S. Sullivan, A. N. Thorpe, and P. Hambright Howard University Washington, D.C. 20001
An Inexpensive Magnetic Susceptibility Balance
Magnetic susceptibility measurements on substances are an important means of elucidating details of atomic and molecular structure and bonding (1, 3). While a number of physical and inorganic lab texts feature susceptibility experiments, the equipment required is usually rather expensive, and designed for ambient temperature measurements only. We would like to describe a Faraday-type susceptibility apparatus that has been used successfully in our courses for several years. This balance is relatively inexpensive and useful for measurements on solids and solutions in the milligram range from 300°K to 77'K. This balance is a modification of a previous system (3). We shall describe in the following sections the theory of the balance and a general treatment of susceptibility data, then the design and constrnction of the balance, and finally the details of an experiment. Apporatus
Figure 1 shows the design of the susceptibility apparatus for room temperature measurements. An essential component is the quartz helical spring to which glass fibers of various lengths are attached. Helices having various force constants can be obtained (Microchemical Specialties Co., 1825 Eastshore Highway, Berkeley, California 94710) and d i e r e n t ones used depending on the expected susceptibility of the sample. For most samples, a spring having a 20-cm deflection with a mass of 20 mg is sufficient. The endmost fiber
has a loop perpendicular to its length on which an approximately spherical sample is placed. The mass of the sample is determined with a cathetometer. The spring and sample are enclosed in the glass apparatus during all measurements to eliminate air currents. The movement of a horn type permanent magnet riding on an aluminum lab jack is used to cause a deflection of the sample, which is measured by a travelling microscope (Microchemical Specialties, Co.). Permanent magnets of varying field strengths (950-3000 gauss) are commercially available (Permanent Magnet Company, Inc., 4437 Bragdon St., Indianapolis, Indiana 46226). The support frame for the apparatus can be made from sturdy wood or aluminum, and the balance should be isolated to prevent vibrations. Figure 2 shows the modifications required for making magnetic susceptibility measurements as a function of temperatnre from 300°K to 77°K. The sample chamber is evacuated and carefully filled to within a few millimeters below atmospheric pressure with helium gas, which serves as the heat transfer medium. The sample is suspended in such a manner that it is a t a distance of two to three millimeters from a Au-Co Thermocouple (Sigmund Cohn Carp., Mt. Vernon, New York). The temperature of the sample is controlled to within one degree by varying the flow rate of pre-cooled nitrogen gas passing through the outer section of the low temperature tube. The nitrogen gas is pre-cooled by passing it through a copper coil which is submerged in a liquid nitrogen bath. The temperatnre
* M
W
L.6
,.*
Cold i.", ",a
"-","-*
Figure 1. The magnetic rurceptibility apparatus for meoruremenh a t room temperature.
Figure 2. The opparotur of Figure 1 modifled for *umoptibility measurements down to 77-K.
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dependent emf of the thermocouple can be measured with either a digital voltmeter or regular potentiometer. Theory
The force in dynes (F) acting on a sample in an inhomogeneous magnetic field is mX,(HdH/dS) where m is the mass of the sample in grams, X , its gram susceptibility in ergs/(oersted)'g, (emu/g), and H and dH/dS are the applied magnetic field strength (oersteds) and the field gradient (oersteds/cm) a t the location of the sample, respectively. In this work, the sample is suspended on a sensitive quartz helical spring, and the displacement of the sample is observed as the position of a horn type permanent magnet is slowly changed from above to below the sample. The magnetic force on the sample is proportional to the displacement of the spring, and is maximum when HdH/dS causes maximum deflection. At the points of maximum deflection, F,., is given by F,,,
=
mX.(HdH/dS),,
=
KY
(1)
where K is the force constant of the spring in dynes/cm and Y is the maximum displacement of the sample in em caused by the magnet. The displacement of the spring caused by the mass of the sample is given as where g is the gravitational constant in cm/sec2 and D the observed extension of the quartz helix in cm due to the sample in the absence of an applied magnetic field. With the elimination of K from eqns. (1) and (2) we obtain where a' is characteristic of a given magnet. Once a' is determined, the gram susceptibility of an unknown sample can be calculated from the expression X.
=
Y/(Dr.')
(4)
I n order to obtain a', a sample of known susceptibility is required. Pure platinum has a susceptibility at 20°C of 0.971 X emu/g which is temperature independent around room temperature. CuS04.5He0, Fe(NH4)r (SO& ,6H20, and Hg[Co(SCN),] are solids commonly used for calibrations (2, 4). These species have strongly temperature dependent susceptibilities, and we will present such data for Hg[Co(SCN)r]. The observed susceptibility X , can be written as a sum of individual susceptibilities. The most often encountered expression for X , is
X,,, is the negative, usually temperature independent, diamagnetic susceptibility, and X,,, the positive paramagnetic susceptibility which depends on temperature. X,,. is equal to M/H where M is the magnetization of the substance in ergs/(oersted g) when the applied field is H. At room temperatnre and low fields, the ratio M/H is constant. Xte+ the temperature independent paramagnetism. X,6,,. is the ferromagnetic term and is given by u/H, where u is a constant defined as the saturation magnetization. At room temperature, eqn. (5) can thus be expressed as 346
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Journol of Chemical Education
For a plot of X , versus 1/H, the slope of the curve is u, and the intercept a t 1/H = 0 is the sum of the field independent susceptibilities. The presence of appreciable amounts of ferromagnetic impurities in a sample is shown by a positive u. The paramagnetic susceptibility varies inversely with temperature, and is expressed by the Curie Law. where N is the number of atoms per gram, p, the number of Bohr magnetons; b, the unit Bohr magneton (9.27 X ergs/oersted); k, Boltzman's constant (1.38 X 10-l6 ergs/degree); T, the absolute temperature; and C, the Curie constant. In the absence of ferromagnetic impurities, eqn. (6) can he written as X.
