Field Emission Fluctuation Method Research Articles

The diffusion of oxygen on W(001)

The diffusion of oxygen on the W(001) plane has been studied by the field emission fluctuation method as function of coverage, temperature, preanneal and direction of diffusion. Diffusion is complex, showing a number of maxima and minima at a given coverage, and depends on preanneal. It is reversible without anneal only to 600 K. These findings suggest oxygen-induced reconstruction, in agreement with other work. Diffusion is also anisotropic, indicating the existence of ordered reconstructed and unreconstructed domains of preferred orientation. The activation energies E vary from 2 to >8 kcal mol −1 and prefactors D 0 are generally very small, as low as 10 −10 cm 2 s −1. E and D 0 increase with coverage for unannealed layers, suggesting that the low values correspond to substrate assisted hopping, with stiffening of the lattice resulting from increases in O coverage. Such stiffening removes low E, low probability hopping events. Prediffusive “flip-flop” characterized by exponentially decaying correlation functions was also observed, with fast and slow components, down to temperatures as low as 78 K, suggesting a tunneling component.

The diffusion of oxygen on W(110) revisited

The diffusion of oxygen on the (110) plane of tungsten has been reexamined via the field emission fluctuation method, using a digital correlation apparatus. Measurements were carried out over a coverage range of 0.13⩽O/W⩽0.79. Where overlap exists activation energies agree well with previous work; there is qualitative but not quantitative agreement with prefactors D0. Mean-square fluctuations show very little temperature dependence. The present results show that E rises almost linearly from 14 kcal/mol at O/W⩽0.2 to 23 kcal/mol at O/W=0.4, then shows a slight dip at O/W=0.56 and then rises again to 27 kcal/mol at O/W=0.79. D0=4×10−8 cm2/s at O/W=0.13, and rises by six orders of magnitude to 5×10−2 cm2/s at O/W=0.79. It is postulated that the increases in E and D0 with coverage have their origin in polaronic effects, to wit the participation of substrate atoms in the diffusion process and a progressive stiffening of the substrate by O atoms as coverage increases.

Diffusion of oxygen on the Re(20 [formula omitted]1) plane

The diffusion of oxygen on the Re(20 2 1) plane was studied by the field emission fluctuation method. At low coverages E = 22 kcal/mol, decreases to 16 kcal/mol at θ = 0.3, and increases to 25 kcal/mol at θ ⩾ 0.6. Mean square fluctuations are nearly temperature independent. It is argued that this behavior implies stronger effects of neighboring O atoms on diffusion saddlepoints than on occupied binding sites, and can be explained qualitatively by assuming that a single neighbor to a saddlepoint lowers E while two neighbors on opposite sides raise it.

Diffusion of 1H and 2H on W(001)

The diffusion of 1H and 2H on the (001) plane of a tungsten field emitter has been studied by the field emission fluctuation method, employing a rectangular probe for anisotropy determinations. Diffusion was found to be temperature independent for T < 140K, followed by a slightly activated regime between 140 and 220 K. In this range E = 1−2kcal/mol and D 0 = 10 −9−10 −10cm 2/s. For T > 220K a third regime with E = 4−7kcal/mol and D 0 = 10 −5−10 −7cm 2/s occurs. There is some diffusion anisotropy for both tunneling and weakly activated diffusion, and also for high temperature diffusion at very low coverage, presumably corresponding to surface reconstruction with a single domain predominating. For T < 200K evidence for the coexistence of two diffusion regimes was found and is tentatively attributed to fluctuations caused by single atoms and by collective modes, respectively. Isotope effects were small under all conditions, including tunneling. Mean square fluctuations were temperature dependent, except below 140 K. The resultant “activation” energies suggest that much of this dependence involves substrate compression. The small isotope effect in tunneling and the small values of E and D 0 in the first activated regime are attributed to the involvement of substrate distortions in diffusion, essentially via polaronic effects and adsorbate-substrate atom phasing requirements for H hopping. The self diffusion of thermally generated W atoms at 660 ≤ T ≤ 775K was also investigated: E ≈ 18kcal/mol and D 0 ≈ 10 −7cm 2/s.

