Magnetic Susceptibility Aspects of Instrumentation and Applications to Chemistry and Solid State Science I . N. Mulay,’ Solid State Science Programt2 Materials Science Department, and lndumati I . Mulay, Center for Air Environment Studies, and Materials Research Laboratory, Pennsylvania State University, University Park, Pa. 7 6802
I
this fourth review on magnetic susceptibility, we survey some selected aspects of instrumentation and applications to chemistry including the solid state. The first three reviews (&A, 46A, 47A) appeared in 1962,1964, and 1966. This review covers selected features of literature from about November 1965 to about November 1967. We offer below comments from a previous article (47A) to clarify our position in writing this review. The elements of arbitrariness, which may appear to some readers concerning the selection of the material, continue to exist in the present review. Hence, i t should not be regarded as an extensive review of a complete bibliographic nature on what may be commonly regarded as “magnetochemistry.” This statement partly reflects the agony of discovering the vast and everincreasing growth in magnetics literature and one’s inability to cover all important aspects. The reviewer is then baffled by deciding what to select and what not to select. The titanic growth in magnetics literature refers to the overall growth in magnetics “technology” and in part to its “science.” K e do not, therefore, review literature on magnetic materials and devices, magnetic measurements such as permeability, remanence, etc., which characterize magnetic materials; however, references to new books and review articles on magnetic materials research are included. Jt7e shall outline a few aspects of solid state chemistry or magnetic materials such as nonstoichiometric oxides. Readers who want a thorough bibliographic list of references on all branches of magnetics, or on magnetic susceptibility alone, must be directed to the voluminous pages of chemical and other similar abstracts. N
GENERAL LITERATURE
Abstract Services. The Cumulative Solid State Abstracts a n d the STAR compilation of the National Aeronautics and Space Administration (NASA) of the E.S. Government continue t o provide excellent abstracts in magnetics. The “Index t o Literature in Magnetism,” published by t h e Bell Telephone Laboratories, is highly specialized b u t unfortunately ignores many interesting aspects of magnetochemistry. The general scope and use 440 R
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of these abstracting and indexing services were outlined in a previous review
(47A). Monographs and Books. Several books with a direct or indirect bearing on magnetic susceptibility, magnetic materials, and on “magnetochemistry,” have recently appeared. Static magnetic susceptibility, magnetic relaxation, magnetic resonance, and Mossbauer spectrometry are intricately related. Because resonance and Mossbauer spectrometry have developed as separate “disciplines,” literature in these areas will not be reviewed here, in the belief that these will be covered by other reviewers. However, because magnetic relaxation is likely to be ignored by others, we have included appropriate references on this subject. These are grouped below under different categories for the benefit of the reader. hf AGNCTOCHEMICAL ASPECTS. A monograph on “Magnetic Susceptibility” by Mulay (44-4) appeared as a paperback reprint. This contains a few additional references to the original contribution. Judging from its favorable reviews, which appeared in this journal and in the “Journal of Chemical Education,” the monograph seems to have been useful in the research laboratory as well as in the classroom. Texts by Brailsford (5d) and Williams (MA) provide excellent theoretical outlines of magnetism which should be of interest to the chemist. Schieber’s (64Aa) “Experimental Magnetochemistry” dealing with nonmetallic magnetic materials was brought to our attention by the publishers during the course of proof corrections of this article. ;idvances in the experimental and theoretical aspects of magnetochemistry will be surveyed in a forthcoming volume by Boudreaux and Nulay (4Aa). THEORY.An outstanding sequel t o Van Vleck’s 1932 classic has appeared under the title, “Theory of Electric and Magnetic Susceptibilities of Molecules.” The author, Davies (ISA), offers the following comments in his preface; these comments explain the purpose and rigor of the book : “iJ7ewere all inhibited by the thought, supported by rumour, that Van Vleck hiinself might extend the territory of which he was the master. I n 1963, I decided to ignore rumour and this book started to take shape on the foundation of my posegraduate lectures at the
Cniversity of Groningen. I n pursuit of understanding, I travelled in the United States and France as well as in Holland and Britain, and, like all authors, I benefitted from those who suffered my importunity and answered my inquiries.” Tyabikov (62A) has virtually produced a treatise on “Methods in Quantum Theory of Magnetism.” Slater (57d) has presented the third volume of “Quantum Theory of Molecules and Solids.” Equally valuable are Kittel’s “Quantum Theory of Solids’’ (35A) and the second edition of his famous “Introduction to Solid State Physics” (3SA). Marshall (39.4) has edited a volume on the “Theory of Magnetism in Transition Metals”; this covers aspects of ferromagnetism in metals and alloys and does not deal with “transition metal ions,” in which chemists are primarily interested. lfanenkov and coworkers (37A) cover several aspects of spin lattice relaxation in ionic solids. “Hyperfine Interactions,” edited by Freeman and Frankel (23A), outlines theoretical advances in various aspects of magnetism of the electron and nuclei. As companions to the above theoretical volumes, we recommend Hameka’s (29-4) book on quantum chemistry, Stevenson’s (60A) “Lfultiplet Structure of Atoms and Xolecules” and Uhagvantam’s ( 4 A ) “Crystal Symmetry and Physical Properties.” FERROMAGNETISM AND METALS. K i j n (65A) has edited Volume 18 of “Encyclopedia of Physics” and covers extensively ferromagnetism. Sparks (58-4) and Vonsovskii ( S S A ) deal with “Ferromagnetic Relaxation Theory” and “Ferromagnetic Resonance,” respectively. Carey and Isaac (8A) have an interesting volume on “Magnetic Domains and Techniques for Their Observation”; the chapter on colloids should be of interest to chemists. Rad0 and Suhl’s (50-4) Volume I I B on “hIagnetism” is devoted to interactions in metals and Volume IV in the same series by Herring (%?A) covers 1 Also affiliated with the Materials Research Laboratory. Enquiries should be addressed to this author. 2 Interdisciplinary graduate program in the physical sciences leading to R1.S. and Ph.D. degrees in Solid State Science. 3 Laboratory for interdisciplinary research in Chemistry, Physics, Planetary sciences, etc.
exchange interactions among itinerant electrons. ~ I A T E R I ASCIEKCE. LS The concept of “materials science” is not new; the name was introduced about a decade ago and, as outlined below, several excellent contributions to magnetism have resulted from this “materials science” approach. It is unfortunate that some chemists (and physicists) find it difficult to comprehend the “materials science” concept. Briefly stated, it is a newly emerging “interdisciplinary” discipline in which the chemist, the metallurgist, the physicist, the engineer, etc., take an integrated look a t both old and new problems of science and attempt to solve them. Indeed “materials” cover a wider territory than “chemical compoundsJ’ of well defined stoichiometry, with which the chemist is most familiar. In the “materials science” approach, attempts are made to synthesize IIPW materials, to characterize materials (old and new), and to understand their structure a t the macroscopic and microscopic (or electroiiic) level. Characterization a t the macroscopic level includes efforts especially to understand the widely variable “defect state” of the material by various techniques including those related to magnetic, electrical, optical, and mechanical properties. X study of certain properties on the one hand helps in the characterization of mateiials, and on the other in the elucidation of their electronic structure. I n this respect. magnetic susceptibility and other related magnetic properties play ai1 important role. Returning to our review of new books on materials, we should like to point out a contribution by Rose, Shepard, and n’ulff (52d), who lucidly describe magnetic properties froni the materials point of view; this volume is evcellent both for introductory aspects of teaching arid research. Martin (40A) has authored a book on “1Iagnetimi in Solids.” It has good sections on dia- and paramagnetism of ionic solids; however, the discussion on molecular solids, in which most chemists are interested, is rather sketchy. Sussbauni (48-4) discusses electromagnetic and quantum properties of materials, and has an excellent chapter on magnetic materials. “Applied Magnetism” by Olsen (49A) represents a unique approach to basic theory and technological aspects of magnetism. Several excellent hooks under the title “Solid State Chemistry” have appeared: of these, Hedvall (30.4) discusses the magnetic state, and Moore (43-4)provides a clear picture of the physical phenomena in nickel oxides, ruby, steel, etc. The well known “Magnetism and Magnetic Materials Digests” for 1966 and 1967 have been edited by Haas and Jarrett (27.4) and by Doyle and Harris (18d). I n addition to topics on chem-
istry, structure, and crystal growth of magnetic materials, these digests cover latest aspects of superconductivity, magneto-optic and resonance phenomena, The digest provides references to proceedings of conferences on magnetism, magnetic materials, etc. Thompson (61A) has recently written a book on the “Magnetic Properties of Materials.” Standley (69A) has surveyed oxide magnetic materials. In addition to these, there are a large number of volumes on “Materials Science,” “High Temperature Materials,” etc., which contain references to maglietic properties of several materials. Almost every major publisher in the U.S.A. currently has a special listing for materials science. Gco- AND SPACEL~AGKCTISJI.The past decade accelerated the activity in the materials science area to facilitate the exploration of outer space; it also seems to have enhanced the activity of taking a good look a t our o m planet. I n this respect, the geochemist and the space chemist, may be interested in the following new books: Collinson, Creer, and Runcorn (14A); Natsushita and Campbell ( @ A ) ; Hindmarsh, Lowes, Roberts, and Runcorn (MA) ;and finally a book by Rikitake (61A). Reviews, Chapters, and Articles of General Interest. Haberditzl ( M A ) has revieived very effectively t h e advances in molecular diamagnetism. He shows t h a t , a t the present state of instrumentation and quantum mechanical approximations, diamagnetic measurements can supply information on chemical structure which complement- the results of other approachessuch as infrared and nuclear magnetic resonance. He seems to have reviewed the literature to the beginning of 1966. Guy (26-4) has a short review on theoretical methods of calculation of diamagnetic susceptibilities. He discusses very briefly various theoretical formulas for predicting susceptibilities, and the application of the variational method, which has produced rather encouraging results. Results for several simple hydrocarbons, amines, alcohols, etc., are given. Guha (25A) has reviewed especially the theory of diamagnetic susceptibility and anisotropy developed by Pauling and London. I n an extensive chapter in his new book, Haineka (29d) discusses elegantly and in a somewhat detailed fashion the theory of diamagnetic susceptibility and magnetic shielding constants. Dehn and RIulay (17A) discuss in a forthcoming paper their calculations of diamagnetic susceptibilities of several atoms based on the recent aspects of Clementi’s (Ilil, 12A) and Burns’ (7.4) wavefunctions and also on earlier wavefunctions of Slater (56A) and Angus (SA). These values are extensively tabulated and compared with
