Process, a structure, and a supercapacitor
10910165 ยท 2021-02-02
Assignee
Inventors
Cpc classification
Y10S977/842
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
H01G11/28
ELECTRICITY
H01G11/34
ELECTRICITY
B82Y40/00
PERFORMING OPERATIONS; TRANSPORTING
H01G11/26
ELECTRICITY
B82Y30/00
PERFORMING OPERATIONS; TRANSPORTING
Y02E60/13
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
Y10S977/948
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
H01G11/36
ELECTRICITY
Y10S977/734
GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
International classification
H01G11/36
ELECTRICITY
H01G11/28
ELECTRICITY
C23C28/00
CHEMISTRY; METALLURGY
H01G11/34
ELECTRICITY
H01G11/26
ELECTRICITY
Abstract
A process for forming high surface area graphene structures includes: depositing at least one metal on a surface of silicon carbide; heating the at least one metal and the silicon carbide to cause at least one of the metals to react with a portion of the silicon carbide to form silicide regions extending into an unreacted portion of the silicon carbide and graphene disposed between the silicide regions and the unreacted portion of the silicon carbide; and removing the silicide regions to provide a silicon carbide structure having a highly irregular surface and a surface layer of graphene.
Claims
1. A process for forming high surface area graphene structures, the process comprising: (i) depositing a thin film of elemental nickel on a surface of silicon carbide; (ii) heating the elemental nickel and the silicon carbide to cause the deposited elemental nickel to react with a portion of the silicon carbide to form silicide regions extending into an unreacted portion of the silicon carbide and graphene disposed between the silicide regions and the unreacted portion of the silicon carbide; (iii) removing the silicide regions to provide a silicon carbide structure having a rough or porous surface and a surface layer of graphene; and (iv) repeating steps (i) to (iii) one or more times to increase the roughness or porosity of the surface layer of graphene.
2. The process of claim 1, wherein the silicon carbide is initially in the form of a thin film of silicon carbide supported by a substrate.
3. The process of claim 2, wherein, prior to said depositing, the method comprises patterning the thin film of silicon carbide so that, after said steps of depositing, heating and removing, the silicon carbide structure is in a form of mutually spaced electrodes having a porous surface and a conformal surface layer of graphene.
4. The process of claim 3, wherein the electrodes are in the form of interdigitated finger electrodes.
5. The process of claim 3, comprising introducing an electrolyte into a region between the mutually spaced electrodes to form a supercapacitor.
6. The process of claim 5, wherein the electrolyte is a gel electrolyte.
7. The process of claim 1, wherein the deposited nickel has a thickness of about 2 nanometers.
Description
BRIEF DESCRIPTION OF THE DRAWINGS
(1) Some embodiments of the present invention are hereinafter described, by way of example only, with reference to the accompanying drawings, wherein:
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
(10)
(11)
(12)
(13)
(14)
(15)
(16)
(17)
DETAILED DESCRIPTION
(18) The described embodiments of the present invention include a process for forming graphene structures, and a process for forming supercapacitors incorporating those graphene structures. The graphene structures formed by the described processes are characterised by having highly non-planar or rough surfaces that provide a relatively high surface area per unit volume or footprint, making them advantageous for use in many applications requiring high surface area structures, including, for example, many types of sensors and capacitors.
(19) In particular, the described processes include processes for forming electrochemical capacitors or capacitor structures having very high capacitances, known in the art as supercapacitors. Supercapacitors can be used with or in place of batteries, and they can be charged and discharged much faster than batteries (e.g., they can be fully charged in just a few seconds). They are also less affected by charging and discharging than rechargeable batteries, and thus are preferred for applications requiring many charge-discharge cycles.
(20) Supercapacitors are capable of an order of magnitude larger (10,000 W kg.sup.1) power density than lithium-ion batteries, and two orders of magnitude higher (10 Wh kg.sup.1) energy density than electrolytic capacitors. They also do not suffer from the relatively slow power output and limited life cycle of lithium-ion rechargeable batteries.
