Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 156

The expansion or contraction of a material upon heating or cooling is commonly quantified by its linear coefficient of thermal expansion α defined by the equation

(4.48)

where, Δl is the change in length of a specimen of length l_o due to a change in temperature ΔT. The thermal expansion coefficient has the unit °C⁻¹ (or K⁻¹) but is often expressed in units of 10⁻⁶ °C⁻¹ because of its low value. The thermal expansion coefficient of one material relative to another is dependent on its interatomic bonding energy versus displacement curve (Section 2.2).

Although α varies slightly, depending on the temperature range of measurement, ceramics and glasses typically have low α values relative to other classes of materials, in the range ~5 × 10⁻⁶ to ~15 × 10⁻⁶ °C⁻¹ over a temperature range of a few hundred degrees Celsius above room temperature. On the other hand, some glasses, such as fused silica glass, and a few glass‐ceramics have values as low as ~0.5 × 10⁻⁶ °C⁻¹. Metals have higher α values, in the range ~10 × 10⁻⁶ to ~25 × 10⁻⁶ °C⁻¹ but tungsten and a few metal alloys, for example, have values lower than ~5 × 10⁻⁶ °C⁻¹. Polymers have the highest values, typically ~100 × 10⁻⁶ °C⁻¹ and over.

A difference in thermal expansion coefficient leads to the development of mechanical stresses between two adherent materials upon heating or cooling. If high enough, these stresses can lead to cracking and delamination of one material from the other, such as a coating deposited on a three‐dimensional material. Metal implants, such as Ti6Al4V for example, have been coated with a bioactive material such as hydroxyapatite or bioactive glass, of thickness several tens of microns to a few hundred microns, to improve their bioactivity and osseointegration with host bone. These coatings are often formed on the metal implant at several hundred degrees Celsius. Ti6Al4V, for example, has a thermal expansion coefficient of ~9.5 × 10⁻⁶ °C⁻¹. Consequently, coating materials for Ti6Al4V should have a thermal expansion coefficient that is not significantly different from this value to minimize stresses in the coating and reduce the potential for cracking or delamination of the coating during cooling from the fabrication temperature. Bioactive glass‐coated implants have seen little clinical application despite efforts to design glass compositions having thermal expansion coefficients that match those of implants such as titanium or Ti6Al4V (Peddi et al. 2008). In comparison, hydroxyapatite (thermal expansion coefficient of 10.0 × 10⁻⁶–10.5 × 10⁻⁶ °C⁻¹) has been used for a few decades to coat dental and orthopedic implants, particularly those composed of titanium or Ti6Al4V. While considerable efforts have been devoted to creating adherent hydroxyapatite coatings using a variety of techniques, indications for the capacity of these coatings to enhance the long‐term viability of the implants remain controversial (Le Guéhennec et al. 2007).