Bound electron screening effect on ion-ion potential of warm and hot dense matter

The effects of bound electron screening in warm and hot dense matter are investigated analytically and a theoretical description of screened short-range repulsion is given meanwhile. An empirical ion-ion potential including the classic charge screening and chemical bond attraction at various temperatures and densities is proposed. By solving hypernetted chain equations and comparing the obtained radial distribution function (RDF) with ab initio simulations, the proposed ion-ion potential is found to be promising over a wide range of temperatures and densities for warm dense aluminum and iron. The elastic scattering amplitude and the x-ray absorption near the edge structure of warm dense aluminum calculated from the obtained RDF are in good agreement with experiment results.

Figure 1

RDFs of warm dense Al at various densities and temperatures. The QMD simulation results in (a)–(c) are from Ref. [3]. The results of $\mathrm{HNC}\text{−}\mathrm{Y}+a/r^4$ and DFT-MD in (d) are from Ref. [19]. The charge numbers $Z$ calculated by Yukawa model are 0.207, 0.260, 0.413, and 0.700 in (a)-(d), respectively.

Figure 2

(a) The elastic scattering amplitude as a function of scattering wave number $k$ for Al at $\rho =8.1$ g/${\mathrm{cm}}^3$ and $T=10$ eV. The results of experiments and $\mathrm{HNC}\text{−}\mathrm{Y}+a/r^4$ are from Ref. [13]. (b) The elastic scattering amplitude as a function of scattering wave number $k$ for Al at $\rho =6.3$ g/${\mathrm{cm}}^3$ and $T=1.75$ eV. The results of experiments, DFT-MD simulation, and $\mathrm{HNC}\text{−}\mathrm{Y}+a/r^4$ are from Ref. [14]. (c) $K$-edge XANES of Al at various densities and temperatures. The experimental results are from Ref. [16]. The charge numbers $Z$ calculated by Yukawa model are 2.071 in (a), 1.100 in (b), and 0.344, 1.090, 1.347 for $T$=0.3, 2.8, 4.6 eV in (c).

Figure 3

RDFs of warm and hot dense Fe at various densities and temperatures. The TFMD simulations results in (a)–(d) are from Ref. [21]. $r_{\mathrm{WS}}={(3/4\pi n_i)}^{1/3}$ is the Wigner-Seitz radius. The charge numbers $Z$ calculated by Yukawa model are 2.11, 6.11, 19.97, and 25.47 in (a)–(d), respectively.

Figure 4

The RDFs of warm dense Fe at 240 eV with densities from 1.6 $\mathrm{g}/{\mathrm{cm}}^3$ to 40 $\mathrm{g}/{\mathrm{cm}}^3$. The OFMD results are from Ref. [20]. The charge numbers $Z$ calculated by Yukawa model are 16.34, 15.55, 14.99, 14.67, 14.5, 14.59 for $\rho$=1.6, 4, 7.9, 16, 32, 40 g/${\mathrm{cm}}^3$, respectively.