Reversibility of the Coercive Force in Alnico 5M. G. Van Der Steeg and K. J. De Vos Citation: Journal of Applied Physics 27, 1250 (1956); doi: 10.1063/1.1722242 View online: http://dx.doi.org/10.1063/1.1722242 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/27/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetization reversal and coercivity of magnetic-force microscopy tips J. Appl. Phys. 89, 6098 (2001); 10.1063/1.1368872 Microstructure and domain studies in Alnico 5 and Alnico 7 (abstract) J. Appl. Phys. 57, 4173 (1985); 10.1063/1.334654 Intercrystalline Fracture in Alnico 5 J. Appl. Phys. 37, 1106 (1966); 10.1063/1.1708355 Hot Working of Alnico 5 Alloys J. Appl. Phys. 31, S84 (1960); 10.1063/1.1984614 Shape and Crystal Anisotropy of Alnico 5 J. Appl. Phys. 26, 1217 (1955); 10.1063/1.1721876

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1250 LETTERS TO THE EDITOR

8r-----,------.------,-----,------,

~~----~W~-----Z~O~O~--~3~O~--~~~~~500

-~ FIG. 1. Average energy product It in gauss oersteds XIO-' plotted as

a function of apex angle of cone containing [100] axes.

crystal. The correction is in both cases about the same and is given in Fig. 1. The calculated value of E with correction for a textureless polycrystalline magnet is 4.9X 106 gauss oersted, which is consistent with experiment._This indicates that the averaging of (1) is justified.

Another type of texture can be achieved by casting the alloy in a narrow cylindrical mold. In this case the columnar crystals are oriented radially from the chilled periphery to the center.

For the properties along the axis of the cylinder a similar averaging as mentioned above is carried out assuming the same deviation of the [100J axes from the columnar directions:

E=[6.1-2.9 sin~+2 sin~+0.03 sin6'1JXlOG gauss oersted. (3)

In Fig. 1 a correction for constant induction is given, analogous to the first case with axial texture.

1 See also D. G. Ebeling and A. A. Burr, J. Metals 5, 537-544 (1953).

Reversibility of the Coercive Force in Alnico 5 M. G. VAN DER STEEG AND K. J. DE VOS

Philips Metallurgical Laboratories, N. V. Philips' GloeilamPenfabrieken, EindhafJen-Netherlands

(Received June 22, 1956)

T HE current theory to explain the remarkable properties of permanent magnet alloys of the Fe-Co-Ni-Al type is

based on the precipitation of a Fe-Co rich phase during the permanent magnet heat treatment. During the first step of this treatment (cooling down from a temperature above 1200°C), the nucleation is controlled by a magnetic field. In this stage the coercive force is about 300 Oersteds. During the second step (aging at a temperature of about 600°C) the nuclei develop into plates, and this process causes a further increase in the coercive force to about 650 Oersteds.1- a

From an extensive analysis of this treatment on Alnico 5 (51 % Fe, 24% Co, 14% Ni, 8% AI, and 3% Cu) we have found several phenomena which cannot be explained simply by this theory. If, for example, during the cooling down step a magnet is water­quenched above a temperature of 750°C, it has a coercive force of only 10 Oersteds, although x-ray diffraction shows that in this stage the precipitate is already present. Aging of this specimen at 600°C again yields a coercive force of 650 Oersteds. After this sample is annealed for 3 min at 750°C, the coercive force is once more reduced to 10 Oersteds. Re-aging at 600°C restores the coercive force to 650 Oersteds. After prolonged annealing at 750°C or higher temperatures the coercive force can be only partially restored by re-aging at 600°C,'

In our opinion these phenomena mean that different reactions are taking place during the two steps of the permanent magnet heat treatment. The first reaction is the precipitation of the above-mentioned phase, which is believed to be rich in iron and

cobalt,2 An order-disorder reaction could be responsible for the phenomena during aging, Since the parent metal is already ordered, even at high temperatures, we initially supposed that an ordering in the Fe- Co precipitate occurred analogous to the well-known ordering reaction in the binary Fe-Co system. Up to now we have found no conclusive evidence for this supposition.

