Symposium on Glass Papers presented before the Division of Industrial and Engineering Chemistry a t the 85th Meeting of the American Chemical Society, Washington, D. C.. March 26 to 31, 1933.
Diffusing Glasses for Illumination Recent Developments in Light-Diffusing Glasses of the Spontaneous and Controlled Types HENRYH. BLAU,Macbeth-Evans Glass Company, Charleroi, Pa.
M
0 DE R N illumination
flexible means of obtaining a far Glasses which diffuse the light by means of has presented unusual greater range of degrees and their internal structures (inclusions within the problems to glass techtypes of light diffusion. Thus, glasses) have outstanding illuminating advannologists. Some of these have the development of internally tages over those which diguse light as a result of resulted from the commercial dediffusing glasses offers a promissurface irregularities. Theoretical and empirivelopment of new types of illuing solution to many problems of the illuminating engineer. minants, such as ultra-violet cal studies show that the properties of internally Recent progress along these lines lamps, sodium, and other lumidiffusing glasses may be largely controlled by has been made possible by the nous-vapor tubes, etc. Others fixing the size, number, and character of the inapplication of physics and physiof more immediate and general clusions. Composition and thermal history cal chemistry. importance have arisen from the largely determine these factors in glasses in which Glasses, which diffuse light improvement of gas-filled, incanas a result of their internal descent-filament l a m p s . N o t the inclusions are certain types of crystallites. structures, do so because they only have these lamps been Spontaneous crystallization during cooling accontain myriads of tiny inclurendered more efficient, but their counts for the light diffusion in many of these sions of different indices of reuse in higher wattages has beglasses; but unusual illuminating properties can fraction from those of the surcome much more extensive. The be obtained by controlled crystallization resulting rounding glasses. Thus, light proper distribution of light from is scattered in the course of its such sources, as well as the refrom definite time-temperature schedules. passage through the glass by duction of their brightnesses, reencountering one or more of quires the use of modifiers, which are ordinarily formed of diffusing glasses. these inclusions with resulting reflection, refraction, or diffracLight falling upon such glasses is diffused by means of tion. The results of the studies of these physical relations either surface irregularities or internal structures. The gen- afford a suitable basis for the development of the proper eral aspects of the principal methods of obtaining diffusion physico-chemical means for fulfilling these requirements. This in glasses are illustrated in Figure 1. The irregularities are work has been so extensive and involved that only its more ordinarily imparted to the glass surfaces by such processes as general aspects may be set forth here. etching or sand-blasting. However, the degrees of diffusion PHYSICS OF LIGHTSCATTERING so obtainable are limited, and, in general, the resulting glasses The fundamentals for these studies were derived by Rayleigh ( I S , 14) in his mathematical considerations of astrophysical phenomena. In these he investigated the scattering of light by a single electrically nonconducting particle and set forth the relations of the intensity of the scattered light t o the properties of the particle and the surrounding medium, in the following equation:
Molded or configurated glass
Ir Mat glass
Cloudy glass
FIGURE 1. SCHEMATIC REPRESENTATION OF THE PRINCIPALTYPESOF DIFFUSINGGLASSES
are far more difficult to keep clean and are of lower mechanical or thermal resistance than are the corresponding glasses with smooth or glazed surfaces. Conversely, glasses which scatter light by virtue of their internal structures are not only relatively free from these objections, but also afford a more
The wave length factor (A) was originally used as the basis for explaining the colors of the sky and sunsets, but it is equally applicable to the causes of opalescence in many glasses, with the accompanying reddish or fiery appearance of the images of common light sources viewed through them. This factor also indicates that the equat,ion was derived primarily from the consideration of particles of dimensions smaller than the maximum wave length of visible radiation. cos%) factor accounts for the distribution of the The (1 light as well as for the degree of polarization of the scattered light when observed a t various angles. The Rayleigh relation was shown by Mie (IO) to be a simplified analysis and to hold rigorously only for values of n J n ~
+
I ?; D U S T R 1.4 L A N D E N G I N E E R I S G C H E M I S T R Y
August, 1933
approximating unity and for very small valuw of r. hlie (10) and Gans (4, 5 ) introduced more general and refined analyses of the problem to cover particles of shapes other than spherical, as well as greater ranges of dimensions. Although the views of previous workers were based primarily on the behavior of individual particles, Schuster (17“1carried out corresponding derivations for large numbers of particles and resolved the scattered light into two diffuse fluxes moving in opposite directions through the medium. He also introduced the assumption that the particles functioned as though they, themselves, were emitting light. Ryde and Cooper (15) have recently applied the Rayleigh and Schuster relations directly to opal glasses by introducing such factors as those which include the surface or boundary effects, thus obtaining equations which they have confirmed within reasonable limits by direct measurements. The problem has also been approached empirically through the study of models consisting of liquid suspensions. Thus, Cheneveau and Audubert (3) confirmed Mie’s yiew that the Rayleigh equation holds only as a limiting case. Ryde and Tates ( I C ) found from studies of the behavior of suspensions of shellac in water that the qualitative inferences from the Rayleigh relations mere valid for opal glasses. Lax, Pirani, and Schonborn (9) similarly investigated suspensions of paraffin in water and others consisting of alumina in dilute acetic acid solutions, to obtain the following empirical relations:
+ K4 log F.Q = h-dog S + K ; FD
- 1 = K,S
(3)
(4)
The diverse approachej of theoretical physics and empirical studies of models of diffusing media have led to the general equations: Fo = Ft
+ F, +
kLt =
IO
(5)
Fa
K ~ ( F+, F,) = 1 - e-
(Nq
+ p)t
(7)
849
ever, in the present study it is more significant to consider the effectixe wave length, which may be assumed to approximate 5700 9.for commonly used, gas-filled incandescent lamps. Aside from this assumption, a physical rather than a physiological viewpoint may be maintained to adrantage in the
L Tb
FIGLRE 2.
