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Ferromagnetism and order in nickel manganese alloys Piercy, George Robert 1952

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FERROMAGNETISM AND ORDER IN NICKEL MANGANESE ALLOYS  by GEORGE ROBERT PIERCY. '  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of Physics  We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of MASTER OF APPLIED SCIENCE.•  Supervisor i n Metallurgy Department. Head of Department of Physics.  THE UNIVERSITY OF BRITISH COLUMBIA OCTOBER 1952  SYNOPSIS  An investigation of ferromagnetism  i n n i c k e l manganese  alloys up to f o r t y atomic percent manganese has been carried out.  Twenty  a l l o y s within t h i s composition range were subjected to three heat t r e a t ments such that the conditions within the a l l o y s varied from atomic disorder to a high degree of long range order. The degree of order of Ni Mn calculated from measured 3  saturation magnetisation using the Ising model of ferromagnetism  was  consistent with the value calculated from the r a t i o of measured integrated i n t e n s i t y of the (110) x-ray d i f f r a c t i o n superlattice l i n e to that of l i n e (111). The r e l a t i o n s h i p between saturation magnetisation and concentration f o r the disordered alloys can be explained adequately by the existence of short range order.  A value of 3 . 4  Bohr magnetons was  obtained f o r the e f f e c t i v e magnetic moment of manganese atoms i n a nickel lattice.  Acknowledgement  The author i s g r a t e f u l f o r f i n a n c i a l a i d i n the form of a National Research Council Bursary during the winter of 1951-52 and the summer of 1952.  Without such a i d t h i s work could not have been c a r r i e d  out. The author i s also g r a t e f u l to the s t a f f of the Department of Mining and Metallurgy f o r t h e i r co-operation, encouragement, and advicej i n p a r t i c u l a r to R. Butters f o r the chemical analysis of the a l l o y s and to Dr. E. R. Morgan, the supervisor of t h i s research.  TABLE OF CONTENTS  page Introduction  1  Previous Work  7  Procedure . .  . . . . . .  9  Results Preliminary experiments  . . . . .  14  Quenched a l l o y s  . . . . . . . . . . . . . .  Annealed a l l o y s  . . . . . . . . . . . .  .  14 14  Intensity measurements . . . .  . . . . . . . .  15  Discussion Preliminary experiments  24  Quenched a l l o y s  24  Annealed a l l o y s Conclusions  .*  . . . . . . . . . . . . .  28 31  Appendices 1.  Vacuum melting and casting apparatus . . . . . . . .  33  2.  Description  39  3.  Derivation of the general equations f o r the order  and c a l i b r a t i o n of magnetic balance  . .  parameter at any composition . . . 4.  Equations f o r the quenched a l l o y s . . . . . . . . . .  5.  Calculation of order parameter of Ni Mn  49 54  3  - from magnetisation results . - from superlattice l i n e i n t e n s i t y Bibliography . . . . . . . .  . 56 58 62  ILLUSTRATIONS  page 1.  Magnetic moment per atom plotted against atomic number . . .  2.  Saturation magnetisation plotted against percent manganese results of Kaya and Kussmann . . •  3.  0  8  L a t t i c e parameter o f n i c k e l manganese a l l o y s - r e s u l t s of Valentiner  5.  6  Curie temperature of n i c k e l manganese a l l o y s - r e s u l t s of Kaya and Kussmann . . . . . . .  4.  4  and Becker . . . . . .  8  Change i n saturation magnetisation of an a l l o y with 23.7 percent manganese with increasing annealing time at 380, 400, 420 and 450°C . . . . . . . . . v  6.  •  •.  X-ray d i f f r a c t i o n films showing that the d i f f u s e l i n e s were not produced by an oxide layer . . . . . . . . . . . . .  7.  20  X-ray d i f f r a c t i o n films o f an a l l o y with 23.7 percent manganese a f t e r the f i n a l heat treatments  10.  18  Results o f saturation magnetisation of a l l three heat treatments . . . . . .  9.  17  Change i n saturation magnetisation of an a l l o y with 23.7 percent manganese with increasing annealing time at 490°C  8.  1°  21  Results of saturation magnetisation f o r alloys near stoichometric composition Ni Mn . . . . . . . . . . . . 3  22  11.  X-ray d i f f r a c t i o n f i l m s showing superlattice l i n e s . . . .  23  12.  Diagramatic view of vacuum pumping system  35  13.  Diagramatic view of high frequency induction furnace and vacuum casting unit  36  page 14.  Photograph of vacuum melting and casting unit, front view . . 37  15.  Photograph of vacuum melting and casting unit, rear view . .  38  16.  Front view of magnetic balance  40  17.  Top view of magnetic balance, showing furnace  18.  Top view of magnetic balance showing dewar f l a s k  42  19.  Test of probe f o r e l e c t r o s t a t i c measurements  45  20.  P o s i t i o n of p o t e n t i a l readings . .  .........  45  21.  Plot of e l e c t r o s t a t i c p o t e n t i a l readings . . . . . . . . . .  46  22.  Potentials along magnet pole axis . . . . . . . . . . . . .  47  23.  C a l i b r a t i o n of magnetic balance f o r sample weight . . . . .  48  •  41  FERROMAGNETISM AND ORDER IN NICKEL MANGANESE ALLOYS  Introduction  A ferromagnetic  material i s defined as a material that has  a large force exerted on i t when placed i n a magnetic f i e l d gradient.  The  source of the ferromagnetism i s thought to be the spin of the electrons* Although the o r b i t a l motion of the electrons may also have a magnetic moment, t h i s i s thought to be small compared with the spin magnetic moment i n a s o l i d , as the gyromagnetic r a t i o i s nearly equal to that of an e l e c t ron spin.  For a substance t o be magnetic, i t i s necessary to have more  of the electron spin moments oriented i n one d i r e c t i o n than i n the other. If equal numbers of electrons have t h e i r spins aligned i n each d i r e c t i o n , t h e i r magnetic moments w i l l cancel and the material as a whole w i l l not be magnetic.  In ferromagnetic materials there i s a spontaneous  2  alignment of the electron spins i n the p a r t i a l l y f i l l e d s h e l l s of each atom.  Because one energy l e v e l can only contain one electron of each  spin orientation, the alignment of electron spins w i l l r a i s e some of the electrons into higher k i n e t i c energy states.  I f a magnetic material does  not have a high density of states i n the u n f i l l e d electron s h e l l , then the a l i g n i n g of the electrons w i l l require more energy than i s a v a i l a b l e . In the Heisenberg theory^, the energy that aligns the electrons i s a r e s u l t of the e l e c t r o s t a t i c exchange i n t e r a c t i o n between the electrons of the atoms.  The outer, valence electrons w i l l not take part i n the magnet-  ism because the density of states i s not s u f f i c i e n t l y high.  In the trans-  i t i o n metals, however,' there i s an u n f i l l e d 3d s h e l l i n the iron group and an u n f i l l e d 4f s h e l l i n the rare earths.  It i s found that n i c k e l , 2  cobalt, iron, and gadolinium are the only magnetic elements.  Slater ,  using the Heisenberg theory, a t t r i b u t e s the lack of magnetism i n other elements of the t r a n s i t i o n groups to the large radius of t h e i r 3d s h e l l compared with t h e i r r e l a t i v e l y small interatomic distance.  Under t h i s  condition the 3d s h e l l s of adjacent atoms w i l l overlap too much causing a negative exchange i n t e r a c t i o n . The r e l a t i v e values f o r the saturation magnetisation  of d i f f -  erent elements and a l l o y s are often compared with the number of electrons i n the 3d s h e l l .  There are f i v e quantized energy l e v e l s i n the 3d s h e l l ,  each of which can hold two electrons of opposite spin.  I f t h i s band i s  divided into two half bands, each of which can hold f i v e electrons of one spin d i r e c t i o n , the maximum magnetisation w i l l occur when one of the bands i s completely f i l l e d and the other band has the remaining 3d electrons. Because the 3d and 4s bands overlap, i t i s not necessary to have an i n t e g r a l number of electrons i n e i t h e r band, but the t o t a l number of  3.  electrons i n the 3d plus 4s bands must be the same as that of the free atoms.  Because the experimental value f o r the saturation magnetisation of  n i c k e l i s 0.6 Bohr magnetons, there must be 0.6 holes i n the 3d s h e l l of nickel.  This allows 0.6 valence electrons i n the 4s s h e l l .  I f we assume  that the number of 4s electrons i s constant f o r atoms with atomic number near that of n i c k e l , then the magnetisation w i l l decrease with atomic number as shown i n Figure 1. l i n e i n Figure 1.  