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Relationships between crystallographic textures and properties of columnar Alnico magnets

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1974 J. Phys. D: Appl. Phys. 7 1233

(http://iopscience.iop.org/0022-3727/7/9/309)

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J. Phys. D: Appl. Phys., Vol. 7, 1974. Printed in Great Britain. 0 1974

Relationships between crystallographic textures and properties of columnar Alnico magnets

J R Moon Department of Metallurgy and Materials Science, University of Nottingham, University Park, Nottingham, NG7 2RD

Received 27 December 1973, in final form 11 February 1974

Abstract. The crystallographic textures of a series of columnar castings of Alcomax I11 have been determined and related to their magnetic properties. The textures are described by histograms for the angle made by the magnet axis with the nearest <loo) directions and by the standard deviation of these angles (SO). The BHmax of the magnets decays rapidly with SO when SO < 10". Calculations based on the histograms and the Stoner-Wohlfaxth theory of permanent magnets give results for BHmax which are within 10% of the measured values. A continuously cast sample had inferior properties which could not be accounted for on the same basis.

1. Introduction

It is well known that the ideal permanent magnet should be highly anisotropic (eg Stoner and Wohlfarth 1948, Wohlfarth 1959). Two practical approaches are available to achieve this aim : either materials with inherently large magnetocrystalline anisotropies may be searched for and developed, as exemplified by the cobalt/rare-earth compounds ; or anisotropy can be induced by metallurgical methods, as in the Alnico alloys.

Alnico alloys are brittle and cannot be formed except by powder metallurgy tech- niques or more usually by casting. They have body-centred-cubic crystal structures and, when cast, solidify fastest along (001) directions (Barrett and Massalski 1966). Columnar crystals, several centimetres long and several millimetres in diameter, are formed by unidirectional solidification, the columnar axes being approximately parallel with the solidification direction. Thus, columnar magnets tend toward a strong (001) fibre texture (Gould 1964a, b, 1971).

When such magnets are appropriately heat-treated, particles of a second ferro- magnetic phase are precipitated by a spinodal type of transformation (de Vos 1966, Cahn 1963) and grow to occupy about 50% of the volume. The precipitates are rod- shaped and grow with their long axes parallel to (001) in the matrix. Application of a magnetic field of not less than about 80 kA m-1 parallel to the solidification axis while the precipitates are forming encourages the rods to grow along the nearest (001) direction and suppresses growth in the other two (001) directions. The result is an assembly of single-domain particles, all aligned approximately parallel to the solidification direction. The demagnetizing factors parallel and perpendicular to the length of the particles differ by about 0.4.

Magnets produced in this way are available commercially (eg Columax, Hycomax), but achieve typical values of BITmax of only about 0.7 BrHc. This could be due to a number

97 1233

1234 J R Moon

of factors, including crystal defects and compositional variations arising from dendritic coring. However, the most important variable indicated by previous studies is the scatter of columnar grain orientations. For example, Gould (1964a, b) has shown that the BHmax of a semi-columnar casting progressively improved as material was ground away to leave a greater proportion of well-aligned grains. Nevertheless, few quantitative studies have been made. All the available results have been collected together in table 1.

Table 1. Relationship between magnet properties and scatter of crystal orientations (previous data for Alcomax 111)

Average Origin disorientation Br(T) Ho(kA m-l) BHmax(kJ m-3)

McCaig and Wright (1960) 4.8" 1.430 61.5 70.0

4.5" 1.355 62.5 64.5 9.2" 1.380 57.2 58.0

Gould (1968, private communication) 12.0"

9.0" 7.75" 8.9" 8.05'

Combined result? 8.1" Ideal [OOl] Random$

Hinsley (1962) Random$

1.40 54.1 1.35 56.5 1.37 57.7 1.40 57.7 1.43 56.1 1,365 57.4

63.6 1.33 51.2

1.26 51.6

Koch etal(1957) Single-crystal [OOl] 1.40 Random: 1.27

Zijlstra (1956); [OOlI heat-treated with field [Oll] in directions listed, and [I 111 tested in [OOl] direction Random (calculated)$

