Thermal expansion of interlayer spacing and thermal vibrational displacement of carbon atoms in petroleum coke

Abstract

On petroleum coke heat-treated at various temperatures in the range from ∼ 1600 to ∼ 3000°C, thermal expansion of the interlayer spacing and the mean-square displacement along the c-axis due to thermal vibration of carbon atoms were measured from room temperature to ∼ 1050°C by means of X-ray diffractometry. The static mean-square displacement due to imperfect crystallization was also estimated for each sample. The c-axis spacing increases linearly with temperature and the slopes had almost the same values (1.85×10−4 to 1.89×10−4A/°C) for all samples. The mean-square thermal vibrational displacements of carbon atoms increased almost linearly from 0.012A2 at room temperature to ∼ 0.047A2 at 1000°C for all samples, except for the sample heat-treated at 1640°C. A mean “free space” between the layer planes, that is the interlayer spacing minus twice the total root-mean-square displacement of carbon atoms along the c-axis direction, was obtained in consideration of the mean-square thermal vibrational displacement and the mean-square static displacement. The mean “free space” increases abruptly with decrease of c-spacing from 6.86 to 6.85A (heat-treatment temperatures of 1640 and 2100°C respectively), then decreases slowly and eventually again begins to increase with further decrease of c-axis spacing to 6.73A.