side where diffusion is faster.

Thermoelastic Martensitic Transformation

When the shape change during martensitic transformation is coordinated by elastic deformation, it is referred to as thermoelastic martensitic transformation.

Amorphous Material

Atoms lack long-range periodic arrangement, and the material has no fixed melting point, exhibiting isotropy.

Packing Density

The percentage of total volume occupied by atomic volume in a crystal structure.

Multiple Slip

When the shear stress on several slip systems equals and simultaneously reaches the critical shear stress, the phenomenon of simultaneous slip occurs.


During the phase transformation process, a transition occurs at a temperature below the phase transition point after cooling to a certain temperature. The difference between the equilibrium phase transition temperature and this actual transition temperature is called undercooling.

Interstitial Phase

When the ratio of the radii of non-metallic (X) and metallic (M) atoms, rX/rM, is less than 0.59, the phase formed with a simple crystal structure is called an interstitial phase.

Full Dislocation

A dislocation for which the Burgers vector is equal to the lattice vector or its integer multiples is referred to as a full dislocation.

Slip System

A combination of a slip plane and a slip direction on that plane in a crystal is referred to as a slip system.

Eutectic Segregation

In a eutectic alloy, the α phase attached to the primary α phase grows, pushing the other phase β to the final solidified crystal boundary. This separation of the two phases in the eutectic alloy is called eutectic segregation.

Homogeneous Nucleation

The new phase nuclei grow uniformly within the parent phase, meaning the nuclei are formed directly from some atomic groups in the liquid phase without being influenced by impurity particles or external surfaces.

Edge Dislocation

On a certain crystal face, if there is an excess half-plane of atoms, it appears as if a knife blade is inserted into the crystal, causing atomic misalignment between the upper and lower parts of this crystal face, known as an edge dislocation.

Grain Refinement

As the grain size decreases, the total length of grain boundaries increases, leading to greater hindrance to dislocation slip and higher yield strength of the material. Grain refinement increases in material strength.

Double Cross Slip

If after cross-slip, a dislocation returns to and continues to move on a slip plane parallel to the original slip plane, it is termed double cross slip.

Unit Dislocation

A dislocation with a Burgers vector equal to the unit lattice vector is referred to as a unit dislocation.


The diffusion associated with the formation of a new phase due to a chemical reaction is called reaction diffusion.

Grain Boundary Segregation

Enrichment of solute or impurity atoms at the grain boundaries due to differences in distortion energy or the presence of vacancies.

Kohler Cluster

The phenomenon where solute atoms, after interacting with dislocations, tend to cluster around dislocations. Proposed by Kohler, it is also known as the Kohler cluster.

Deformation Texture

The phenomenon of preferred crystallographic orientation during the deformation process in polycrystals is called deformation texture.

Lattice Distortion

Within a local range, atoms deviate from their normal lattice equilibrium positions, causing lattice distortion.

Steady-State Diffusion

In steady-state diffusion, the concentration of diffusing species only changes with distance and remains constant over time.

Peritectic Reaction

A process where two solid phases react to form another solid phase.

Non-Coherent Grain Boundary

When the atomic arrangement at the interface between two phases differs significantly, i.e., with a large mismatch δ, a non-coherent grain boundary is formed. Similar to high-angle grain boundaries, it can be considered as a very thin transition layer with irregular atomic arrangement.

Substitutional Solid Solution

When solute atoms dissolve in a solvent to form a solid solution, either occupying lattice sites of the solvent or replacing some solvent atoms, it is called a substitutional solid solution.

Interstitial Solid Solution

A solid solution where solute atoms occupy interstitial positions in the solvent lattice is called an interstitial solid solution.

Secondary Recrystallization

The phenomenon where a few grains grow abnormally large after recrystallization is completed, having escaped normal growth inhibition.

Pseudo-Eutectic Transformation

In non-equilibrium transformation processes, alloys near eutectic compositions of hypo or hyper eutectoid alloys may exhibit a microstructure that appears entirely eutectic.

Schottky Defect

In a crystal, when an atom has sufficient vibrational energy to increase its amplitude to a certain extent, it may overcome the restraining effect of surrounding atoms, jump from its original position to a normal lattice point on the crystal surface or internal surface, leaving a vacancy inside the crystal. This is known as a Schottky defect.

Frankel Defect

Atoms departing from equilibrium positions insert into interstitial positions in the lattice, simultaneously creating an equal number of vacancies and interstitial atoms in the crystal.

Non-Steady-State Diffusion

Diffusion where the concentration of diffusing species not only changes with distance (x) but also varies with time is termed non-steady-state diffusion.


The process where a supersaturated solid solution undergoes solute atom precipitation at room temperature or above.


Refers to the stage of substructure and performance changes that occur before the appearance of new undistorted grains.

Phase Rule

The phase rule provides a relationship between the number of phases, components, and temperature and pressure in a system at equilibrium and can be expressed as: f=C+P-2, where f is the degree of freedom of the system, C is the number of components, and P is the number of phases.


A substance composed of two or more metals or a combination of metal and non-metal that is formed by melting, sintering, or other methods and exhibits metallic properties.


When two crystals (or two parts of a crystal) form a mirror-symmetric relationship along a common crystal plane, these two crystals are called twinned, and the common crystal plane is called the twin plane.

Phase Diagram

A graphical representation describing the conditions for phase equilibrium or coexistence in a system, also known as the geometric trajectory of thermodynamic parameters at equilibrium.


The shear process is undergone by crystals in a way that produces twinning after being subjected to external forces.

Grain Boundary

A boundary between grains with the same composition and structure.

