New measurements on time decrease of permeability

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New measurements on time decrease of permeability

A.J. Bosman, P.E. Brommer, G.W. Rathenau

To cite this version:

A.J. Bosman, P.E. Brommer, G.W. Rathenau. New measurements on time decrease of permeability. J.

Phys. Radium, 1959, 20 (2-3), pp.241-243. �10.1051/jphysrad:01959002002-3024100�. �jpa-00236025�

241

NEW MEASUREMENTS ON TIME DECREASE OF PERMEABILITY

A. J. BOSMAN, ^{P. E.} BROMMER, ^{G. W.} RATHENAU,

Natuurkundig Laboratorium der Universiteit van Amsterdam, Amsterdam, ^The Netherlands.

Résumé.

La désaccommodation des alliages FeSi est mesurée dans le domaine où la cons-

tante de magnétostriction h1 disparaît. ^On trouve que cet effet a peu d’influence.

Il semble que le carbone soit plus efficace que l’azote pour produire ^la désaccommodation, ^tandis

que le contraire ^est vrai pour le frottement interne.

En remplaçant le 12C par 13C le changement ^du coefficient de diffusion s’obtient par la mesure

de la désaccommodation. On trouve une diminution de (4 ± 1) %.

Abstract.

The disaccommodation of Fe-Si alloys has been measured. In the region ^where

the magnetostriction ^constant h1 changes sign the disaccommodation is little affected.

It seems that the disaccommodation due to carbon is larger than the effect due to a corresponding

atomic percentage ^of nitrogen, although ^the contrary ^{is true} for internal friction. The ratio of the diffusion coefficients of 12C and 13C in pure iron has been determined, again by measuring ^the

disaccommodation. We find a value of (1,04 ± 0,01) ⁱⁿ agreement ^{with a} (m)-1/2 relationship

for the diffusion coefficient.

LE JOURNAL DE PHYSIQUE ^{ET LE RADIUM TOME} 20, ^FÉVRIER 1959,

Introduction.

The time decrease of _permea-

bility (disaccommodation) ^{due to} interstitials in iron according ^{to Néel} [1, 2] originates ^{from a}

direct non-mechanical interaction between the interstitials and the magnetization ^{vector. It is} argued ^{that a} magnetostrictive interaction alone is too small to account for Snoek’s [3] observations.

Brissonneau [4] ^has brought additional evidence in showing ^{that besides 900} walls, 1800 walls also contribute to the disaccommodation in iron. It

seems worth-while to present ^more data which

strengthen ^the theory.

We have measured the disaccommodation of

alloys ^{in the} silicon-iron system for which Carr and Smoluchowski [5] ^{have shown the} magneto- striction constant h1 (3/2 03BB100 ) (3/2 100 ^to change sign ^{in a}

range of composition ^{in which} h2 is small. We also want to stress the différence in disaccommo- dation produced by ^{the same amount} of intersti- tial carbon and nitrogen ^and compare ^{this with} the difference in opposite direction in internal friction.

Finally it is shown that the disaccommodation is a tool adapted ^{to measure small} changes ^{in rela-}

xation time. It can give information about the diffusion process upon which it is based.

Measurements in the silicon-iron system. - Four alloys of Si and pure iron produced by ^vacuum melting ^and casting [6] ^{have been} kindly put ^at

our disposal by ^Professor J. D. Fast of Eindhoven.

Rings made from all of these alloys ^{have been heat-}

ed together ^{in an} atmosphere ^of purified dry hydrogen ^{and methane} for 30 hours ^at 1000 C.

After this ^{water was} suddenly poured upon the

quartz container ^to gas quench ^the specimens.

After 20 hours annealing ^{the 4.5 wt} % ^Si rings

scemcd already saturated with carbon with respect

to the gas atmosphere.

