APRIL 1952 293

THE STRUCTURE OF·GLASS·

.by' J. M. STEVELS. 666.1 :539.213:1

Although the material "glass" has now been knownfor some thousands ofyears, the variationsin which it may be obtained a~e nOJ by any means exhausted. This is evident from the fact thatduring the last decades many kinds of glass with new properties have been developed and foundapplication in various technical direcdons. For the man of science it is gratifying to see thatnow, after centuries of empiric rule in this domain, in many cases theoretical conceptions asto the structure of glass are serving as a guide to the development of new materials.

Introduetion

For many uses of glass, particularly in thefield of electrotechnology, the requirements whichhave to be met nowadays go far beyond the proper-ties that are usually to be found in normal kinds ofglass. To illustrate this we have only to take afew cases occurring in the field of activity of ourlaboratories. For radar transmitting valves a glassis required which shows no excessive dielectriclosses in an alternating field with frequencies inthe order of 1010 cis (3-cm waves). For the trans-mitting valves used for normal radio broadcastingat frequencies round about 106 cis (300 metres)the glass must likewise not have too high dielectriclosses, whilst it must also have a low softeningpoint for easy manufacture, The developmen,t. ofthe cathode-ray tubes for television receivers-particularly involves special glass-technical prob-lems. For the small projection-television tubes,in which electrons are accelerated by voltages of25 kilovolts or higher, a glass is required whichis able to withstand lengthy bombardment bythe electrons and by X-rays without being subjectto discoloration.

It was fortunate that at the moment when suchvery special requirements as these were placedbefore the glass technologist some insight had alreadybeen obtained into the structure of glass in general.This suggested the lines. on which further workcould be done to reach the desired 'results.

The foundations for our present-day knowledge ofthe structure of glass were laid by Zacharias en 1)',who in 1932 wrote a classical article on the subject.The theories he expounded have already been setforth in this journal ~), so that it will suffice to recallthem here quite briefly .We shall then proceed to dealwith the refinements which Zachariasen's theoryhas subsequently undergone on various points, and

1) W. H. Zachariasen, J. Amer. Chem:Soc. 54, 3841, 1932.2) J. M. Stevels, Philips Techn. Rev. 8, 231-237, 1946.

which are due mainly to the work of Warren andWeyl in the U.S.A. and of Dietzel and Smekalin Germany. It is due to these refinements in par-ticular that we are not only able to grasp a numberof peculiarities in the already known physicalproperties of glass but are now better preparedto cope with the new requirements of technicalscience.

Zachariasen's theory

There are a number of oxides, called glass-formingoxides, which may occur in the vitreous as wellas in the crystalline state (Si02, B203, P205)'According to Za chariasen, in the crystallineand in the vitreous state these oxides are built upof the same elements, namely polyhedrons (tetra-hedrons or triangles) of oxygen ions with thehighly. charged cations Si4+, B3+, p5+ at theircentres. The only difference is that in the crys-talline state these polyhedrons are arrangedregular-ly, whereas in the vitreous state they are not. Aschematic representation of this is given in fig. 1.

For the network of oxygen polyhedrons, tooccur in these two forms it is necessary that thestructure of the oxide in the crystallinestate satisfies a number. of conditions given byZa ch ar iase n, which (see the article quoted infootnote 2)) involve the following.1. Every oxygen ion must be bound to not more

than two positive ions which must be highlycharged and small.

2. The number of oxygen, ions which surroundsuch a positive ion (forming a polyhedron)must be neither very large nor small' (3 or 4).

3. The oxygen.polyhedrons adjacent to each othermust have common corners (bridging oxygenions), but no common edges or faces.

4. Each 'polyhedron must have at leastthree oxygenions in common with neighbouring polyhedrons.

294. PHILIPS TECHNICAL REVIEW VOL. 13, No. 10

• Cationo Oxygen ion 68469

Fig. 1. Two-dimensional representation a) of a crystallinelattice A203 (A is a cation) and b) the corresponding networkin the vitreous state.

