六方最密堆积密度的计算-《集美大学学报（自然科学版）》

文章信息/Info

Author(s):: ZOU Zongfeng; (School of Science,Jimei University,Xiamen 361021,China)

Keywords:: sphere packing problem; sphere packing density; face-centered cubic packing; hexagonal closest packing

摘要:: 本文提出一种计算六方最密堆积(hexagonal close packing,HCP)密度的新方法。针对3维等径球堆积问题，验证了HCP的密度最大值，为该经典几何问题的教学与计算提供新的思路。从HCP的晶胞结构出发，通过分析晶胞中球体半径与晶胞参数之间的几何约束关系，建立比例关系，进而计算单个晶胞中球体的总体积占晶胞体积的百分比。经计算，HCP的空间利用率约为74%，该值与面心立方堆积的空间利用率相等。

Abstract:: This paper presents a new method to calculate the density of hexagonal close packing (HCP).In the context of equal-sphere packing in three-dimensional space,the aim is to verify the maximum density of HCP,thereby offering a new approach for both teaching and computation of this classic geometric problem.Starting from the unit cell structure of HCP,the geometric constraints between the sphere radius and the unit cell parameters are analyzed to establish a proportional relationship.Based on this,the percentage of the total volume of spheres occupying the unit cell volume in a single unit cell is calculated.The calculation shows that the space utilization of HCP is approximately 74%,which equals that of face-centered cubic close packing.