US3089056A

US3089056A - Storage tube

Info

Publication number: US3089056A
Application number: US9080A
Authority: US
Inventors: Norman H Lehrer
Original assignee: Hughes Aircraft Co
Current assignee: Raytheon Co
Priority date: 1960-02-16
Filing date: 1960-02-16
Publication date: 1963-05-07
Anticipated expiration: 1980-05-07

Description

N. H. LEHRER 3,089,056

STORAGE TUBE 2 Sheets-Sheet 1 May 7, 1963 Filed Feb. 16. 1960 N. H. LEHRER May 7, 1963 STORAGE TUBE 2 Sheets-Sheet 2 Filed Feb. 16. 1960 my, i@ W/. s au. M WQ 4 -7 W |5/ t 5 14M ...am M 2 0. f 4, M .d m

UnitedStates Patent O 3,089,056 STORAGE TUBE Norman H. Lehrer, Los Angeles, Calif., assignor to Hughes Aircraft Company, Culver City, Calif., a corporation ofv Delaware Filed Feb. 16, 1960, Ser. No. 9,080 4 Claims. (Cl. 315-12) This invention relates to a visual display storage tube and more particularly to a cathode ray tube incorporating -a storage screen adapted to operate with a high energy level Writing beam in a manner to effect high writing speed and simultaneously provide a presentation having a high resolution.

Application for patent entitled, Storage Tube, Serial No. 800,180, filed March 18, l959, now abandoned, and assigned to the present assignee, is continued herein.

Present day storage tubes generally depend on secondary electron emission or electron bombardment induced conductivity charging mechanisms to effect writing on a storage surface. In the case of secondary electron emission mechanism, positive charging takes place in that region of electron beam energies where the secondary electron emission ratio is greater that unity, that is, intermediate the first and second crossover potentials of the secondary emission characteristic. Since the secondary electron emission ratio is highest for the lower range of beam energies and space-charge considerations dictate that the maximum amount of current that can be focused into a given spot size is proportional to the three-halves power of the beam voltage, it is evident that increased writing speed achieved by increasing the beam current can only be achieved by sacrificing resolution.

For the bombardment induced conductivity mechanism, on the other hand, application of presently available data to the design of a storage tube results in inherent limitations in writing speed. For example, dielectric materials employed for the storage surface film are generally of from one to two microns thick as thinner films result in increased persistence but slower writing speed, while thicker films decrease the persistence but increase the writing and erase speeds. In practice, it requires an electron beam having an energy level of the order of i4 kilovolts to produce a reasonable value of bombardment induced conductivity through a film of silicon monoxide of from one to two microns thick. At thisenergy level, a potential drop of 150 volts across the storage surface film results in a conduction ratio of approximately 30. At this value of potential drop, however, operation of a half-tone storage tube is erratic since backplate potentials that are greater than the first crossover of the secondary electron emission characteristic, generally around 40 to 50 volts, cause the electrons of the viewing or fiood beam to land with sufficient energy on the storage surface as to drive portions of it to the potential of the collector grid.

It is apparent, therefore, that the potential applied to the backplate is a limiting factor in the operation of half-tone storage tubes in that it may not exceed 30 to 40 volts. This reduced potential drop across the storage surface film necessitates the use of a thinner film to obtain the necessary electric field strength which will produce reasonable values of the conduction ratio. the thickness of the storage surface film, however, produces substantial increases in the capacity of such a target and, as compared with the aforementioned conventional target, the increased capacity is not compensated for by the increase in the gain of the writing mechanism due to the increase in the conduction ratio whereby the resulting writing speed is actually substantially decreased. In addition to the foregoing, decreasing the thickness of the Decreasing v 3,089,056 Patented May 7, 1963 ICC storage surface film of -a conventional target also increases the persistence and erasure time which may also be objectionable.

It is therefore an object of the present invention to provide a storage tube incorporating an improved storage screen adapted for use with a high energy writing beam with its concomitant high resolution without loss of writing speed.

Another object of the present invention is to provide a visual display half-tone storage tube incorporating a storage screen which utilizes secondary electron emission and electron bombardment induced conductivity mechanisms to effect writing.

Still another object of the present invention is to -provide a visual display half-tone storage tube incorporating a storage screen having a thin storage Surface film having bombardment induced conductivity characteristics and which requires a sufficiently low electric field -thereacross as to be consistent with stable half-tone operation of the tube.

