US2699505A - Mass spectrometry - Google Patents

Description

Jan. l1, 1955 T, E, Usl-1ER ET AL 2,699,505

MASS SPECTROMETRY Filed Sept. 24, 1952 2 Sheets-Sheet 1 Jan. 1l, 1955 T, E USHER ET AL MASS SPECTROMETRY 2 Sheets-Sheet 2 Filed Sept. 24, 1952 75 Vapo/1 71%; l

United States Patent Oiiice 2,699,505 Patented Jan 11, 19.55

MASS SPECTROMETRY Thomas E. Usher, Scotia, and George Jernakol, Schenectady, N. Y., assignors to General Electric Company, a corporation of New York Application September 24, 1952, Serial No. 311,199 ti Claims. (Cl. Z50-41.9)

This invention relates generally to mass spectrometry and,` more articularly, to methods and apparatus for stabilizing tie sensitivity of the measurement of ions according to mass-to-charge ratio.

This application is a continuation in part of our copending application Serial No. 302,724, tiled August 5, 1,952, and assigned to the assignee of the present application.

Mass spectrometry can be defined as the art f anali/Zinc a gas or vapor by ionizing molecules of the gas or vapor, separating the ions according to mass-,to-charge ratio and selectively measuring the separated ions. Mass spectrometry is employed as a means of determining qualitatively and quantitatively the constituents of a vapor or gas,` or al mixture of vapors or gases, and as a means of measuring the isotope abundance ratios of the elements.

Several forms of mass spectrometer apparatus have been evolved to enable the practice of mass' spectrometry. All such apparatus are characterized by certain common elements which are required to perform the desired analyses. For example, all mass spectrometer apparatus include sample reservoirs from which the gases of vapors undergoing analyses are admitted through a leak to the apparatus for ionization and separation according to mass-to-charge tained within the regions of ionization and ion separation, the several forms of mass spectrometer apparatus also include a vacuum pump system for continuously evacuating such regions of the apparatus.

We have found that the effect of the aforementioned common elements of mass spectrometer apparatus can produce deleterious operational characteristics. Thus in the operation and utilization of mass spectrometer apparatus, unless the sensitivity of the apparatus is essentially independent of the pressure at which a sample is admitted, the speed of evacuation and the ultimate pressure to which the evacuable portions of the apparatus can be evacuated, the sensitivity varies greatly due to normal changes in the elements which determine such factors. As employed herein, sensitivity is defined as the amount of measured ion current, representing selec` tively separated ions, per unit of pressure of the admitted sample of gas or vapor. Since the magnitude of the measured ion current is the basis for the quantitative determination of the constituents of a sample, it therefore is apparent that sensitivity variations obviate the attainment of fully accurate analyses.

According to the present invention sensitivity variations from the above-.described causes are minimized or essentially eliminated by making the Sensitivity of mass spectrometer apparatus substantially independent of changes in sample, pressure, speed of evacuation and ultimate pressure. This is accomplished by providing certain specified interrelationships among the speed of evacuation, sample pressure, ultimate pressure, and ow conductances of the apparatus.

The features of the invention desired to be protected are set forth in the appended claims. The invention itself, together with further objects and advantages thereof, may best be understood by reference to the following specification taken in connection with the accompanying drawings in which Fig. l is a simplified schematic View, partially in section, of mass spectrometer apparatus according to the invention; Fig. 2 is a partly schematic view of an alternative flow construction which can be employed in the apparatus of Fig. l; and Fig. 3 is a ratio. A nd since a vacuum must be main- 2, simplified section view of a portion of a mass spectrometer tube which can be utilized in connection with certain of the apparatus of Fig. 1 according to the invention.

Referring particularly now to Fig. 1 there is shown in simplified schematic fashion mass spectrometer apparatus according to the invention. The apparatus comprises a mass spectrometer tube 1 which can be continuously evacuated through a pump connection 2 by means 0f a diffusion pump 3 and a mechanical rough vacuum pump d. Diusion pump 3 and rough pump 4 can be of couventional, commercially available types well known to those familiar with vacuum techniques. A vapor trap 5 is provided in the pump connection 2 between mass spectrometer tube 1 and diffusion pump 3 for the purpose of removing condensible vapors from the vacuum system. Vapor trap 5 is partially surrounded by a cooling medium 6, such as liquid nitrogen or air, contained within an insulated vacuum flask 7.