We shall not enter into' the arguments on whichthese rules have been formulatèd. Suffice it to saythat oxides which in the crystalline state satisfythese conditions have a very open structure,so that the polyhedrons need not necessarilyarrange themselves according to a periodic patternwhen, upon cooling of the melt, the solid phaseis formed.

The structure of the many glasses that can bemade by fusing these glass-forming oxides togetherwith a large number of metallic oxides, such asCaO, BaO, PbO, Na20, is likewise described by thetheory of Zachariasen. While the metal ions finda place in the interstices of the open network justmentioned, the added oxygen ions are taken upthrough a number of oxygen bridges in the networkbeing broken, each bridging' oxygen ion beingreplaced'by two non-bridging oxygen ions. Obviouslyany continued change of tills nature will greatly in-fluence the properties of the glass.

Fig. 2. ia-a diagrammatié representation of thestructure of such a glass.Actually, of.course, it is not each metal ion that

seeks a place in an interstice of the network. It isbetter to say !hat while the melt is solidifying theoxygen chains arrange. themselves around the metalions. Thc presence of these ions modifies to someextent the form that the network finally assumes,and for that reason they have been given the nameof network modifiers. The ions occurring inthe centres of the oxygen polyhedrons, and which,therefore, together with the oxygen ions actuallyform the network, are called network formers.

This simple theory of the structure of glasses

was, verified about, 1938 with the aid of X-raydiffraction photographs; mainly by Warren andhis associates 3).

We shall now proceed to discuss some of theaforementioned refinements of the theory that havebeen made in' the course of the last ten years.

The structure of borate glasses

It willhe obvious that the addition of metallicoxides to a glass-forming oxide cannot be continuedat will. It has already been pointed out that thebreaking down of oxygen bridges greatly in-fluences the properties of a glass, and one canimagine that if this is carried too far the typicalvitreous structure of coherent tetrahedrons ortriangles 'ultimately becomes unstable. It can readilybe understood that a network completely spatiallybonded is no longer possible as soon as the numberof contact points (bridging oxygen ions) per polyhe-dron, denoted by Y, becomes less than two 4)."Islands" are then formed, which in themselvesmay .consist of a rather l~rge number of poly-hedrons. The smàller the value of Y, the smallerare the islands. For Y = 1 these islands averagetwo polyhedrons, whilst for Y= 0 the "structure"

6R~7r

• Network-forming ion® Network-modifying iono Bridging oxygen iono Non-bridging oxygen ion'

Fig. 2. Two-dimensional representation of the network of aglass containing, in addition to oxygen ions, both network-forming and various network-modifying iOIlS.Non-bridgingoxygen ions occur.

3) B. E. Warren and J. Bi sco e, J. Amer. Ceram. Soc. 18,49, 1935; J. Biscoe and B. E. Warren, J. Amer.Ceram. Soc. 21, ,287, 1938.

4) J. M. Stevels, J. Soc. Glass Techn. 30, 31, 194·6;Ned. T.Natuurkunde 12, 257, 1946.

APRIL 1952 .STRUCTURE OF GLASS 295

consists of isolated polyhedrons. Obviously thestructures with small, Y values will have a strongtendency to order themselves, thus readily changinginto the crystalline state.

The number of contact points, per polyhedron, Y,can quite easily he calculated from the compositionof the glass. In this connection the composition ischaracterized by the ratio R of the total numberof oxygen ions to the total number of network-forming ions. For glasses with tetrahedrons aselements, i.e. with network-forming ions havinga coordination number of 4 (silicate and phosphateglasses), the relation is 5):

y= 8 - 2R,

whilst for glasses with triangles as elements, i.e.with network-forming ions having a coordinationof 3, the rule is:

'y= 6-2R ....

Silicate glasses can, indeed, only be formed aslong as R < 3; in other words, as soon as Y < 2(i.e. as soon as islands begin to form) it is no longerpossible for the melt to solidify in the vitreousstate. With phosphate glasses it appears thatone can go a little farther in adding metallicoxides, as far as R = 3.2. Then Y = 1.6, whichmeans that it is possible to reach the vitreous statenotwithstanding the occurrence of [not too small)islands.