(21) The graphene structures described herein have not only a large surface area, but also low sheet resistance and high conductivity. Moreover, the graphene structures are formed on a silicon carbide (SiC) surface, SiC being an extremely robust refractory material suitable for use in harsh and extreme environments. The described processes can also be integrated into existing semiconductor manufacturing processes, allowing the graphene structures and supercapacitors to be combined with other structures and devices on a single die, including integrated circuits, in order to provide integrated or on-chip energy storage, offering advantageous miniaturisation prospects for a number of integrated microsystems such as sensors and energy harvesters, for example.
(22) As shown in the flow diagram of
(23) At step 104, the metal(s) and the SiC body are heated to cause the metal(s) to react with the SiC to form one or more silicide regions and graphene layers disposed at the interface between the silicide regions and the unreacted SiC. The general phenomenon by which this occurs is described in International Patent Application No. PCT/AU2014/050218, entitled Process for Forming Graphene Layers on Silicon Carbide, the entirety of which is hereby expressly incorporated herein by reference. Metals such as nickel (Ni), cobalt (Co), titanium (Ti), tungsten (W), and iron (Fe), for example, can be deposited and reacted with SiC as described above to form stable silicides, typically at temperatures of at least 1000 C.
(24) However, the inventors have determined that the morphology of the silicide regions is highly dependent upon the particular metal(s) that is/are deposited. In particular, some metals or combinations of metals (a mixture of nickel (Ni) and copper (Cu), for example) form a relatively uniform and smooth layer, whereas other metals result in the formation of silicide regions having a highly irregular and complex morphology. In accordance with the present invention, at least one metal is selected such that, when reacted as described above, it forms spatially irregular or non-uniform silicide regions 302 that intermittently penetrate or protrude into the SiC layer or body, as shown in
(25) The inventors have determined that the metal nickel (Ni) is a particularly suitable choice for this purpose, although other metals may be used in some embodiments. Nickel is a fast diffusing element in SiC, and is found to be efficient at dissociating SiC bonds and forming morphologically non-uniform nickel silicide regions and graphitic carbon. At least some of the released carbon (from SiC) is graphitized at the SiC/Ni interface, i.e. deposits as graphene. The overall reaction can be simplified as follows:
yNi+xSiC.fwdarw.Ni.sub.ySi.sub.x+xC(graphene)(1) (where x,y=1-2)
(26) Having formed these silicide protrusions, they are removed (e.g., by an etching process) at step 106, together with any remaining metal. Due to the highly non-uniform morphology of the silicide regions, the surface of the remaining unreacted SiC has a correspondingly rough and non-uniform morphology, as shown in
(27) For the sake of completeness, if the SiC is completely reacted, then the graphene layers can still remain, but are of poorer quality than when there is still some remaining SiC.
(28) As described above, the resulting structure can be used for a wide variety of applications, and is particularly well suited for applications requiring a large surface area, including sensors and capacitors, for example. Depending on the specific requirements of any given application, the degree of porosity or surface roughness can be tuned, tailored, or otherwise determined as required, by simply repeating steps 102 to 106 any number of times until the porosity or surface roughness is sufficient for the desired application (as assessed at step 108).
(29) As described below, this graphene layer has a high conductivity and a large surface area relative to its footprint, making it particularly suitable for use as the mutually spaced electrodes or plates (notwithstanding that they are non-planar) of a capacitor.
(30)
(31) At step 506, these SiC islands 606 are processed using the process 100 described above in order to react at least a portion of each SiC island 606 with at least one metal to form spatially non-uniform silicide regions, and to remove these silicide regions and any remaining metal such that the surfaces of the remaining SiC structures 608 are porous, highly textured or rough, and have a surface coating of graphene, as described above and shown in
(32) At step 508, electrically conductive electrodes 610 are formed on selected portions of each capacitor structure 602 in order to provide the mutually spaced electrodes or plates of each capacitor. At step 510, an aqueous or gel electrolyte (for example, H2S04 in a PVA gel) is added to the regions between the capacitor plates 612, so that the structure can function as an electrochemical capacitor or supercapacitor. As shown in
EXAMPLE I
(33) To demonstrate the properties of the porous graphene on SiC structures formed using the processes described herein, a (300 nm thick) 3CSiC layer was grown on (100) Si wafers via calcination at 1000 C. with SiH.sub.4 (99.9994%) and C.sub.3H.sub.6 (99.9999%) supplied alternatively into a horizontal hot wall, low-pressure chemical vapour deposition (LPCVD) furnace. The resulting crystalline 3CSiC layer was found to have an unintentional doping concentration of 10.sup.16-10.sup.17 cm.sup.3 n-type carriers.
