920 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



in the early stages the intensity increases in the 111 zone "steps" and in 

 the region beyond the 211 plane going toward the 111 plane. 

 j^ We have repeated similar experiments, about 20 times, varying the tem- 

 perature and field. The rate at which the changes take place increases with 

 temperature and with field. The rate increases more rapidly than the first 

 power, perhaps as the square or cube of the field. In one experiment the 

 direction of the field was reversed; this did not affect the kind of changes 

 nor the rates. In another experiment, the temperature was reduced to 800°K 

 while a field of about 40 million volts/cm was applied; in one hour the 211 

 planes enlarged perceptibly, the intensity increased just beyond this plane 

 in the 111 direction, and the "steps" in the 111 zone appeared. For fields 

 >40 X 10® volts/cm and T = 1500 to 1600°K, most of the surface can be 

 developed into planes; the highest emission comes from broad lines where 

 the planes intersect; and the voltage necessary to obtain a given current is 

 greatly reduced. 



Many of these observations can be explained readily if we postulate that 

 W atoms can be polarized and that such atoms will tend to move from low 

 to high fields. The effects of such polarization forces will of course be super- 

 imposed on the forces which tend to hold the W atoms in certain crystalline 

 positions. Consider normal clean tungsten after glowing at 2400°K, and 

 concentrate attention on the 211 plane. In the previous section we con- 

 cluded that above 1050°K, W atoms are mobile on the surface and travel 

 in the 111 direction until they reach the adjoining paraboloidal surface. A 

 model of the 211 plane for W shows that, in the 111 direction, the atoms 

 touch each other but the rows of atoms are separated by 1 .635 atom diam- 

 eters; hence we would expect that atoms on this plane could move quite 

 readily in the 111 direction. Now consider the effects of a high field. At the 

 edge of the 211 plane the field will be larger than average, while at the cen- 

 ter it will be less than average so that the field must increase toward the 

 edge. Hence there should be a net force due to the field tending to take atoms 

 off the edge of the plane, and the rate at which the planes develop should be 

 greater with a field than without. Furthermore the extent to which the 

 plane develops should be greater with a field. Since the polarization and the 

 field gradient are probably proportional to the field, and the force is the 

 product of the two, one would expect the field effect to increase with the 

 square of the field. Because the force on the polarized atom due to the field 

 is away from the surface for both positive and negative fields, the field effects 

 should be independent of the direction of the field. 



The polarization postulate also explains the observation that after 39 

 minutes of applied field most of the emission comes from the 111 region 

 and regions surrounding the 211 and 110 planes; and that the emission from 



