126 PHILlPS TECHNICAL REVIEW VOLUME 22

X-RAY DETERMINATION OF CRYSTAL STRUCTURES

by P. B. BRAUN and A. J. van BOMMEL. 548.735

Since the fundamental work of Van Laue and Bragg (1912), X-ray diffraction analysishas grown into an extremely important technique for studying the solid state. It has led to animpressive series of structure determiruuions, including such spectacular ones as vitamin B 12,strychnine and penicillin.

The article below deals with the principles underlying X-ray diffraction, discussing therelation between the structure and the diffraction patterns, and how the one can bederived from the other. By way of illustration, examples of structures determined in Eindhovenare discussed, special mention being made of work on a substance from Cl class of magneticmaterials known as ferroxplana.

Crystals of differing structure also differ in theway they scatter X-rays. This fact underlies amethod of identifying crystalline substances, bymeans of the characteristic diffraction patterns towhich these substances give rise when irradiatedwith X-rays 1). (Diffraction patterns have thereforebeen described as the finger prints of crystals.) Dif-fraction patterns can moreover be used for deter-mining the crystal. structures of substances. The

detailed analysis of the crystalline and molecularstructure of penicillin is one of the remarkableresults achieved in this way. As appears in jig. 1,the structure of the penicillin molecule is verycomplicated, and its elucidation was therefore alandmark in the development of X-ray analysis.Other outstanding results in this field have been thedeterminations of the structure of strychnine andof vitamin B 12 2).

Fig. 1. Model of the benzyl penicillin molecule, obtained from the "Fourier maps" alsoshown. The latter represen t three projections of the molecule, the "contours" being linesof constant electron density, and the "peaks" corresponding to the projections of atoms.These Fourier maps were constructed from data obtained from X-ray diffraction patterns.(From: E. Chain, Endeavour No. 28, Oct. 1948, p. 152.)

At the same time X-raydiffraction studies can leadto a better understandingof those physical andchemical properties thatare related to the crystalstructure of solids andmolecules. Structure anal-ysis is accordingly indis-

2593

') See e.g. W. G. Burgers,Philips tech. Rev. 5, 157,194.0; W. Parrish and E.Cisney, Philips tech. Rev.IO,157,1948/49.

2) D. Crowfoot, C. W. Bunn,B. W. Rogers-Low andA. Turner-Joues, The chem-istry ofpenicillin, PrincetonU niversity Press, 1949.J. H. Robertson and C. A.Beevers, The crystal struc-ture of strychnine hydrogenbromide, Acta cryst. 4,270-275,1951. C. Bokhoven,J.C. Schoone and J. M. Bij-voet, The Fourier synthesisof the crystal structure ofstrychnine sulphate penta-hydrate, Acta cryst. 4,275-280, 1951. D. CrowfootHodgkin et al., The struc-ture of vitamin B 12, Proc.Roy. Soc. A 242, 228-263,1957.

1960/61, No. 4 DETERMINATION OF CRYSTAL STRUCTURES 127

pensable in the study of ceramic magnetic materi-als, such as ferroxdure and ferroxplana 3).To understand the principles on which X-ray

structure analysis is based, it is necessary first of allto know what information is contained in an X-raydiffraction pattern, and how the structure of asubstance can be deduced from such a pattern. Thiswill be the subject of the first half of this article 4).The second half deals briefly with three examplestaken from researches carried out in recent years atthe Philips Research Laboratories in Eindhoven.

Electron and neutron diffraction analysis areanalogous to X-ray diffraction analysis. Thesemethods are all based on the same principles, butdiffer in technique. They also differ to some extentin the information they yield, so that they supple-~-ent one another very usefully. An article onneutron diffraction will appear in these pages in thenear future; the various differences from X-raydiffraction will be further discussed there. Theexamples of structure determinations given in botharticles will relate to the same substances, so thatit will be readily possible to compare the twomethods.

One final prefatory remark: X-rays are scatteredsolely by electrons. This means that the data derivedfrom X-ray diffraction patterns can only relate <to

3) See e.g. J. J. Went, G. W. Rathenau, E. W. Gorter andG. W. van Oosterhout, Philips tech. Rev. 13, 194, 1951/52;G. H. Jonker, H. P. J. Wijn and P. B. Braun, Philips tech.Rev. 18, 145, 1956/57.

4) Details of this subject will be found in such works as:J. M. Bijvoet, N. H. Kolkmeyer and C. H. MacGillavry,Röntgenanalyse van kristallen, Centen, Amsterdam 194B;H. Lipson and W. Cochran, The determination of crystalstructures, BeU,London 1953; R. W. James, The crystallinestate, Vol. 11. The optical principles of the diffraction ofX-rays, Bell, London 19itB; J. Bouman, Theoreticalprinciples of structural research by X-rays, Handbuch derPhysik, Vol. 32, 95-237, Springer, Berlin 1957. For thetechniques used for recording diffraction patterns, see e.g.M. J. Buerger, X-ray crystallography, Wiley, New York1942; H. P. IUug and L. E. Alexander, X-ray diffractionprocedures, Wiley, New York 1954.

Cl Na

these particles. To determine a crystalline structureit is necessary to find the sites of the atoms, but thiscan be done by localizing the electron clouds. We canthus formulate the direct objective of the X-rayanalysis of crystal structure as the determination ofthe spatial distribution of the electron density in acrystal.

A useful way of describing the electron density ina crystal

It is characteristic of a crystal that it possessesthree-dimensional periodicity. This means that it ispossible to choose a volume element, by the regularstacking of which the whole crystal can be built up.The smallest volume element with which this canbe done is called the unit cell.The three-dimensional periodicity is, of course,

shared by the electron density.Now a periodic function having a period d can

always be resolved into a series of sine waves whoseperiods are d, dj2, dj3, etc. The process by which afunction is resolved into these components is calledFourier analysis, whilst the building-up of a functionfrom these components is referred to as Fouriersynthesis.In view ofits periodicity, the electron density in a

crystal can also be resolved into Fourier components.These constitute a colle~tion of plane .stationarywaves having different d,irections. All the waveshaving anyone directiorr" comprise a set havingwavelengths which are sub-multiples ofthe periodic-ity d in that direction. The Fourier components arereferred to here as density waves or density compo-nents (see figs. 2 and 3).The electron density may thus be expressed as

follows:

(1)

Cl

L__ ~ _

2583 0

Fig. 2. The thick upper curve is ob-tained by adding together the lowerseries of cosinewaves (Au, Al' A2 etc.)whose wavelengths are all integralsub-multiples of d. The thick curverepresënts the electron density (e.)between the octahedral planes of rock-salt, while Au, AI' A2, - ét'è. are theamplitudes of the Fourier componentsof this curve, referred to here as"density waves". z is the directionthrough the crystal (viz. normal tothe octahedral planes), d the latticespacing in that direction.