=
+ X d + C/T
(Xdion,
(8)
Thus a plot of X , versus 1/T has a slope of C and the intercept as the sum of the temperature independent terms. Xea, can usually be estimated from tables of diamagnetic corrections (2). In many cases, the X,T data is better represented by the Curie-Weiss Law X,.. = C / ( T 8 ) (9) where the 0 is the Weiss constant.
+
Experimental
A typical experiment is run in the following manner. With the lower tube in position during measurements, the difference (D) between the cathetometer readings with the sample unloaded and loaded on the quartz helix is recorded. The magnet is then positioned around the sample, with the sample equidistant from and centered between the pole faces. A convenient reference on the glass fiber is observed through the telescope. The magnet is then moved above and below the sample with the lab jack, while noting if there is an appreciable deviation in the sample motion from a vertical direction. The magnet may be repositioned slightly to minimize any motion of the sample other than vertical. With the magnet below and moving up toward the sample, the position of maximum deflection is recorded. The magnet is then moved above the sample and the other maxima located. During this process, the sample will describe the motion as shown in Fig. 3. The difference between these maxima is 2Y. This process is
Figure 3. The displacement of the smmple coured by tho magnet, Y, versus the distance beheen tho center of the magnet and the sample, S.
rapidly repeated several times and the data averaged. For example with a 1.509 rng (D) sample of Hg[Co(SCN)r] at 303"K, successive microscope readings denoted by 1,2,3,. . . .in mm X 10-'were as follows .$AMPLE
50-
3
O3IUPLE i
40-
The 1,3 and 3,5 readings were averaged and the 2 and 4 readings subtracted, respectively, giving the average 2Y as 0.1322 mm. The field strengths of the magnets can be measured with a rotating coil gauss meter (Rawson Electric Instrument Company, Cambridge, Mass., Types 501 and 720.) This magnet had an H at maximum HdH/dS (where Y = Y,. or Y,,, Fig. 3) of 960 oersteds, with an a' determined by using pure platinum of 2.874 X 10%. By means of eqn. (4), XO(303"K) = 15.24 X lo-=. This process was repeated with. magnets having H values of 1250 and 2080 oersteds, with two independently prepared (5, 6) samples of Hg[Co(SCN)4]. Figure 4 shows a X, versus
I
I
I
I
I
;
5
20
-
8 0
I
I
o,l'
?PI
Figure 5. The grom susceptibility versus reciprocal temperature for two samples of HgCoISCN)+
wo
I
100
10
ol",.
30-
x'
200
M O
T PKI
,be,-,
Figure 4. The gram susceptibility versus reciprocal magnetic field for H~COISCN)~.
Figure 6. The reciprocal molar susceptibility versus temperature for two sampler of HgCo1SCN)r.
1/H plot of the data in terms of eqn. (6). The absence of appreciable ferromagnetic impurities in the samples is thus indicated by the zero slope. Figure 5 shows X, versus 1/T data for the two samples in terms of eqn. (8). The least-squares fit of the line was
The magnets remain calibrated for several months if kept well apart at normal temperatures, and free from shocks or stray ferromagnetic particles. The keepers should not be replaced after a calibration. A typical room temperature determination by two students takes about fifteen minutes, and a temperature dependence can be done in three hours with about one-third of a tank of nitrogen gas and 8 1of liquid nitrogen. The field dependence of the susceptibility is readily demonstrated on a sample of platinum rubbed with a nail.
X,
=
-1.32 X
lo-= + (48.39 X
10-')IT
(10)
Many workers prefer to report their results in terms of the Curie-Weiss Equation used in the form 1/X, = T/C B/C where X, is the molar susceptibility corrected for diamagnetism. For Hg[Co(SCN)4], the molar diamagnetism (6) is - 137 X 10- emn/mole, and the molecular weight is 491.84 g. This type of plot is shown in Figure 6. It is seen that the magnetic moment of the species is temperature independent in the range (300-77"K), and is equal to 4.38 BM. The temperature dependence (X rn T-l) is similar to that found by Candela and Munday (b),but slightly different from that originally (6,6)reported (X rn (T 10)-3.
+
+
Literature Cited (1) Lie~wooo. P. W.. "Magnetoohemiatry." NewYork. 1956. (2) F ~ a a ~ sB., N . . A m8 L*wI% J., (Edifora: Lswm, J., AND WUI York. 1960, Ch , " ( 3 ) TRonPa. A,, AND I
2nd ed.. Wiley-Interscience,
Coordination Chemistry." .). Wiiey-Intel raoience, New
G. A.. . . C*ND.L*.
(4)
( 5 ) Fmars, B. N., m o Nrrro~la,R. 8.. J. Cham. Soc., 4190 (1958). (8) Floara,B.N., ~ w o N r a o mR.S., , J. Cbm. Sao..338 (1959).
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