+
+
1696
Langmuir 1996, 12, 1696
Additions and Corrections Optical Second Harmonic Generation as a Probe of Selective Dissolution of Brass G. Nagy and D. Roy* Langmuir 1995, 11, 3457-3466. In line 3 of column 1 on page 3461, “lateral mode” is misprinted as “lateral model”. The quantity within the square bracket on the right-hand side of eq 36 should be (2) (V)|/|χ(2) read as: [f|l| + |χCu br (V)|]. The correct quantities (2) (Vr) and on the left-hand sides of eqs 37 and 38 are χCu (2) χbr (Vr), respectively. Equation 39 should be read as:
[ ] |χ(2) Cu(Vr)| |χ(2) br (Vr)|
≈ 1.17
[
]
2|χ(2) N′′Cuabr Cu(Vr)| ≈ N′′braCu 3ωτ|χ(2) br (Vr)|
2.34
In the first line below eq 42, the expression for η at 2.34 eV should be read as (3ωτ/2). In line 1, column 2, page 3464, 3τ ∼ 1 ps. Line 5 of the same column should read: “... square bracketed quantity on the right hand side of eq 36”. The approximation sign used in eq 29 has not been explicitly discussed in the paper. It has been brought to our attention that a discussion of this point may be useful to choose the appropriate expressions for the optical data in further SHG studies of alloys. Equations 27 and 28 are more general expressions for the surface SHG signal while eq 29 represents an approximation specific to our reported experimental system. This approximation is explained 2 below. Equation 28 states that |χ(2) r | ) [(x1 + x2) + (y1 + (2) (2) 2 1/2 y2) ] , where x1 ) Re[fl], y1 ) Im[fl], x2 ) Re[χCu/χbr ], and (2) (2) y2 ) Im[χCu /χbr ]. Here, x1 and y1 are found from l given on page 3461; x2 and y2 are found by using eqs 37 and 38 (2) (2) (2) ≈ χCu (Vr)FCu, χ(2) in 32 and 33: χCu br ≈ χbr (Vr)Fbr; FCu ) 1 + ∆Cu(V - Vr), Fbr ) 1 + ∆br(V - Vr). For the optical and electrochemical parameters used in the paper, x2(1.17 eV) ≈ [N′′Cuabr/N′′braCu][FCu/Fbr]1.17 ∼ 1, y1(1.17 eV) ≈ 0.1 and y2 (1.17 eV) ) 0. Within the limitations of eqs 37 and 38, and considering the simple order of magnitude estimate used for τ, these results at 1.17 eV are qualitatively combined as x1y2 ∼ y1x2 ∼ 0. This condition similarly applies to the 2.34 eV data. Using the appropriate optical parameters and br(2.34 eV) ) -6.25 + i1.86 from ref 49, we find x2(2.34 eV)/y2(2.34 eV) ≈ (36ω2/τ - 2/τ3)/(27ω3 12ω/τ2) ≈ 0 and x1(2.34 eV)/y1(2.34 eV) ∼ 0.3. These values allow for the simple estimate x1(2.34 eV)/y1(2.34 eV) ∼ x2(2.34 eV)/y2(2.34 eV) ∼ 0. From these considerations, we take x1y2 ≈ y1x2 for both the 1.17 and 2.34 eV data. This gives (x1y2 - y1x2)2 ≈ 0 and, subsequently, x1x2 + y1y2 ≈ [(x21 + y21)(x22 + y22)]1/2. This is equivalent to writing [(x1 + x2)2 + (y1 + y2)2]1/2 ≈ (x21 + y21)1/2 + (x22 + y22)1/2. This later expression leads to the simple, approximate form of eq 29 from eq 28. LA9600053
