INVESTIGATION OF MICROSTRAIN FIELDS BY NEUTRON SCATTERING AND DEPOLARIZATION

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INVESTIGATION OF MICROSTRAIN FIELDS BY NEUTRON SCATTERING AND DEPOLARIZATION

W. Schmatz, K. Berndorfer, G. Durcansky

To cite this version:

W. Schmatz, K. Berndorfer, G. Durcansky. INVESTIGATION OF MICROSTRAIN FIELDS BY NEUTRON SCATTERING AND DEPOLARIZATION. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-679-C1-680. �10.1051/jphyscol:19711237�. �jpa-00214065�

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JOURNAL DE PHYSIQUE Colloque C 1, supplkment au no 2-3, Tome 32, Fkvrier-Mars 1971, page C 1 - 679

INVESTIGATION OF MICRO STRAIN FIELDS BY NEUTRON SCATTERING AND DEPOLARIZATION

W. SCHMATZ, K. BERNDORFER and G. DURCANSKY

Institut fur Festkorperforschung der KFA Jiilich und Physik-Department der TH Munchen

R6sum6. - L'observation combinee de la diffusion des neutrons aux petits angles et de la dkpolarisation des neutrons permet dVtudier les champs de microtension. Des rksultats expkrimentaux obtenus avec des cristaux de Nickel Ccrouis contenant des dislocations en forte densitk montrent que la longueur de correlation du champ des micro-tensions et la densit6 de dislocation peuvent Stre dkterminkes. Dans tous les cas on constate que l'approche a la saturation magnktique prksente une variation normale en fonction du champ. Dans des monocristaux l'anisotropie des dislocations dans l'espace a kt6 Btudiee au moyen de figures de diffusion.

Abstract. - The combined observation of neutron small angle scattering and neutron depolarization allow conclu- sions on the microstrain fields. Experimental results on cold-worked nickel crystals with high dislocation densities show that the correlation length of the microstrain field and the dislocation density can be determined. In all cases the approach to magnetic saturation shows the correct field-dependence. For single crystals the anisotropy of the dislocations in space has been investigated by means of the scattering patterns.

Strain-, respectively stress-fields around dislocations causes by magnetoelastic coupling deviations of the magnetization direction from its average value. Near magnetic saturation these deviations are small and they can be calculated straight forward by minimiza- tion of free energy [I]. For nickel, as we have used, exchange energy, magnetoelastic coupling energy, magnetostatic energy and stray-field energy must be taken into account, whereas anisotropy energy can be neglected. Using the Fouriertransformed of the stress- field one obtains the Fouriertransformed of the magnetization vector, whereby changes of the absoluie value of magnetization can be neglected.

The magnetic small angle scattering cross section per atom is [2]

a is the magnetic scattering length, Va the atomic volume. y(r) is the unit vector in magnetization direction as a function of position r.

T(K)

is the Fourier- transformed of y with K the scattering vector. For small angle scattering K is perpendicular to the incident beam and its absolute value is 2 n0/1 (0 scattering angle, 1 neutron wavelength).

F(K)

is the projection of

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into the plane perpendicular to ^K (+). V is the volume used for calculation of ?(K).

For a single straight dislocation of length L, do/dQ is :

K: is the component of the scattering vector parallel to the dislocation, ^K: the component perpendicular to it. The reciprocal exchange length ^IC, is proportional t o the magnetic field H, for nickel and for

(*) In [2] erroneously instead of

7'

has been used.

K, is A-.I. do/dQ vanishes for H + co. Ccontains material properties, A ( q ) is a constant depending of relative orientations to each another o f : scattering vector, magnetic field, cubic crystal axis and direction of dislocation. A ( q ) is also different for various types of dislocation.

A cylindrical nickel single crystal deformed plasti- cally in tension parallel to its axis Z was used as scattering sample. Angles ^E= 3 ([I 1 I], Z) and 1 = 3 ([loll, Z) have been ^E= 46.00 and 47.50 and 1 = 440 and 42.50 before and after deformation respectively. The final tension axis was parallel to H and perpendicular to the incident beam. All scattering patterns have been taken with quantitative neutron photography-technique. Patterns for various magnetic fields and various rotation angles q of the sample around the field axis H have been taken. In figure 1 a few representative patterns, obtained for

IC = 2,2 A - l ,

for p =O,i.e.; N [ I l I ] -scattering dimetion Of7 FIG. 1. - A few scattering patterns from dislocations in a

nickel single crystal.

are shown. 0 is the direction of scattering vector K.

It is 0 = 0 for K I H. For rcL > 2 7 ~ , a condition, which is fulfilled according to electron microscope studies, the neutrons are mainly scattered into the intersection of the plane perpendicular t o the dislocation line and the scattering plane. This direction

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711237

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C 1 - ⁶⁸⁰ W. SCHMATZ, K. BERNDORFER AND G. DURCANSKY varies with sample rotation cp. Calculations for nearly

all types of dislocations revealed that A ( q ) changes within orders of magnitude. Figure 2 gives an example.

This behaviour allows to identify special dislocation types. For instance peak N in figure 1 is originated by dislocation type of figure 2, because cp and 0 have

FIG. 2. -Scattering strength A (9) sinz(lc;Llc)/1c:2 and scatter- ing direction W of a dislocation parallel to [Oil] with Burgers

vector [OOl].

the expected values. Otherwise the mainpeak M couldn't be explained by any A ( q ) of a single dislo- cation. It was necessary to assume groups of disloca- tions of the same sign within the (111) primary glide plane. Then maximum scattering parallel to [ I l l ]

direction is obtained as observed (Fig. 1). From the absolute value of da/dS2 reasonable dislocation densities have been calculated.

Summing-up over dislocations in the vicinity of one special dislocation there is always one dislocation more of opposite sign than the sign of the special one.

Therefore in equation (2) a correlation factor I ( K ) must be introduced. I(K) + 0 for ^K^-+0. For K 3- lld with d as the mean dislocation distance I ^-+1. If I(lcc) ^E.112 then I / K , as approximately the mean distance do of dislocations of opposite sign. This quantity do is important for understanding the problem of plastic deformation. In small angle scattering decrease of I(K) ^-+0 has not been observed because K , is too small.

Neutron depolarization measurements have been performed therefore.

A well-defined fraction F(K) of neutrons, scattered according to Eq. (2) is spinflipped. Intensity of spin- flipped neutrons can be calculated by multiplying eq. (2) with I(K) and F(K) and integrating afterwards.

Spinflip is roughly proportional to N/K,. Using N as determined from small angle scattering experiments we obtained a mean dislocation distance of 3 000 A

for our specimen. Similar experiments have been performed with polycrystalline nickel samples and do values from 700 to 2 000 have been obtained.

These samples have been more deformed than the single crystal. In all experiments correct field- dependence according to eq. (2) has been observed.

References

[I] KRONMULLER (H.), SEEGER (A.), J. Phys. Chem. Sol., 1961, 18, 93, and 1960, 12, 298.

[2] KRONMULLER (H.), SEEGER (A.), WILKENS (M.), Z.

Phys., 1963, 171, 291.