recently-reported experimental data (%%I). For the benefit of theoreticians and experimentalists who need to update continually their guessing of diamagnetic corrections to various systems-such as organometallic and coordinationswe provide here a preview of their final results shown in Figures 1(a) and 1( b ) . Another topic of theoretical interest by Flygare (2lA) considers the electric and magnetic interactions and the ground state electronic structure of molecules. Carlin (9A) has reviewed the stereochemistry of cobalt(1) complexes and their electronic structure with reference to their magnetic susceptibility and ESR spectra. Brow1 (6-4) also has a similar chapter on organometallics and the entire series on Transition Metal Chemistry, edited by Carlin (9A), contains valuable information on magnetic susceptibility and ESR of coordination compounds. The magnetochemistry of chromia-alumina catalysts has been reviewed by Pool and MacIver (49Aa). Magnetic properties and crystal chemistry of oxides with ordered rock salt structure have been described theoretically and tabulated by Wickham (64A). Markham (%A) has a short section on the paramagnetic susceptibility of Fcenters in alkali halides in his book on this subject which describes several other aspects, especially ESR. Mulay (45-4) has suggested the possibility of elucidating by Mossbauer spectrometry the electronic binding in diamagnetic organometallic compounds, with special reference to the molecular orbital theory and in antiferromagnetic coordination complexes, with special reference to the computation of exchange interaction in such complexes. Collins, Dehn, and Mulay (1SA) have reviewed applications of this spectrometry to superparamagnetic systems. It is gratifying to note that magnetic susceptibility is finding its way into undergraduate and advanced laboratory instruction; the pedagogical value of the following articles is undoubtedly great. Adams and Raynor (%4) suggest several informative experiments on the magnetochemistry of nickel(I1) and iron complexes, which can be performed very easily by the Gouy method; details of calculation are given. Dunne (19A) also recommends basic experiments on a simple Gouy balance in an undergraduate laboratory. Carlin (10A)has an interesting article on the quantum mechanical calculations of paramagnetic susceptibility. Abeles and Bos (2A) outlined the dimensional analysis in the calculation of magnetic susceptibilities. This paper helps partly to unravel the mystery surrounding the fact that most workers, while agreeing that susceptibility is a dimensionless quantity, continue to use units such as “cgs” or “emu” or “cgsVOL. 40, NO. 5 , APRIL 1968
e
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v Experiment01 o Slater
3c
D
t
s o
3 m
Angus Burns
Clernenti 5 Ctcrnenti 5' Burns' H,-like
k orbitals
?; -x 2c x I
J
f
m
3
m
0
IC
I 0
c
a He
0
Li I
2
v o
Be
B
,
N
C I
0
F
I
I
Ne
Na
10 ATOMIC NUMBER,
6
4
Mg
I
AI
-
i
Si
Cu ~
P
S
I2
8
Z
CI
14
16
Sloter
Figure 1(a) and (b).
-
Riamagnetic susceptibilities of atoms
Comparison of various theoretical calculations and experimental values by Dehn and Mulay (I7A)
442 R
ANALYTICAL CHEMISTRY
I
18"29
Experimental
ATOMIC NUMBER, 2
Go
A A/
1
Zn
1
30 31
emu” for specific and molar susceptibilities while some use the unit ‘ ‘ ~ m - ~ per mole” for the molar susceptibility [cf. Mulay (44.4)]. Compilations of Magnetic Data. Coordination, organometallic, and free-radical chemists will be delighted CAMPING MAGNET to find t h a t the new series of Landolt(OPTIONAL) Bornstein tables [editor-in-chief, ALUMINUM DAMPING VANE Hellwege (31A ) ] contains voluminous PALLADIUM STOPS data on the magnetic susceptibility of coordination and organometallic compounds, and on magnetic properties (mostly ESR) of free-radicals. Eyring’s (20A) third volume on rare earth research also contains references to and tabulation of some magnetic susBEAM SUSPE:NSIONS ceptibility data. The same is true of Sinha’s ( 5 5 A ) book on rare earth comSAMPLE SUSPENSO plexes. Samsonov (53A) has compiled PROTECTION LOOP physicochemical data, including magPERMANENT MAGNET netic susceptibility, on high temperature BALANCING (OPTIONAL) compounds of rare earth metals such as the borides, carbides, silicides, and sulTARE WEIGHT fides. Samsonov (54.4) has another SU S PE N SlON useful handbook on the physical properties of the elements. Torp (61Aa) reports magnetic susceptibilities and spectra for several halogen complexes of niobium(1V) and tantalum(1V). Jain REFERENCE POINTER \ (34ii) has written a book on properties BEAM POINTERof electrical engineering materials. The research materials information ~ S E N S I T I V I Y Y ADJUSTMENT center [T. F. Connoly (15A)l of the Oak HOOK SUSPENSION Ridge Sational Laboratory has produced an excellent bibliography of magnetic materials of groups IV, V, and VI SAMPLE HOOK transition metals. A report and its Supplement I provide selected references (and short abstracts) on the prep/TARE SENSITIVITY ADJUSTMENT HOOK aration, structure, physical properties (including magnetic), metallography, Figure 2. Constructional details of an all-quartz microbalance and transport properties. These concf. Mulay and Worden (82B) tain over a thousand references; the latest compilation, (ORSL-R?*IIC-7), gives a tabulation of magnetic transition adsorption, thermogravimetric (or therHence, there is a certain unavoidable temperatures. The formidable task of momagnetic) measurements. The allmixing of instrumental descriptions in compiling such enormous data has inquartz construction is especially useful the following sections classified variously deed been handled successfully. as the “Faraday,” “Gouy,” and “anisoin studies on adsorption, etc., involving Last of all, Grigsby’s ( 2 4 A )contribucorrosive gases, which affect metallic tropic” techniques. Readers seeking a tion needs attention. He presents a knowledge of selected advances in one parts in other balances. Some features guide to the literature (Volume 2) on of a Worden Model 4301 Fused Quartz electronic properties of materials. This area are therefore urged to read the microbalance are shown in Figure 2, other sections also. The above classifialso refers to transport properties of which is self-explanatory. The entire cation has been adopted for organizamaterials. balance is enclosed in a quartz cylindritional convenience only. Sections of books on “Vacuum Microcal case about 4 inches in diameter. INSTRUMENTATION balance Techniques’’ edited by Behrndt The balance is of two-pan, equal-arm design. Construction of the balance ( 4 B ) and Czanderna (QB)contain valuGeneral Aspects of Force Measureable information for constructing magelement is entirely of fused quartz. ments. Some general references in Frictionless fused quartz flexure hinges the next section are particularly netic balances of utmost precision. One specific section, for example, by van den are used instead of the conventional helpful in the construction of magBosch (SQB)is devoted to such instrunetic susceptibility apparatus, based knife edges or taut bands. The readout of the beam deflections is accommentation. Thomas and Williams on the measurement of force. These include the basic Gouy and Faraday plished by viewing a beam pointer with (37B) provide a special review of microbalances. I t should be noted t h a t a micrometer microscope. -4resolution balances. Reference should be made to some of the sensitive force measuring of better than 1 pg is readily achieved. a recent survey (1967, 1968) by Hirsch devices used for the “average suscepti(20B) of laboratory balances of all types -4 feature of the balance which seems bility” measurements on powdered including the microbalance. advantageous in susceptibility work is solids by the Faraday method also can that the user may adjust the sensitivity Mulay and Rorden (32B) outline the be used for the measurement of “anisoadaptability of an “all-quartz’’ microso that para-, dia-, or even ferromagnetic tropic susceptibility” of single crystals. balance for magnetic susceptibility, samples can be studied with about same
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accuracy while using perhaps one instrument. Of course, the sample weight and the applied field will need suitable variation to keep the changes in weight within the available range. There are numerous optional features such as magnetic damping, magnetic weight loader for adding additional tare weights under vacuum, etc., which make the instrument more versatile. This “manual balance” has provision for changing to a “semiautomatic” balance, by winding solenoids on the outside of the enclosure tube, and measuring the current to obtain a null balance. The cost (of about $800.00) appears to be within the reach of most research laboratories. A new balance, the Worden hIode14302 Auto-Xu11 Micro-Balance, is now available. The unit affords the same allfused quartz element as used in the Model 4301, but incorporates a servodriven automatic nulling device for the readout. Three field coils are mounted around the outside of the chamber to provide magnetic fields for nulling and damping. The electromagnetic circuit provides sufficient force to null u p to a 200-mg weight change in the sample. The precision of the balance is i 2 pg, which includes resolution and repeatability. The advantage of this system for magnetic susceptibility work is that in the servo mode the beam is automatically held at the null position, so that the sample remains in the same position in the magnetic field. The readout may be accomplished by manually nulling the microvolt readout instrument which has a digital display with units of micrograms/microvolt, or by using the 0- to 0.5-volt signal from the control system to drive a potentiometric recorder. This balance also appears to be well suited for measurements of change in susceptibility with temperature and/or time, etc. The cost of servomechanism is naturally more than the “manual” or “semi automatic” balance. hlackinon (28B) describes magnetic measurements at low temperatures; this text is useful for classroom as well as laboratory instruction. Sections of a n earlier book by Hoare and Jackson (21B), not previously reviewed, also depict some experimental procedures for measurements a t low temperatures. A detailed study of the magnetic susceptibility of borosilicate glass, fused quartz, and polytetrafluoro-ethylene (Teflon) generally employed in the fabrication of vessels for holding samples in the force methods, has been made by Hurd (22B). “Pyrex” glass, which is generally regarded as paramagnetic at all temperatures, shows a transition (to diamagnetism) around 34’ K and is strongly temperature dependent below this temperature. Fused quartz (diamagnetic) is found to be almost independent of temperature. Teflon (diamagnetic) shows a transition around 80” 444 R
