Stability of Grain Boundary Cavities in Copper
Stability of Grain Boundary Cavities in Copper
复制标题
铜晶界空洞的稳定性
作者：
A. Gittins
在高温蠕变和疲劳过程中，多晶铜的晶界上会形成空洞，导致密度降低。在蠕变条件下，空穴核在经历正常拉伸应力的边界上生长，这是由于空穴从晶界扩散到空穴表面1。对于高温疲劳，有人提出，形成了过量浓度的晶格空位2;然后通过晶格扩散3使空位到达腔表面。由高温蠕变或疲劳形成的空洞在应力消除后会因空位的丢失而缩小，这是不言自明的。使球形空腔塌陷的驱动力是2γ/r，其中γ是空腔的表面能，r是空腔半径。在没有应力的情况下，使半径为r的空腔塌陷所需的时间ts由下式给出：其中kT具有通常的意义，a是空腔间距（10 - 3 cm），Dg是晶界原子扩散系数（Cu在400° C时为10−8 cm 2/sec），δZ是可用于扩散的晶界的厚度（1.10 × 10−7 cm），Ω是原子体积（1.2 × 10−23 cm 3）。对于铜，γ = 1，500尔格/cm 2。因此，半径为5 × 10 - 5 cm的铜腔在400° C下大约5小时内就会塌陷。
DURING both creep and fatigue at high temperatures cavities form on the grain boundaries of polycrystalline copper and cause a decrease in density. Under creep conditions cavity nuclei grow on those boundaries experiencing a normal tensile stress by the diffusion of vacancies from the grain boundary to the cavity surface1. For high temperature fatigue it has been proposed that an excess concentration of lattice vacancies is formed2; the vacancies then reach the cavity surface by lattice diffusion3. It is axiomatic that cavities formed by either high temperature creep or fatigue should shrink by losing vacancies when the stress is removed. The driving force to collapse a spherical cavity is 2γ/r where γ is the surface energy of the cavity and r is the cavity radius. In the absence of stress the time ts required to collapse a cavity of radius r is given by where kT has its usual significance, a is the cavity spacing (∼ 10−3 cm), Dg is the grain boundary atomic diffusion coefficient (∼10−8 cm2/sec for Cu at 400° C), δZ is the thickness of the grain boundary available for diffusion (∼ 10−7 cm) and Ω is the atomic volume (1.2 × 10−23 cm3). For copper γ ∼ 1,500 ergs/cm2. Thus a cavity of radius 5 × 10−5 cm in copper should collapse in about 5 h at 400° C.