53.4 54.1 58.9 58.1 57.3 48.9 71.6 44.6

42.9

58.1 63.6 50.6 39.8

60.5 36.5 33.5 39.0

t The combined result represents the overall disorientation of five specimens cut from one casting. The magnetic properties were measured independently before cutting the casting. The other results due to Gould are the individual measurements for each specimen. $The average disorientation of a random sample is calculated to be 35".

The average disorientations quoted by McCaig and Wright (1960) and by Gould (1968, private communication) were estimated by using the Laue technique to determine the angle between the magnet axis and the nearest (001) direction in each of about twelve grains per specimen. This method may be criticized on two points: firstly, only those grains large enough to contain the incident x-ray beam completely were sampled; secondly, no allowance was made for the differing volumes of the grains that were sampled. The work reported here attempted to overcome these problems by using an x-ray diffractometer.

Textures and properties of Alnico magnets 1235

2. Experimental methods

2 . I. Materials and sampling methods

The materials studied were a series of columnar castings of nominal composition (by weight) 24.5 %CO, 13.5 %Ni, 8 %Al, 3 %Cu, 0.6 %Nb, balance Fet. These were kindly provided and heat-treated by the Permanent Magnet Association, Central Research Laboratory, Sheffield. All magnets were heat-treated according to the standard PMA schedule; that is, cooled in a magnetic field of greater than 220 kA m-1 applied parallel to the solidification direction from 1250 "C at 1.2 "C s-1, held for 48 h at 590 "C, and then held for a further 48 h at 560 "C.

Magnets I A to 3B. These were cut from 50" cubic castings, two specimens (eg 1A and 1B) being obtained from one casting. Each specimen measured 25 mm in the solidification direction and 30 x 15 mm2 in cross section.

Magnet 4 . This was also cut from a 50 mm cubic casting. The specimen was cylin- drical, 25 mm long by 15 mm in diameter, and was taken from the centre of the casting.

Magnet 5 . This was 25 mm long and was cut from a continuously cast rod of circular cross section 15 mm in diameter.

The rectangular magnets were cut into twelve specimens as illustrated in figure 1. The cylindrical magnets were cut into discs about 2.5 mm thick. Each cut face was metallographically polished and etched before being used for orientation determination.

Solidification direction and magnet axis

I

Each cut removed-2 mm o f material

Figure 1. Subdivision of rectangular magnet blocks into specimen slices.

2 .2 . Orientation determination

The principle of the method was to determine the distribution of [OOl] about the solidifica- tion direction. This was done by examining each face that had been cut perpendicular to the solidification direction and measuring the variation in intensity of x-rays diffracted from (002) as the angle between the incident beam and the specimen face was varied.

Known commercially as Alcomax I11 or Columax.

1236 J R Moon

surface

(002) surface

Figure 2. Arrangement of specimen in diffractometer.

The specimen was arranged in a diffractometer in the conventional manner (figure 2). A counter tube was placed to measure the intensity of diffracted x-rays at the constant angle 26' to the incident beam, where 6' is the Bragg angle for (002). This angle was deter- mined independently for each specimen. Cobalt K, radiation was used, and this gave 6' close to 38.4". The smallvariations from specimen to specimen, representing a maximum variation in lattice parameter of 0.4 %, were not systematic.

The incident beam sampled a strip, 12 mm high and about 0.3 mm wide, perpendicu- lar to the plane of figure 2. The aperture of the detector slit was 0.1".

The specimen was rotated about an axis parallel to its face and formed by the inter- section of the incident and diffracted beams. The diffracted intensity Z(p) was monitored as a function of the angle p defined in figure 2. Ideally, /3 should range symmetrically between limits of i- 54.7" (ie from 001 to 11 1) for cubic crystals, but in the present work it was found that ,B need be varied only between 525". Subsidiary experiments also showed that absorption corrections were unnecessary.