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K. Reliable experimental data for these materials over a range of temperature are reported. This information is particularly useful for making accurate corrections for the susceptibility of vessels, etc., in the course of making precise measurements on samples over a wide temperature range. ASPECTSOF THE FARADAY MAGNETIC BALANCE. Hill (19B) discusses the influence of positioning errors on susceptibility measurements by the Faraday method, especially using the Heyding, Muir, and Taylor poles [cf. hlulay (44A)l. This is a careful analysis of errors, seldom described by other workers and is recommended as a “must read” article to all experimentalists using this technique. In particular, the influence of the field profile upon susceptibility measurements is discussed, taking into account changes in size and position of the sample. Hill (19B) shows that by using suitable pole tips, measurements of susceptibility can be reproduced to 0.2%, if a movable magnet is employed. For specimens limited in size to 2 mm, no corrections for dimensions are required to maintain this accuracy. He gives excellent graphs and tables for variation of magnetic force as a function of the length of the specimen, and of vertical displacement of the sample, etc. Rakos and coworkers (34B) also have made a detailed study of the errors in the Curie-Cheneveau and Pascal balances, which are based on the Faraday principle. They used NiCl2 solution and studied the effects of the diameter and the thickness of the test tube on the accuracy of measurement of the magnetic susceptibilities. They considered errors arising from the “tangent error” in optical systems. They suggest that corrections for the empty tube have to be made if the reference compounds and sample differ markedly in their susceptibilities. A modification of the Senftle balance [cf. Mulay ( M A ) ] is described by Baidakov and coworkers ( 2 B ) . I t s major advantage is that it minimizes the effect of oxygen adsorbed on the solid sample by incorporating a gas-purification system. Measurements can be made on a few milligrams of samples from - 100’ to 150’ C either in vacuum, up to torr, or in helium gas up to one atmosphere. The apparatus was used for magnetic susceptibility studies on lead sulfide. An automatic apparatus for simultaneous thermogravimetric and magnetic susceptibility measurements is reported by Simmons and Wendlandt (36B). It is based on the Faraday method; the changes in weight during thermal decomposition and with the field on and off are recorded with a semimicro recording balance. The thermal decomposition of diamagnetic [Co (”&]
Ch with dZsp3 structure to paramagnetic CoCl2 with d7 configuration-Le., 3 unpaired electrons-is reported, A complete thermogravimetric and thermomagnetic analysis is described. This apparatus allows a quick determination of the Curie constant (c) and the Weiss constant (e) in the Curie-Weiss law, A Faraday magnetic balance for measurement of susceptibilities of highly reactive materials is reported by Kirchmayr and Schindl (25B). This is useful for ferromagnetic or strongly paramagnetic materials in the range 80”1600” K. Accuracy of f1% is claimed. The apparatus features temperature regulation for the study of phase changes by magnetic methods. ASPECTSOF THE GOUYMETHOD. An outstanding contribution for the micro measurement of magnetic susceptibilities using a novel “Cartesian diver” approach has been made by Gersonde (14B). His paper sounds impressive in that measurements on a sample containing as little as 50 pg of Fe3+ ions show change in the molar susceptibility of 130 X cgs units. This is said to correspond to a change of 6 x 10-9 cgs units for 1g. of Fe3+ ions. The operations and principles of the apparatus appear complicated at first glance; however, considering that the method was developed to study small changes in magnetic susceptibility of microgram quantities of biological materials-e.g., hemoproteid undergoing a change to the tertiary structure-the technique should be of great interest to microanalysts, despite its complexity. The method combines some aspects of (a) the Gouy method and (b) the Rabi method ( S S B ) of measuiing susceptibility, although the latter aspect is not clearly stated by the authors. The mathematical treatment is, however, quite clear. The equations of the Gouy method are employed inasmuch as a tiny cylindrical (sealed) sample tube moves in and out of a uniform field. The sample tube is suspended by a glass fiber from a Cartesian diver floating in a liquid which surrounds the entire assembly in a larger outer tube. The principle of the Cartesian diver as a micromanometer for variations of hydrostatic pressure of a liquid has been found to be better by a factor of 1000 than the Warburg apparatus. This has been used cleverly in essentially observing “apparent” displacement of the sample tube. I n actual practice the displacement of the sample is counterbalanced by “adjusting” the susceptibility of the surrounding float liquid. This type of balancing has been previously used by Rabi to measure the (anisotropic) susceptibilities of crystals which are suspended by a fiber and surrounded by an inert solvent. The paramagnetic susceptibility of the surrounding float liquid is controlled by an ex-
ternal “magnetic titration” technique. The molar susceptibility of the sample is given by
where V is the volume of the external tube containing the reference liquid, M is the molecular weight of the sample, and rn,its amount. xuis the specific susceptibility of the float liquid. C,f is the concentration of the paramagnetic salt in the float liquid. Because the apparatus is used in a relative manner, changes in C, -L e . , AC, -are employed to achieve a “magnetic equivalence point” or a “null point.” This simply means that the concentration of the surrounding floating liquid is changed (AC,) so that the sample tube will not move a t all with the field on or off. (Thus when the volume susceptibility of the sample equals that of the displaced liquid, there is no magnetic force on the sample.) The factor (1/u) enters as a constant of proportionality between AC, and AC,, where C, is the concentration of the paramagnetic salt solution in the tube, using the same paramagnetic salt and solvent as in thelouter float tube. The “null point” is observed by an optical microscope focused on the Cartesian diver. The apparatus has to be free from mechanical vibrations; this is achieved by placing even the heavy magnet in a sand bath mounted on “oscillation elements,” which seem to imply heavy “spring mounts.” These precautions are necessary for measuring forces as small as 2 X dyne in this flotation balance. I’ENDULUM 1 f C T H O D S (HIGH PRESSURI: VCSSCLS,CTC.). Measurements of magnetic susceptibility (or magnetization) under high pressure have posed several problems. One of the first attempts by Broersma using an inductance bridge and very small pressures was reviewed before (46A). I t had all the limitations of an inductance bridge [ c j . Mulay (44A)l. A remarkable advance in average and anisotropic measurements on weakly magnetic samples under high pressure in conjunction with a pendulum method has been made by Kawai and Sawaoka (24B). They use a pressure vessel (or bomb) made of nonmagnetic Cu-Be alloy in which the sample is subjected to a hydrostatic pressure up to 12 kilobars using liquids like kerosene and a Bridgman-type intensifier. The tube which feeds the pressure liquid to the vessel is disconnected after reaching the desired pressure; the internal oil pressure is maintained in the vessel through the use of a cone shaped no-return valve. The enclosed sample and the vessel can now be handled in a routine fashion. (In our
judgment, this vessel or its appropriate modification could be used with any “magnetometer” or perhaps even with a “magnetic balance” for susceptibility measurements.) The authors have used a torsion pendulum magnetometer in which the vessel is suspended from a horizontal arm attached to a pendulum and is essentially allowed t o swing in a nonuniform field (H) with a gradient dH/dx. The vessel is affected by the following magnetic attraction:
F
=
(mx
- m’x’)
d
-H 2
dx
where m and x are the mass and the specific susceptibility of the sample respectively; m’and x’ correspond to the vessel. The deflection of the pendulum is magnified by an optical device and a photoelectric amplifier. The rest of the arrangement is essentially the same as described before by Mauer (29B). The potential use of this pendulum as B null method for automatic recording of susceptibility is discussed. Examples are given for the magnetization as a function of the field for the Cu-Be vessel (diamagnetic) and for Nohr’s salt (ferrous ammonium sulfate), which is paramagnetic. Other instrumentation is described for enclosing inside the vessel a thermocouple (for temperature measurements) and a manganin wire (for pressure measurement via its electrical resistance). Measurements up to 200’ C can be made, beyond which the Cu-Be alloy is not stable. For anisotropy measurements, which are illustrated by results on a single crystal of nickel, the same vessel is used. I n it a crystal oriented along a desired direction is fixed and subjected to a known pressure as before. I t is suspended from a wire between the poles of an electromagnet with a high degree of field homogeneity. The magnet is rotated and the torque exerted on the sample is measured a t the other end by a strain gage. The lateral motion of the vessel is prevented by an airjet bearing system. The strain gage could detect + 2 dyne; this sensitivity is said to be enough for measurement on ordinary ferromagnets. The authors give equations and values for the pressure dependence of the anisotropy constants for nickel. Dubrovskaya and coworkers (11B) seem to have used a “pendulum principle” in which the sample, attached to the lower part of a pendulum and placed in a nonuniform field, experiences a force. This “rocking force” is compensated by a current flowing through two solenoids which generate a magnetic force on the top part of the pendulum. The method is claimed to be suitable for weakly paramagnetic materials, and the sources of error are discussed.