(34) The resulting SiC/Si wafers were then coated with a thin (2 nm) nickel film by DC Ar.sup.+ ion sputtering using a deposition current of 100 mA at a base pressure of 810.sup.2 mbar. The wafers were then annealed in a flowing (20 sccm) N.sub.2 atmosphere at 1000-1200 C., some by conventional furnace annealing for a period of 2 hours (denoted FA, temperature ramping at 25 C. min.sup.1), and others by rapid thermal annealing for only four minutes (denoted RTA, temperature ramping at 5 C. s.sup.1). For convenience of reference, samples with different annealing conditions are denoted as F.sub.1 (1000 C. via FA), F.sub.2 (1200 C. via FA), R.sub.1 (1000 C. via RTA), and R.sub.2 (1100 C. via RTA).
(35) The annealed wafers were then etched using a Freckle solution (70:10:5:5:1085% H.sub.3PO.sub.4:Glacial acetic acid:70% HNO.sub.3:50% HBF.sub.4:H.sub.2O) to remove the resulting nickel silicides and any unreacted nickel, using extreme care to retain the graphene layers.
(36) All the samples were characterized by Raman Spectroscopy on a Renishaw spectrometer with a laser excitation at 514 nm on four sites of each sample. Raman spectroscopy is a powerful and non-destructive technique to assess the graphitic structure by comparing the D and G Raman bands.
(37)
(38) For example, SiC-derived carbon powders processed by halogenation have a small pore size with a high value of I.sub.D/I.sub.G, indicating defective sites in abundance. In contrast, the graphitized carbon (graphene) in the samples prepared as described above is characterised by relatively low I.sub.D/I.sub.G values (0.7-1.2, see Table 1 below), suggesting that the graphene produced as described above is of relatively high quality with relatively few defects. It is apparent from the values in the table that the annealing procedure makes a significant difference in the amount of defects and the final thickness of the graphene layers.
(39) TABLE-US-00001 TABLE 1 Sheet resistance, Raman ID/IG ratio, RMS roughness, number of graphene layers, area capacitance, and gravimetric capacitance of samples F1, F2, R1, R2 and reference SiC/Si samples. Number Sheet RMS of Area Gravimetric Resistance Raman Roughness Graphene Capacitance* Capacitance* Samples () I.sub.D/I.sub.G (nm) Layers (F cm.sup.2) (F g.sup.1) F.sub.1 680 10 1.2 0.1.sup.# 23 2 8.3 0.5 31.8 50.8 F.sub.2 80 10 1.2 0.1 41 2 13.7 0.5 37.5 36.2 R.sub.1 80 10 0.7 0.1 66 2 14.1 0.5 69.5 65.0 R.sub.2 236 10 0.7 0.1 70 2 24.8 0.5 34.4 18.3 Reference 4-7 10.sup.3 N/A 3.8 0.8 N/A 6.2 N/A SiC/Si *Capacitance obtained at a scan rate of 5 mV s.sup.1 .sup.#uncertainty values represent the variation in measured values over 4 sites per sample
(40) The chemical compositions of the surface regions of the samples were determined by X-ray Photoelectron Spectrometry (XPS) in an ultrahigh vacuum (UHV) system using a non-monochromatic Mg K (1253.6 eV) X-ray source (DAR 400, Omicron Nanotechnology) operating at a power of 300 W, at an incident angle of 65 to the sample surface, using a 125 mm hemispherical electron energy analyser (Sphera II, 7 channels detector, Omicron Nanotechnology). The resulting photoelectrons were collected at a take-off angle of 90. Survey scans were taken at an analyser pass energy of 50 eV, and high resolution scans at an analyser pass energy of 20 eV. The survey scans were carried out with 0.5 eV steps and a dwell time of 0.2 s, whereas high-resolution scans were run with 0.2 eV steps and 0.2 s dwell time. The pressure in the analysis chamber during XPS scans was kept below 4.010.sup.10 mbar.
