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Intensity distribution in charge-exchange continua formed in a 180-degree, magnetic deflection mass spectrometer
International Journal of Mass Spectrometry ad Iool:Physics
EIsevierPublishingCompany, Arnderdam. Printedin the Nether&r&
INTENSITY DISTRIBUTION IN CHARGE-EXCHANGE CCWIINUA FORMED IN A 180-DEGREE, MAGNETIC DEFLECTION MASS SPECTROMETER J. M. blCCREA
P-0. Box 172, Monroedie,
Pa. 1.5146 (U.S.A.)
(Received September2701, 1971)
ABs-rRAcr
e The intensity distribution for charge-exchange continua produced in a 180degree, direction-fotiussing, magnetic deflection mass spectrometer has been deduced theoretically assuming uniform exchange probability along equal lengths of primary ion trajectory. Distributions for the 2-k to 1 -t charge exchange are compared with the case of the Mattauch-Herzog instrument geometry. In an earlier paperl, equations fo;_ the intensity distribuzion in the chargeexchange cor;tinua produced in the magnetic sector of a Mattauch-Herzog mass spectrometer were developed. This treatment is modifiable to obtain results applicable to a 180” magnetic mass analyzer. The modified treatment and results obtained for the 180” case are presented here. The geometric conditions for the trajectory of the ion undergoing a charge change from +p to +p--n at a point E are illustrated in Fig. 1. The radii of the initial circular arc OE and of the final arc ES are in the ratio (p-n)/p, and may be denoted by (p-n)r and pr, respectively. The coordinates of E, the point of charge exchange, and C, , the center for the final arc may be written by inspection as (p-n)r
sin 0,
(p-n)r(l
-cos
0)
and --nr sin 8,
(p-n)r+-nr
cos 0.
By simplification of the quadratic equation for thi arc ES subject to the condition x = 0, a quadratic in y, 3J”-22yrCy-41 I&. J.
-cos
e)]-2&(p-?zn)(l
Mass Spectrom. Ion Phys., 9 (1972)
-cos
e) =: 0 167
0
X
Fig. 1. Schematic diagram for charge-exchange trajectory. The ion enters the uniform 180” magnetic field perpendicularly at 0, traverses a circular arc about center C sweeping out an angle B and then undergoes charge exchange at E. From E it continues on a circular arc of larger radius with center C1 until it strikes the focal plane OY at S. S1 and S2 are, respectively, the locations where ions not undergoing charge exchange and ions undergoing charge exchange immediately on entry into the field at 0 would intercept OY.
is obtained. The resulting solution for the ordinate OS is ___~ y = r[p--n(lcos i3)]+r’jp2--n2 sin2 8
(11
With the assumption that the cross-section for charge is independent of 8 and that the total amount of charge exchange is a small proportion of the primary ion beam, equal amounts of charge exchange take place over equal increments of the angle 6. The ions resulting from char ge exchanges corresponding to an increment df? are thus detected along an increment dy in the focal plane of the 180” analyzer, and their relative intensity is given by dQ/dy or (dy,ld6)-‘. Differentiation of eqn. (1) yields
dv -= d0
-nr
sin 8
(2)
the necesshlry expression for computing relative intensity in terms of 8. The resuits obtained by evaluating y and d0/dy from eqns. (1) and (2) at various values of 6 describe the intensity variation to beobserved in a chargeexchange continuum recorded on an ion-sensitive plate detector placed in the focal pl&e of a 180” direction-focussing mass spectrometer. The quantity S,S,/S,S2 or (y-y&y,-y,); the ratio of the lengths of the straight line segments S,S and 168
Int. J. Mass Spec?rom. Ion Phys., 9 (1972)
Fig. 2. Rulative intensity of a 2+ to 1 f charge-exchange continuum as a function of displacement. Solid line, case of detectionby an ion-sensitiveplate along 0‘ with SISjSISz as abscissa; dashed
line, case of fixed slit and magnetic scan with (H-H,)/B, exponentialvoltage scan with t/4 as abscissa.