The experimental curves are shown as a dotted  I t i s seen that a l l o y s of n i c k e l and manganese follow  the t h e o r e t i c a l curve at high n i c k e l concentrations but leave the curve at manganese concentrations greater than eight atomic percent, 3  The Ising approximation , i n which only the z component of the 3d spin i s used i n the Heisenberg exchange energy term, can be used t o predict the magnetisation of a l l o y s i f the magnetic moment of the i n d i v i d u a l atoms i s known. When using t h i s approximation, i t i s usually assumed that the exchange interaction which aligns the electron spins i s constant f o r small changes i n interatomic distance.' This approximation has been used by Neel^ , Vonsovsky-', B i t t e r ^ , Smoluchowsky'', and others, to explain -  ferromagnetism and antiferromagnetism i n f e r r i t e s and a l l o y s . The a l l o y s of manganese and n i c k e l are an i n t e r e s t i n g example of the Ising approximation.  When the manganese atoms are added to  the n i c k e l l a t t i c e t h e i r magnetic moments w i l l l i e i n the same d i r e c t i o n as the n i c k e l atoms i f the exchange i n t e r a c t i o n between the manganese and n i c k e l atoms has a positive sign.  Because there are more holes i n the 3d  s h e l l of manganese than of n i c k e l , one would therefore expect a l i n e a r increase i n saturation magnetisation with increasing manganese concentration.  This was found to be true up to s i x atomic percent manganese by 8  Kaya and Kussmann • ation extrapolated to  Their r e s u l t s f o r the values of saturation magnetiszero degrees Kelvin, are shown i n Figure 2.  The  4  CO  z o  Cr  Mn  Fe  Co  Ni  Cu  2 4  25  26  27  28  2 9  ELECTRONS  Figure 1.  PER  ATOM  A. p l o t o f magnetic moment p e r atom a g a i n s t number.  atomic  The s o l i d l i n e i s the t h e o r e t i c a l v a l u e ;  • 18  the d o t t e d l i n e s show t h e e x p e r i m e n t a l  measurements.  5.  bending over of the curve at eight atomic percent manganese i s attributed  9 by Carr  to the negative exchange i n t e r a c t i o n of the nearest neighbour  manganese atoms causing adjacent manganese atoms t o have opposite spin. The p e r f e c t l y ordered face centered cubic structure would, however, have no nearest neighbour manganese atoms below twenty-five atomic percent manganese.  One would therefore expect the completely ordered a l l o y to have a  value of saturation magnetisation on the l i n e tangent to the curve at zero percent manganese.  The tangent i s shown dotted i n Figure 2.  The  ordered a l l o y of Kaya and Kussmann at twenty-five atomic percent manganese has a value of saturation magnetisation f a r below the expected value on the tangent.  A preliminary heat treatment on an a l l o y of t h i s composition  made during the present work, showed that the saturation magnetisation of Ni Mn was much higher than the value found by Kaya and Kussmann. 3  An  i n v e s t i g a t i o n of the l i t e r a t u r e on n i c k e l manganese a l l o y s confirmed t h i s higher value.  However, no other measurements of saturation magnetisation  have been,made on alloys other than the stoichiometric composition.  The  other investigators used d i f f e r e n t heat treatments and thus obtained d i f f erent values f o r the saturation magnetisation of Ni Mn. 3  I f the a l l o y i s  ordered, superlattice l i n e s should occur on the x-ray d i f f r a c t i o n pattern. Because the i n t e n s i t y of the superlattice l i n e s depends on the difference between the atomic scattering factors of n i c k e l and manganese, which i s small, the superlattice l i n e s were not seen u n t i l monochromatic radiation 10 and an evacuated camera were used recently by Averbach •  Superlattice  l i n e s had previously been seen by neutron diffraction"^". Because i t was apparent that the heat treatment f o r much of the work on these a l l o y s has been inadequate t o give maximum ordering, i t was decided to make a thorough i n v e s t i g a t i o n of the magnetic  6.  10 0 0  5  10  ATOMIC  Figure 2 .  PERCENT  15 MANGANESE  Values o f s a t u r a t i o n m a g n e t i s a t i o n  e x t r a p o l a t e d t o 0°K  p l o t t e d a g a i n s t atomic percent manganese. - results  2 5  2 0  of Kaya and Kussmann.  .,  properties of n i c k e l manganese a l l o y s .  I t was proposed to make a l l o y s i n  the range zero to t h i r t y - e i g h t atomic percent manganese, to f i n d the heat treatment that w i l l give maximum magnetisation, to measure the saturation magnetisation, and t o f i n d the necessary conditions to explain the change i n saturation magnetisation with composition using the Ising approximation. It was also proposed to f i n d the order parameter f o r a l l o y s near the stoichometric composition by measuring the i n t e n s i t y of the x-ray super-  Q lattice lines.  Unfortunately, a paper by Carr , which explained the change  of saturation magnetisation with composition f o r the quenched a l l o y s , was published when the present work was half f i n i s h e d . Previous Work  The change i n saturation magnetisation of n i c k e l manganese a l l o y s has been measured from zero to f o r t y weight percent manganese by 8 Kaya and Kussmann •  Their r e s u l t s f o r the values o f saturation magnetis-  ation extrapolated to zero degrees Kelvin are shown i n Figure 2. measured the Curie temperature at a l l compositions. shown i n Figure 3.  They also  These r e s u l t s are  After a heat treatment at 430° C f o r three days, t h e i r  value of magnetic saturation of composition Ni Mn was 3  4TTI = 7800 Gauss,  compared with a value of 6400 Gauss f o r n i c k e l under the same conditions. The a l l o y Ni Mn has been investigated by several people. 3  12 Thompson  obtained p a r a l l e l e f f e c t s  f o r the change of magnetisation and  r e s i s t i v i t y on both annealed and quenched samples. Curie temperature  at  He measured the magnetic  46O C, the c r i t i c a l ordering temperature at 520° C, 0  and the naximum saturation magnetisation at 6~- 91.5.  This i s equivalent  to 4TTI = 9500 Gauss i f the density of Ni Mn i s taken to be 8.25grams per 3  8  i  i  10  20  ATOMIC F i g u r e 3.  PERCENT  — — - r  30  40  MANGANESE  Change o f C u r i e temperature w i t h i n c r e a s i n g manganese c o n c e n t r a t i o n i n n i c k e l manganese a l l o y s . 8  - results  o f Kaya and Kussmann.  10 ATOMIC F i g u r e 4. '' » •  20 PERCENT  30 MANGANESE  L a t t i c e parameter o f n i c k e l manganese a l l o y s - r e s u l t s o f V a l e n t i n e r and B e c k e r . ' ' 1  5  40  cubic centimeter.  13 Guillard  The saturation magnetisation of Ni Mn was measured by 3  , a f t e r a heat treatment of three weeks at 470° C.  The value of  the extrapolated curve t o 0°K was <5~ = 98.16 Gauss ( 4 F I = 10200).  The  saturation magnetisation of Ni Mn, measured by Komar and Volkenstein 3  14 ,  was 9300 Gauss.  The change i n l a t t i c e parameter of quenched a l l o y s with 15 composition, shown i n Figure 4, was measured by Valentiner and Becker. 10 The l a t t i c e parameter of ordered Ni Mn was 3.59 A° 3  Procedure  The a l l o y s were made from the following metals: n i c k e l powder from Fisher S c i e n t i f i c Company with 0.1$ Fe and less than 0,1% Co as the main impurities; e l e c t r o l y t i c manganese donated by the Electromanganese Corporation with 0.018% S as sulphide and 0.01555 H as the main impurities.  2  The alloys were melted under an argon atmosphere  because a magnetic manganese n i t r i d e forms when manganese a l l o y s are melted under a i r .  The a l l o y s could not be melted under vacuum because  manganese i s too v o l a t i l e .  To obtain the proper argon atmosphere the  vacuum melting and casting unit described i n Appendix 1 was designed and built.  The oxide surface on the n i c k e l powder was reduced by heating the  n i c k e l and manganese i n the induction furnace at 600° C. f o r t e n minutes under a hydrogen atmosphere.  After the oxide had been reduced, the  furnace was evacuated to 0.5 microns and argon, which had been p u r i f i e d by passing over magnesium chips and copper turnings at to a pressure of one atmosphere.  400° C, was l e t i n  The metal was then melted and the a l l o y  was cast under the argon atmosphere i n t o the cold brass mold.  This c h i l l  casting produces a high concentration gradient f o r short distances i n the  10.  cored structure, thus decreasing the homogenizing time required to remove detectable heterogeneity.  To test the ingot f o r segregation, samples  taken from the top, center, and bottom of a cast ingot were analyzed; t y p i c a l results were: 22.9, 22.6, and 22.7 weight percent manganese.  The  ingots were homogenized f o r f i v e days at 1000° C under a p u r i f i e d argon x atmosphere. The saturation magnetisation of the alloys was measured 16 on a Fereday magnetic balance. 2.  This instrument i s described i n Appendix  The samples f o r the magnetic balance were cut and f i l e d to shape from  the homogenized ingot. analysis sample.  The adjacent piece of the ingot was used f o r the  The magnetic samples were annealed at 420° C f o r two y  weeks, then at 400° C f o r one week.  