A further object of the present invention is to provide a half-tone storage tube incorporating a storage screen having a storage surface with enhanced secondary electron emission characteristics.

A still further object of the present invention is to provide anA electron storage tube including a storage screen constituted of a uniformly thin layer of cubic zinc sulfide disposed over a conductive substrate.

According to the present invention, a visual display half-tone storage tube is provided which incorporates an improved storage screen which includes a conductive screen covered with a layer of dielectric material one or more microns thick, which material exhibits enhanced bombardment induced conductivity. In addition, an extremely thin film of high secondary emitting material such as magnesium fluoride may be coated over the dielectric material exhibiting enhanced bombardment induced conductivity. The thickness of this film is made `as thin as possible consistent with the retention of its high secondary electron emission characteristics so as to allow penetration therethrough into the underlying dielectric material by a high energy level writing beam. In operation, a positive potential drop of a magnitude that is less than the first crossover potential is maintained across the composite storage surface layer and the writing beam is scanned over the storage screen to produce a charge pattern on the storage surface by both secondary f electron emission and electron bombardment induced conductivity charging mechanisms. Lastly, a viewing gun illuminates the storage screen with fiood electrons which vpenetrate therethrough in proportion to the charge thereon and are directed to a viewing screen.

The above-mentioned storage screen is realized by producing a thin film of cubic zinc sulfide on a conductive substrate which preferably also has material with an exposed cubic lattice structure in contact with the cubic zinc sulfide. It has been found that of the three types of zinc sulfide, only cubic zinc sulfide possesses the desired properties suitable for use in the present invention. Arnorphous zinc sulfide was found not to possess bombardment induced conductivity characteristics and hexagonal zinc sulfide, although having bombardment induced conductivity characteristics, has a resistivity that is sufficiently low to make it unusable for charge storage purposes. Also, cubic zinc sulfide is not normally obtained by conventional evaporative processes. Further, as described above, a thin film of magnesium fluoride may be evaporated over the layer of cubic zinc sulfide to enhance the secondary electron emission characteristics of the storage surface.

The above-mentioned and other features and objects of this invention, and the manner of obtaining them, will become more apparent by reference to the following description taken in conjunction with the accompanying drawings, wherein:

FIG. 1 is a cross-sectional schematic view of the halftone visual display storage tube of the present invention;

FIGS. 2 and 3 are an enlarged cut-away perspective and an enlarged cross-sectional view, respectively, of the storage screen in the device of FIG. l; and

FIG. 4 shows the writing speed characteristic of the device of FIG. 1.

Referring now to the drawings, FIG. 1 shows a halftone visual display storage tube in accordance with the present invention. This tube comprises an evacuated envelope which includes a comparatively large cylindrical section 1'1 having a face plate 12 at the right extremity as viewed in the drawing, and a non-axially aligned neck portion 13 at the left extremity thereof. The neck portion 13 houses an electron gun 14 for producing an electron beam of elemental cross-sectional area. Horizontal and vertical magnetic deflecting coils 15 are disposed concentrically about the neck portion 13 adjacent the cylindrical section 11 for controlling the deflection of the electron beam. The electron gun 14, of course, may be electrostatically deflected if desired. A viewing gun 16 for producing a viewing beam of flood electrons is disposed concentrically within the cylindrical section 11 at the left extremity thereof as shown in the drawing.

