In the condition of constant pressure, the change of the length or volume of graphite material is caused by the change of temperature. The extent of expansion is expressed in line (body) expansion coefficient or swelling rate. The linear expansion coefficient α and the volumetric expansion coefficient β are defined as follows: The expansion rate of length and volume is expressed by L and V respectively. T is the temperature, p is the pressure, L and V are the length and volume of the specimen respectively. α and beta are sometimes called true expansion coefficients, which are used to differentiate between average expansion coefficients. Temperature from T1 to T2, the length of the object from L1 to L2, its volume from V1 to V2, the average line expansion coefficient α and the average body expansion coefficient β by the following expression.Graphite Material

Greenessen Theory of graphite thermal expansion the thermal expansion of solids is an increase in the average distance between neighboring atoms in solids. The potential energy of the neighboring two atoms in the crystal is the function of the distance r between the nuclei. The potential energy curve u-r is an asymmetrical curve (Fig 1), the atomic distance increases with the increase of the vibration energy, because the resonant does not change the average distance between atoms, strictly speaking, the distance should be increased with the increase of the non harmonic motion. This is the starting point of Greenessen (E. Grtinecsen) Thermal expansion theory. In a certain vibrational energy, the distance of the two atoms is changed near the equilibrium position, because of the asymmetry of the potential energy curve, the mean distance r is greater than the equilibrium distance r0, and the average distance is greater under higher vibrational energy. The vibration energy increases with the increase of temperature, and the average distance between the two atoms increases with the increase of temperature, resulting in swelling. When the crystal expands, the elastic energy increases and the lattice vibration frequency decreases. Greenessen constant γ is usually introduced to describe the change of frequency w with volume V.Graphite Material

Greenessen according to the equilibrium volume is the smallest volume of free energy, and that the vibration frequency of all lattice points is roughly the same as the dependence of volume, that is, γ is a constant. For isotropic crystals, such as the Zirconia series, the following relations are derived: the β= (Γ/KCV)/V (6) is the crystal expansion coefficient, the k is the volume elastic modulus, the CV is the molar constant Jons-Bugejon, and V is the molar volume.Graphite Material