HYDROGEN DIFFUSION IN AMORPHOUS FeCrB RIBBONS

The article deals with the study of hydrogen absorption (hydrogenation) and desorption (dehydrogenation) in amorphous ferromagnetic FeCrB ribbons prepared by rapid quenching from the melt. A simple theoretical model was proposed for description of hydrogen concentration and determination of diffusion coefficient in these materials. Using this model diffusion coefficient can be calculated using experimentally obtained values of average hydrogen concentration in the sample during dehydrogenation process. The values of diffusion coefficients are comparable with those obtained by hydrogen permeation test. The proposed method is not only simple but it also makes possible to determine diffusion coefficient under the same conditions as the changes of other properties of these materials during their dehydrogenation.


INTRODUCTION
The parameters that characterize ferromagnetic material from the point of view of its possible technical applications are closely related to its physical properties and structure.Amorphous ferromagnetic alloys are materials widely used for electronics purposes.The study of their structural properties is very important because their magnetic, electric properties and stability in the operating conditions depend on their structure.
Heat treatment of amorphous materials is often used in the study of their structure and its possible modification although it can result in irreversible changes in amorphous structure.Significant predominantly reversible changes of some properties of amorphous ferromagnetic materials can be created by hydrogenation of amorphous material and subsequent dehydrogenation.Interaction of hydrogen with the structure of amorphous alloys has been intensively studied in last decades since hydrogen can influence electrical and magnetic properties of these materials and can also serve as a probe for the study of their structure [1].That is why the study of hydrogen absorption (hydrogenation) and desorption (dehydrogenation) and determination of parameters of hydrogen diffusion in these alloys are of great importance.It has to be taken into account that this treatment is suitable only for materials which do not contain elements with a strong affinity to hydrogen.Basic parameter of hydrogen diffusion is diffusion coefficient that reflects mobility of hydrogen atoms in studied materials [2].The standard method to study the diffusion of hydrogen in ribbon-shaped amorphous samples is hydrogen permeation test [3,4].In this paper we propose an alternative method for determination of diffusion coefficient from the measurement of average hydrogen concentration in amorphous samples during their dehydrogenation.This method provides a possibility to determine the diffusion coefficient and the concentration profile during the dehydrogenation of the sample.
The main advantage of this method consists in the facts that it is simple and diffusion coefficient is determined under the same conditions as the changes of other properties of these materials during their dehydrogenation [5].

EXPERIMENTAL
The studied samples Fe 85 B 15 , Fe 81.5 Cr 0.8 B 17.7 , Fe 80 Cr 4.3 B 15.7 and Fe 77.4 Cr 6.5 B 16.1 were prepared by rapid quenching from the melt in KFKI MTA in Budapest.Elements of these materials do not exhibit affinity to hydrogen.The width w of the samples was about 12 mm and thickness L was a few tens of millimeters (in detail see the first two rows in Table 1).The length of samples used in experiments was 104 mm.Atomic hydrogen was introduced into samples electrolytically from air side of ribbons [6] (Fig. 1).The duration of hydrogenation was 2 hours.Then the sample was placed into a closed chamber.The hydrogen content was determined from the measured changes of pressure and temperature [7] (Fig. 2).

THEORY
Hydrogenation and dehydrogenation of ribbon-shaped amorphous FeCrB samples can be described by Fick's laws of diffusion where j is a flux of hydrogen atoms, D is diffusion coefficient and c is hydrogen concentration.For the material under study it is correct to assume that D does not depend on c.The solution of Eq. 2 strongly depends on the initial and boundary conditions.If a ribbon-shaped sample of thickness L is hydrogenated from one side, hydrogen atoms diffuse from one side of the sample where their concentration is of maximum value c 0 to the opposite side where the concentration is equal to zero (Fig. 3a), then the initial and boundary conditions are: c(x,0) = 0 for x > 0 and c(0,t) = c 0 , c(L, t) = 0 for all t > 0. The solution of Eq. 2 satisfying these conditions is from which also the flux of hydrogen atoms j(x,t) (Eq. 1) can be calculated (see Fig. 4).
Both quantities c(x,t), j(x,t) can be measured on the opposite side of the sample (x = L) in hydrogen permeation test.Fitting experimentally obtained c(L,t), j(L,t), values to the Eq. 3 and 1, the hydrogen diffusion coefficient can be obtained [3,4].
Diffusion coefficient as well as the maximum of hydrogen concentration in the sample can be obtained from experimental data obtained during dehydrogenation also using a new and relatively simple procedure which will be described now in detail.As was mentioned above dehydrogenation process (Fig. 3b) obeys Eq. 2, for which the initial concentration of hydrogen atoms c(x,0) inside the sample is given by Eq. 3 where t 0 is the time of hydrogenation and the boundary conditions are: c(0,t) = c(L,t) = 0 for all t > 0, where t is current time of dehydrogenation.
The concentration c(x,t) satisfying these conditions is: In the experiment an average hydrogen concentration   t c is obtained.It can be also calculated using equation This gives The experimental results of average hydrogen concentration vs. time can be fitted to the function   for 50 hours (it is obvious that that time is enough for hydrogen to be released from the ribbon sample) of dehydrogenation for D = 2.3×10 -15 m 2 s -1 , calculated using Eq. 5.

