【作者】 朱湘萍；

【导师】 廖树帜；

【作者基本信息】 湖南师范大学 ， 理论物理， 2007， 硕士

【摘要】 弹性模量是材料的工程应用、构件设计和科学研究等方面的重要物理量,也是金属材料评定和选用以及加工工艺选择的主要依据。随着社会发展和国防的需要,近代航空、航天、无线电及其精密仪器工业对金属材料的弹性有更高要求,不仅要有高的弹性模量,而且还要稳定,所以我们要不断地改善金属材料的性能和探究新的金属及金属合金材料,并不断地开发超高强高韧、高耐腐蚀、超耐热和高弹性模量的金属、金属合金、复合材料和合成材料。本学位论文应用改进分析型嵌入原子（MAEAM）模型和非简谐理论,研究了FCC结构金属Al、BCC结构金属Fe的体弹性模量,以及它们的体弹性模量与温度、压强的关系,并得到如下创新结果:1采用改进分析型嵌入原子模型计算金属Fe、Al趋向绝对零度时的体弹性模量,所得结果与实验测量数据吻合的很好,说明改进分析型嵌入原子模型能很好地描述BCC结构金属Fe、FCC结构金属Al趋近绝对零度时的体弹性模量。2结合改进分析型嵌入原子模型和非简谐效应,研究发现BCC结构金属Fe、FCC结构金属Al的体弹性模量是温度的二次函数:金属Fe为B（T）:1.732-1.871×10^-4T+7.333×10¹¹T² Mbar金属Al为B（T）=0.802-1.236×10^-4T+3.275×10^-11T² Mbar这一结果说明非简谐效应是导致金属材料体弹性模量随温度变化的主要因素。3结合改进分析型嵌入原子模型和非简谐效应,研究发现金属Fe的体弹性模量B随压强P规律:B=1.732×10¹¹+7/9P+7.927×10¹¹ln(P×5.773×10^-12+1),即金属Fe的体弹性模量B随压强P增加而增大,并且遵循以下而且当压强小于4×10¹¹Pa时与已有数据吻合很好,并发现简谐系数和第二非简谐系数都不影响体弹性模量随压强的变化规律。在压强小于10¹¹Pa时,B-P曲线相当的平坦,即在压强增大时,金属的弹性模量变化很小;在压强大于10¹²Pa之后,曲线相当陡,即在压强增大时弹性模量急剧增大。这说明当压强较小时,晶体间距较大,引力起主要作用;当压强增大时,原子间距逐渐减少,原子间斥力逐渐占主导作用;当压强继续增大时,原子问斥力迅速增大,固体难被压缩,弹性模量迅速增大。这说明铁的体弹性模量是一个与压强有关的物理量。更多还原

【Abstract】 The elastic properties of materials play an essential role in the aspect of engineering design and application,scientific research et al.Also,it is the primary foundation for the evaluation and the preference of metal materials and the processing technical option of materials.For the development of society and the national defense,such as modern aviation and space industry,radio industry, precise instrument and precision meter industry,there are great higher demands for the elastic properties of the metals materials.That is to say,the elastic modulus of the metals materials must be higher and invariable.Therefore,we much try our best to improve the properties of the metal materials continuously,to explore the new metal materials and the new alloys materials,and to develop the metals and the alloy composite materials with the properties of ultra-high strength and malleability,high corrosion resistant,superheat resisting and high modulus.The Modified Analytical Embedded Atom（MAEAM）Model and the anharmonic effect are used to study the bulk modulus of FCC Al metal and BCC Fe metal.In the paper,the following results are obtained:1.The bulk modulus calculated by the MAEAM model for BCC Fe metal and FCC Al metal at zero temperature is in good agreement with the experiment data available.It indicates that the MAEAM model can be applied to investigate the bulk modulus for BCC Fe metal and FCC Al metal. 2.Considering the anharmonic effect,applying the MAEAM model and the anharmonic theory,the variation of the bulk modulus with temperature can be described successfully.That is,the bulk modulus for BCC Fe metal can be described by a quadratic function of temperature B[T]= 1.732-1.871×10^-4T + 7.333×10^-11T², And the bulk modulus for FCC Al metal can be described by a quadratic function of temperature B[T]=0.802 - 1.236×10^-4T + 3.275×10^-11T².The result demonstrates the feasibility of the present method.3.The MAEAM model and the anhannonic theory are used to study the bulk modulus and we find that the bulk modulus increases with the pressure for Fe metal.The relationship can be described by a quadratic function of pressure B = 1.732×10¹¹+ 7/9 P+ 7.927×10¹¹ln(P×5.773×10^-12+ 1),and the result is in good agreement with the data available.When the pressure is less than 4×10¹¹pa,pressure have nothing to do with the harmonic coefficient and the second anharmonic coefficient. The B-P curve is flat within the pressure less than 10¹¹Pa,That is to say,with the increase of the pressure,the bulk modulus grow slowly.And there will be a great steep B-P curve when the pressure is greater than 10¹²Pa.The bulk modulus increases greatly with the increases of the pressure.These can be explained with the interatomic interaction:when the pressure is small,there is great interatomic distance,and the attractive force is relatively bigger.With the increase of pressure, the interatomic distance decreased,and the repulsive force is predominate gradually;with the continually increasing of pressure,the repulsive force increased greatly,it’s becoming very difficult to compress,and the bulk modulus is therefore reinforced greatly.The result demonstrates the influence of the pressure on the bulk modulus for Fe metal.更多还原