The correct annealing treatment  was found by annealing alloys of 15.35, 19.92, 23.70, and 32.07 atomic percent manganese at temperatures of 370, 400, 420 and 450° C, and x.  A standard quartz tube furnace with rubber bungs at the end of the tube and a heating element sixteen inches long was used.  A  rubber gas analysis bag connected to the furnace, kept the pressure s l i g h t l y above one atmosphere,  y.  Some previous investigators have used a slow cooling heat treatment on t h e i r a l l o y s .  I f t h i s i s done they must assume  the a l l o y i s completely ordered a f t e r the heat treatment.  By  using a constant temperature heat treatment, the degree of order f o r the a l l o y can be found from the t h e o r e t i c a l curve of order against temperature.  11.  measuring the room temperature saturation magnetisation of each sample a f t e r d i f f e r e n t annealing times.  A l l magnetic balance samples were heat  treated i n evacuated glass tubes with a piece of pure manganese i n the tube to absorb any remaining oxygen or nitrogen.  The glass tube was  heated before i t was sealed to remove any occluded gases.  Other  samples  were annealed at 800° C f o r two hours i n evacuated vycor tubes and were quenched i n water. When Debye-Scherrer powder patterns were taken on the annealed a l l o y s , a l l alloys above eighteen atomic percent manganese had d i f f u s e back r e f l e c t i o n l i n e s .  This effect i s due to a change i n l a t t i c e  parameter i n the sample, which can be produced by any of the following: 1.  an oxide layer on the surface of the powder.  2.  small order domains r e s u l t i n g i n many Mn-Mn interactions betvreen manganese atoms with the same spin d i r e c t i o n at the domain i n t e r faces.  3.  i n t e r n a l stresses produced during f i l i n g .  To check f o r the p o s s i b i l i t y of an oxide layer, a powder sample of 23.7 atomic percent manganese was heated at 420° C f o r sixteen hours. x-ray pattern was taken showing diffuse l i n e s . at 800° C f o r two hours and quenched. had sharp l i n e s .  An  The powder was reannealed  The pattern of the quenched sample  This showed that no oxide layer was present.  To check  for the p o s s i b i l i t y of i n t e r n a l stresses s t i l l being present, a powder sample of 23.7 atomic percent manganese was annealed at 550° C f o r sixteen hours and then at 420° G f o r fourteen hours. back r e f l e c t i o n l i n e s . the  The r e s u l t i n g f i l m had sharp  This confirms the presence of r e s i d u a l s t r a i n from  f i l i n g , i n the a l l o y s annealed at 420° C f o r two weeks plus 400° C  for one week.  Apparently the r e c r y s t a l l i s a t i o n temperature of n i c k e l  12  manganese alloys increases with manganese content because the a l l o y s with less than eighteen percent manganese had sharp back r e f l e c t i o n l i n e s with the same heat treatment i n which a l l o y s with higher manganese concentration had d i f f u s e l i n e s .  This, however, does not, eliminate the p o s s i b i l i t y  of small order domains causing the diffuse l i n e s , as the a l l o y with heat treatment at  550° C f o r sixteen hours plus fourteen hours at 420° C may  not be s u f f i c i e n t l y ordered to produce t h i s e f f e c t .  17 It has been shown by Sykes and Jones  that the order domain  size i s increased by annealing just below the c r i t i c a l order temperature,, A preliminary heat treatment was given samples of 23.7 atomic percent manganese to determine the length of annealing time at essary to produce large order domains. at  490° C that i s nec-  Samples of the a l l o y were annealed  490° C f o r d i f f e r e n t times, and were then annealed at 420° C f o r two  weeks.  It was found that the saturation magnetisation of the a l l o y i n c r -  eased with the time of annealing at 490° C up to a period of 200 For the f i n a l heat treatment, a l l o y s of composition 19.9, 21.8, 24.1, 25.0, 25.7, 27.9,  hours* 23.7,  and 30.3 atomic percent manganese were annealed at  555° C f o r fourteen hours, plus 250 hours at 490° C, plus 260 hours at 420° C, plus 260 hours at 400° C.  Powder patterns were taken of these  alloys and t h e i r saturation magnetisation was measured. .The i n t e n s i t y of the (110) superlattice l i n e on the a l l o y of twenty-five atomic percent manganese was measured on the P h i l i p s goniometer by taking the t o t a l count f o r an hour with the geiger counter o s c i l l a t i n g across the l i n e .  The background was taken under the same  conditions on both sides of the l i n e . was then measured i n a similar manner.  The i n t e n s i t y of the (111) l i n e  13.  Results In the f i r s t set of preliminary samples f o r the magnetic balance, a heavy oxide formed when the samples were annealed i n •evacuated* pyrex tubes that were i n c o r r e c t l y sealed.  The curve o f magnetisation  against annealing time f o r these samples followed the curve l a t e r found f o r magnetisation against decreasing manganese content.  The oxide,was obviously  reducing the manganese concentration of the samples.  To prevent t h i s  oxide from forming, pieces of pure manganese were put i n the evacuated tubes with the magnetic balance samples.  After being sealed, the pure  manganese was s l i d to one end of the tube and the tube was heated at the manganese end with a gas flame.  I t was hoped that the hot manganese would  absorb any o f the remaining oxygen and nitrogen.  I t was found a f t e r  several t r i a l s , that the l o c a l heating of the manganese introduced more gas into the tube from the softened glass than was absorbed by the manganese. the  The l o c a l heat treatment was therefore stopped' and a l l samples on  f i n a l runs were annealed i n evacuated tubes with a piece of manganese  and were not contaminated.  Several other investigators have noticed a  decrease i n manganese content on annealing.for a few hours and attributed i t to the sublimation of the manganese atoms. putting i n the pure manganese.  This e f f e c t i s reduced by  To check f o r any gain or loss i n manganese  concentration during the heat treatment, the sample f o r the magnetic balance with 23.7 atomic percent manganese was analyzed at 24.0 atomic percent manganese a f t e r annealing f o r two weeks at  420° G and one week  at 400° C. The following r e s u l t s were obtained from the preliminary runs:  1.  The saturation magnetisation of the alloy with 15.4 atomic  percent manganese was unchanged by annealing at 380, 400, 420, or 450° C. 2.  The curves of saturation magnetisation against annealing time at  380, 400, 420, and 450° C for an alloy with 23.7 atomic percent manganese are shown i n Figure 5« The curves for the other alloys are similar. 3. In the course of the magnetic measurements for the preliminary runs, the magnetisation of the standard nickel sample was measured twenty times on different days.  It gave a room temperature value of 6000 with a  standard deviation of 60. 4. The x-ray diffraction pattern of the 23.7 atomic percent manganese alloy annealed at 420° C for sixteen hours i s shown in Figure 6, film A. The pattern for this same alloy after an additional anneal at 800° C with a water quench, i s shown i n Figure 6, Film B. 5.  The saturation magnetisation of samples with 23.7 atomic percent  manganese annealed for varying times at 490° C plus an additional two weeks at 420° C i s shown in Figure 7. For the results of the f i n a l runs, the following notation is used for the heat treatments: Heat treatment A - Two hours at 800° C followed by a water quench. Heat treatment B - Two weeks at 420° C plus one week at 400°C. Heat treatment C - Sixteen hours at 555°C, plus 250 hours at 490°C, plus 260 hours at 420°C, plus 260 hours at 400°C. The following results were obtained from the f i n a l runs: 1.  The values of the saturation magnetisation for heat treatment A  measured at room, dry ice, and liquid oxygen temperatures are shown i n Table 1. The value of saturation magnetisation after extrapolation of the 2 magnetisation against T curve to zero degrees Kelvin i s also given for  15.  the samples i n which the curve was linear. 2. The values of saturation magnetisation for heat treatment B are shown i n Table 1. The extrapolated values of saturation magnetisation for heat treatments A, B and C are shown i n Figure 8. 3. Figure 9, films A, B, and C show the x-ray diffraction patterns obtained for alloys with 23.7 atomic percent manganese after heat treatment A, B, and C respectively. 4. The values of saturation.magnetisation for the samples after heat treatment C are shown i n Table 1. The results of the extrapolated curve to zero degrees Kelvin are shown i n Figure 10. The corresponding curve for heat treatment B i s drawn on the same graph. 