With borate glasses, considering that the B203structure consists of triangles, one would expectthe addition of metallic oxides to cause formationof islands (Y<2) as soon as R>2. With borium-containing glasses, however, a peculiar complication'arises, in that in such glasses metallic oxides mayhe taken up according to a mechanism differingsomewhat from that described above. When metallicoxides are added to B203 - for instance Na20-the Na+ ions will find a place as network modifiersbut the mechanism of bridge breaking does not

. take place. The excess of added oxygen is taken upowing. to the property of the- n:~+ion being ableto occur in the centre of an oxygen triangle butalso in the centre of an oxygen tetrahedron.Thus the network is then built up from both oxygentriangl~s and oxygen tetrahedrons, while thereis not a single non-bridging oxygen ion. Such astructure is represented in fig. 3.

5) Denoting the average number of non-bridging oxygenions per polyhedron by X and the total number of oxygenions per polyhedron (the coordination number} by Z, then,as may be verified by simply counting the ions, X+ Y=Zand X+!Y=R, from which it follows that Y=2Z-2R.

It is remarkable that this process of taking upoxygen, whereby a change takes place in the coor-dination number for some of the Ba+ ions and thenetwork gains more and more in strength, continues'until a certain concentration is reached, which, forthe system Na20-B203, ,is 18 mol. % Na20. Withgreater' concentrations of Na20 the previouslydescribed bridge-breaking mechanism comes intoaction again, non-bridging oxygen .ions then beingformed., These ranges of concentrations have beennamed respectively the accumulation regionand the destruction r egion .

(1)

(2)

~Na

00• B

68471

Fig. ,3. Two-dimensional representation of a borate glass withsmall Na20 content. This is characterized by the absence ofnon-bridging oxygen ions. (Bê+ions intriangular or tetrahedralsurroundings are represented in the diagram by' a coordina-tion of 3 and 4 respectively in the plane of the drawing.)

The 'state of affairs outlined here implies thatin such a borate glass relatively more metallicoxides can be taken up, before island formationarises. In "the accumulation region, where nonon-bridging oxygen ions occur, Yalways equals2R (cf. footnote 5)), so tb-at the average number ofcontact points per polyhedron increases. withincreasing R! In the destructien region the ratioof the munher oftriangles to'.the' number of,tetra-hedrons remains constant, such thät the averagecoordination number of the B3+ion Z = 3.22.In this region, therefore, the relation (cf. footnote 5)is:

Y= 6,44-2R. (3)

'/ " " .Island-forming (Y <2) will then not 'take placeuntil R > 2.22. Actually it appears that mostborates may become ~itreous up to R = 2.4,so that .he;e again, just as in the case of phosphate

,,-------~---------------------------~-

296 ,I;'HILl~S TECHNICAL REVIEW VOL. 13, No. 10

glasses, a small degree of island-formation is nohindrance to vitrification.The foregoing is illustrated graphically in jig. 4.Of particular importance in practice are the

consequences that the changing of the coordination'number and the accompanying s,trengtheningof the network have for the physical propertiesof this, group of glasses. By way of example, injig. 5 the coefficient of thermal expansion. of thepure sodium-borate glasses is plotted as a function

4Y \

r \V\\\ ~i,P

__"

'\ \\(a) \ .