A typical variation of Z(p) with f l is shown in figure 3 . A peak in I @ ) occurs when the normal to (002) in a sampled grain is coplanar with the incident and diffracted beams and bisects the angle between them. The height of each peak is proportional to the sampled

Figure 3. Typical variation of Z(j3) with j3.

Textures and properties of Alnico magnets 1237

area of the diffracting plane. Small peaks, arising from small grains, are not usually resolved individually, but overlap with others to contribute to the net intensity. In effect, figure 3 represents the distribution with ,8 of the volume of material oriented such that [OOl] is at an angle f l with the magnet axis.

The only planes which are brought into diffracting positions as f l is varied are those whose poles lie on a single diameter of the stereographic projection about the specimen surface normal. Other diameters were sampled by repeating measurements after rotating the specimen about its surface normal.

Traces such as figure 3 were analysed in two ways, in both cases to give a single number which characterizes the dispersion of grain orientations. Either the average value of coszg and the corresponding ,8 were calculated; or the trace was treated as a sample from a gaussian distribution and the mean p and standard deviation SB were estimated. A variation on this latter practice which is physically more meaningful was to assume the mean value of ,6 was zero, ie that the distribution was symmetrical about the magnet axis, and to estimate the standard deviation SO on that basis. Experi- mental justification for this assumption will be presented in the Results section.

3. Results

3.1. The symmetry of the distribution about the magnet axis

A few specimen slices were taken from the rectangular magnets to estimate the symmetry of the crystallographic texture about the magnet axes. This was done by repeating meas- urements about different axes of rotation in the specimen surface. In three cases, only two orthogonal axes were used. In a fourth case, four axes spaced at 45" intervals were used. All measurements were repeated after demounting and resetting the specimen, and both top and bottom faces of each slice were examined.

The combined results for each specimen and rotation axis are given in table 2. In only one case is p comparable with either S, or SO; in all other cases SB and SO are significantly greater than 8. Furthermore, with only one exception, the values of SB and SO are generally very similar to one another. These results were taken as a reasonable justification for the assumption that the textures were cylindrically symmetrical about the magnet axis and that the true value of 8 was zero.

Table 2. The effect of rotating specimens about the surface normal

Magnet

2A

2B

2B

Angle of rotation axis Sample (deg)

1 0 45 90

135

8 0 90

-~

-

10 0 90

1.1 1.0 2 . 5 3.9

0 .2 3 . 8

2.6 6.4

~~ - _. . ~~ ~

2B 12 0 2.4 8 . 5 8.8 90 2.9 8.1 8.6

1238 J R Moon

5-

3 . 2 . Variations from magnet to magnet

The assumption that the textures were spherically symmetrical enabled a more economic assessment of the overall dispersions of orientations in the magnet blocks as a whole.

One trace of I@) against /3 was obtained for each of the twelve specimen slices taken from the rectangular magnets. The face examined was chosen randomly, and the rotation axis was varied systematically through each magnet block. Specimens 1, 3, 5 , 8, 10, 12 were rotated about an axis parallel with an edge, and specimens 2, 4, 6, 7, 9, 11 were rotated about an axis at 45" to an edge.

The cylindrical magnets were treated differently. Only three thin disc specimens

L

- v

IO- - - - Magnet I A - 5- - -

I

5 10 15 20

Magnet IB

L 5 IO 15 20

I O 151 Magnet 28 n - 5 - I -

r

0' 5 IO I5 20

5 IO 15 20

hl I . magnet 5

I O 1 I I h i m

0' 5 IO 1'5 p (deg)

Figure 4. Histograms illustrating dispersions of [MI] about magnet axis

Textures and properties of Alnico magnets 1239

were available from each. Each specimen was used to generate four traces about axes at 45" to each other, two being taken from one face and two from the other.