5. The x-ray diffraction patterns of alloys with 23.7, 25.0, and 25.7 atomic percent manganese after heat treatment C are shown i n Figure 11, films A, B, and C. The prints were over-exposed to bring out the order lines.  This i s the reason why the. doublets are not resolved,  6. The results for the line intensity measurements are given below: oscillating angle min. i max.  1 Line 1 background  '  1  (no)  42.96  44.02  i  (no)  44.28  45.49  1 background  i  (no)  1 background  1  Total Counts i os d i l a t i n g | angle(20) i  Time  72450 \  1  1 hour  1  1 hour  1  74314 ,  1 hour  1  72889 I  1  45.61  ;  j  46.58  ;  53.95 [  54.92  1  20 min. 26584 !  i  (LID  ;  54.83 |  56.36  1  20 min. 85387 ;  56.71 J  57.70  ' 20 min. 28079 [  (111)  1.53°  1  1  (in)  1  |  1  i  1 background  1.21°  1  1  ;  1  16.  9000 -  8000  420°G  7000 o  rO  CD  6000  <  5000  CVI  cn CO  4000  < 3000 <3"  2 000 380°C 1000  0  100 ANNEALING  F i g u r e 5.  300  200 TIME  IN  HOURS  Change i n s a t u r a t i o n m a g n e t i s a t i o n f o r an a l l o y o f 23.7%  Mn w i t h i n c r e a s i n g a n n e a l i n g t i m e . A l l  measurements were done a t room  temperature.  400  Figure 6,  Film A - 23.1$ Mn a f t e r 16 hours at 420°C. - u n f i l t e r e d Cu radiation Film B - same sample as f i l m A with an additional 2 hours at 800°C followed by a water quench. - u n f i l t e r e d Cu radiation.  «8.  9 3 0 0  9 2 0 0  -  9 1 0 0  9 0 0 0  o ro cn  8 9 0 0  -  8  8 0 0  -  8  7 0 0  -  CM  CO CO  < 8 6 0 0  8 5 0 0  100  A N N E A L I N G  F i g u r e 7.  T I M E  A T  4 9 0 ° C  2 0 0  IN  H O U R S  Room temperature v a l u e s of s a t u r a t i o n m a g n e t i s a t i o n f o r samples of 23.7/5 Mn annealed f o r v a r y i n g times at  490°C w i t h an a d d i t i o n a l 400 hours a t 420°C.  19. Saturation Magnetisation 4TTI i n Gauss Heat Treatment C  Heat Treatment B  Heat Treatment A  '293°K 200°K : 90 K : O°K £93° K :200°K : 90 K : O°K £93 °K :200°K : 90° K : O°K 0  0  • : :  : 6203 : 6400 : 6400 : 6400  0  3  -  :  9  :  6880 : 7250: 7690 *. 7810 . 6940 . 7340'; 7530 : 7600 (  .' 4.8 : '6940 :7440.: 7730 . 7810 : 6960' 7510;: 7750 : 7800 :  6.4 . 7120 : 7700 : sioo:: 8200 : 7190 7810': 8240 ' .8330  j  7 . 4 ' 7060 ''7740 : 8130 .: 8210': 7320" 7980:: 8380 : 8480.  :  i i . i : 6680 : 7610: 8410: 8550:: 6700: 7730: 8290 : 8470.  :  12.7: 5860 : 7070: 7800: 8000: 6050: 7180: 7990 : 8170"  :  15.4. 4740 . 6210:. 7020:: 7220: 5470: 6830:. 7660 : 7850:  :  16.0: 4270 : 5900'. 6647'. 6890' 4720: 6230' 7090 : 7340:  :  is.3: 1984; 4460.' .  (  (  (  :  1 9 , 9  :  21.8. 100 ' 1030  :  2 3  7  5  2  0  :  ' 5820: 4250: 5840: 6702 ' 6870:  740 : 3670: 4850: 5140: 3860: 5450: 6210 ': 6350: 3750: 5360:' 6186 ' 6540 :  :  * :  5  8540. 9050. 9270 : 9320: 7630: 8300:' 8540 : 8590 :  2780.  100 . 370..  1  4  5  9440:. 9500: 9450': 9480]. 9890] 9880: 9850 : 9880 :  :  0  60 . 180 '[ 890' \  25.0  50 : 110 : 400:  *  25.7  40 ' 100 | 300:  :  28.0  50 ; 70  ;  30.3  32  50  64:•  :  32.1.  32 :  46 :  28.  *  37.0:  :  :  1  4  :  0  Table 1.  9370: 9340; 9330;: (  \  k  : 10730: 11010: 10910 :nooo : i  7830: 8240: 8350;[ 8380: 10130: 10260: 10340: 10350 : 9510: 9750: 9910: 10020 l  . 7360: 7710: 7800:. 7820: 7070: 7950: 7840: 7900 :  130:  :  9 3 5 0  7 1  i ' 6850: 7160: 7270] 7310: 6710: 6890: 7010: 7070 :  0 . 590:  640:  620;  620 j  0 \  320]  330:  330:  340:  The above values were obtained r e l a t i v e to the standard n i c k e l sample, with a correction f o r the change i n weight of the average atom and the change i n l a t t i c e parameter as shown i n Figure 4,  HEAT  5  10 ATOMIC  Figure  8.  15  20  PERCENT  25  TREATMENT  30  35  MANGANESE  Values o f s a t u r a t i o n m a g n e t i s a t i o n e x t r a p o l a t e d t o zero degrees and  C.  K e l v i n f o r heat treatments A, B,  C  40  21.  Figure  9. X-ray d i f f r a c t i o n patterns f o r an alloy with 23.7 atomic percent manganese a f t e r heat treatment A, B, and C are shown i n films A, B, and C respectively. U n f i l t e r e d i r o n r a d i a t i o n was used.  22-.  ' 20  1  1  1  I  I  10.  L_  1  I I  25 A T O M I C - P E R C E N T  Figure  L  30 MANGANESE  Values of s a t u r a t i o n magnetisation  extrapolated to  zero degrees K e l v i n f o r heat treatments  B and  C.  Figure l l .  X-ray diffraction patterns for alloys with 23.7, 25.0, and 25.7 atomic percent manganese after heat treatment C are shown i n films A , B, and C respectively.  Unfiltered iron radiation was used.  24.  Discussion  1.  Preliminary Runs. From Figure 5 showing the change of magnetisation with  annealing time at 420°C, i t i s evident that saturation magnetisation i n c r eases progressively with annealing time f o r periods up to two weeks.  Most  other investigators have only used times i n the order of f i f t y hours.  The  value of the saturation magnetisation a f t e r annealing at 420°C i s influenced by the length of the previous anneal at 490°C.  This change, shown i n Figure  7, i s due to the size of the order domains increasing at the high temperature anneal.  2.  F i n a l Runs. a.  Disordered case a f t e r heat treatment  A.  The t a i l above twenty-five atomic percent manganese i n the curve of saturation magnetisation against concentration f o r the quenched alloys i s probably due to the- slow quenching rate, as the vycor tubes were not broken when they were quenched into the water.  The curve of Kaya and  Kussmann, shown i n Figure 2, has no t a i l . 2 It was noticed that the curve of magnetisation against T was not l i n e a r f o r the quenched samples between twenty and t h i r t y atomic percent manganese.  These a l l o y s had much too low a value of saturation  magnetisation at 200°K to f i t the T m the work of Kaya and Kussmann . 0  2  curve.  This e f f e c t i s also present  It i s probably due to the magnetic f i e l d  strength not being s u f f i c i e n t to saturate the samples.  I f the samples had  a coercive force that was small at 90°K and 293°K, and was large at 200°K, then i t would be possible f o r the magnetic f i e l d to saturate the samples  25.  t at 90.K and 293°K but not be strong enough to saturate them at 200°K. The only alloys that have non l i n e a r curves are the quenched a l l o y s near the order composition.  I f l o c a l order exists, then these a l l o y s w i l l have an  order domain size that i s larger than the domain size of the other quenched alloys and smaller than the domain size of the annealed alloys near the order composition.  I t i s a known f a c t that the magnetic coercive force reaches  a maximum at one magnetic domain size and i s smaller f o r either larger or smaller domains.  Because the maximum size of the magnetic domains i s less  than the size of the order domains, the non l i n e a r curves f o r the quenched alloys can be explained by assuming that the order domains o f these alloys are the proper size to produce the c r i t i c a l magnetic domain size f o r maximum coercive f o r c e . Carr , i n a recent paper, q u a l i t a t i v e l y explains the behaviour of the saturation magnetisation of the quenched alloys i n terms of the number of Mn-Mn interactions.  He proposes the following theory:  •For a disordered a l l o y with an appreciable percentage of manganese atoms, the Mn-Mn interaction begins t o outweigh the weaker Ni-Mn interaction, and one eventually f i n d s the manganese spins s t a r t t o cancel one another.  This behaviour becomes clearer i n the energy  calculations which follow and which indicate that the bending over of the curve as observed i n Figure 2, should occur f o r q r e l a t i v e l y small f r a c t i o n of manganese.  Beyond t h i s point, the magnetic moment  i s derived p r i n c i p a l l y from the n i c k e l ions and diminishes with increasing manganese content because o f the replacement of n i c k e l and to the f i l l i n g up of the n i c k e l 3d s h e l l .  Assuming the manganese  ions t o have f i v e electrons i n the 3d s h e l l , one finds that the n i c k e l s h e l l s become completely f i l l e d at about 30 percent manganese. The  26.  moment thus goes t o zero at t h i s composition i n approximate agreement with experiment.' If we assume that f o r low manganese concentrations there are no Mn-Mn interactions, then from the i n i t i a l slope of the curve i n Figure 8, we f i n d that the addition of manganese atoms to a n i c k e l l a t t i c e produces a r i s e i n magnetisation s i m i l a r to that produced by an atom with a magnetic moment i n the order of 3.4 Bohr magnetons. 18  Other values f o r the magnetic  moment of manganese are: MnAs - 3.40  Mn Sb - 0.94  MnBi - 3.52  MnSb - 3.53  Mhz^N - 0.24  Mn Sn - 0.86  . MnP  -  2  2  1.2  The value obtained i n t h i s a l l o y i s 5.7 times the magnetic moment o f a 19 n i c k e l atom.  I f we use the Zener assumption  that the manganese atoms  w i l l r e t a i n f i v e of t h e i r 3d electrons and the rest w i l l be given t o the n i c k e l , then each manganese atom w i l l give n i c k e l atoms.  