SILICATE GLASSES Calculation of Densities, Refractive Indices, and Dispersions from Glass Composition --hIAURICE
Equations and constants are given for the calculation of densities, refractive indices (n,), and dispersions (nF nc) of silicate glasses from their compositions. For glasses in the NazO-SiOz system the average differences between calculated and the
-
PECIE’IC and molar volumes and refractions of glasses
S
are approximately additive functions of the composition, expressed in terms of the component oxides ( I , 4, 6, 7, 8, 11). The best experimental data, however, show that the volume-composition and refraction-composition relations, which should be strictly linear for true additivity, are best represented by curved lines, with more or less sharp breaks a t certain values of the composition (different for different systems). These breaks have been interpreted (unnecessarily) as evidence for the existence of definite chemical compounds in the glasses. Since the constants of the curves and the positions of the breaks vary from system to system, no general method applicable to complex glasses has been available. This unsatisfactory situation is now changed. A series of articles (5) shows that the densities, refractive indices, and dispersions of silicate glasses can be calculated fairly accurately from their compositions by means of some simple equations and a set of constants-approximately three (one each for density, refractive index, and dispersion) per component oxide. The purpose of this paper is to outline the method, give the equations and constants, and discuss briefly the order of accuracy attainable.
L. HUGGINS, Eastman Kodak Company, Rochester, N. Y.
best observed values of these properties are about 0.002, 0.00035, and 0.00007, respectively. In general, the deviations between calculated and experimental values seem to he due largely to inadequate knowledge of the actual compositions.
The composition of any given glass composed of oxides , preshaving formulas M,O, and molecular weights W M and ent in relative amounts given by weight fractions jM,may be expressed by a set of atom fractions, N M . Each such atom fraction is the number of atoms (or gram atoms) of the element M per atom (or gram atom) of oxygen in the glass under consideration. The values of NAu may be calculated from the relation,
The denominator contains one term for each of the component “metallic” elements, M-i. e., one term for each component oxide. The volume, VO,of the glass mhich contains one gram atom of oxygen is related to the density, p, by the equation,
T h e s u m m a t i o n is t h e same as in Equation 1. We consider here only the density (and other properties) a t ordinary room temperature (-20’ C.). The refraction, R o , ~ for the amount of glass containing one gram atom of oxygen, is related to the refractive index, n,, for the wave length, A, by the following equation of the Gladstone-DaIe type :
Equations and Constants The relations b e t w e e n composition and the properties under discussion are simplest when one deals throughout with t h a t quantity of glass which contains one gram atom (or 16 grams, equivalent to A v o g a d r o ’ s n u m b e r of atoms) of oxygen. 1433
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VOL. 32, NO. 11
TABLE I. VALUESOF CONSTANTS ba Range of Nsi 0 . ?7(?)-0.345 0 . 3 4 5 -0.40 -0.436 0 . 4 3 5 -0.50 0.40
AND
csi
bsi
E91
5.69 4.21 2.G6 0.00
13.00 17.27 21.14 27.26
TABLE 11. GLASSCONSTANTS A4 Si
FIGURE1. DEPENDENCE OF V0.s~ ON Nsi (418,10, 1 1 )
FOR
+
- nx,)Vo
(4)
The following additivity equations have been shown (5) to hold m i t e closelv for well-annealed silicate glasses of a wide variety of compositions, using the data collected by Morey ( 8 ) :
+ + + Z’Vo,nr Nsi + Z’CMNM
V o = k -I-Vo.si k bsi RO.D= ZRO,N.D
CEi
= Za,v.DNlcr
aM,D 12.506
aAf,F --“M,C
0.18355
The other constants listed in Table I1 are a p plicable over the whole range of silicate glass compositions, in so far as can be determined from data now available, except in the case of lead. The a P b , D and ( ~ P I , , F - ~ P I , , c ) values given are not accurate for N P b greater than about 0.2 (Figure 5). Different constants are found to be necessary for boron atoms (13’) surrounded by four oxygens and for boron atoms (B”) surrounded by but three. This result is in agreement with theoretical expectation, with the structure determinations which have been made (chiefly by Zachariasen, 12) for various crystalline borates, and with the x-ray studies of Biscoe and Warren (2) on sods-boric oxide glasses. The relative amounts of the two kinds of boron depend on
NazO-Si09 GLASSES
The refraction may also be defined by means of an equation of the Newton (ni -1) or Lorentz-Lorenz (n: - 1)/(7~: 2) type. At least from an empirical standpoint, however, the simpler Gladstone-Dale equation appears to be quite as satisfactory as the others. The dispersion, DO,^,,,^, for the quantity of glass containing one gram atom of oxygen may be defined by the relation: D o . x ~=x ~ (nxI
M (Table I)
(5) (0)
DOJC = ZDO.M.FC
- a m )NM
(7) Here k is a small constant, probably characteristic of the annealing technique, which must be included to give agreement between the data published from different laboratories. We assign to k the value 0 for data from the Geophysical Laboratory, 0.01 for Bureau of Standards data, and 0.05 for data from the University of Sheffield. The constants 68, and cgi are different for different ranges of Ne;, as shown in Table I. They correspond to the changes in slope of the VO,R,us. Ns, curve in Figure 1. (As would be expected on theoretical grounds, the experimental points indicate a slight rounding of the curve a t the intersections of the straight line portions. For simplicity, this rounding will be neglected for the present.) = Z(aM.F
OF VO.N. FIGURE 2. DEPENDENCE
ON
NN.
