טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentBen-Bashat Bergman Liron
SubjectThe Origin of Surface Instabilities in Fracture of
Brittle Crystals
DepartmentDepartment of Materials Science and Engineering
Supervisor Dr. Dov Sherman
Full Thesis textFull thesis text - English Version


Abstract

Cracks in brittle crystals are atomically sharp and propagate by breaking bonds in a complicated manner. Post-mortem fracture surface analyses demonstrate a large spectrum of surface undulations. These undulations are so called fracture surface instabilities and have been addressed by numerous scientific studies attempting to reveal the underlying physics of dynamic fracture in brittle materials. Past numerical and theoretical calculations implied that crack front may be disturbed by small heterogeneities in fracture toughness.

This study aims to gain a comprehensive understanding of fracture surface instabilities and investigate whether their multi-scale nature originates at the atomic scale and dictated by the lowest energy crack path.

In this research, surface instabilities in the form of micron scale ridges in brittle single crystal silicon were investigated by cleaving silicon specimens along the {111} and {110} low energy cleavage planes under three-point bending (3PB) and tension. Fundamental query was arisen regarding the origin of these ridges, what caused them to initiate and how? What are the material properties that constitute this behavior, and more generally, under which conditions the fracture of a brittle single crystal would be atomically flat.

To gain some understanding of the origin of these instabilities, specimens containing boron dopants with two distinct dopant concentrations (1015 and 1019 atoms/cm3) extracted from specimen’s resistivity were cleaved and analyzed. While the same specimen geometry and same experimental conditions were taken, the results were astonishingly different. The fracture surface ridges were generated at a critical crack speed below 1100 m/sec and their density has been shown to increase significantly with increasing boron concentration. The origin of the above ridges was experimentally revealed by in situ fracture experiments of miniaturized bending specimens under ultra-high vacuum (UHV) and their surface analysis using scanning tunneling microscope (STM). These suggest a speed dependent crack tip-dopant interaction mechanism, generating atomic height jogs which grow by over 3 orders of magnitude and terminating as micron scale ridges. Interestingly, this phenomenon was generalized by additional fracture cleavage experiments of silicon with oxygen as interstitials, and silicon and germanium doped with phosphorus and gallium, respectively. The results correlate the surface instabilities to atomic chemical strain. Surprisingly, the {110} cleavage plane showed no evidence for crack interaction with point defects on the fracture surface. Apparently, the {111} plane demonstrates atomic phenomena due to the anti-symmetric atomistic arrangement of the cleavage plane surrounding, while other planes shields them. These results enabled the establishment of a complete understanding of the fracture surface instabilities herein. The findings were also encouraged by multi scaled quantum mechanical molecular mechanics calculations.

An energy balance model describing dynamic fracture instability was developed, demonstrating the relationship between fracture surface jogs, chemical strain, crack speed, and material anisotropy. The requirements for finding the critical conditions of speed and strain to perturb a brittle crack from its initial path are defined, determining the origin of fracture surface instabilities at the lowest scale.