the materials according to the present invention are prepared using the following generic method : stoichiometric amounts of the precursor materials are intimately mixed together and pressed into a pellet . the resulting mixture is then heated in a tube furnace or a chamber furnace using either an ambient air atmosphere , or a flowing inert atmosphere ( e . g . argon or nitrogen ), at a furnace temperature of between 400 ° c . and 1500 ° c . until reaction product forms ; for some materials a single heating step is used and for others ( as indicated below in table 1 ) more than one heating step is used . when cool , the reaction product is removed from the furnace and ground into a powder . using the above method , active materials were prepared , examples 1 to 14 , as summarised below in table 1 : all of the product materials were analysed by x - ray diffraction techniques using a siemens d5000 powder diffractometer to confirm that the desired target materials had been prepared , to establish the phase purity of the product material and to determine the types of impurities present . from this information it is possible to determine the unit cell lattice parameters . the operating conditions used to obtain the xrd spectra illustrated in fig1 ( a ) 12 ( g ), and fig1 ( a ) and 14 ( a ) are as follows : the target materials were tested either i ) using a lithium metal anode test cell , or ii ) using a na - ion test cell using a hard carbon anode . it is also possible to test using a li - ion cell with a graphite anode . cells may be made using the following procedures : a na - ion electrochemical test cell containing the active material is constructed as follows : the positive electrode is prepared by solvent - casting a slurry of the active material , conductive carbon , binder and solvent . the conductive carbon used is super p ( timcal ). pvdf co - polymer ( e . g . kynar flex 2801 , elf atochem inc .) is used as the binder , and acetone is employed as the solvent . the slurry is then cast onto glass and a free - standing electrode film is formed as the solvent evaporates . the electrode is then dried further at about 80 ° c . the electrode film contains the following components , expressed in percent by weight : 80 % active material , 8 % super p carbon , and 12 % kynar 2801 binder . optionally , an aluminium current collector may be used to contact the positive electrode . the negative electrode is prepared by solvent - casting a slurry of the hard carbon active material ( carbotron p / j , supplied by kureha ), conductive carbon , binder and solvent . the conductive carbon used is super p ( timcal ). pvdf co - polymer ( e . g . kynar flex 2801 , elf atochem inc .) is used as the binder , and acetone is employed as the solvent . the slurry is then cast onto glass and a free - standing electrode film is formed as the solvent evaporates . the electrode is then dried further at about 80 ° c . the electrode film contains the following components , expressed in percent by weight : 84 % active material , 4 % super p carbon , and 12 % kynar 2801 binder . optionally , a copper current collector may be used to contact the negative electrode . the cells are tested as follows , using constant current cycling techniques . the cell is cycled at a given current density between pre - set voltage limits . a commercial battery cycler from maccor inc . ( tulsa , okla ., usa ) is used . on charge , sodium ( lithium ) ions are extracted from the cathode active material . during discharge , sodium ( lithium ) ions are re - inserted into the cathode active material . fig1 ( a ) , 1 ( b ), 1 ( c ), 1 ( d ) and 1 ( e ) show the third cycle discharge voltage profiles ( na - ion cell voltage [ v ] versus cathode specific capacity [ mah / g ]) for several hard carbon // nani 0 . 5 − x ( mn 0 . 5 − x mg x ti x o 2 cells . the cathode materials used to make these cells were nani 0 . 5 mn 0 . 5 o 2 ( fig1 ( a ) , prior art ), nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 ( fig1 ( b )), nani 0 . 40 mn 0 . 40 mg 0 . 10 ti 0 . 10 o 2 ( fig1 ( c )), nani 0 . 35 mn 0 . 35 mg 0 . 15 ti 0 . 15 o 2 ( fig1 ( d ) ) and nani 0 . 30 mn 0 . 30 mg 0 . 20 ti 0 . 20 o 2 ( fig1 ( e )). the data shown in fig1 ( a ) , ( b ), ( c ), ( d ) and ( e ) are derived from the constant current cycling data for the nani 0 . 5 − x mn 0 . 