- Email: [email protected]
Two-process diffusion of titanium on the (1 1 1) tungsten plane by the current fluctuation method in FEM
Vacuum 63 (2001) 113}118
Two-process di!usion of titanium on the (1 1 1) tungsten plane by the current #uctuation method in FEM T. Biernat*, A.M. Da9 browski Institute of Experimental Physics, University of Wroc!aw, pl. M. Borna 9, 50 - 204 Wroc!aw, Poland
Abstract Field emission current noise of titanium adsorbed on the (1 1 1) tungsten crystal face was investigated. Measurements were carried out for coverages ranging from 0.2 to approximately 2 monolayers in the temperature range 300}1500 K. A linear combination of two theoretical functions obtained by Gesley and Swanson for the di!usion model of current #uctuations was "tted to the experimental autocorrelation functions. In such a way two di!usion coe$cients and two activation energies for titanium surface di!usion were determined. The theoretical model is applicable to a temperature range of 800}1450 K. The energy of each di!usion process decreases with increasing coverage, from a value of 1.77 eV (the "rst process) and 1.42 eV (the second process) until the saturation value of about 0.3 eV is reached for both di!usion processes. The "rst process occurs below the phase transition point of titanium (1156 K) and the second process occurs above it. 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction Since the experimental and theoretical results on "eld emission current noise were reported by Kleint [1] and Gomer [2] the phenomenon has not been submitted to an exact description and, consequently, its interpretation has been far from exactitude. In the basic approach it is assumed that an adsorption layer on the substrate surface occurs in the state of thermal equilibrium, which means that the average density of the adlayer remains constant. This density, however, is subject to #uctuation which is responsible for the occurrence of "eld emission current #uctuations. The #uctuation mechanism is connected with the process of surface
* Corresponding author. Fax: #48-71-328-7365. E-mail address: [email protected] (T. Biernat).
di!usion. This process represents a speci"c type of di!usion in which the resultant amount of the material displaced in all directions is equal to zero. This model was employed in the theoretical work by Gesley and Swanson [3]. Using a di!erent formalism, these authors have obtained a result similar to that of Gomer [2]. Both papers deal with the presentation of a theoretical formula for the current #uctuation autocorrelation function. The autocorrelation function depends on the energy dependent coe$cient of surface di!usion. The direct connection of the physical characteristic of di!usion with "eld emission current #uctuations in the theoretical model o!ers a bene"t to surface research workers. Measurement of the current #uctuations can yield data about some physical parameters related to a given adsorbate deposited on a given substrate. Gomer has successfully used his theory for investigation of some gases [4] on refractory metals. The
0042-207X/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 1 7 8 - 6
114
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
same method was employed in studies of alkali metals: potassium layers [5}7] and microcrystals [8], lithium layers [9}11] as well as for selfdi!usion of tungsten [12]. Recently the method of analysis of the autocorrelation function for "eld emission current #uctuations has been employed in a surface di!usion study of titanium [13,14]. Besides treating the autocorrelation function one can analyse the cross-correlation of current #uctuations measured for two emitter surface regions not too far away from each other [15]. Such measurements yield information on the interaction between atoms as well as the material transport on the emitter surface. Gomer's theory has been successfully adopted in the paper [16] to calculate the theoretical cross-correlation function. Not all experimental facts, however, could be understood by an advanced theory based on the adsorbate density #uctuations. Certain phenomena appear which need explanation based on the notion of soliton movement [17,18]. Interpretation of experimental results in the present work goes beyond the explicit formalism of Gesley and Swanson's theory. Part of these results are described by introducing a linear combination of two theoretical functions. In this way the interpretation can be done by referring to the general properties of titanium. Titanium di!usion on a "eld emitter surface was studied many years ago [19,20], such studies included the measurement of material transport caused by the presence of the concentration gradient. The present interest in titanium metal is due to its great importance in power engineering and ultrahigh vacuum technology. Titanium appears to be an ideal material for the power industry to store an ecologically clean fuel. Upon increasing air pollution by exhaust gas the new e$cient means of clean fuel storage has become a clue task. In order to examine the interaction of titanium with gases, the primary data required are ones about the temperature behaviour of the metal under well-de"ned ultrapurity conditions. Bulk titanium itself undergoes a high temperature phase transition from the hcp structure to bcc titanium. The transition occurs at 1156 K, which is well below the melting point of titanium at 1941 K. Measurements in the present
work were carried out at temperatures from 300 K to about 1500 K.