128 PHILlPS TECHNICAL REVIEW VOLUME 22

Fig.3. Schematic representation of various density waves, inwhich the electron density is depicted by the geometricalamplitude. Two of the waves shown have the same direction,their wavelengths being in the ratio 1 : 2; the two other wavesshown have different directions. To find the electron densitydistribution in a crystal, a number of such waves must beadded together.

The term on the left is the electron density as afunction of the coordinates x, y and z. The terms onthe right constitute the corresponding electrondensity waves. The wavelength and direction ofeach wave are expressed, with the aid of theintegers h; k and I, in terms of the longest repetitiondistances a, band c of three waves whose directionsdo not lie in one plane 5). AHl is a complex quantitywhose modulus and argument indicate the ampli-tude and phase, respectively, of the relevant densitywave.

The volume of the parallelepiped whose edges area, band cwill generally be taken as small as possible;in this way we thus arrive at the above-mentionedunit cell.

5) In the text books quoted the symbols h, k and 1 are giventhe meaning of indices of lattice planes. In a brief discussionof the principles of structural analysis, this is neithernecessary nor desirable. No mention will therefore be madeof lattice planes in this article, and the Bragg law willaccordingly appear in a somewhat modified form.

Sometimes to bring out the symmetry of the crystal, a unitcell is adopted that is an integral number of times larger thanthe smallest possible. In that case the quantity Ahkl informula (1) corresponding to given combinations of h, k andI is reduced to zero (a case of general extinctions).

We shall now show that the electron densitywaves can be deduced directly from diffractionpatterns. We shall consider the simplest conceivablecase, in which the electron density may be describedin terms of a single density wave (this is never so inreality), and show what the form of the diffractionpattern is in that case. We shall then do the samefor an electron distribution consisting of a numberof density waves, as found in an actual crystal.

Diffraction by electron density waves

The question in what directions a single densitywave scatters is answered most easily if we considerthe effect of successive "cross-sectional layers" ofthe density wave, as depicted in fig. 4. Each of theselayers acts as a kind of mirror. The scattered radia-tion is thus to be sought in the direction correspond-ing to simple reflection from these layers.

In general, the total yield in reflected radiationfrom alllayers is zero. A perceptible reflection occursonly under the condition that the angle of incidencee satisfies the relation:

2d sin e = ?c, (2)

where J, is the wavelength of the radiation and d thewavelength of the density wave. In that case theamplitude of the reflected waves has a value pro-portional to the amplitude of the density wave.

Fig. 4. Representation of a density wave with an X-ray beamincident upon it. The variation of the electron density in thewave is indicated by the shading. On the right, three "layers"of the density wave are represented, each of which acts as areflector for X-rays. Rays reflected from the various layersinterfere with one another and cause, in general, extinction,except at one specific angle of incidence, where a reflectionof finite intensity occurs.

1960/61, No. 4 DETERMINATION OF CRYSTAL STRUCTURES 129

These two relations, concerning the angle and theamplitude of reflections, are the foundations of theX-ray analysis of crystal structures. They show thata reflection provides information on no less thanthree properties of a density wave, viz. the ampli-tude, the wavelength and the direction. The int en-sity of the reflection is a measure of the amplitudeof the density wave. Given the wavelength of theradiation, we can calculate the wavelength of thedensity wave from the angle of reflection. Thirdlythe position of the crystal together with the directionand angle of the reflection determines the directionof the density wave. ,I i.e. the amplitude of the reflected ray is proportional to the

amplitude of the electron density wave considered 6).The above can easily be demonstrated vectorially with the

aid of fig. 5.The difference in path length of the rays drawn in fig. 5 is

equal to the component of the vector r along S minus thecomponent of r along So, or:

r . (S - So).

The corresponding phase difference is:

2n r· (S-So);.

The total amplitude F of the radiation, caused by thescattering volume, is obtained by adding together the contri-butions from all volume elements dV, each having an electrondensity e(r), and taking the mutual phase differences intoaccount:

JA _2nir·(S-So)

F = e(r)e ;. dV.V

Regarding the scattering body as an electron density wave,we can write for e(r):

. (3)

2ni~e(r) =A e d,....... (4)

where z is the unit vector indicating the direction of the densitywave, and A and d represent the amplitude and the wavelength,respectively. Using (4), the expression (3) becomes:

,. 2 . (z S-So)F = .JA e n H ä--;.- dV. . .. (5)

V

Only when the exponent is zero will this integral have a valuethat is significantly different from zero.

2585

Fig. 5. Determination of the reflection condition for a densitywave. So and S are unit vectors denoting respectively thedirections of incidence and scattering of an X-ray beam, tworays of which are shown. r is the vectorial distance betweentwo scattering points, dV is a volume element of the totalvolume V, and e is the semi-angle of reflection.

This gives us the condition for reflection:

z S - Sod=-;,-·

This means:a) The two vectors (S- So)and z must have the same direction,î.e, the directions of incidence (So)and reflection (S) lie with zin one plane and make the same angle with z. In other words,the layers into which we have divided the density wave act asreflectors.b) The magnitudes of the vectors must be equal. SinceIS- Sol= 2 sin e (see fig. 5), lId = 2 sin el). or 2d sin e = ;..These conditions being fulfilled, the integral gives:

F= VA, (6)

We have seen that the electron density in a crystalcan be described in terms of a group of densitywaves. Each such wave, independent of the otherwaves, is capable of "reflecting" in the mannerdiscussed. A further point of importance is that eachreflection can generally be intercepted separatelyfrom the other reflections. (Since no two waves areidentical in direction as well as wavelength, they all"reflect" under different conditions.) This makes itpossible to derive from each density wave the in-formation present in its reflection.

To obtain this information it is convenient to usevarious different ways of irradiating the crystal(s).Weissenberg patterns are particularly valuable instructural analysis, but Laue and Debye-Scherrerpatterns and rotation photographs are also oftenuseful for this purpose (see fig. 6). The reflectionsmay be recorded photographically or they may bemeasured with the aid of Geiger counters, propor-tional counters or scintillation counters 7).

The underlying principle of structure analysis

Summarizing the foregoing, the principles of theX-ray determination of crystal structures may beexpressed as follows.

