Leonard F. Lindoy, W a d io i , and Daryle H. Busch The Ohio State University
Columbus, Ohio 43210
I
I
A Variable-Temperature Faraday Magnetic Balance
The measurement of magnetic susceptibilities and magnetic moments is as basic to the study of compounds of transition elements as are the application of the more broadly encountered spectroscopic techniques. The results of magnetic measurements often provide a count of the number of unpaired electrons. Further, the magnitude of the quantities measured is useful in indicating the degeneracy and nature of the ground state of the transition element species. This, in turn, leads to strong inferences concerning the oxidation state of the metal ion and/or its coordination number and stereochemistry (1-4. The determination of the susceptibility as a function of temperature both greatly enhances the certainty of deductions related to number and orbital states for unpaired electrons, and it also provides much insight into systems that might, on the basis of measurements at one temperature, seem anomalous. These so-called auomalous cases may involve cooperative effects, such as intramolecular spin-spin coupling (5), or a variety of circumstances resulting from the coexistence of two or more species having different numbers of unpaired electrons (6, 7). In view of the long-standing critical need for magnetic susceptibility data it is surprising that the development of instrumentation has remained largely in the hands of users and still less pleasing to realize that most of the evolved expertise has remained relatively unavailable to those first encountering the need for such measurements. These criticisms are particularly appropriate to the preferred technique for susceptibility determination, the Faraday method. The magnetic susceptibility of a sample can be determined from the force exerted on it when placed in an inhomogeneous magnetic field. An element of matter having a volume of dv and mass, dm in a horizontal magnetic field (H, x direction) experiences a force in the z direction (vertical) given by eqn. (1) (8).
Because of the design of pole pieces in the usual magnetic susceptibility apparatus, the field in the y and z directions is much smaller than H, and hence eqn. (1) reduces to
where x is the volume susccptibilit,y of the sample. Two methods, the Gouy and Faraday, are in common use for determination of magnetic susceptibilities. Both are based on the use of a balance to measure the force on a sample suspended in a magnetic field. In the past, the Gouy method has been the most widely used. In this method, the sample is packed into a
cylindrical tube of length, 1, and uniform cross sectional area, A. The sample is suspended between the poles of a magnet such that one end is subjected to the full effect of the field (HI) while the other end is at a region of essentially zero field (Ho).Integration (of the force) over the total length of the sample, yields
where v = sample volume. Hence F
-
1/wi(HLa
- Hp)
For the case where Ho is zero F
=
'IFAH,"
(4)
This method has frequently been used in the past since it requires relatively unsophisticated, easily constructed equipment. A1t)hough it has adequate sensitivit,y, the method requires a relatively large sample (0.1 to 1.0 g) and the accuracy of the measurement is dependent on the sample homogeneity (i.e., uniformity of packing for a powdered sample), which can introduce up to approximately 5% error in the measurement. The use of this method for studying ferromagnetism is of uncertain significance a t the present time. Recently the Faraday method has gained popularity for susceptibility measurements. Typically, a small sample (5-50 mg) is needed for such measurements and this sample is suspended in a magnetic field between poles whose characteristics provide a region of constant H (bH/&) about the sample. From eqn. ( Z ) , the force on the sample is given by F
= xuC
where C is a constant = H @HI&); but F = w/u, and K = x p = x/(w/v); therefore
(5) =
gAw, p