ENCOURAGING ADVANCESin “FLUX CHANGE” and “INDUCTANCE” METHODS. Ingenious techniques for susceptibility measurements based on the unique properties of superconductors and the well-known dc inductance method have been successfully developed by Deaver and Gorre (10B). Compared with all the modifications of other methods, ranging from the force measurements to magnetic resonance, this technique provides much higher accuracy and is quite novel in its theoretical and practical approach, The cost of instrumentation and operation (equivalent to the cost of a good superconducting magnet and liquid helium) would be perhaps beyond the reach of the average research laboratory. This would seem to be its only limitation. However, the principle and operation are elegant and allow measurement of susceptibility as small as 10-10 cgs unit per gram (units specified by these authors) in a lo4oersted field and a wide range of temperature (2O-3OO0 K). The basic idea here is to measure the total change in flux of two coils (wound in apposition) when the sample is moved from one coil to the other. This situation is reminiscent of the well known Barnetts method [cf. Mulay ( & A ) ] . The high sensitivity seems to result from the very high fields employed and from the sophistication used in the measurement of the change in flux, This sophistication is based on the Meissner effect in superconductors, described below. The Meissner effect refers to the expulsion of the magnetic field from the interior of a solid superconductor when it is cooled below its transition temperature; fluxoid quantization comes into play, which means that the only possible values of magnetic flux trapped inside a thick superconducting ring are integral multiples of hc/2e = 2 X 10-7 G-cm2. This quantization makes it possible to produce a region of zero magnetic field, Now, if a superconducting cylinder is cooled below its transition temperature in an external field which produces less than half a quantized flux through it, a current is induced in the superconductor to exactly cancel this flux and thus produces the lowest quantized state, that is, zero magnetic field. The current in the cylinder is a direct measure of the flux which initially existed in the cylinder. The magnetic field can thus be measured, so to speak, without access to the volume occupied by the field, and with no motion of the superconductor. I n the apparatus, a small sample (0.1~ m - is ~ placed ) in a superconducting coil L1 which is connected (in opposition) to coil L2,and then on t o coil La. Because LI and LZare wound in opposition, the flux change in the entire assemblyL I ,Ls,and L-is twice that which would have resulted from simply removing it from L I (this trick of doubling the flux VOL. 40, NO. 5 , APRIL 1968
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change is well known in inductance circuits). The voltage induced in another coil which is coupled to LJ is proportional to the persistent current resulting from the movement of the sample. The authors discuss appropriate circuits for this purpose and several alternate refinements. Allied instrumentation includes a low field magnetometer for measuring magnetic fields as low a s0.5 X 10-7 oersted, and a low field superconducting shield developed for testing low-field magnetometers. This shield has been used to provide stable fields of less than 10-6 oersted over a six-day period. I n general the entire approach reflects a significant advance in susceptibility instrumentation. Recently several modifications of vibrating magnetometers based on the “change-in-fluu” principle have been reported. Kaeser, Ambler, and Schooky ( d S B ) have compared the relative merits of the “vibrating coil” and the “vibrating sample” magnetometers, various versions of which have been reviewed before ( 4 6 A ) . The authors recommend the use of the vibrating coil magnetometer for use at very low temperatures (below 0.3” K) obtained by adiabatic demagnetization of paramagnetic materials. The authors discuss experimental difficulties in reaching such temperatures and describe a vibrating coil magnetometer and a special cryostat designed for overcoming these difficulties. Experimental results on irradiated SrTiOs (paramagnetic) are presented. For spherical samples about 3 mni in diameter, the sensitivity of magnetic moment measurements is 10-8 emu. The entire approach is very encouraging and it would seem that with further modifications accurate measurements will be possible on diamagnetic samples. I n our experience none of the homemade or commercial “Foner type” vibrating magnetometers are actually capable of measuring diamagnetic susceptibilities. Technical literature on commercial instruments confuses this issue and unwary customers by saying that “the magnetometer detects changes in diamagnetic susceptibility.” Goldberg, Dent, and Miller (16B) outline a compact device for studying phase changes in (magnetic) solids a t elevated temperatures. The need for coolant and/or vacuum is eliminated by making t h r primary and secondary coils of a “permeability transformer” of platinum and winding them on a ceramic insulator. Simultaneous magnetic and dilatometric measurements on a maraging steel sample are reported up to 815” C, although the apparatus is capable of providing temperatures to 1150” C in air. Other advances in inductance techniques are listed under the section on anisotropy. 446R
ANALYTICAL CHEMISTRY
N M R METHODS.Tompa and coworkers (S8B) have successfully applied the broad-line N M R method for measuring the magnetic susceptibility of powdered MnO over a range of temperature. This is one of the few detailed investigations which shows that such parameters as the Nee1 temperature, etc., for antiferromagnets can be accurately determined by the broadline NRIR method. This method has been reviewed before (44A) and consists of detecting the proton resonant signals for a reference material in a cross-shape probe enclosed inside the powdered solid. This arrangement provides directions parallel and perpendicular to the applied field so that the separation between the signals is directly proportional to the susceptibility. The authors used for reference “rubber” and “Cu/I/Cl” powder in polystyrene for measurements below and above room temperature, respectively. These were made in magnetic fields of approximately 4000 and 8000 oersted. The meaning of the composition “Cu/I/Cl” is not clear to us in terms of internationally accepted chemical nomenclature. The authors are associated with the Central Research Institute for Physics in Budapest, Hungary. Another measurement of paramagnetic susceptibility using a high resolution NMR spectrometer is described by Adams ( I B ) for paramagnetic solutions and for certain powdered solids, The author describes a method for paramagnetic solutions, which resembles in toto a method previously reported by Evans (22B) and modified by others. This method and several other modifications (based on the chemical shift of protons in a reference liquid produced by a surrounding sample) have been described and extensively reviewed in the literature (44A,46.4). A few papers appeared in the Review of ScientiJic Instruments, prior to .%dams’ ( I B ) publication in the same journal. The author failed to cite even a single reference to any of the N l I R susceptibility methods; the only reference is to the Foner magnetometer used for verifying some data. This is quite surprising. I t is disenchanting to see such amateurish treatments in print; it would seem that the editorial policies and procedures for reviewing papers for publication in certain instances are totally arbitrary, and these, as ever, continue to be enigmatic. AXISOTROPICSUSCEPTIBILITY MEASUREMENTS. I n the preceding sections, reference was made to anisotropic measurements which could be carried out with the pendulum methods. Other selected advances are presented below. Chose (15B) discusses the covariant matrix in the determination of the magnetic susceptibilities of triclinic crystals. He points out that for any
triclinic crystal, five observations suffice to determine the absolute values of principal susceptibilities and principal axes. I n a mathematical treatment of the susceptibility tensors, he shows that the maximum susceptibility, -11, and any error, dJI, in its measurement cancel out. Based on this treatment, he outlines a method for measurements on triclinic crystals with a n even greater accuracy than before. Bosch (7B) has developed a torsion balance for the measurement of magnetic force on a sample with a high degree of accuracy. Samples as small as 1 mg can be used. Fields u p to 17,000 gauss and temperatures from 61” to 300” K were used for measurements on a single crystal of K2NiF4. Van Mal (4OB) has developed a novel method for measuring the magnetic susceptibility anisotropy of single crystals by the Hartshorn inductance bridge. I t consists of a low temperature sample holder which can hold samples as wide as the inner diameter of a solenoid magnet and which can be rotated into any position. This is indeed a great improvement over the conventional techniques [flip-angle, etc., cf. Mulay ( 4 4 A ) ] ,in which mounting crystals by delicate quartz fibers is difficult. The performance of the method using a crystal of “DYES” (Dysprosium ethyl sulfate) is described. I n the bridge method, a pick u p coil which rotates along with the sample is employed. This is said to improve the sensitivity by a factor of 30 over the fixed coil method. An anisotropy torquemeter previously described by Birss and Wallace in 1963 (and reviewed before) has been adapted to measure the magnetocrystalline anisotropy at high pressures. Birss and Hegarty (5B) describe modifications for use up to 6 kilobars pressure. The apparatus has been tested with a single crystal disk (1120) of gadolinium. For differential anisotropy measurements on ferromagnetic samples, such as hematite and orthoferrite, Flanders and Pearson (1SB) have considered the feasibility of using a torque magnetometer in which a steady de field is applied at right angles to the usual magnetizing field. I n this method the torque output, which is proportional to u = (x,,- xu) H is measured as a function of the applied field. For samples which have a small magnetic moment due to their small quantity or due to small spontaneous magnetization, this instrument serves as a good (hysteresis) loop tracer. For single crystals, differential susceptibility can also be measured. Hagedorn (18B) has constructed a new rotating field technique for the measurement of anisotropic properties of materials. Illustrative data for permalloy film ( p = 5 x emu) are
given. The method has a high precision (-0.5%) and an absolute accuracy of 2%. The technique is based on the harmonic analysis of the signal induced in a pick-up loop when the anisotropic material is immersed in a spatially rotating field. The harmonics generated are related in a simple way to the Fourier coefficients of the anisotropic energy. This represents an important theoretical and experimental advancement in anisotropy measurements. A low frequency hysteresis measurement of small magnetic torroids has been outlined by Grover (17B). This apparatus displays hysteresis loops on an oscilloscope and incorporates a n economical method for supplying the output to an r-y plotter with increased signal-tonoise ratio. A re-entrant hysteresis loop tracer for ferromagnetic wires is outlined by Wolfe and Haszko (41B). They have modified a conventional loop tracer by the addition of a pulse generator and an extra coil coaxial with the specimen. Metz (SOB) has derived equations for the torque produced by the interaction of an applied field and a superconducting torus. She discusses a possible use of this arrangement for the measurement of any torques of interest (at low temperatures), such as in a “radiation balance,” and points out that the method is adaptable to a null technique and provides measurement of torques over a very wide range. Useful limits for superconductors cooled through various transition points are discussed. I n our opinion, the method has great potential for the measurement of small magnetic anisotropies a t very high fields and low temperatures. However, this aspect is not discussed and perhaps was not even intended by the author. Chambers and coworkers (8B) have developed a novel optical method for the measurement of crystal anisotropy in magnetic films. This uses the transverse initial susceptibility and the transverse magneto-optic effect and avoids the use of delicate suspensions or pick-up coils. Observations on a (100) oriented nickel film and associated theoretical discussion are reported. Banbury and Nixon (SB) give a description of preliminary work showing the ability of the scanning electron microscope to resolve magnetic surface detail or anisotropic properties. Examples with a cobalt crystal are provided. TEMPERATURE COXTROL. Birss, Gibbs and Wallis (6B)describe a cryostat using liquid helium for their magnetometer. Temperatures between 4.2’ K and room temperature are easily obtained by controlling heat exchange between the specimen and helium vapor. Details of its performance in relation to specimen temperature and rate of boil-off of
helium gas are also described. Readers may recall that Birss has contributed extensively to instrumentation of magnetometers and temperature control equipment. This work has been reviewed before (46.4, 47A). Kroon (d6B) has constructed a liquid helium glass dewar for work a t a fixed temperature. Its special feature is that it has a narrow tail with a working space of 14 mm (internal diameter); the outside is about 24 mm in diameter. This has been made possible through the inclusion of a molybdenum-glass seal and a copper tube serving as a radiation shield for liquid helium. Reithler (35B) describes a cryostat for use with a magnetic balance. Different refrigerants are used to obtain a constant temperature within certain ranges. Lim and coworkers (d7B) describe a cryopump for temperature control. Although its easy adaptability to susceptibility measurements is doubtful, the paper presents an interesting aspect of recovering the refrigerant (such as liquid helium) almost completely. Temperature control using commercial dc amplifiers is discussed by Miller (SIB). The design of “three-term” temperature controllers and details are given for a high temperature furnace working up to 1000’ C ; an accuracy of ~ t 0 . 5 C~ is claimed. The circuits appear to be of general applicability for controlling low temperatures as well. APPLICATIONS TO CHEMISTRY AND SOLID STATE SCIENCE
I n addition to selected applications, we have included a few theoretical aspects of magnetic susceptibility a t appropriate places; for example, in discussing some applications of magnetic anisotropy, it seems appropriate to point out advances in its theory. Other features of applications and theory have been covered in some of the references cited under “General Literature.” Some facets of solid state applications are described under “nonstoichiometric oxides,” superparamagnetic materials, etc. COORDINATION COMPLEXES.Magnetic susceptibility continues to be used as a criterion of “bond type” in the study of coordination compounds. This aspect is not now particularly new and, as such, no reference will be made to this routine aspect of the literature. The exciting future in coordination chemistry now lies in synthesizing and characterizing complexes with (a) unusual coordination, (b) ferromagnetic and (c) antiferromagnetic ordering, and finally (d) with semiconducting properties. (a) Unusual Coordination. As examples of complexes involving rather unusual coordination number, the work of Martin and White (28C) may be cited.
