Physics. - "Ma,qnetic Researches. XXVI. Measurements of Magnetic Pel'meflbilities of C!tl'omiwn Chloride OIul Gadolinium Sulplwte at t!te BOl;lin,q Point of Liquid Hydl'ogen in A lte1'nflting Fields of F~'equency 369,000 PIJ}' Secoud." BJ G. BRm', Nalional Resaal'ch Fellow, U.S.A., and H. KAT\n:ULINGH ONNES. (Commu­uication N°, 168c f!'Om the Physical Labol'atory at Leiden .)

(Communieated at the meeting of December 29, 1923).

~ 1. Introdnction. 11 has been suggested by EHR~]NFE~T 1) that at very low tempel'atures paramagnetic substances may show pheno­mena of hysteresis. The expel'Ïments I'eporled ou iJl this commnni­cation were made in ordel' 10 see whellrel' Ibis effect is pl'esent at I'easonab ly high fl'equencies. 'rhe quantities measured were magnelic susceptibililies. 'fhe measurements were made 011 samples previously IIsed ill sleady field delerminatiolls 10 as 1.0 enable a direct (~o lllpa­

risoll. Tlle measUl'emeuts made do IIOt give one sutJicient ('onfideuce 10 daim great lIumerical accuracy of the results . However, they seem to indicate definitely that Ihe order of magnitude of Ihe sus­ceptibilities fOl' sleady ano altel'OEtling fields is Ihe same. The nume~ rical values obtained fol' both salts are smaller thau the values obtained in dil'eet tields alld the apparent consistency of trial measure­ment given below suggests thai Ilris discrepancy may be not due 10 expel'imenlal el'I'or.

t 2. Methods and A ppa1'fltus. The melhod was similar to that described by HELTZ ') . Two electr'0I1 lube circllits (NI'. 1, NI'. 2) welte set np to generale suslained oseillations of high frequency . 'rhe fl'equencies of Ille Iwo were adjusled so as to be nearly integral mnltiples of each olher. A Iwo stage audio frequency amplifier was conpled loosely 10 both. 'rhe audible beats pl'oduced in the amplifier wel'e made to gi"e beats with an andible nole produced bya th i 1'11 electroll lube ('il'CUit, say NI'. 3. The para­magnetic sample was pnt inlo the iuductance of ( ~ il'cuit Nl'. 1. Tlre cl'yogenic appal'atns slll'rounding Ihe sample was plnced inside the same eoil. The eoil was shielded on Hs inside by means of linfoil. Thc linfoil was cut inlo 8 segmenls so as to allow the magnetic field to pass 10 lire inside of the shield. The cryogenic

I) P. EHRENFEST, these Proc. 23, p. 989; Leiden Uomm. SuppJ. N°. 44b. S) Phi\. Mag . 44 (1922) p. 479.

841

appamtus consi sted of two nOIl-si I vel'ed vacu 11 m glasses - the 0111-

side being used fol' air and the inside fOl' hydrogen in the usuul man nel', Fig, 1 shows the sbielded box B into which cil'cuit NI'. j

was put. C is tlre top of the inductance coil slrield., L is the lid of tlre box. P is the paekillg. Under t/re hood circuits Nl'. 2 alld Nl'. 3

Fig. 1.

are al'l'anged as shown. Tlre amplifiel' A is on the table to Ihe right. .. The small cOlldenser J( (used at a pluee wlrel'e i t has 313 Illl f capacity) is eonnected in sel'ies with a lal'ger tixed con­denser (eapacity 2847 Illlf) between the filament and grid of circuit NI', 2, The rod R 270 ems. long controls the motion of 1<, being attached to a serew adjustment S. Adjnsting S changes the frequency of circuit Nr. 2 by smal! arnounts . On lig. 2 8 view isgiven of the inside of tlre box B, tIle shield of Ule coil C and its windings W being plainly visible. The shield segments are connected by Ule wÎl'e D and when the lid is lowered Ule wire D is connected to the box shield by a short wire alld a clip. The windings of the coil W al'e sllpported by a piece of glass tllbing to which t/rey are weil fastened with parafiine. The uppel' pal't of . the shield is made of pasteboat'd tubing thorollghly boiled ill paratline and hal'dened by seveml coats of shellac. The filament and plate battel'ies al'e also showlI on this pietul'e. The filament r11t~ostat which is shown on Ule right wall /ras bean shol'l eircuited in Ihe final meaSlll'ements so as 10 eliminate fluctuations in the

55 Proceedings Royal Acad. Amillerdam . Vol XXVI.

842

Fig. 2.