However, we have found by x-ray diffraction that after pro­longed aging at 600°C (70 days), in addition to the Fe-Co rich precipitate, a new phase, having an f.c.c. structure with a lattice constant at room temperature of 3.62 A, becomes detectable. This 'Y phase disappears on reheating the sample at 820°C. As the precipitation of the 'Y phase during aging and its re-dissolution at higher temperature runs parallel with the above-mentioned reversibility, we believe that this phase plays an important role in achieving the coercive force of Alnico 5.

A full description of our experiments will be published soon.

I A. H. Geisler, Trans. Am. Soc. Metals 43,70 (1951); Phys. Rev. 81, 478 (1951).

'Kittel, Nesbitt, and Shockley, Phys. Rev. 80. 302 (1950). 3 R. D. Heidenreich and E. A. Nesbitt. J. Appi. Phys. 32, 352 (1952). • Hansen reported a similar behavior of a material of the same type at

the Conference on Magnetism and Magnetic Materials. Pittsburgh (June. 1955).

Electron Cyclotron as a Source of Megavolt Bunched Electron Beams*

IRVING KAUFMAN AND P. D. COLEMAN

Ultramicrowave Group. Electrical Engineering Research Laboratory. University of Illinois, Urbana, Illinois

(Received June 22. 1956)

AN electron cyclotron has been shown to be a compact source of million volt electrons.1,2 Recent calculations carried out

in this laboratory have discovered a phase compression in one of the orbits, which indicates that such a device can in addition be a source of tightly bunched electron beams. Such beams, when passed through an appropriate coupling device, can potentially produce appreciable amounts of power in the submillimeter range of the electromagnetic spectrum. S

The scheme of the electron cyclotron, first publishedt by Veksler'in 1944, is shown in Fig. 1. A microwave cavity supplied with external power and a source of electrons is immersed in a uniform, static magnetic field. Electrons accelerated by the cavity travel in circular orbits. Proper adjustment of magnetic field and

MAGNETIC FIELD, PERPENota.JL.AR TO ORBITAL PlANE

FIG. 1. Scheme of electron cyclotron.

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LETTERS TO THE EDITOR 1251

-0- -b- -c-

FIG. 2. Phase compression in an orbit.

o:A 0=8 x=c

cavity power causes a fraction of the initial beam to be returned to the cavity repeatedly, to accrue additional energy each time, resulting in electron orbits of discrete radii. The electrons of these orbits lie in a "phase-stable" region of the RF cycle, in which they oscillate about a "resonant" particle.

The presence of a phase-stable region alone means that the current in an outer orbit has a strong harmonic content up to the 25th harmonic of the cavity frequency (for a phase stable region of 12°-15°). Detailed calculations have shown that an additional phase compression in the phase-stable region is possible in one of the orbits. This phase compression can enhance the harmonic content up to the SOOth harmonic of the cavity frequency.

Phase compression is illustrated in Fig. 2. Here three particles are shown. On emerging from the cavity, let the order of the particles be CBA. Let the electrons travel through the gap during the portion of the cycle that imparts more energy to ethan B and A, to B than A. With energy increments possible in the resonator, inversion of arrival times may result. This is because A, B, and C all travel at nearly speed c, while the orbit of C may be larger than that of B, that of B larger than A. Therefore, if the order of arrival at the cavity is ABC, somewhere in the orbit two particles will have been side by side. If conditions are favorable, all three are bunched longitudinally during a small arc of the orbit. If the magnetic field is terminated at this favorable point, a tightly bunched beam can emerge.

Results of computations carried out for a specific set of param­eters, including the integration of the relativistic equation of motion in the cavity, are shown in Fig. 3.5 Here it is seen that an initial phase increment of 8° is compressed into 0.5°, correspond­ing to an additional effective frequency multiplication of 16.

o ORBIT ANGLE

(S}I Resonant PorIic:Ie

Conditions: f=2600mc S .. 995 gauss

I-:=~-:-~--:_-:-:-..,....,:--_-,--..,.-llnitial Injection v=O Nate~ A resonant particle here entered Cavity Gap = I an

the cavity initially (Orbitl) at &-60 Cavity Field = 5.2266 x lel VIm

FIG. 3. RF phase<deviatlon (rom resonant particle vs orbit angle (8th orbit).

