Bulk modulus

It is defined as the ratio of the infinitesimal pressure increase to the resulting relative decrease of the volume.

[1] Other moduli describe the material's response (strain) to other kinds of stress: the shear modulus describes the response to shear stress, and Young's modulus describes the response to normal (lengthwise stretching) stress.

For a complex anisotropic solid such as wood or paper, these three moduli do not contain enough information to describe its behaviour, and one must use the full generalized Hooke's law.

The reciprocal of the bulk modulus at fixed temperature is called the isothermal compressibility.

The inverse of the bulk modulus gives a substance's compressibility.

Strictly speaking, the bulk modulus is a thermodynamic quantity, and in order to specify a bulk modulus it is necessary to specify how the pressure varies during compression: constant-temperature (isothermal

is given by When the gas is not ideal, these equations give only an approximation of the bulk modulus.

Solids can also sustain transverse waves: for these materials one additional elastic modulus, for example the shear modulus, is needed to determine wave speeds.

It is possible to measure the bulk modulus using powder diffraction under applied pressure.

It is a property of a fluid which shows its ability to change its volume under its pressure.

A material with a bulk modulus of 35 GPa loses one percent of its volume when subjected to an external pressure of 0.35 GPa (~3500 bar) (assumed constant or weakly pressure dependent bulk modulus).

Since linear elasticity is a direct result of interatomic interaction, it is related to the extension/compression of bonds.

On the other hand, when two atoms are very close to each other, their total energy will be very high due to repulsive interaction.

Together, these potentials guarantee an interatomic distance that achieves a minimal energy state.

Its potential energy-interatomic distance relationship has similar form as the two atoms case, which reaches minimal at r0, The Taylor expansion for this is: At equilibrium, the first derivative is 0, so the dominant term is the quadratic one.

When displacement is small, the higher order terms should be omitted.

Note that the derivation is done considering two neighboring atoms, so the Hook's coefficient is: This form can be easily extended to 3-D case, with volume per atom(Ω) in place of interatomic distance.