(41) High resolution XPS spectra of the C1s peak of all samples are shown in
(42) To quantitatively determine the number of produced graphene layers (t) on the SiC/Si wafer, the intensity ratio of the photoelectron peaks corresponding to graphene (N.sub.G) and SiC (N.sub.R, as a reference) in the high resolution XPS spectra was calculated as follows, given the interlayer spacing of 3.35 for graphene:
(43)
(44) where T represents the transmission function of the analyser; E represents the photoelectron kinetic energy; represents the atomic density of the materials; C represents the differential cross section; and represents the inelastic mean free path from the TPP-2M formula. Taking photoelectron diffraction into account, a geometrical correction factor, F, is also included in the equation. The superscript indicates quantities corresponding to the graphene overlayer as opposed to the SiC bulk. By solving t from the equation, the number of graphene layers for each sample was calculated to be 8.3, 13.7, 14.1, and 24.8 for F.sub.1, F.sub.2, R.sub.1 and R.sub.2, respectively, as shown in Table 1.
(45) To investigate the surface morphology, samples were examined by Scanning Electron Microscopy (SEM) using a JSM-6610LV facility.
(46) Transmission Electron Microscopy (TEM) was used to generate cross-sectional images of the samples. TEM samples were prepared using a Focused Ion Beam (FIB) lift-out technique. Prior to ion milling, the samples were protected with a 5 keV e-beam deposited Pt cap to preserve the initial surface integrity. The samples were then prepared by FIB milling with a Ga ion beam at 30 keV to a thickness of 1 m and then polished using an Ar ion beam at 500 eV to remove the Ga ion damage and to obtain electron transparency for high resolution imaging. Then the samples were inserted into an FEI Titan Cs corrected TEM operated at 80 keV.
(47)
(48) Additionally, further away from the surface, several dark areas with a size in the range of 30-50 nm of nanometers are found, showing that some of the pores are formed deeper in the SiC film.
(49) A NT-MDT Integra spectra system was used to measure the surface texture on the samples by Atomic Force Microscopy (AFM). AFM images and line scan profiles of the graphene samples F.sub.1, F.sub.2, R.sub.1, and R.sub.2 over a scanning area of 20 m20 m are shown in
(50) The sheet resistances of the graphene on SiC/Si and the reference SiC/Si wafer were measured using macroscopic Van der Pauw structures over an area of 12 cm.sup.2. Sheet resistance classically represents a measure of the resistance of a thin film of uniform thickness, and is useful in the assessment of the electrical conduction of thin films.
(51) Electrochemical Analysis
(52) All samples (12 cm.sup.2) were dried and used as working electrodes with a Ag/AgCl reference electrode and a platinum counter electrode in a three-electrode cell configuration. Electrochemical tests were performed in a 3 M KCl aqueous electrolyte. Cyclic voltammetry (CV) tests were carried out at a voltage range of 0 to 0.8 V (against Ag/AgCl) on a Princeton Applied Research VersaSTAT 4 potentiostat unit. The scan rates ranged from 5, 10, 20, 50 to 100 mVs.sup.1. Electrochemical Impedance Spectroscopy (EIS) was performed on the same instrument over a frequency range of 100 kHz to 100 MHz, with an alternating current amplitude of 10 mV. Galvanostatic charge and discharge performance was evaluated using a Radiometer Analytical Voltalab 40 device at current densities of 1, 2, 3, and 4 A cm.sup.2.
