Magnetochemistry

By Pierce W. Selwood

A comprehensive treatise on the subject of Magnetochemistry. This is an essential textbook for those studying the subject and anyone interested in the magnetic properties of chemical compounds. Sections include: Part I: Measurement and Susceptibility. Part II: Atomic Diamagnetism. Part III: Molecular Diamagnetism. Part IV: Atomic Paramagnetism. Part V: Molecular Paramagnetism. Part VI: Complex Compounds. Part VII: Metallic Dia- and Paramagnetism. Part VIII: Ferromagnetism. Part IX: Applied Magnetism Analysis

• Language: English
• Publisher: Read Books Ltd.
• Release date: Jun 11, 2013
• ISBN: 9781473389090

Book preview

CHAPTER ONE

MEASUREMENT OF MAGNETIC SUSCEPTIBILITY

1. Explanation and Definition of Terms

The intensity of a magnetic field is expressed in oersteds, although the word gauss is often used in the same sense. A field of one oersted (or one gauss) is of such intensity that a unit magnetic pole placed in it is acted on by a force of one dyne.

If a substance is placed in a magnetic field of a certain intensity, then the intensity of the field within the substance may be either smaller or larger than the intensity in the surrounding space. (Fig. 1.) In the first case the substance is called diamagnetic, in the second paramagnetic. There is also the case of ferromagnetism in which the intensity of field within the substance may be increased a million-fold or more. But ferromagnetism, although of great technological importance, is rare in nature. It occurs in only a few metals, alloys, and compounds. Paramagnetism is common in nature, especially among the transition group elements. Diamagnetism is a universal property of matter. All substances, even though paramagnetic, have at least an underlying diamagnetism that must be corrected for in precise determination of the permanent magnetic moment. A substance may be both diamagnetic and paramagnetic, but generally whenever paramagnetism is present it is so much larger that it hides the diamagnetism.

FIG. 1.—Diamagnetic bodies (left) are less permeable than a vacuum to magnetic lines of force. Paramagnetic bodies are more permeable than a vacuum.

If a substance is placed in a field of intensity H, then the intensity within the substance is given by B, where

B = H + 4π

The quantity is called the intensity of magnetization, and /H = κ is the magnetic susceptibility per unit volume. The magnetic susceptibility per unit mass is obtained by dividing κ by the density. The symbol χ will be used throughout this book for the magnetic susceptibility per gram. The molar susceptibility, χM, is the magnetic susceptibility per gram-molecular weight.

In general the susceptibility of diamagnetic substances is independent of temperature and of field strength. The susceptibility of paramagnetic substances is of ten inversely proportional to the absolute temperature, and is independent of field strength. The susceptibility of ferromagnetic substances is dependent on both temperature and field strength in a rather complicated way.

There are many methods available for the measurement of magnetic susceptibility. The more important of these methods are described in detail in the following pages. Literature references are given to a number of other methods. A few highly specialized methods are described later. The given general references may be useful.¹–⁴

2. The Gouy Method

⁵a

If a cylindrical sample of matter is suspended between the poles of a magnet so that one end of the sample is in a region of large field intensity and the other end in a region of smaller field, then the sample will experience a force along its length. The magnitude of this force, f, is given by the expression

where κ1, κ2 are the volume susceptibilities of sample and surrounding atmosphere respectively; H1 H2 are the maximum and minimum fields to which the sample is subjected; and A is the cross-sectional area of the sample.⁵b The arrangement is shown diagrammatically in Fig. 2. In practice H2 may be made negligible, and, by using hydrogen or nitrogen for the surrounding atmosphere, κ2 may also be made negligible. It is convenient to measure f by suspending the sample from a balance, in which case we may have

where g is the gravitational constant, and Δw the apparent change in weight of the sample on application of the magnetic field.

FIG. 2.—Gouy magnetic balance.

For many types of investigations it is convenient to use a magnetic field of from 5000 to 15,000 oersteds. For strongly paramagnetic samples Δw may then be of the order of several tenths of a gram. An ordinary analytical balance therefore gives a sufficient degree of accuracy for some purposes. But for more refined measurements, especially on solutions, it is necessary to use a microbalance.