where x, is the mass susceptibility and Aw is the change in weight of the sample in and out of the field. g is the gravitational constant, p the bulk density of the sample and w is the weight of the samplc. In practice, Aw must be corrected for the corresponding change in weight of the sample container. The value of 0 is usually obtained by using a standard compound of known susceptibility, such as HgCo(NCS)a or [Ni(en)a]SzOs(9). Alternatively, 0 could be calculated directly provided the characteristics of the field are known accurately. Unlike the Gouy method, the accuracy of the Faraday method does not depend on the homogeneity of the sample but only on the uniformity of H (bH/bz) Volume 49, Number 2, February 1972
/
1 17
in the region of the sample. In addition, the latter method is capable of measuring ferromagnetic s u e ceptibilities. In the past, the additional complexity of this type of apparatus together with the nonavailability of suitable commercial components has tended t.o limit the construction of Faraday balances. Although suitable for restricted use, such balances have often not proved sufficientlyrobust for general laboratory use. For several reasons, this is no longer the case and recently an increasing number of research departmentas have phased out their Gouy apparatus in favor of a Faraday sctup and it seems likely that this trend will gain impetus in the future. What follows is a description of a variable-temperature Faraday balance which has been constructed in the authors' laboratory and which is suitable for duplication elsewhere since it is designed around a number of readily available commercial components. These components arc a major factor in the increased robustness of the present setup and have been proven to be mutually compatible and particularly suitable for their respective roles. I t has been shown that thc design is suitable for a general laboratory instrument since the balance has been in continuous use, by a range of operators for some two years. A number of Faraday balances have been described previously in the literature (9-11); however, many of thesc suffer from limitations of thc sort mentioned above. The balance to be described here is based, in part, on designs by Hatfield (10) and by Morris and Wold (11). Basic Design Features
The Faraday magnetic susceptibility equipment for mcasurcmcnts over a temperature range of SO300% consists of the following main components (for complctc parts list write to authors, DHB): Automat,ic Elcctrobalancc, cryostat, temperature controller and clcct,rornagnet (see Fig. 1). The sample (10-20 mg) is suspended between the constant force pole picces of an clectromagnct in a region where H (bH/bz) is constant. The sample is contained in a small quartz boat (Fig. 2) and is suspended from the balance arm by a quartz fiber. For room temperature measure-
Figure 1. 1. 2. 3. 4.
/
Arrangement of romple b o d .
ments the sample is protected by a cylindrical glass tube. The change in weight of the sample in and out of the field is measured with an automatic Electrobalance and is recorded with a potcntiometric (1 mV) recorder. For variable temperature measurements (SO-300%) the sample is suspended wit,hin a cryostat (Fig. 3). Around the sample compartment of the cryostat is a copper block wound with a heater element and this is used to control temperature by balancing the heat loss to the coolant against current supplied to the heating coil by a temperature controller. The controller, activated by the output of a t hermocouple placed in the copper block, supplirs current to the heater as required. In this manner a given set point temperature can be maintained. Independent temperature monitoring is achieved by the use of a calibrated copper-constantan thermocouple embedded in the glass wall adjacent to the sample. The output from this thermocouple is fed to eit,her a galvanometer-potentiometer system or
Diogrom of Farodoy balance system.
Helium cylinder BASF catalyst tower Drying Tower Safety tube 5. Barometer 6. Vacuum manifold 7. Liquid NI trap 8. Vacuum pump 9. Electrobalance 10. Cryortat 1 I. Electromagnet
118
Figure 2.
12. 13. 14. 15. 16.
Cryostot elevotor Liquid NZdewor Nitrogen cylinder Solenoid valve Voltage divider circuit 17. Thermocouple cold junction campenrotor 18. Liquid N2 level circuit 19.20. Recorders 21. Electrobalonce circuit9 22. Thermoregulator 23. Potentiometer and galvmometer
Journol of Chemical Education
Figure 3.
Cryostat.