They report a simple method for synthesizing five coordinated iron(II1) complexes with the square pyramidal configuration and spin S = 3/2. The magnetic moments lie close to that expected for a system with the central metal ion in dSP3 hybridization; this indicates the presence of three unpaired electrons and no orbital contribution. The complexes are monomeric both in the dissolved and the solid state, which excludes the possibility of intermolecular exchange interaction. The infrared spectra are reported and a detailed analysis of the magnetic energy levels and anisotropic g-values is given. (b) Ferromagnetic Complexes. While the phenomenon of ferromagnetism in various metals, alloys, and oxides, (and that of ferrimagnetism in ferrites, which are used for permanent magnet devices) has been known for many years, attempts to produce ferromagnetic ordering in coordination complexes are of recent origin. Ginsburg, Sherwood, and Martin ( I 7 C ) report that a trimeric complex of nickel, bis(acety1acetonato) nickel(I1) shows the positive or ferromagnetic ordering. These compounds facilitate the study of exchange coupling since the handling of magnetic data for a small cluster (isolated short range ordering) is much simpler than for a n entire lattice (long range ordering), where integration over various lattice sites becomes mathematically difficult. We had emphasized this aspect of cluster compounds in our last review (47A). The three nickel ions in this complex are nearly ocollinear, equally spaced a t about 2.896; the shortest nickel-nicks1 intermolecular distance is about 86, which prevents any long range coupling between molecules. The superexchange mechanism (cf. 5A) operates through the oxygen atoms. The magnetic susceptibility of this complex was measured by a pendulum magnetometer, originally described by Bozorth [cf. reference (31) in Nulay (44‘4 ) I. (c) Antiferromagnetic Complexes. Cotton (9C) has reviewed cluster compounds of transition metals. Hence a detailed review of cluster compounds will not be presented here. However, we should like to point out the following work as representative in the area. Colton and Tomkins (8C) studied the halides and oxyhalides of molybdenum and tungsten. They report the presence of trinuclear clusters (11,) in halides such as MCls and oxyhalides like 11OCl4. The susceptibilities were studied as a function of temperature. This revealed the temperature independent paramagnetic contributions. After correction for these terms, the moment of the pentahalides was found t o be 1 Bohr magneton per tungsten atom, which is exactly one-third of an electron atom. The original anomalous magnetic moVOL 40, NO. 5, APRIL 1960
e
447 R
300-
280-
260-
b
t
-
I
-
I
SLIGHTLY REDUCED Y
~
TiOz
Figure 3(a). Plot of molar magnetic susceptibility xm cgs units) vs. temperature T (OK) for the Magneli phases of titanium oxygen system. [Keys and Mulay ( 7 9C-24C)I
ment is rationalized on the basis of trinuclear clusters of tungsten atoms in the compounds. The paper gives several syntheses for the halides and oxyhalides. I n a recent paper, Mulay and Hofmann (S4C) report the magnetic susceptibility, E P R and X-ray crystal structure studies on the binuclear orthophenanthroline complexes of Fe(111). This work, which first appeared in an abstract of a meeting of the American Chemical Society, has been reviewed extensively before (47-4). It will suffice to point out here that a detailed X-ray crystal structure of a triclinic crystal of this complex and Nossbauer studies are quite challenging and are expected to elucidate in detail the magnetic ordering in these complexes. (d) Semiconducting Compounds (Coordination and Organic). The area of 448 R
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ANALYTICAL CHEMISTRY
semiconduction in certain intermetallic compounds is very fascinating and several books on this subject have been written largely by the solid state physicists and the materials scientists. So far we have not even mentioned semiconductivity in our previous reviews, somewhat conveniently assuming that this area of magnetic materials (which has given rise to the “transistor” technology) may not be of interest to the average chemist. Second, we feared that even introducing i t sketchily to our readers and reviewing even a small fraction of its titanic literature would be a very difficult task and would occupy considerable time and space. However, recent reports that some chemists have undertaken attempts to synthesize tailor-made intermetallic polymers with semiconducting properties, has importuned us to review those facets of coordination (and organic) chemistry,
where again magnetic susceptibility will continue to play an important role in their characterization and structural elucidation. It should be noted that the idea of using “ir-electron ring currents” in aromatic molecules such as anthracene, ferrocene (and corresponding polymers), etc., for semiconducting applications appealed to several workers many years ago. Therefore, extensive studies of diamagnetic anisotropy which elucidate these ring currents and the transport phenomena were undertaken in several laboratories. Most texts on seniiconduction refer to these experiments and there exist special books devoted to semiconduction in organic compounds. However, there has not been much technological progress in this area. generally because of their thermal instability and difficulties in establishing metallic contacts to the organic crystals. Kow, intermetallic coordination polymers, with better thermal properties, etc., are likely to open a new avenue of approach. I n a recent report, Collman, llonteith, Ballard, and Pitt (7C) outlined the possibility of using planar dS organometallic complexes with a polymeric chain for possible use as semiconductors. Platinuni and iridium are known to form such compounds easily and the exploratory work on these complexes appears to be very encouraging. I t is hoped that their forthcoming publications will have fruitful results, and we also look forward to revieiving any use of magnetic susceptibility in their extensive and interdisciplinary studies on intermetallic polymers. ~ O K S T O I C H I O h l E T R I C OXIDES-SEMICOKDUCTIKG PROPERTIES. During the past few years, it became clear that the electronic band-gap picture of certain ionic solids had been imperfectly understood in the past. These ionic solids include oxides of varying stoichiometry (or nonstoichionietry) and have atiracted the attention of materials scientists. An impetus to research on oxides with varying stoichiometry or nonstoichiometry was provided by the work of illagneli and ;inderson (cf. ZlC). Their work and subsequent developments summarized by Keys and Mulay (19C, %$C) showed that osides of transition metals ( N o , IT,Ti, V, etc.) eshibit many stable phases depending on the stoichiometry. These are known as the “Magneli phases” and have definite structural and compositional ranges; in the case of titanium, these could be w i t t e n as TinOSn--l. The nonstoichiometry may be said to arise from the “defect structure” of these solids. The term “defect structure” is quite broad; indeed, there exists a wide variety in these defects and in the ordering of the cations and anions. Tests on solid state chemistry and solid state physics, referred to under “General Literature” should be con-
sulted to fully appreciate this beautiful, perplexing, and challenging area of the solid state, which has been generally ignored by the chemists, who seem to have preferred t o focus their attention on compounds of well defined stoichiometry, As outlined below, magnetic susceptibility measurements have helped the characterization and electronic structural elucidation of some of the nonstoichiometric compounds, especially those with interesting properties such as semiconduction. The Hall effect is generally used in obtaining energy band-gap information for semiconducting solids; however, this study needs single crystals of sufficient size for establishing electrical contacts, etc. Because such crystals could not be obtained in our magnetochemistry laboratory, we studied magnetic susceptibility of polycrystalline oxides of titanium, essentially for their characterization and structural elucidation; work on the energy gap is still in progress. Because most of the work by Keys and Mulay (f9C,24C) was reported in the physics-type journals, we have included Figures 3(a) and (b) which summarize their extensive studies and interpretive approaches. The magnetic susceptibilities of a number of Ti-0 phases were studied over the range 80' to 900' K by the Faraday method. These phases may be described by stoichiometric formulae, TinOa,%Os, Ti&, Tib09, Ti6011, Ti7Ola, Tisols, TigOl7,and TiloOlg. The molar magnetic susceptibilities per Ti3+ ion, corrected for the underlying diamagnetism of these phases, were plotted m a function of temperature, as well as those for two reduced rutile samples. The reciprocal of the corrected molar magnetic susceptibility of the Ti3+ ion was also plotted as a function of the temperature for all but the Ti203, Ti&, and Ti02 phases (Figure 3b). The Ti203 and Ti305 phases show, respectively, a noncooperative and a cooperative semiconductor to metal transition. The Ti02 phase has a temperature-independent molar magnetic susceptibility of f5.15 X cgs units. The Ti407, Ti509, and Ti6011 phases sholv antiferromagnetic behavior with Keel temperatures ( T N )of about 130' K. The other phases show an apparent paramagnetic effect, but deviate from the normal Curie-Weiss law behavior. There is evidence of free carriers in these samples as shown by optical absorption studies. The molar magnetic susceptibility increases with increasing stoichiometry up to TiloO19 and then it decreases sharply as one approaches the value observed for Tion. The variation in the molar magnetic susceptibility of these phases with temperature is quite similar to that seen for VB and CrB. The magnetic susceptibility of all the
180.0
-
I70.0
-
160.0
.. .-
h
;
1500-
rn
= 1400-
N 0
E
I" ?O-I
Ej 120.0-
I8i
ED
110.0-
3
v)
3 0
=
-I
'OoO90.0-
Q
8
3
800-
LL 70.060.0-
-
50.0
400-
300 :
ob
I d o z b o & o 4 L o & & 7 d o e d o & TEMPERATURE.O K
Figure 3(b). Plot of the reciprocal molar magnetic susceptibility, 1 /xm (1 O'cgs units) vs. temperature T ( O K ) for the Magneli phases of the titanium oxygen system. [Keys and Mulay ( I 9C-24C)I
phases, except Ti01.5 (ie., Ti203) and TiOl.67(Le., TiaOs) when plotted above the Nee1 temperatures obey a CurieWeiss law of the form given below. The stoichiometry of the phases may be also expressed as TiO(2n-l)/n,as in Figure 3b. X=-
T+e
+A
The slightly reduced rutile is Ti02-,J and the highly reduced rutile is TiOz-,~~. The values were obtained from a least squares best fit by a computer program utilizing an approximation technique. The observed increase in the Curie constant C is surprising if one considers that diamagnetic Ti4+ ions are being added to Ti3+ ions. One would normally expect a decrease in the Curie value because of the dilution effects; however, apparently only the electronic structure of Ti01.6 and TiO1.67 is being modified.