5 − x mg x ti x o 2 active materials in a na - ion cell where these cathode materials were coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cells were fully charged , they were potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active materials , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active materials . the third cycle discharge processes for these cells correspond to the following cathode specific capacities : ( a ) nani 0 . 5 mn 0 . 5 o 2 = 88 mah / g ; ( b ) nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 0 . 5 o 2 = 77 mah / g ; ( c ) nani 0 . 40 mn 0 . 40 mg 0 . 10 ti 0 . 10 o 2 = 86 mah / g ; ( d ) nani 0 . 35 mn 0 . 35 mg 0 . 15 ti 0 . 15 o 2 = 116 mah / g ; and ( e ) nani 0 . 30 mn 0 . 30 mg 0 . 20 ti 0 . 20 o 2 = 109 mah / g . it should be noted from fig1 ( a ) , ( b ), ( c ), ( d ) and ( e ) that as the levels of mg and ti increase , there is a smoothing of the discharge voltage profile . this is an important observation as it is not advantageous for application purposes to have voltage ‘ steps ’ in the discharge voltage profile , thus the materials according to the present invention , nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 , nani 0 . 40 mn 0 . 40 mg 0 . 10 ti 0 . 10 o 2 , nani 0 . 35 mn 0 . 35 mg 0 . 15 ti 0 . 15 o 2 , and nani 0 . 30 mn 0 . 30 mg 0 . 20 ti 0 . 20 o 2 , provide significant advantage over prior art material nani 0 . 5 mn 0 . 5 o 2 . fig2 ( a )-( e ) show the third cycle differential capacity profiles ( differential capacity [ mah / g / v ] na - ion cell voltage [ v ]) for several hard carbon // nani 0 . 5 − x mn 0 . 5 − x mg x ti x o 2 cells . the cathode materials used to make these cells were : nani 0 . 5 mn 0 . 5 o 2 ( fig2 a , prior art ), nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 0 . 5 o 2 ( fig2 ( b )), nani 0 . 40 mn 0 . 40 mg 0 . 10 ti 0 . 10 o 2 ( fig2 ( c )), nani 0 . 35 mn 0 . 35 mg 0 . 15 ti 0 . 15 o 2 ( fig2 ( d ) ) and nani 0 . 30 mn 0 . 30 mg 0 . 20 ti 0 . 20 o 2 ( fig2 ( e ) ). the data shown in fig2 ( a )-( e ) are derived from the constant current cycling data for the nani 0 . 5 − x mn 0 . 5 − x mg x ti x o 2 active materials in a na - ion cell where these cathode materials were coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cells were fully charged , they were potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active materials , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active materials . the data shown in fig2 ( a )-( e ) characterize the charge - discharge behaviour of the na - ion cells under test . differential capacity data have been demonstrated to allow characterization of the reaction reversibility , order - disorder phenomenon and structural phase changes within the ion insertion system . the differential capacity data for the nani 0 . 5 mn 0 . 5 o 2 cathode ( fig2 a ) shows a very structured charge - discharge behaviour characterized by several sharp differential capacity peaks in both the charge and discharge processes . peaks in the differential capacity data correspond to plateaux ( voltage steps ) in the voltage versus capacity profiles . it should be noted from fig2 ( b )-( e ) that as the levels of mg and ti increase , there is a dramatic change in the differential capacity profiles ( see for example the difference between the data derived from the na - ion cell incorporating the nani 0 . 5 mn 0 . 5 o 2 cathode material ( fig2 a ) and that for the na - ion cell incorporating the nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 cathode material ( fig2 b )). this is an important observation as it is not advantageous for application purposes to have voltage ‘ steps ’ in the discharge voltage profile . increasing levels of mg and ti in the cathode materials ( fig2 ( c ) to fig2 ( e ) ) cause a further loss of structure in the differential capacity data and reflect directly the smoothing of the voltage profile due to the mg and ti incorporation into the structure of the cathode material . these observations demonstrate that the materials according to the present invention , i . e . nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 ( fig2 ( b )), nani 0 . 40 mn 0 . 40 mg 0 . 10 ti 0 . 10 o 2 ( fig2 ( c )), nani 0 . 35 mn 0 . 35 mg 0 . 15 ti 0 . 15 o 2 ( fig2 ( d ) ) and nani 0 . 30 mn 0 . 30 mg 0 . 20 ti 0 . 20 o 2 ( fig2 ( e )), provide further significant advantageous over prior art material nani 0 . 5 mn 0 . 