CRYSTALLIZATION C U R V E S FOR SPOXT.4KEOUS
OPAL G ~ . s s s
study of diffusing glasses. The relation of wave length to scattering coefficient may be expressed as: q = K’/X” Rayleigh (13) showed that theoretically K may possess a limiting value of 4; but others (16) have shown that it has a value of about 2 for most opal glasses and as low as 0.2 for some alabaster glasses. Obviously, if K is equal t o 0, the light scattering becomes independent of the wave length, and this has been approached only in the cases of glasses containing relatively large inclusions. The absorption coefficient of the glass, F, is not actually independent of the scattering coefficient, q , although it seems to be primarily a function of the content of the usual glasscoloring impurities or constituents, as well as the distance traversed b y the light nithin the glaqs. Various m-orkers
I
c
I t should be noted that the scattering - coefficient, 0, - is ~-propor.,2 - no*) tional to 2n,q]’ for nionochroniatic light and suspensions of spherical, dielectric particles. This coefficient is so complex that the various factors introduced may well be considered independently. I n summarizing, these relations show that the diffusion in glasses of the type undm consideration is primarily a function of: +
$
The wave length of the light Eource The thickness of the glass The absorption coefficient of the glass The values of the indices of refraction of the inclusions and the glassy matrix ( 5 ) The character of the incluqions (6) The number of inclusions per unit of volume (7) The dimensions of the inclusions
(1) (2) (3) (4)
FACTORS IXFLVEXCIXG LIGHTSCATTERIKG Some of tliece properties are usually stipulated by the illuminating engineer so as to conform to his pal ticular purpose. For example, the thickness of the glass is usually determined by the mechanical properties required in a particular installation or the methods by which the glassware may be satisfactorily produced. The spectral characteristics of the light source are also usually a matter of similar selection and are ordinarily defined in terms of “color temperature.” How-
FIGURE 3.
CRYSTALLIZ.4TION CURVES FOR CONTROLLED
OPALGLASS
(6, 9) have estimated that the light actually passes through the equiyalent of four to eight times the thickness of opal glasses, but there is not complete accord in their several estiniates (6, 9) of the relative absorption of light b y the glassy matrix and by the inclusions. The discrepancies in the data may be attributed to such differences between the aqueous suspension models and the actual glasses as adsorption of light-absorbing substances by the inclusions, the character of the inclusions, or the lack of homogeneity of the crystallites. I n general, it is even more essential in diffusing glasses than in
1 X D U S T K I A I, A N D E N G I N E E R I N C C H E M 1 S T H Y
U.3
trailsparent, w e b to niioiriiize t,lie coirte~rtsof such impurities as iron. That tlie indiccs of refraction of tlie inclusions and of tlre glass? matrix have a marked influence on the scattering coefficient, q I is iliovrn by tlie relation:
Vol. 25, No. 8
arid for ordinary opals bas been dctemiined (9, 16) to be of the order of magnitude of 1 X 10" to 1012percc. In general, the greater the number of inclusions, the longcr is the average light pat11 through the glass, and, in all actual glasses, the peater is the light absorption. Accordingly, practical considerations limit the extent to which this variable should he enrployed to obtain light scattering. The influerices of tlie particle number on the gcneral illuminating properties have been tliorouglily investigated by Lax, Pirani, and Schonhorn (9) aid are set forth in Equations 2, 3, aird 4. 130th tlre theoretical and empirical approaches indicate that the size of the iiiclusions affords tlie most flexible means of determiuing internal diffusion if othcr factors are properly fixed. The logaritlim of the efficiency of the direct transmission decreases 8s tlre first power of the particle number, N , hut it varies as a higher pover of tlie radius of the particles, T (according to tho Rayleigh equation, as the sixth power). Ilampton (7) has derived the following values for tlie relativc scattering power on the basis of the metliods suggested hy Ryde and Cooper:
Crn.