Keys and Mulay (19C, 247) suggest that the molar magnetic susceptibility apparently increases, because the band picture of Ti015 and Ti01.67 is being modified. They consider two mechanisms for explaining an increase in the Curie constants. One could be observing a fractional electronic character as observed for some metals, with a substantially reduced magnetic moment. One could also be observing the effects of diluting the Ti3+ ions which contribute electrons to the conduction band with Ti4+ions. As Ti4+ionsare added, some localized states (possibly high energy, nonionized, donor states) are being created and these could exhibit a normal paramagnetic behavior. They further discuss the increase in Curie constant in terms of exchange interactions between the cations. The authors propose the following bonding scheme in these oxides: VOL. 40, NO. 5 , APRIL 1968
449 R
(I) a shallow, broad conduction band; (2) a dense, narrow 3d band; and (3) a narrow, covalent-bonding band lying below but near the Fermi level. Thus, the properties of these phases are said t o be similar to those in CrB and VB and cannot be described by a Curie-Weiss law over the whole temperature range, and the observed paramagnetism is attributed to an incompletely filled 3d band. The magnetic behavior thus indicates that rather than a strong covalent bond, a weak exchange interaction is encountered in these phases. By assuming that (1) the electrons can be considered as free, (2) the Ti3+ ions are the only source of conduction electrons, (3) the Ti3+ ions are completely ionized, (4) the Fermi surface is a sphere, and (5) the conduction electrons can be considered as a degenerate electron gas, the authors show that the Pauli-Peierls relation reduces to
600
c
-
'"0 n
E
x
0 1
I
400
where A' is the number of conduction electrons, p B is the Bohr magneton, m and m* are the free and effective electron masses, respectively, p is the density, h is Planck's constant, and X I is the mass susceptibility. By considering that the Ti305phase is formed as Th3+ Ti4+ Os2- and correcting for the diamagnetic contribution of these ions-i.e., x,,- the authors further show that an effective mass of about 20 m is obtained for the metallic phase of Ti30sand an effective mass of 4.4 m for the semiconductor phase. These results are in excellent agreement with recent studies on TiOz in which effective masses of 10-30 m were found. I n the course of the above magnetic investigations, some surprising magnetic transitions have been observed. Mulay and Danley (31C) report a "thermal hysteresis" in the change in susceptibility of oxides, such as Tisos as a function of temperature. This is shown in Figure 4. Generally a metal-to-semiconductor transition reflects itself as a change from a low to a high susceptibility in going from a low to a high temperature. Such transitions are also expected to be reversible. However, as shown in Figure 4, one such transition is observed while increasing the temperature; this is not quite reversible in that the curve obtained on cooling is quite different. This is being further investigated by X-ray crystal structure, thermogravimetric, and possibly dilatometric techniques; any final interpretations will be correlated with similar observations on other oxides, which are now continually appearing in the literature. Several scattered and uncoordinated magnetic studies on oxides of vanadium, etc. have been reported during the
+
450 R
ANALYTICAL CHEMISTRY
+
I
I
1
450
T E M P E R A T U R E
500 (OK.)
Figure 4. Molar magnetic susceptibility for Ti305, 7 ( l o + cgs units) as a function of temperature T (' K) showing thermal hysteresis. [Mulay and Danley (32C)]
past decade. We give below a few selected references to publications which appeared in 1965 and 1967. This work may be regarded as representative in the nonstoichiometric field and is expected to provide leads to a detailed bibliography. Some features of the work on such oxides have been appropriately surveyed by Keys and Mulay (I9C, 24C). It is important to note that related magnetic techniques such as N X R , EPR, and Mossbauer spectrometry are being used to supplement the magnetic susceptibility approach. Feinleib and Paul (13C) d'lSCUSS electronic transitions in VzOa with hydrostatic pressure and temperature. Adler, Feinleib, Brooks and Paul ( I C ) analyze the theory of semiconductor-tometal transitions in transition metal compounds outlined in the previous reference. Kosuge (15C) studied magnetic and other phase transitions especially in VOz by using, among other techniques, Mossbauer spectra of iron doped in this oxide. Shinjo and coworkers (S9C) also report similar studies on Vz03 which supports its antiferromagnetic ordering. Umeda (41C) outlines possible correlation of NMR spectral changes in VOZ and electronic transitions. Vasilev and Ariya (41C) report extensive magnetic susceptibility measurements on oxides of titanium ranging in stoichiometry from Ti203 to TiOz. RAREEARTHRESEARCH. A practical application of the Pluecker and Gouy susceptibility methods for the determi-
nation of paramagnetic traces in diamagnetic substances is outlined by Rutzen (38C). He used an electron-magnetic scale to measure traces of paramagnetic substances in lanthanum oxide and showed that purity determination to 99.996% in La203is feasible. Deb-Ray, Ryba, and Mulay (IOC) measured the magnetic susceptibility of several intermetallic compounds of S d , Sm, Gd, Th, Ho, Yb with zinc (MZn2) over 77" to 300' K. All compounds except YbZnz were found to obey the Curie-Weiss law. YbZnz showed a negative susceptibility a t room temperature but a positive value a t lower temperatures. The data obtained from the paramagnetic region for compounds except GdZnz yield magnetic moments in agreement with the theoretical values for the tripositive ions. The electronic bonding in these compounds is discussed. The paper contains several references to earlier work on intermetallic compounds. YOVEL SUPERPARAMAGNETIC SYSTEMS. In a previous review (47A)we introduced and surveyed the area of super (or collective) paramagnetism. The catalytic activity of finely divided transition metals is related to the superparamagnetism of the metallic clusters. Considerable work in this field is generally reported in journals devoted to catalysis and surface phenomena. Magnetochemistry of catalysts continues to be interesting and quite informative; however, it is no longer a novelty and as such will not be reviewed
here a t all. As pointed out before, Pool and MacIver (49da) have surveyed the magnetochemistry of the chromiaalumina catalysts. Recently new methods have been evolved to disperse iron, nickel, etc., either in their atomic state or as ions (which are then stabilized as oxides, etc.) within a silicate matrix. RIulay and coworkers ( S I C ) point out that by controlling variables such as total metal concentration, partial pressure of any reducing gas like CO, and subsequent thermal treatment (sintering a t different temperatures, for varying periods of time, annealing, etc.), it is possible to control and t o limit the size of clusters, within the matrix-and so to speak “encapsulate the clusters.” As opposed to this, in supported catalysts, there is a wide distribution of metallic particle sizes on the surface of the support; this is unavoidable because the ‘Isurface,” as compared with the “internal spaces,” is highly irregular. Starting with this idea, they report the synthesis and superparamagnetic behavior of iron dispersions within a silicate matrix ( S I C ) . They point out that a superparamagnetic system follows the Langevin function, which reduces to in the low field region. Here M, is the intrinsic inagnetization of a cluster, Ji, is the saturation magnetization of the system and u is the volume of the cluster. Figure 5 shows their data in which magnetization -11 for total iron is plotted as a function of H I T ; the observed trend in the low field region is taken as evidence of superparamagnetic behavior. From a value of the saturation magnetization, Jia, (-37 gauss), obtained by plotting Ji us. l/ZI, and extrapolating to H , and assuming that saturation magnetization for Fe” is 1750 gauss, the authozs calculate a cluster radius of -12A. This is found to be compatible with cluster sizes observed in other superparamagnetic systems and it is concluded that metallic iron, Fe”, is most likely the species responsible for superparamagnetism. Their work is supported by LIossbauer spectra. I n yet another novel approach, Mulay and Collins (5C, SOC), introduced iron pentacarbonyl, Fe(CO)5and FeCL in a molecular sieve (Linde 1 3 X ) , which has essentially a zeolite matrix. On firing the material to different temperatures (uli to 900’ C) and cooling, they observed clustering of iron t o different extents. This is evidenced by the variation in their magnetization observed as a function of HIT; this leads to cluster parameters, which are consistent with superparamagnetism and the thermal treatment. The clustering species appear to be of Fe203as determined by X-ray studies, and these definitely are introduced inside the zeolite matrix
-1
/
0 -
M i M,v 3k
M, gouss 6-
4.