10-5-3.4 - 1.6 electrons to the  This w i l l make the magnetic moment o f the n i c k e l atoms equal  zero at twenty-seven atomic percent manganese. 9 Carr assumes that the magnetisation near twenty-five atomic percent manganese i s due to the n i c k e l atoms alone. I f t h i s i s true, then the curve near twenty-five atomic percent manganese w i l l have a slope  640O  .  equal to 25" =~250.6 using the units on Figure 8. -S6P4..  The a c t u a l slope i s  This discrepancy can be eliminated by having the manganese atoms  contribute to the magnetism up t o twenty-five atomic percent manganese and above t h i s concentration having a l l the manganese atoms paired o f f . I t can be accomplished i n either of two ways: 1. by assuming that the strength of the Mn-Mn i n t e r a c t i o n i s such that  27.  i t f i n a l l y overpowers the Mn-Ni i n t e r a c t i o n at twenty-five atomic percent manganese. 2.  by assuming that l o c a l order exists that tends t o keep the mang-  anese atoms from becoming nearest neighbours i n the quenched a l l o y s . The degree of order i s such that below twenty-five atomic percent manganese there are i n s u f f i c i e n t Mn-Mn interactions to make the contribution o f the manganese atoms to the magnetic moment of the a l l o y equal to zero. Of these two assumptions, the l a t t e r i s preferable f o r the following reasons: a.  I t i s shown i n Appendix four, that when the f i r s t assumption i s  used, the value obtained f o r the f i n a l slope of the curve near twentyf i v e atomic percent manganese i s only h a l f the experimental value. b.  The Mn-Mn i n t e r a c t i o n should outweigh the Ni-Mn i n t e r a c t i o n at a  manganese concentration lower than twenty-five atomic percent because the strength of the Mn-Ni i n t e r a c t i o n becomes weaker as the 3d s h e l l s of the n i c k e l atoms become f i l l e d . c.  In a previous section of the discussion, i t was shown that the  non-linearity of the saturation magnetisation against T^ curve f o r some of the quenched a l l o y s can be explained by assuming short range order. 20 d.  Some degree of short range order i s present i n a l l a l l o y s .  Examples of t h i s are the l o c a l order i n AgAu f o r which there i s no long range order, and the l o c a l order i n quenched samples of Cu Au. 3  e.  The saturation magnetisation i s the same f o r quenched and annealed  alloys up to nine atomic percent manganese.  The Curie temperature i s  the same f o r quenched and annealed alloys up to seventeen atomic percent manganese.  Because the annealed alloys w i l l be ordered, then so w i l l the  quenched alloys i f t h e i r magnetisation and Curie temperatures  are the same.  28.  2b.  Ordered A l l o y s . The maximum i n saturation magnetisation f o r the ordered  a l l o y s occurs at a concentration less than twenty-five atomic percent manganese because the a l l o y i s not completely ordered.  An incompletely  ordered a l l o y at twenty-five atomic percent must have some of i t s manganese atoms w i t h . l e f t spin, but an incompletely ordered a l l o y at less than twenty-five atomic percent manganese may accomplish i t s disorder by having n i c k e l atoms i n manganese s i t e s and therefore does not need to have any manganese atoms with l e f t spin.  I t i s seen from figures 8 and  10, that heat treatment C produces a maximum i n the graph of saturation magnetisation versus composition at 24.1 atomic percent manganese and heat treatment B, which produces less long range order than heat treatment C, r e s u l t s i n a niaximum i n saturation magnetisation at 23.7 atomic percent manganese. The drop i n magnetisation of Ni Mn from the ordered value 3  of 13"1?00 to the value of 8380 a f t e r heat treatment B, can be explained by assuming that the magnetic moment of a manganese atom with reversed spin, w i l l cancel the magnetic moment of one manganese atom with right spin.  To account f o r the magnetic moment found experimentally i n heat  treatment B using the above assumption, we must have 0.187of the manganese atoms with l e f t spin. positions.  Therefore these atoms must occupy face centered  Using t h i s value we get S = 0 . 8 J from the Bragg and Williams  theory and <T = 0.63 from equations 14 of Appendix 3, using the l o c a l order theory, i f we assume that each manganese atom with l e f t spin produces three Mn-Mn interactions. 5.  The calculations are shown i n Appendix  The short range order parameter of heat treatment B gives a value of  S = O.f? f o r the long range order parameter.  Similar values f o r heat  29.  treatment C were:S = 0.8$ f o r the Bragg and Williams, and 6" = 0.77 f o r the short range order theory which makes S = 0.88 f o r t h i s theory. References 21 and 22 give the following equilibrium values of S at A00°C with a c r i t i c a l order temperature  of 520°C:  Bragg and Williams theory  S = 0.79  Bethe and P e i e r l s theory  S=.0.95  Cu Au experimental  S=0.98  3  The low value of S obtained from the r e s u l t s of heat treatment B may be p a r t i a l l y due to the small order domain s i z e . of the theories includes a f a c t o r f o r the domain s i z e . reason f o r the low value of S, i s the assumption  Neither  Another possible  that a manganese atom i n  a face centered p o s i t i o n reverses i t s spin and does not influence the spin of i t s nearest neighbour manganese atoms.  I f the reversed spin of  one manganese atom reduced the e f f e c t i v e spin of i t s three adjacent manganese atoms, then a small amount of disorder  would produce a larger decr-  ease i n the magnetisation than that calculated.  This would r a i s e the  value of the order parameter calculated from the experimental r e s u l t s of saturation magnetisation. The values of saturation magnetisation f o r the annealed a l l o y s above t h i r t y and below twenty-one atomic percent manganese are not as high as those expected, because long range order i s not present and thus there are more Mn-Mn interactions than i f i t were present. The Curie temperature of a magnetic material i s d i r e c t l y proportional to the strengths of the interactions between the magnetic moments of the atoms of the material. From the decrease i n Curie temperature with the addition of manganese atoms i n the n i c k e l l a t t i c e , shown i n Figure 3, i t i s concluded that the Mn-Ni i n t e r a c t i o n i s much smaller  30.  than the Ni'-Ni i n t e r a c t i o n at t h i s composition.  The high Curie temper-  atures of the ordered a l l o y i s probably due to the second nearest neighbour i n t e r a c t i o n between-t<he manganese atoms on the cube corners. This would account f o r the rapid r i s e i n Curie temperature hear twenty ' atomic percent manganese when long distance order i s increasing r a p i d l y . It also accounts f o r the maintaining of the high Curie temperature f o r compositions greater than twenty-five atomic percent manganese because there are s t i l l the same number of second neighbour Mn-Mn interactions that are present i n the a l l o y with twenty-five atomic percent manganese. The value of the order parameter of the a l l o y with twentyf i v e atomic percent manganese a f t e r heat treatment C was  calculated from  the measured i n t e n s i t y of the (110) planes compared with the (111) planes. The calculations are shown i n Appendix 5. S  The value obtained  was  =0.84 * 0.07. The order parameter f o r the same a l l o y calculated from  the saturation magnetisation was S = 0.88.  This agreement i s f a i r l y good  and j u s t i f i e s the assumption that the Mn atoms i n the face centered position invert t h e i r spins and thus cancel the magnetic moment of one of the manganese atoms at the cube corner. Probably the weakest point i n the explanation of the change i n saturation magnetisation with concentration i s the assumption that the 3d s h e l l s of the n i c k e l atoms are being f i l l e d with increasing manganese  19 content.  This p r i n c i p l e i s i n accord with Zener's theory  but does not  necessarily occur i n a l l a l l o y s , as evidenced by neutron d i f f r a c t i o n experiments on FeCo.  I f we do not assume that the 3d s h e l l s of the n i c k e l  atoms are f i l l e d , then there i s no explanation f o r the decrease i n saturation magnetisation to zero at twenty-five atomic percent manganese for the quenched a l l o y s .  Unfortunately, there i s no way to test t h i s  31.  assumption f o r the quenched a l l o y s .  In the case of the ordered a l l o y s i t  could be checked by an evaluation of the magnetic moments of the manganese and n i c k e l atoms by neutron d i f f r a c t i o n on a completely ordered a l l o y .  Conclusions  The annealing times used by most other investigators t o produce complete order i n alloys near the composition Ni Mn have been 3  inadequate.  