as abscissa; dotted line, case of
S,S, in Fig. 1, forms a useful dimensionless measure of position along the continuum. It is used as one abscissa scale in Fig. 2 where data calculated for a 2-k to 1 + charge excha.nge are shown. When an ion collector located at a fixed point in the focal plane of +he spectrometer is used to study continua, the distance OS is geometrically fixed and different values of 8 can be obtained only by changing the effective value of I-. The effective value of r for the case of a 2+ to 1+ charge exchange should cover all values between $(OS) for 8 = 0 and *(OS) for 8 = 180”. For a given ion, r is determined by the magnetic field strength H and ion accelerating voltage V, and is proportional to V*/H. Thus with V constant, the field H, will locate S2 at S, and the field HI = 2H, will locate S, at S. Similarly, with H constant, the voltage V2 wiL locate S, at S, and the voltage
V,
= &V, will locate S, at S. The field H
may be conveniently scanned through the required range by adjusting the magnet current, and the dimensionless expression (H- H&H2 is a convenient variable for recording the progress of the scan. In the case of V, an appropriate RC circuit may be used to let Vdecrease exponentially from the value V+ towards zero as time t progresses. The ratio f/f* is a convenient variable for following progress of the scan where t-, is defined as the time required for the accelerating voltage Y to drop to one quarter of its initial value. Relative intensity data for continua obtained by magnetic and exponential vohage scanning are shown in Fig. 2 along with data for the ion-sensitive plate method. Figure 3 gives a comparison between the Mattauch-Herzog case reported before’ and the 180” case discussed here. Both cases show a high intensity in the Inf. 3. Mass
Spectrom. Ion Phys., 9 (19?2)
_.
169
2.0 -
7.6 -
1.2 -
Q8-
o.4, 0
Q2
08
0.4
0.8
)
Fig. 3. Relative intensity of a 2 + to 1 -I- charge-exchange continuunr as a function of displacement for different instrument geometries, with SIS&St as abscissa. Solid line, case of 180” instrument with ion-sensitive plate detection; dotted line, case of Mattauch-Herzog geometry with ionsensitive plate detection.
continua where the charge exchange takes place near the end of the primary trajectory and the secondary trajectories are effectively short tangents to the primary trajectory. The second high intensity end for the 180” case- results from the entry of the primary ion beam in a direction normal to the focal plane of the spectrometer.
REFERENCE J. M. MCCRW, Int. J. Mass Spectrom. Ion Phys., 5 (1970) 381. The author would two errors on p. 383 of this reference. The left-hand side of eqn. (3) should read the word “directly” should be added to the sentence immediately preceding The corrected sentence thus should read: “The irtensity variation along OS is proportiona! to cLazq2 per increment de in 6, or directly to de/&.”
170.
:
hf.
-.
J. Muss
like to correct -2dxjd6 and the equation. thus inversely
Spictrom. Ion Phys.; 9 (1672)
EIsevierPublishingCompany, Arnderdam. Printedin the Nether&r&
INTENSITY DISTRIBUTION IN CHARGE-EXCHANGE CCWIINUA FORMED IN A 180-DEGREE, MAGNETIC DEFLECTION MASS SPECTROMETER J. M. blCCREA
P-0. Box 172, Monroedie,
Pa. 1.5146 (U.S.A.)
(Received September2701, 1971)
ABs-rRAcr
e The intensity distribution for charge-exchange continua produced in a 180degree, direction-fotiussing, magnetic deflection mass spectrometer has been deduced theoretically assuming uniform exchange probability along equal lengths of primary ion trajectory. Distributions for the 2-k to 1 -t charge exchange are compared with the case of the Mattauch-Herzog instrument geometry. In an earlier paperl, equations fo;_ the intensity distribuzion in the chargeexchange cor;tinua produced in the magnetic sector of a Mattauch-Herzog mass spectrometer were developed. This treatment is modifiable to obtain results applicable to a 180” magnetic mass analyzer. The modified treatment and results obtained for the 180” case are presented here. The geometric conditions for the trajectory of the ion undergoing a charge change from +p to +p--n at a point E are illustrated in Fig. 1. The radii of the initial circular arc OE and of the final arc ES are in the ratio (p-n)/p, and may be denoted by (p-n)r and pr, respectively. The coordinates of E, the point of charge exchange, and C, , the center for the final arc may be written by inspection as (p-n)r
sin 0,
(p-n)r(l
-cos
0)
and --nr sin 8,
(p-n)r+-nr
cos 0.
By simplification of the quadratic equation for thi arc ES subject to the condition x = 0, a quadratic in y, 3J”-22yrCy-41 I&. J.
