Abstract

The density transformation according to Seidel, Dt=log[(d0/d)−1] results in a calibration curve that is nearly straight in the wavelength region normally used in spectrographic analysis.

The properties of the “transformed density curve” are studied in detail and it is shown that by choice of favorable conditions the remaining curvature is negligible. This offers the possibility to extend the density difference method to the (H and D) density range 0.1–2.

© 1951 Optical Society of America

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References

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  1. H. Kaiser, Spectrochim. Acta 2, 1 (1941).
    [Crossref]
  2. Honerjaerger-Sohm and H. Kaiser, Spectrochim. Acta 2, 396 (1944).
    [Crossref]
  3. H. Kaiser, Spectrochim. Acta 3, 159 (1948).
    [Crossref]
  4. H. K. Hughes and R. W. Murphy, J. Opt. Soc. Am. 39, 501 (1949).
    [Crossref] [PubMed]
  5. E. H. Cohen, “Investigations on the emulsion calibration for quantitative spectrochemistry” (Dutch), Thesis, Amsterdam, 1950.
  6. J. R. Churchill, Ind. Eng. Chem. Anal. Ed. 16, 653 (1944).
    [Crossref]
  7. R. Schmidt, Rec. trav. chim. 67, 737 (1948).
    [Crossref]
  8. Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).
  9. R. Schmidt and A. Schuringa, Rec. trav. chim. 64, 349 (1945).
    [Crossref]

1949 (1)

1948 (3)

R. Schmidt, Rec. trav. chim. 67, 737 (1948).
[Crossref]

Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).

Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).

H. Kaiser, Spectrochim. Acta 3, 159 (1948).
[Crossref]

1945 (1)

R. Schmidt and A. Schuringa, Rec. trav. chim. 64, 349 (1945).
[Crossref]

1944 (2)

J. R. Churchill, Ind. Eng. Chem. Anal. Ed. 16, 653 (1944).
[Crossref]

Honerjaerger-Sohm and H. Kaiser, Spectrochim. Acta 2, 396 (1944).
[Crossref]

1941 (1)

H. Kaiser, Spectrochim. Acta 2, 1 (1941).
[Crossref]

Churchill, J. R.

J. R. Churchill, Ind. Eng. Chem. Anal. Ed. 16, 653 (1944).
[Crossref]

Cohen, E. H.

E. H. Cohen, “Investigations on the emulsion calibration for quantitative spectrochemistry” (Dutch), Thesis, Amsterdam, 1950.

Honerjaerger-Sohm,

Honerjaerger-Sohm and H. Kaiser, Spectrochim. Acta 2, 396 (1944).
[Crossref]

Hughes, H. K.

Kaiser, H.

H. Kaiser, Spectrochim. Acta 3, 159 (1948).
[Crossref]

Honerjaerger-Sohm and H. Kaiser, Spectrochim. Acta 2, 396 (1944).
[Crossref]

H. Kaiser, Spectrochim. Acta 2, 1 (1941).
[Crossref]

Manders,

Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).

Murphy, R. W.

Schmidt,

Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).

Schmidt, R.

R. Schmidt, Rec. trav. chim. 67, 737 (1948).
[Crossref]

R. Schmidt and A. Schuringa, Rec. trav. chim. 64, 349 (1945).
[Crossref]

Schuringa, A.

R. Schmidt and A. Schuringa, Rec. trav. chim. 64, 349 (1945).
[Crossref]

v. Wijk,

Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).

Verkerk,

Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).

Compt. Rend. du 10-ième Congrès du Gams (1)

Schmidt, Manders, and v. Wijk, with Verkerk, Compt. Rend. du 10-ième Congrès du Gams (1948).

Ind. Eng. Chem. Anal. Ed. (1)

J. R. Churchill, Ind. Eng. Chem. Anal. Ed. 16, 653 (1944).
[Crossref]

J. Opt. Soc. Am. (1)

Rec. trav. chim. (2)

R. Schmidt, Rec. trav. chim. 67, 737 (1948).
[Crossref]

R. Schmidt and A. Schuringa, Rec. trav. chim. 64, 349 (1945).
[Crossref]

Spectrochim. Acta (3)

H. Kaiser, Spectrochim. Acta 2, 1 (1941).
[Crossref]

Honerjaerger-Sohm and H. Kaiser, Spectrochim. Acta 2, 396 (1944).
[Crossref]

H. Kaiser, Spectrochim. Acta 3, 159 (1948).
[Crossref]

Other (1)

E. H. Cohen, “Investigations on the emulsion calibration for quantitative spectrochemistry” (Dutch), Thesis, Amsterdam, 1950.

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Figures (2)

Fig. 1
Fig. 1

A comparison between the shapes of the density ratio curve, the density curve, the transformed density ratio line, and the transformed density curve. These four curves are based on the same experimental data.

Fig. 2
Fig. 2

Transformed density curves of Gevaert normal plates at different wavelengths.

Tables (4)

Tables Icon

Table I Values of δ in Eq. 17 for various values of ΔDt and .

Tables Icon

Table II Estimates of relative systematic errors in concentration (percent) arising from changes in the curvature of the T.D. curve.

Tables Icon

Table III Parameters of the T.D. curve for a Gevaert normal plate at different wavelengths; step sector calibration logn=0.301.

Tables Icon

Table IV ΔDt for Fe 2936/Co 2990 and Ni 3051/Co 2990 as found on three plates, after correction for differences between the T.D. curves of these plates. Correction factors 1.00, 1.04, and 1.06, respectively. Gevaert Normal plates.

Equations (22)

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D t = log ( d 0 - d / d ) ,             or             D t = log [ ( d 0 / d ) - 1 ] ,
D t k = p + q D t k + 1 .
E k + 1 = n E k .
D t 1 = D t 0 - p q ;
D t 2 = D t 0 - p ( 1 + q ) q 2 ;
D t i = D t 0 - p ( 1 + q + q 2 + + q i - 1 ) q i .
D t i = D t 0 - p ( q i - 1 / q - 1 ) q i ,
log E i = log E 0 + i log n .
D t i = p q - 1 { q - ( log E i / log n ) - 1 } .
D t = p q - 1 { E - ( log q / log n ) - 1 } .
δ ( Den. ) δ q = 1 ;             δ ( Num. ) δ q = - p · E - ( log q / log n ) ;             0.4343 q · log n · log e E
[ D t ] q = 1 = - p log n · log E .
D t max = - p / q - 1.
D t A - D t S = p q - 1 { I A - - I S - } ,
Δ D t = p q - 1 { I S - ( m - - 1 ) } .
Δ D t = p q - 1 { ( I s · δ ) - ( m - - 1 ) } .
Δ D t - Δ D t = ± 0.005 = p q - 1 · I S - ( m - - 1 ) ( δ - - 1 ) ,
Δ D t ( δ - - 1 ) = ± 0.005.
Δ D t A - S = p q - 1 { I A - η - I S - η } ,
K = ( p / q - 1 ) { I c 1 - η - I c 2 - η } ( p / q - 1 ) { I c 1 - - I c 2 - } .
1 / K Δ D t A - S = χ · Δ D t A - S ,
I c 1 - - I c 2 - I c 1 - η - I c 2 - η = χ I A - - I S - I A - η - I S - η .