x
0.2 0.5
Cm. x
IO' 1
87
1.0 2.0
10'
1.730 95,000
fie tias also showii that the weight of the scattering particles is somewhat less than 4 per cent of the total weight of a typical opal glass. It seems probable that inclusions of diameters somewhat greater than the maximum wave lengths of visible light are most desirable for approaching pcrfect diffusion with tlie efficient transmission or reflection of light. The general conclusion of the workers in this field seems to he that the size of tlre inclusions has a preponderating influcnce on tlre diffusion of liglit and associated properties of glasses. SPOh..I'AX.EOUS FlJRl\I.4TIoli OF CRYXTALLITES
FKXJT~E 4. BLOWING OF STREET-LWHTIVG (;L*Wv*RE
reported Srorri their x-ray studies t,liat the inclusiiuis in tlie commoner fluoride opal glasses are crystallites of calcium and sodium fluorides, tlie relative amounts of each varyiug with the particular coinpositions used. However, the cryst.& lites in glasses characterized by other basic constituents have not been definitely ident.ified up to the present. Tile values of the indices of refraction of the identified crystallites and of typical glasses, in wliielr t.lrcy may be iinbediled, are as followx: Cxieiem fluoridc 1.48 norosiiicate piBrs 1.49 Sodium Huoride Sods-iirne Ylh98
1 . 3 8 High-lead glans 1.52
1.85
Calculations using the above data reveal that tlie scattering coefficients may be varied thirty fold by the extreme combinations of refractive indices. However, these views are entirely on an optical basis, and there are usually other physical, as well as ciiemical, limitations which tend to restrict the use of this entire range of refractive indices. Moreover, it will be sliovn that the diffusion of light may be more satisfactorily controlled on the basis of the size of the inclusions and their number per unit volume. Tlie number of inclusions per unit of volume, N , is a flcxihle, although limited, means for obtaining the desired illuminating properties. For a given glass it is usually simpler and more precise to refer to the number of inclusions per unit of mass, rather than per unit of volume, when therc are extensive temperature ranges sucli as those in tlic thermal treatments to be described. The ialue of A' is usually quite liigli,
I t may reasonably bc concluded that tlie number of inclusions per uuit of volume, and their dimensions, are importarit factors in determiuing the properties of internally diffusing glasses. In the cases of many of these glasses, in which tire inclusioirs are crystallites such as fluorides, rncans are available for fixing these factors within Sairly satisfactory limits. These methods are based on molecular-kinetic conceptions of crystallization developed by de Coppet and Tammann (18, 18). Although direct nieasuremcnts to substantiate their views were carried out on supercooled organic r ; n b stances, this hypothesis ha8 liccrr satisfactorily applied to metals and the devitrification of glasses. Indirect measurements (8, 8)l have confirmed the view that it may be adapted equally well tu many types of opal and certain colored glasses. The determining factors in the formation of crystallites are tlre rates of nucleus formation and tlie velocity of crystallization. Their application to tire more widely known types of opal glasses ("spontaneous opals") ruay be deliionstrated hy Figure 2, in which tlre curves represent, respectively, as functions of temperature: A . Viscovity of the glass B. Rdte of nucleus formation (number of riuclei fwmed per unit mass of glass per minute) C. Crystallization velocity (vectorial rate of crystalline growth, microiis per minute)
The process of cooling and the attendant dcvelopinciit of diffusing properties may be briefly outlined as follows from F i y r e 2: The opal glass at a relatively high temperature, 1 The nnpIio&tion oi the Tammann Oryslsiiiratiun hypothesis to opal nnd similar g188888 wag described b y the sulhor. P I ~ O to I the Pubiioation oi references 6 and 8.in a talk given at the Melion Institute in Pitiahurth. P a , April 14. 1931. and reviewed by F. \V. Preston [Glass Ind.. 12, 110-11 (1931)l.