(4, 9,10,1 1 )
FOR
Pia200SiOs GLASSES
NOVEMBER, 1940
INDUSTRIAL AND ENGINEERING CHEMISTRY
1435
The dispersion, np - nc, is similarly computed, with the aid of Equation 1, Equation 7, and either Equation 2 or 5 , substituting finally into Equation 12:
- nc
T~F
Do,FC
= --
(12)
VO
Accuracy of the Results The most precise measurements available for testing the foregoing relations are those by Morey and Merwin (9) and by Finn and co-workers (4, 11) on the sodium silicate glasses. For these, the average deviation between observed and calculated values is about 0.002 for the density, 0.00035 for nDl and 0.00007 for np - nc. For other systems, as would be expected, the agreement is not so good, largcly because of inaccuracies in thc experimental values (especially the compositions) and to insufficient annealing. An extensive comparison of the calculated with the experimental results for those silicate glasses for which the requisite data are in the literature has been presented, largely in graphical form (6). This comparison need not be repeated here. Several of the graphs, however, are reproduced to indicate the OF V O , ~ON . Nc. FIQURE3. DEPENDENCE GLASSES (3, 4, 9)
FOR
NazO-CaOSiO~
the annealing treatment and on the values
of Ng and N R . For well-annealed glasses, approximately, = NB N p = 0
Ngi
] for Nsi +
N B
N B ~= 2 - 4x8, - 3N13 NB* = 4Nsi ~ N -B2
+
for Nsi
t
0.50
(9)
The summations in Equations 6 and 7 are over all the component “metallic” atoms, including silicon. The summation, E’, in Equation 5 is over all except silicon. T o calculate the density of a glass from ita composition by weight, one need only compute the N M values by Equation 1, substitute these and the appropriate constants from Tables I and I1 (also the appropriate value of k , for greatest accuracy) into Equation 5 , and finally substitute into Equation 10, which is obtained by rearranging Equation 2 :
To calculate the refractive index for the sodium D line, one calculates N M by Equation l, Ro,D by Equation 6 and Table 11, Vo either from the observed density by Equation 2 or from the constants of Tables I and I1 by means of Equation 5 , and substitutes into Equation 11, which is readily deduced from Equation 3: RO,D
n o = I + y ,
a 0‘ 0:
I
0
01
O?
0.3
I
I
0.4
0.5
Npb
FIGURE 5. DEPENDENCE O F R0,pb.D ON N p b FOR NazO-K+PbOSiO, GLASSESACCORDINQ TO MERWIN AND ANDEMEN (8) The slope of the straight line is 30, rather than 29.1, the value later ohooen as beat for N , , < 0.16
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mined. Thelarge deviations shown in Table 111 between observed and calculated quantities are, in the writer's opinion, almost entirely the result of inaccurate knowledge of the actual compositions.
Plea for More Precise Data 0.0113
No
0.07 -0.03
0.0050 -0.oW4
-0.W63
No
0.07 -0.01
0.0057 -0.w1s
0.0118 -0.~28
ChsnceBros. 't c o .
34 34
Yes
Para-Alantois
10 16
Yes
The author wishes to enter a olea for the determination and 0.00033 0.00084 .. . of a larger amount of +O.ooMu , , ~ ~ ~ . .publication precise data on densities, refractive indices, dispersions, and other properties for glasses of accurately known composition, to make it possible t o correct, refine, and extend the table of constants presented here (and other similsr tables) and to study adequately the deviations from the simple relations represented by the equations of this paper. o.000~7 -0.00011
o.ooo~8 -0.000a5
~~
Acknowledgment The writer is glad to acknowledge the assistance of Dorothy Owen with the computations on which the results summarized in this paper are based.
Literature Cited (1) Bilts. W.. and Weibke, F.. 2. anore. allem. Cha., 203. 345 (1932); 241, 39, 421 (1939).
FIGURE6 . DEPENDENCE OF DO.N~.FC ON FOR NalO-SiO. GLASSES (9)
#we
( 2 ) Biscoe, J., and Wsrien, B. E., J . Am. Ceram. Soc.. 21, 287
.."-_,.
(1 W U i
~
Endish, S., and Turner, W. E. S., J . SOC.Glasa Tech., 4 , 126 (1920).
