中文摘要：

使用德拜模型和准谐近似，结合第一性原理方法，考察Nb、Zr、Sn加入对beta钛合金热膨胀系数的影响。研究表明：Nb对beta钛合金的热膨胀系数有较大的影响，而Zr、Sn的加入对热膨胀系数影响很小；beta钛合金热膨胀系数的变化主要源于合金元素对体系体模量的影响；体模量升高，体系热膨胀系数降低；但当体模量随成分变化较小时（如Zr、Sn），其它因素如体积因素的共同作用将使体系的热膨胀系数变化趋于复杂。

英文摘要：

Using the first principles method in combination with quasi-harmonic Debye model, the effects of the alloying elements Nb, Zr, and Sn on the coefficient of thermal expansion of beta titanium alloy were investigated. The results show that the addition of Nb remarkably reduces the coefficient of thermal expansion of beta titanium alloy, whereas the effects of Zr and Sn are less significant. It is found that bulk modulus may account well for the variation of coefficient of thermal expansion brought about by Nb, while for addition of Zr and Sn, the scenario turns out to be complicated as other index such as volume has comparable contribution to the effect on thermal expansion in addition to bulk modulus.