5 o 2 ( fig2 ( a ) ). fig3 ( a )-( e ) show the first four charge - discharge cycles ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for several hard carbon // nani 0 . 5 - x mn 0 . 5 − x mg x ti x o 2 cells . the cathode materials used to make these cells were : nani 0 . 5 mn 0 . 5 o 2 ( fig3 ( a ) , prior art ), nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 ( fig3 ( b )), nani 0 . 40 mn 0 . 40 mg 0 . 10 ti 0 . 10 o 2 ( fig3 ( c )), nani 0 . 35 mn 0 . 35 mg 0 . 15 ti 0 . 15 o 2 ( fig3 ( d ) and nani 0 . 30 mn 0 . 30 mg 0 . 20 ti 0 . 20 o 2 ( fig3 ( e ) ). the data shown in fig3 ( a )-( e ) are derived from the constant current cycling data for the nani 0 . 5 − x mn 0 . 5 − x mg x ti x o 2 active materials in a na - ion cell where these cathode materials were coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cells were fully charged , they were potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active materials , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active materials . the data in fig3 ( a )-( e ) indicate the reversibility of the sodium ion extraction - insertion reactions . it is clear from inspection that the voltage profiles for the cathode iterations incorporating mg and ti ( i . e . fig3 ( b )-( e )) show a less - structured profile . in addition , the level of voltage hysteresis ( i . e . the voltage difference between the charge and discharge processes ) is extremely small , indicating the excellent kinetics of the extraction - insertion reactions . this is an important property that is useful for producing a high rate active material , thus materials nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 ( fig3 ( b )), nani 0 . 40 mn 0 . 40 mg 0 . 10 ti 0 . 10 o 2 ( fig3 ( c )), nani 0 . 35 mn 0 . 35 mg 0 . 15 ti 0 . 15 o 2 ( fig3 ( d ) and nani 0 . 30 mn 0 . 30 mg 0 . 20 ti 0 . 20 o 2 ( fig3 ( e ) ) exhibit still further advantages over prior art material nani 0 . 5 mn 0 . 5 o 2 ( fig3 ( a ) . fig4 shows the constant current cycling data for the nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 active material ( prepared according to example 2 ) in a na - ion cell where it is coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cell was fully charged , the cell was potentiostatically held at 4 . 00 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . it is evident that sodium ions are extracted from the cathode active material , nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 , and inserted into the hard carbon anode during the initial charging of the cell . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 cathode active material . the first discharge process corresponds to a specific capacity for the cathode of about 87 mah / g , indicating the reversibility of the sodium ion extraction - insertion processes . na - ion cells reported in the literature commonly show relatively rapid capacity fade on cycling . it is common for these cells to fade in capacity by more than 50 % in the first 30 cycles . the data shown in fig4 , show that the hard carbon // nani 0 . 45 mn 0 . 45 mg 0 . 05 ti 0 . 05 o 2 cell demonstrates quite exceptional cycling behaviour . there is almost no capacity fade over the first 100 cycles . the initial specific capacity for the cathode is about 87 mah / g and after 100 cycles the specific capacity for the cathode is about 85 mah / g , indicating a capacity fade of less than 3 %. fig5 ( a )-( c ) show the third cycle discharge voltage profiles ( na - ion cell voltage [ v ] versus cathode specific capacity [ mah / g ]) for several hard carbon // nani v mn w mg x ti y o 2 cells . the cathode materials used to make these cells were : nani 0 . 5 ti 0 . 5 o 2 ( fig5 a )), nani 0 . 40 ti 0 . 50 mg 0 . 10 o 2 ( fig5 ( b )), and nani 0 . 40 ti 0 . 40 mg 0 . 00 mn 0 . 10 o 2 ( fig5 ( c ) ). the data shown in fig5 ( a )-( c ) are derived from the constant current cycling data for the nani v mn w mg x ti y o 2 active materials in a na - ion cell where these cathode materials were coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cells were fully charged , the cells were potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active materials , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active materials . from inspection of fig5 ( a )-( c ) we can detect that with the incorporation of mg and mn in the cathode active material there is a dramatic increase in the reversible cathode specific capacity . the third cycle discharge processes for these cells correspond to the following cathode specific capacities : nani 0 . 