To produce the equilibrium degree o f order at 420°C, at  least two weeks annealing time i s necessary. The maximum value f o r the saturation magnetisation of any a l l o y of n i c k e l and manganese less than f o r t y percent manganese, a f t e r heat treatment C, i s 4 THE = 1Q5J80 Gauss.  This i s the highest recorded  value f o r any n i c k e l manganese a l l o y after any heat treatment. The order domain s i z e i n Ni Mn increases with annealing 3  time at 490°C up to periods of 2 0 0 hours.  When t h i s annealing treatment  i s followed by an a d d i t i o n a l 2 5 0 hours at 420°C, and 2 5 0 hours at 400°C, the order l i n e s can be seen on an x-ray powder pattern using i r o n r a d i a t ion.  For these long heat treatments, i t i s necessary t o have a piece of  pure manganese with the sample t o prevent the sublimation o f the manganese atoms from the sample. The order parameter of Ni Mn a f t e r the heat treatment given 3  i n the paragraph above i s S = 0 . 8 8 , calculated;from the saturation magnetisation, and S = 0 . 8 4 * 0 . 0 7 , calculated from the order l i n e intensity. The addition of manganese atoms to a n i c k e l l a t t i c e produces a r i s e i n saturation magnetisation that i s s i m i l a r to that produced  32.  by an atom with a magnetic moment of 3#4 Bohr magnetons. To explain the change i n saturation magnetisation of a l l o y s quenched from 800°C, i t i s necessary to assume that some of the 3d electrons from the manganese atoms go into the 3d s h e l l of the n i c k e l atoms.  Once t h i s assumption has been made, the curve of saturation magnet-  i s a t i o n against composition f o r the quenched alloys can be explained most s a t i s f a c t o r i l y by the existence of short range order.  33.  APPENDIX 1  Vacuum Melting and Casting Apparatus  To prevent the contamination of the metals by nitrogen and oxygen;, a high frequency vacuum melting apparatus was designed and b u i l t . The apparatus consisted of two parts; a general vacuum pumping unit shown i n Figure 12, and a high frequency induction furnace shown i n Figure 13. Photographs of the complete unit are shown i n Figures 14 and 15. The brass pumping u n i t consisted of a Welsh duoseal forepump with a pumping speed of 0.37 l i t e r s per second at 0.1 millimeters pressure, a VMF 50 o i l d i f f u s i o n pump, a cold trap, a Kinney vacuum valve, a p i r a n i gauge, and an i o n i z a t i o n gauge. connected to the end of the u n i t .  A three inch brass tee was  A l l parts of the unit were connected  with eight-bolt companion flanges using greased rubber gaskets.  The  gasket groove had a beveled edge to prevent the gasket from being pinched when the b o l t s were tightened.  For argon melting, a bourdon gauge was  connected to the pumping u n i t .  This was necessary to measure the pressure  when the argon was l e t i n t o the system. The high frequency induction furnace was attached to the brass tee of the pumping unit with a companion flange.  The quartz tube  (fourteen inches long and one and one half inches i n diameter) was connected to the brass by using a mixture of graphite, o c t o i l , and digested rubber i n vacuum wax.  This mixture had p h y s i c a l properties similar t o  plasticene except that i t s vapour pressure was lower. end of the furnace was water cooled.  The s e a l at the top  The power was supplied by a Lepel  34.  7.5 KVA high frequency u n i t .  The x^ater cooled high frequency c o i l had  sixteen turns i n four inches length.  The crucibles were Norton extraction  thimbles made of alundum, with powdered alumdum packed between them. The inner crucible, which could be used f o r several melts, held f i f t y grams of powdered n i c k e l .  The loaded crucible was inserted into the top of the  quartz tube when the mold was removed. the  The crucible was then lowered into  middle of the high frequency c o i l by lowering the rod through the vac-  uum compression seal a t the bottom of the furnace. at the top of the furnace and the forepump started.  The mold was replaced I t took approximately  seven minutes pumping time to reduce the pressure to 0.1 millimeters, which i s the forepressure of the o i l d i f f u s i o n pump.  The t o t a l pumping time to  reach 0.5 microns pressure was from t h i r t y to f o r t y minutes.  After the  metal was melted i n the crucible, the rod at the bottom of the furnace was pushed up, thus l i f t i n g the crucible containing the molten metal to the height of the brass mold.  The whole furnace was then rotated through one  hundred degrees about the 0-ring seal and the metal flowed into- the cold mold.  35.  Figure 12.  Diagramatic view of the vacuum pumping system.  36.  f i g u r e 13.  D i a g r a m a t i c view o f the h i g h frequencyi n d u c t i o n f u r n a c e and vacuum c a s t i n g  unit.  37.  Figure 14.  Photograph of vacuum melting and casting unit - front view.  38.  Figure 15  Photograph of vacuum melting and casting unit - rear view.  39.  APPENDIX 2  Magnetic  1.  Balance  Description. The saturation magnetisation of the alloys was measured on a 16  magnetic balance s i m i l a r to that of Fereday turns and produced a f i e l d of 3000 Oersteds.  .  'The electromagnet had 7000  The s p e c i a l magnet poles  designed by Fereday produced a magnetic f i e l d such that the force on a sample was constant along the pole axis near the center of the gap. The samples were — x — x i inches. The sample holder was attached t o the end * 4 20 20 of the suspension arm shown i n Figure 16, When the current was on i n the electromagnet, the sample was displaced toward one of the poles. then restored to i t s i n i t i a l p o s i t i o n by twisting the suspension.  It was The  angle through which the suspension was twisted was controlled and measured by a worm gear at the top o f the suspension.  The i n i t i a l position of the  arm could be found by shining a l i g h t to the mirror on the suspension and back to a scale.  The angle through which the suspension was turned was  d i r e c t l y proportional to the force on the sample caused by the magnetic gradient.  field  The saturation magnetisation f o r a sample was found by comparing  the force on i t to the force on a standard n i c k e l sample.  To measure the  saturation magnetisation at high and low temperatures, the furnace shown i n Figure 17 and the dewar flask shown i n Figure 18 were used.  Figure 16.  Front view of magnetic balance showing magnet, suspension and sample holder.  Figure 17.  Top view of magnetic balance showing worm gear control and furnace arrangement•  42.  Figure  18.  Top view of magnetic balance showing dewar f l a s k arrangement.  43.  2.  Calibration. a.  P l o t t i n g of magnetic f i e l d i n the a i r gap. The r e l a t i v e change of the magnetic f i e l d i n the a i r gap  investigated using the analogy between magnetostatic fields.  was  and e l e c t r o s t a t i c  Because the magnetic f i e l d between the. pole pieces i s constant with  time, the magnetic p o t e n t i a l s a t i s f i e s Laplace's equation.  Therefore, i f  the boundary conditions f o r the magnetic and e l e c t r i c f i e l d s are the same, the potentials w i l l be r e l a t i v e l y the same over a l l points i n the f i e l d . Using t h i s p r i n c i p l e , r e l a t i v e values of the magnetic f i e l d i n the a i r gap of the magnetic balance were found by measuring e l e c t r o s t a t i c p o t e n t i a l s . To obtain s i m i l a r boundary conditions, the pole pieces of the magnet were removed and. placed the same distance apart i n a tank of water. p o t e n t i a l was  An e l e c t r i c  put on one of the pole pieces and the other pole was  grounded}  the p o t e n t i a l was then measured at a l l points on a h o r i z o n t a l plane through . the center of the pole pieces. The v e r t i c a l probe was made from a piece of insulated wire with a t i p bare.  To ensure that the insulated section of the probe d i d  not d i s t o r t the f i e l d , readings were taken on a l i n e along the axis of the probe, perpendicular to the axis of the magnet poles and midway between them.  I f the insulated part of the probe was d i s t o r t i n g the f i e l d , the  readings f o r which the probe point was below the pole axis would not be the same as the readings above the pole axis.  Figure 19, a plot of these  readings, shows that the insulated wire does not d i s t o r t the f i e l d .  Figure  21 gives a plot of the potentials f o r the positions i n the f i e l d shown i n Figure 20.  The potential along the pole axis i s shown i n Figure 22.  The results of t h i s investigation were:  44.  1,  The f i e l d was constant over the cross-section of the sample per-  pendicular to the pole axis. 2.  The force on the sample, which i s proportional to grad H, was  constant f o r a distance of approximately one h a l f inch along the f i e l d axis i n the center of the gap. The choice of rest point for. the suspension i s therefore not c r i t i c a l . b.  