2-
Figure 5. Magnetization M as a function of the field/ternpemture quotient H I T for 0.70 SiOz-0.16Ca0-0.14NazO 0.025 Fez03. [Mulay, Collins, and Fisher (3 7 C)]
+
rather than on the surface, as shown by electron microscopy. These conclusions are supported elegantly by Mossbauer spectrometry; the beauty of this technique is that the spectra reveal gradual transitions from paramagnetism to superparamagnetism and on to ferromagnetism. The spectrum for paramagnetic Fe3+ are observed in materials a t relatively low temperatures (-100’ C produced by the heat of adsorption), which cause a dispersion and provide magnetic dilution of Fe3+. The spectra for superparamagnetic behavior are observed in materials fired a t medium temperatures (-500’ C) which seems to promote appropriate clustering to “protodomain” limits. The typical sixline spectrum for a ferromagnetic condition is observed in materials treated a t high temperatures (-900” C). At this temperature, the zeolite structure appears to be considerably modified. The new dispersion techniques suggest a possibility for studying the superparamagnetic phenomena a t a more basic level than before. h I S O T R O P Y AND a-ELECTRON RING CURRENTS. The molecular susceptibility and the relative ring currents in pyridine, thiophene, furan, and pyrrole are discussed by Murthy and Le Fevre (36C). The molar Cotton-RIouton constants a t infinite dilution are reported. By correlating these with available polarizability and susceptibility data, the diamagnetic anisotropies of the solutes are derived. The ?r-electron ring currents relative to benzene as 1 appear to decrease in the order 1.06: 0.79:0.57 :0.37 for the four heterocyclic compounds listed above. The a-electron density per cyclopentadienyl ring in ferrocene, ruthenocene and osmocene (4.6; 3.1; 2.6) derived from their magnetic susceptibility an-
isotropy by Mulay and coworkers [reviewed before (47A)j has been successfully correlated with the molecular orbital descriptions of Dah1 and Ballhausen by RIulay and Dehn (SSC). The agreement of experimental values with those derived from the M.O. theory [4.65; 3.05; 2.751 is surprisingly good and suggests that diamagnetic susceptibility anisotropy provides a sensitive method for testing molecular wave functions. German and Dyatkina (142) have calculated the anisotropy of ferrocene, bisbenzene chromium, and bisbenzene cobalt by assuming that contributions to the two rings and metal atoms can be taken independently; the value for ferrocene is compared with the experimental data. Lasheen ( W C ) has shown that the molecular anisotropy of naphthalene tetrachloride has almost the same value as that of a benzene ring with two hydrogen atoms substituted. From this, he concludes that the cyclohexane ring has no or very small magnetic anisotropy and hence it does not contribute to the whole molecule. The molar anisotropy of the central ring in 1:3 : 5triphenyl benzene is 45.9 and that of any three phenyl rings is 55.1. Another application to myoglobin is discussed under bioscience. Borovinskii and Egorova (4C) discuss the shortcomings of the theory of diamagnetic susceptibility based on the 1-electron approximation. They made calculations for cyclic polyenes with 4n electrons (where n = 1, 2 , 3 ) using wave functions consisting of one and more configurations. Kasiyan and Kon (18C) outline the theoretical calculation of susceptibility of an ideal electron gas in a linear approximation. A method of “double time” Greens temperature function was used to calculate the susceptibility x in a VOL. 40, NO. 5, APRIL 1968
451 R
S-91 MELANOTIC MELANOMA 14 DAYS
S - 9 1 MELANOTIC MELANOMA 32 DAYS
S-91 MELANOTIC MELANOMA 42 DAYS
S 9 I A AMELANOTIC MELANOMA 32 DAYS
X /
-
S-9iA AMELANOTIC MELAYOMA 42 DAYS
S-91A AMELANDTIC MELANDMA 63 DAYS
Figure 6. Typical EPR spectra for melanotic and amelanotic melanoma mouse tissues. These show increasing order of magnetic susceptibility (x)and EPR signals with the growth of tumor. [Mulay and Mulay (35C)]
weak field. I n a homogeneous external field at low temperatures the following relation is obtained: x = x o p ~ o - ~ , where x0 is the Landau susceptibility at zero degrees, and p is the temperature independent potential. Theoretical calculations of atomic susceptibilities by Dehn and Mulay (I‘i‘A) have been outlined before. STUDYOF REACTIONS. Zeilmaker and Drotschman (4SC) have essentially used the Gouy method to study the discharge of electric current in a galvanic cell containing M n 0 2 . The diagrams for susceptibility and emf changes during discharge for y and p MnOz are compared showing different reaction mechanisms which are discussed in detail. I n both cases A h 4 + is reduced to &In?+;the difference appears in the phase changes relating to the solid state. Early work in this area was done by Selwood [cf. Mulay (44-4)]. Gersonde and Netter (16C) have studied the small changes in the magnetic susceptibility when certain hemoproteids undergo a change to the tertiary structure. Poole and MacIver (49Aa)discuss the magnetochemistry of the chromiaalumina catalysts in the latest volume of “Advances in Catalysis.” 452 R
ANALYTICAL CHEMISTRY
Kortia (S’i’C) measured the magnetic susceptibilities of complex ions of I\;a3+, Gd3f, Ho3+,Er3+ and the anions CoC142-, CoBr2- and NiC14?-, which had been adsorbed on suitable ion exchange resins. The Gouy method was used; values of the Weiss constant calculated from the results showed good agreement with earlier data, except in the case of NiC14?-. BIOSCIENCE.Mulay and Mulay (S5C) studied the magnetic susceptibility and electron spin resonance (EPR) spectra of Cloudman S91 and S91A melanomas and various mouse tissues and correlated these with trace-metal analysis and known biochemical reactions. Average magnetic moments obtained from temperature-dependence studies showed the following order for tissues: S91 > S91A > leg muscle. These results indicated a similar order in the relative concentration of magnetic species (free radicals and/or paramagnetic ions) and were confirmed by E P R . Figure 6 shows the increasing order of magnetic susceptibility and EPR signal heights as a function of tumor growth. The EPR spectra at different power levels showed that the free radical activity and the Cu*+ and Fe3+ activity attributed to
different signals was generally higher in S91 than in S91A, which did not show a n Fe3+ type signal. Normal tissues such as liver, spleen, heart, kidney, brain, and leg muscle showed varying amounts of free radical activity but not signals attributable to paramagnetic ions. EPR spectra and trace-metal analysis at different stages of S91 tumor growth indicated a systematic increase in the free radical activity, total copper and iron concentrations, and paramagnetic ions, presumed to be Cuz+ and Fe3+. The S9lA melanoma showed increase in total copper, but not in free radical and paramagnetic ion (Cu2+) activity after the initial growth. Correlation of these findings with known biochemical reactions suggests that the free radical activity may be attributed partly to melanin and intermediates of various enzymatic reactions. Presumed paramagnetic ion activity cannot yet be ascribed to specific biostates. Bauman and Harris (SC) have used a susceptibility transformer method [originally designed for geological samples by Collinson and coworkers (SC)] for the measurement of changes in susceptibility in living rats. Their purpose was to measure changes in hepatic overload during progressive iron loading. Their calculations indicated that each grain of ferritin-hemosiderin (storage iron) would be expected to increase the magnetic susceptibility of a human liver emu per cc. by about $0.08 X Employing the transformer method both in vivo and in vitro measurements of magnetic susceptibility, they claim that satisfactory agreement with the predicted value was obtained by in vitro measurements of rabbit livers which contained different but known amounts of iron. I n our opinion, biomedical work of this nature must be taken with great caution. The number of experimental parameters, which can cause considerable variation in the apparent susceptibility measurement is great, and as such the method should not be applied to iron-storage measurements in biosystems without a prior analysis of systematic and random errors. Dmitriyeva and Korin (11C) found that the specific magnetic susceptibJity is about the same for the following: blood serum of normal persons, serum patients with disseminated sclerosis, and cerebrospinal fluid in this and other diseases of the nervous systems. The specific susceptibility was found to be very close to that of water (-0.72 X 10-8). The authors compare their results with thoseobtained previously from patients with diseases like epilepsy, cerebral arachnoiditis, etc., and conclude that “the animal body has strictly defined parameters of certain physical characteristics of its biofluids (in particular magnetic susceptibility) which with the onset of pathological processes in the