~'ig. 3.

843

filament CIIITent. Fig; 3 shows circuits Nr,2, Nr,3 and the amplifier in more detail. C' is the inductance of NI', 2, The valves used have been MUJ.J,ARD Ol' PHIUPS receiving valves, The circuit connections in NI', 1 aJld Nr, 2 have beeJl those ofthe usual HARTJ,EY cil'cuit a tap off at the middle of the coil leading to the filament and the extre­mities going 10 tbe grid and plate battery terminals, Acondenser wa.s connected aCl'oss the eoil terminals, All the parts of circuit NI', 1 were thorougbly shielded, Tlle conpling to tbe amplifier A was accomplished by a wit'e entering the box B thl'ough a hole 011 the side opposite to thai shown Fig, 1, This wire was connected to the input of A either dil'ectly Ol' thl'ough a tt'ansformel', The input terminal of A was also coupled by a wire 10 circuit Nr, 2, The 1008e end of this wil'e was stl'etched ill ovel' a I'ope towards circuit NI', 2, Cil'cnit NI'"3 was controlled by a pulley al'l'angement allowing one to tnl'll its cOJldensel' plates withont introducing capacity dne to tile observer's body, Tlle observel' was situated at Ihe onlst.anding COl'lIel' of B in Fig, 1, The telephoJles were lIsed on Ihe observel"s head, The conpling iJl Ihis appal'atus was sntficiently loose to make the capacity effect thl'Ollgh Ihe phones negligible fOl' the small motions of the observel"s body during the measul'ement. The liquid air ill Ihe vacuum glass inside C produced sufficienl cooling of it to cause Ilnsteadiness, It thus was necessary to have a I'apid method of meaSUl'ement.

For tbis pllrpose a syslem Q (Fig, 1) was attached to the I'od sliding throngh p, Q consists of a hol'Ïzontal metal rod cal'rying three collars, Tlle eentl'al one is attached 10 a vertical gnide passing throngh a collar al most directly above V The motion of this gnide (',an be contl'olleo by t.he level' shown, The eollar on the right is eonnected 10 P by a vertical I'Od and the collar on Ihe left cal'l'ies El. glass rod from Ihe lower end of which is snspended a glass tube by llIeaJlS of a thread, The mfllal rod passing tlll'ough P ellded weil inside Ihe tube of Gel'lllan silver supporting Pand was thlls shielded from Ihe action of Ihe magnetie field ~f C. To lhe lowel' end of that rod a glass tube was fixed with sealing wax and this 'tube supporled the pal'amagnetic specimen, The 'pal'amagnelic specimen and the suspended tube eould be t.hus moved in and out of C simultaJleously, Inside t.he glass tube a single Ol' sevel'al eopper wil'es were pilt and these wel'e seleeted in s11eh a way as 1.0 make Ihe nllmbel' of beats pel' second in the upper and lowel' positions UIa- same, The combillat.ioll was recol'ded and a subsequent ealibratioll detel'mined the magJlitllde of the effect, The range of motioll was fixed by pet'manent stops on the sliding I'ods, This was necessal'y

55*

844

becallse balallce in the end positiolls was fonnd not to mean always a balance in the illterrnediate ones.

~ 3. P1'eliminary Tests.

a. Necessity of shield jOl' eoil. The faet that the coil had to be shielded on the inside was ascertained by first. trying the al'l'angement witholl t the sh ield. A glass bott Ie lowered inside the coil by a thread proàuced all appreciable effect on the beats. This effect was absent when the inside of the eoil was covered witl! thin tinfoil stdps .

b. Bending of box lid. Many blank tests have been made t,o aee whether the strains in the lid due to the up ano dowlI motion of the rod system Q affected the beats. No sllch effect was observed.

c. Interaction between circuits has heen observed to be generally vet'y smal!. Thus by adjnsting the beat frequellcy between Nr. 1 and Nr. 2 to a low value like J 00 110 tendeucy of pulling into one has beeu 1I0ted. Putting a pat'amagnetic sample in and then out again under these circumstances did not alter the beat frequency noticeably. Tlte beat frequency employed in the measurements was of the ordet· of 500 or 1000 pet' second and the illteraction must have been still smaller. A further test of this was made by Ih'st compensating a sample by changing K, say with set Nr. 1 going at a higher' frequency than Nr. 2 ; then Nr. 2 was set to the higher freq uency and the measut'emellt t'epeated. 'rhe following tabJe gives the results of tho changes of the scale S.