Table 3. Relationships between magnetic properties and the scatter of grain orientations

Magnet

1A IB 2A 2B 3A 3B 4

Scatter of grain orientations

<cos2 8)

0.9832 0.9862 0.9909 0.9770 0.9852 0.9763 0.9938

~ -..

B (deg)

7.45 6.72 5.46 8.71 6.98 8.84 4.49

. .

So(deg)

7.33 6.84 5-53 8.82 7.01 8.75 4.50

5 0,9933 4.67 4.68

Br(T)

1.34 1.34 1.35 1,355 1.32 1.33 1.40

1.34 ~~ .

Hc(kA m-l) BHmax(kJ m-3)

55.7 46.95 57.3 54.91 61.7 57.30 609 1 54.11 59.3 49.34 60.1 51.33 58.5 61.67

59.7 50.13

Thus, in all cases, twelve individual traces were obtained for each magnet. The total data for each magnet were reduced to histograms giving the proportion of total diffracted intensity in intervals of 1" from zero. The results are given in figure 4. The calculated values of SO, (cosZP> and the corresponding P are given in table 3 together with the

- " I " ' I " I I I I I I 0 5 IO 15 20 25 30 35

So(deg)

Figure 5. The relationship between BHmax and SO: + measured, this work; 0 calcu- lated, this work; x other work, table 1 .

magnet properties. The relationship between BHmax and SO is shown in figure 5, which also includes data taken from table 1. Gould's data are included only as the combined result, which was considered to be more representative than the individual results since it was based on a larger sample.

1240 J R Moon

4. Discussion

4.1. Accuracy of results

The major factor influencing the accuracy of SO is the extent by which those grains which were sampled represented the magnet as a whole. Some indication of the sampling error was obtained by observing how SO settled toward a value as the size of the sample was increased. This was done by combining individual results for randomly chosen specimen slices in increasing numbers. The results are shown for two magnets in figure 6 , from which it can be seen that the variations in SO reduce to less than +2% when nine or more individual results are combined. Since each result in table 3 is based on the combination of twelve individuals, the sampling error is estimated to be about 4 2 %.

1 2 4 6 8 IO I2 N h u m b e r o f individual results used to estimate So)

Figure 6. The effect of sample size on estimates of So for two magnets.

4.2 . The relationship between textures and properties Figure 5 shows that BHmax decreases rapidly with SO when SO is small, and more slowly when SO is large. This suggests that worthwhile improvements in magnet properties might be obtained by improving casting techniques to give modest reductions in the dispersion of grain orientations.

There is some uncertainty about the causes of the observed relationship between BHniax and SO. The properties might be determined by the orientation dispersion alone, or interactions between adjacent grains might also be important.

The extent to which the orientation dispersion affects BHmax in the absence of other affects was assessed by using the method of Stoner and Wohlfarth (1948) to calculate BHma,. Each magnet was assumed to consist of an assembly of non-interacting prolate spheroids. BHma, was calculated for individual spheroids as a function of their orienta- tion, and the weighted average for each magnet was estimated using the observed orienta- tion dispersions. Although this method is not rigorous, it was considered to be compat- ible with the precision of the observations.

The results of this calculation were obtained as fractions of the ideal BHmax for a perfectly aligned set of spheroids. These fractions and the BHmax of each magnet were

Textures and properties of Alnico magnets 1241

Table 4. Comparison of observed and calculated BHmax

BHmax (kJ m-3) - .____ - -~ -

Ratio of BHmax with that Calculated for Magnet of an ideal crystal Measured an ideal crystal

1A 0.613 46.95 76.61 1B 0,625 54.91 87.84 2A 0.656 57.30 87.42 2B 0.577 54.11 93.54 3A 0.631 49.34 78.20 3B 0.591 51.33 86.86 4 0.691 61.67 89.28