to a 1 mV recorder. The temperature of the sample is followed graphically on a recorder, and after equilibrium is reached the accurate temperature is measured using the potentiometer. (A good digital voltmeter could replace both components.) The liquid nitrogen level in the cryostat is maintained virtually constant by use of an automatic liquid nitrogen leveling device. An electromagnet equipped with a power supply and a current regulator is used to develop the magnetic field. The magnet is equipped with constant force pole caps and a 1.5-in. pole gap is used. With our magnet it is possible to attain magnetic fields of up to 8 kG. The electromagnet is mounted on a trolley and track so that the magnetic field can be removed from the area of the sample. Apart from its sensitivity, the use of an electrobalance is preferred for Faraday measurements since it operates on the null-principle and thus the position of the sample relative to the magnetic field is always the same. In addition, the balance is relatively insensitive to vibration. A small vacuum line, as shown in Figure 1, adds considerably to the flexibility of operai tion of the balance for it enables measurements to be taken over a range of pressures, in either helium or air. The use of helium at a pressure of 50 mm proved to be satisfactory for most routine dcterminations. The low density of this diamagnetic gas lessens bouyancy effects and its high thermal conductivity aids sample temperature equilibration. A glove-box attachment for loading samples (for room-temperature measurements) in an inert atmosphere was also constructed. Basically the attachment consists of a cornmcrcial polyethylene glove bag which surrounds the vertical sample suspension tube. For room temperature operation, the temperature was measured using a copper-constantan thermocouple which was inserted in the sample compartment such that the hot junction was just below the sample position. The output from this thermocouple was fed directly to a recorder which had been calibrated in degrees. The small mass of the sample results in its rapid response to small temperature variations, and for this reason measurement of the air temperature near the sample compartment by means of a mercury thermometer is not satisfactory. For variable temperature measurements the hot junction of a standardized thermocouple was placed in the wall of the cryostat adjacent to the sample compartment. Equilibrium is usually reached after about 11/% hr. The commercial temperature controller is an off-on proportional output type, capable of operating within the range -200°C to +240°C. The commercially available cryostat was based on a design by Richardson and Beauxis (13) which was later modified by Hatfield (10). The cryostat was mounted on a horizontal arm attached to a vertical post (Fig. 1). The arm and cryostat could be lowered or raised by means of a counterweighted rack and pinnou mechanism; this greatly simplifies the placement of a sample in the balance. The ahgnment of the sample with respect to the dewar can be checked by placing a light immediately beneath the bottom of the dewar and viewing the sample from above the balance weighing mechanism. The position of the samplc is changed by altering the posi-
tion of the balance mechanism inside its vacuum bottle. The thermocouple was standardized against a standard nlatinum resistance thermometer. Details of the design and construction of this Faraday Magnetic Susceptibility balance can be obtained from the authors (DHB). Experimentd Procedure
The procedure for setting up, calibration, and use of the Eleetrohalsnce is given in the manufacturer's manual and will not be repeated here (IS). I t is noted that, part,icularly on dry days, strttie electricity can affect the reproducibility of the balance. In general it has been found necessary to irradiate the sample and boat with a small redioactive source prior to beginning a determination. Other methods of dealing with static are listed by the balance manufacturer (15). Initially the quartz boat must be calibrated for the various field strengths that will he employed for susceptibility measurements. For measurement in helium, two constants need to be determined for each field strength. First, i t is necessary to messure the diamagnetic force ( ~ w a on ) the empty quartz boat, and, since there is a possibility of the presence of paramagnetic im~uritiesin the ouartz. this measurement should be made over rhr v x i w . Iemperuww IIIIICP> 1 0 lte t 1 ~ 15 e c ~ ) d l vR. w u h r d compou!d of k m ~ ?wwplildity ~ n is t ~ e d0, delermiue llae ccm-
where x,T is the gram susceptibility of calibrant a t temperature T; w, the weight of sample; Aw, the change in weight of sample and boat in snd out of field; and Awb, the change in weight of empty boat in and out of field. H ~ C O ( S C Nand ) ~ INi(en)alSsOa are commonly used calibrants (8). The latter compound has a lower susceptibility and therefore is suitable for use with higher fields. These standard substances are very easily prepared and are not hygroscopic. The nondependance of 6 on temperature was confirmed by determination of its v d u e using HgCo(SCN). as a calibrant over a range of temperature (120-30O0K). The x, of I I ~ C O ( S C Nis) ~ given by Figgis and Nybolm (14) to be 16.44 X 10- a t 20% with a 0 of 10°K. I t can be celouleted for m y temperature from eqn. (8).
Substituting into eqn. (7) yields eqn. (9)
The values of B mensured on our equipment over a range of temperature (120-30O0K) were identical within 1%. In order to check the performance of the equipment, the magnetic susceptibility of the standard compound Ni(en)&Os was
Figure 4. Voriotian of mognetic rvrceplibility temperature (TI.