- On the inner surfa'ce of the face plate 12opposite the electron gun 14 and the viewing gun 16, there is disposed a viewing screen 18 which includes a phosphor screen 19 covered with a thin lm of aluminum 20. Adjacent to and coextensive with the viewing screen 18, there is disposed, in the order named, a storage screen 22 and its associated collector grid 24. Referring to FIGS. 2 and 3, there is shown an enlarged perspective portion and an enlarged cross-sectional portion, respectively, of the storage screen 22. Referring to these figures, storage screen 22 includes an electroformed nickel mesh 25 having from 100 to 400 meshes per inch and preferably of the order of 250 meshes per inch, a thickness of the order from 1 to 2 mils and an overall transparency of the order of 60%. When nickel is used for the mesh 25, it is desirable to plate it with a thin film of rhodium to prevent chemical reaction with the storage surface material. On the side of the electroformed nickel mesh 25 facing the electron gun 14 and viewing gun 16, there is disposed a thin layer 26 of insulative material which exhibits a secondary electron emission ratio greater than unity and bombardment induced conductivity characteristics throughout overlapping ranges of electron energies. As is generally known, the secondary electron emission ratio is greater than unity from the first to the second crossover potentials, the second crossover potential being the higher potential level which is sometimes otherwise known as the sticking potential. The layer 26 constitutes a coating of cubic zinc sulfide disposed coextensive with the meshes of electroformed nickel mesh 25 and having a thickness of the order of 0.65 micron. This layer 26 of cubic zinc sulfide is disposed on the electroformed nickel mesh 25 by an evaporation process, which process may be performed in a conventional manner. In order to convert all of the zinc sulfide to the cubic lattice form, however, the mesh 25 is first etched in an acid bath to expose its cubic-type lattice structure. Subsequent to the evaporative process, it was found that aging the storage screen 22 in a dark place either in a vacuum or at atmospheric pressure and at a temperature of from 70 to 80 F. for a period of approximately one month converted all of the zinc sulfide to the cubic lattice type. There are also other methods for producing cubic zinc sulfide which are known to the art. In the event that it is desired to enhance the secondary electron emission characteristics of the storage screen 22, a thin film 27 of magnesium fluoride of the order of 500 Angstroms in thickness is evaporated over the layer 26 of zinc sulfide. In general, the thin film 27 of magnesium fluoride should be as thin as possible consistent with preserving the high secondary electron emission characteristics of the magnesium fluoride so as to allow a high energy beam of electrons to penetrate therethrough into the layer 26 of cubic zinc sulfide to raise electrons therein to the conduction energy level. Thicknesses in both cases may be determined by the use of an interferometer. Lastly, a thin fllm of gold is evaporated on the side of mesh 25 opposite the side on which layer 26 is disposed so as to cover any dielectric particles which may have been inadvertently deposited on this side.

Referring again to FIG. l, the collector grid 24 is provided by a conductive screen having a transparency that is preferably of the order of which screen is supported about its periphery by an annular ring 30. Further, an annular electrode 32 or can is juxtaposed to the annular ring 30 of collector grid 24 and extends away from the face plate 12 for a distance of several inches, the exact distance depending on the size of the tube. During operation, the viewing screen 18 is maintained at a potential of the order of 6,000 volts positive with respect to ground by a suitable connection from the aluminum film 20 to the positive terminal of a battery 34, the negative terminal of which is referenced to ground. Also, the electroformed nickel mesh 25 of storage screen 22 and the collector grid 24 are maintained at potentials of +20 volts and +120 volts relative to ground, respectively. This may be accomplished, for example, by a connection from the annular support ring 30 of collector grid 24 to the positive terminal of a battery 36, the negative terminal of which is referenced to ground. A potentiometer 37 is connected across the terminals of battery 36, and an adjustable tap 38 is connected therefrom to the nickel mesh 25 of the storage screen 22 and set to provide the desired voltage. Next, the annular electrode 32 is maintained at a potential of the order of +40 volts positive with respect to ground by means of a connection therefrom to an appropriate intermediate tap of battery 36.

Lastly, an equal potential region is maintained throughout the neck portion 13 and the remaining left portion of cylindrical section 11 by a conductive layer 40 disposed about the inner periphery of neck portion 13 coextensive with the gun 14 and about the inner periphery and left appendage of the cylindrical portion 11. During operation, conductive layer 40 is maintained at a potential of the order of +5 volts positive with respect to ground by a suitable connection therefrom to the positive terminal of a battery 42, the negative terminal of which is referenced to ground.

As previously specified, neck portion 13 of evacuated envelope 10 houses electron gun 14 whichv is of conventional construction. The electron gun 14 includes a cathode 46 and an intensity grid 47. The cathode 46 of gun 14 is maintained at a potential of the order of -7000 volts with respect to ground by means of a connection therefrom to an intermediate negative terminal of a battery 48, the positive terminal of which is referenced to ground. Further, the intensity grid 47 of gun 14 is maintained at a quiescent potential of the order of 30 volts negative with respect to the potential of cathode 46 by means of a connection therefrom through a load resistor 50 to the negative terminal of the battery 48. Means for modulating the intensity of the electron beam is provided by a connection from an input terminal 53 through a capacitor 54 and across the load resistor 50 to the intensity grid 47 of gun 14. The electron beam produced by electron writing gun 14 is scanned over the storage screen 22 in a desired manner by means of horizontal and vertical deflection currents generated by horizontal and vertical deflection current generator 56. The horizontal and vertical deflection signals are applied to the horizontal and vertical deection coils by means of appropriate connections thereto.