Mass spectrometer tube 1 can be any one ofthe several types known heretofore. For example, tube l can be of the type disclosed in U. S. Patent No. 2,535,032, issued to Willard H. Bennett on December 26, 1950, wherein ions are separated according to mass-to-.charge ratio by a plurality of linearly arranged unidirectional and radio frequency potentials, Altet-natively, tube 1 can be of the form disclosed in U. S. Patent No. 2,570,158, issued to Paul O. Schissel on October 2, 1961,v and assigned to the assignee of the present invention. In the Schissel tube, ions formed therein are accelerated by means of an alternating electric field against the force of an electrostatic or direct current electric lield having a linear space distribution, whereby the ions become separated in space according to mass-to-charge ratio. Also tube 1 can be as shown and described by Robert V. Langmuir in U. S.

patent application Serial No. 669,044, filed May 1l, 1946, and assigned to the assignee of the present invention. In the Langmuir tube ions are accelerated in spiral paths by an alternating electric tield. in the presence. of a maar netic field, whereby ions having natural frequency cora responding to the frequency of the alternating electric field are spatially separated from the remaining ions. As yet another alternative, tube 1 can be of the type disclosed by Gaylord W. Penney in U. S. Patent No. 2,581,813, issued January 8, 1,952, wherein ions are separated according to mass-to-charge ratio by a divergent alternating electric iield and a magnetic held. That still other forms of mass spectrometer tubes may be employed will be apparent as the description of the present invention proceeds.

Vapors or gases to be analyzed within mass spectrometer tube 1 are admitted from a sample reservoir 3 through a leak 9 which can consist of `a diaphragm of thin metal foil having minute holes therethrough. The metal foil is sealed about its periphery to a tubular connection lil' between reservoir 8 and tube l as illustrated. To assure desired ionization of admitted samples, connection 10 preferably extends within tube 1 to an ionization chamber 10 which is diagrammatically illustrated by the dotted lines. The vapors or gases admitted to tube 1 are ionized by electron bombardment within the ionization region and then separated according to mass-to-charge ratio. Indications of the magnitudes of the constituents of the gases are obtained as the ion currents representing each of the mass-to-charge ratios are selectively measured upon a current responsive measuring instrument 1l.. The various means for collecting and selectively measuring the ion currents are shown and described in the aforementioned patents relating to alternative forms of mass spectrometer apparatus.

As has been mentioned heretofore, the sensitivity of mass spectrometer apparatus as commonly employed has been found to vary with changes in the pressure within sample reservoir 8, the speed of evacuation, the ultimate pressure and the flow conductances of the apparatus. The reasons for this will be apparent from the f ollowing derivations of the flow relationships,

Assume that equilibrium conditions for a given sample analysis have been reached within the described apparatus of Fig. 1. Then where Nr. is the number of molecules per unit time entering through leak 9 and NP is the number of molecules per unit time exhausting through diffusion pump 3 and rough pump 4. Now, if F1. is the equivalent flow conductance of tubular connection including leak 9 and SP is the speed of evacuation (or conductance) of the vacuum pumping system at the juncture of pump connection 2 with tube 1 (neglecting any pressure differential within tube 1), we may write where n is the molecular density within the sample reservoir 8, n1 is the molecular density at the place where ions are formedin this case the same as the density within mass spectrometer tube 1, and nu is the molecular density corresponding to the ultimate pressure Pu to which the mass spectrometer tube 1 can be evacuated under dynamic conditions. Solving Equation 2 for n1, we obtain In practice, Sr is usually of the order of liters per second while FL is of the order of 105 or 10-4 liters per second, thus it may be stated that SP FL whereby Equation 3 may be simplified to F L n1=1 nl-n We know, however, that at equilibrium conditions and that obtained:

ne In 1 Within mass spectrometer tube 1 the number of ions formed per second is proportional to n1 and also proportional to the ion current measured by instrument 11. Denoting these proportionality constants by C, it follows that the magnitude of the ion current measured by instrument 11 equals Cn, whereby from Equation 7 we can write C' FLP P.,

0* k SPTTT1 (8) If the sensitivity of the mass spectrometer apparatus is dened, in accordance with the denition stated heretofore, as the ratio of the ion current measured by instrument 11 to the pressure P within sample reservoir 8, We obtain from Equation 8 Equation 9 shows clearly that the sensitivity of the described apparatus of Fig. l varies with changes in SP, Py and P. Thus, the characteristic changes in the pumping speed of diffusion pump 3-occurring from boiler temperature changes, alterations in the level of coollng medium 6, etc.-Vary the sensitivity of the mass spectrometer. Similarly, a change in the pressure of the sample has the effect of altering the sensitivity of the apparatus.

