利用密度泛涵理論討論鎂、鍶和鋅摻雜對氫氧基磷灰石機械性質的影響

隨著經濟以及醫療產業的蓬勃發展，大家對醫療品質要求越來越高，促使越來越多人投入生醫材料的研究，氫氧基磷灰石(Hydroxyapatite,HA)為一種骨填補材料，雖然有優異的生物相容，但在臨床上希望能在提高HA機械強度。本次研究利用密度泛含理論在HA單位晶胞內摻雜鎂、鍶、鋅離子去替換原本的鈣離子，並計算HA的機械強度，由於HA的單位晶胞內鈣原子可以替換的位置有十個，在本次研究中有單顆、雙顆、三顆以及混合離子摻雜故在選定摻雜結構時，我們利用排列組合將所有摻雜位置都先做過結構優化的計算，再觀察在哪個摻雜位置的時候會有最為穩定的結構，其中將鈣的位置分成Ca(1)以及Ca(2)的位置，可以觀察出摻雜鎂和鍶的結構中在Ca(1)位置中比較容易產生較穩定的結構，在摻雜鋅的結構中可以發現鋅摻雜在Ca(2)的位置中比較容易產生較穩定的結構。在機械強度上的計算我們分別將材料以2%的應變為一個單位拉伸以及壓縮至10%，接著利用能量和體積以及應變的關係擬合二次曲線並計算C11與C33彈性常數和體積模數(bulk modulus)，其中影響彈性常數的原因分別有氫氧基磷灰石中鈣之間的距離、磷之間的距離、電負度以及離子半徑，可以發現在單顆鍶摻雜、雙顆鍶摻雜、雙顆鎂單顆鍶混合摻雜、三顆鎂雙顆鍶混合摻雜的結構中可以增加C11彈性常數；在單顆鎂摻雜、單顆鎂單顆鍶混合摻雜、雙顆鎂雙顆鍶混合摻雜可以使C33彈性常數增加，在體積模數部分則是全部都下降，其中彈性常數的改變以單顆鎂單顆鍶以及雙顆鎂雙顆鍶的混合摻雜結構最符合本次實驗的目標，這兩個摻雜結構在提升C33彈性常數的同時其體積模數沒有太大的下降。

關鍵字

密度泛涵理論；氫氧基磷灰石；機械性質

並列摘要

As the economy is growing and blooming, customers expect high-quality medical treatments and services. Hydroxyapatite (HA) is used in filling the bones because of its biocompatibility. However, HA does not have sufficient mechanical strengths for clinical usage. In this research, we used density functional theory to study the mechanical properties of Mg, Sr, and Zn substituted HA. The Ca ion in HA was replaced by Mg, Sr, and Zn. We calculated single doped, double doped, triple doped, and mixed doped systems. Doped Mg and Sr ions were more stable in the Ca(1) than in the Ca(2) site. On the other hand, doped Zn ions preferred the Ca(2) sites. In the mechanical strength calculations, we stretched and compressed the material with a strain from 2% to 10%. Then, we used the energy-volume and energy-strain relationships to calculate C11 and C33 elastic constants and bulk modulus. The factors to influence the elastic constant are the distance between Ca and P atoms in HA, electronegativity, and radius of ions. The C11 elastic constant increased in single-Sr-doped, double-Sr-doped, double-Mg-doped single-Sr-doped, and triple Mg-double-Sr-doped HA. The C33 elastic constant increased in single-Mg-doped, single-Mg-Sr-doped, and double Mg-Sr-doped. We found that all doped HA had lower bulk modulus than pure HA. Nevertheless, the bulk modulus of single-Mg-Sr-doped and double Mg-Sr-doped decreased slightly and improved the C33 elastic constant. The Mg-Sr mixed doping shows improvements on the mechanical strength of HA.