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Ingredients of Pyrotechnic Compositions
Published in Ajoy K. Bose, Military Pyrotechnics, 2021
The metal oxide ratio, also known as N. Pilling and E. Bedworth ratio (or P–B ratio), is the ratio of the volume of the elementary cell of a metal oxide to the volume of the elementary cell of the corresponding metal (from which the oxide is created). In other words, it is the ratio of volume of the oxide formed to the volume of the metal consumed. This can be shown in the equation: RPB=Voxide/Vmetal=(Moxide×ρmetal)/(n×Mmetal×ρoxide)where RPB is the Pilling–Bedworth Ratio, M is the molecular or atomic mass, n is the metal atom per oxide molecule (Example n = 1 for MgO, n = 2 for V2O5 and Cr2O3), V is the molar volume, ρ is the density. P–B ratio provides an idea about the type of such films.
The Importance of Magnesium and Its Alloys in Modern Technology and Methods of Shaping Their Structure and Properties
Published in Leszek A. Dobrzański, George E. Totten, Menachem Bamberger, Magnesium and Its Alloys, 2020
Leszek A. Dobrzański, George E. Totten, Menachem Bamberger
Magnesium rather easily oxidises in air, but, as in the case of aluminium, the corrosion process is inhibited by passivation. In contrast to aluminium (PBR = 1.28), magnesium, however, has an unfavourable Pilling–Bedworth ratio PBR = 0.80 [11,12], as a result of which the passivation coating is less effective. Magnesium is also passivated in concentrated (98%) sulphuric acid and in the presence of iodine vapours. A passivation layer of the poorly soluble magnesium fluoride protects it to the temperature of 600°C, and also against the activity of hydrofluoric acid [13]. Magnesium reacts slowly with hot water with temperature of >70°C, forming magnesium hydroxide. It is completely resistant to the activity of alkali, and vigorously reacts with acids, by creating corresponding salts and releasing hydrogen [10]. Magnesium is a flammable substance, the flash point is approx. 760°C. Magnesium dust is pyrophoric, its flash point is approx. 470°C. Magnesium in the air burns with a blinding white flame, whose temperature is 3000°C–3100°C. The main product is magnesium oxide, accompanied by magnesium nitride. Incineration is also maintained in an atmosphere of water vapour and carbon dioxide. Magnesium dissolves when heated in methanol and ethanol by producing relevant magnesium alcoholates. Such reactions are initiated by iodine and inhibited by water with the fraction of over 1%. They are used to produce alcoholates and to obtain the so-called absolute ethanol, i.e., the product with a very small fraction of water.
Mechanistic model for stresses in the oxide layer formed on zirconium alloys
Published in Journal of Thermal Stresses, 2019
Isha Gupta, J. R. Barber, M. D. Thouless, Wei Lu
Zirconium oxide has a higher molar volume than zirconium, so a biaxial compressive stress is developed in the oxide film owing to the constraint exerted by the substrate while the oxide forms. The Pilling–Bedworth ratio, VPB, defined as the ratio of the molar volume of the oxide to the molar volume of the metal, is equal to 1.56 for zirconium oxide [1]. If the volumetric expansion during unrestrained growth is assumed to be isotropic, the resulting compressive strain within the oxide would be given by implying in-plane compressive stresses within the oxide of around 57GPa. It can be seen that substitution of such stress levels into Eq. (8) results in huge plastic strain rates, implying a very rapid relaxation of stresses to more reasonable levels. Previous studies [6, 20] have assumed that the oxide forms at an in-plane compressive stress of about 2GPa, but stresses as high as 4GPa have been measured experimentally [21, 22], suggesting that the value 2GPa is merely an arbitrary temporal point for a rapidly relaxing compressive stress. However, the precise details of how the stresses relax from the theoretical initial value is beyond the scope of this work.