C a l i b r a t i o n f o r a change i n sample weight. The Alhico n i c k e l samples used f o r t h i s c a l i b r a t i o n were of  two d i f f e r e n t shapes.  One shape was c y l i n d r i c a l with the r a t i o of length  to diameter equal to f i v e .  The other shape was the same except i t had a  square cross-section instead of a c i r c l e . the same f o r a l l samples.  The r a t i o of width to length was  The r e s u l t s are shown i n Figure 23. The c i r c l e s  are values f o r samples with a round cross-section; the dots are f o r samples with a square cross-section.  I t was therefore shown that the d e f l e c t i o n  on the magnetic balance divided by the weight of the sample was constant. The constant was the same f o r both shapes and a l l weights of the samples investigated.  1  ro  1  1  1  PROBE -• V O L T S  X  •  :  '  mm  2 O  i POTE  Z  1 3 i  1  1.5  2.0 DEPTH  Figure 1 9 . •  OF  1 . 2.5 PROBE  INTO  TANK  1  1  3.0  3.5  IN  INCHES  Test of probe used i n measurement of the e l e c t r o s t a t i c potentials between the magnet poles.  98765432  98 7654 32  Figure 2 0 .  Position i n a i r gap between the magnet poles for the potential measurements shown i n Figure 2 1 .  4.<  I  I I I I I I I  I I I I I I I I  I I I I  22 -  20  18  16  14 ro x co o >  ,o  Q-  I2  10  6  I  I  I I I I !• I • I '» I' 'I' I j  DISTANCE  F i g u r e 21.  SMALL  POLE  LARGE  POLE  PARALLEL  TO  POLE  I I I I •»  FACE  P o t e n t i a l at v a r i o u s p o i n t s i n t h e a i r gap between the magnet p o l e s . shown i n F i g u r e  The p o s i t i o n of t h e r e a d i n g s i s '  20.  5 DISTANCE  F i g u r e 22.  6 ON  POLE  7 AXIS  FROM  8 CONCAVE  P o t e n t i a l s a l o n g t h e magnet p o l e  POLE  axis.  1  f  WEIGHT  F i g u r e .23.  OF  1  SAMPLE  I  IN  1  1  T  MILLIGRAMS  C a l i b r a t i o n o f magnetic b a l a n c e f o r sample w e i g h t . The dots a r e measurements on samples w i t h square section;  the c i r c l e s on samples w i t h round  cross-  cross-section.  49.  APPENDIX  THREE  S t a t i s t i c a l Derivations  1.  Definitions„ Let the face centered cubic l a t t i c e be divided into four  simple cubic l a t t i c e s L]_, L?, L3, and L^, such that an atom i n one sublattice has four nearest neighbours i n each o f the other three sublattices but no nearest neighbours  i n i t s own s u b l a t t i c e .  Let the order parameters of L]_, L2, L 3 , and L4 be a, b, c, and d, respectively. Let  a =  I f :A i s the f r a c t i o n of L, s i t e s occupied by A atoms  2 fiA-l  1  when a = 1  a l l atoms on L^ are A atoms  when a = 0  one half the atoms on L j are A atoms  when a = -1 no atoms on L l are A atoms similarly:  b = 2 ^A" c  d  - ISA" 2  =  2  f A-  1  1  1  3  We therefore get the equations / J1A"  1  * 2  {  A  = JIB  1 -  -P  =  J l A  1  -  a  2  with s i m i l a r equations f o r the other s u b l a t t i c e s . Let  (a + b + c + d) = R  Let  . . . . . .  2  be the t o t a l f r a c t i o n of A atoms i n the a l l o y . FA  = f =  IA +  j~2A +  1/2 + 1/8  f 3A 4  +  fkA  ( a + b + c + d)  50.  F  A  = 1/2 + 1/8 R  3  F  B  = 1/2 - 1/8 R  4  Let z. be the coordination number of the l a t t i c e . 2.  Derivation of Equations. Consider the nearest neighbour interactions of the atoms i n  s u b l a t t i c e L i with the atoms i n L2, L3, and L 4 . and B atoms i n L i i s ^i_±_§_^  I  a n  d ^  ~ ^ ^ a  The t o t a l number of A atoms respectively.  The.probab-  i l i t y of any one atom i n l a t t i c e L]_ being an A atom, i s equal to the f r a c t i o n of A atoms i n L^. Using these l a s t three f a c t s , the number of A-A interactions where one of the A atoms i s i n L]_ i s : . /l +  aA N f  V—;  4  Z: (l  [ 3\ — )  which equals  '2  + b\  Y1 + c\  3 { — )  , Z: / l + d \  vrr-/  3 N? f -l J^g I 3 + 2a + R + ab + ac + ad I +  +  S i m i l a r l y , the number of B-B interactions, where one of the B atoms i s i n L]_ i s :  (H*) i [ f M - f M ' f M ] which equals  jj^  £ 3 - 2a - R + ab + ac + a d j The number of A - B interactions i n which the A atom i s i n  L^ i s :  ^  [3 + 4a - R - (ab + ac +  ad)J  51.  The number of B - A interactions i n which the B atom i s i n L i i s : J3 - 4a  +R-  (ab + ac + ad)J  Since A-B interactions are equivalent  to B-A interactions,  the sum of the l a s t two equations w i l l be the number of A-B interactions i n which one of the atoms i s on L^.  j-jp" '  This equals  (6 - 2 (ab + ac + ad)~]  7  Equations s i m i l a r to 5> 6, and 7 are derived using L?, L 3 , and  i n turn as the reference axis.  The t o t a l number of A-A interactions  i s the sum of equation 5 with the three s i m i l a r equations obtained by considering the A-A interactions using 1%, L-j, and  as the reference l a t t i c e ,  a l l divided by 2. Let Q,pj^, Q gg and Q^  be the t o t a l number of A-A, B-B, and A-B  B  interactions, respectively. QAA -  [ 1 2 + 6R + 2 (ab + ac + ad + be + bd + but  AA  =  Q  BB  =  Q  AB.  Q  cd)j  Zr = 12 f o r the •$•<*-. l a t t i c e .  I £ l 2 + 6R + R  2  - ( a +b 2  2  +c  2  +d )]  + c  2  + d )]  . . 8  2  similarly  =  I  [L2 - 6R + R  2  I Q24 - 2R  2  - (a + b 2  + 2(a + b 2  2  2  + c  2  2  + d ) 2  . . . . . . . .  J  9 10  It i s seen that the t o t a l number of interactions obtained by adding equation 8, 9 and 10 i s 6N. This i s i n agreement with the coordination Case 1.  number of twelve.  Disordered l a t t i c e . When the l a t t i c e i s completely disordered,  52.  = b = c = d = 2j-  a  - 1 = 2F - 1  lk  A  R = a + b + c + d = 4 a = 4 (2F - l) A  Putting these values of a, b, c, d, and R into equations 8, 9 and 10 we get 2 ( Q A A )  dis  ( BB) .  =  Q  D  S  ( AB)  d i s  Q  6  A  F  11  N  =  6N  [ F /- 2F  -  12 H ( P - F A  2 A  A  +  1  ]  12  )  .13  Case I I . Ordered L a t t i c e , Let L]_ be the sublattice containing the B atoms when f u l l y ordered. Assume:  (1) that a l l B atoms l i e i n the one sublattice L^ ( i t i s immaterial  which sublattice they are i n as long as they a l l l i e i n the same one) (2) the other three sublattices are indistinguishable, i . e . , b = c =d Case I l a .  F  > \  A  4  A  then b = c = d = 1  . . . . as these l a t t i c e s have no B atoms  buta + b+ c + d = R = 4 (2F - l) A  a = 8F - 7 A  putting these values of a, b, c, d into equations 8, 9, 10, we get (QAA) . = ord toB>ord" (QAB)  ord  IQ  -  N ( 1 2 AF -  (-96F + 96) N  =  12N ( 1 - F )  (96 F  A  - 48)  A  6)  0  -  A  8  A  14  lib.  Assume lq_ l a t t i c e i s f i l l e d with B atoms, i Let b = c = d b u t a + b + c + d = R = 4 b = | F  A  (2FA - l )  - 1  putting these values into equations 8, 9, 10 we get ( Q A A*ord )^ -  (QBB)ord  ^J i . F  F/  6  12F, A  2 A  - 12F + 6 A  - I32-  N F  F, A  2  N  these check with case H a f o r F. =  2 4  A  £  54  APPENDIX 4  Equations f o r the Quenched Alloys  The object of t h i s Appendix i s to f i n d the slope o f the curve of saturation magnetisation of the quenched alloys near twenty-five atomic percent manganese assuming the alloys are disordered. Near twenty-five atomic percent manganese the 3d s h e l l of the n i c k e l w i l l be nearly f i l l e d .  One would therefore expect the Mn-Mn  i n t e r a c t i o n t o be much stronger than the Mn-Ni i n t e r a c t i o n , which i n turn w i l l be much stronger than the Ni-Ni i n t e r a c t i o n .  Therefore the  f r a c t i o n of manganese atoms with l e f t spin should be proportional to Q g, the number of Mn-Mn i n t e r a c t i o n s . B  Because the Mn-Ni i n t e r a c t i o n i s  much stronger than the Ni-Ni i n t e r a c t i o n , one would also expect the spin of a n i c k e l atom t o be i n the same d i r e c t i o n as the spin of i t s adjacent manganese atom.  This i s equivalent to saying the f r a c t i o n of n i c k e l  atoms with l e f t spin i s the same as the f r a c t i o n of manganese atoms with left  spin. If we assume the i)»m'bcr of manganese atoms with l e f t  spin i s KQBB, then the f r a c t i o n with l e f t spin i s ^BB . when the value FN K  B  of Qgg f o r the disordered a l l o y i s substituted from equation 12, Appendix 3, the f r a c t i o n of manganese atoms with l e f t spin i s 6KFg.  For the mang-  anese contribution to the magnetic moment t o equal zero at twenty-five atomic percent manganese, 6KFg must equal 1/2 at FB equal t o 1/4.  There-  fore K = ^ . Therefore the f r a c t i o n of manganese and n i c k e l atoms with l e f t spin i s 2Fg.  55.  If the 3d electrons of the manganese go into the n i c k e l 3d s h e l l , then the magnetic moment of a manganese atom i s f i v e Bohr magnetons, and that of a n i c k e l atom i s - ^ j j i = 0.6 -  Fg . When  the ordinate i s changed to makex( j_ = 1 - 3.8 Fg, then ^i.^ N  = 8.3 .  Therefore the manganese contribution to the magnetic moment of the metal i s 8.3 FgN(l - 4Fg)  and the n i c k e l contribution to the  magnetic moment i s F N(1 - 3.8Fg)(l - 4 F g ) . A  T n e  t o t a l magnetic moment i s  the sum of these and equals: M T = [8-3F  B  + (1 - F g ) ( l - 3.8Fg)] t 1 - 4Fg]N  ,  -  -8.4  The experimental curve i n the same units has a slope of - 15.00.  