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A model to calculate the effective elastic modulus of a single crystal cantilever used as a substrate for magnetostrictive measurements of thin films is given. Calculations are presented for Si (110), sapphire (11̄00) (M plane) and (12̄10) (A plane) cantilevers. Numerical calculations using the finite element method for sapphire show a very high accuracy of the proposed model.

Refractory Metals and their Application in the Chemical Process IndustrySpecial metals, such as titanium, zirconium and tantalum, are being used increasingly for chemical plant. The exceptional resistance of special metals to many corrosive chemicals -they show it even at high temperatures and pressures -arises not from natural immunity but from the formation of a protective oxide passivp layer on the metal surface. Special metals are well suited for welding. Their reactions with gases of the atmosphere must be taken into account though. Welding is therefore possible only under inert gas or a high vacuum. Similarly, alloying with iron-based materials during welding must be avoided under all circumstances. It should be taken into consideration that the melting point of tantalum, for example, is about twice as high as that of steel. Tantalum and niobium are machined with high-speed cutting steels; the cutting speed and cutting angle are similar to those used for stainless steels. In detail, the outstanding properties of special metals in chemical plant are as follows: -the stability of titanium under oxidizing conditions -the stability of zirconium under reducing and alkaline conditions -the resistance of molybdenum to hydrofluoric acid and fluoride -the stability of tantalum under oxidizing and reducing conditions. In pure mineral acids the passive behaviour generally improves in the order titanium -zirconium -tantalum. Except where molybdenum is concerned, the medium should not contain fluoride. The material with the widest range of applications is tantalum. The addition of niobium as an alloying element leads to favourably priced but similarly resistant materials whose prospects of becoming established in the chemical industry and playing a part similar in importance to that of tantalum itself are good.