We have investigated the anisotropic thermal expansion of graphite using ab-initio calculations of the implicit and explicit anharmonicity of phonons, which occur due to change in volume and increase in the thermal amplitudes, respectively. We find that the negative thermal expansion (NTE) in the a-b plane below 600 K and very large positive thermal expansion along the c-axis up to high temperatures arise due to various phonons polarized along the c-axis. While the NTE arises from the anharmonicity of transverse phonons over a broad energy range up to 60 meV, the large positive expansion along the c-axis occurs largely due to the longitudinal optic phonon modes around 16 meV. We find that these phonons have large implicit anharmonicity, but very little explicit anharmonicity. We also find very significant increase in the linear compressibility along the c-axis with increase in volume, and this has important role to quantitatively explain the thermal expansion behavior along the c-axis. The hugely anisotropic bonding in graphite is found to be responsible for wide difference in the energy range of the transverse and longitudinal phonon modes polarized along the c-axis, which are responsible for the anomalous thermal expansion behavior. This behaviour is in contrast to other nearly isotropic hexagonal structures like water-ice, which show anomalous thermal expansion in a small temperature range arising from a narrow energy range of phonons.

我们使用声子的隐式和显式非谐性的从头算计算研究了石墨的各向异性热膨胀，这是由于体积的变化和热振幅的增加而发生的。我们发现，由于各种声子沿c轴极化，因此在600 K以下的ab平面中负热膨胀（NTE）和沿c轴直至高温的非常大的正热膨胀会出现。NTE是由横向声子在高达60 meV的宽能量范围内的非谐性引起的，而沿c轴的大正膨胀主要是由于16 meV附近的纵向声子声子模引起的。我们发现这些声子具有很大的内在非谐性，但很少有显式非谐性。我们还发现随着体积的增加，沿c轴的线性可压缩性显着增加，这对于定量解释沿c轴的热膨胀行为具有重要作用。发现石墨中的巨大各向异性键是造成沿c轴极化的横向和纵向声子模的能量范围差异很大的原因，这是异常热膨胀行为的原因。此行为与其他近似各向同性的六角形结构（如水冰）相反，后者由于声子的能量范围狭窄，在较小的温度范围内显示出异常的热膨胀。发现石墨中的巨大各向异性键是造成沿c轴极化的横向和纵向声子模的能量范围差异很大的原因，这是异常热膨胀行为的原因。此行为与其他近似各向同性的六角形结构（如水冰）相反，后者由于声子的能量范围狭窄，在较小的温度范围内显示出异常的热膨胀。发现石墨中的巨大各向异性键是造成沿c轴极化的横向和纵向声子模的能量范围差异很大的原因，这是异常热膨胀行为的原因。此行为与其他近似各向同性的六角形结构（如水冰）相反，后者由于声子的能量范围狭窄，在较小的温度范围内显示出异常的热膨胀。