It is realized that our calculations are exploratory. Such problems as electron injection, physical structure (use of a race­track cyclotron to facilitate external injection, for example), and tolerances need to be considered before a practical device is built. Nevertheless, it is felt that the initial calculations have demonstrated the principle satisfactorily.

The authors gratefully acknowledge the aid of Dr. J. E. Robert­son of the University of Illinois Digital Computer Laboratory in the coding of the problem for use on the Illiac.

* Work supported by Air Force Cambridge Research Center, under Contract No. AFI9(604)-S24.

I Redhead, Le Caine, and Henderson, Can. J. Research 28 73-91 (1950) , H. F, Kaiser, J. Franklin Inst. 259, 25-46 (1955),' . • P. D .. Coleman and M. D. Sirkis, J. App!. Phys. 26, 1385-1386 (1955) . . t The Idea. of ~he electron cyclotron was also suggested independently,

WIthout publtcatlOn, by others such as Alvarez and Schwinger. • V. Veksler. Compt. rend. acado sci. URSS 43, 329-331 (1944)' also

J. Phys. USSR 9, 153-158 (1945). • . • Quarterly Report No. I, Contract AF19 (604)-524, Electrical Engineer­mg Research Laboratory, University of Illinois, Urbana, Illinois.

Dislocation Damping J. WEERTMAN AND E. I. SALKOVITZ

Naval Research Laboratory, Washington, D. C. (Received July 2, 1956)

GRANATO and Lucke! have raised a serious objection to a dislocation damping model proposed by us.2 They state

that even at comparatively large stresses dislocation loops of the length of Frank-Read sourCes vibrate with an amplitude of the order. of 0, the interatomic distance, or less. Our theory requires amplItUdes of the order of blel or greater where c is the impurity concentration. We wish to give a calculation to show that even at the lowest strain amplitudes (5 X lO--8) used in damping experi­ments the amplitude may be, in fact, quite larger than b.

According to Koehleil the maximum displacement of a disloca­tion loop of length 1 is equal to.l2j 4b where. is the strain amplitude of vibration.* The length of an F-R source is equal to (N 13)--i in a three dimensional dislocation network of density N. The x-ray measurements of Noggle and Koehler' indicate N is of the order of 106/cm2• It should be noted that this density is rather low compared to other x-ray estimates. There is another independent way, however, of obtaining the lengths of the F-R sources, namely a measurement of the critical shear stress. Lauriente5 has m~~e the most precise measurements, to our knowledge, of the cntlcal shear stress of aluminum single crystals. He finds critical shear stresses as low as 6XlOb d/cm2• In high temperature creep measurements of aluminum crystals6 extensive plastic flow show­ing well defined slip markings occurs at resolved shear stresses as low as 106 d/cm2• This stress will activate an F-R source of length 7X 10--3 em, a length which compares favorably with that calculated from the Noggle-Read density (1.7XlO-3 cm). The critical shear stress method should give a larger value of l since the longest F-R sources are activated first upon application of a stress.

At the lowest resolved strain amplitude (2.SXlO-S) the total maximum displacement, twice that given by the expression above, in a loop of length 1. 7 X 10-a cm is around 60 atom spacings for b.=2.5::<10-s em, the interatomic distance in copper. This amplItude IS large enough to allow our model to be operative to impurity concentrations below 10-5, contrary to the criticism of Granato and Lucke. For very small stresses or for superpurity materials the model breaks down.

1 A. Granato and K. LUcke, J. App!. Phys. 27, 583 (1956). 'J. !"eertman, J. App!. Phys. 26, ~02 (1955); J. Weertman and E. I.

Salkovltz. Acta Metallurgica 3. 1 (1955). • J. S. Koehler. Imperfections in Nearly Perfect Crystals Uohn Wiley

and Sons, Inc .. New York, 1952), p. 197. * Actually Koehler gives a displacement of one-half of the above ex­

pression. In deriving his formula he had used a dislocation line tension of I'b' where p is the shear modulus. Later estimates of the line tension give the value tl'b'. Thus Koehler's formula should be corrected with a factor 2 .

• T. S. Noggle and J. S. Koehler, Acta Metallurgica 3.260 (1955). • M. Lauriente. thesis. Johns Hopkins University (1955). 'J. Weertman. J. ADP!. Phys. 27, 832 (1956).

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