The electron density in a crystal can be describedas the sum of a number of Fourier components. Each

G) In the derivation given here we have assumed that a ray,once reflected, leaves the crystal without again beingreflected. The so-called "dynamic theory", which takesaccount of multiple reflections, produces slightly differentresults from the "kinematic theory" used here. The lattertheory proves to be adequate for most crystals in practice,but corrections may sometimes be called for (extinctioncorrections). The situation is different where perfect crystalswith no defects are concerned. In their case "dynamic"effects are very important. See e.g. L. P. Hunter, Anoma-lous transmission of X-rays by single cryetal-gèrmanium,Proc. Kon. Ned. Akad. Wet. B 61, 214-219, 1958.

7) Seee.g,W. Parrish, E. A. Hamacher and K. Lowitzsch, The"Norelco" X-ray diffractometer, Philips tech. Rev. 16,123-133, 1954/55; P. H. Dowling, C. F. Hendee, T. R.Kohler and W. Parrish, Counters,for X-ray analysis, Philipstech. Rev. 18, 262-275,1956/57.

b

130 PHILIPS TECHNICAL REVIEW VOLUME 22

Fig. 6. Various types of X-ray diffraction patterns.a) Debye-Scherrer pattern, produced by monochromaticirradiation of a powder consisting of differently orientedcrystallites. These patterns are widely used for identifyingcrystalline substances and for determining the size of the unitcell.b) Rotation photograph, obtained by monochromatic irradia-tion of a rotating single crystal. It can be seen that the reflec-tions form straight lines (layer lines), from the spacing of whichthe lattice parameter in the direction of the rotation axis canbe calculated. The size of the unit cell of a crystal is oftendetermined from three such patterns, the crystal being rotatedabout the three crystallographic axes.c) Laue pattern obtained by polychromatic irradiation of astationary single crystal. These patterns bring out very clearlythe symmetry of crystals; in the present case the symmetry ishexagonal.d) Weissenberg pattern, produced by monochromatic irradia-tion of a rotating single crystal, the camera being movedparallel to the axis of rotation. A screen ensures that only thosereflections appear on the film that would form a single layerline in a rotation photograph (see b). The spots on a Weissen-berg pattern thus correspond to the spots of a single layer linein a rotation photograph, the difference being, however, thatthe spots are here spread all over the film as a result of thedisplacement of the camera perpendicular to the direction ofa layer line. This dispersion is in itself an advantage, in thatreflections that produce overlapping spots on a rotation photo-graph can be separately identified on a Weissenberg pattern.More important, however, is that the positions of the reflectionsin a Weissenberg pattern depend not only on the deviation ofthe X-ray beam but also on the angle through which the crystalhas had to turn in order to arrive at a reflection position (thecamera being translated synchronously with the crystalrotation). The coordinates of a reflection in a Weissenhergpattern therefore provide information on the direction of thecorresponding density wave, as well as on its wavelength. Thisinformation is difficult or impossible to obtain from patternsproduced on a stationary film. Considering further that theamplitudes of the density waves can he calculated from theintensities of the reflections, it is evident that Weissenbergpatterns are a particularly valuable aid to structure analysis.

a

c

d

1960/61, No. 4 DETERMINATION OF CRYSTAL STRUCTURES 131

density component gives rise to an X-ray reflectionwhich provides information on the amplitude, wave-length and direction of that particular component.From "all the "reflections from a crystal we have a(virtually) complete picture of all the electrondensity components, and hence in principle of theelectron distribution in a crystal. The determinationof this electron distribution - and with it thestructure of the crystal - amounts to carrying outa Fourier synthesis, i.e. adding all componentsof the Fourier series to yield the required electrondistribution function. It should be noted that thesynthesis involved is three-dimensional, and istherefore extraordinarily complioated. A commonpractice is therefore to carry out one-dimensionaland two-dimensional Fourier syntheses, which pro-"duce projections of the structure (projections on aline and on a plane, respectively). From two or threesuch projections it is possible to deduce the spatialconfiguration of the atoms. (This is well brought outin fig. 1.)

The phase problem

However close the solution may now seem, there isstill a lot to be done before we can determine thestructure of a crystal from the summing of thedensity components. Although at first sight it mightseem that a mere addition is called for, closerexamination shows that one quantity is still missing.This brings us up against an obstacle briefly referredto as the "phase problem". Overcoming this obstacleoften costs the crystallographer most of the time hespends on analysing the structure of a crystal.

To carry out the Fourier summation correctly wemust know, apart from the amplitude, wavelengthand direction of the constituent waves, the phase ofthe waves, which is given by the argument of Ahklin equation (1). This is demonstrated in fig. 7.

Unfortunately, the phase of the density compo-aents cannot be observed; unlike the amplitude,

25U 0 0,5

wavelength and direction, it cannot be deduced fromthe reflections. The intensity of a reflected ray is ameasure of the amplitude of the' correspondingdensity wave, but tells us nothing about its phase.

It is for this reason that the diffraction pattern ofa crystal cannot be directly interpreted to give apattern of the electron density in a crystal. Not untilthe phases have been determined, by the methodsabout to be discussed, is it possible to carry out thesuperposition of Fourier components and so producethe required picture of the electron clouds whichshow the arrangement of the atoms or molecules ina crystal.

Phase determination

Just as knowledge of the phases of the reflectionsfound by experiment would enable' us to solve thestructure of a crystal, it is possible conversely tocalculate the phases from a known structure. Thisimplies a possible method of solving the phaseproblem, for if we can produce a model representinga reasonable approximation of the true structure,the phases of the strongest reflections can often bedetermined with a fair degree of accuracy. Thesedata are then used for carrying out a (provisional)Fourier synthesis. Although the picture obtained inthis way is usually very rough, it often leads to abetter approximation to the actual structüre thanthe original model. With this improved approxima-tion, better calculation of the phases can be made,and so on. In this procedure, phase calculationalternates with Fourier synthesis, thus producingstep by step an increasingly more accurate pictureof the electron density in the crystal.The question now is how to arrive at an initial

model to start the above procedure. The search fora suitable model leads along well-trodden paths,each attempt requiring from the investigatorconsiderable crystallographic experience, deductiveability and intuition. For each attempt we have to

Fig. 7.. Result o£,.a Fouriersynthesis, dohe with 'tire sameFourier components as in fig. 2,but with the component ADhaving a different phase. Theresult is entirely different fromthe density distribution ob-tained in fig. 2.

132 PHILIPS TECHNICAL REVIEW VOLUME 22

ask the question: what is known of the crystal underinvestigation, apart from the X-ray data, which canhelp us to make a provisional guess at the structure?