Ix,~of
Ni(enlsS~0,with
Volume 49, Number 2, February 1972
/
1 19
measured over the temperature range (80-300°K). The gram susceptibility of the Ni(en)&Ot is reported to be xo = 10.82 X 10-8 cgs units a t 25°C (16). However, ,previously reported result that the suceptibility obeys a Cune-Weiss law with B = -43' has been found to be incorrect (5, 16). More detailed measurements (16) over a wider temperature range have shown that the plat of l/xMe"' versus T passes through O'K and hence the msgnetio properties of the compound follow the Curie law. The various values of the gram susceptibility in the range from 80 to 300°K, as determined on the present apparatus are given in the table and a plot of x, against the inverse of temperature is shown in Figure 4. x, st any temperature can be calculated from eqn. (10) xoT
=
(10.82) X (293.2)
T x h o l wt)
(11)
The corrected molar magnetic susceptibilities xMwwis obtained by substrscting from x,. the correction for diamagnetic substituents XMI"v
= XH
- xdio
The corrections for diamagnetic substituents are obtained from Pascal's constants (17) and are x s i ~= -199 X lo-' cgs units. The values of XM~O*' are given in the table.
Literature Cited ( 1 ) Froore, B. N . . "Introduation to Lisand Fields," Interscienoe, New York, l%6. ( 2 ) Froara, B. N.. nno LEVIS, J.. " P r o g r e ~in ~ Inorgania Chemistry" F . A,). Intersoiance. New York. 1964. Vol. 6 . (Edilor; COTTON. ( 3 ) Floa~s,B . N., AND LEVIS, J.. "Techniques of I~organioChemistry." (8ditors: J o n ~ s s m ,H . B.,*no Wszaan~noen.A,), Interscience. New Y o r k , 1965, Vol. 4. pp. 137-248.
120
/
lournol o f Chemical Education
(Mol w t = 351.5.
T"K
81.3 83.5 142.0 166.5 186.8 205.4 224.5 283.0
Diamagnetic correctianx = - 199.0) x. X 10' xxC"' X lo6 39.96 39.09 23.06 19.39 17.53 15.76 14.37 11.12
14,250 13,940 8,304 7,014 6,361 5,739 5,250 4,108
(10)
The molar magnetic susceptibilitiesare calculated from eqn. (11) XM =
The Temperature Dependance of the Susceptibility of Ni(en)&Oa
( 4 ) E A R N B R I A,. ~ . " I n t m d ~ ~ t i oton Magnetochemistry," Academic Press. London. 1965. (5) BALJ.,P. W., C o w d . Chdm. Ra..4 , 361 (1868); SINN,E., AND H A B R ~ C. M., Coord. Chem. RN..4 , 391 (1968). ( 6 ) B m e n m o . E. K.. Bwcx,, D. H., A N D N E ~ S O N S., M., Quavi. Re"., XXII, [4], 457 (1968). ( 1 ) MABTIN.R. L.. A N D W a r ~ s .A. H.. ransi sit ion ~ e t a Chemistry." l (Editor: Cnnr.1~. R. L.),Maroel Dekker. Inc.. New York. 1968, Vol. 4. p. 113 R. ( 8 ) BATES,L. F.. "Modern Mapnetism" (4th Ed.), Cambridge University Press. London, 1961. ( 9 ) HATFIELD, W . E.. FAT R. C., PFLUNOER, C. E.. AND PIPER.T. S.. J . Amer. Chcm. Soc., 8 5 , 2 6 5 (1963). (lo) xi. E., l . ~ ~ ~ h ~ thei ~cabn ~ ~~ . i ~ ~ t ~ No. 14. Cahn ~natrumentCo. (11) MORRIS, B. L., A N D WOLD,A., SCI.Inal?'., 39, 1937 (1@68). (12) R ~ c ~ ~ n n sJ. o aT.. . A N D B ~ n a r l sJ. . 0.. RW. s c i . ~ n a c .34,877 , (1063). ( 1 3 ) Instruotion Manual for the Cahn RG Automatic Eleotrobalanee, Cahn Instrument Co.. Paramount, Calif., 1967. (14) Fzoa~s,B . N., AND NIHOLU. R. S.. J . Chem. Soc., 331 (1959). (15) CURTIS,N. F., . I . Clbem. SOC., 3147 (1961). (16) ALYEA, E., Ph.D. Thesis, University of London, 1968. (17) F~eors. B. N . . AND L ~ w m ,J., "Modern Coordination Chemistry" (h'ditora: Lswra. J.. a m Wxmms. R. G . ) . Interscience Publishers. Inc.. New York. 1960.
~
b
~