Other methods are available for obtaining f. For instance the sample may be suspended from a spring, the extension of which, on application of the field, may be observed with a microscope, or interferometrically. Or the sample may be suspended horizontally from a torsion, or bifilar, suspension. The horizontal suspension methods lack nothing in sensitivity, but they become cumbersome when high or low temperature ranges are necessary.

Measurements on metals or alloys are very simple by the Gouy method. The sample has only to be cast or machined into the desired cylindrical shape. The accuracy of the magnetic measurement will generally be limited by the reproducibility of the sample. The Gouy method gives, of course, the volume susceptibility so that an independent determination of the density is necessary for calculation of the mass susceptibility.

Powdered samples may be measured by packing them into cylindrical glass sample tubes. Correction must be made for the susceptibility of the glass, which is generally diamagnetic with a slight temperature coefficient. The accuracy of measurements on powdered samples is severely limited by the uniformity and reproducibility of packing. It is difficult to exceed an accuracy of ±1%. Theoretically there is no particular reason why the accuracy with powders should not be considerably greater.⁶

The susceptibility of pure liquids is also conveniently measured in glass sample tubes. As the difficulty of packing does not arise with liquids, the accuracy may be considerably greater.

Much magnetochemical research is done on solutions. Very accurate semi-differential methods are available for solutions. The glass sample tube may be double-ended, extending below the magnetic field just as far as above. The two ends are separated by a glass partition, in the region of which the magnetic field is applied. The solution under investigation is placed in one end of the sample tube, while the pure solvent is placed in the other. The arrangement is shown in Fig. 3. This sample tube must be supplied with a reservoir for change in volume of the solvent in the lower compartment with temperature. Otherwise the tube would break whenever the temperature was raised, or, when the temperature was lowered a bubble of vapor would form at the partition. In the tube shown, solvent completely fills the lower half of the main tube, and half fills the reservoir. Then, as the solvent warms up, it expands through a capillary tube into the reservoir, or if the solvent contracts, it sucks up more solvent from the reservoir without forming a bubble at the partition. For the most accurate measurements, it is necessary to use sample tubes of constant internal diameter. With all refinements, measurements to four significant figures are possible.

FIG. 3.—Sample tube used in the Gouy magnetic balance.

FIG. 4.—Temperature control arrangements for the Gouy balance. Thermocouples, heating coil, and other subsidiary equipment are not shown.

The Gouy method is not well adapted to the investigation of gases although rough measurements on oxygen and on other paramagnetic gases and vapors have been made.

Most magnetic measurements require a range of temperature and often a very accurate control of the temperature. During measurements on solutions, using a microbalance, it is often necessary to control the temperature to within 0.1° C. This is not because of any very large temperature dependence of magnetic susceptibility but because the buoyancy effect of the surrounding atmosphere is markedly dependent on the temperature.

High temperatures are easily obtained by surrounding the sample tube with a tubular electric furnace. The only precautions necessary are to protect the balance from warm currents of air, and the magnet pole-pieces from extremes of temperature. Actual measurement of the temperature may be done with a thermocouple, or in some cases, the buoyancy effect of the surrounding atmosphere may be calibrated in terms of temperature.

Low temperatures may be achieved by surrounding the sample tube with a Dewar flask of appropriate design to go between the pole-pieces. Various low boiling liquids may be used as refrigerants. The author prefers to use a large lead block suspended by plastic tubes inside the Dewar flask. This block has a central cylindrical opening in which the sample hangs. It is also supplied with a spiral opening into which liquid air may be injected. A small heating coil is available as required. The apparatus is shown diagrammatically in Fig. 4. Temperatures are measured by a multi-junction thermocouple. This apparatus has proved very satisfactory for the temperature range − 190° to + 100° C.