In the first place the constituent atoms of a crystalare usually known from chemical analysis. Thescattering contribution of each atom ("atomicstructure factor") has been calculated for allelements and these are published in tables. We canalso measure the density of crystals and calculatethe number of atoms contained per unit volume. Forour purposes it is particularly interesting to knowthe number of atoms contained in the unit cell, sincethe dimensions of this cell can be derived from thediffraction pattern. Having ascertained the numberof atoms of each kind contained in this volume ofknown dimensions, it remains to find the spatialarrangement of the atoms.

Obviously, only those arrangements will beconsidered that agree with the properties of thecrystal (chemical, optical, magnetic, morphologicaland particularly the symmetry properties). Takingthese data into account, many possibilities can beeliminated, but it is hardly ever possible to reducethe remaining possible structures to one. Neverthe-less, if only a few models are left after this elimina-tion, it is now usually a practicable proposition totry each of them in turn. This is referred to simplyas the "trial and error" method.

Knowledge of the interatomie distances can be ofgreat help in the construction of a model. Thisknowledge is useful in the process of eliminationdescribed, and is sometimes decisive for the successof the analysis.

Information on the distances (magnitude anddirection) between the atoms in a crystal (but notthe sites of the atoms) can be obtained by Patter-son's method. This is based on the dependence oftheintensities of the reflections on the interatomiedistances. The method consists in carrying out' aso-called Patterson synthesis, which is a Fouriersynthesis in which the components to be summedare simply the reflection intensities. This can be donewithout the phases ofthe reflections being known.

To show that something can indeed be learnt about inter-atomic distances from the reflection intensities, we shall firstwrite formula (1) in a simpler notation:

e(r)= IAu e2n iH . r, . . . . .. (7)

uwhere r is the vector from the origin to the point x, y, zand

x . y -Hvr represents h. - + k-b+ I:.

a cFrom this equation we shall now derive another in which

the intensities occur. In this connection the following pointsshould be noted: a) AB is in general a complex quantity;b) the square of the modulus of this quantity, lAB 12 or ABA~,

wIrere • denotes the complexconjugate ofAH' is related, fromeq..(6), to the intensity In (ex:: FF*) of the correspondingreflection by:

A * IBnAu = V2' ••...•. (8)

Of course, eq. (7) is also valid when An is replaced by itscomplex conjugate. Moreover, the equation also remains validwhen the independent variable r is replaced by r-u, where u isany arbitrary vector. (By this device, as will be shown, weintroduce the interatomie distance u.) We may thus write:

*( ) \'A* -2niH'(r-u)e r--u = L..J He.H

Multiplication of (7) and (9), distinguishing the vectors H in(7) and (9) by H and H', gives:

• • (9)

().( ) \' \'A A* 2niH/·u 2ni(H-H/)'rere r-u=~L..J BH' e e .. B B' • • • • (10)

We shall henceforth omit the * sign in e*(r-u), since thisquantity is real and thus identical to its complex conjugate.Integrating both sides over the whole volume of the unit cellgives:

I e(r)e(r-u) dVer) =

v= LLABAfre2niH/,uI e2ni(H-H')'r dV(r).(ll)

H B' V

The integralon the right is always zero, except when H = H',in which case the integral is equal to V. Using (8) we may.~hus write for (11):

I1 \' 2niH' ue(r)e(r-u) dV(r) = V~ IB e .

v B. • (12)

The right-hand side represents a Fourier summation, per-formed with intensities instead of amplitudes; compare (12)with (7). The significanee of this Patterson function, as it iscalled, appears from the left-hand side: it is a volume integralof the product of two electron densities at places lying atvector distances of u apart. This implies that the integral inquestion will assume high values when u is a distance betweenpeaks in electron density, i.e. when u is an interatomic distancereally present in the crystal. By performing a Fourier synthesis,using the intensities of the reflections as Fourier coefficients,we thus obtain a function whose maxima provide indicationsof the atomic distances.

The clues to interatomie distances obtained by thePatterson method are sometimes so.clear that theyreveal the whole structure; sometimes they throwlight only on certain details of the structure. Muchdepends on the ingenuity of the researcher's inter-pretation of the Patterson synthesis. However thismay be, information is always present, which canhelp in the construction of the model.

We should mention finally that other methodsexist which lead directly, i.e. not via models, to thephase constants required. One such is the "methodof inequalities", which is based on the fact that theelectron densityin a crystal can nowhere be negative,and another is the "statistical method", where useis made of knowledge concerning the constituent

1960/61, No. 4 DETERMINATION OF CRYSTAL STRUCTURES 133

atoms of the crystal. Particulars of these methodswill be found in the treatise byBouman, mentionedin footnote 4).

These, then, are the broad lines of structuredetermination. We shall now say something aboutthe "strategy".

We have seen that each reflection corresponds toa density componcnt, providing information on itsamplitude, wavelength and direction, and that todetermine the phases a provisional model is devised.Now every incorrect model is shown to be wrongonly after a timeconsuming procedure. The lessprobable models should therefore be avoided as faras possible. The time can better be used to look fara more reasonable model; again, the search for sucha., "good" model should not take too long. Animportant aspect of structure analysis is thus theart of finding, with the available data, the shortestway to this "good" model. Since the data involved'are different in every case, one should always beprepared for other possibilities and difficulties, andbe ready to try one way after another. The questionoften arises later whether one should persist witha choice once made, when the work based on themodel adopted does not lead directly to results. Inthis way, experimenting and doubting, the crystallog-rapher may be busy for months before he sees thefirst signs of success, indicating that he may at laststart on the actual determination of the structure.This element of uncertainty imparts to structuredeterminations the interest and excitement ofadventure.

Examples

Having sketched the broad outlines of the X-rayanalysis of crystal structure, we shall now give amore detailed description of three cases, the first twobeing quite simple and making only partial use ofthe above procedures, and the third relating to acomplicated structure, which necessitated a broaderapproach.

Analysis of the compound Alo.89Mnl'1l

It was known as early as 1900 that various alloysof manganese are ferromagnetic, even thoughmanganese itself is not ferromagnetic (HeusIeralloys 8)). The compound AlO.80Mnl'1lhaving turned

8) F. Heusler, Üher Manganhronze und üher die Synthesemagnetisierharer Legierungen aus unmagnetischen Metal-len, Z. angew. Chem. 17, 260-264, 1904.

out to be a material suitable for permanent magnets,a study vwas made of the relation between themagnetic saturation and the structure of thissubstance.