A .point source of flood electrons is provided by the viewing gun 16 which is disposed along the longitudinal axis of the cylindrical portion 11 of the evacuated envelope 10 at the left extremity thereof as viewed in the drawing. Viewing gun 1-6 includes a cathode 80 and an intensity electrode 81 which encloses the cathode 80 except for a small circular aperture 82 disposed over the central portion of the cathode 80, and an annular electrode 84 disposed adjacent to the periphery of intensity electrode 81, as shown in the drawing, and concentrically about the circular aperture 82. In operation, cathode 80 of viewing gun 16 is referenced to ground by means of a connection therefrom to ground. Further, the intensity electrode 81 and the annular electrode 84 are maintained, respectively, at potentials of the order of -20 and +100 volts with respect to ground by means of connections therefrom to adjustable taps 87, 88 of potentiometer 90. The potentiometer 90, in turn, is connected across the positive and negative terminals of a battery 92 and an intermediate terminal thereof referenced to ground.

In operation of the device of the present invention, voltages are applied to the various electrodes in the manner hereinbefore specified. In particular, a potential of +20 volts is applied to the nickel mesh 25 of storage screen 22. Because of the capacitance between the nickel .mesh and the storage surface, it is evident that the storage surface will initially assume a potential of +20 volts also. In that this potential is less than the first crossover potential of the secondary electron emission characteristic, the flood electrons from viewing gun 16 which emanate from cathode 80 which is maintained at ground potential, charge the storage surface -in a negative direction until the ood electrons can no longer impinge thereon; that is, until the storage surface is charged negatively to the extent that it repels the flood electrons. In order to operate the device in a half-tone mode, however, it is desirable to maintain the storage surface at a quiescent potential that is negative relative to the potential of the cathode 80 of viewing gun 16. In order to accomplish this, positive pulses are applied to the nickel mesh 25 of storage screen 22 at a repetition rate that is in excess of the icker rate.

This may `be accomplished by inserting a load resistor 98 in the lead from adjustable tap 38 of potentiometer 37 to the mesh 25 of storage screen 22. A pulse generator 100 is then coupled across the load resistor 98, the lead which connects from the generator 100 to the junction between load resistor 98 and the adjustable tap 38 1being referenced to radio-frequency ground. The amplitude of the pulses developed across load resistor 98 by the pulse generator 100 determines the extent to which the storage surface will be charged negative with respect to the potential of cathode 80 of viewing gun 16. -In particular, the leading edge of each pulse applied to mesh 25 also drives the storage surface positive yby a corresponding amount because of the capacitance therebetween. In that the storage surface is now positive with respect to the potential of the source of flood electrons, namely, the potential to cathode 80 of viewing gun 16, the flood electrons commence discharging the storage surface to ground for the duration of the pulse interval. Upon the occurrence of the negative excursion at the trailing edge of each pulse, the storage surface which is capacitively coupled to the mesh 25 goes negative to the extent of the amplitude of the negative excursion of the pulse whereby it is driven negative by the amount that it is discharged during the pulse interval. Thus, over a series of pulses, it is apparent that the storage surface will be charged to a potential that is negative with respect to the potential of cathode 80 by an amount equal to the amplitude of the pulses. Thus, for example, if pulses having an amplitude of +5 volts are developed across the load resistor 98, the storage surface will assume a quiescent potential of -5 volts relative to the potential of cathode 80, which potential is referenced to ground and -25 volts relative to the potential of the mesh 25 of the storage screen 22. It is necessary that this latter potential difference, i.e., 25 volts, be less than the iirst crossover potential of the secondary electron emission characteristic of the storage surface in order to achieve stable operation of the tube. That is, if this potential were exceeded, portions of the storage surface would charge to the potential of the collector grid 24 and could not be readily discharged or erased.