5 ti 0 . 5 o 2 = 79 mah / g ( fig5 ( a )); nani 0 . 40 ti 0 . 50 mg 0 . 10 o 2 = 103 mah / g ( fig5 ( b ) ; and nani 0 . 40 ti 0 . 40 mg 0 . 10 mn 0 . 10 o 2 = 125 mah / g ( fig5 ( c ) . fig6 ( a )-( c ) show the third cycle differential capacity profiles ( differential capacity [ mah / g / v ] na - ion cell voltage [ v ]) for several hard carbon // nani v mn w mg x ti y o 2 cells . the cathode materials used to make these cells were : nani 0 . 5 ti 0 . 5 o 2 ( fig6 ( a )), nani 0 . 40 ti 0 . 50 mg 0 . 10 o 2 ( fig6 ( b )), and nani 0 . 40 ti 0 . 40 mg 0 . 10 mn 0 . 10 o 2 ( fig6 ( c ) ). the data shown in fig6 ( a )-( c ) are derived from the constant current cycling data for the nani v mn w mg x ti y o 2 active materials in a na - ion cell where these cathode materials were coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cells were fully charged , the cells were potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active materials , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active materials . the data shown in fig6 ( a )-( c ) characterize the charge - discharge behaviour of the na - ion cells under test . differential capacity data have been demonstrated to allow characterization of the reaction reversibility , order - disorder phenomenon and structural phase changes within the ion insertion system . the differential capacity data for the nani 0 . 5 ti 0 . 5 o 2 cathode ( fig6 a ) show a structured charge - discharge behaviour characterized by a sharp differential capacity peak at about 2 . 85 v on discharge . peaks in the differential capacity data correspond to plateaux ( voltage steps ) in the voltage versus capacity profiles . it should be noted from fig6 ( b )-( c ) that on incorporation of mg and mn into the cathode material , there is a dramatic change in the differential capacity profiles ( see for example the difference between the data derived from the na - ion cell incorporating the nani 0 . 5 ti 0 . 5 o 2 cathode material ( fig6 ( a ) ) and that for the na - ion cell incorporating the nani 0 . 40 ti 0 . 40 mg 0 . 10 mn 0 . 10 o 2 cathode material ( fig6 ( c ) ). this is an important observation because , as described above , it is not advantageous for application purposes to have voltage ‘ steps ’ in the discharge voltage profile . fig7 ( a )-( c ) show the first four charge - discharge cycles ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for several hard carbon // nani v mn w mg x ti y o 2 cells . the cathode materials used to make these cells were : nani 0 . 5 ti 0 . 5 o 2 ( fig7 ( a )), nani 0 . 40 ti 0 . 50 mg 0 . 10 o 2 ( fig7 ( b )), and nani 0 . 40 ti 0 . 40 mg 0 . 10 mn 0 . 10 o 2 ( fig7 ( c ) ). the data shown in fig7 ( a )-( c ) are derived from the constant current cycling data for the nani v mn w mg x ti y o 2 active materials in a na - ion cell where these cathode materials were coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cells were fully charged , the cells were potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active materials , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active materials . the data in fig7 ( a )-( c ) indicate the reversibility of the sodium ion extraction - insertion reactions . it is clear from inspection that the voltage profiles for the cathode iterations incorporating mg and mn ( i . e . fig7 ( b ) and 7 ( c ) ) show a less - structured profile . in addition , the level of voltage hysteresis ( i . e . the voltage difference between the charge and discharge processes ) is extremely small , indicating the excellent kinetics of the extraction - insertion reactions . this is an important property that is useful for producing a high rate active material . thus the compounds of the present invention , nani 0 . 40 ti 0 . 50 mg 0 . 10 o 2 ( fig7 ( b )), and nani 0 . 40 ti 0 . 40 mg 0 . 10 mn 0 . 10 o 2 ( fig7 ( c ) ) demonstrate significant advantages over prior art material nani 0 . 5 ti 0 . 5 o 2 ( fig7 ( a ) ). the data shown in fig8 ( a )-( c ) are derived from the constant current cycling data for a nani 0 . 40 mn 0 . 40 mg 0 . 05 ti 0 . 05 al 0 . 