A simple form of Gouy balance has recently been described by Wartman.⁷

3. The Quincke Method

⁸

This method is similar in principle to the Gouy method except that the force on the liquid sample is measured in terms of the hydrostatic pressure developed when the liquid is placed in a capillary tube so that the meniscus stands in a strong magnetic field. The apparatus is shown diagrammatically in Fig. 5. On application of the field, the meniscus will rise if the liquid is paramagnetic or will fall if the liquid is diamagnetic. It is often possible and convenient to use fields of the order of 25,000 oersteds. For a diamagnetic liquid such as water the change in height of the meniscus may be several millimeters. When the reservoir is of large diameter compared with the capillary, and when the susceptibility of the vapor above the meniscus is negligible, the mass susceptibility of the sample is given by

where Δh is the change in vertical height of the meniscus, and the other terms have their usual significance. This method has, therefore, the advantage that independent measurement of the density is not necessary.

Sometimes rise or fall of the meniscus is observed directly. More frequently the meniscus is returned to its original position by changing the height of the reservoir, or by changing the gas pressure over the meniscus. Accuracy of the readings may be increased slightly by inclining the capillary.

The Quincke method is well adapted to the measurement of liquids, and the accuracy possible is at least as great as with the Gouy method. Unfortunately, arrangements for changing the temperature over a wide range are not convenient. For measurements near room temperature it is possible to control the temperature with a high degree of accuracy. The method has recently been used by C. S. Marvel and co-workers in extensive studies of free radicals.

FIG. 5.—Diagrammatic representation of the Quincke magnetic balance. Many modifications have been described.

The Quincke method may also be used for gases. If the susceptibility of the vapor over the meniscus is not negligible, the hydrostatic pressure developed on application of the field is

p = 1/2(κ − κ0)H²

where κ, κ0 are the volume susceptibilities of the liquid and vapor, respectively.

Some very sensitive adaptations of the Quincke balance as applied to liquids and to gases are described by Wills and Hector,⁹ Bauer and Piccard,¹⁰ Bitter,¹¹ and Woodbridge.¹²

4. The Faraday Method

¹³

If the poles of a magnet are inclined toward each other (Fig. 6), there is produced a non-homogeneous field with an axis of symmetry. If a substance is now placed in a region where the strength of the field (H) changes rapidly with displacement along the axis of symmetry (x), then the substance will be subjected to a force along the axis

where m is the mass of the sample, χ the mass susceptibility, H the field strength, and the rate of change of field strength along the x axis.

FIG. 6.—Faraday magnetic balance. The sample, shown here at the origin, is placed where the product Hy∂Hy/∂x is a maximum. The sample is free to move along the x-axis and may be suspended on a torsion arm.

This method is convenient and sensitive. Small amounts of material are required, and no separate determination of density is necessary. The method was used extensively by Pierre Curie¹⁴ in his classical measurements, and has been used by many investigators since then. The sample may conveniently be mounted on a torsion arm. Displacements may be observed directly, or by a mirror, lamp, and scale arrangement. The sample is generally restored to its original position with the aid of a torsion head. The electrical torsion head is very satisfactory for this purpose.¹⁵

Although the torsion method is sensitive it becomes complicated when temperature control is necessary. Alternatively, the force may be measured as a horizontal force or as a vertical force. The horizontal force method, involving a bifilar suspension, has been developed by Weiss. A null method is used, the force being compensated by the attraction between two current-bearing coils. The method is described at length by Foëx.¹⁶,¹⁷

FIG. 7.—Sucksmith modification of the Faraday balance.

The vertical force method has been developed in a very useful piece of apparatus by Sucksmith.¹⁸ Instead of using a balance as in the Gouy method, he suspends the sample from a ring of phosphor bronze which is fixed at its upper side. Two small mirrors are fixed to the ring at the optimum positions so that on a scale at one meter distance the image of a lamp filament may be observed. Movement of the filament image is at least 150 times the movement of the sample under investigation. A diagram of the apparatus is shown in Fig. 7. The method appears to combine some of the most valuable features of the Faraday and the Gouy methods. Recently, Sucksmith¹⁹ has modified the balance in such a way that susceptibility determinations may be made in vacuum or in a controlled atmosphere up to 1500° C.