Next, the electron gun 14 is modulated with an intelligence signal and scanned across the storage screen 22 in synchronism therewith to produce a charge pattern on the storage surface. This is accomplished by impressing the intelligence signal on intensity grid 47 of grid 14 through input terminal 53. The horizontal and vertical current generators 56 produce currents which are applied to the horizontal and vertical deflection coils 15 in a manner to scan the electron Ibeam produced by gun 14 over the storage screen 22 in the desired -manner to produce a charge pattern that is constituted of potentials that are positive with respect to the quiescent potential of the storage surface, i.e., -5 volts, but which are, in general, negative with respect to the potential of cathode 80. When this is the case, the flood electrons from viewing gun 16 will not erase the charge pattern except during the pulse intervals but will penetrate through the interstices of the viewing screen 22 in proportion to the charge thereon and accelerated towards the viewing screen 18 to produce a visual presentation of the charge pattern.

Reference is now made to FIG. 4 which shows the write characteristic of the storage screen 22 of the device of FIG. 1 for 4an electron beam of 0.020 inch spot size having a progressively increasing energy level and a constant current of 30 microamperes. In particular, the abscissa of the characteristic of FIG. 4, proceeding from left to right, as shown -in the drawing, there is indicated the progressively increasing energy levels for the electron beam which scans the storage screen 22. The ordinate, on the other hand, shows the writing speed of the electron beam on' storage screen 22. In particular, the line 94 illustrates the characteristic of the storage screen 22 with the layer 26 of zinc sulde disposed uniformly over the elcctroformed nickel mesh 25, in the hereinybefore described manner, to a depth of the order of 0.65 micron. On top of the layer 26 there is disposed the film 27 of magnesium fluoride having a thickness of 500 Angstroms. As is evident from the drawing, an electron beam having `an energy level of approximately 2 kilovolts can write at a speed of the order of 300,000 inch-volts per second on the storage screen 22. An increase in the energy level of the beam effects a decrease in the possible writingspeed until at an energy level of approximately 4.5 kilovolts the writing speed becomes approximately equal to 230,000 inch-volts per second. A further increase in the energy level of the beam, however, causes the beam to charge the storage surface of screen 22 at a faster rate until at an energy level of approximately 7 kilovolts, the electron beam will .again write on the storage surface at a speed of the order of 300,000 inch-volts per second. At this latter energy level, however, it should be noted that substantially greater currents could be concentrated within the same spot size thus substantially increasing the writing speed or, alternatively, the electron beam could be focused into a smaller spot size to improve the resolution of the presentation.

One theory which may be advanced to explain the above described phenomenon is that the electron beam of gun 14 simultaneously charges the storage surface of storage screen 22 by secondary electron emission and by electron bombardment induced conductivity when operating at the higher energy levels. As can be seen from the characteristic 94 of FIG. 4, the writing speed is decreased as the energy level of the writing beam of gun 14 is increased from 2 to 4.5 kilovolts. Throughout this range of energy levels, charging of the storage surface can be attributed primarily to secondary electron emission. This being the case, the decrease in writing speed would be due to a decrease in the secondary electron emission ratio; that is, as the beam electrons impinge upon the storage surface at greater velocities, they penetrate deeper into the molecular matrix constituting the dielectric material which provides the storage surface, thus making it more diicult for electrons to be ejected free of the surface. At the higher energy levels, however, the beam electrons penetrate into the layer 26 beneath the storage surface with sufficient energy to raise increasing numbers of electrons to the conduction energy level. These conduction electrons are attracted by the positive potential gradient maintained across the

dielectric layers

26, 27 to the nickel mesh 25 to charge the storage surface in a positive direction by means of electron bombardment induced conductivity. Thus, as is evident from characteristic 94 of FIG. 4, when the electron beam of electron gun 14 is operated at an energy level of the order of 7 kilovolts, the storage surface of storage screen 22 is charged in a positive direction by both secondary electron' emission and by electron bombardment induced conductivity.