We assume that all alloys ^were saturated after 30 hours. The carbon contents relative to the 4.5 % ^Si alloy ^can then be calculated for all spe- cimens (Smith [7]). The values of the disaccom- modation reproduced ⁱⁿ figure ^{1 have been reduc-}

ed to the same amount of carbon in all alloys assuming proportionality between time decrease and carbon concentration. We think that this amount is about 5/1000 ^wt % ^of carbon, ^{on the}

basis of separate experiments ^{on the 4.5} % ^Si alloy.

In figure ^{1 two kinds} of measurements are

reproduced : a) gives ^the change ⁱⁿ reluctivity à(l iti)

^{Ar at 262 °K} during ^{1 hour} after dema-

gnetization. ^{For all} alloys investigated ^{the relax-}

ation is then completed for about 50 % ; b) ^shows

the change ⁱⁿ reluctivity ^{at a} higher temperature (290 OK) during very long ^{times of} waiting. ^The reluctivity for t = 0 is arrived at by extrapolating

measurements performed ^{at lower} temperatures.

yo (2,6.10-4 Oe, ²⁹⁰ °K) ^{has a} maximum value of about 870 for the 6 % ^Si alloy ^{while for the other} alloys ^{it is between 600 and 700. The} points ⁱⁿ a) ^and b) ^{indicate that the influence of} magneto-

striction on time decrease and consequently ^inter-

action energy [1, 2, 4] ^{is small.}

We have also measured the field of stabilization for iron and the 4 . 5 % ^{and the 6} % alloy. ^{For a}

carbon content of 0.005 wt % ^{this field is about}

10 times larger in iron than in the alloys. ^We sup- pose ^{this to} be due to the (preferential) occupation

of sites near the Si atoms. We also suspect ^that the magnetic strain energy due ^to interstitials is lowered by ^this.

^{The fact that} the disaccom-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3024100

242

modation in the alloys ^is larger than for iron while the field of stabilization is small can be explained by ^a smaller wall area in the case of the alloys.

FIG. 1.

Disaccommodation of Fe-Si’’’’’alloys reduced for

a carbon content of about 0.005 wt % ^C.

Demagnetization ^{in an} alternating ^{current field of} diminishing amplitude ^{at t = 0.} Measurement in a mean effective field of 2.6 X 10-4 Oe.

a) Change ⁱⁿ reluctivity r

1/u during ^{1 hour after} demagnetization. Temperature : ^{262 °K.}

b) Change ⁱⁿ reluctivity ^{at 290 OK} during ^{at least}

10 hours of waiting. The initial value of the reluctivity

has been arrived at by extrapolating the values measured for lower temperatures ^{to 290 °K.}

c) Magnetostriction ^constants after Carr and Smolu- chowski for quickly ^cooled respectively ^annealed alloys.

If in contradistinction to internal friction the time decrease of permeability is ^{based on electronic} effects, ^{and not on} lattice strains due to interstitials

one cannot expect ^{that carbon} and nitrogen

influence time decrease and internal friction in a

similar way. Experiments ^{on iron} point ^{in this}

direction. We find the same disaccommodation and stabilizing ^field for N and C if the ratio of the

increase in resistivity ^{due to the} interstitials is

( -D- ) / _R ^(D.:J =3.8 while according ^to Dijks-

" 1 C

tra [8] ^{the same} internal friction (for single crys-

tals) ^{results if} i AR ^W)N (D.J:) c = 1 .8. ^{B /c Since per}

atomic percent ^the internal friction of C is about

0,8 times that of N [9, 10, 111, ^{it seems} that magne-

tically the effect of C is about 1. 7 times that of N.

Measurement of the dependence ^{on mass of the}

diffusion constant.

In another _paper [12] ^{it has}

been shown that the time decrease of permeability

for interstitial nitrogen ^{in iron can be} represented by

where the Tk ^are different relaxation times and the ro, rlk ^are constant with respect ^to time. If it is desired to measure a small relative change ^{of a} particular ^T, say T2, due ^{to some} external influence,

such as the application ^of hydrostatic pressure, the relative change ^{of ’t’i can be deduced} [13] ^{from the}

course of a function Z(t)

rx- rx ^{in a} time inter-

r - To val 0.7-ri ^t 2-ri.

