Dielectric Relaxation and Hopping Conduction in La<sub><b>2</b></sub>NiO<sub><b>4+<i>δ</i></b></sub>

<table>Frequency dependence of the imaginary part (<svg height="17.7125" id="M14" style="vertical-align:-0.0pt" version="1.1" viewbox="0 0 20.075001 17.7125" width="20.075001" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,17.65)"><path d="M698 636l-541 -596q60 -5 176 -5q91 0 138.5 5t69.5 24q44 36 85 124l29 -15q-38 -125 -64 -173h-559l-9 16l545 598h-182q-81 0 -109 -8t-48 -31q-26 -29 -55 -103l-29 3q23 86 42 200h22q11 -16 21 -20.5t34 -4.5h428z" id="x1D44D"></path></g>
<g transform="matrix(.012,-0,0,-.012,12.313,9.488)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g><g transform="matrix(.012,-0,0,-.012,15.846,9.488)"><path d="M227 744l-123 -338l-31 15l73 368q12 3 41.5 -8t36.5 -20z" id="x2032"></path></g>
</svg>) of impedance at various temperatures for <svg height="15.65" id="M15" style="vertical-align:-3.3907pt" version="1.1" viewbox="0 0 67.612503 15.65" width="67.612503" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.362)"><path d="M495 163l30 -6q-19 -99 -36 -157h-453v28q63 5 77.5 20t14.5 78v400q0 63 -13 77t-75 19v28h261v-28q-61 -5 -74.5 -19t-13.5 -77v-395q0 -41 5 -59t18 -25q24 -13 96 -13q85 0 112 31q30 33 51 98z" id="x4C"></path></g><g transform="matrix(.017,-0,0,-.017,9.446,11.362)"><path d="M433 39l-85 -51q-27 0 -47 20q-16 16 -24 44q-5 -3 -24 -16.5t-27 -18.5t-23 -13.5t-25 -12t-19 -3.5q-52 0 -86 36.5t-34 85.5q0 71 81 99q128 43 155 65v17q0 54 -23 83.5t-62 29.5q-28 0 -45 -19t-29 -66q-7 -23 -29 -23q-15 0 -29 13t-14 30t31 40q25 19 68.5 40.5
t81.5 29.5q49 0 82 -27q45 -39 45 -123v-185q0 -60 35 -60q18 0 36 11zM275 84v156q-12 -6 -49 -23t-41 -19q-31 -14 -46 -31t-15 -43q0 -35 22.5 -55.5t48.5 -20.5q19 0 42 10.5t38 25.5z" id="x61"></path></g>
<g transform="matrix(.012,-0,0,-.012,16.925,15.45)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g>
<g transform="matrix(.017,-0,0,-.017,23.262,11.362)"><path d="M719 650v-28q-43 -2 -62 -15t-22 -44q-6 -47 -6 -169v-403h-31l-426 524h-2v-251q0 -111 6 -169q4 -37 24 -50.5t72 -16.5v-28h-237v28q45 2 64.5 16t23.5 49q6 62 6 171v220q0 54 -3 68.5t-17 32.5q-16 19 -34.5 26.5t-54.5 10.5v28h147l418 -502h3v246q0 117 -7 166
q-4 34 -24.5 47t-73.5 15v28h236z" id="x4E"></path></g><g transform="matrix(.017,-0,0,-.017,35.536,11.362)"><path d="M135 536q-20 0 -35 15.5t-15 35.5q0 22 15 37t36 15t35.5 -15t14.5 -37q0 -21 -15 -36t-36 -15zM252 0h-220v26q48 5 59 17t11 63v206q0 47 -9 58t-54 18v24q78 12 142 39v-345q0 -51 11.5 -63t59.5 -17v-26z" id="x69"></path></g><g transform="matrix(.017,-0,0,-.017,40.091,11.362)"><path d="M381 665q131 0 226.5 -93t95.5 -239q0 -158 -96 -253t-238 -95q-137 0 -231 95t-94 238q0 142 92.5 244.5t244.5 102.5zM359 629q-89 0 -151 -74.5t-62 -208.5q0 -141 69 -233t175 -92q90 0 150.5 74t60.5 211q0 152 -69 237.5t-173 85.5z" id="x4F"></path></g>