Surface diffusion of lithium across and along atomic rows on the W(112) plane

The surface diffusion of lithium on the W(112) plane was investigated using the field emission fluctuation method. A rectangular slit was applied as a probe hole which could be rotated in situ. The spectral density functions of the field emission current fluctuations for two perpendicular slit positions (along the [111] and [110] crystallographic directions) were measured. On the basis of the theoretical results obtained by Gesley and Swanson the surface diffusion coefficients were calculated. From the temperature dependence of the diffusion coefficient in the temperature range of 390–530 K the activation energies for chosen coverages of lithium were determined. An anisotropy was found for the wide range of lithium coverages. The surface diffusion energy is higher for the [110] than that for the [111] direction. For the relative Li concentration 0.6 the values of 0.54±0.03 and 0.46±0.03 eV were obtained, respectively. The anisotropy is explained by the substrate atomic structure.

Surface diffusion parameters for potassium and lithium on tungsten field emitter tip

The field emission fluctuation method has been applied to determine surface diffusion parameters. Experimental results both for lithium and potassium on (112) and (111) tungsten planes are presented.The values of the diffusion coefficients are evaluated on the basis of the experimental spectral density functions as well as the cross-correlation functions. The values of the diffusion parameters obtained previosly are compiled and compared with the new results. Physical conditions of various diffusion experiments are analyzed. The surface diffusion processes for potassium andlithium are compared.

Surface self-diffusion studies on the W(112) plane by the field emission method

The surface self-diffusion anisotropy of tungsten on the W(112) plane has been measured along (∥) and across (⊥) the channels, which exists on this plane, by using the field emission fluctuation method with two forms of probe holes. For most measurements the slit probe-hole dimensions, 0.4 × 4 mm, correspond to 40 × 400 Å at the emitter and the round probe-hole dimension, 1 mm, corresponded to 100 Å. In the round probe hole the thermal activation energy is E = 13.0 kcal and the prefactor of the surface self-diffusion coefficient D 0 = 4.8 × 10 −7 cm 2 s −1; in the long narrow rectangular slit E(∥) = 13.2 kcal, D 0(∥) = 7.1 × 10 −7 cm 2 s −1 and E(⊥) = 6.2 kcal, D 0(⊥) = 1.8 × 10 −9 cm 2 s −1 at T = 500−700 K. The experimental data suggest that a W atom diffusing across channels should not climb over the channel wall, which would almost certainly require a much higher activation energy, but displace an atom in the wall. This process can require a much smaller activation energy, but since it involves concerted motion of at least two atoms it will also have a much smaller prefactor.

Surface self-diffusion anisotropy of tungsten atoms on W(112) plane

Surface self-diffusion anisotropy of tungsten on W(112) plane has been measured along (∥) and across (⊥) channels existed on this plane by using the field emission fluctuation method in two forms of the probeholes. In the round probehole the thermal activation energy E=13.0kcal, and the prefactor of the surface self-diffusion coefficient D0=4.8×10-7 cm2s-1; in the long narrow rectangular slit, E(∥)=13.2kcal, D0(∥)=7.1×10-7 cm2s-1 and E(⊥)=6.2kcal, D0(⊥)=1.8×10-9 cm2s-1 at T=500 ∼ 700K. The experimental data suggest that a W atom diffusing across channels should not climb over the channel wall, which would certainly require a much higher activation energy, but instead, displace an atom in the wall. This process requires a much smaller activation energy; however, since it involves concerted motion of at least two atoms, it will also have a much smaller prefactor.

