SINGLE-CRYSTAL ELASTIC MODULI + HCP TO BCC TRANSFORMATION IN TI,ZR, + HF
SINGLE-CRYSTAL ELASTIC MODULI + HCP TO BCC TRANSFORMATION IN TI,ZR, + HF
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DOI：
10.1103/physrev.135.a482
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发表时间：
1964-01-01
期刊：
影响因子：
--
通讯作者：
RENKEN, CJ
中科院分区：
文献类型：
--
作者：
FISHER, ES;RENKEN, CJ
本文用超声波干涉技术测定了六方晶系Ti、Zr和Hf单晶在4~1155 K温度范围内的弹性模量随温度的变化。c 11、c 33和c 44在三种金属之间差别很大，而Ti和Zr的c 66剪切模量在4 - 300 K之间相差不超过1%，在1100 K时小于10%。Ti和Zr的剪切模量随温度的变化具有非常显著的各向异性，在4~1100 K之间，c 66降低75%，而c 44降低40%。在与已发布的电阻率数据中的异常曲率相一致的温度下，c 66的线性温度依赖性出现非常明显的偏差。在hcp → bcc相变温度下，c66剪切模量相对较小，这与Burger提出的相变剪切机制相一致。对六方晶系金属弹性模量和热膨胀数据的研究表明，C_（66）具有较高的温度依赖性，并发生hcp → bcc转变，这是C_（66）<1.60的金属的特征。有人建议，这些特点是由于在基面的横向热振动，并从非谐贡献的自由能，这是由比热数据表示的转换结果。与其他hcp金属的比较相反，由Ti、Zr和Hf的4K弹性模量得到的德拜θ与已发表的比热数据非常一致。一个轻微的异常，在18 K的钛，这可能与发表的电阻率最小值钛合金。
The variations with temperature of the elastic moduli in single crystals of hcp Ti, Zr, and Hf have been experimentally determined from 4 K up to 1155 K, using an ultrasonic wave interference technique. The c 11, c 33, and c 44 differ considerably among the three metals, whereas the c 66 shear moduli for Ti and Zr are similar to within 1% between 4 and 300 K and less than 10% at 1100 K. There is very marked anisotropy in the temperature dependence of the shear moduli in Ti and Zr, c 66 decreasing by 75% between 4 and 1100 K whereas c 44 decreases by 40%. A very pronounced deviation from a linear temperature dependence of c 66 occurs at a temperature which coincides with the anomalous curvatures in the published electrical resistivity data. The relatively small c 66 shear moduli at the hcp→ bcc phase transformation temperatures are as expected from the transformation shear mechanisms suggested by Burger. A survey of existing elastic modulus and thermal expansion data in hcp metals leads to the conclusion that a relatively high temperature dependence in c 66 and the occurrence of hcp→ bcc transformations are characteristic of metals with c a< 1.60. It is suggested that these characteristics due to the transverse thermal vibrations in the basal planes, and that the transformation results from anharmonic contributions to the free energy which are indicated by specific heat data. Contrary to comparison in other hcp metals, the Debye θ from 4 K elastic moduli in Ti, Zr, and Hf are in excellent agreement with published specific heat data. A slight anomaly at 18 K in Ti is indicated which may be associated with published resistivity minima in Ti alloys.