Unit Cell

A representative basic unit (smallest parallelepiped) is extracted from a lattice as the building unit of the lattice, referred to as a unit cell.


A line defect in a crystal, is characterized by a regular arrangement of atoms along a line; this defect is described by a line direction and a Burgers vector.


Non-uniformity in the chemical composition of an alloy.

Metallic Bond

The bonding force is generated by electrostatic interaction between free electrons and atomic nuclei.

Solid Solution

A uniform mixture of elements in a crystalline structure, where one element (solvent) incorporates atoms of other elements (solutes) into its lattice.


Several grains with slightly different orientations within a single grain are referred to as subgrains.

Subgrain Boundary

The interface between adjacent subgrains is called a subgrain boundary.

Grain Boundary Energy

Regardless of whether it is a small-angle or large-angle grain boundary, atoms deviate to some extent from their equilibrium positions. Thus, relative to the interior of the crystal, the grain boundary is in a higher energy state. The excess energy is termed grain boundary energy or interfacial free energy.

Surface Energy

Surface atoms experience an uneven force field, leading to a significant increase in their energy. The excess energy is known as surface free energy or surface energy.

Interfacial Energy

Atoms at interfaces are in a state of broken bonds, possessing excess energy. The average excess energy per unit area on the interface is called interfacial energy.


Hardenability refers to the ability of an alloy to transform into martensite upon quenching, primarily associated with the critical cooling rate, which is represented by the depth of the hardened layer.


Hardenability refers to the ability of steel to achieve the highest hardness after quenching, primarily influenced by the carbon content of the steel.

Habit Plane

During a solid-state phase transformation, the new phase often begins forming on a specific crystal plane of the parent phase. This plane is called the habit plane.


An intermediate product of the pearlite transformation in the mid-temperature range, consisting of lamellar ferrite and cementite with a smaller interlamellar spacing and thinner lamellae.


A product of the eutectoid transformation in iron-carbon alloys, consisting of lamellar structures of ferrite and cementite.


A product of the eutectic transformation in the iron-carbon phase diagram, composed of eutectic austenite and eutectic cementite.

Burgers Vector

An important vector describing the characteristics of a dislocation, it reflects the magnitude and direction of the total distortion within the dislocation region, enabling the relative sliding of crystals after the passage of a dislocation.


Refers to a three-dimensional array formed by the periodic arrangement of geometric points in space, an abstraction of the crystal structure.

Van der Waals Bond

A physical bond composed of intermolecular forces generated by instantaneous and induced dipoles.

Dislocation Slip

The movement of dislocations along slip planes under the influence of applied stress.

Heterogeneous Nucleation

Nucleation of crystals favored by foreign surfaces in liquid metal or at temperature gradients.

Structural Fluctuation

In the atomic arrangement of liquid structures, there is long-range disorder and short-range order. Short-range ordered atomic clusters are not fixed and exhibit continuous changes, resulting in structurally unstable configurations. This phenomenon is known as structural fluctuation.

Lever Rule

For an alloy in three-phase equilibrium, the composition points must lie at the center of mass of a conjugate triangle.

Strain Aging

After the first tension, if a second tension is immediately applied without an apparent yield stage on the stress-strain curve, and the specimen is allowed to stand at room temperature before the second tension, a yield stage will reappear on the stress-strain curve. However, the strength of the re-yield is higher than the initial yield strength. This phenomenon is called strain aging.

Dendritic Segregation

Under non-equilibrium cooling conditions, the internal composition of the newly formed solid solution grains after homogeneous transformation is uneven. The core of the first crystallized grains contains more high-melting-point component atoms, while the outer region of later crystallized grains contains more low-melting-point component atoms. Usually, solid solution crystals grow dendritically, resulting in uneven composition within the same grain.

Critical Deformation

The minimum pre-deformation required for a metal to undergo recrystallization at a given temperature.

Electron Compound

A class of compounds where the crystal structure is determined by the concentration of electrons, also known as the Hume-Rothery phases. If they have the same electron concentration, their crystal structure types are identical.

Polymorphous Allotropy

Different crystal structures are formed by the same chemical composition due to different thermodynamic conditions.

Recrystallization Temperature

The lowest temperature at which deformation metals complete recrystallization within a certain time period (generally 1 hour).

Bravais Lattice

A lattice is formed not only by considering the shape of the unit cell but also by considering the arrangement of lattice points.

Coordination Polyhedron

A polyhedron is formed by the central connection of atoms or ions with their directly adjacent atoms or ions, called the coordination polyhedron.

Schmid Factor

Also known as the orientation factor, it is defined as cosΦcosλ, where Φ is the angle between the slip plane and the central axis of the applied force (F), and λ is the angle between the slip direction and the force (F).

Topologically Close-Packed Phase

A class of intermediate phases composed of two different-sized metal atoms, forming a complex structure with high space utilization and coordination numbers. Because these structures exhibit topological features, they are called topologically close-packed phases.

Interstitial Compound

When the ratio of the radii of non-metallic (X) and metallic (M) atoms, rX/rM, is greater than 0.59, a phase with a complex crystal structure is formed, commonly referred to as an interstitial compound.

High-Angle Grain Boundary

The grain boundary between grains in polycrystalline materials is called a high-angle grain boundary, where the misorientation between adjacent grains is greater than 10º.

Low-Angle Grain Boundary

The boundary between adjacent subgrains with a misorientation of less than 10º is called a low-angle grain boundary, generally less than 2º, and can be further classified into tilt boundaries, twist boundaries, and coincidence boundaries.

Critical Shear Stress

The minimum shear stress required to initiate the movement of dislocations, and it is a constant value related to the material’s inherent properties, independent of the orientation of the applied force.

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