关注：

1） 金属化密度；the metallization density of water (ice)

2） Weigner radius在分析中应用

Forefword:

   I met two nice professor. Thanks must be given to Neil. He spared one hour to meet me every week, though Roald can decide nearly all the things. The following words from him:

  The average polarizability of  H₂O is 1.45 cubic Angstroms. The average polarizability of H2O2 is around 2.30 cubic Angstroms (could you  check this?).

    This means that the (number ) density at which H2O2 will become metallic should be LOWER than the equivalent for water by a fraction

according tho the GH criterion.

   Please check the recent estimates for the metallization density of water (ice) and

2)  

   Metallization of ice in our calculations occurs only near 4.8 TPa, where the metallic

C2∕m phase becomes most stable. In this regime, zero-point energies much larger than typical enthalpy differences suggest possible melting of the H sublattice, or even the entire crystal.

1)     金属化标准The Goldhammer-HerzfeldCriterion for Metallization

  A very old and often considered question incondensed matter physics is that of which properties give rise to metallicversus insulating character.

  Today, the most common description is that metals contain a partiallyfilled conduction band while insulators have a completely filled valence bandseparated by a large gap from an empty conduction band.

  The modern theory o f band structure provides a comprehensive picture ofthe behavior of electrons in a solid however, accurately predicting such bandstructures generally requires powerful computers and sophisticatedcomputational techniques.

  Long before the theory of band structure in solids was developed,Goldhammer [63] and later Herzfeld[64] developed a simple and remarkably accurate theoryable to account for the onset of metallic character.

  The GH critieron is based upon the Lorenz-Lorentz or Clausius-Mosstottirelation:

Where n is the index of refraction[折光, 折射度]，ε is the relative permittivity【[电]介电常数,电容率】，αis the molecular polarizability[极化率,极化度],V is the molar volume, NA is the Avagodro’s number and R=(4π/3 α)N_A is called the molar refractivity.

  Clearly, as R/V→1,n→∞ and ε→∞; this can only happen if electrons are no longer bound, as in ametal.  Thus, the GH criterion is

    R/V <1 → insulating;

     R/V ≥ 1 → metallic.

A simple physicalinterpretation of the GH criterion becomes apparent when one notes that thepolarizability of a conducting sphere of radius r is equal to r³.

Thatapproximating the atom as aconducting sphere can produce reasonable radii is clear if one considers forexample the polarizability of Ar, α～0.988 ų[66]

So that r=α^1/3~1 Å.

    Now , the meaning of R, the molarrefractivity, becomes clear: R=(4π/3 α)N_A=(4π/3 r³ )N_Ais nothing more thana measure of the volume occupied by one mole of counducting spheres.

   Usually R can be taken to be independent ofdensity allowing straightforward estimates ofmetallization density given knowledge of the atomic/molecularpolarizability.【R作为一种独立的密度量，常用来在已知原子或分子极化率的情况下估算金属化的密度】

    Imagine compressing a material whereinitially R/V<1 which means that r<R_WS(in analogy to the situation shown at the left of Figure 2.5).  The material is insulating because the “conductingspheres” do not overlap.

    Upon increasing the pressure, R/Vincreases to 1 and the spheres touch.

    At this and higher pressures, when R/V≧1 the material is metallic because the conductiongspheres overlap, allowingthe electrons to freely wander throught the material.

  Theaccuracy of the simple GH　criterionwith respect to the metallic character of elemental solids is strikinglyillustrated in Figure 2.7;

Notethat as one scans from left to right across the figure, the elements of theperiodic table turn from metal to non-metal around columns 13-16 just as theR/V values curve below the dashed line at R/V=1.

    If we define V0 as theambient pressure volume and Vc as the critical pressure for transition to themetallic state, it is clear that metalliztion occurs when the relative volumeVc/V0=R/V0.

    As an example, consider Xe. From Figure2.7, R/V0~0.29 forXe leading one to expect Xe to become metallic when compressed to the poingwhere V/V0~0.29.

    According to the measured equation ofstate of Xe[69], one would expect toreach this relative volume at a pressure of ~150 GPa. Indeed, this isapproximately the pressure where Xe is found to enter the metallic state[70-72]. In many cases, the prediction of the GHcriterion is as accurate as significantly more complicated theoreticaltreatments such as the augmented plane wave(APW) method[73]. Iｎ　Appendix A we list calculated R/V values for several compounds and in Section 4.2.3we will retrun to the GH criterion in the context of the search forsupercondcting low-Z materials.

* There are caseswhere R changes significantly with density, causing the GH criterion to fail . Someof these cases are discussed in Reference[67]

关注：

 1）金属化标准：Goldhammer-Herzfeld criterion

 2) 高压下，在不发生结构相变的情况下，物质电子结构变化的普遍规律；

^ The Goldhammer-Herzfeld criterion is a ratio that compares the force holding an individual atom's valence electrons in place with the forces, acting on the same electrons, arising from interactions between the atoms in the solid or liquid element. When the interatomic forces are greater than or equal to the atomic force, valence electron itinerancy is indicated.

   Metallic behaviour is then predicted.^[65] Otherwise nonmetallic behaviour is anticipated.

网络问答：

A:

有人说 “当介质的相对介电常数εr 趋于无穷大时，其效果相当于导体”  和 "金属的介电常数无穷大" ，请问这种说法对吗， 有没有什么理论依据或者公式啊？

Q:

完美电导体=电导率无穷大，内部没有电磁场，来源于外场激发金属的电子使得电子在金属表面产生一层感应电荷，完全抵消外部电场，电磁场将被完全反射，对应于边界两侧的电场切向分量为0，法线方向分量差对应着表面电荷。
金属的介电常数在低频时候非常大，相当于完美电导体；在光频段是有限值，不是完美电导体

Q:这种说法对！
设介质的相对介电常数为εr，则介质内的电场强度为Eo/εr，其中Eo为无介质时的电场强度；
对于金属，在静电平衡时，其内部电场强度为0，等同于εr趋于无穷大！

Q::

如果相对介电常数无穷大，效果相当于导体，应该是对的。介电常数无穷大时，根据泊松方程Q/ε，趋于0，其效果相当于，Q=0，即材料内部没有电场。可以说效果相当于导体。
金属的介电常数无穷大，这个结论应该是不对的