,

I First Side·lsecond Side·1 Difference,

I Iron wire Nr. 7 in suspended tube 22,3 22.5 - 0.2 -1%

Iron wire Nr. 8 in box 13.9 13.2 0,7 5.4%

Combined action 34.3 33.6 0.7 2%

The iron wire NI'. 8 was het'e put in a tube fastened to the para­magnetic sample in . the warm condition with thread and sealing wax. This tube was approximately at the axis of the coil while Nt'. 7 was in t.he suspended tube alrnost at the shield. There appeal's to be no tme systematic difference bet ween meaSUl'ements made with the two frequencies reversed .

d. Di1'eet test of balanee. I t so happened that a copper wire ('2 N) when used in the sllspended tube balanced by its diamagnetic eddy cmrent effect the paramagnetic effect of iron wire (NI', 8). When the

845

effeet of 2 N was balanced by means of K, 13.4 scale divi siolls were necessary while Nr.8 took - 14.2, scale divisiolls. The I'esidnal effect of the combilIed action was estimated al -0.5. The equalioll 14.2 = 13.4 + 0.5 is satisfied to about 2 0

/ 0 ,

e. Ej/eGt of lmgtlt of IJlll'alnagneÜc sal/lple. '1'0 test this four iroll wil'es of differellt lengths were cut from one piece. They had lengtlis : 6 .73 cm., 7.80 cm ., 10.00 CIII . Two glass tubes were faslelled 1.0

the Inbe of CrCI, in the warlll cOllditioll. Tests wilh these were made on Ma} 12 and 011 J uly 1 a, Hl22 . [11 the th'st set of test s t he pammagllel.ic action of t he i 1'011 W i res used i 11 one of t.he 1.11 bes at the axis was blllallced by the diamagnetic aclioll of sllitably chosen co 111 binat ions of copper w i res pu I i 11 to t he slIspellded til be and besides ft copper wire was put into Ihe otllel' tube at the axis so as to take lip the blllk of Ille pal"iunagllelic actioll of the iroll wire. The measurellIellts \,\'ere th ell repeated with the iroll wires tllrned IIpside dowlI . No ditferellce of IIsillg one elld up rather than the ' other was fOlllld thus showing thnt Ihe iron wires are homo­gelleolls. Both sets of measuremellts ag reed in showillg that the effects of the wires havillg lellglhs 7.80 cm. alld 8 .80 cm. are lIearly eqlla! alld slightly greater thall the effects of wires having lellgths 6 .73 cm., 10.00 cm. The etrect of Ihe wire ha\"ing 10 CIII. tength was only slightly smaller than the maximlllli. The copper alld iron wires used at the axis wel'e made 10 challge places alld the obser­vaiions wel'e cOlltirmed the effect of the illterchallge beillg vary smal\. 011 J 11 IJ' 13 flllthe!' COII fiJ'matioll of t he obse!'ved affaet of length was obtained the effeet of Iho iroll wires beilIg this time compellsated by challges ill K . The IIl1mber of scale divisiolls of S req lIi I'ad fol' COOl pellsatioll was tOl' Ille same wi ras i n i IIcl'easing ordel' of langth 18.4, 22,6, 22 .5, 21.1.

The reason fol' t.he decraase in the paramaglletic effect allO cm. is 1I0t cleal'. The illcrease ill the ragioll of 7 cm. - 8 CIlI. must be dlle lo the simple increase in the length ill a fairly homogeneous

22.6 7.80 field because 18.4 = 1.17 while 6 .73 = 1.16. lt may be that the

shiald canses a peeul ial' d ist ri bil lioll of llIaglletic field resllJti lig 111

the upper pOl'tioll of the 10 cm. wil'e beilIg ill a sll'ongel' field Irt

Ihe "up" position thall in the "dowIl".

I Ellect 0/ cl'iterion of C07njlensation. Whell Ihe heat fl'equellcy of eil'cllits NI'. 1 and NI'. 2 beeomes nead} equal to the f\'equal\c} ofN\'. 3, i!. heeOllles at times ditlicult 10 distingllish thelll. Also ill theol'y olie cannol dany a possible adion of NI'. 3 on the combilIed system Nl'. 1 alld Nl'. 2 :tlld lhll s all effect 011 lheil' heat freqllellcy . Iftheseeffacls

846

are present, olie should expect the result of lIIaking settings by adjusting beats to zel'o and by adjusting beats to a fixed nnmber to be different. The results IlOwevel' indicate that. this effect is ahsent. Thus 13.2 and 13.1 al'e the readings obtained on the scale S by the two melhods.