1 o 2 active material in a na - ion cell where this cathode material was coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to fully charge the cell , the na - ion cell was potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active material , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active material . fig8 ( a ) shows the third cycle discharge voltage profile ( na - ion cell voltage [ v ] versus cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 40 mn 0 . 40 mg 0 . 05 ti 0 . 05 al 0 . 1 o 2 cell . the cathode specific capacity corresponds to 73 mah / g . fig8 ( b ) shows the third cycle differential capacity profiles ( differential capacity [ mah / g / v ] na - ion cell voltage [ v ]) for the hard carbon // nani 0 . 40 mn 0 . 40 mg 0 . 05 ti 0 . 05 al 0 . 1 o 2 cell . these symmetrical data demonstrate the excellent reversibility of the ion extraction - insertion reactions in this na - ion cell . fig8 ( c ) shows the first four charge - discharge cycles ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 40 mn 0 . 40 mg 0 . 05 ti 0 . 05 al 0 . 1 o 2 cell . these data demonstrate that the level of voltage hysteresis ( i . e . the voltage difference between the charge and discharge processes ) is extremely small , indicating the excellent kinetics of the extraction - insertion reactions . the data shown in fig9 ( a )-( c ) are derived from the constant current cycling data for a nani 0 . 45 mn 0 . 45 cu 0 . 05 ti 0 . 05 o 2 active material in a na - ion cell where this cathode material was coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cell was fully charged , the cell was potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active material , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active material . fig9 ( a ) shows the third cycle discharge voltage profile ( na - ion cell voltage [ v ] versus cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 45 mn 0 . 45 cu 0 . 05 ti 0 . 05 o 2 cell . the cathode specific capacity corresponds to 90 mah / g . fig9 ( b ) shows the third cycle differential capacity profiles ( differential capacity [ mah / g / v ] na - ion cell voltage [ v ]) for the hard carbon // nani 0 . 45 mn 0 . 45 cu 0 . 05 ti 0 . 05 o 2 cell . these symmetrical data demonstrate the excellent reversibility of the ion extraction - insertion reactions in this na - ion cell . fig9 ( c ) shows the first four charge - discharge cycles ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 45 mn 0 . 45 cu 0 . 05 ti 0 . 05 o 2 cell . these data demonstrate that the level of voltage hysteresis ( i . e . the voltage difference between the charge and discharge processes ) is extremely small , indicating the excellent kinetics of the extraction - insertion reactions . the data shown in fig1 ( a )-( c ) are derived from the constant current cycling data for a nani 0 . 40 mn 0 . 40 ca 0 . 10 ti 0 . 10 o 2 active material in a na - ion cell where this cathode material was coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cell was fully charged , the cell was potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active material , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active material . fig1 ( a ) shows the third cycle discharge voltage profile ( na - ion cell voltage [ v ] versus cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 40 mn 0 . 40 ca 0 . 10 ti 0 . 10 o 2 cell . the cathode specific capacity corresponds to 109 mah / g . fig1 ( b ) shows the third cycle differential capacity profiles ( differential capacity [ mah / g / v ] na - ion cell voltage [ v ]) for the hard carbon // nani 0 . 40 mn 0 . 40 ca 0 . 10 ti 0 . 10 o 2 cell . these symmetrical data demonstrate the excellent reversibility of the ion extraction - insertion reactions in this na - ion cell . fig1 ( c ) shows the first four charge - discharge cycles ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 40 mn 0 . 40 ca 0 . 10 ti 0 . 10 o 2 cell . these data demonstrate that the level of voltage hysteresis ( i . e . the voltage difference between the charge and discharge processes ) is extremely small , indicating the excellent kinetics of the extraction - insertion reactions . the data shown in fig1 ( a )-( c ) are derived from the constant current cycling data for a nani 0 . 40 mn 0 . 40 zn 0 . 10 ti 0 . 10 o 2 active material in a na - ion cell where this cathode material was coupled with a hard carbon ( carbotron p / j ) anode material . the electrolyte used is a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 10 ma / cm 2 between voltage limits of 1 . 50 and 4 . 