PHYSICAL REVIE% B VOLUME 26, NUMBER 6 15 SEPTEMBER 1982 Enhancement by Li+ of the diffusion of Mn2+ in MgFz crystals J. Toulouse and A. S. Nowick Henry Krumb School of Mines, Columbia University, New York, New York l0027 L. E. Halliburton Department of Physics, Oklahoma State University, Stillwater, Oklahoma 74078 (Received 21 January 1982) A particularly striking example of solute enhancement of cationic diffusion is observed in the case of Mn + diffusion in MgF2 crystals doped with Li+. Mn + is diffused in from the vapor at 920'C and detected by its electron-spin-resonance spectrum. In the ab- sence of Li+, DM„at 920'C is (9X 10 " cm /sec, but in the presence of -600-ppm Li+, values =2&(10 cm'/sec are obtained. This large enhancement apparently ori- ginates in the fact that Li+ enters the lattice predominantly as interstitials, thereby great- ly increasing the cation vacancy concentration. The present results also permit lower- limit estimates to be made for the formation enthalpy of the predominant intrinsic defect in MgF2. INTRODUCTION The ability of solutes to enhance self-diffusion is well known, particularly in metallic systems, where enhancement may be a consequence of an increase in the vacancy concentration due to association be- tween vacancy and solute atoms, or to easier jumps of solvent atoms when located close to solute atoms. ' The concept of enhancement of diffusion has not been much discussed in the case of ionic crystals. Yet, a strong enhancement effect can oc- cur in the case of an aliovalent impurity that intro- duces the defect required for solvent diffusion. Such an effect was demonstrated for NaC1 doped with SrC12, where Na diffusion is much enhanced in the extrinsic range, though not in the (higher temperature) intrinsic range of diffusion. ~ This behavior is readily understood in terms of the in- troduction of cation vacancies along with the Sr + impurities by way of charge compensation. The present work shows a particularly striking example of an enhancement of cation diffusion in the case of magnesium fluoride crystals doped with LiF, i. e. , with a homer-valent cation. Because self- diffusion of Mg is difficult to measure, however, we have instead employed MnF2 and carried out a chemical diffusion experiment. Since Mn + is similar in charge and size to Mg +, and MnF2 possesses the same crystal structure as MgF2 (the tetragonal rutile structure), chemical diffusion in this case may be regarded as very similar to self- diffusion of Mg +. The great advantage of using MnF2 is that Mn + is easily detected with great sensitivity by means of electron-spin-resonance (ESR) measurements. A convenient way to introduce Li+ into MgF2 crystals is through diffusion by heating in LiF va- por. Because of its relatively high diffusion coef- ficient (7)&10 cm jsec at 920'C), Li+ can penetrate relatively deeply into the crystal by such a treatment. The form that the Li defect takes at low temperatures was determined, by internal fric- tion measurements, to be a Li-Li pair located about a single Mg + site. The fact that the pres- ence of Li+ greatly enhances the ionic conductivi- ty, however, shows that at elevated temperatures the Li pairs must be converted to other forms. In the present experiments, we have attempted to introduce Mn + into the crystals by the method of diffusing it in from the surface exposed to MnF2 vapor. The experiments were carried out in two ways: (a) exposing the crystal to MnF2 powder only, and (b) exposing it to a mixture of MnF2 and LiF powders so as to diffuse Mn and Li into the crystal simultaneously. All experiments were car- ried out so that diffusion took place primarily along the c axis, i.e. , along the tetragonal axis of the crystal. It is in this direction that both dif- fusion and ionic conductivity take on their greatest values in MgF2 crystals. We will see that the re- sult of this study leads to important conclusions about the nature of defects present in Li+-doped MgF2 at elevated temperatures. THEORY The present experiment involves diffusion into a thin slab of thickness 2L exposed to the vapor of 2926 1982 The American Physical Society