固化在許多製程中扮演著中重要的角色，而不同的固化過程對生成物的機械性質也有很大的影響。而由固化所得的晶體，晶格排列越規則則其機械性質越佳，例外強度、延展性。單向固化製程由於其鑄造物有較佳的機械性質，所以常用於渦輪葉片的製造，但由於其在固化過程中往往會出現一些缺陷，使的良率降低，這是和生長過程中，固液介面上會產生過冷現象而導致形態的不穩定所造成。本文的目的是探討週期性調變溫度對單向固化形態穩定的影響，並希望藉由改變流場中的一些參數來抑止其形態不穩定的發生。 The main goal of this thesis is to investigate into the influence of temperature modulation on the morphological stability of directional solidification. We study the morphological instability of the melt-solid interface of a dilute binary alloy. The alloy is assumed to undergo directional solidification into a modulated temperature field. Under such a circumstance, the molten zone is oscillated back and forth in a periodic way. The basic state is solved analytically assuming the melt-solid interface is flat and the bulk melt is quiescent by expanding the governing equation in terms of the assumed infinitesimal modulation amplitude. By further neglecting the flow field, we investigate the interfacial stability of the base state by considering two specific instability modes: the synchronous and sub-harmonic modes. The synchronous modes vary with time having the same frequency as that of the oscillatory molten zone, while the sub-harmonic modes are of the half frequency.