The analysis ofthis structure went very smoothly.The Debye-Scherrer diagram showed the (tetra-gonal) unit cell to be very small, which indicatedthat there were not many different possibilities as tothe atomic positions. It further appeared from thedensity and the chemical formula that the unit cellcould in fact contain no more than two atoms.Finally, the symmetry found left no other choice butto place the atoms at the corners and at the centre.

It is very rare that the atomic sites can be deter-mined with such accuracy at such an early stage ofan analysis. Usually, it may be recalled, only theapproximate positions of the atoms would be knownat this stage, and on the basis of this rough modelone would try by Fourier syntheses to obtain a moreaccurate picture of the structure. In this case. thatwas not necessary because the symmetry had al-ready pointed the way to the precise positions forthe atoms.

This would have concluded the structural analysishad it not been that the non-stoichiometric formulaAlo.89Mnl'1lshowed that the aluminium and man-ganese atoms could not possibly occur in a com-pletely regular arrangement in the crystals If, forexample, all aluminium atoms were situated at thecorners and all manganese atoms in the centres, theformula would be AlMn exactly. This suggested thatthe atoms were not so strongly bound to their ownposition in the cell, in other words that aluminiumatoms might well occupy some of the sites ofmanganese atoms, and vice versa (the latter caseprevailing) .

In such cases we want to know the ratios in whichthe various kinds of atoms occur at the various sites.This information, too, can be deduced from theintensities of the reflections. If in this case we cal-culate the reflection intensities on the basis of a unitcell that is everywhere identical - containing forexample one manganese atom at site A (corner) andone aluminium atom at site B (centre) - the resultsobtained will differ from the observed values. Theeffect on the intensities of the random atomicdistribution described is as if each lattice sitecontained not one single particular atom butfractions of different atoms. These fractions on onesite must, of course, together add up to, one; and ifwe add the fractions of the same atoms in theirdifferent positions, the sum must obviously be inagreement with the chemical formula. In our casewe can therefore write:

134 PHILlPS TECHNICAL REVIEW VOLUME 22

Site A Site B0.89,- r

0.11 + r,AluminiumManganese

r1- r

where T is the fraction of the number of A sitesoccupied by aluminium atoms.

We now- calculate the reflection intensities forvarious values of r, and find the value of T that bestagrees with the observed intensities. In our case thisvalue was 0.03.

Finally, there was the crucial question whetherthis structure indeed corresponded to the magneticproperties of the substance. It was found, forexample, that the magnetic saturation decreasedwhen the substance was subjected to mechanicaldeformation. An X-ray investigation of this phe-nomenon revealed that r increases under theseconditions to 0.13.

This meant that the drop in magnetic saturationmust be accompanied by an increase in the numberof manganese atoms on the "wrong" B sites (onlythe manganese atoms are considered, since theyalone possess a magnetic moment). The conclusionwas drawn that the magnetic moment of the man-ganese atoms on the B sites must be opposite inorientation to that of the manganese atoms on theA sites.

Weshall not go further into this subject, but itmay be mentioned that neutron diffraction analysishas confirmed this conclusion, making it possible torelate the magnetic saturation quantitatively withthe above picture of the structure.

O Th{Z=OZ=C

o...-,I \\ I'-_/

y

i

Analysis of the compound Th2Al

In the course of research on thorium-aluminiumcompounds, which are important for their getteringproperties, the structure of Th2Al was analysed 9).This is an example of a fairly simple "trial and error"analysis, calling for no Fourier syntheses.In this case the unit cell (again with tetragonal

symmetry) contained four aluminium and eightthorium atoms. On grounds of crystal symmetry,the aluminium atoms could immediately be assignedto special positions in the cell, as was done for allatoms in the first example. Itwas not immediatelyclear where the eight thorium atoms should belocated. The task of determining the 24 coordinatesof these atoms was fortunately simplified by the factthat the symmetry severely limited the mimher ofpossibilities, inasmuch as a choice of one coordinateestablished the other 23.The procedure thereafter was as follows. Various

values of this coordinate were chosen, the reflectionintensities were calculated with the models producedand the results were compared with the observedintensities. In this way the structure was determinedby trial and error.Here, too, the structure found threw light on to

the other properties of the substance. The structurecontains fairly large tetrahedral interstices (seejig. Ba and b). These interstices may be supposed to

9) See also P. B. Braun and J. H. N. van Vught, Acta cryst. 8,246, 1955.

OTho AI

_X

2587

bFig. 8. The unit crystal cell of Th2Al, a substance 'with gettering properties. The thoriumatoms form tetrahedrons, a number of which are shown. Absorbed gas atoms or ions takeup positions in the interstices of these tetrahedrons. a) Projected positions of the atomslooking along the c axis (5.86 Á). The levels of the various atoms (z) are given in fractionsof the c axis. The x and y directions are those of the a and b axes, respectively (both 7.62Á).b) Perspective view of unit cell, showing atomic positions. The x, y and z directions areagain the a, band c axes.

1960/61, No. 4 DETERMINATION OF CRYSTAL STRUCTURES 135

have some connection with the gettering propertiesof the substance. This supposition was later con-firmed by nuclear magnetic resonance measure-ments 10)and by neutron diffraction analysis, fromwhich it was possible to demonstrate the presenceof gas atoms or ions in:these interstices.

Analysis of the compound Y-Ba2Zn2Fe12III022

As our last example we shall take the analysis ofà highly complex structure. Y-Ba2Zn2Fe12III022is asubstance from the class of ceramic magneticmaterials which have been given the collective name"ferroxplana" 11). These materials, whose propertiesresemble those of the familiar ferroxcube materials,can he used up to even higher frequencies than thelatter (>100 Mc/s)... .The fact that the unit cell in this case contains114 atoms, viz. 6 barium, 36 iron, 6 zinc and 66 oxy-gen atoms, makes it evident that this analysis wasa great deal more difficult than the two describedabove. The following outline of the analysis will givea good general picture of how such a complicatedstructure can he tackled.

One could not start on such a structure if it werenot for the knowledge gained of simpler relatedstructures. In this case, for example, we assumedthat parts of the structure must resemble _thestructure of spinel P].

With the aid of Debye-Soherrer patterns, Lauepatterns and rotation photographs (the first ob-tained with an X-ray diffractometer) it was foundthat the crystal is hexagonal and that the unit cellhas one very long edge (c axis, 4.3.6Á) and two shortedges (a and b axes, 5.9 Á).

