# 纳米级电子器件&纳米级磁性材料和器件&纳米材料|EEE6215& MAT6390 Nanoscale Electronic Devices&Nanoscale Magnetic Materials and Devices代写

$$V-E+F=2(1-g)$$
For bulk three-dimensional solids, $g$ is equivalent to the number of cuts required to transform a solid structure into a structure topologically equivalent to a sphere (for instance, $g=0$ for a polygonal sphere such as $\mathrm{C}{60}$ or $\mathrm{C}{70}$, and $g=1$ for a torus). Suppose, further, that the object is formed of polygons having different (i) number of sides. The total number of faces $(F)$ is then
$$F=\sum N_{i}$$
where $N_{i}$ is the number of polygons with $i$ sides. Each edge, by definition, is shared between two adjacent faces, and each vertex between three adjacent faces, which is represented as
$$E=(1 / 2) \sum i N_{i}$$
and
$$V=(2 / 3) E$$
By substituting Euler’s postulate for $i \geq 3$ is represented as
$$\begin{array}{r} 3 N_{3}+2 N_{4}+N_{5}-N_{7}-2 N_{8}-3 N_{9}-\cdots-=12(1-g) \ \sum(6-i) N_{i}=12(1-g) \end{array}$$

## EEE6215& MAT6390 COURSE NOTES ：

$$\delta=d A$$
where $d$ is carbide density and $A$ is the mass fraction of carbon in the carbide. Theoretical total pore volume $V_{\Sigma}$ was calculated on the basis of pycnometric density of carbon $\left(d_{C}=2.00 \mathrm{~g} / \mathrm{cm}^{3}\right)$ by the formula
$$V_{\Sigma}=\frac{1}{\delta}-\frac{1}{d_{\mathrm{C}}}$$
It was found that the theoretical $\delta$ and $V_{\Sigma}$ values are generally in satisfactory agreement with experimental data taking into account the porosity of the initial carbide granules.
According to the IUPAC definition, porosity in solids is classified by pore size