No abstract

Cylindrical/ring-shaped permanent magnets with diametrical magnetization can be found in many applications, ranging from electrical motors to position sensory systems. In order to correctly calculate the magnetic field generated by a permanent magnet of this kind with low computational cost, several studies have been reported in literature providing analytical expressions. However, these analytical expressions are either limited for an infinite cylinder or for computing the magnetic field only on the central axis of a finite cylinder. The others are derived to calculate the magnetic field at any point in three-dimensional (3D) space but only with low accuracy. This paper presents an exact analytical model of the magnetic field, generated by a diametrically magnetized cylindrical/ring-shaped permanent magnet with a limited length, which can be used to calculate the magnetic field of any point in 3D space fast and with very high accuracy. The expressions were analytically derived, based on geometrical analysis without calculating the magnetic scalar potential. Also, there is no approximation in the derivation steps that yields the exact analytical model. Three components of the magnetic field are analytically represented using complete and incomplete elliptical integrals, which are robust and have low computational cost. The accuracy of the developed analytical model was validated using Finite Element Analysis and compared against existing models.

A series of biocompatible high-porosity (up to 72.4%) TiZr-based porous bulk metallic glass (BMG) scaffolds were successfully fabricated by hot pressing a mixture of toxic element-free TiZr-based BMG powder and an Al particle space holder. The morphology of the fabricated scaffolds was similar to that of human bones, with pore sizes ranging from 75 to 250 μm. X-ray diffraction patterns and transmission electron microscopy images indicated that the amorphous structure of the TiZr-based BMG scaffolds remained in the amorphous state after hot pressing. Noncytotoxicity and extracellular calcium deposition of the TiZr-based BMG scaffolds at porosities of 32.8%, 48.8%, and 64.0% were examined by using the direct contact method. The results showed that the BMG scaffolds possess high cell viability and extracellular calcium deposition with average cell survival and deposition rates of approximately 170.1% and 130.9%, respectively. In addition, the resulting TiZr-based BMG scaffolds exhibited a considerable reduction in Young’s moduli from 56.4 to 2.3 GPa, compressive strength from 979 to 19 MPa, and bending strength from 157 MPa to 49 MPa when the porosity was gradually increased from 2.0% to 72.4%. Based on the aforementioned specific characteristics, TiZr-based BMG scaffolds can be considered as potential candidates for biomedical applications in the human body.