.8

.7

.6

.5

~.4 Z <

<

.2

- . 1

940 920 900 880 860 ~40 820

WAVENUMBER, cm -1

Fm. 3. In f ra red spectrum of cyclo- hexane. : major curve from Fig. 1 corrected for baseline; ++++++: the corresponding sum of Cauchy funct ions; : (bottom curve) the difference between ob- served and calculated spectra.

where PIPe is the intensi ty rat io of t ransmi t ted to incident radia t ion passing through a layer of thick- ness b, of a solution of mater ia l having a concentra- tion c and an absorpt iv i ty a. I f the spect rum is ob- ta ined at two thicknesses in a variable space cell, assuming tha t the unwanted losses are the same for the cell windows and solutions, then the relat ion be- tween the rat io of intensities and the two thicknesses is

Pf/P1 = exp [ -- ac (bf-- bl) ],

or, in absorbance units,

Ae--Al=ac(bf--bl) .

This relat ion should be t rue for systems which obey Sougue r ' s law. 3

To i l lustrate this technique, in f ra red spectra of cy- clohexane were obtained at two thicknesses in a vari- able space cell without removing the cell f rom the instrument . A baseline was also obtained with no cells in the instrument . Spect ra were obtained on a P e r k i n - E lmer model 521 spectrophotometer equipped with a D D R - 1 digitizer. The spectra, shown in Fig. 1, were digitized at 0.2-cm -1 intervals, processed and plot ted by computer.

The absorbance difference between the " t h i c k " and " t h i n " spectra of Fig. 1 and a synthetic spec- t r u m calculated as the sum of two Cauchy functions are plot ted in Fig. 2. The Cauchy functions are cen- tered at 903.28 and 861.26 cm -1 and have half-widths of 5.82 and 9.50 cm-< The difference between the ob- served and calculated spectra is also shown. Fo r com- parison, the " t h i c k " spectrum f rom Fig. 1, corrected

for ins t rument baseline, and the a t t empt to fit it with Cauchy distr ibutions is shown in Fig. 3.

We have successfully used this technique for the s tudy of ins t rument spectra l slit funct ions and dy- namic response as well as for the s tudy of in f ra red band contours.

J~eeeived 14 July 1965

*Present address: Universal Oil Products Co., Des Plaines, Ill.

1. R. N. Jones, K. S. Seshadri, N. B. W. 5onathan, and 3". W. Hopkins, Can. J . Chem. 41, 750 (1963). 2. J-. U. White and W. W. Ward, Anal. Chem. 37, 268 (1965). 3. 1~. P. Bauman, Absorption Spectroscopy ( John Wiley & Sons, Inc., New York, 1962).

Device for Measuring Spectral Linewidths*

Paul R. Barnett U. S. Geological Survey, Denver, Colorado 80225

Conventional methods of microphotometry measure the port ion of an incident beam of l ight tha t is t rans- mit ted through a given spectral line on a photo- graphic Mm or plate. This percentage t ransmit tance is, in effect, a measure of the densi ty of the l ine; for density is equal to the logar i thm of the reciprocal of the t ransmit tance. These methods are well founded and are not l ikely to be replaced for those densities

128 Volume 21, Number 2, 1967

on or near the linear port ion of the t t and D curve. However, as the density approaches the photographic saturat ion level, the methods become less reliable and eventually fail. The chief causes for this fa i lure are (1) the diminishing efficiency of the photographic emulsion when most of the silver halide has been ex- posed, and (2) the lack of reliabili ty of the micro- photometer when the t ransmit tance is below about 3%.

Many methods have been employed to reduce the density to usable values. They include diluting the sample, using step filters, reducing the exposure of the whole spectrogram, or placing a filter at the plate in order to reduce the exposure of a l imited wave- length reg ion- -a l l of which require expenditures of addit ional t ime and /o r materials.

Another photographic phenomenon tha t bears the same relationship to incident l ight as does density is broadening of the image. This broadening is due to scattering of the l ight by the silver halide grains into the shaded area adjacent to the image. 1 The more in- tense the incident light, the greater is the scat ter ing and, hence, the broader the photographic image. The width of the spectral line in spec t rography is a reli- able measure of the amount of rad iant energy pro- ducing the line. The width is, in fact, direct ly pro- port ional to the logar i thm of the in tegrated incident light.

In an excellent paper on the use of line width as an al ternat ive for density measurement in spectro- chemical analysis, Junkes and Salpeter 2 point out tha t astronomers had used the principle of image broadening for est imating stellar brightness for half a century before it began to be used in spectrography. Eisenlohr and Alexy 8 in 1937 first demonstra ted its usefulness for concentration measurements in spec- trochemistry. Although this innovation was a signif- icant milestone in spectrographic analysis, the line- width method has been slow in coming into general use dur ing the ensuing years.

FiG. 1. Top view of the device. (a) Micrometer depth gauge, (b) 4-in. base, (e) 6-in. rod, (d,d') stainless-steel blocks, (e) aluminum wheel, (f) millimeter scale.

FIG. 2. Leaf spring for returning plate.

The chief reason for this slow development has been the lack of a technique or an ins t rument for rapidly and accurately determining the width of the line. Ea r ly workers 4,5 measured the width of the recorder t racing of a line at some more or less a rb i t r a ry base (percent t ransmission). This technique is good in theory but is inaccurate in practice because of the inconstant ra te of movement of the plate carriage on most recording microphotometers and, hence, poor precision in the width of the tracing.

