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I.

INTRODUCTION

IN previous work,[1] it is theoretically predicted that hydrogen-trap binding enthalpy, HB, is substantially linearly related to the temperature of hydrogen release peak, TP, in hydrogen evolution experiments as HB 1 DH' 5 g (N, m0)kBTP

[1]

where DH' is a constant, g (N, m0) being a function of trap site density N and parameter of detrapping or release m0.[1] It should also be noted that linearity of the relationship has been shown to be valid for a range of values of trap parameters broad enough for substantially all the possible conditions of hydrogen diffusion in steel to be covered. The assumed values of activation enthalpy, HL, and pre-exponential factor, D0, for lattice hydrogen diffusion are HL 5 0.082 eV (1900 cal/mol) and D0 5 0.78 z 1023 cm2/s. In the present work, the influence on the aforementioned HB-TP relation of parameters of lattice hydrogen diffusion (i.e., activation enthalpy and pre-exponential factor for lattice diffusion and other influential factors, i.e., initial temperature of heating, heating rate, and specimen size) will be considered.

trap sites. First, trap sites are of such a depth that hydrogen atoms on these trap sites are released upon being heated in hydrogen evolution experiments. Second, trap sites are deep enough for a substantial fraction of hydrogen atoms on these trap sites to be kept bound up to a maximum test temperature, usually 1000 K or lower. The physically permissible maximum test temperature is limited by the thermostability of the heat-resisting glass pipe used in the carrier gas flow line in the experimental system, and is normally 1000 K. It is impossible to measure the deepest binding enthalpy by the hydrogen evolution experiment, but the fraction of hydrogen atoms captured by such strong trap sites, if any, is to be analyzed by vacuum fusion or carrier gas fusion method. Further, it may be postulated that hydrogen atoms on shallow enough trap sites, including a diffusible hydrogen,* have little influence on the evolution *A diffusible hydrogen is defined by hydrogen atoms that are released from the specimen upon heating the specimen up to 318 K.

peak temperature. Hydrogen diffusion in a cylindrical specimen containing the aforementioned two kinds of trap sites can be described by the following three equations in nondimensional form: ]u/]t 1 ]v1/]t 1 ]v2 /]t 5 ] 2u/]r 2 1 (1/r)(]u/]r)

II.

THEORY

In order to know the physical meaning of the proportionality factor g (N, m0) and constant DH' in Eq. [1], we will first examine a possible change in relation [1] caused by a virtual change in activation enthalpy, HL, of lattice hydrogen diffusion. We are now considering the problem of hydrogen evolution during ramp heating, at rate ε, a system which contains the following two kinds of hydrogen

MAKIO IINO, Professor, is with the Department of Mechanical Engineering, Faculty of Engineering, Yamaguchi University, Ube City, 755 Japan. Manuscript submitted June 6, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A

[2]

]v1/]t 5 k1u(1 2 u1) 2 m1v1

[3]