The numerator in this expression ^{for Z is related}

to the experiment giving ^ri, the denominator to

the experiment ^{with the} relaxation time

’ri

’t’i(1 + 3).

By applying ^{this formalism a small} change ^of temperature ^{leads to the correct} change ^{of the}

mean time of stay ^{of the} interstitials in iron as can be calculated with the known activation energy for diffusion. Also the change ^{of the mean time}

of stay ^{due to the} application ^of hydrostatic pres-

sure and the so-called activation volume have been deduced [13].

The same method now has been applied ^{to com-}

pare the diffusion coefficients in iron of natural carbon (99 % 12C) and of carbon enriched in 13C

(95 % 13C).

The ^{reason for} doingthis experiment ^is the follow-

ing. Recently ^{in the case of} substitutional ^diffu- sion indications have been presented ^{[14; that the} dependence ^{of the} diffusion coefficient ^{on mass} is much larger ^than (M)-112 . ^{The current} simple theory [15] ^{however leads to a} (m)-l’2 ^relation- ship. ^{We wanted to test this} relationship.

Almost the same amount of 12C respectively

13C has been alternately introduced in the ^same iron rings (0.005 ^wt %). ^{The relative} change

in relaxation time for the same temperature (248 OK) ^was determined by making ^{use of three}

different experiments ^{with 13C and two} experi-

ments with 12C. The results give ^{a mean relative} change ^of (4 + 1) %. ^The (m)-1/2 relationship

would demand 4 % ^{for the} pure nuclides.

243

As a check ^on the method of evaluating ^the

results also two experiments with 13C have been

compared giving a ^relative change of the relaxation time less than 0.5 %.

In performing ^these experiments ^{we have found}

that the method employed ^{did not} give ^reliable

results in some cases, where the unrelaxed initial permeabilities ⁱⁿ the experiments ^{to be} compared

differed more than 30 %.

The authors _{are very} much indebted to Mr. C. J.

Schinkel, ^who took part in many of the experiments.

This work has been financially supported by ^the

General Electric Research Laboratory ^{in Schenec-} tady.

The carbon nuclides have been separated ^{in the}

F. 0. M.-laboratory ^{for Mass} Separation ^{in Ams-}

terdam.

REFERENCES

[1] ^NÉEL (L.), ^J. Physique Rad., 1951, 12, ^339.

[2] ^NÉEL (L.), ^J. Physique Rad., 1952, 13, 249.

[3] ^SNOEK (J. L.), Physica, 1939, 6, 797.

[4] BRISSONNEAU (P.), C. R. Acad. Sc., Paris, 1954, 239,

346.

[5] ^CARR (W. J.) and SMOLUCHOWSKI (R.), Phys. Rev., 1951, 83,1236.

[6] ^FAST (J. D.), ^LUTEYN (A. I.) and OVERBOSCH (E.), Philips ^tech. Rev., 1953, 15, 114.

[7] ^SMITH (R. P.), J. Amer. Chem. Soc., 1948, 70, 2724.

[8] ^DIJKSTRA (L. J.), Philips ^Res. Rep., 1947, 2, ^357.

[9] ^FAST (J. D.) and VERRIJP (M. B.), ^{J. Iron and Steel} Inst., 1955, 180, 337.

[10] DAHL (W.) ^{and LÜCKE} (K.), ^Arch. Eisenhüttenwes.,

1954, 25, ^241.

[11] ^PITSCH (W.) ^{and LÜCKE} (K.), ^Arch. Eisenhüttenwes., 1956, 27, ^45.

[12] ^BOSMAN (A. J.), ^BROMMER (P. E.), ^DAAL (H. ^J. van)

and RATHENAU (G. W.), Physica, 1957, 23, 989.

[13] ^BOSMAN (A. J.), ^BROMMER (P. E.) and RATHENAU

(G. W.), Physica, 1957, 23,1001.