2. Experimental Measurement of "eld emission current #uctuations for titanium adsorbed on the region of the W(1 1 1) plane were carried out using the probehole "eld emission microscope and the experimental arrangement described in Ref. [13]. Titanium was evaporated in situ onto the W tip from a source made of a Ti block which could be heated by electron bombardment. The emitter tip temperature could be changed from room temperature to high values: it was stabilized and controlled using the temperature dependence of the resistance of an emitter loop segment with potential leads. The emission current from the W(1 1 1) plane was magnetically directed via a probe-hole to the Faraday collector for the probe region of approximately 10\ cm. After ampli"cation of the probe-hole current, its a.c. component was processed in an analog-digital converter PC card. The sampling time was 2;10\ s and one realization consisted of 400 000 samples. In order to control the thickness of the titanium adlayers, the work function versus the deposition time (corresponding to Ti coverage) was investigated. The initial portion of saturation of the curve is assumed to correspond to one monolayer of titanium. Data on the work function changes can be found in Ref. [13] and they are in general agreement with former ones [19,20]. The values of average work function versus deposition time of titanium used for investigation of "eld emission current #uctuations in this work are presented in Fig. 1.
3. Results and discussion Typical experimental autocorrelation functions of "eld emission current #uctuations are represented in Fig. 2. These results were obtained for the deposition time of titanium equal to 9 min (Fig. 1, point d). Curves from a to e are shifted by 0.4 of the unit along the vertical axis for better viewing. Each
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
115
Fig. 1. Average work function of tungsten versus the deposition time of titanium. Points a}f correspond to Fig. 4a}f. Point d corresponds to the Figs. 2 and 3.
Fig. 3. Experimental autocorrelation functions of the Ti/W(1 1 1) system for the deposition time of titanium t "9 min (the same as in Fig. 2) in double logarithmic scale (dots). Solid lines represent the theoretical autocorrelation functions "tted to the experimental values. Curves are shifted in the vertical direction by one decade each for better viewing.
Fig. 2. Experimental autocorrelation functions of the Ti/W(1 1 1) system, for the deposition time of titanium t "9 min, determined at the emitter temperatures indicated in the "gure. Curves are shifted in the vertical direction by 0.4 each for better viewing. Plots a}e correspond to plots a}e in Fig. 3 and points a}e in Fig. 4d.
curve starts at a value of 1 and diminishes to 0 with increasing time. The higher the temperature, the faster the autocorrelation functions diminish to
zero. The measurements were made in a broad temperature range of 300}1500 K. Thermally activated di!usion was observed above 875 K. In order to determine the di!usion coe$cient a theoretical curve was "tted to the experimental autocorrelation function by the least squares method. The theoretical autocorrelation function was calculated and given in analytical form in Ref. [3, Eq. (45)]. The diagram in Fig. 3 represents the curves of Fig. 2 in log}log scale. Points show the experimental data (as they were measured) and solid lines represent the theoretical functions. Curves in the "gure are shifted relative to each other by an order of magnitude for better viewing. It is seen that curves a, b and c are all well approximated by the theoretical function A. Curves d and
116
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
e, however, are well approximated by the function A only for long delay times, while for small times, the curves need approximation by introducing an additional function B. At high temperatures only the sum of functions A and B gives a good approximation of the experimental curves. In the "tting procedure described above the diffusion coe$cients were obtained at di!erent temperatures and titanium deposition time. In Fig. 4 the di!usion coe$cients D are shown as a function of reciprocal temperature 1/¹ in a semi-logarithmic diagram. It is clear from the "gure that certain ranges of temperature appear suitable for the di!usion coe$cients D to satisfy the Arrhenius equation with a constant activation energy E. In these temperature ranges the surface di!usion seems to be thermally activated. In Fig. 4 this is represented by the points that lie at the marked straight line segments with the corresponding values of energy and estimation error given at each segment. Filled circles correspond to the di!usion coe$cient computed by "tting with the theoretical function A and empty circles represent "tting by the function B. It may be noticed that the high temperature di!usion coe$cients D (marked by "lled circles) decrease with increasing temperature, while those of low temperature practically remain unchanged. In the range of high temperature, the di!usion coe$cients D represented by empty circles are arranged along a line of negative slope. Based on these results it seems that two di!usion types should be involved, or certainly two processes by which the di!usion proceeds could be discriminated. The di!usion energy for these processes as a function of the titanium layer thickness (which is expressed by the evaporation time) is represented in Fig. 5. Based on the literature [19] one can assume that the maximum thickness of the titanium in the present work corresponds to about two monolayers. It results from Fig. 5 that the energy for the process A is as high as 1.77 eV for small coverage and it diminishes with increasing coverage. For coverages in excess of a monolayer the diminution saturates and the energy reaches a value of approximately 0.3 eV. A similar behaviour is observed for the energy of the process B, where the saturation is reached at about the same value of energy, though this process starts from the initial value of energy
Fig. 4. Temperature dependence of the di!usion coe$cients for di!erent coverages of titanium. The deposition times of titanium are: (a) t "1 min, (b) t 3 min, (c) t "6 min, (d) t "9 min, (e) t "12 min, (f) t "22 min. The activation energies of di!usion calculated from the slope of Arrhenius plots are indicated at the plots.