<g transform="matrix(.012,-0,0,-.012,52.788,15.45)"><path d="M456 178h-96v-72q0 -51 12.5 -62.5t72.5 -16.5v-27h-256v27q65 5 78 17t13 62v72h-260v28q182 271 300 426h40v-407h96v-47zM280 225v295h-2q-107 -148 -196 -295h198z" id="x34"></path></g><g transform="matrix(.012,-0,0,-.012,58.499,15.45)"><path d="M113 -12q-24 0 -39.5 16t-15.5 42q0 24 16 40.5t40 16.5t40 -16.5t16 -40.5q0 -26 -16 -42t-41 -16z" id="x2E"></path></g><g transform="matrix(.012,-0,0,-.012,61.212,15.45)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g>
</svg>; (a) <svg height="11.825" id="M16" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 55.349998 11.825" width="55.349998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g><g transform="matrix(.017,-0,0,-.017,16.092,11.55)"><path d="M512 -3l-437 233v51l437 233v-58l-378 -200v-2l378 -199v-58z" id="x3C"></path></g><g transform="matrix(.017,-0,0,-.017,30.796,11.55)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,38.956,11.55)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,47.115,11.55)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> K (b) <svg height="11.825" id="M17" style="vertical-align:-0.1638pt" version="1.1" viewbox="0 0 55.349998 11.825" width="55.349998" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
<g transform="matrix(.017,-0,0,-.017,.062,11.55)"><path d="M649 676l-22 -187l-33 -2q3 56 -12 94q-8 20 -31.5 26.5t-86.5 6.5h-74l-90 -491q-4 -23 -6 -36.5t1 -25t7 -16.5t18 -9t27 -5t41 -3l-6 -28h-286l4 28q68 5 84 18.5t28 76.5l94 491h-55q-74 0 -100.5 -6t-41.5 -23q-24 -29 -54 -98l-32 1q32 98 53 188h22q7 -18 15 -22
t37 -4h417q23 0 33.5 5t25.5 21h23z" id="x1D447"></path></g><g transform="matrix(.017,-0,0,-.017,16.092,11.55)"><path d="M512 230l-437 -233v58l378 199v2l-378 200v58l437 -233v-51z" id="x3E"></path></g><g transform="matrix(.017,-0,0,-.017,30.796,11.55)"><path d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" id="x31"></path></g><g transform="matrix(.017,-0,0,-.017,38.956,11.55)"><path d="M412 140l28 -9q0 -2 -35 -131h-373v23q112 112 161 170q59 70 92 127t33 115q0 63 -31 98t-86 35q-75 0 -137 -93l-22 20l57 81q55 59 135 59q69 0 118.5 -46.5t49.5 -122.5q0 -62 -29.5 -114t-102.5 -130l-141 -149h186q42 0 58.5 10.5t38.5 56.5z" id="x32"></path></g><g transform="matrix(.017,-0,0,-.017,47.115,11.55)"><path d="M241 635q53 0 94 -28.5t63.5 -76t33.5 -102.5t11 -116q0 -58 -11 -112.5t-34 -103.5t-63.5 -78.5t-94.5 -29.5t-95 28t-64.5 75t-34.5 102.5t-11 118.5q0 58 11.5 112.5t34.5 103t64.5 78t95.5 29.5zM238 602q-32 0 -55.5 -25t-35.5 -68t-17.5 -91t-5.5 -105
q0 -76 10 -138.5t37 -107.5t69 -45q32 0 55.5 25t35.5 68.5t17.5 91.5t5.5 105t-5.5 105.5t-18 92t-36 68t-56.5 24.5z" id="x30"></path></g>
</svg> K.</table>

Journal of Materials

fig3

Figure 3

Figure 3: Dielectric Relaxation and Hopping Conduction in La<sub><b>2</b></sub>NiO<sub><b>4+<i>δ</i></b></sub> 

Journal of Materials

Dielectric Relaxation and Hopping Conduction in La2NiO4+δ

Figure 3

Dielectric Relaxation and Hopping Conduction in La₂NiO_4+δ