,1/. Calih1'l1tion . Since all tlle changes in the fl'equency are very sm all the change iu the frequency is very nearly propol'tional to the change in capacit,v Ol' to Ihe change ilJ inductance that causes it. Thel'efore (~hanges in K necessal'J 10 compensale fOl' two different changes in induclance are propol,tiolJal 10 these changes. [f one change ilJ inductance is knowIJ Ol' if its meaning as a susceptibility is knowIl the olher is derived by OIlIltiplicalion into the ratio of Ihe two settings of K. Tllis is Ihe pl'ÎlJciple of Ihe calibration em­ployed. The calibration divides itRelf into Ihe following pal'ts :

a. 1'0 fn'oduce a change in inductance wltich /tas a direct inte1'­p,'etation as a susceptibility.

FOI' Ihis plll'pose Iwo glass tubes were attached to the paramag­nelic sample at opposite sides of a diameter - while the sample was in the warm conditiou. Copper wires accuralely drawn and meas\lI'ed coulrl be insel'led into these . The lellglh of the wires was nearly equal to Ihe length of Ihe column of paramagnetic subslanee 8mployerl. ROllghly the wires may be said to exclnde the high fl'e­queuc,}' magnetic field from their interiol'. To a fil'sl approximalion

tlley al'e thel'efore equivalent to a matel'ial of sllsceptibility -~. 4n

If the positive effect of a pal'amagnetic sample is equal to the effect of a wire of a certain si:r.e, its sllsceptibility must be then equal to

~ times the I'atio of the volume of the wire to Ihe volume of the 4.11' substanct>. Since the field is not quile t>xcluded from Ihe interiol' of the wÎl'e, its diamagnetic action is 1I0t qllite as lal'ge as we ha"e just supposed but a cOI'l'ection for Ihis may be applied . Taking Ihe field to be a homogeneous one along the axis of the wire the correctiolJ factor is - I-' ~ (q) + 1 w here

2 he1' q hei' q - he1" q hei q S (q) = - . . q her' q + hel' q

V4~I-'W . where q = - (j- a, bel' and bet are the KETJVIN functions, and

1-', (j, (( al'e respectively the permeability, resistivity, and radius of w

t he wil'e used at the frequellcy . ~ . 2~

847

h. Now "he pal'umaglletic sumple wus halaneed agaillst. Wll'e~ put 1I0t in its immediate neighbodlOod but at the shield, A correctioJl factor musl be applied fOl' this. The faclor was determined exp(>l'i­melltally lIy halallcing the effeel of Ihe same wil'e by 1(, fil'sl al Ihe tubes attached to the pammagnelic sample and second ill lhe suspended tube useo ilJ tlle eompensatioll of the paramagnetic salt. The I'atio of Ihe I'eadings 011 S gave the cOl'l'ectÏon factor . The detel'minatiolls of the cOITeclioll factol' var)' somew hal and a COII­siderable part o.f the experimelllal uncerlainly is due to this.

c. Finally a oelermillatioll had 10 be made of the I'alios of lire ellanges ill f( which had 10 be made ill order to eompellsale Ille change ill illdllctanee pl'Odlwed liJ' Ihe combinalioll of wil'es \Vhieh compeJlsaled the paramagllelic sample allO the challges produced hy Ihe slandal'd accurately OI'RWII wires,

,4. l(,/'su!ts lol' anltydl'otls Ch,'omiltllt Cltlm'ide rrt t!te boiün,q poiut of hydrogen.

At a fl'equeney of . 3 .69 X 10' tlle sample of chromium chloride was halallced uy a comhiJlalioll of wire~ the effect of which was SOOII afterwanb cOlllpared with Ihe effeet of one of Ihe stalldal'd wires (2N). The I'atio of the effecIs of the eombination of wires

6.0 to the effect of 2N as measlll'ed by f( was 6.3 ' 'fhe cOITeet.ioll

factor due 10 the inhornogeneity of Ihe field as lIleasul'ed 011 2 N

was 6'63

. [<'inally tlle cOl'I'ection 1'01' t.he lellgtlt (Ihe sample of ehl'Omium 4,

18.3 chloride was largel' thall 2N) was 21.5' (Th is was detel'lllined from

the results on Ï1'OII wires cited above). The I'esultanl cOl'I'ection is

6.0 , 6.3 ., 18.3 _ 111 then 6.3 X 4.6 A 21 .5 - . .