Fig. 5. Di!usion activation energy versus deposition time of titanium determined from the Arrhenius plots in Fig. 4. Curves A and B correspond to di!erent processes of di!usion for a lower and a higher temperature range, respectively.
1.42 eV. Taking into account the estimation error, both "nal values of energy may be recognized to be equal in the high coverage limit. Besides the surface di!usion energy E also the pre-exponential factor D is obtained (Fig. 6) which
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117
Fig. 6. Titanium coverage dependence of the pre-exponential factor D determined from the Arrhenius plot in Fig. 4. Filled circles correspond to process A, empty circles correspond to process B.
Fig. 7. Temperature ranges of the thermally activated di!usion yielding an Arrhenius straight line of a semi-log plot (see Fig. 4). Region between the curves marked by "lled circles and triangles corresponds to the process A. Curve of empty circles represents the onset of process B.
is related to the entropy di!erence between trough and saddle position of the di!using adparticles. According to Zener [21] and Frenkel [22] the simplest model for D reveals D "a, where a is a jump-length and an attempt frequency. If a is taken as the tungsten lattice constant, a"3.16 As , and "10 s\, the pre-exponential D will be 10\ cm s\ which is not observed for both processes. D for the process A is 10\ cm s\ and D for the process B is 10\ cm s\ when the coverage of titanium tends to zero. Then D for both processes decreases with rising deposition time t more than one order of magnitude to 10\ cm s\ for the process A and 4;10\ cm s\ for process B. It seems that so large D variations are not only due to the adatom oscillation frequency but also due to adatom jump-lengths and may be caused in part by changes in the thermodynamic factor exp(S/k) which is lacking in the above expression of D . For the interpretation of the obtained results it may be understood that bulk titanium metal undergoes at 1156 K the phase transition from the hcp structure to bcc titanium. It is seen from Fig. 4 that the Arrhenius straight lines for both processes are displaced with increasing coverage towards low temperature. This e!ect is clearly seen in Fig. 7, where "lled circles represent the initial temperature and "lled triangles the "nal temperature of the range typical of the process A. The upper curve of
empty circles shows the initial temperature for the process B; its "nal temperature cannot be reasonably represented because of the low accuracy of measurement at higher temperature. The horizontal dashed line in Fig. 7 marks the ordinate 1156 K, or the phase transition point of titanium. Temperature regions of both processes are separated almost entirely by this line. Only for low coverage the process A proceeds at a temperature higher than 1155 K. For coverages in excess of a monolayer each process can be assigned to a di!erent range of temperature. The di!usion process A proceeds at a temperature at which bulk titanium has the hcp structure, while the di!usion B occurs at one where the bcc structure occurs. It can be supposed that adsorption sites or con"gurations of di!erent energy are involved in each process. The occurrence of two processes in the adsorption layers below and above the titanium phase transition point hcp/bcc is in accordance with the FEM results of Ti/W by Anderson and Thompson [23]. In their paper the formation of an alloy was not supposed to be probable. A similar point of view has been expressed in a recent paper [24], although the phase diagram titanium}tungsten [25] admits the possibility of an alloy formation of a bcc structure. A conclusion about the possible occurrence of a Ti/W surface alloy could be made based on LEED examination or atom*probe FIM
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
118
analysis rather than by the interpretation of FEM patterns of the Ti/W adsorption system. It can be concluded that the behaviour of the ultrathin titanium layers on the W(1 1 1) substrate probably is connected with a precursor of the phase transition of titanium at high temperatures. Acknowledgements The work was supported by the University of Wroc"aw, Grant 2016/W/IFD/99. Helpful discussions with Dr. S. Surma are gratefully acknowledged. The authors are also indebted to Krzysztof Biernat for the computer programming. References [1] [2] [3] [4] [5]
Kleint Ch. Surf Sci 1971;25:394,411. Gomer R. Surf Sci 1973;38:373. Gesley MA, Swanson LW. Phys Rev B 1985;32:7703. Gomer R. Rep Prog Phys 1990;53:919. Be9 ben J. Solid State Phenom 1990;12:17.