5 0.710 50.13 70.62

__ ._

_~~~ -~ _ - ~_ ~~~ _

Average calculated ideal BHmax: samples 1A to 4, 85.7k6.1 kJ m-3; all samples, 83.8 +. 7.8 kJ m-3.

used to estimate the magnitude of the ideal. The results are given in table 4; those obtained from magnets 1A to 4 differ by less than 10%. Magnet 5, which was continuously cast, gave a result which differed from the others by about 20 %. The average ideal BHmax is about 85 kJ 171-3. The best experimental value for a single crystal is 71.6 kJ m-3. At present, the causes of this difference cannot be identified, although it is not unexpected that real samples should fall short of ideal. Important factors in this respect might be defects in the crystal or that the reversal of magnetization occurs not by the coherent processes assumed but by one of the processes of buckling or curling described by Wohlfarth (1959).

The calculations give the correct form of variation of BHmax with So. This is shown in figure 5, in which the calculated points are the appropriate fractions of 85 kJ m-3.

The properties of magnet 5 differ substantially from those expected from the orienta- tion dispersion. This magnet was taken from a continuously cast bar, and there is independent evidence (Johnson 1970, private communication) that such material has poorer properties than would be expected from its microstructure, which shows well- aligned columnar grains. The crystallographic data support the contention that the grains are well-aligned; from this point of view it was the best of the magnets studied. It seems that some other factor, as yet unidentified, contributes deleteriously to the properties of the magnet. Its chemical analysis is (by weight) 24.75 % CO, 13.7 % Ni, 7.84 % Al, 3.05 % Cu, 0.59 % Nb, 0.07 % Si, which is within the range usual for these alloys.

5. Conclusions

The BHmax of the magnets studied decreases rapidly with So when SO is small. This suggests that improvements in casting techniques to give modest improvements in SO might produce significant improvements in BHmax.

With the exception of the continuously cast magnet, the properties seem to be adequately described by the theory of Stoner and Wohlfarth (1948) and the observed orientation dispersions. To obtain a good fit with measured data, it is necessary to assume a BHma, for an ideal sample which is between 15 % and 20 % larger than the best value obtained for a single crystal. These results suggest that interactions at the bound- aries between adjacent grains exert relatively small effects on the properties of the magnets.

1242 J R Moon

Continuously cast material exhibited good alignment of orientations, but its proper- ties cannot be interpreted on the same basis as the other magnets.

Acknowledgments

The support of this work by the Centre d’Information du Cobalt, Bruxelles is gratefully acknowledged. It is a pleasure to acknowledge also the considerable help and encourage- ment given by Mr J E Gould, formerly director of the central research laboratory of the Permanent Magnet Association, Sheffield. The materials for this work and the measurements of magnetic properties were all provided by Mr Gould and his staff at PMA.

References

Barrett CS and Massalski T B 1966 Structure of Metals (New York: McGraw-Hill) pp 535-8 Cahn J W 1963 J. appl. Phys. 34 3581-6 Gould J E 1964a Cobalt No. 23 1-6 __ 1964b Journe‘es International des Applications du Cobalt pp 127-33 - 1971 Cobalt Alloy Permanent Magnets (Bruxelles: Centre d’Information du Cobalt) Hinsley J F 1962 Permanent Magnets ed D Hadfield (London: Iliffe) chap 5, pp 105-90 Koch A J J, van der Steeg M G and de Vos K J 1957 Pvoc. 2nd Con$ on Magnetism and Magnetic Materials,

Boston, 1956 (New York: Am. Inst. Elect. Engng) pp 173-83 McCaig M and Wright W 1960 Br. J . appl. Phys. 11 279-81 Stoner E C and Wohlfarth E P 1948 Phil. Trans. R. Soc. A 240 599-642 de Vos K J 1966 Thesis Technische Hogeschool, Eindhoven, Netherlands Wohlfarth E P 1959 Adv. Phys. 8 87-224 Zijlstra H 1956 J . appl. Phys. 27 1249-50