August, 1933
I N D U S T R I A L .k N D E N G I N E E R I N G C H E pI.I I S T R Y
T I ,such as that obtaining when the glass is molten and in the pot or furnace, is transparent, because all of its constituents are in solution. It remains transparent until cooled to temperature, Ts, because, even though i t has passed through the temperature range, T pto T3, where crystalline growth is possible, none occurs because the crystalline nuclei necessary for the formation and growth of crystals, are wanting; that is, the glass is supercooled. From temperature T3 to T4 nuclei form, and the crystals grow so that the glass is rendered diffusing. Below temperature T4 no further effective crystallization occurs because the glass on cooling becomes highly viscous and solidifies without further change of diffusing properties other than those which result from the variations of such properties as the refractive indices with changes of temperature. Since a relatively small section of a time-temperature curve for the cooling of glass approximates a straight line, the abscissa may be considered either as time or temperature for Figures 2 and 3, if proper proportionality factors are used. The actual curves for the several properties as a function of time really differ so slightly from those for temperature as hardly to justify the consideration of a second set of curves. On this basis the entire horizontally hatched area in Figure 2 is proportional to the number of crystals present per unit mass of opal glass. Similarly, the cross-hatched area yields definite information as to the maximum size of the crystals developed. A fairly satisfactory estimate of the size distribution of the crystals may be obtained readily by considering the vertically and horizontally hatched areas in relation to each other. These considerations indicate that the diffusFIGURE5 . ing properties depend largely on the rate of cooling of opal glass and that quite a range of sizes of crystallites is formed in opal glasses of this type. Unfortunately the temperature ranges, which determine the size and number of crystallites, overlap those in which the glasses are formed or shaped by hand as well as mechanical processes. This results in even greater variations in those factors which determine light diffusion in different parts of the same piece of glass. These relations are further complicated by the fact that there are frequently two, or possibly more, species of crystallites present, each of which has characteristic relations like those depicted in Figure 2. Although much can be accomplished by efforts to separate the crystallization temperature ranges from those in which the glass is formed, or by properly shaping the hatched areas under the curves, the practical limitations are evidently great. COXTROLLED FORMATION OF CRYSTALLITES A more satisfactory method is offered by the possible reduction of the hatched areas to zero-that is, by the separation of the curves so that these processes do not appreciably overlap, and the nuclei form only below the temperatures a t which the glass is shaped. On first consideration this may not seem feasible, since the rate of nucleus formation and the velocity of crystalline growth are both dependent on such closely interrelated factors as: 1. The number of crystalline substituents (molecules, atoms, or ions) per space lattice element 2. The orientation of the crystalline substituent5
EFFICIEMCY
851
OF UNlT&!P7
PHOTOHETRIC ANALYSIS OF DIFFERENTIALLY OPACIFIED, INDIRECT LIGIITING LUMJNAJRE
SEMI-
The kinetic energy of the crystallizing substituents The viscosity of the glass The concentration of the crystallizing substituents The magnitude of the energy changes involved (latent heats of crystallization or solution) (12) 7. The thermal conductivity or rates of transfer of heat to or from the region of crystallization (18) 8. The rate of diffusion to or from the region of crvstallization 9. Interfacial concentrations (adsorptik) 10. The influences of polar forces 11. Variations in the fugacities of crystallites with their radii of curvature, etc. However, the relative influences of these factors and particularly the roles of the last cited probably make it possible to obtain glasses yielding a single species of crystallites whose characteristic curves may be represented as in Figure 3. Opal glasses of this type may well be termed “controlled opals.” On removing such a glass from the furnace, it cools from temperature TI’ to “4’ before nuclei start to form. It is then below the temperature range conducive to crystalline growth. The number of crystallites may be determined by fixing the time during which the glass is held within the range of curve B. Crystallites of definite and uniform dimensions may be obtained by reheating the glass to a temperature such as T7’. Their dimensions are proportional to the areas included under curve C between the temperatures T,’and T3’. If the rate of heating of the glassis identical with the cooling rate previously considered, twice the integral under 3. 4. 5. 6.
I N D U S T 11 I A I.
8 s
A
N D :1 3 G 1 N E E R I N G C H E M I S T 1%Y
curve C between tlic limits T7'and T8' is Importioiial lo tlie value d the radii of crystallites forrned in the elass. Tl,c resultant crystals are of unifonn a.nd definite size in contrast to the wide ranees of sizes obtained in the svontaneous ooal glasses previously described, since all of the nuclei are foniied hefore growth begins. This affords a method for obtaining 13pal glasses nf uniform and predetermined difiusing, transrnitting, or reflccting proprrtics.