\ I

\~~~ \ir\ \\ \\\ \

\

, Completespatialcoherence

t

2Beginning of

+- islandformation

Islands of; on+-- anaveragc,two

polyhedrons

o1,5 2,5

Isolated4 +-- polyhedrons3 3,5

~RFig, 4" Relation between Y, the average number of bridgingoxygenions per polyhedron, and R, the total number of oxygenions divided"by the total number of network-forming ions. Themore metallic oxides are added to the glass-formingoxide, thegreater is the value of R. The line Si,P applies for a network oftetrahedrons (eq. 1), the broken line (B) for a network oftriangles (eq. 2). 'From Y = 2 onwards island-formation occurs. In the case

of silicate glasses this indicates the limit to which R can heraised without dcvitrifieation occurring (point I). In phosphateglasses the vitreous state is still tenable up to Y = 1.6, i.e.R = 3.2 (point IJ).In the case of borate glasses the addition of metallic oxide

is at first accompanied by a transition of B3+ions from thecoordination number 3 to the number 4; then Y = 2R (begin-ning of the sharply bent, fully-drawn line B). When the coor-dination number has reached the average value Z=3.22 itremains constant and Y drops with increasing R according tocq. (3). Island formation (Y=2) then begins at R = 2.22, butfor most borate glasses the vitreous state appears to be stillpossible up to R'= 2.4. (point Ill).

2

of their composition. This curve shows a rmmmumjust at that composirion where, according to theforegoing . considerations, the network has thestrongest structure.Something' similar is found in the case of boro-

silicate glasses. On the boundary line between theaccumulation region and the destruction region(jig. 6) are the glasses which, compared with other

.'

-, ..

'\ -If\.

"\ ./~

<,----7120

100

80

60

40

20

oo 20 ·25 30 35'~ % Na20 68473,

Fig. 5. The expansion coefficient of pure sodium-borate glassesas a function of the Na20 content, expressed in weight %.

10· 155

borosilicate glasses, are characterized by a maximumstrength of structure (small expansion coefficientand high softening point), for example the "Pyrex"glasses.The changing of the coordination number of the

B3+ ion is therefore responsible for the fact that,under suitably chosen conditions, the incorporationin glass of B203, which itself has a very high ex-pansion coefficient and very readily melts, resultsin a reduction of the expansion coeffiicent and araising of the softening point. Various other

68474

Fig. 6. PHase diagram of the system (MI MII)O·B203-Si02,

where MI and MIl represent respectively a monovalent and abivalent metal, which may occur in any proportions. Thediagram can be divided into an accumulation region and adestruction region.

APRIL 1952 STRUCTUREOF GLASSe297

properties of the glass are likewise influenced bythe structural change described, as for Instance thedielectric losses. This will be discussed in greaterdetail in another article to be published shortlyin this journal.

The conceptions of network-forming and network-modifying ions

Zachariasen thought that the positive ionscould be divided into two groups, which in the fore-going have been denoted as network formers andnetwork modifiers, but it has meanwhile becomeapparent that this division does not hold in all cases.It is now known that there arc a large number ofions which may occur in glass in both forms, andoften simultaneously. This means that in glassthere are some ions of a certain type which have 4oxygen ions surrounding them, thus being situatedin the centre of the tetrahedrons forming the net-work typical for glass, while other ions of that typeare surrounded by a larger number of oxygen ions.In some cases the positon of the "equilibrium" be-tween the two forms may be roughly deiel'mined bythe col 0u r of the glass, as is the case, for instance,with the nickel ion. Ni2+ions may occur in a glassmainly as network formers, in which case the glasshas a purple colour; under other circumstances theseNi2+ions mainly occur as network modifiers, theglass then being yellow. Such differences in colour incases where the coordination number is changedhave been found, for example, with Cu2+, C02+,Fe2+, Fe3+, Mn2+, Mn3+ and UH. But it is also pos-sible to detect these changes in the coordinationnumber among non-colouring ions, by a methodwhich has recently heen indicated 6) and which willbe discussed in our next article,

Thc "equilibrium" between the forms of coordi-nation depends not only upon a number of externalfactors (temperature and furnace atmosphere whenmaking the glass, and the rate of cooling) but alsoto a large extent upon the quantities of the differentions contained in the glass. The simple theory ofZachariasen could not "furnish any explanationfor this, but it has been made comprehensible bymeans of a "colDpetition principle". In general, thesmall, highly charged ions which are capable ofattracting the oxygen ions close to them, ~nd strong-ly binding them, will easily surround themselveswith only four oxygen ions (or three in the case ofB3+). The larger and less charged cations are thensurrounded by a larger number of oxygen ions, '~o

6) J. M. Stevels, Venes et Rëfractnires2, 2, 194,8.

which they are less strongly bound. In principle;however, also these latter cations may be surroundedby only four oxygen ions, thus entering into com-petition with the small, highly charged ions, inwhich they may be successful, for instance, whenrelatively few oxygen ions are present.