Diffusion of tungsten on stepped tungsten surfaces

Self-diffusion of thermally generated tungsten atoms near (123) and (257), on the zone (011)–(112) and on (023), on the zone (011)–(001) of a tungsten field emitter has been investigated by the field-emission fluctuation method, using a rectangular probe in order to investigate diffusion anisotropy. In agreement with earlier findings of Gong and Gomer [J. Chem. Phys. 88 (1988) 1359, 1370] diffusion of single W atoms along and across (011) terraces separated by (011) steps, i.e. step edges running along [111] is essentially isotropic with E d = 16 kcal, D 0 ≈ 10 −4 cm 2 s −1, while atoms can cross (001) oriented steps only with much activation energy: E d ≈ 35 kcal, D 0 = 10 −2 cm −2 s −1. Slow diffusion parallel to steps attributed previously by Gong Chem. Phys. 88 (1988) 1359, 1370] to kink motion was also seen along the zone (011)−(112) but seems more complicated than previously assumed, with several regimes, which may correspond to motions of different kink configurations. Distinct dips in the slow regime diffusion coefficients occurred at 910 K, somewhat higher than the previously seen onset of dips, 875 K, and may indicate roughening, as previously hypothesized. Slow diffusion perpendicular to steps was also seen in this zone and is not fully understood. It may arise from some step components always perpendicular to the short slit dimensions, or may correspond to more complicated surface configurations than the step and terrace pattern on an ideal emitter surface.

Diffusion of CO on Ni(111) and Ni(115)

Diffusion of CO on the Ni(111) and (115) planes as a function of coverage was studied by the field-emission fluctuation method from 130–219 K. On (111) E d = 6.8 kcal, independent of coverage, while D 0 ≅ 10 −3 cm 2 s −1. Near CO Ni = 0.4 there is a peak in D at all temperatures. Mean square fluctuations increase only slightly with increasing T but show strong oscillations in the coverage range 0.3 ⩽ CO Ni ⩽ 0.5 at all temperatures probed. D divided by the “thermodynamic factor”, i.e. D 〈(δN) 2〉 〈N〉 is not constant as a function of coverage, indicating a compensation between the thermodynamic factor and the remaining terms in D. On (115), which consists of terraces of varying width of (100) orientation, E d = 6.4 kcal, D 0 ≅ 10 −3 cm 2 s −1 up to CO Ni = 0.6 or CO = 0.96 × 10 15 molecules cm 2 . Above this coverage E d and D 0 drop rapidly, reaching 4.5 kcal and 2 × 10 −6 cm 2 s −1 respectively near saturation. 〈(δN) 2〉 〈N〉 decreases markedly with increasing coverage but is only slightly temperature dependent. There is again a strong compensation between changes in the thermodynamic factor and the remaining terms in D.

Surface self-diffusion and thermal roughening of tungsten surfaces studied by field emission fluctuation method

Surface self-diffusion measurements of tungsten atoms and other defects were carried out by means of field emission fluctuation method at various positions along the zones (011)-(112) and (011)-(001). The experimental results show that the self-diffusion on stepped surface can be used to investigate thermal roughening procedures.

Thermal roughening on stepped tungsten surfaces. II. The zone (011)–(001)

Self-diffusion measurements by the field emission fluctuation method have been extended to the (011)–(001) zone. Some evidence for roughening at 700–900 K is seen on (023), (012), and (017). On (013) there is much less indication of roughening. In all cases diffusion appears to be one dimensional below 900 K where it becomes two dimensional. These results are in contrast to those obtained on the zone (011)–(112), where steps are better defined and close packed, so that a sharper transition is observed at higher temperature.