(53) Cyclic Voltammetry (CV) curves of F.sub.1, F.sub.2, R.sub.1, R.sub.2 and reference SiC/Si samples at different sweep rates are shown in
(54) The area capacitance (C.sub.A, F cm.sup.2) was converted to gravimetric capacitance (C.sub.G, F g.sup.1) as follows:
(55)
(56) where .sub.a is the atomic areal density of monolayer graphene (3.810.sup.15 atoms cm.sup.2); N.sub.A is Avogadro's Constant (6.02210.sup.23 mol.sup.1); M.sub.C is the molar mass of carbon (12.01 g mol.sup.1), and t is the number of graphene layers as obtained from Equation (2). The values of the areal and gravimetric capacitance at a scan rate of 5 mV s.sup.1, as well as the sheet resistance, RMS roughness (Rq, nm), and the number of graphene layers from XPS of each sample are listed in Table 1.
(57) The galvanostatic charge-discharge (GC) curves of F.sub.1, F.sub.2, R.sub.1, R.sub.2 and reference SiC/Si electrodes are shown in
(58) Electrochemical Impedance Spectroscopy (EIS) is a technique used to assess the internal resistance of supercapacitors.
(59) All the Nyquist plots exhibit nearly vertical slopes in the low frequency region, indicating good capacitor behaviour of all supercapacitor cells. The intercept of the real part of the axis in the high frequency region, as seen in the magnified view in the inset of
(60) As known by those skilled in the art of electrochemical impedance spectroscopy, the impedance curves begin with an approximately semicircular portion and then become generally linear. The semicircular regions on the plot reveal the charge transfer resistance (R.sub.CT); the reference SiC/Si sample has a larger semicircular portion than the curves for the other four catalytic graphene samples (which are not visible at the scale shown), indicative for a much larger R.sub.CT, which is related to the low carrier doping and leads to limited capacitance. As high-quality graphene forms on the SiC/Si wafers, the charge transfer resistance of the cell is further decreased, as evidenced by the presence of smaller semicircles. These EIS results further confirm the improved conductivity of the supercapacitor cell with the catalytic graphene-on-chip electrodes, which deliver enhanced electrochemical performance compared to the reference SiC/Si.
(61) Table 1 above summarizes the measured physical, electrical, chemical and electrochemical properties of the graphene samples and the corresponding SiC reference sample. These stand-alone graphene-on-chip electrodes are free of conductive additives and binders, and the double-layer capacitance of these electrodes is only dependent on the quality and the accessible surface area of the active material (graphene) on the electrodes.
(62) It is clear that R.sub.1 has the best electrochemical performance in terms of areal capacitance (69.5 F cm.sup.2) and gravimetric capacitance (65.0 F g.sup.1) among all of the graphene samples. This can be ascribed to its low sheet resistance (80/), as evidenced by the much decreased electrolyte resistance in
(63) Sample F.sub.2 has similar sheet resistance (80/) and numbers of graphene layers (13.7 vs. 14.1) as sample R.sub.1, but its electrochemical properties are much poorer than R.sub.1, owing to its smaller RMS roughness (41 nm), which provides a lower accessible surface area. R.sub.2 has similar values of I.sub.D/I.sub.G (=0.7) and RMS roughness (70 nm vs. 66 nm) compared to R.sub.1, but yields lower area capacitance and gravimetric capacitance, which can be attributed to its larger sheet resistance (236/). Similarly, sample F.sub.1 has worse electrochemical properties than R.sub.1, also due to its larger sheet resistance (680/) and smaller RMS roughness (23 nm) with a smaller surface area.
(64) The I.sub.D/I.sub.G values in Table 1 indicate the quality of the graphene samples in terms of defectivity. However, even with a higher I.sub.D/I.sub.G value of 1.2, the sheet resistance of graphene is still as low as 80 in the case of F.sub.2. This indicates that the graphene defectivity as estimated with Raman spectroscopy in the investigated range does not correlate with the measured sheet resistance. The likely reason for the larger sheet resistance of R.sub.2 and F.sub.1, compared to that of R.sub.1 and F.sub.2, is a different degree of continuity or coverage of the different graphene films, an attribute not captured by the Raman measurements.