RESULTS AND DISCUSSION
In metals hydrogen atoms occupy interstitial sites.The maximum hydrogen concentration then can be 3.0 [H/Me], however experimentally obtained values are much lower (e.g. for steel 1.8×10 -3 [H/Me], where Meinstead of a chemical symbol of metal).The situation in amorphous materials is even more complicated since they are materials with only short-range order and hydrogen solubility is influenced also by the energy distribution of available interstitial sites [1,3].
The values of average hydrogen concentration in the studied samples obtained experimentally during dehydrogenation were fitted to the function    Experimentally obtained values and corresponding fitted curves are shown in Fig. 7. Magnetic measurements on the samples studied in this paper revealed that chromium introduces stress in amorphous structure proportional to the Cr content [4].

Fig. 3
Fig. 3 Scheme of a) hydrogenation and b) dehydrogenation

(Fig. 4 Fig. 5 Fig. 6
Fig. 4 Experimental results and theoretical dependence of the concentration of H in amorphous ribbon Fe 85 B 15 vs. time calculated using fitting parameters c 0 and D obtained from the fit of experimental data during dehydrogenation (see Tab. 1).For fitting the least square method was used.Using obtained fitting parameters c 0 and D the profiles of concentration during hydrogenation and dehydrogenation can be calculated.In Figs. 5 and 6 these profiles are depicted for the same sample Fe 85 B 15 .
using the least square method.The obtained values of maximum H concentration c 0 and hydrogen diffusion coefficient D are listed in Tab. 1.

Table 1
The values of width w, thickness L, maximum concentration c 0 and diffusion coefficient D of samples: A-Fe 85 B 15 , B-Fe 81.5 Cr 0.8 B 17.7 , C-Fe 80 Cr 4.3 B 15.7 ,D-Fe 77.4 Cr 6.5 B 16.

Fig. 7
Fig. 7 Experimental and calculated values of average hydrogen concentration in FeB and FeCrB ribbons during dehydrogenation.The stress centers are then probably less accessible for hydrogen atoms because for the samples with chromium admixture the c 0 values are distinctly lower than for FeB sample (Tab.1).The calculated values of diffusion coefficient are of the same order as those obtained for amorphous FeNiMoB and NiP alloys by hydrogen permeation test [1,4].Obtained values indicate that chromium up to 4.3 at.% increases hydrogen mobility in amorphous materials since the values of diffusion coefficient for Fe 81.5 Cr 0.8 B 17.7 and Fe 80 Cr 4.3 B 15.7 are almost three times higher than for Fe 85 B 15 sample.However, further increase of Cr content results in material with lower hydrogen mobility (Fe 77.4 Cr 6.5 B 16.1 ).This corresponds also with character of calculated distributions of concentration in samples depicted in the Figs. 8 and 9.In the samples Fe 85 B 15 and Fe 77.4 Cr 6.5 B 16.1 after 4 hour dehydrogenation these distributions are markedly asymmetrical.For Fe 81.5 Cr 0.8 B 17.7 after the same time the distribution is less asymmetric and for Fe 80 Cr 4.3 B 15.7 it is almost symmetrical.

Fig. 8
Fig. 8 Asymmetrical distribution of hydrogen in the amorphous ribbon Fe 85 B 15 for 4 hour dehydrogenation calculated using Eq. 5