The effect of finite resolution on the determination of diffusion coefficients by the field emission fluctuation method

Equations for the current correlation functions for round and rectangular probeholes, taking the finite resolution of the field emission microscope into account, are derived and discussed. The effect of finite resolution introduces a fictitious time shift, so that the argument of the previously derived functions t/ τ 0 → t/ τ 0 + 2( λ/ r 0) 2 where λ is the resolution parameter for an assumed Gaussian resolution function and r 0 the radius of a round probehole or the full dimension of a rectangular slit, and τ 0 the previously defined relaxation time. This shift causes the current correlation function to decay more slowly than it would for λ = 0 and thus makes apparent diffusion coefficients, determined by neglecting non-zero λ smaller than they in fact are. Roughly speaking the effect can also be interpreted as causing an increase in the effective probe dimensions by an additive amount 0.75λ. It is also shown that the importance of resolution decreases linearly with increasing emitter radius.

The effect of finite resolution on the determination of diffusion coefficients by the field emission fluctuation method

The effect of finite resolution on the determination of diffusion coefficients by the field emission fluctuation method

Extensions of the field-emission fluctuation method for the determination of surface diffusion coefficients

The use of scanning tunneling microscopy and related techniques for the determination of surface diffusion coefficients of adsorbates is discussed. Three schemes, all extensions of the field-emission current fluctuation method are presented and analyzed. The first consists of determining single site correlation functions with a STM in its more or less normal operating mode. The second consists of retracting the tip approximately one tip radius so that a circular region of high field is created on the flat surface from which field emission and diffusion-induced current fluctuations can be obtained. The third considers creation of a long narrow region of high field by placing a very fine cylindrical wire parallel to and above the plane substrate. This last scheme allows determination of diffusion anisotropy. Detailed expressions for the current correlation functions for the three schemes and criteria for allowed vibrational amplitudes and drift are derived. It is concluded that all three schemes should be feasible but probably would differ in the range of diffusion coefficient values they would be able to handle.

Compared mobilities of Cs and Na on W(110) at low coverage

The surface diffusion coefficient and compressibility if Cs on the (110) face of tungsten are measured by the field emission fluctuation method for coverages of 0.32 and 0.63 × 10 14 atoms/cm 2. An activation energy of 0.42 eV and preexponential of 10 −4 to 10 −5 cm 2 s −1 for diffusion are obtained. The compressibility is about 10 −3 to 10 −2 time that of the perfect gas. Comparisons with previous results of Na on W(110) are made.

Diffusion and compressibility of sodium on the (110) plane of tungsten

The surface diffusion parameters and the compressibility of sodium on the (110) plane of tungsten have been measured using the field emission fluctuation method for sodium coverages from 0.2 to 3 × 1014 atoms cm−2 and for temperatures from 170 to 500 K. Two temperature regimes can be defined. In the high temperature regime (≳ 300 K) the diffusion is essentially normal with an activation energy ranging from 0.28 to 0.58 eV and a preexponential coefficient D0 from 10−8.1 to 10−2.7 cm2 s−1. In this regime the compressibility increases with temperature indicating an effective repulsive adatoms interaction. In the low temperature regime (≲ 300 K) the diffusion coefficient decreases with temperature at high coverage and slowly increases with temperature at lower coverage. The transition between both regimes appears on the compressibility versus temperature curve as an inflection point. The comparison of the present results with slow electron diffraction results furnishes strong evidence that the observed transition corresponds to a continuous short-range order-disorder transition.

Diffusion and compressibility of sodium on the (110) plane of tungsten

Abstract The surface diffusion parameters and the compressibility of sodium on the (110) plane of tungsten have been measured using the field emission fluctuation method for sodium coverages from 0.2 to 3 × 10 14 atoms cm −2 and for temperatures from 170 to 500 K. Two temperature regimes can be defined. In the high temperature regime (≳ 300 K) the diffusion is essentially normal with an activation energy ranging from 0.28 to 0.58 eV and a preexponential coefficient D 0 from 10 −8.1 to 10 −2.7 cm 2 s −1 . In this regime the compressibility increases with temperature indicating an effective repulsive adatoms interaction. In the low temperature regime (≲ 300 K) the diffusion coefficient decreases with temperature at high coverage and slowly increases with temperature at lower coverage. The transition between both regimes appears on the compressibility versus temperature curve as an inflection point. The comparison of the present results with slow electron diffraction results furnishes strong evidence that the observed transition corresponds to a continuous short-range order-disorder transition.

