Stress Analysis of KDP Single Crystals Caused by Thermal Expansion Mismatch during Traditional Growth

Abstract

To further elucidate the relationship between the growth stress and cracking of KDP (KH2PO4, potassium dihydrogen phosphate) crystals of different sizes, a three-dimensional finite element calculation was conducted to analyze the growth stress of KDP single crystals grown from Z-plate seeds with varying cooling rates. The mismatch in the coefficient of thermal expansion (CTE), between the cap region and its close vicinity, and among the transparent region, was taken into account. The results indicate that when the cap region is a solid region (when the seed was regenerated with a cooling rate of 0.1 °C/day), the difference in material properties between the cap region and its close vicinity, especially the CTE mismatch along the a-axis, is the main reason of the high stresses. When the cap region is a box-like structure filled with solution (when the seed was regenerated with a cooling rate of 0.3 °C/day), the calculated stress is in proportion to the CTE gradient of the transparent region. Under both models, the stresses induced from an incremental CTE value (from the cap region to the growth front) are greater than those calculated from a diminishing CTE value, implying that the impurities reduce the CTE of KDP crystals, causing the crystals to crack more easily. Despite the maximum stresses inside the crystals changing slightly with an increase in crystal size, the decreased fracture stress of large brittle crystals leads to a higher cracking risk in a large-sized crystal.

Keywords

• KDP crystals
• cracking
• mismatch in coefficient of thermal expansion
• thermal stress