Junkes and Salpeter 2 designed a variable slit of large ape r tu r e for a microphotometer and measured "effect ive l inewidths" in the following way. With the slit set at nar row opening, the t ransmit tance of a clear port ion o f the plate is observed. Wi th the line placed in f ront of the slit, the slit is opened unti l the t ransmit tance is the same as for the nar row slit on the clear plate. The new opening is called the effective width of the line. This method has been shown to work but requires the construction of a somewhat complicated variable slit and the modification of the microphotometcr to which it is affixed.

Bastron, Barnet t , and Mura ta 6 clocked with a stop- watch the t ime required for the microphotometer to scan the line between 5% transmission values on opposite sides of the line. This technique works well for microphotometers with a light-weight, moving slit pulled across the line by a constant-speed motor. The method will not work on most microphotometers where the slit remains s ta t ionary and the carriage must move to scan the line. This is due to the incon- s tant rate at which a heavy carriage is moved by an underpowered motor and a long mechanical linkage.

F igure 1 is a top view of a device tha t may be at- tached to a microphotometer of the moving-carr iage type to convert i t into an ins t rument for the accurate and relat ively rap id measurement of linewidths. The device is essentially a micrometer depth gauge (a) with a 4-in. base (b) , a 6-in rod (c), and a run of 1 in. The gauge is secured to the end of the plate car- r iage as follows: two ¼ in.×¼ in. × i ~ in. stainless-steel blocks (d,d') are fastened to the bed of the plate car- riage with two Allen screws countersunk in each

APPLIED SPECTROSCOPY 129

5O

I00

..~ 150

200 I I O.OO2 0.OI O.I

CONCENTRATION. PERCENT Sr

~'IG. 3. Working curve for strontium (4607-~ line).

block. Holes are dril led through the na r row por t ion of the ends of the base of the gauge and the gauge screwed to the steel blocks through these holes. The geometry is such tha t the project ion of the plane of the lower surface of the spectrographic plate is tangent to the gauge rod at the lower end of its ver- tical diameter. This prevents the rod f rom hi t t ing the rhomb (or slit) of the microphotometer and possibly damaging it.

In order that small movements of the depth gauge may be read more accurately, an a luminum wheel (e) approximate ly 4 in. in diam is fr ict ion fitted a round the knur led thimble of the depth gauge. The wheel has a ½-in. flange and a hub to accommodate a set screw. A mill imeter scale ( f ) is fastened to the circumfer- ence of the wheel. An index made of brass extends out f rom the near end of the base of the depth gauge.

As the wheel is tu rned to the right, the rod of the gauge pushes the spectrographic plate to the lef t with respect to the plate carriage. When the wheel is ro- ta ted to the left, a leaf spr ing (Fig. 2) a t tached to the ways of the pla te carriage with a thumbscrew pushes the plate back to the right. B y reading the wheel scale to the nearest ½ mm, movements of the plate can be read to 0.001 ram, or 1 ~, for the device with a micrometer screw of 1/40-in. pi tch and a wheel with a circumference of 317.5 ram.

To use the device in connection with the micro- photometer in order to measure the width of a line, the plate carr iage is moved unt i l the line is jus t to the r ight of the l ight beam entering the pickup slit. The plate carr iage is then secured so tha t i t will not move. This can be done by pu t t ing small but powerful magnets on the steel top of the microphotometer and against the ends of the plate carriage. To always have the plate carr iage so positioned tha t nei ther end extends beyond the top of the microphotometer,

i t is sometimes necessary to insert a rectangle of a luminum with dimensions approx imate ly the same as a half-plate between the rod of the depth gauge and the plate being read.

With the carr iage secured, the depth gauge is ro- ta ted to the r ight unt i l the microphotometer reads 5%, or some other preselected value. A t this position the scale on the wheel is read. The gauge is then advanced, moving the line across the slit of the micro- photometer, with the percent t ransmission dur ing the operat ion being less than the preselected value. The gauge movement is s topped when the percent t rans- mission again reaches the preselected value, and the wheel scale is again read. The difference between the two scale readings is propor t ional to the width of the line.

This device is being used in our labora tory for routine analysis of elements whose best lines are too dark for density measurements. Al though not as rap id a procedure as densitometry, it is less t ime con- suming than redoing the sample at a lesser exposure or greater dilution.

S tandards are always exposed on the same plate with the unknowns. Working curves are d rawn by plot t ing the width of the line against the log con- centration. The curves are typical ly S-shaped with a near ly l inear central port ion (Fig. 3). The s tandard deviation for repeat l ine-width measurements has been determined to be about 0.8 ~. This represents a coefficient of var ia t ion of 2% for a line 40 ~ wide and ½% for a line 160 ~ wide.

The device is inexpensive, is easy to fabr ica te and a t tach to the microphotometer , does not impai r the normal functions of the microphotometer , and can be quickly detached. No grea t skill is required for its operation.

~ecei~ec~ 23 hrovember 1965

*Publication authorized by Director, U. S. Geological Survey.

1. C. E. K. lVlees, The Theory of the Photographic Process (The Macmillan Company, New York, 1964), Chap. 25, p. 1001.

2. g. Junkes and E. W. Salpeter, Ric. Spettroscopiche, Lab. Astrofis. Specola Yaticana 2, (5), 205 (1958).

3. F. Eisenlohr and K. Alexy, Z. Physik. Chem. (Leipzig) A 179, 241 (1937).

4. P. Coheur, J. Opt. Soc. Am. 36, 498 (1946). 5. D. J. Hunt and D. L. Timma, c ~ Studies of the Line Width

Method of Spectroehemical Analysis," 4th Annual Pitts- burgh Conference on Analytical Chemistry and Applied Spectroscopy (1953).

6. H. Bastron, P. R. Barnett, and K. J'. Murata, U. S. Geol. Surv. Bull. 1084-G, 165 (1960).

130 Volume 21, Number 2, 1967