Anisotropy in surface ace diffusion: Oxygen, hydrogen, and deuterium on the (110) plane of tungsten

Abstract The field emission fluctuation method of measuring surface diffusion coefficients has been extended to a determination of anisotropy by using as probehole a long, thin, rectangular slit, which can be rotated in situ. For oxygen on W(110), D (110) D (100) = 2 (where the subscripts indicate directions in the plane) under almost all conditions of coverage and temperature. This is the expected result if actual jumps occur along (111) directions. For 1H and 2H very little anisotropy was found for θ > 0.25, and D (110) D (100) ⩽1.3 at θ ⩽ 0.25. This result is tentatively explained by symmetry breaking: It has recently been found by Estrup that H adsorption causes surface reconstruction consisting of a shifting of the top layer along the (110) direction. This Jahn-Teller effect leads to inequivalence of the two asymmetric bridge sites at the ends of the “hourglass” wells on (110) and this can be shown to favor diffusion along (100) over that along (110), relative to the unreconstructed plane, thus decreasing D (110) D (100) . Anisotropies in the mean square fluctuations were also seen in all cases. These can be explained by assuming that the correlation lengths of the fluctuations differ along the (110) and (100) directions and that the correlation length along the former is at least 40 A. A mean field theory calculation in terms of nearest, next nearest and next-next nearest neighbor interaction energies is carried out, and it is shown that values of these parameters in good agreement with those invoked to explain the O/W(110) phase diagram and the increase in activation energies of diffusion for that system give the required correlation lengths and anisotropies. In particular it is shown that the anisotropies in interactions along the (110) and (100) directions are largely responsible for the mean square fluctuation anisotropy for oxygen. For 1H and 2H similar but even larger mean square fluctuation anisotropies are found, and vary more strongly with coverage and temperature than for oxygen, suggesting even more complex interactions.

Anisotropy in surface diffusion: Oxygen, hydrogen, and deuterium on the (110) plane of tungsten

The field emission fluctuation method of measuring surface diffusion coefficients has been extended to a determination of anisotropy by using as probehole a long, thin, rectangular slit, which can be rotated in situ. For oxygen on W(110), D(110)D(100) = 2 (where the subscripts indicate directions in the plane) under almost all conditions of coverage and temperature. This is the expected result if actual jumps occur along (111) directions. For 1H and 2H very little anisotropy was found for θ > 0.25, and D(110)D(100) ⩽1.3 at θ ⩽ 0.25. This result is tentatively explained by symmetry breaking: It has recently been found by Estrup that H adsorption causes surface reconstruction consisting of a shifting of the top layer along the (110) direction. This Jahn-Teller effect leads to inequivalence of the two asymmetric bridge sites at the ends of the “hourglass” wells on (110) and this can be shown to favor diffusion along (100) over that along (110), relative to the unreconstructed plane, thus decreasing D(110)D(100). Anisotropies in the mean square fluctuations were also seen in all cases. These can be explained by assuming that the correlation lengths of the fluctuations differ along the (110) and (100) directions and that the correlation length along the former is at least 40 Å. A mean field theory calculation in terms of nearest, next nearest and next-next nearest neighbor interaction energies is carried out, and it is shown that values of these parameters in good agreement with those invoked to explain the O/W(110) phase diagram and the increase in activation energies of diffusion for that system give the required correlation lengths and anisotropies. In particular it is shown that the anisotropies in interactions along the (110) and (100) directions are largely responsible for the mean square fluctuation anisotropy for oxygen. For 1H and 2H similar but even larger mean square fluctuation anisotropies are found, and vary more strongly with coverage and temperature than for oxygen, suggesting even more complex interactions.