MgO和MgB2高壓物性的第一性原理計(jì)算

作為地球形成的主要礦物質(zhì)之一，方鎂石（MgO）在壓強(qiáng)高達(dá)227GPa時都始終以氯化鈉（B1）結(jié)構(gòu)穩(wěn)定存在，研究它的彈性性質(zhì)對解釋地幔內(nèi)部地震波速的變化以及構(gòu)造地球內(nèi)部礦物學(xué)理論模型具有重要的作用，也是經(jīng)常用于發(fā)展固體物理第一性原理計(jì)算的模型材料。近年來，無論是在實(shí)驗(yàn)上還是理論上，研究材料在高壓下的性質(zhì)一直是個熱門課題。2001年1月10日，日本青山學(xué)院大學(xué)教授秋光純宣布二硼化鎂具有超導(dǎo)電性，超導(dǎo)轉(zhuǎn)變溫度高達(dá)39K。發(fā)現(xiàn)二硼化鎂超導(dǎo)電性迫使人們重新考慮，在BCS理論的框架內(nèi)是否存在更高臨界溫度的超導(dǎo)體。二硼化鎂結(jié)構(gòu)簡單，易于制備和加工，有著廣闊的應(yīng)用前景。本文主要包括兩部分內(nèi)容：
1) 利用平面波贗勢密度泛函理論和準(zhǔn)諧德拜模型研究了氧化鎂（MgO）的晶格常數(shù)a、體彈性模量B0、狀態(tài)方程以及彈性常數(shù)（C11、C12和C44）等基本性質(zhì)參數(shù)。得到了壓強(qiáng)0～130GPa范圍內(nèi)，溫度分別為300K和800K的彈性常數(shù)（C11、C12和C44）、等溫體彈性模量Bs、剪切模量G、德拜溫度 和壓縮波速VP、剪切波速VS。所得到的C12的等溫線不同于Karki等人的理論計(jì)算結(jié)果。由于對材料增加壓強(qiáng)和降低溫度的效果幾乎相同，我們認(rèn)為本文結(jié)果應(yīng)該更正確。另外，還研究了在300K、800K的彈性常數(shù)、彈性各向異性以及偏差 ，發(fā)現(xiàn)壓強(qiáng)小于20GPa時，彈性各向異性為正值且隨壓強(qiáng)增加而降低，在20GPa時為零，呈現(xiàn)各向同性。MgO的偏差 絕對值隨壓強(qiáng)增加而增加，意味著MgO在高壓下受到非中心多體力場作用。 
2) 利用基于線性綴加平面波的密度泛函理論研究了二硼化鎂（MgB2）在壓強(qiáng)0～60GPa下的態(tài)密度、能帶結(jié)構(gòu)以及晶體的彈性常數(shù)。比較分析了體積的壓縮和晶格常數(shù)c/a的減小對能帶結(jié)構(gòu)的影響，得出c/a對導(dǎo)電性質(zhì)的影響是主要的。另外，還研究了MgB2力學(xué)性質(zhì)的各向異性，包括體彈性模量（B、Ba和Bc）、壓縮波 和剪切波（ 、 ）與壓強(qiáng)的關(guān)系。由于Mg原子層與B原子層之間的金屬鍵相對B原子層內(nèi)原子之間的共價鍵相對較弱，所以隨著壓強(qiáng)的增大呈現(xiàn)晶體力學(xué)性質(zhì)的各向異性。
關(guān)鍵詞：密度泛函，贗勢，線性綴加平面波，彈性常數(shù)，能帶結(jié)構(gòu)，態(tài)密度
第First-Principles Calculations for the Properties of MgO and MgB2 at High Pressure
第
Major in Atomic and Molecular Physics
Postgraduate:  Zhao Jian-zhou     Tutor:  Chen Xiang-rong

As one of the main compositions of the earth minerals, periclase (MgO) is stable as sodium chloride (B1) structure at pressure up to 227 GPa. It has great usage of explain the change of earth-shock wave inside of the mantle and the model of mineral theory of composing the earth. It also used as the model of the first principles calculations of solid state physics. Recently, properties of material at high pressures and high temperatures have been the objects of intensive experimental and theoretical investigations. In Jan. 10, 2001, Professor of Aoyama-Gakuin University, Nagamatsu, Jun, announced magnesium diboride has properties of superconductivity, and its transition temperature up to 39 K. It forced people to reconsider whether it exist such superconductor with ever higher transition temperature. Magnesium diboride has simple structure, easy to preparation, and has wide exercise future. This paper conclude two part:
1) The thermodynamic properties and the equations of state (EOS) of rocksalt (RS) structure MgO are investigated at a wide range of pressure 0~170 GPa, using plane-wave pseudopotential density functional theory. We obtain the pressure dependences of the elastic constants, the adiabatic bulk modulus BS, the shear modulus G, aggregate acoustic velocities and the Debye temperature at several temperatures (300 K and 800 K) and pressures (0~130 GPa). Our calculated isotherm of C12 is different from the predicted result by Karki et al., who found that the isotherm for high temperature is above the isotherm for low temperature. Based on that the effect of increasing pressure on the material is the same as decreasing temperature of the material, we think that our calculated isotherm of C12 should be correct. The elastic anisotropy A is investigated at the temperatures of 300 K and 800 K. When P < 20 GPa，it is found that the elastic anisotropy of MgO decrease dramatically with increasing pressure, becoming elastically isotropic at the pressure of 20 GPa. The increase of the deviation   in absolute with pressure means that MgO is affected by the non-central many-body force at high pressure.
2) We have investigated the density of states, band structure, and elastic constants of magnesium diboride at pressure 0 ~ 60 GPa based on density functional theory with linear augmented plane wave. We compared the impact of volume compression and decrease of c/a ratio to the band structure, and conclude the conductivity is mainly affected by c/a. Beside, we investigated the mechanics anisotropy of MgB2, includes the relationship of bulk modulus (B, Ba and Bc), compression wave   and shear wave ( ,  ). As the metal bond between Mg atom layer and B atom layer is weaker than the covalent bond between the B atoms in a B atom layer, the mechanics anisotropy was shown obviously while pressure increased.
Key words: density functional theory, pseudopotential, Linear augmented plane wave, elastic constants, band structure, density of states