nervous system do not change appreciably.” We must suggest that any small changes in paramagnetism (of free radicals, etc.) are masked by the high diamagnetism of water, and these changes could be detected by careful temperature-dependent studies with a sensitive instrument. EPR of course provides another possibility. Aisen, Koenig, and Lilienthal (2C) have carried out a careful analysis of the magnetic susceptibility of ceruloplasmin a t very low temperatures (2’ to 4.2’ K and 77” K). They provide a very enlightening discussion of the limitations of and correlations between EPR and susceptibility measurements. They find that the paramagnetic contribution of the cupric ions of ceruloplasmin t o the susceptibility obeys the Curie law above 2’ K. B y combining the Curie constant with published EPR data, they conclude that 0.44 + 0.02 of the total copper in the protein is in the cupric paramagnetic state. Ehrenberg and Kamen (12C) measured the magnetic susceptibilities and electron-spin-resonance spectra and temperature difference spectra for a number of haem proteins and for an iron protein. These proteins function in the photosynthetic apparatus of the purple photosynthetic bacteria. It is shown that the variant Rhodospirillum rubrum type (RHP-type) proteins which are chemically related to C-type cytochromes, resemble alkaline ferrimyoglobin and ferrileghemoglobin when in the ferri form in that they exist as thermal mixtures of low- and high-spin forms. The temperature-difference spectra suggest that when the temperature is decreased the amount of the highspin form is increased, contrary to the temperature effect found with ferrileghemoglobin and alkaline ferrimyoglobin but similar to that found with acidic ferrimyoglobin. C-type cytochrome (one example) and iron protein (one example) are both low-spin compounds. Reduced (ferro) RHP-type proteins appear to be pure high-spin compounds. These results are discussed in terms of the known structural and chemical features of the proteins. I n a recent paper, Tasaki, Otsuka, and Kotani (40C) discuss their measurements on hemoproteins down to 4.2’ K. A summary from their paper is given below. To obtain information on the electronic state of the iron ion in various hemoproteins [(myoglobin, hemoglobin, Rhodospirillum rubrum henioprotein (RHP) and cytochrome c (Cyt. c)], the magnetic susceptibilities of these substances u-ere measured from room temperature down to 4.2” K. After plotting the experimental susceptibility data against the reciprocal of temperature, the diamagnetic part of the magnetic susceptibility could be easily determined
by extrapolating the X us. 1/T curve to the point where I/T was zero. The temperature dependence of the effective number of Bohr magnetons was calculated from the paramagnetic part, which was obtained by subtracting the diamagnetic part from the total magnetic susceptibility. The following compounds were of highspin type: Nb(Fe3+)pH = 6; Mb(Fe2+) p H = 6; Illb(Fea+)F, Hb(Fe3+) p H = 6 ; Hb(Fe2+) p H = 6; RHP(Fe3+) p H = 6; RHP(Fe3+) p H = 11; RHP(Fe2+) p H = 6; RHP(Fe2f) p H = 11; catalase (Fe3+) pH = 6; and catalase (Fe3+)F. From the temperature dependence of neff,the value of D (where H = DS,2) of hlb(Fe3+) p H = 6 was estimated to be 10 cm-1, which was in good agreement with the value obtained from the anisotropy of the susceptibility. Mb(Fe3+)CN; Cyt. c(Fe3+) p H = 6; Cyt. c(Fe3+) p H = 11; Cyt. C(Fe2+) p H = 6; Cyt. c(Fe2+) pH = 11; catalase (Fe3+)CN; and catalase (Fe3+)S3were of low-spin type and n e f f for Mb(Fe3+) pH = 9 had a medium value, between the high- and low-spin types. Related studies are reported by Gersonde, Seidel, and Netter (16C). Lindskog and Ehrenberg (27C) studied the magnetic susceptibility and near infrared spectra of bovine cobalt carbonic anhydrase. They consider in detail the crystal field effects of Co(I1) complexes on the basis of magnetic measurements and optical spectra. By assuming that the cyanide inhibited enzyme contains tetrahedral Co(I1) with A = 5300 cm-1, they obtain an expected effective magnetic moment in the range 4.26 to 4.37 Bohr magnetons in good agreement with the experimental value of 4.41 =k 0.05 B.M. Their magnetic measurements had to be restricted to room temperature due t o the limitations of Theorell’s magnetic “suscetometer” or balance [cj. Xulay ( & A ) ] , They further discuss the spectral changes occurring on the interaction of cobalt carbonic anhydrase with protons and inhibitors, and the effects of coordination in the active enzyme. Morimoto and coworkers (89C) discuss elegantly in a short paper their results on a single crystal of myoglobin. They point out that the F e is trivalent, its ground state is 6S, and spin-orbit interactions split the sextet into three Kramers doublets. By considering the following well known spin Hamiltonian, H = DSZ2 E ( S Z 2- SV2)
+
(cf. S4C), and EPR, they find that E < 0.01 D and D 2 5 cm-1. Thus it is shown that the susceptibility can be calculated with only one parameter D, based on the orientations of the haem planes, which were determined from EPR studies. The anisotropy, AX (1.1 X 10-7) was measured by an oscillation
method on a single crystal of myoglobin, (0.7 mg). They find that D ,- 12 cm-1 to correspond to this AX value. They give several reasons for ignoring the diamagnetic susceptibility of the aromatic rings of the amino acids and of the porphyrin rings. ACKNOWLEDGMENT
We thank Carmella Moore and Betty White for their expert help in typing and in making drawings, respectively. We thank our colleagues Fred and Valerie Trexler for proofreading the manuscript. Some of our work was supported by the U. S. Atomic Energy Commission, the American Cancer Society, National Institutes of Health, and by Professor R. Myers, Director, P.R.I. at the Kent State University, Kent, Ohio. LITERATURE CITED
Introduction and General Literature (1A) Abeles, T. P., Bos, M. G., J . Chem. Ed. 44,438 (1967). (2A) Adams, D. hl., Raynor, J. B., “Advanced Practical Inorganic Chemistry,” Wiley, New York, 1965, (3A) Angus, W. R., Proc. Roy. SOC. (London)A136, 569 (1932). (4A) Bhagvantam, S., “Crystal Symmetry and Physical Properties,” Academic Press, New York, 1966. (4Aa) Boudreaux, E. A., Mulay, L. N., “Advances in hlagnetochemistry,” Marcel Dekker, New York, in press. (5A) Brailsford, F., “Physical Principles of Magnetism,” Van Nostrand, New York, 1966. (6A) Brown, D. A., Chapter I in “Transition Metal Chemistry,” Vol. 3, R. L. Carlin, Ed., Marcel Dekker, New York, 1966. (7A) Burns, G., J . Chem. Phys. 41, 1521 (1964). (8A) Cafey, R., Isaac, E. D., “Magnetic Domains and Techniques for their Observation,” Academic Press, New York, 1966. (9A) Carlin, R. L., Ed., Chapter I in “Transition Metal Chemistry,” Vol. 1, Marcel Dekker, New York, 1965. (10A) Carlin, R. L., J. Chem. Ed. 43, 521 (1966). (11A) Clementi, E., Ramondi, D. L., J . Chem. Phys. 38,2686 (1963). (12A) Clementi, E., Ramondi, D. L., Reinhardt, W. P., Ibid., 47, 1300 (1967). (13A) Collins, D. W., Dehn, J. T., Mulay L. N., “Mossbauer Methodology,” Vol. 111, I. Gruverman, Ed., Plenum Press, Xew York, 1967. (14A) Collinson, D. W., Creer, K. M., Runcorn, S. K., “Methods in Paleomagnetism,” American Elsevier, New York, 1967. (15A) Connoly, T. F., Bibliography on Transition Metals (RMIC-3) and Research Materials. Information Center, Oak Ridge National Laboratory, P. 0. Box X, Oak Ridge, Tenn. (16A) Davies, D. W., “The Theory of Electric and Magnetic Properties of Molecules,” Wiley, New York, 1967. (17A) Dehn, J. T., Mulay, L. N., J. Chem. Phys. 47, (1965) ( I n press). (18A) Doy!e, W. B., Harris, A. B., “fiIagnetism and Magnetic Materials Digest 1967,” Academic Press, New York, 1967. (19A) Dunne, T. G., J. Chem. Ed. 44, 142 (1967). VOL 40, NO. 5, APRIL 1960
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Prentice Hall, Englewood Cliffs, N. J., 1966. (49A) Olsen, E., “Applied hlagnetism,” Phillips Technical Library, Erinhoven (Netherlands) and Springer-Verlag, New York, 1966. (49Aa) Poole, C. P., RIacIver, D. S., “Physical Chemical Properties of Chromia Alumina Catalysts,” p. 224 in “Advances in Catalysis,” Vol. 17, D. D. Eley, H. Pines, and P. B. Weisz, Eds., Academic Press, New York, 1967. (50A) Rado, G. T., Suhl, H., Eds., “Magnetism,” Vol. IIB, “Interactions in Metals,” Academic Press, New York, 1966. (5lA) Rikitake, T., “Electromagnetism and the Earths Interior,” American Elsevier, New York, 1967. (52A) Rose, R. bl., Shepard, L. A,, Wulff, J., “Electronic Properties: The Structure and Properties of Materials,” Vol. IV, Wiley, New York, 1966. (53A) Samsonov, G. V., “High Temperature Compounds of Rare Earth RIetals,” Consultants Bureau, New York, 1965. (54A) Samsonov, G. V., Ed., “Handbook of the Physicochemical Properties of the Elements,” Plenum Press, Sew York, 1967. (54Aa) Schieber, 31. M., “Experimental Magnetochemistry” North Holland, Amsterdam (Wiley, Sew York), 1967. (55A) Sinha, S. P., “Complexes of the Rare Earths,” Pergamon Press, New York, 1966. (56A) Slater, J. C., Phys. Rev. 36, 57 (1930). (57A) Slater, J. C., “Quantum Theory of Molecules and Solids,” Vol. 111, McGraw-Hill, Sew York, 1967. (58A) Sparks, AI., “Ferromagnetic Relaxation Theory,” LlcGraw-Hill, Sew York, 1967. (59A) Standley, K. J., “Oxide Magnetic Materials,” Clarendon ,Press, Oxford, 1962. (60A) Stevenson, R., “hlultiplet Structure of Atoms and Alolecules,” W. B. Saunders, New York, 1965. (61A) Thompson, J. E., “The Magnetic Properties of Materials,” Chemical Rubber Co., Cleveland, 1967. (61Aa) Torp, B. A., Doctoral Ilissertation in Chemistry, Iowa State University, Ames, Iowa (1964). Available from University blicrofilms, Inc. (No. 64-10, 672), Ann Arbor, hlich. (62A) Tyabikov, S. V., “Methods in Quantum Theory of Magnetism,” Plenum Press, New York, 1967. (63A) Vonsovskii, S. \’., Ed., “Ferromagnetic Resonance,” Pergamon Press, Kew York, 1966. (64A) Wickham, I). G., Record. Chem. Progress 27, .58(1966);< (65A) Wijn, I€. P., Encyclopedia of Physics,” Vol. 18, Springer-Verlag, Berlin, New York, 1966. (66A) Williams, D. E. G., “The Magnetic Properties of hlatter,” American Elsevier, New York, 1966. Instrumentation (1B) Adams, J. Q., Rev. Sci. Instr. 37, 1099 (1966). (2B) Baidakov, L. A., Blinor, L. N., Zubenko, Y. V., Ka?ennov, A., Strakhov, P., Vcstn. Lrnzngr. L:niv. 21(4), Ser. Fiz. i. Khim., S o . 1, 40 (1966). (3B) Banbury, J. R., Sixon, W. C., J . Sci. Instr. 44,889 (1967). (4B) Behrndt, K. H., “Proceedings of 1 acuum 3\licrobalance Techniques,” (Princeton Conference), 5’01. 5 , Plenum Press, New York, 1966. (5B) Birss, R. R., IIegarty, B. C., J . Sci. Instr. 44, 621 (1?67). (6B) Birss, R. R., Gibbs, J. I., Wallis,
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(IC) Adler, D., Feinleib, J., Brooks, H., Paul, W., Phys. Rev. 155,841 (1967). (2C) Aisen, P., Koenig, S. If., Lilienthal, 13. R., J . diol. Bzol. 28, 225 (1967). (3C) Bauman, J. I