Again at. Ihe fl'equellcy 3 .69 . JO ' Ille \VlI'e 2 N ha~ n q = 9.0J and hence 1 - iJ (q) = 0.8,1,1. Thlls Ihe volume sllsceplibilit.y of the

wit'e is ,,= - 0.841 = - 0.0669. Now Ihe I'Lldii of the wire alld of 4.1l

the sample wel'e 0,705 mmo and 3.5 mlll . I'espoctively. Hence Ihe

(0.705)' volume susceptibility of tlle sample is " = 1.11 X \. ----a.5 X

X 0.06692 = 0.00305. The weighl of !'I1l'omiulII ehloride was 3.192 3.192

grams and ilt' length ~.7 cm .; Ihe dellsily i~ .1l X 9.7 X (0.35)' = 0.85

848

alld the specific sl1sceptibility X = 0.0036. The value obtained ' in dil'ect fields, according to unpublished results of Dr. H. R. WOLTJER is 0.004t:l 1 j.

~ 5. Resu/ts J01' Gadolinium Sulphate at tlte boiling point oJ Itydrogen. At the same frequency of 3.69 X 106 the gadolinium sulphate

was balanced against a different combination of wires which when compared with 2 N had an effect smaller than 2 N in t.he ratio

1.48 f 8 -0--' The length 0 the sample was .74 cm. and the cOl'responding 1 .1

18.3 corl'ection 22.7' The weight of the sample is 2.897 gl'ams. The

specific susceptibility is hellce X = 0.00051. The value obtained at the same temperatul'e for the same sample in a steady field was 0.0010 '). Measurements on manganic and nickel sulphate have been also made and gave results of the same order of magnitude as those for steady fields.

~ 6. Conclusions and Discussion . A. The order of magnitude of the susceptibility is unchanged if

the freq uency is incl'eased to 3.69 X 10'. B. The I'esults seem to indicate that the susceptibility is smaller

than for direct fields. The values obtained in altel'llating fielde for OrCI. and Gd sulphate are 0.75') and 0.51 C) respectively of what

-1) This value is obtained by the method of weighing a rod of the material in

an inhomogeneous magnetic field (KAIIERLINGH ONNES and PERRIER, these Proc. 16, p. 689, Leiden Comm. N°. J 39a) . However, the susceptibility seems to depend on the field strength, decreasing with increasing magnetic force. The value given relates to a field ranging from 4500 gauss at the top of the rod to 2!0 gauss at the bottom. The limit for very weak magnetic fields may be about !O% higher (as fouod by ex trapolating the susceptibility-magnetic force curves), so the ratio 0.75, given in § 6B for the susceptibilities in alternating and direct fields, may be too large.

I) KUIERLINGH ONNES and OOSTERHUJS, these Proc. 15, p. 3!~, Leiden Comm, N°. 129b, § 6. However, it has to be pointed out, that it was not sure the sample was really at the temperature of the bath, as it appeared afterwards, that in the experiments of KAMERLINGH ONNES and OOSTERHUJS it took some , hours before the susceptibility had taken a definite value, probably owing to lag in the tempe­rature equilibrium. Even in order to avoid this difficulty and to ensure a belter temperature equilibrium of the powder and the batb, tbe tubes fOl' tbe magnetic investigations were later on not evacuated but filled with a small quantity of non condensing gases (hydrogen or helium). The value 0.00051 obtained witb tbe present tube is probably too Iow.

S) See note § ,. ') See Dote I 5.

849

they are in direct fields. However, il would be preposterous to COI1-eillde thaI the slisceplibi I i ty is actually deereased by I he amoullt found . Fm'theJ' work will be necessary fOl' thaI. The choice of the place of the suspended tube was l"at.heJ' u IIfort.1lnat.e. [t was siluated J'atheJ' close 10 one of the slit.s in Ihe tinfoil. Even Ihol1gh <,apacily etfects appeal' 10 be aosent Ihis is dangel'ous beeallse Ihe rnagnetie field in the neigh borhood of I he si i t is not homogeneous. h is pos­sible thai the di\'el'genee bet ween the values for alternaling and direrl fields is olie 10 insufficient caulion in the manipulalion of the sus­pended tube alld a !-llighl displacement of il dIlring the experiment. This would hardly explaill, however, Ihe similal'ity 1) of Ihe result" for t he I wo 811 bstalH~es i 11 vestigated .

The wJ'iters wish 1-0 express theil' sincel'e thanks to Dr. H. R. WOL'l'.H:H fOI" help in comparillg the resllits with those in steady fields alld rol' makilIg IInpubli shed results of liis measnrements available .

I) Especially, if the value 0.75 is too high and 0.51 too low (see notes §§ 4 and 5, thi!i similarity is perhaps not only qualitative, but also more or less quantitative.