Various investigators have attempted to expressthis "competition capacity" ofthe ions numerically.A suitable measure has been found to he the' "fieldstrength" of the ion at the centre of an adjacentoxygen ion, z/a2, where z is the charge of the ionand a the distance between the centres of the twoadjacent ions 7). When the ions are arranged in theorder of their calculated field strength (see table I)their sequence gives an idea of the preference thatthe various ions have for occurring either as net-work formers or as network modifiers. When dif-ferent cations occur in a glass simultaneously, thosewith the highest z/a2 value will preferably occupythe network-forming positions (smallest coordina-tion numbers), while those with the" lowest :z/a2value show a preference for the ,network-modifyingpositions (largest coordination numbers).

Table I. The'.'fieldstrength" z/et2 for a numberof cations,accordingto Dict ecl"};z = chargeof the ion, expressedinelementary charges; a == distance (in Angstrom)from thecentre of the ion to the centreof an adjacent oxygenion. (Ifthe cationis rather large it then no longerfitsin the intersticeof a tetrahedronformed by four oxygen ions, and for thisreason alonethe natural coordinationnumber is greater thanfour). '

~3 4 6 8

nr

p5+ 2.08B3+ 1.65 1.45Si4+ 1.57A13+ , .97 0.84,Zr4+ 0.78Be2+ 0.87Ni2+ 0.61 0.55'Zn2+ 0.59 0.53Mg2+ 0.51 0.405Ca2+ 0.35 0.33Bu2+ '. 0.24,Li+ 0.23Na+ 0.19

l'0.17

K+ 0.13

Some striking examples can be given to illustratcthis.

When silicon ions and phosphor ions enter intocompetition. with each other, as in the glass of thecomposition SiP207 (i.e. Si02.P205), from the table

7) A. Dietzel; Glastechn. Ber. 22, 4,1, 19'1.8.

.-----~-----------------~-~-_. -

, tJ

298 PHILIPS TECHNICAL REVIEW VOL. 13. No, 10

it is to be predicted th'at the phosphor ions will"win". For this glass it 'is difficult to determinedirectly with what coordination numbers the ionsSi4+ 'and p5+ occur in it. The crystalline SiP207 hasnever heen examined in this respect either, butcrystalline ZrP207, which is isomorphoush, as. ByX-ray diffraction analysis it was found that eachp5+ion ie; indeed surrounded 'by four bridging oxygenions and' each Zr4+ion by six bridging oxygenions. Since it may he assumed that the coordina-tion numbers will be the same in the vitreous stateand in the crystalline state, we have here a case'where sr+ occurs in a 'coordination of 6, i.e. the

• Si4+ion, the network former par excellence, occupiesonly a network-modifying position.The opposite effect is seen in the following exam-

ple. Of the compound 2CaO.Si02 only a crystallineform is known. This is, in conformity with theaforementioned considerations about Y and R: forfour oxygen ions there is only one network-formingion, thus R =4 and therefore, according to eq. (1),Y = O. Though this substance is built up from Si04