00 v . to ensure that the na - ion cell was fully charged , the cell was potentiostatically held at 4 . 0 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at room temperature . during the cell charging process , sodium ions are extracted from the cathode active material , and inserted into the hard carbon anode . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active material . fig1 ( a ) shows the third cycle discharge voltage profile ( na - ion cell voltage [ v ] versus cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 40 mn 0 . 40 zn 0 . 10 ti 0 . 10 o 2 cell . the cathode specific capacity corresponds to 72 mah / g . fig1 ( b ) shows the third cycle differential capacity profiles ( differential capacity [ mah / g / v ] na - ion cell voltage [ v ]) for the hard carbon // nani 0 . 40 mn 0 . 40 zn 0 . 10 ti 0 . 10 o 2 cell . these symmetrical data demonstrate the excellent reversibility of the ion extraction - insertion reactions in this na - ion cell . in addition , the charge - discharge behaviour is now largely without structure . fig1 ( c ) shows the first four charge - discharge cycles ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for the hard carbon // nani 0 . 40 mn 0 . 40 zn 0 . 10 ti 0 . 10 o 2 cell . these data demonstrate that the level of voltage hysteresis ( i . e . the voltage difference between the charge and discharge processes ) is extremely small , indicating the excellent kinetics of the extraction - insertion reactions . referring to fig1 ( b ) , this shows the constant current cycling data ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for the first 4 cycles of the na 0 . 7 mno 2 . 05 ( x1386 ) active cathode material ( p2 structure ) in a na - ion cell where it is coupled with a capacity balanced hard carbon ( carbotron p / j ) anode material . the electrolyte used was a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 20 ma / cm 2 between voltage limits of 1 . 00 and 4 . 20 v . to ensure that the na - ion cell was fully charged , the cell was potentiostatically held at 4 . 20 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at 25 ° c . it is evident that sodium ions are extracted from the cathode active material , na 0 . 7 mno 2 . 05 , and inserted into the hard carbon anode during the initial charging of the cell . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active material . the first charge process corresponds to a specific capacity for the cathode active material of only 81 mah / g . the first discharge process corresponds to a specific capacity for the cathode of 47 mah / g , indicating the poor reversibility of the sodium ion extraction - insertion processes . clearly the specific capacity performance for the na 0 . 7 mno 2 . 05 material ( which has a p2 structure ) is inferior to the performance from the o3 cathode materials . referring to fig1 ( b ) , this shows the constant current cycling data ( na - ion cell voltage [ v ] versus cumulative cathode specific capacity [ mah / g ]) for the first 4 cycles of the na 0 . 95 ni 0 . 3167 mn 0 . 3167 mg 0 . 1583 ti 0 . 2083 o 2 ( x1380 ) active material according to the present invention in a na - ion cell where it is coupled with a capacity balanced hard carbon ( carbotron p / j ) anode material . the electrolyte used was a 0 . 5 m solution of naclo 4 in propylene carbonate . the constant current data were collected at an approximate current density of 0 . 20 ma / cm 2 between voltage limits of 1 . 00 and 4 . 20 v . to ensure that the na - ion cell was fully charged , the cell was potentiostatically held at 4 . 20 v at the end of the constant current charging process until the current density dropped to 20 % of the constant current value . the testing was carried out at 25 ° c . it is evident that sodium ions are extracted from the cathode active material , na 0 . 95 ni 0 . 3167 mn 0 . 3167 mg 0 . 1583 ti 0 . 2083 o 2 , and inserted into the hard carbon anode during the initial charging of the cell . during the subsequent discharge process , sodium ions are extracted from the hard carbon and re - inserted into the cathode active material . the first charge process corresponds to a specific capacity for the cathode active material of 228 mah / g . the first discharge process corresponds to a specific capacity for the cathode of 151 mah / g , indicating the excellent active material utilization and the good reversibility of the sodium ion extraction - insertion processes .