(65) Sample R.sub.1, with 14 graphene layers, delivers the best areal capacitance, whereas R.sub.2 with 25 layers shows the worst gravimetric capacitance, revealing that a larger number of graphene layers do not translate into better electrochemical performance. This may be because only a few top graphene layers are fully accessible for electrochemical double-layer charge storage, and thus determine the overall capacitance.
(66) The described embodiments of the present invention include processes that simultaneously form porous SiC and high-quality graphene on the porous SiC, using a metal-assisted catalytic process. The resulting graphene samples have high surface areas due to extensive pitting of the underlying SiC, and display typical supercapacitive behaviours as stand-alone on-chip electrodes, with specific capacitances up to 65.0 F g.sup.1 (or 69.5 F cm.sup.2). The electrochemical performance of these on-chip electrodes is closely related to the surface area and the quality and coverage of the synthesised graphene layers, as indicated by the measured sheet resistance values.
(67) The described processes for forming graphene are transfer-free and can eliminate the use of conductive additives and/or binders for electrochemical applications. By combining these processes with patterning (e.g., to form an interdigitated finger structure), the described processes can be used to create micro-scale supercapacitors on low cost (e.g., silicon) substrates, enabling energy storage at the wafer level and numerous opportunities for on-chip integrated energy storage applications.
EXAMPLE II
(68) An epitaxial 3CSiC layer (500 nm) with an unintentional n-type doping of 10.sup.16-10.sup.17 cm.sup.3 was initially grown on a Si (100) wafer. A thin nickel film (2 nm) was sputtered onto this 3CSiC/Si wafer by using a DC Ar.sup.+ ion sputterer (deposition current of 100 mA and base pressure of 810.sup.2 mbar) and transferred into a tube furnace. The coated 3CSiC/Si wafer was annealed for 2 h under vacuum with a temperature ramping rate of 25 C. min.sup.1 at 1000-1200 C. The graphitized samples were allowed to cool down to room temperature and immersed in Freckle solution (70:10:5:5:10-85% H.sub.3PO.sub.4:Glacial acetic acid:70% HNO.sub.3:50% HBF.sub.4:H.sub.2O) overnight to eliminate nickel silicides and unreacted nickel. This whole process was repeated for three times to produce samples of graphene on porous SiC.
(69) All electrochemical measurements were conducted on an Electrochemistry Workstation (CHI660E) in the presence of a 3 M KCl aqueous electrolyte. The CV tests were carried out in a voltage range of 0.2 to 0.8 V (against SCE) from 10-100 mV s.sup.1. Galvanostatic charge-discharge (GC) performance was evaluated at current densities of 3-10 A cm.sup.2. The cyclic stability of a representative sample was examined at the current density of 10 A cm.sup.2 for 10,000 cycles.
(70) The long-term cycling test of this representative sample at a current rate of 10 A cm.sup.2 is shown in
(71) Some of the samples were then subjected to etching in an O.sub.2 plasma to remove the graphene surface layer.
(72)
(73) Three all-solid-state supercapacitor cells were produced using two identical graphene, etched, or reference 3CSiC/Si samples arranged face-to-face and a layer of a gel electrolyte in a two-electrode configuration. The gel electrolyte was prepared by mixing 0.03 g of fumed silica and 1.0 g of the ionic liquid, 1-butyl-3-methylimidazolium bif(trifluoromethylsulfonyl)imide. The all-solid-state cells were left for 2 h prior to the measurements.
(74)
(75)
(76) TABLE-US-00002 TABLE 2 Areal capacitances of cells formed using unprocessed reference SiC, processed (high surface area graphene electrodes), and processed + etched (graphene removed, high surface area SiC only) samples, respectively. Areal Capacitance Sample (F/cm2) Ref SiC 86 F1100-3 (porous graphene) 139 Plasma Etch F1100-3 (porous/rough SiC) 84
(77) Many modifications will be apparent to those skilled in the art without departing from the scope of the present invention.