Pinning force is a

force In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a p ...

acting on a pinned object from a pinning center. In

solid state physics Solid-state physics is the study of rigid matter, or solids, through methods such as quantum mechanics, crystallography, electromagnetism, and metallurgy. It is the largest branch of condensed matter physics. Solid-state physics studies how the l ...

, this most often refers to the

vortex In fluid dynamics, a vortex ( : vortices or vortexes) is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in th ...

pinning, the

pinning Pinning may refer to: * Pinning, the effect of certain weapons that cause their targets to be pinned down * Pinning ceremony (nursing), a symbolic welcoming of new graduates into the nursing profession * Pinning force, a force acting on a pinned ...

of the magnetic vortices ( magnetic flux quanta,

Abrikosov vortices In superconductivity, fluxon (also called a Abrikosov vortex and quantum vortex) is a vortex of supercurrent in a type-II superconductor, used by Alexei Abrikosov to explain magnetic behavior of type-II superconductors. Abrikosov vortices occu ...

) by different kinds of the defects in a

type II superconductor In superconductivity, a type-II superconductor is a superconductor that exhibits an intermediate phase of mixed ordinary and superconducting properties at intermediate temperature and fields above the superconducting phases. It also features the ...

. Important quantities are the ''individual'' maximal pinning force, which defines the depinning of a single vortex, and an ''average'' pinning force, which defines the depinning of the correlated vortex structures and can be associated with the

critical current density Critical or Critically may refer to: *Critical, or critical but stable, medical states **Critical, or intensive care medicine *Critical juncture, a discontinuous change studied in the social sciences. *Critical Software, a company specializing in ...

(the maximal density of non-dissipative current). The interaction of the correlated vortex lattice with system of pinning centers forms the magnetic phase diagram of the vortex matter in superconductors. This

phase diagram A phase diagram in physical chemistry, engineering, mineralogy, and materials science is a type of chart used to show conditions (pressure, temperature, volume, etc.) at which thermodynamically distinct phases (such as solid, liquid or gaseous ...

is especially rich for

high temperature superconductors High-temperature superconductors (abbreviated high-c or HTS) are defined as materials that behave as superconductors at temperatures above , the boiling point of liquid nitrogen. The adjective "high temperature" is only in respect to previ ...

( HTSC) where the thermo-activation processes are essential. The pinning mechanism is based on the fact that the amount of

grain boundary In materials science, a grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are two-dimensional defects in the crystal structure, and tend to decrease the electrical and thermal ...

area is reduced when a particle is located on a grain boundary. It is also assumed that particles are spherical and the particle-matrix interface is incoherent. When a moving grain boundary meets a particle at an angle

\beta

, the particle exerts a pinning force

F

on the grain boundary that is equal to

F = 2\pi \sigma \cos \beta \sin \beta

; with

r

the particle radius and

\sigma

the

energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...

per unit of grain boundary area.

References

See also