Our first object was to find the pOSItIOnof theheaviest atoms, barium, iron and zinc. Thesecontribute most to the scattering and thereforedominate the intensity pattern of the reflections.For this reason the position of such atoms must be

.' .accurately known. Only then is there any sense inlooking for the sites of the lighter atoms. At thisstage, however, no distinction could be madebetween iron and zinc atoms, the difference in theirscattering power being relatively small.

It was assumed, from analogies and other indica-tions, that the structure concerned would be one oflayers perpendicular to the hexagonal axis, con-

10) See D. J. Kroon, Nuclear magnetic resonance, Philips tech.Rev. 21, 286-299, 1959/60 (No. 10), in particular page 297.

11) See P. B. Braun, The crystal structures of a new group offerromagnetic compounds, Philips Res. Repts. 12, 491-548,1957, and G. H. Jonker, H. P. J. Wijn and P. B. Braun,Philips tech. Rev. 18, 145-154, 1956/57.

12) Cf. E. J. W. Verwey, P. W. Haaijman and E. L. Heilmann,Philips tech. Rev. 9, 185, 1947/48.

sisting mainly of closely packed oxygen and bariumatoms, most of the other atoms being in the inter-stices. First of all we tried to establish in whichlayers the barium atoms occurred. To do this it wassufficient to investigate a one-dimensional projectionof the unit cell perpendicular to the hexagonal axis.The projection of the structure on to a plane wasdetermined at a later stage, and finally the three-dimensional structure.

w

1

·1"

oL___ -===~==~==~_pw 2589

Fig. 9. Patterson plot of a one-dimensional Patterson synthesisP(w) carried out with reflections from Y-Ba2Zn2Fe12III022'The10 direction is that of the c axis. The various peaks provideinformation on the projections of the interatomie distances onthe c axis. The peak at 3.2 Á indicated a projected spacing ofthat amount hetween harium atoms. This indication made itpossible to build the first, provisional model.

A one-dimensional Patterson synthesis providedinformation on the projected distances between theatoms along the hexagonal axis (fig. 9). The largepeak at 3.2 Á was taken as an indication of theprojected spacing between the heavy barium atoms,11 to the c axis, Knowledge of this spacing (howeverinaccurate due to the width of the peak) decided thechoice between a number of models already drawnup on the basis of analogies. With the model thusobtained we set out to calculate the phases of thereflections.

This model represented, of course, a very roughstructure, devoid of detail: all the light atoms andeven part of the iron or zinc atoms hadbeen dis-regarded. What is more, it was still only a proj ection.Using this incomplete model we determined thephases of 15 reflections and then carried out aFourier synthesis. The resultant picture contained,

136 PHILlPS TECHNICAL REVIEW VOLUME 22

D

0 -0C) 0

20

U 00 c:::::::>

0

Fe.....Z=o ...

2590

Fig. 10 Fig. 11

Fig. 10. Result of a one-dimensional Fourier synthesis, obtained from the reflections from Y-B~Zn2Fe12III022'The curve representsthe variation of electron density (in electrons per lingström) in one sixth of the unit cell projected on to the c axis (z direction).The positions of the various projected atoms are denoted by their chemical symbols. This concluded the first stage of the analysis,in which only the projection on the c axis was considered. In order to reach this result, however, it was necessary to make manytrials to determine the location of the iron (or zinc) atom, the peak of which is just perceptible beside the large peak for thebarium atom. The next stage in the investigation is illustrated by fig. 11.

Fig. 11. Map of a two-dimensional Fourier synthesis, obtained from the reflections from Y-Ba2Zn2Fe12III022'The content of onesixth of the unit cell is projected on to a plane. The contours shown represent lines of equal electron density. The "peaks" indicatethe presence of atoms, denoted by their chemical symbols. The small peaks in the map are due to unavoidable experimentalerrors. The crosses are centres of symmetry. The z direction represents the c axis. The relation of the map to the projection offig. 10 is seen directly simply by projeering the atoms on to the c axis. (It is only necessary to determine the one-sixth of theunit cellshown, because the rest of the unit cell can be obtained by inversion operations with respect to the centres of symmetry.)

as .we had hoped, numerous indications regardingthe possible situations -of the other atoms. Thisenabled us to venture on to new models, whichwere successively supplemented with more of theiron atoms still unused. When devising these modelswemade repeated checks with the Patterson synthesis(as we did on several occasions later) to ensure thatthe models chosen were not in conflict with thePatterson plot.

The model containing all the iron atoms was agood step forward, but still not sufficient to allow

oÓ

z

I

us to distinguish between the iron and the zinc atomsand to find sites for the light oxygen atoms. We hadthe impression that this was because one of the ironatoms was not yet on its proper site. By analogywith the structures of other similar materials, wehad allocated it a position in the same plane as thebarium atoms. Various other positions were tried,at first with little success. Finally it was found thatthe answer was to place this iron atom just outsidethe plane containing the barium atoms. After thisit was a fairly straightforward procedure to complete

o

Q

_~O~20

o o

o

2Fe

o

1960/61, No. 4 DETERMINATION OF CRYSTAL STRUCTURES

the structure determination and extend it into twoand three dimensions, thereby localizing the zincand oxygen atoms. It is interesting to note that thezinc atoms and some of the iron atoms were foundto compete for the same sites (exactly as in the case

of the manganese and aluminium atoms III

Alo.s9Mnl.n). In this way, then, the final structurewas arrived at step by step. Figures 10, 11 and 12mark the three most important steps of the deter-mination.

Fig. 12

5

The result of a one-dimensionalFourier synthesis (projection on thec axis), carried out after all therequired phases had been calculated,is shown in fig. 10. Note the smallpeak beside the large peak of thebarium atom: this is the iron atomthat caused so much trouble. Atwo-dimensional Fourier synthesis- obtained analogously with the aidof two-dimensional models and thephases calculated on the basis of thesemodels - gives the electron densityof the structure proj ected on to a plane(fig. 11). (Projection of the peaks in thisfigure on to the c axis again producesthe one-dimensional projection offig. 10.) Finally, fig. 12 illustrates thethree-dimensional structure found.Looking along the a axis we canrecognize, between z = 0 and z = c/6,the projection given in fig. 11.