Vol. 2.5, No. 8
varying the iliffusirrgproperties in different parts of t.lie same niece of iz1a.s. are now heinrr introduced.
I
Tlie applications of these plrysico-cheinical relations to diffusing glasses Imve been sketched to show that opal glasses merit further detailed study for improving their illuminating properties. Tlicir investigation also offers unusual a p ~iroacliesto greater insight into the broader conception of .\FFLICATIOSS OF CUXTIWLL>:D CllYS'~.~LI,l~.~'~lUX tlie structures of glasses. The evidence of crystallinity in Tlie application of the descrihed conceptions iias resnlt,ed most glasses is cartninly inconclusive (11, 1Q), but the fact in marked improvement and better control of the prnperties remains that identical means of investigating opalescent or d illiiminatiiig glasses wliicti arc of generally uniform striic- opal glasses containing relatively sniall crystallites yield t.ilrc. This has been true of the spontaneous opals, altiiougtl broadly similar results to those obtained fur glasses usually the inore outstamling results cansidered as truly amorplious. liave bceii attained with the A c c o r d i n g l y , the st,iidies of opal and similar glasses may controlled opals. Se'erni-indirect become links in the chain of ligliting howls I i a r e been prothe general kn~iwleclgcof the diieed wliieli Iiava illuminating efficieiiciesvitlr extremely low solid state a i d may demonstrate that the term "glass" is hrightncsses in spite of their not a misiiomer when applied use vith higli-wattage lamps a t small d i s t a n e c s from tlx: to snch substances. Since tlie glass surfaces. These glasses s t r u c t u r e s of m a n y o p a l in 'Ig-inch thicknesses yield glasses definitely involve crystalliiiity, otlier applieations wefficients US reflectioii greater o f pririeiples previously apt h a n t h a t of polislied ehroiiiiurn plating. The eliaracplied to the study of inetala t e r i s t i c s o f t h e s e special may also l i e fruitful. In these s t n d i c s t h e d i f f e r e n c e s in glasses may bc most satisfacsue11 properties as the thermal torily illustratcd on the basis conductivities of metals arid of the phot,ornetric analyses of li gh t.ing uriibs incorporating glasses s h o u l d a c c e n t u a t e them. Available space preIJNIT~ such contrasting features as dudes introducing more t.lian t h e more satisfactory cnnthe single (base shown in Figure 5 . This indicates that trol of crystallization in tire case of the glasses. Simitire controlled processes bring about further advanta,gr~sre- larly, tlie method described for obtaining controlled opals sulting from the aiiiity to vary bhe ilifhsing and rcfli:cting also affords a xiew basis for fundarnental studies of light-scatpri,perties in definite parts of a single piece: of glass. Thus, tering plienorneiia using test specimens of more permaiicnt, marked advances in .x:ini-inilirect illuminating glolies (2) as w?ll as predett:rmined inclusion cllaractcristics. Such 1mve Iieeri obtained by tlie dcvelopnient of erystallitcs in tlie work should assist in t h e furtlier approach to perfection in lower or b,o.sl portions of the gloLr, so that most of tlie Iiglbt iiluniinatirig properties and afford a means for providing is reflected up~mrdtliruogli liighly trailsparent sections wliich glasses to keep apace a i t h the develiipments of the illuniinatare virtually free from these crystallites. I l o u m w , tlicre ing enginerr. may be introduced into this highly transmitting Ixirtion othrr kinds of iiiffiicing inclusions which are virtually indep~nrlent l o = intensity oi incident light of the tlrenrinl treatment a t higher viscosities. Sitice time I , = i,,tensity scuttereclligkl+, I,' = intensity of directly transmitted light may be used in tlic same glass compositions in wliidi lites are also capable of development, a wide range of light= illcident W t flux F D = t o t d transmitted light flux inoilifying propert,ies may he incorporated in variiius parts of Fn = reflected light flux a single piece of glassware. ~ g n r 5 e sets forth thr ability F, = total light flux F. = alisorbed light flux of semi-indirect light,ing glassware of this type to distrilrritc E = directly transmitted liglrt flux the light properly, efficiently, and witli resulting low tirightIIPSS values. Tlic relative advantages of this type of liglit,ing '* = from specime" (Or par.'ie1e) A = amplitude of incident light rrare beeomr evident from the examination of corresponding N = nun,i)erof inclusions per ",,it volume T = radius of inelusiorrs photometric data for senii-indirect lighting glassware made by = index oi refraction of ir~clusious n d i incthods as the enameling of transparent glass or the 761 partin1 "casilig" of clear glass uritll