F. W., Youns, J. C., and Finn, A. N.. B w , Slandaida 3. Research. 9,799 (1932). Huggina, M. L . , J . U p l i d SOC.Am., 30,420 (Sept.), 495 (Oct.), - (Nov.). 1940. Knapp. 0.. Sprsehsaal. 63. 61 (1930); Glastech. BBI.. 8, 154 (1930); J . SOC.Glass Tech., 24,3i (1940). Kordes. E., Z. anorg. allgem. Chem.. 241, 1, 418 (1939); 2. phyaiic. Chem., B43, 119, 173 (1939). Morey, G.W.. "Propertiesof Glass", New York, Reinhold Pub. Gorp.. 1938. Marey. G.W., and Merwin, H. E., J . Uptical Soc. Am.. 22, 632 Glaae,
degree of agreement between the assumed equations and constants and the experimental data. It seems worth while to consider the question of the a p plicability of the derived equations and constants to the calculation of the properties of complex commercial glasses. Accurate composition data on such glasses, with precise density, refraction, and dispersion data on the same samples, are practically nonexistent in the literature. h'evertheless, ealculatiom have been made for the Chance Brothers and ParaMantois optical glasses for which approximate compositions are quoted by Morey (8). The results are summarized in Table 111. Three glasses containing fluorine and one containing triangularly surrounded horon (B") are not included in the averages,,sinee the requisite constants have not been deter-
(1932).
Winks, F., and Turner. W. E. S., J . Soc. Glass T e d . , 15. 185 11"11\
i l l Y I , .
Young, J. C.. Glase, F. W.. Faick. C. A., and Fim, A. N., J. Research Nall. Bur. Standards. 22, 466 (1939). Zachariasen. W. H., 2. Krisl.. 88, 150 (1934). 98, 266 (1937); Zaohariasen. W. H.. and Zieglsr, G. E . , l b i d . . 83,354 (1832). C o n ~ s r e u ~ r772 o ~from the Xodak Reeesioh Laborstories
Couifrsy,
Owcn8-IItinoia Oiaas cornpmv
INSUWTINO GLASSBLOCKS WHICHARETRANSLUCENT BUT NOTTRANSPARENT
Courtesy, De Vilbiss Rubber Company
GOODHOUSEKEEPING WILLREDUCEACCIDENTS
Dollars and Sense of Safety F. J. VAN ANTWERPEN N. Y .
60 East 42nd Street, New York,
T
HE theme and plot that money can be saved by a safety program is not new and is not original with this generation. As a premise for safety work it was advanced many years ago. But it is a delicate and unpopular subject, almost taboo among safety men and executives alike. The reason for this attitude is the conception, real or fancied, that safety must be practiced for humanitarian reasons and for those reasons only. This is commendable, an outlook with which we must and do agree. However, there are other benefits, aside from the prevention of human misery, which accrue from safety programs, and the purpose of this article is to inspect these-to examine safety from an economic standpoint to show that i t is profitable, in a dollar interpretation, to install and maintain safety measures. Emphasis on safety work seems to have had its inception around the years 1908-12. There are examples of safety consciousness which go back farther, but in the main these years saw the start of the mass safety movement. The iron and steel industry provides a classical example Beginning in 1907, when frequency rates were 82.06, the rate had been reduced to 60.3 by 1913. In 1938 a representative group of companies from this industry showed a frequency of 13.85, while a select group, known to be industriously interested in safety, had a rate of 6.56, a 92 per cent reduction in 31 years. (Frequency is the number of lost-time accidents per million man-hours of work or man-hours of exposure.)
Economics of Safety One of the earliest studies on monetary gain through reduction of accidents was published by the Massachusetts Industrial Accident Department in a series of bulletins which give an interesting picture ( 7 ) . Table I is taken from the first bulletin ( 7 ) , published in 1912, and shows the comparative accident rates for various industries in Massachusetts. TABLE I. ACCIDENTS IN MASSACHUSETTS INDUSTRIES, JULY, 1912 All manufacturing industries
Chemical and allied products Textiles Iron steel and their products Misc'ellandous products Leather and its finished products Paper Metal and metal products other than steel Food and kindred products Lumber and its remanufacture Printing and bookbinding Liquors and beverages Clay, glass, and stone products Clothing
Employees 584,599 4,883 196,827 72,125 54,685 97,660 24,534 27,449 18,861 24,748 15,603 2,367 7,879 19,1173
I nj uries % Injured 3051 45 888 645 581 233 154
0.5 0.9 0.4 0.8 1. o 0.2 0.6
146 120
0.5 0.6 0.4 0.2
115 39 31 30 24
1.3 0.3 0.1
This analysis covers only one month, July, 1912, and cannot be' considered conclusive. It is indicative, however; chemical industry had a rate well above the average and is 1437