-cos
e)]-2&(p-?zn)(l
Mass Spectrom. Ion Phys., 9 (1972)
-cos
e) =: 0 167
0
X
Fig. 1. Schematic diagram for charge-exchange trajectory. The ion enters the uniform 180” magnetic field perpendicularly at 0, traverses a circular arc about center C sweeping out an angle B and then undergoes charge exchange at E. From E it continues on a circular arc of larger radius with center C1 until it strikes the focal plane OY at S. S1 and S2 are, respectively, the locations where ions not undergoing charge exchange and ions undergoing charge exchange immediately on entry into the field at 0 would intercept OY.
is obtained. The resulting solution for the ordinate OS is ___~ y = r[p--n(lcos i3)]+r’jp2--n2 sin2 8
(11
With the assumption that the cross-section for charge is independent of 8 and that the total amount of charge exchange is a small proportion of the primary ion beam, equal amounts of charge exchange take place over equal increments of the angle 6. The ions resulting from char ge exchanges corresponding to an increment df? are thus detected along an increment dy in the focal plane of the 180” analyzer, and their relative intensity is given by dQ/dy or (dy,ld6)-‘. Differentiation of eqn. (1) yields
dv -= d0
-nr
sin 8
(2)
the necesshlry expression for computing relative intensity in terms of 8. The resuits obtained by evaluating y and d0/dy from eqns. (1) and (2) at various values of 6 describe the intensity variation to beobserved in a chargeexchange continuum recorded on an ion-sensitive plate detector placed in the focal pl&e of a 180” direction-focussing mass spectrometer. The quantity S,S,/S,S2 or (y-y&y,-y,); the ratio of the lengths of the straight line segments S,S and 168
Int. J. Mass Spec?rom. Ion Phys., 9 (1972)
Fig. 2. Rulative intensity of a 2+ to 1 f charge-exchange continuum as a function of displacement. Solid line, case of detectionby an ion-sensitiveplate along 0‘ with SISjSISz as abscissa; dashed
line, case of fixed slit and magnetic scan with (H-H,)/B, exponentialvoltage scan with t/4 as abscissa.
as abscissa; dotted line, case of
S,S, in Fig. 1, forms a useful dimensionless measure of position along the continuum. It is used as one abscissa scale in Fig. 2 where data calculated for a 2-k to 1 + charge excha.nge are shown. When an ion collector located at a fixed point in the focal plane of +he spectrometer is used to study continua, the distance OS is geometrically fixed and different values of 8 can be obtained only by changing the effective value of I-. The effective value of r for the case of a 2+ to 1+ charge exchange should cover all values between $(OS) for 8 = 0 and *(OS) for 8 = 180”. For a given ion, r is determined by the magnetic field strength H and ion accelerating voltage V, and is proportional to V*/H. Thus with V constant, the field H, will locate S2 at S, and the field HI = 2H, will locate S, at S. Similarly, with H constant, the voltage V2 wiL locate S, at S, and the voltage
V,
= &V, will locate S, at S. The field H
may be conveniently scanned through the required range by adjusting the magnet current, and the dimensionless expression (H- H&H2 is a convenient variable for recording the progress of the scan. In the case of V, an appropriate RC circuit may be used to let Vdecrease exponentially from the value V+ towards zero as time t progresses. The ratio f/f* is a convenient variable for following progress of the scan where t-, is defined as the time required for the accelerating voltage Y to drop to one quarter of its initial value. Relative intensity data for continua obtained by magnetic and exponential vohage scanning are shown in Fig. 2 along with data for the ion-sensitive plate method. Figure 3 gives a comparison between the Mattauch-Herzog case reported before’ and the 180” case discussed here. Both cases show a high intensity in the Inf. 3. Mass
Spectrom. Ion Phys., 9 (19?2)
_.
169
2.0 -
7.6 -
1.2 -
Q8-
o.4, 0
Q2
08
0.4
0.8
)
Fig. 3. Relative intensity of a 2 + to 1 -I- charge-exchange continuunr as a function of displacement for different instrument geometries, with SIS&St as abscissa. Solid line, case of 180” instrument with ion-sensitive plate detection; dotted line, case of Mattauch-Herzog geometry with ionsensitive plate detection.
continua where the charge exchange takes place near the end of the primary trajectory and the secondary trajectories are effectively short tangents to the primary trajectory. The second high intensity end for the 180” case- results from the entry of the primary ion beam in a direction normal to the focal plane of the spectrometer.
REFERENCE J. M. MCCRW, Int. J. Mass Spectrom. Ion Phys., 5 (1970) 381. The author would two errors on p. 383 of this reference. The left-hand side of eqn. (3) should read the word “directly” should be added to the sentence immediately preceding The corrected sentence thus should read: “The irtensity variation along OS is proportiona! to cLazq2 per increment de in 6, or directly to de/&.”
170.
:
hf.
-.
J. Muss
like to correct -2dxjd6 and the equation. thus inversely
Spictrom. Ion Phys.; 9 (1672)