tetrahedrons, these are all isolated and thereforearrange themselves into a well-ordered structure,with Ca2+ions as "binder". The remarkable factis that the entirely analogous compound 2ZnO.Si02may indeed occur in the vitreous state. An explana-tion for this may find support in the fact that Zn2+stands some steps higher in table I than Ca2+. Itis therefore feasible that in the system in questionCa2+ occurs exclusively with a coordination numbersix or higher, i.e. as a network modifier, whereasunder suitably chosen conditions Zn2+ may occuralso with coordination number four, thus possiblyplaying the part of a network-forming ion. If in thecompound 2ZnO.Si02 only 16.7% of the Zn2+ionsoccur as network' formers :__ instead of writingZn2Si04 the composition can then be better writtenas ZnSj3 (Znl/3Si)04 - then the quotient R is al-ready reduced to exactly 3 and thus vitrification ispossible (Y = 2). Actually slightly more than 16.7%of the Zn2+ions will he present as network formers.Vitrificàtion in the system ZnO-Si02 continues untilroughly the composition 2.2 ZnO.Si02 is reached.The condition R < 3 can then only he satisfied if atleast 18.2% of the Zn2+ions occupy a network-forming position S).

8) Here it is tacitly assumed that the limit found in practicefor the occurrence of the vitreous silicates (R=3) wouldlikewise apply for the glasses containing Si4+ and fewZn2+ ions as network formers. A priori this need notstrictly be the case, it being possible for the limit to lie at asomewhatgreatervalue ofR (Y <2) (cf. the phosphate andborate glasses). Then smaller percentages of network-forming Zn2+ions would be sufficient to account forvitrification in the case of the compositions mentioned.

Certain barium-containing silicate glasses (theheavy barium crown glasses) have been shown tocontain a number of barium ions forming part of atypically tetrahedral formation. Thus even Ba2+ionsmay sometime play the part of network formers.

Resuming, the following advances have, thusbeen made upon the old theory. According toZachariasen's criteria Zn2+ and Ba2+ionsshould always behave as network modifiers. Thenew conception (the competition principle) makesit feasible that such ions mayalso accur asnetwork formers, and that such is more likely tobe the case the greater' the concentrations inwhich these ions are present. This is of greatpractical importance; since the addition of on~and the same ion to a glass may influence the pro-perties to a different extent (or even in the oppositedirection), depending upon the position it takes inthe network: the Mg2+ion, for instance, yields, asnetwork modifier, a contribution towards the dielec-tric losses of a glass at 106 cis, whereas as a networkformer it is harmless in this frequency range.

How the nature of the bond influences vitrification

The theory of Zachariasen has undergone aconsiderable evolution in recent years in yet an-other respect. Whereas Zachariasen never dis-cussed the nature of the bond in vitreous systemsand, moreover, regarded the elements (the polyhe-drons) as being invariable, in recent years it hasbeen pointed out, especially by German investigators,that the nature of the chemical bond in theelements is of great importance in determiningwhether a certain substance mayor may not oc-cur in the vitreous state. Sm ek a 1, to whose workthis theory is mainly to be ascribed, has indicatedthat it is feasible 9) that a condition for vitrificationis that the system must contain "mixed" bonds.By this it is meant that, in addition to directedbonding forces (homopolar bonds, which are con-fined to certain mutual "valence angles", such as,e',g., in CO2 or NHa or SiCI4), also non-directedbonding forces (heteropolar bond or Van del'Wa aIs bond) must be in action. The two kinds ofbonding forces may be united in one bonding direc-tion, such as, e.g., in the Si-O bond, which is to bedescribed as a combination of a force of the type ofa homopolar bond and one of the type of aheteropolar bond, or they may be present in differ-ent bonding directions. The latter is found to be thccase, for instance, in the vitreous selenium and in

0) A. Smekal, Nova Acta Leopoldina 11,511, 1942; workedout in more detail in Glastechn. Ber. 22, 278, 1949.

,APRIL 1952 STRUCTURE OF GLASS 299

the chain macromolecules, where in the directionof the chains- a homopolar bond prevails while thechains are mutually kept together mainly by aVan der Waals bond 10).

These considerations are of great importance be-cause they relate to all kinds of glasses, whereasZachariasen's theories apply exclusively tokinds of glass formed by inorganic oxides.