Attention may be called to someof the more important features ofthe structure thus determined. Theiron atoms are located in octahedralinterstices (atom C in fig. 12) or intetrahedral interstices (atom B infig. 12). Some of the tetrahedral

2591

Fig. 12. Three-dimensional model of part ofthe unit cell of Y-Ba2Zn2Fel2III022. Thecoloured spheres indicate the positions of thevarious atoms: green = barium atoms, red =iron atoms in octahedral interstices, blue =iron or zinc atoms in tetrahedral interstices,yellow = oxygen atoms. The long c axis runsin the vertical (z) direction. A projection ofthe cell between z = 0 and z = c/6 lookingalong the a. axis (x direction) produces themap of fig. 11. In this three-dimensionalrepresentation it is possible to distinguishlayers consisting of close-packed oxygen andbarium atoms. The iron or zinc atoms arecontained in certain of the oxygen interstices.Other important features of the structure arethe presence of centres of symmetry (shownonly at A, but others shown by X in fig. 11)and of three 3-fold axes parallel with thec axis (not indicated). S denotes a blockpossessing the same structure as spinel. Thefact that the interstices may be surroundedby either four or six oxygen atoms (tetra-hedral or octahedral interstices) is clearly tobe seen at Band C, respectively. B is also theiron (or zinc) atom which, as mentioned inthe text, caused such trouble.

137

138 PHILlPS TECHNICAL REVIEW VOLUME 22

interstices are occupied by zinc atoms instead ofiron atoms. Further, at either side of centres ofsymmetry (such as A in fig. 12) barium atoms arefound which are relatively close together and arelocated in adjacent layers. (This had already beenestablished, it may he recalled, from the result of th~one-dimensional Patterson synthesis in fig. 9.) Owingto the proximity of these "large" atoms, the ironatom (or zinc atom) B is "pushed aside" slightly, sothat this atom lies outside the plane, perpendicularto the c axis, through the layer of barium atoms (this,too, had emerged at an earlier stage, see fig.IO). 13)

The knowledge gained of the structure has beenused for estimating the magnetic interactionsbetween the various iron atoms, as described in thisjournal some years ago 11). It was found that all ironatoms on tetrahedral sites have parallel orientedmagnetic moments, while those of the iron atoms onoctahedral sites are for the most part anti-parallel.Such a distribution of the magnetic orientationsexplains the low magnetic saturation of this sub-stance.Another investigation concerned the property

which this substance shares in common with othermaterials of the "ferroxplana" group, namely theexistence of a preferred plane of magnetization. Inthis plane the magnetization is fairly free to rotate,enabling these substances to be used as a "soft"

13) Afull descriptionisnot possible in the compass of this article.No mention is made, for example, of the method of leastsquares, of difference Fourier synthesis, etc. A full descrip-tion will be found in the article in Philips Research Reportsquoted under 11).

magnetic material in rapidly alternating magneticfields. The magnetic moments are tightly bound tothe plane perpendicular to the c axis. Various cal-culations have been made to explain this effect, butthey cannot be dealt with here 14). It will suffice toremark that, as illustrated by the above "casehistories", structure determinations can evidentlylead to a better understanding of the properties ofthe substance investigated.

14) See § 39 in "Ferrites" by J. Smit and H. P. J. Wijn, PhilipsTechnical Library, 1959. .

Summary. The principles and some applications of the X-raydetermination of crystal structures are discussed. The electrondistribution in a crystal can be described as the sum of anumber of Fourier components, here termed "density waves".The diffraction by a crystal can be regarded as due to thescattering causedby these density waves. When a density waveis irradiated by X-rays, a perceptible reflection"occurs only ata particular angle of incidence. The resultant reflections makeit possible to determine the amplitude, wavelength and direc=tion of these density waves. It then remains to determine thephase of the waves in order to calculate the electron distribu-tion in a crystal by means of Fourier synthesis. The phases arefound by successiveapproximation, on the basis of provisionalmodels of the structure. Various means of arriving at suchmodels are discussed, including the Patterson projection, whichprovides information on interatomie distances. Finally, variousstructure analyses carried out in the Philips Research Labora-tories are described. Analysis of the structure of the compoundAlo.s9Mnl'11made it possible to infer that the manganese atomsare present in two non-equivalent sites in the unit cell and thattheir magnetic moments at these sites are oppositely oriented.The structure of Th2AIwas found to contain fairly large inter-stices, which explained the gettering properties of this sub-stance. The structure of Y-B~Zn2FeI2IIr022' a ceramic mag-netic material (ferroxplana), proved to be exceptionally compli-cated (114 atoms in the unit cell). The successful analysisof its structure contributed to a deeper understanding of themagnetic properties of this substance.

dihydrotachysterol , (Rec. Trav. chim. Pays-Bas 78, 659-662, 1959, No. 8).

The results are presented of investigation on pre-paring dihydrotachysterol , from dihydrovitaminsD2-I and D2-II.

2771: E. J. W. Verwey: Synthetische keramiek(Chem. Weekblad 55, 553-556,1959, No. 41).(Synthetic ceramics; in Dutch.)

In the last decennia, especially in the last 10years, there has been a rapid development of a newbranch of ceramics, called here "synthetic ceramics",characterized by the use of synthetic starting mate-rials and by the circumstance that the final compo-sition corresponds to compound materials synthe-tized purposely in view of specific physical properties.These materials are mainly appliedin high-frequencyelectrical technique. They comprise insulators,semiconductors and magnetic materials .. A surveyis given of this branch of ceramics. A number ofmaterials developed in the Philips laboratories arediscussed in some detail. .

f r PH/UPS' r.{ f'JE .1960/61, No. 4 () .U ./ U ",;:H! t !/{..' D 139

.J ; Ij Lir 'itnRI E K ft?ABSTRACTS OF RECENT SCIENTIFIC PUBLICATIONS BY THE STAFF OF

N.V. PHILIPS' GLOEILAMPENFABRIEKEN

Reprints of these papers not marked with an asterisk * can be obtained free of chargeupon application to the Philips Research Laboratories, Eindhoven, The Netherlands,where a limited number of reprints are available for distribution.

2767: M. Koedam: Sputtering of copper singlecrystals bombarded with monoenergetic ionsof low' energy (50-350 eV) (Physica 25,742-744, 1959, No. 8).

Experiments on the sputtering of copper atomsejected from Cu single-crystal surfaces of variousorientations bombarded with rare-gas ions at normalincidence show an anisotropy in the directionaldistribution. The ejection patterns in the case of abombardment of Cu (Ill) and (110) surfaces aregiven.

The number of copper atoms ejected per incidention in the normal (110) directionis given as a functionof the ion energy for a copper (110) surface bombardedwith rare-gas ions at perpendicular incidence. Thenumber varies from 0.01 at 75 eV to about 0.04 at350 eV, depending on the bombarding ion and itsenergy. For comparison the sputtering yield of silveris given as a function of the ion energy. The silversurface was bombarded with normally incidentHe+, Ne+, Ar+ and Kr+ ions, with energies ranging'from 50 to 250 eV. The yield varies from 0.1 at50 eV to about 1.5 at 250 eV ion energy.