According to the present invention, sensitivity variations are minimized or essentially eliminated by making the sensitivity of the mass spectrometer apparatus essentlally independent of SP and P over the operating range of pressure P. This is accomplished by inserting a constnction 12 between the region of ionization with- Sensitivity--l 1 P 1 in mass spectrometer tube 1 and diffusion pump 3, and relating the ow conductance of the constriction to the remainder of the evacuation system in a manner which will be described presently. As illustrated in Fig. 1, constriction 12 can comprise a rotatable vane 13 mounted upon a shaft 14 Within pump connection 2. Near one edge of vane 13 is attached a magnetic slug 15, the weight of which maintains vane 13 in a normally closed position. Vane 13 can be rotated into its open position by means of a solenoid 16 which is energized by a source of current 17 upon closure of a switch 18.

If the flow conductance of constriction 12 with vane 13 in its closed position is denoted as FR, we may state for equilibrium conditions that where Nn. is the number of molecules per unit time passing through constriction 12. And, in a manner similar to the foregoing analysis, it follows that FL Pu :I S'PT+PT1 Now, with the proper adjustment of the ow conductances of leak 9' and constriction 12, the ratio FL/Fn can be arranged such that over the desired operating range of the mass spectrometer apparatus Pu FL FL PT, FRT S'PT With this adjustment, Equation 13 reduces to approximately Sensitivity=-g -FF-IZLT--l- (13) C FL Sensitivity-16T E] (15) and the sensitivity becomes essentially independent of P, Pu and SP.

It may be further shown that FL-:aIIB-f 16) and mig 17) where a and b are geometrical constants and M is the mass of the constituents of the sample considered individually. Equation 15 may now be written as aC' Sens1t1v1ty kMfmTO (18) Equation 18 shows that the sensitivity of the mass spectrometer apparatus under lthese latter specified conditions according to the invention is independent of all the above mentioned factors except the temperature of the sample vapor or gas and the temperature within the mass spectrometer tube. If these temperatures are maintained at constant values, or are permitted to change only in such manner as always to satisfy Equation 18 for a given constant value of sensitivity, the sensitivity of the mass spectrometer apparatus does not vary for given geometrical configurations which result in FL and FR.

In order to assure constancy of temperature of the sample gas or vapor and within mass spectrometer tube 1, there is shown in Fig. l in simplified, schematic fashion an enclosure 19 of heat insulating material whichis subdivided into sections 20 and 21. Heat is supplied to sample reservoir 8 and the portion of tubular connection adjacent sample reservoir 8. boy-:a current-carrying winding wrapped around sample reservoir 8 in any 1- venient manner and energized from a souree of eu nt 23 through a variable resistor; 24` and a disconneet switch 2.5.. Similarly, heat is Supplied to mass Spectremeter tube l by means of a winding 26 which is energized from source 2??. through switch 25 and a variable resistor 27. The temperature of sample reservoir- 8 can be measured with a thermocouple 28` connected to a calibrated` millivoltmeter 29, and the temperature of mass spectrometer tube 1 can be measured with a thermocouple 30 connected to a calibrated millivoltmeter 31. It is contemplated that a suitable automatic temperature regulating system can also 0e @replayed for the purpose of regulating the Current through windings 22 and 26 and thus maintaining the temperatures of sample reservoir S and mass speotrometer tube 1 desired constant or properly varying values. Furtherrngre, windings .2.2 and 26 need not be Placed as illustijated around reservoir 8 and tube 1, respectively, but can be distributed around the interior of sections and 211. Other well known forms of supplying heat to sections 2f) and 21 can be employed alternatively to obtain the desired temperatures.