The difference between Sm ekal' s theory andthat of Zachariasen may be formulated by sayingthat the latter theory ascribes the irregular struc-ture of the network exclusively to the irregularpacking of the oxygen polyhedrons. According toSmekal' s theory, applied to the oxide glasses, thetype of bond within the polyhedrons may change, inthat the bond may bear a more homopolar or a moreheteropolar character. Consequently, therefore, in-teratomie distances in those polyhedrons maychánge, and this mayalso contribute towards theirregular structure ofthe networkin vitreous systems.

Inorganic glasses in which Zachariasen's rules donot hold

Having accepted this line of thought' as beingcorrect, one will not be surprised to find that inor- ,ganic systems exist which do not at all obey therules given by Zachariasen and nevertheless oc-cur in the vitreous state.Excluding those resembling selenium (such as

vitreous sulphur and tellurium), the earliest knownexample is the system of carbo nat es K2C03-MgC03. According to Zachariasen's rules, asapplied to the oxide CO2, there would be no ques-tion of vitrification here; one would rather expecta regular crystallattice formed by the positive metalions and negatively charged CO;-groups. It has nowbeen found, however, that the heating of a mixtureof K2C03 and MgC03 in equimolecular quantitiesdoes indeed lead to vitrification. The glass certainlyhas a strong devitrifying tendency: at 300°C it com-pletely devitrifies in an. hour, but at temperaturesbelow: 150°C the vitreous state is maintained.Quite analogous systems,' such as Na2Ca(C03)2'K2Ca(C03h, Na2Mg(C03b NaLiC03 and KLiC03,on the other hand, show no trace of vitrification.

Looking back at table I, it is seen that of all thecations in question here K+ and Mg2+ differmost in"field strength". The fact that of the systems men-tioned only K2Mg(C03h forms a glass is an indica-

10) In the light of these considerations it will he realized thattheoretically it is difficult 'to find justification' for theclassification of the ions according to Dietzel's criterion,which is based entirely upon a heteropolar bond picture.Nevertheless it has been found very useful as a heuristicand didactic principle.

tion that the condition favourable for vitrificationis created by the combination of a very weak and amuch stronger cation. It may, therefore, be so inter-preted that the greatly varying electric fieldsprevailing in the system deform the CO;- groups ina different way, thereby, according to Smekal,promoting vitrification ..

Something similar has been found with the ni-t rat e s. A mixture of equimolecular quantities ofCa(N03)2 and KN03 becomes vitreous when cooledfrom the molten state, whereas such is not the casewith the system Ca (N03)2-NaN03. Apparently thedifference in strength of the Ca2+ion and the Na+ion is not large enough for a sufficient deformationof the NO;-groups. On the other hand the systemMg(N03kKN03 would, indeed, be expected to oc-cur in the vitreous state, and this has in fact beenfound to be the case. This is not so easily proved be-cause it is difficult to obtain anhydrous Mg(N03)2in' a chemically pure state. In the procedure fol-lowed by us a mixture ofMg(N03h.4H20 was meltedin a platinum crucible (the melting point is 92°C)and then carefully heated further, thereby removingall the water contained in it. As soon as the meltbegins to give off nitrous vapour (at about 290°C)an equimolecular quantity of KN03 is added. Thehomogeneous melt of KMg(N03h thereby obtainedis quenched by decanting in droplets in liquid air.X-ray diffraction photographs showed that the pro-duct was vitreous.

With the sulphates there is a still more strikingexample. The system K2S04-MgS04 does not, in anycomposition, yield a vitreous product, notwithstand-ing the great difference in strength between theK+ and the Mg2+ions. When, however, the Mg2+ionis replaced by an ion with a still stronger field, viz.the H+ion, vitrification is possible: by. heatingKHSO 4 to just above the melting point and thenquenching by decanting onto an iron plate, a glassis obtained. At a temperature of 70°C this glass canbe drawn into threads.