2768: A. Venema: The measurement of pumpspeed (Le Vide 14, 113-120, 1959, No. 81;in French and in English).

Discussion of the various factors, in particular thedefinition and measurement of pressure, involvedin the measurement of pump speeds at low pressures.A number of conclusions are reached concerning thelocation and nature of the pressure gauge to be usedin order to obtain meaningful results.

2769: K. H. Hanewald: Analysis of fat solublevitamins, IV. Discussion of the chemicalroutine determination of vitamin D (Rec.Trav. chim. Pays-Bas 78, 604-621, 1959,No.8).

Details of the already published procedure for thechemical routine determination of vitamin D havebeen investigated, especially the colorimetrie deter-mination with antimony trichloride and the elimi-nation of tachysterol by addition of maleic anhy-dride.

2770: P. Westerhof and J. A. Keverling Buisman:Investigations on sterols, XII. The conver-sion of dihydrovitamin D2-I and D2-II into

2772: J. te Winkel: Drift transistor (Electronic and, Radio Engr. 36, 280-288, 1959, No. 8).

Equivalent circuits for a drift transistor aredeveloped starting from a set of parameters derivedfrom the physical principles underlying the device.It is shown what approximations are possible iflimited frequency ranges or large values of thedrift field are considered. Further simplificationsare obtained from the introduetion of suitablychosen frequency parameters. The resulting equiva-lent circuits appear to be simply related to thosecommonly used for a normal alloy transistor. Theform is the same and the values of the circuitelements can be found by means of a number ofmultiplying factors that depend on the drift fieldonly. These are given in graphical form.

2773: C. Jouwersma: Die Diffusion von Wasser inKunststoffe (Chem. Ing. Technik 31,652-658,J959, No. 10). (The diffusion of water inplastics; in German.)

The application of classical diffusion theoryto the water uptake of plastics is described. Inthe cases investigated experimentally, it was foundthat Fick's law was obeyed. In such cases, the

140 PHILlPS TECHNICAL REVIEW VOLUME 22

variables - viz. form and size of specimen, natureof surrounding medium, time and temperature, andsolubility and diffusion coefficients of the material-can be separated. This enables one to make exactpredictions concerning the water uptake of speci-mens of any form and size provided the characteris-tic constants of the plastic material in question areknown.

2774: P. Penning and G. de Wind: Plastic creep ofgermanium single crystals in bending (Phy-sica 25, 765-774, 1959, No. 9).

The vertical displacement of the centre of a barsupported on two knife-edges and loaded in thecentre, caused by plastic How, is measured as afunction of time. First the creep rate increasesgradually <and then becomes constant. The param-eters describing the behaviour in these two regionshave been determined as a function of the appliedstress, for crystals of low and high dislocation den-sities and for crystals doped with oxygen.

2775: H. G. van Bueren: Theory of creep of ger-manium crystals (Physica 25, 775-791, 1959,No.9) .•~... ~t;

To explain the shape of the creep curves of ger-manium single crystals loaded in tension and inbending, a simple kinetic model is proposed, in whichthe dislocations are generated by (surface) sourcesand move with a uniform velocity over their glideplanes. In this model a quantitative interpreta-tion of the parameters of the creep curve in termsof the velocity of the dislocations, the incubationtime of the sources and the density of the sourcesis possible. From the observations at "high" stresslevels the velocity of dislocations in the germaniumlattice can be determined; from those at "low"stress levels the rate of generation of the dislocationsfrom the sources. The observed stress and tempera-ture dependence of the creep process leads to similardependences of incubation time and velocity. Thesedependences are used to form a quantitative theoryof dislocation production and motion in the ger-manium lattice. This theory is shown to reflectsemi-quantitatively various observed peculiaritiesof the creep phenomenon. Th~ influence of otherdislocations and of oxygen as an impurity on theelementary creep process can now also be qualita-tively understood.

2776: J. S. C. Wessels: Dinitrophenol as a catalystof photosynthetic phosphorylation (Biochim.biophys. Acta 36, 264.-265, 1959, No. I).

The insensitivity of photosynthetic phosphoryla-tion to dinitrophenol shows that the mechanismsof photosynthetic and respiratory generation of

ATP may be quite different. The present notereports that, surprisingly enough, DNP is able tocatalyse the generation of ATP by illuminatedchloroplasts. In this respect it is more active thanFMN but less active. than vitamin K3'2777: H. Koelmans, J. J. Engelsman and P. S.

Admiraal: Low-temperature phase transi-tions in ,B-Ca3(PÛ4)2 and related compounds(Phys. Chem. Solids 11, 172-173, 1959,No. 1/2).

On measuring the temperature dependence ofthe luminescence of ,B-Ca3(P04)2 activated withdivalent Sn, strong hysteresis effects' were found<.These effects are interpreted as being due to phasetransitions occurring at about 20°C and at about- 40 °C.The presence of these two phase transitionshas been confirmed calorimetrically. A numberof modified Sr-orthophosphates, which have astructure closely related to that of ,B-Ca3(P04)2'show similar behaviour.

2778: J. Davidse: Transmission of colour televisionsignals (T. Ned. Radiogenootschap 24, 255-272, 1959, No. 5).

The paper discusses the transmission of colour-télëvision signals according to the NTSC system.The choice ofthe chrominance signals, of their band-widths and of the subcarrier frequency is discussed.The consequences of the method of gamma cor-rection and of dcviations from the constant-lumi-nance principle are considered. The significance ofthe statistics of the chrominance signal is pointedout. This article has since been published in I.R.E.Trans. on Broadcasting BC-6, 3, Sept. 1960.

2779: A. G. van Doorn: Studio equipment forcolour television (T. Ned. Radiogenootschap24, 237-253, 1959, No. 5).

This paper gives a broad survey of the equipmentconstructed in the Philips Research' Laboratoriesfor the generation of colour-television signals andthe testing of the different pick-up systems. Itdescribes three colour cameras, one using imageorthicons as pick-up tubes, while in the <other twoexperimental vidicons are used. Further the principleof the flying-spot scanner is described, as well asthe colour-film camera. The special problems en-countered in designing simultaneous pick-up systemsand concerning colour-image registration, signaluniformity and gamma correction are discussedin more detail. In conclusion more is said about thedifferent pick-up tubes and their use in colour-television cameras, their sensitivity, picture qualityand overall performance.