What is claimed is:

1. A half-tone visual display storage tube comprising a storage screen including a conductive screen and a uniformly thin layer of cubic zinc sulfide disposed over at least a portion of one side of said conductive screen, said cubic zinc sulfide having a secondary emission ratio greater than unity throughout a first continuous range of electron energy levels from a first crossover potential level to a second crossover potential level relative to a predetermined reference potential level and exhibiting electron bombardment induced conductivity characteristics throughout a second range of electron energy levels which substantially overlaps said first range: a viewing screen disposed adjacent to and coextensive with said storage screen on the side thereof opposite from said one side of said conductive screen; means for maintaining said conductive screen positive with respect to the potential of said storage surface by an amount less than the potential difference between said first crossover potential and said reference potential level; means for collecting secondary electrons ejected from said storage screen; means for producing an electron beam of an electron' energy level that is within said second range of energy levels; means for scanning said storage screen with said electron beam thereby to charge said storage surface in positive directions at least partially by bombardment induced conductivity in proportion to the intensity of said beam at the instant of impingement thereof to produce a charge pattern; and means including a viewing gun for directing flood electrons through said storage screen to said viewing screen to produce a visual presentation of said charge pattern.

2. The half-tone visual display storage tube as defined in' claim 1 wherein the energy level of said electron beam is common to both said first and second ranges of electron energy levels.

3. The half-tone visual display storage tube as defined in claim 1 wherein a thin film of magnesium fluoride having a thickness of less than 2000 Angstroms is disposed over said uniformly thin layer of cubic zinc sulfide thereby to enhance the secondary electron emission characteristics of said storage surface.

4. A half-tone visual display storage tube comprising a storage screen including a conductive mesh, and a layer less than two microns thick of cubic zinc sulfide disposed over one side thereof; a viewing screen disposed adjacent to and coextensive with said storage screen on the side thereof opposite from said one side of said conductive mesh; means including a viewing gun having a cathode maintained at a substantially fixed reference potential for directing flood electrons uniformly over said storage screen; means for maintaining said conductive mesh at a predetermined potential level that is in the range of from 5 to 30 volts positive with respect to said reference potential; means for discharging said storage surface to a quiescent potential that is negative relative to said substantially fixed reference potential; means for collecting secondary electrons ejected from said storage screen; means for producing and scanning said storage screen with a high energy electron beam of elemental cross-section area thereby to charge said storage surface in positive directions by both secondary electron emission and electron bombardment induced conductivity in proportion to the intensity of said beam at the instant of impingement thereon to produce a charge pattern whereby said flood electrons penetrate through said storage screen to said viewing screen in' proportion to the charge on said storage surface to produce a visual presentation of said charge pattern.

References Cited in the file of this patent UNITED STATES PATENTS 2,435,436 Fonda Feb. 3, 1948 2,527,652 Pierce Oct. 31, 1950 2,527,981 Bramley Oct. 3l, 1950 2,790,929 Herman et al. Apr. 30, 1957 2,887,597 Smith May 19, 1959 OTHER REFERENCES The Encyclopedia of Chemical Technology, volume 15,

o page 281 (1956).

Claims

1. A HALF-TONE VISUAL DISPLAY STORAGE TUBE COMPRISING A STORAGE SCREEN INCLUDING A CONDUCTIVE SCREEN AND A UNIFORMLY THIN LAYER OF CUBIC ZINC SULFIDE DISPOSED OVER AT LEAST A PORTION OF ONE SIDE OF SAID CONDUCTIVE SCREEN, SAID CUBIC ZINC SULFIDE HAVING A SECONDARY EMISSION RATIO GREATER THAN UNITY THROUGHOUT A FIRST CONTINUOUS RANGE OF ELECTRON ENERGY LEVELS FROM A FIRST CROSSOVER POTENTIAL LEVEL TO A SECOND CROSSOVER POTENTIAL LEVEL RELATIVE TO A PREDETERMINED REFERENCE POTENTIAL LEVEL AND EXHIBITING ELECTRON BOMBARDMENT INDUCED CONDUCTIVITY CHARACTERISTICS THROUGHOUT A SECOND RANGE OF ELECTRON ENERGY LEVELS WHICH SUBSTANTIALLY OVERLAPS SAID FIRST RANGE: A VIEWING SCREEN DISPOSED ADJACENT TO AND COEXTENSIVE WITH SAID STORAGE SCREEN ON THE SIDE THEREOF OPPOSITE FROM SAID ONE SIDE OF SAID CONDUCTIVE SCREEN; MEANS FOR MAINTAINING SAID CONDUCTIVE SCREEN POSITIVE WITH RESPECT TO THE POTENTIAL OF SAID STORAGE SURFACE BY AN AMOUNT LESS THAN THE POTENTIAL DIFFERENCE BETWEEN SAID FIRST CROSSOVER POTENTIAL AND SAID