An interferometric adaptation of the Faraday method is described by Bhatnagar and Mathur.²⁰

Many observations, using the Faraday method, have been made at high and at low temperatures. But for absolute measurements a careful and tedious mapping of the field is necessary. The method has its principal application in work on powders, for which small samples only are required, and for which the problem of uniform packing would otherwise arise. Cabrera has recently described refinements in which the accuracy reaches 1/1000.²¹

5. The Curie-Chéneveau Balance

²²

This balance is similar in principle to the Faraday method except that mapping of the field and careful setting of the sample are neatly avoided. The balance is shown diagrammatically in Fig. 8. It consists of a torsion arm suspended by a fine wire. One end of the torsion arm supports the sample which is free to move between the poles of a small permanent magnet. The magnet may be moved forward or backward with respect to the sample, and, because of its magnetic susceptibility the sample is either repelled or attracted. Movement of the torsion arm may be followed by a pointer or by a mirror, lamp, and scale. The sample automatically places itself in the region of maximum attraction or repulsion. The force acting on the sample is zero when the sample is between the poles. It is also zero when the sample is well removed from the poles. There are then two regions in which the force is a maximum as the magnet is moved from far on one side of the sample to far on the other side. The mass susceptibility of the sample is given by

where χ0, m0 are the mass susceptibility and mass, respectively, of a substance of known susceptibility, m is the mass of the sample of unknown susceptibility, Θ is the difference in corresponding maximum deflections on either side of zero for the sample under investigation, Θ0 the difference for the standard substance, and Θt the difference for the empty tube.

Various refinements have been suggested by Gray and Farquharson²³ and by others. Relatively small quantities of sample are required and the measurements may be made rapidly. On the other hand, it is difficult to introduce temperature control, and the sensitivity is not very high. The Curie-Chéneveau balance is of most use in magnetochemical analyses such as are required in rare earth work. Useful elaborations of the Curie-Chéneveau balance are described by Wilson,²⁴ Oxley,²⁵ and Vaidyanathan.²⁶

FIG. 8.—Curie-Chéneveau balance.

6. The Rankine Balance

If a bar magnet stands parallel to a plane surface, the induced polarity on the surface exerts a force on the magnet. This force is an attraction if the surface consists of a paramagnetic substance, a repulsion if the substance is diamagnetic. The magnitude of the force depends on the magnetic susceptibility of the substance. Use of this principle for magnetic measurements was suggested by Rankine²⁷ and developed by Iskenderian.²⁸ The arrangement is shown diagrammatically in Fig. 9. The magnet is suspended by a quartz fiber from a horizontal beam supported by another quartz fiber. This arrangement minimizes the effects of the earth’s magnetic field and of stray accidental fields. The relative magnetic susceptibilities of different materials can be deduced from the magnitudes of the torques produced in the torsion fiber.

FIG. 9.—Rankine magnetic balance.

Owing to the effects of stray fields the method is rather difficult and it is necessary that all parts of the balance, other than the magnet, be constructed of non-ferromagnetic materials. The apparatus is capable of giving accurate results, with the interesting difference from other methods that very weak fields are used. The fields may be of the order of 100 oersteds.

7. Other Special Methods

There is an almost endless number of methods and modifications of methods which have been suggested for the measurement of magnetic susceptibility.

If an elongated specimen is suspended by a fiber between the poles of a magnet, it will tend to take up an equilibrium position. A diamagnetic specimen will set itself at right angles to the field, a paramagnetic specimen parallel to the field. The force acting on the specimen depends on the difference in mass susceptibilities of specimen and surrounding atmosphere. This affords a convenient method for the investigation of liquids. The specimen may be made of glass or quartz, and the liquid takes the place of the surrounding atmosphere. The method was developed by Decker,²⁹ and has been used by the author.³⁰a Reber and Boeker³⁰b have recently adapted the method for use on vapors.