It is preferable that sample reservoir 8 and the portion of tubular connection 10 s s s at essentially the same constant temperatures. lf reser- Voir 8 and the portion off tubular connection 10 preceding leak 9 are at widely different temperatures, undesirable thermal diffusion and thermal transpiration effects may occur. Thermal diffusion results in a gas or vapor of lighter mass traveling toward the cool portion of the system faster than a gas or vapor ofheavier mass, whereby the true proportions of light and heavy gas molecules in al sample are not measured. Thermal transpiration results` from a temperature gradient and causes'a` pressure differential of gases or vapors having thel same mass. Both of these effects are negligible if the temperature throughout the system including sample reservoir 8 and tube 1` is essentially the same. Of` course, it will be undersstood that these effects are frequently of no substantial significance and, if little variation of the temperatures of sample reservoir 8y and tube 1 occurs during equilibrium conditions of operation, no heating or cooling means for reservoir 8 and tube 1 need be utilized to secure the desired constant sensitivity in accordance with 'the invention.

In the operation of the mass spectrometerapparatus of Fig. 1, sample resem/oir 2")` can be closed off from tube 1y by means of a suitable valve (not shown) inserted into tubular connection 10 between reservoir 8 and leak" 9.

Reservoir S is evacuated and a sample for analysis introduced thereto by means of a vacuum pump and sample supply arrangement, which has not been shown for the purpose of simplifying the drawing, connected to a tubulation 31'. An arrangement which can be employed for such purpose is shown and described in U. S. Patenty No. 2,412,236, issued to Harold W. Washburn on December l0, 1946. The vane 13 is rotated to its open position and spectrometer tube 1 is exhausted by means of diffusion pump 3 and rough pump 4. Thereafter, vane 13, is rotated to its closed position and the sample gas or vapor is admitted to spectrometer tube 1 from reservoir 8 through leak 9. If the conditions as set forth above are observed, the sensitivity of the apparatus remains constant throughout the analysis of the sample,

It will be understood that the ilow conductance-xs of leak 9 and constriction 12 are arranged to fulfill the aforesaid conditions by constructing the openings therethrough such that the desired amount of resistance to flow is pro vided. In its closed position the vane 13 should not, of course, completely close off pumping connection 2 and, if necessary, a small hole (not shown). may be provided therein in order that the desired conductanee Fa is supplied. The proper pumping speed SP can be obtained by the correct selection of the diffusion pump 3 and rough pump 4 along with the interconnections to spectrometer tube l. The selection of these latter portions of the apparatus also serves in a large measure to determine the ultimate pressure to which "the system can be evacuated. The required pressure within sample reservoir .S can be arranged by the evacuation and admission of sample gas or vapor thereto. The pressure within spectrometer tube 1 is obtained as desired by the amount of sample gas or vapor admitted` to the tube and the speed of the evacuation.

invention:

F 10 microns lt is emphasized that these are order of magnitude values only and that such variations as fulfill the aforesaid equations are permissible to achieve the purpose of this invention, In the foregoing analysis the symbol is intended to refer to a difference in magnitude between two parameters of at least 10. Reduction of such specilied differences in magnitude much below a factor of 10 seriously affects the sensitivity stability of the mass spectrometer apparatus and renders the sensitivity response with sample pressure non-linear over the operating sample pressure range. The equations developed in the foregoing analysis are yvalid only in the molecular iilow range, i. e., when the mean free path of the gas or vapor molecules is at least: of the order of ten times the radius of the smallest aperture or orifice through which they must pass (see chapter 2 of EScientific Foundations of Vacuum Technique by Saul Bushman, Wiley and Sons, 1949).

in 2 there Vis shown an alternative form of constricion`12 which ean'be utilized in a vertically extending portion of pumpv connection 2. As shown this embodiment comprises a valve plate 32 which seats against an inwardly projeoting flange 33 of pump connection 2. Attached to valve plate 32 is a valve stem 34 which extends slidably thijoughbearings 35 and terminates in a magnetic sing 36. To raise the valve into its open position as illustrated by the dotted lines, a solenoid 37 may be energized from a. suitable source of current (not shown). If insufficient leakage to provide the desired conductance FP. according to the invention does not occur when the valve is in its closed position, a small aperture 38 may be provided in valve plate 32.