[14] ^LAZARUS (D.) and OKKERSE (B.), Phys. Rev., 1957, 105, 1677.

[15] ^See e.g. WERT (C. A.) ^{and ZENER} (C.), Phys. Rev., 1949, 76, 1169.

DISCUSSION

M. Ferro.

Puisque-le spectre ^de relaxation du C ou N dans les alliages fer-silicium est très large,

est-il possible ^{de tenir} compte correctement de cela en vue d’une comparaison quantitative ^entre

le pourcentage du carbone et l’intensité des effets de relaxation à une température ^{donnée ?}

Pour ce qui ^est de l’effet de la magnétostriction

de l’alliage ^sur l’intensité de la relaxation, ^il peut

être intéressant de signaler quelques ^mesures que l’on a faites récemment sur du fer silicium 6,4%

dans un domaine très étendu de température ^et publiées ^{seulement en} partie (BIORCI-FERRO- MONTALENTI, Instability of Bloch walls in a ferro-

magnetic lattice, ARDC, ^Res. Rept. ^AF61 (514) 1331, ^March 1958).

Ces mesures semblent donner pour les effets ^à haute température ^{dues au silicium un effet de}

relaxation beaucoup plus petit que l’alliage ^fer-

silicium 3,5 %. ^D’autre part, ^{dans ce même} travail,

nous avons aussi comparé, pour le C dans le fer

.doux, ^{la valeur de} l’énergie ^de couplage magnéto- crystalline par atome de carbône déduite de la valeur expérimentale ^du champ ^de traînage ^avec

la valeur théorique ^{calculée sur la base} de la varia- tion de l’énergie d’anisotropie ^{du fer avec la défor-}

mation due au carbone (NÉEL, ^J. Physique Rad., 1954, ^{et aussi} KITTEL, Rev. mod. Piaysics, 1949).

Les deux valeurs semblent être en accord raison- nable puisqu’on ^{trouve une valeur} théorique ^de 3,3 ^10-16 ergs/atom ^{contre une valeur} expérimen-

tale comprise ^entre 5,3 ^et 6,9.10-16 ergs/atom d’après ^les différentes données expérimentales

obtenues (d’après Snoek, Brissonneau et les nôtres).

Puisque l’expression théorique ^de l’énergie ^de couplage dépend ^dela magnétostriction

où _{cii et} cl2 ^{sont les} constantes élastiques, d ^la

dimension de l’atome interstitiel, ^h la dimension de l’interstice et a le paramètre du réseau. Il nous

semble qu’une dépendance ^du traînage ^{de la} magnétostriction ^{est assez} probable.

M. Rathenau. -a) ^La figure ^{1 b montre la}

relaxation obtenue après ^une durée très longue ^à

des températures comparativement élevées. Pour tous les alliages ^la relaxation est pratiquement complétée.

b) ^Il semble bien difficile à ce moment de tirer des conclusions des mesures faites à hautes tempé-

ratures. Même les constantes de magnétostriction

à des températures ^{élevées sont mal connues. Pour}

le Fe-Si 3.5 % : xioo(400 °C) > Xioo(20 °C) (0160TUR-

KIN, 1947).

M. Brissonneau.

Dans un travail antérieur,

M. le Pr RATHENAU a montré que la diffusion était correctement représentée ^{par un} spectre ^dis-

continu de constantes de temps. Pour l’une d’elles,

on constate un écart de 4 % ^entre les valeurs obte-

nues dans la diffusion de 12C et de 13C. Peut-on détecter de telles variations ^sur les autres cons-

tantes de temps ?

M. Rathenau.

On a des constantes de temps

de très grande durée dont l’origine n’est pas claire

aujourd’hui. ^Ces constantes ne correspondent pas à un saut simple ^{d’un atome} de carbone dans le réseau parfait. ^{Nous ne} connaissons pas le change-

ment relatif de ces constantes si 12C est remplacé

par le 13C.