If the specimen is displaced from its equilibrium position, oscillations will occur, the period of which is a function of the magnetic susceptibilities of the specimen and of the medium. This method has been developed by Frazer and Long³¹ by means of a device used in determination of the gyromagnetic effect. The specimen is suspended by a quartz fiber, and maintained in torsional vibration by the periodic imposition of a magnetic field of suitably adjusted intensity. Fields of the order of 300 oersteds may be used. The method is relative only, but gives the mass susceptibility with a fair degree of accuracy and uses a small (0.5 g.) sample.

A very sensitive balance for gases and vapors has been developed by Bitter³² from a method originally suggested by Glaser.³³ This method is somewhat similar to that of Decker, but much more elaborate. A test body, made of pyrex glass, consists of a cylindrical vessel divided radially into four equal chambers. This vessel is suspended from a torsion fiber between the poles of an electromagnet. Two of the chambers, diametrically opposite one another, are open to the surrounding gas, the other two are evacuated and sealed off. On application of the field the test body turns through an angle which is a function of the magnetic susceptibility of the gas in the open chambers.

Salceanu³⁴ has developed a method of magnetically neutral solutions. If a paramagnetic substance is dissolved in a diamagnetic solvent, such as water, there must be a certain concentration, at a definite temperature, at which the susceptibility is zero. Salceanu determines this condition by the rotation of a glass float placed in the liquid under investigation, between the pole pieces of the magnet. The susceptibility of the solute may be calculated from a knowledge of the concentration at which χ = 0. The method would appear to be of rather limited applicability.

Athenasiadis³⁵ has suggested an original method for liquids. As in the drop method for surface tension measurements, drops of the liquid fall from a tube, the orifice of which is placed in a non-homogeneous magnetic field. The relative susceptibilities of two liquids are a function of the mass of the drops and of the change in mass when the field is turned on or off. The method has been used by Abonnenc³⁶ to find the susceptibility of several inert gases. The basis of the method is determination of the concentration of a solution of CuSO4·5H2O, the weight of a drop of which formed between the poles of an electromagnet remains unchanged whether the field is applied or not. This weight varies according to the susceptibility of the gas in which the drop is formed.

The problem of measurements on non-homogeneous systems has been studied by Bates, Baker, and Meakin,³⁷ particularly with reference to amalgams which separate on standing. One pole tip has a cylindrical surface and the other has a plane surface. When an amalgam is placed in a vertical tube, suspended in the field from a torsion balance, each portion of the amalgam is exposed to the same value of the gradient of H² in the direction along which motion of the tube is possible.

It may seem surprising that no reference has been made to the familiar methods used in determining intensity of magnetization, permeability, and related quantities of ferromagnetic bodies. Such methods are, with few exceptions, not adaptable to the determination of magnetic susceptibilities. The reason for this is that the susceptibilities of non-ferromagnetic substances are invariably extremely small in comparison with the susceptibility of, say, iron. Efforts have been made to develop methods depending on the change of inductance when a substance is inserted into a coil of wire. Some of these efforts are described by Stoner (op. cit.¹), but none has been satisfactory. There are occasions when the ferromagnetic properties of a substance are of great value in determining the composition and structure of a chemical compound. Methods used for these determinations are described later under the heading 9. Measurement of Related Magnetic Quantities.

8. Measurement of Magnetic Anisotropy

The magnetic susceptibility of a solid depends not only on the nature of the molecules present but also on their orientation in the crystal. Measurement of susceptibility on a powdered specimen yields an average of the several different susceptibilities which exist along the different magnetic axes of the many crystals of which the powder is formed. Magnetic anisotropy is the variation of intensity of magnetization with direction in crystalline matter. Sometimes this is expressed as the difference of two principal susceptibilities, sometimes as the ratio. The magnetic axes of the crystal generally correspond with the optical axes. Gases, most liquids, and amorphous, highly powdered, or isotropic solids do not show magnetic anisotropy.