It will be understood from the foregoing analysis that, in order to achieve constant sensitivity according to the invention, the constriction 12 need only be situated between the region of ionization of the molecules of the sample gas or vapor and the diffusion pump 3. ln the forms of mass spectrometer tubes such as some of those mentioned heretofore wherein, it is either impossible or inconvenient to maintain the ionization region within a separate enclosure and at a substantally different pressure from' the region in which the ions are separated according to mass-to-charge ratio, constriction 12 can be positioned within pump connection 2 as illustrated in Fig. 1. However, in mass spectrometer tubes wherein ionization can be performed within a chamber relatively isolated from the region of ion separation, e. g. tubes of the type disclosed in Joseph G. Neuland patent application Serial No. 61,627, filed November 23, 1948, and assigned to the assignee of the present invention, the constriction having the conductance Fa can be located within the mass spectrometer tube. A portion of a mass spectrometer tube of this latter type is shown in Fig. 3 wherein numerals employed heretofore are used to identify similar elements. In this tube gaseous samples are admitted through leak 9 and tubular connection 10 to an ionization chamber or region 40 which is separated from the remainder of the tube by a box-,like structure 41. Within ionization chamber 4i), there is positioned a thermionic filament 42 which, when energized from a source of current (not shown), emits electrcns for the ionization by bombardment of the moleeules of the sample. The ions thus produced are accelerated and focused through a series of suitably charged apertured electrodes 43 and directed into an analyzer tube 44 wherein they are separated according to mass-to-charge ratio. A more detailed description of this tube and the associated energizing equipment making up the complete mass spectrometer apparatus may be found in the aforesaid Neuland patcntfapplication. Mass spectrometer apparatus employing a similar type of tube is also shown and described in U. S., Eatent No. 2,341,551, issued to Herbert Hoover, Ir., on February` 15, 1944.

In the mass spectrometer tube of Fig. 3i the conductance Fn, required to be supplied by a constriction according to the invention, is provided by an aperture 45 in conjunction with any additional passages from ionization chamber 40 into the mass spectrometer tube. The location of the constriction in this manner permits a higher pressure to be maintained within the ionization chamber than is maintained within the remainder of tube 1, whereby a shorter period of evacuation between sample analyses for any given mass spectrometer apparatus can be obtained. As illustrated in Fig. 3, the constriction supplying the conductance FR may be fixed at a desired size in accordance with the above-specified relations and need not be obtained through the employment of a movable valve or vane as described in connection with Figs. 1 and 2. The temperature of the ionization region in the mass spectrometer tube of Fig. 3 can be maintained at a desired constant value by means of a furnace 46 which comprises a current carrying winding 47 around the exterior of the tube between two layers of asbestos tape 48, If desired, heat may be supplied to tubular connection in a similar manner.

While the various direct current voltage supplies, high frequency oscillators, magnets, regulators,.etc., which are necessary for the operation of the several types of mass spectrometer tubes referred to herein have not been shown and described in detail, it will be understood that these components are to be utilized as explained by the pertinent patent applications and patents denoted above. Furthermore, although various portions of the mass spectrometer tubes and the vacuum system interconnections of the flgures of the drawings have been illustrated as being constructed of glass, it will be understood that other suitable material such as metal may be employed if desired. The measurement of the various pressures defined in the foregoing analysis can be accomplished through the use of conventional vacuum gages, e. g. the pressure within sample reservoir 8 can be measured with a McLeod gage or a micro-manometer and the pressure within the mass spectrometer tube may be measured with an ionization gage. Calculation and determination of the size of apertures or orices to give the desired flow conductances required in the performance and utilization of the invention can be made as outlined by Saul Dushman in his aforementioned text (N. B. chapter 2). It should also be noted that the constriction 12 of Fig. 1 can be obtained by any suitable orifice of fixed dimensions, providing the above-specified necessary inter-relationships are satisfied.

While the invention has been described by reference to particular embodiments thereof, it will be understood that numerous changes may be made by those skilled in the art without actually departing from the invention. We, therefore, aim in the appended claims to cover all such equivalent variations as come within the true spirit and scope of the foregoing disclosure.

