Systematic study of the superconducting and normal-state properties of neutron-irradiated ${\mathrm{MgB}}_2$

We have performed a systematic study of the evolution of the superconducting and normal state properties of neutron-irradiated ${\mathrm{MgB}}_2$ wire segments as a function of fluence and post exposure annealing temperature and time. All fluences used suppressed the transition temperature, $T_c$, below $5\mathrm{K}$ and expanded the unit cell. For each annealing temperature $T_c$ recovers with annealing time and the upper critical field, $H_{c2}(T=0)$, approximately scales with $T_c$. By judicious choice of fluence, annealing temperature, and time, the $T_c$ of damaged ${\mathrm{MgB}}_2$ can be tuned to virtually any value between 5 and $39\mathrm{K}$. For higher annealing temperatures and longer annealing times, the recovery of $T_c$ tends to coincide with a decrease in the normal state resistivity and a systematic recovery of the lattice parameters.

Figure 1

(a) (002) and (110) x-ray peaks for undamaged, $4.75\times {10}^{18}$, $9.50\times {10}^{18}$, $1.43\times {10}^{19}$, and $1.90\times {10}^{19}{\mathrm{cm}}^{-2}$, fluence as-damaged samples. The highest two fluence levels show a broadened (002) peak, indicating a decrease in order along the $c$ axis. The inset shows the relative shift of the $a$- and $c$-lattice parameters as a function of the fluence level. (b) The fuller diffraction pattern of the as-damaged $1.90\times {10}^{19}{\mathrm{cm}}^{-2}$ fluence level sample. On this fuller range the broadened (002) peak is clearly visible.

Figure 2

(a) (002) and (110) x-ray peaks used to determine the $a$- and $c$-lattice parameters for the set of $24\mathrm{h}$ anneals on samples exposed to a fluence of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$. (b) The evolution of the lattice parameters as a function of annealing temperature. Closed symbols represent $\mathrm{\Delta }a$ and open symbols are $\mathrm{\Delta }c$.

Figure 3

(a) Normalized magnetization and (b) resistivity curves for the set of $24\mathrm{h}$ anneals on samples exposed to a fluence of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$. (c) The normal state resistivity at $40\mathrm{K}$. The resistivity shows a sharp increase at an annealing temperature of $200°\mathrm{C}$, then decreases approximately exponentially as a function of annealing temperature. (d) $\mathrm{\Delta }\rho$ versus transition temperature.

Figure 4

Restoration of superconductivity by post exposure annealing for samples exposed to a fluence of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$ and subsequently annealed for $24\mathrm{h}$ at various temperatures. Transition temperatures were determined using a 1% screening criteria in magnetization and an onset criteria in resistivity. Annealing at $500°\mathrm{C}$ yields a $T_c$ near $37.5\mathrm{K}$, less than $2\mathrm{K}$ below that of the undamaged sample.

Figure 5

Transport measurements to determine the upper critical field. (a) Resistivity versus temperature and (b) resistance versus field. $H_{c2}$ values were determined using the onset criteria in both measurements.

Figure 6

Upper critical field curves for undamaged as well as for samples exposed to a fluence of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$ and annealed at $150°\mathrm{C}$, $200°\mathrm{C}$, $300°\mathrm{C}$, $400°\mathrm{C}$, and $500°\mathrm{C}$ for $24\mathrm{h}$.

Figure 7

Critical current densities as a function of field at (a) $5\mathrm{K}$ and (b) $20\mathrm{K}$ for samples irradiated with a fluence of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$ and subsequently annealed for $24\mathrm{h}$ at various temperatures. (c) and (d) plot $J_c$ as a function of the reduced field $H∕H_{c2}$.

Figure 8

Normalized magnetization curves for a fluence level of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$ annealed at $300°\mathrm{C}$ for 1/3, 1, 3, 6, 24, 96, and $1000\mathrm{h}$.

Figure 9

(Color online) Semi-log plot of the change of the superconducting transition temperature as a function of annealing time at various annealing temperatures. All samples shown were exposed to a fluence level of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$. Using a linear fit over up to three decades yields non-systematic values in the rate constants for the $200°\mathrm{C}$, $300°\mathrm{C}$ and $400°\mathrm{C}$ annealing temperatures. The activation energy is estimated using the cross cut procedure on extrapolations of these fits to the data (comparison points are given by the x symbols). By comparing points with identical $\mathrm{\Delta }{T}_c$ values, through equation 3 we obtain estimates of $E_a=1.90\mathrm{eV}$ and $2.15\mathrm{eV}$ (see equation 4).