Therefore, the t h e o r e t i c a l curve f o r the saturation magnetisat-  ion near twenty-five atomic percent manganese using these  assumptions  has a slope of approximately one h a l f the experimental value.  56.  APPENDIX FIVE  Calculations o f Order Parameters  1.  Calculation of the order parameter of Ni Mn a f t e r heat treatments 3  B and C. I f we assume that a l l manganese atoms i n face centered s i t e s w i l l reverse t h e i r spin without a f f e c t i n g the spins of the adjacent manganese atoms, and that the number of n i c k e l atoms with reversed spins i s equal t o the number of manganese atoms with reversed spins, then the observed drop i n magnetisation from 14700 on the tangent t o 9500 f o r the experimental value of heat treatment B can be explained by saying that the f r a c t i o n of manganese atoms i n face centered s i t e s i s ^  / ' -9^y^^—  I =.187  When any l a t t i c e s i t e i s chosen at random, the p r o b a b i l i t y f o r i t t o have the right atom i s r , and the wrong atom i s w.  The Bragg  and Williams long range order parameter i s defined as S « r - w. For the cube corner s i t e w • .127 r  = 1 _ w = .8.13  For the face center s i t e w =  .062  r » 1-w = .936 s = r - w =  i ( r - w) + | (r - w) a  b  s = .8.1 This can be checked by f i n d i n g the short range order parameter.  57.  from Appendix 3' Q  B B  Q  a  b  = |  £ l 2 - 6R + R  = |  £24 - 2R + 2 ( a + b  - (a + b  2  2  2  2  2  2  + c  + c  2  .... 9  + d )J 2  + d )J  2  . . . .10  2  3  F . - i + i f a + b + c + dl A 2 8 L  R  -  8F  J  - 4  A  and equation f o r R into 9 and 10  Putting a = b = c = d ^ a QAB -  §  [ 2 4 - 2R + 2 ( a +3b )]  Q B -  N 8  L  B  2  2  2  r 1 2  -  6 ( 8 F  A "  4 )  +  2 ~  R  (  2 a  +  3  b  U  2 1  2 2 Substituting a + 3b from QBB into QAB we get  H But the number of manganese atoms i n face center s i t e s i s (J86)M 4 and each of these has three manganese atoms as nearest neighbours. Therefore, Q  B B  -  3(«^)  N  .  0.14 N-  Substituting t h i s into equation 16 and putting F  A  = ^  QAB = 2.72. N  but  a t  F  =  a  =  4  9 - 9 rand 9 max - 9 rand 9 max =  (Q  AB)ord 6N  1  9  r a  nd -  (Q  '  AB)dis 6N  Therefore, putting i n the values of 9j max and 9 rand found from equation 13 and 15 of Appendix 3, we get o" = 0.66  and S =  =  ,m  This checks with the value of s = .81! found from the theory of Bragg and Williams. When these calculations were repeated f o r heat treatment C,  58  the results were: s = 0.88 & 2.  from Bragg and Williams  = 0.774 and s = 0.88  from the short range order.  The c a l c u l a t i o n of the order parameter of Ni Mn from x-ray3  diffraction line intensities. In t h i s c a l c u l a t i o n the order domain s i z e i s assumed to be very large.  For smaller domain s i z e s , t h i s c a l c u l a t i o n would not  be  valid. The i n t e n s i t y of an x-ray d i f f r a c t i o n l i n e i s given by  23 the equation: I = const..-p.L.e"" where I = integrated  2M  A(e)F  2  . . . . . . . . .  17  intensity  F = structure amplitude f a c t o r p = multiplicity factor L = Lorenz and p o l a r i s a t i o n factor -2M e  = Debye-Waller temperature factor  A( ) e  = absorption f a c t o r  The i n d i v i d u a l factors w i l l be calculated 1.  separately.  M u l t i p l i c i t y factor. This f a c t o r i s equal to the number of equivalent sets of  planes with the same M i l l e r indices, p = 12 f o r the 110 p = 2.  plane  8 f o r the 111 plane.  Absorption f a c t o r .  23 Taylor  gives the following formula f o r the angle between  the incoming x-rays and the compact powder surface equal to  (f  t  59.  A(^)  -  % + s i n <p  const, s i n ^ e l  $ -  In the P h i l i p s spectrometer  O , therefore the absorpt-  ion f a c t o r i s independent o f the Bragg angle Q . 3.  Lorentz and p o l a r i s a t i o n f a c t o r .  L =  4.  23 Taylor gives t h i s factor equal to 2 • ' 1 + cos 2 & f polychromatic beam. cos s i n 6 or  a  For the ( i l l ) planes  L = 6.925  For the (110) planes  L = 11.086  Temperature f a c t o r . 3 h M  2  ff(x), x  " mK ®  1 4  sin  2  0  H = Planck's constant i n erg.sec m = mass of atom i n grams K = Boltzmann's constant i n erg deg" ® = Debye c h a r a c t e r i s t i c x =  @ T  1  temperature  where T i s the absolute temperature  A = wavelength i n cm. = Debye function © = Bragg angle. From the consideration of the Debye temperature  for nickel  and manganese, atoms with s i m i l a r atomic number, and the melting points of these elements, the Debye temperature  of Ni Mn was taken to be 340 K.  This gave a value f o r the Debye f u n c t i o n  2 4  The value of e The value of e  6  3  of  2M  • f o r (110) plane i s 0.9650  _ 2 M  f o r (111) plane i s 0.9485  (p-Q  = 0.' .749.  60.  5.  Structure amplitude a.  factor.  For face centered cubic l a t t i c e s i n general: F =  JE £  n  cos 2 7T (hxn + k y  n  +4%)  where x, y, s are the co-ordinates of the atoms i n the c e l l , h k l are the M i l l e r indices f o r the plane under consideration, and -$~ i s n  the scattering factor of the atom at X n y Z h . n  For the 110 and 111 planes we get: F  F  110 - fcfi l l l " (*L  3* )  +  2  where 6, i s the mean atomic scattering factor f o r the cube corner s i t e s , and ^  i s the mean atomic scattering f a c t o r f o r the face center s i t e s .  The corrections f o r the atomic s c a t t e r i n g factors o f n i c k e l and manganese 25 f o r dispersion due t o the k electrons were taken from James. b.  E f f e c t of ordering on the structure f a c t o r . The mean atomic scattering f a c t o r f o r any of the sublat-  t i c e s can be obtained from the order parameter and the values o f the scattering factors corrected f o r d i s p e r s i o n due to k electrons. Let the f r a c t i o n o f manganese atoms i n face centered s i t e s be P. At cube corner s i t e s  w r  At face center s i t e s  s  w r  - \ ( - ) a I (* " *)b = r  w  +  1  " P  From the values of r and w i n terms of P, the values of ^, and £; are: *»-  |>- )*Mn p  [ ^ - f ^ N i *  +  P  *Ni] fr^Mnj  61.  Therefore  6.  F  l l l ~h  F  110=^l"  +  3*2 • *Mn = (  *2  3^1  +  W  ^  d  "  ^>  Values f o r I n n  i m From the preceding yalues f o r the various factors i n equation 17, we can f i n d the r a t i o of  IJIQ  i n terms of  P.  *LL1  -  h2D  | Il l -- iil £ fj  L  I lml l [  3  J  l [.012303  18  2  Taking the experimental value of I as the average number of counts when scanning across the l i n e once, minus the average.background, the following values are obtained f o r I-QQ ^ d I]j_l from the measurements l i s t e d i n the 'results*. In  =  n  t o t a l no. counts - background no. o s c i l l a t i o n s  where K = angular v e l o c i t y of scanning = 2° (26) per minute 1.21 = angle ( 2 © ) per o s c i l l a t i o n 60 = time of scanning i n minutes. In a s i m i l a r manner 11D Illl I  =  .0075 *  i s found and .0016  This i s equated to the t h e o r e t i c a l hence S.  value i n equation 18 to f i n d P and  The value of S obtained i s S = O . 8 4 + 0.07 where the probable  error was calculated from the uncertainty i n the results intensity.  of the experimental  I t was assumed that a l l constants used were accurate.  62.  BIBLIOGRAPHY  1.  W. Heisenberg, Z. Phys. 49, 619 (1928)  2.  J . C. Slater, Phys. Rev. 3.6, 57 (1930)  3.  E. Ising, Z. Phys. 31, 253 (1935)  4.  L..Neel, Le Magnetisme, I I Ferromagnetisme (Strasbourg 1939)  5.  S. V. Vonsovsky, J . Tech. Phys. (U.S.S.R.) 18, 131 (1948)  6.  F. B i t t e r , Phys, Rev. _5Jt, 79 (1938)  7.  R. Smoluchowsky, J . Phys. et Rad. 12, 389 (1951)  8.  S. Kaya and A. Kussmann, Z. Phys. 7.2, 293 (1931)  9.  W. J . Carr, Phys. Rev. 8J>, 590 (1952)  10.  B. L. Averbach, J . App, Phys. 22, 1088 (1951)  11.  C. G. S h u l l and S. Siegal, Phys. Rev. 7_5_, 1008 (1949)  12.  N. Thompson, Proc. Phys. Soc. J52, 217 (1940)  13.  C. Guilland, Compte Rendu 219, 614 (1944)  14.  A. Komar and N. Volkenstein, J . Exp. Theor. Phys. (U.S.S.R.) 11, 723, (1941)  15.  S. Valentiner and G. Becker, Z. Phys. 93_, 795 (1935)  16.  R. A. Fereday, J . Phys. Soc. 2j2, 251 (1930) J . Phys. Soc. 46, 214 (1934)  17.  C. Sykes and F. W. Jones, P. R. S. A 166, 376 (1938)  18.  R. M. Bozorth, Ferromagnetism» (D. Van Nostrand Company, ,  Inc., New York, 1951). 19.  C  Zener, Phys. Rev. 8j>, 324 (1952)  20.  A. F. Guinier, Proc. Phys. Soc. _5JL, 310 (1945)  21.  C. Sykes and F. W. Jones, P.R.S. A 157. 213 (1936) .  63  22.  F. C, Nix and W. Shockley, Rev. Mod. Phys,  10, 1 (1938)  23.  A. Taylor, An Introduction t o X-ray Metallography (Chapman and H a l l  Ltd., 1949). 24.  A. H . Compton and S. K. A l l i s o n , X-rays i n Theory and Experiment (D. Van Nostrand Co. Inc. 1949)  25.  R. W. James, The O p t i c a l Principles o f the D i f f r a c t i o n of X-rays.  (G. B e l l and Sons, 1950).  

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