Finally, a very striking confirmation of Smekal "stheory has been found with normaloxide glassesthemselves 11) -, According to what has been setforth above, in a system such as, for instance,Na20-B203 vitrification occurs as long as theamount of Na20 does not exceed a certain percen-tage corresponding to a value of RR:l2.4. The samelimit is found for the system K20-B203. Whenexamining, however, the mixed alkali borates, suchas the system Na20-K20-B203, it is found thatthere are kin~s of glass where R is much greater

11) A. W. Bastress, Glass Science Bull. 4, 133, 1946; 6, 9,1947;.6,12,1947.

" .

'lOO PHILlPS TECHNICAL REVIEW VOL. 13, No. 10

than the limit mentioned. The same phenomenonis found with the mixed alkali silicates and alkaliphosphates, such as illustrated for some systemsby the phase diagrams in figs 7 and 8. As far asthe value of R is concerned, the area of vitrificationwould be expected to be bounded in each diagramby the broken line: as a matter of fact vitrification

68475

Fi~. 7. Pha'e d iajrr.uu of the system Na20-Li20-P20.;. Thevitreous stu t e may be obtained with any compo sit.ion in thehatched area. (Figs 7 und B have been taken [ro m thc publica-tirins by BastrI'ss quoted in footnote ").)

occurs within the whole of the hatched area. Themost striking fact i~ that the relative increase ofthe vitrification area is on the whole larger themore the respective cations differ in "field strength";

68476

Fig. H. Phasc diagram of the system Na20-CaO-Si02• Thevitreous state may be obtained with any composition in thehatched area. Contrary to this diagram, according to J. B.Ferguson and H. E. Merwin (Amer. J. Sci. 48,81, ]919)a substance of the composi tion CaO.Si02 (denoted by a crossin the diagram] can occur in the vitreous state; thus here R = 3.

for an exampleexplanation forthreshold value

see table II. Herein lies thethe whole phenomenon. Theof R is related to the fact

that with increasing number of oxygen ions thepolyhedrons, originally considered as being entirelyrigid, are ultimately no longer able to retain theirmutual coherence in a network that is becomingmore and more open. Owing to the great variationsin the electric fields, however, the oxygen polyhe-drons are themselves somewhat deformed. Thisdeformation makes it possible for a coherentvitreous network to be formed also when the valueof R IS somewhat greater (smaller Y).

Table 11. Relative expansion of the vitrification area in thephase diagram of mixed alkali borates, compared with the areain which the condition for R is satisfied ").

System Increase jn %

Na2O-K2O-B203 15Na2O-Li2O-B203 50Li2O-K2O-B203 100

In conclusion it may be said that due to recentrefinements of Za ch ariasen 's theory many de-tails in the phenomenon of vitrification can nowbe better understood. In particular the existence ofall sorts of glasses not fitting in the old scheme hasbecome understandable, while the new conceptionsmay serve as a guide - and in many cases havealready so served - when seeking new glassespossessing entirely new combinations of properties.

Summary. Zachariasen's theory indicates under what con-ditions oxides may occur in the vitreous state. These conditionsare based upon a conception of the structure of glass as anirregular network of oxygen tetrahedrons (or triangles) in whosecentres are situated the small, highly charged ions B3+, Si4+or ps+ (network formers), while in the interstices of the net-work there may be taken up, as network modifiers, all sortsof large, less charged, cations surrounded by a larger number ofoxygen ions. According to new conceptions this picture has to berefined in some respects. The coordination numbers are notfixed to the extent originally supposed. The number of oxygenions surrounding B3+ may change from 3 to 4" thereby ex-plaining various phenomena encountered with borate glasses.Further, under certain conditions typical network modifiers(with normal surroundings of, say, 6 or 8 oxygen ions) mayact as network formers (with coordination number four), andvice versa. The behaviour of the cations in this respect isgoverned by a competition pr-inciple, to which expression isgiven by a classification according to the order of their" fieldstrength". According to Smekal the occurrence of bondingforces of different types between the particles in the networkis essen tial for vitrification. Many facts not covered byZa c har i a s e n ' s theory, or in con tradietion therewi th, thusfind a plausible explanation. A number of examples are givenby way of illustration.