Pilling-Bedworth ratio

Metal oxide scales can be defined as protective and nonprotective using the classical PUling-Bedworth law as the ratio given by [1] 

The PB ratio is used to characterize several oxidation conditions. Thus, 

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Pilling-Bedworth Ratio the ratio of the volume of an oxide film on a metal to the volume of metal used to form that oxide. 

Pilling-Bedworth ratio of 1 96, anatase phase films can show cracks and fissures with, consequendy, a loss of mechanical stability, however a hydrogen reduction treatment above 600°C leads to phase transition from anatase (101) to rutile (110) [43] with XRD detecting TiH2 upon prolonged hydrogen treatment of titania. As shown in Fig. 4.4, introduction of vanadium increases the intensity of the anatase Ti02 peak above 700°C disappearance of the vanadium (001) peak and the simultaneous appearance of the rutile (110) peak are observed, but anatase continues to dominate even after heat treatment at 800° C. A sharp vanadium (001) peak is observed for heat treatments carried out in air, while no vanadium peak has been seen in the case of heat treatment at 600°C in presence of Ar/H2. 

A good indicator of whether an oxide layer is protective is given by the Pilling-Bedworth ratio... 

One factor that is readily assessed is the volume of oxide produced by oxidation of a given volume of metal. This is called the Pilling-Bedworth ratio, XpB, and is most readily expressed in terms of molar volumes ... 

If the Pilling-Bedworth ratio is less than 1 the oxide cannot cover the metal completely and the oxide film has an open or porous structure. Oxidation takes place continuously, and the oxidation kinetics tend to be linear. This type of behaviour is found for the alkali and alkaline earth metals. In the rare cases where the PiUing-Bedworth ratio is equal to 1, a closed layer can form which is stress-firee. When the Pilling-Bedworth ratio is greater than 1, a closed layer forms with a certain amount of internal compressive stress present. 

The cause of stress in this case is the fact that the specific volume of the oxide is rarely the same as that of the metal which is consumed in its formation. The sign of the stress in the oxide may be related to the Pilling-Bedworth ratio (PBR) ... 

Similar situations can be expected for other oxidation reactions, for example, in the oxidation of Ti, Nb, Ta, and so on, even more complex situations, since mostly multilayers of different oxides should be formed. The growth of oxides involving zones with different disorder and insufficient electronic conduction, however, has not been studied and discussed satisfactorily as yet [2]. One reason may be that most of these oxides do not form dense compact oxides, but tend to crack and spall, due to growth by inward oxygen diffusion and a high ratio of the molar volumes of the oxide and metal (Pilling-Bedworth ratio). 

The adherent oxide scale also protects the metal smface from erosion. A general indicator of the protectiveness of the oxide scale is given by the Pilling-Bedworth ratio (PBR), which is defined by the volume ratio of oxide formed to metal consumed. The scale becomes fully protective when PBR 1. PBR 1 means that the oxide is porous and, consequently, loses any protective properties. PBR > 1 means that the oxide scale is highly compressed, thus resulting in buckling and spallation [18]. 

The many causes of corrosion will be explored in detail in the subsequent chapters of this book. In this introductory chapter, two parameters are mentioned the change in Gibbs free energy and the Pilling-Bedworth ratio [5]. 

Although many factors control the oxidation rate of a metal, the Pilling-Bedworth ratio is a parameter that can be used to predict the extent to which oxidation may occur. The Pilling-Bedworth ratio is MdInmD, where M and D are the molecular weight and density, respectively, of the corrosion product scale that forms on the metal surface during oxidation m and d are the atomic weight and density, respectively, of the metal, and n is the number of metal atoms in a molecular formula of scale for example, for AI2O3, n = 2. 

Most metals used at high temperatures have a Pilling-Bedworth ratio greater than 1 (RpB > ) During oxidation, compressive stress therefore develops in the oxide layer. Two mechanisms act to dissipate the stress ... 

Physical factors can play a major role in service, and each investigator should be alert to the significance of these factors. Included here are such factors as the volume of scale to the volume of substrate from which it is produced, the so-called Pilling-Bedworth ratio [72], the coefficient of expansion differences between the scale and substrate, the effect of the relative scale thicknesses, scale transformation stresses, thermal stresses, imposed stresses, plasticity of the scale, and the physical condition of the scale (porosity, presence md nature of any cracking, decohesion, and number of layers). Specimen size and shape can influence test results. Edges md comers behave differently than planar smfaces. 

Therefore, MaOz is theoretically protective as predicted by the Pilling-Bedworth ratio range 1 < PB < 2. 

Chapter 10 deals with high temperature corrosion, in which the thermodynamics and kinetics of metal oxidation are included. The Pilling Bedworth Ratio and Wagner s parabolic rate constant theories are defined as related to formation of metal oxide scales, which are classified as protective or nonprotec-tive. 

Table 2-5. Pilling-Bedworth ratios for some technically important oxides and metal substrates .

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