Within recent years, measurements of magnetic anisotropy have in many cases become complementary to x-ray structural studies of crystals, especially of aromatic compounds. The method has been reviewed by Mrs. Lonsdale.³⁸

The most obvious method of measurement is to determine the magnetic susceptibility by one of the standard methods, but to have the crystal oriented in such a way so that the force of attraction, or repulsion, is exerted along one magnetic axis only. This method is not particularly accurate except for strongly paramagnetic substances, and some difficulty may be experienced in properly orienting the crystals. Jackson,³⁹ however, has had considerable success with crystals of rare earth compounds and other paramagnetic substances. The apparatus used is an adaptation of the Sucksmith modification of the Faraday magnetic balance. Measurements are reported down to the melting point of hydrogen.

An alternative method of high sensitivity has been described by Krishnan.⁴⁰ When any diamagnetic crystal is suspended by a thin fiber in a magnetic field, it will, of course, be subject to a lateral force tending to move it to the weakest part of the field. But there are also two different couples tending to rotate the crystal about the axis of suspension. First, there is a couple due to asymmetry of shape of the crystal and the non-homogeneity of the field. And second, there is a couple due to the magnetic anisotropy. The former effect may be eliminated by using a crystal cut into spherical shape, or more readily, by using a homogeneous field. A field of sufficient homogeneity may be found in a small region between relatively large plane pole faces.

If a crystal is suspended by a torsion fiber in such a field, it may be made to oscillate. The period of oscillation is related to the magnetic anisotropy as follows:

where t and t1 are the periods of oscillation with field on and off respectively; c is the torsional constant of the fiber; m is the mass of the crystal; M is the molecular weight; H is the field; and χ1 – χ2 is the difference between maximum and minimum molar susceptibilities along the magnetic axes lying in the plane of oscillation. A slight modification of this method for very small crystals is described by Krishnan and Banerjee.⁴¹

Krishnan’s elegant method measures only the difference between principal susceptibilities, although it does so with great accuracy. If the absolute values are required, it is necessary to measure at least one of the principal susceptibilities directly. This may be done (in addition to the Jackson method) by a procedure due to Rabi.⁴² The crystal to be investigated is suspended vertically in a non-homogeneous field. The crystal is then surrounded with a solution, the susceptibility of which is varied, and the orientation of the crystal adjusted, until there is no movement of the crystal due to the magnetic field. A diagram of the apparatus is shown in Fig. 10. The susceptibility of the solution is then measured by the Gouy (or other) method. Each axis of the crystal may be investigated in turn, if this is required. The method does not require preparation of crystal sections or measurement of the magnetic field. As many crystalline substances are soluble in water, the solutions used are first saturated with the substance under investigation. The method may, of course, be extended to include non-aqueous solutions. The Rabi method, with some modifications, has been extensively used by Krishnan and his co-workers.

FIG. 10.—Rabi balance for measurement of magnetic anisotropy.

9. Measurement of Related Magnetic Quantities

The relationship between several magnetic quantities is shown in Fig. 11. With increasing field strength, H, the intensity of magnetization, , decreases slightly for diamagnetic substances, and increases for paramagnetic substances. In both cases the slope of the straight line gives the magnetic susceptibility.

FIG. 11.—Relationships between various magnetic quantities.

For ferromagnetic substances the situation is quite different. The intensity of magnetization changes in a complicated, irreversible manner as H is changed, giving rise to the familiar hysteresis curves. Only at high fields, when the specimen is said to be saturated, does the intensity of magnetization become directly proportional to the field.

In the relationship B = H + 4π (cf. Sec. 1) /H is, of course, κ, the volume susceptibility. The quantity B/H is called the permeability, for which the symbol P will be used. The permeability is related to the susceptibility by P = 1 + 4πκ. For dia- and paramagnetic substances both P and κ are independent of field strength, except that at extremely low temperatures and high fields paramagnetic substances approach saturation.

When a ferromagnetic body is placed in a magnetic field and then removed, B may not return to zero as H becomes zero. The body is then said to be permanently magnetized. The magnitude of B under such conditions of permanent magnetization is called the remanence. The field of opposite sign necessary to reduce B to zero is called the coercive force. Specific magnetization is the intensity of magnetization divided by the