What we claim as new and desire to secure by Letters Patent of the United States is:

1. Mass spectrometer apparatus for sample analysis according to mass-to-charge ratio comprising a mass spectrometer tube including means for ionizing the molecule of a sample and means for separating and selectively measuring the ionized molecules according to mass-to-charge ratio, a sample inlet system for admitting samples at a pressure P and a temperature T to said mass spectrometer tube and having an equivalent flow conductance FL, means for evacuating said mass spectrometer tube to an ultimate pressure Pu at a temperature T1 including a vacuum pumping system connected to said mass spectrometer tube, a ilow constriction disposed beyond said ionization means in the direction of ow and having a flow conductance FR at least during the period of sample analysis, said evacuating means having a speed SP at a position in the direction of ow beyond said flow constriction, said flow conduct.- ances` pressures and evacuation speed having the following interrelationships:

tion includes a valve capable of being adjusted to have said flow conductance FR.

3. Apparatus as in claim 1 wherein said iiow constriction includes a member having at least one aperture of lixed dimensions.

4. Apparatus as in claim 2 wherein said valve is disposed in the connection of said evacuating means to said mass spectrometer tube. A

5. Mass spectrometer apparatus for sample analysis according to mass-to-.char'ge ratio comprising a mass spectrometer tube including means for ionizing the molecules of a sample and means for separating and selectively measuring the ionized molecules according to mass-to charge ratio, a sample inlet system for admitting samples to said mass spectrometer tube at a pressure P and a temperature T including a sample reservoir connected to said mass spectrometer tube through a flow conductance F1., means for evacuating said mass spectrometer tube to an ultimate pressure Pu at a temperature T1 including a vacuum pumping system connected to said mass spectrometer tube, a ow constriction disposed beyond said ionization means in the direction of iiow and having a iiow conductance FR. at least during the period of sample analysis said evacuating means having a speed SP at a position in the direction of ilow beyond said flow constriction, said tiow conductances, pressures and evacuation speed having the following interrelationships:

PIl F L FL P7', FRT S'PT means for maintaining the connection of. said sample reservoir to said mass spectrometer tube at a constant temperature, and means for maintaining at least the ionizing means of said mass spectrometer tube at a constant temperature.

6. Apparatus as in claim 5 in which the constant temperatures at which said sample reservoir connection and at least said ionizing means are maintained are essentially the same.

7. Mass spectrometer apparatus for sample analysis according to mass-to-charge ratio comprising a mass spectrometer tube including means for ionizing the molecules of a sample and means for separating and selectively measuring the ionized molecules according to mass-tocharge ratio, a sample inlet system for admitting samples to said mass spectrometer tube at a pressure P and a temperature T including a sample reservoir connected to said mass spectrometer tube through a ilow conductance FL, means for evacuating said mass spectrometer tube to an ultimate pressure P at a temperature T1 including a vacuum pumping system connected to said mass spectrometer tube, a iiow constriction disposed beyond said ionization means in the direction of flow and having a ow conductance FR at least during the period of sample analysis, said evacuating means having a speed Sp at a position in the direction of flow beyond said flow constriction, said ow conductances, pressures and evacuation speed having the following interrelationships:

means for maintaining said sample reservoir and its interconnection to said mass spectrometer tube at a constant temperature, and means for maintaining said mass spectrometer tube at a constant temperature.

8. The method of separating a gaseous mixture into its constituent components in accordance with their mass to charge ratios which comprises introducing a sample of the gaseous mixture into a sample region, maintaining the mixture in the sample region at a desired sample region temperature and pressure, admitting the gaseous mixture from the sample region into an ionizing region undergoing continuous evacuation through an inlet having an inlet flow conductance, ionizing some of the gaseous mixture in -an .ionlzing region, maintaining the gaseous mixture in the iomzing region at a desired ionizing region temperature, evacuating un-ionized molecules of the gaseous mixture at a predetermined speed of evacuation through an outlet having an outlet ow conductance into a region having an ultimate evacuation pressure in a manner such that the speed of evacuation of the ionizing region and the outlet ow conductance are much greater than the inlet ow conductance and the ratio of the ultimate evacuation pressure to the product of the pressure of the gaseous mixture in the sample region times the temperature of the gaseous mixture in the ionizing region is much less than the ratio of the inlet How conductance to the product of the outlet ow conductance times the temperature of the gaseous 10 mixture in the sample region and the last-mentioned ratio is much greater than the ratio of the inlet flow conductance to the product of the speed of evacuation of the ionizing region times the temperature of the gaseous mixture in the sample region, separating the ionized gaseous molecules in the ionizing region in accordance with their mass to chargeratios, and selectively collecting ions having a desired mass to charge ratio.

No references cited.

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