Figure 10

$J_c$ curves (inferred from magnetization data) for the set of $4.75\times {10}^{18}{\mathrm{cm}}^{-2}$ fluence samples annealed at $300°\mathrm{C}$ for various times.

Figure 11

(002) and (110) x-ray peaks for all four exposure levels annealed at $300°\mathrm{C}$ for $24\mathrm{h}$. The highest two levels continue to show a substantially broadened (002) peaks, indicating a degradation of long range order along the $c$ direction.

Figure 12

(Color online) Evolution of the (002) and (110) x-ray peaks for the $1.43\times {10}^{19}$ and $1.90\times {10}^{19}{\mathrm{cm}}^{-2}$ exposure levels annealed for $24\mathrm{h}$ with the annealing temperature increasing from $300°\mathrm{C}$ to $500°\mathrm{C}$. In both cases, the (002) attains a FWHM less than $1°$ $2\theta$ only after the annealing temperature reaches $500°\mathrm{C}$. Note: intermediate temperature anneals at $400°\mathrm{C}$ were performed for longer times to show the persistence of the broadening for $T⩽400°\mathrm{C}$.

Figure 13

(Color online) Calculated lattice parameter shifts for all four damage levels annealed at temperatures up to $500°\mathrm{C}$. Closed symbols represent $\mathrm{\Delta }a$, and open symbols are $\mathrm{\Delta }c$. Lines serve as guides to the eye.

Figure 14

(a) Normalized magnetic transitions as a function of annealing temperature and fluence level for all four damage levels. The time for each anneal was $24\mathrm{h}$. The curves are normalized to a full screening value of $-1$. The set of curves for each successive annealing temperature is shifted upward by 1.2 units for ease of reading. (b) $\mathrm{\Delta }{T}_c$ values, as determined by a 1% screening criteria, as a function of annealing temperature and fluence level.

Figure 15

(a) Normalized magnetic transitions for all four fluence levels annealed at $500°\mathrm{C}$ for $1000\mathrm{h}$. (b) $\mathrm{\Delta }{T}_c$ for samples annealed at $500°\mathrm{C}$ for 24 and $1000\mathrm{h}$. For each of the four fluence levels, extending the annealing time results in a further recovery of $T_c$ toward that of the undamaged sample. Rate constants, $C$, are determined by a linear fit of the semilog plot assuming $\mathrm{\Delta }{T}_c$ follows a decaying exponential as a function of time.

Figure 16

$H_{c2}$ curves for the $4.75\times {10}^{18}$ and $9.50\times {10}^{18}{\mathrm{cm}}^{-2}$ fluence levels annealed for $1000\mathrm{h}$ at $500°\mathrm{C}$. Two sets of data for the low temperature $H_{c2}$ values of the samples exposed to a fluence of $9.50\times {10}^{18}{\mathrm{cm}}^{-2}$ are shown. Both damage levels show a possible enhancement relative to the undamaged sample, but there is some spread in the data as illustrated by the two $9.50\times {10}^{18}{\mathrm{cm}}^{-2}$ fluence level samples shown.

Figure 17

(Color online) A comparison of the different development of $T_c$ with (a) $\mathrm{\Delta }a$, (b) $\mathrm{\Delta }c$, and (c) unit cell volume for neutron-irradiated ${\mathrm{MgB}}_2$ and ${\mathrm{MgB}}_2$ under external pressure. Pressure data are recreated from Ref. 42.

Figure 18

(Color online) A comparison of the different development of $T_c$ with (a) $\mathrm{\Delta }a$, (b) $\mathrm{\Delta }c$, and (c) unit cell volume for neutron irradiation from different groups. Data includes results from Refs. 15, 22. In parts (a) and (b) the error bars on the pure sample represent typical experimental error in determining lattice parameters. In part (c), the error bars represent the propagation of the error in the lattice parameters to the calculated $V∕V_0$ value. All of our data in these plots should be considered to have comparable uncertainty.

Figure 19

(Color online) Interdependencies of $T_c$, $H_{c2}(\mathrm{T}=0)$, and ${\rho }_0$ for carbon doped (Refs. 25, 51), aluminum doped single crystal (Ref. 9), and neutron-irradiated samples. (a) $T_c$ vs ${\rho }_0$, (b) $H_{c2}(T=0)$ vs ${\rho }_0$, and (c) $H_{c2}(T=0)$ vs $T_c$.