[6] Da9 browski AM. Solid State Phenom 1990;12:39. [7] Biernat T, Be9 ben J, Me9 clewski R. Surf Sci 1992;17:266. [8] Biernat T, Kleint Ch, Me9 clewski R. Surf Sci 1983;127: 487. [9] Biernat T. Solid State Phenom 1990;12:61. [10] Biernat T, Kleint Ch, Me9 clewski R. Surf Sci 1991; 246:54. [11] Biernat T, Kleint Ch, Me9 clewski R. Applied Surf Sci 1993;67:206. [12] Biernat T, Kleint Ch. Appl Surf Sci 1987;27:411. [13] Da9 browski AM, Biernat T, Be9 ben J, Gubernator W. Acta Phys Polon A 1997;91:1091. [14] Biernat T, Da9 browski AM. Vacuum 1999;54:99. [15] Da9 browski A, Kleint Ch. Surf Sci 1982;119:118. [16] Da9 browski AM, Kleint Ch. Surf Sci 1986;172:372. [17] Kleint Ch. Acta Univ Wratislaw 1986;936:81. [18] B"aszczyszyn R, Kleint Ch. Surf Sci 1986;171:615. [19] Zubenko YuV. Radiotekhn Electron 1963;8:1239. [20] Vladimirov GG, Medvedev BK, Sokolska IL. Solid State Phys 1970;12:1423. [21] Zener C. In: Proceedings of the Symposium on Imperfections in Nearly Perfect Crystals, Pocono Manor, 1950. [22] Frenkel J. Z Phys 1926;35:652. [23] Anderson JR, Thompson N. Surf Sci 1971;26:397. [24] Szczud"o Z, Ciszewski A. Applied Surf Sci, in press. [25] Hansen M. Constitution of binary alloys. New York: McGraw-Hill, 1958.
Two-process di!usion of titanium on the (1 1 1) tungsten plane by the current #uctuation method in FEM T. Biernat*, A.M. Da9 browski Institute of Experimental Physics, University of Wroc!aw, pl. M. Borna 9, 50 - 204 Wroc!aw, Poland
Abstract Field emission current noise of titanium adsorbed on the (1 1 1) tungsten crystal face was investigated. Measurements were carried out for coverages ranging from 0.2 to approximately 2 monolayers in the temperature range 300}1500 K. A linear combination of two theoretical functions obtained by Gesley and Swanson for the di!usion model of current #uctuations was "tted to the experimental autocorrelation functions. In such a way two di!usion coe$cients and two activation energies for titanium surface di!usion were determined. The theoretical model is applicable to a temperature range of 800}1450 K. The energy of each di!usion process decreases with increasing coverage, from a value of 1.77 eV (the "rst process) and 1.42 eV (the second process) until the saturation value of about 0.3 eV is reached for both di!usion processes. The "rst process occurs below the phase transition point of titanium (1156 K) and the second process occurs above it. 2001 Elsevier Science Ltd. All rights reserved.
1. Introduction Since the experimental and theoretical results on "eld emission current noise were reported by Kleint [1] and Gomer [2] the phenomenon has not been submitted to an exact description and, consequently, its interpretation has been far from exactitude. In the basic approach it is assumed that an adsorption layer on the substrate surface occurs in the state of thermal equilibrium, which means that the average density of the adlayer remains constant. This density, however, is subject to #uctuation which is responsible for the occurrence of "eld emission current #uctuations. The #uctuation mechanism is connected with the process of surface
* Corresponding author. Fax: #48-71-328-7365. E-mail address: [email protected] (T. Biernat).
di!usion. This process represents a speci"c type of di!usion in which the resultant amount of the material displaced in all directions is equal to zero. This model was employed in the theoretical work by Gesley and Swanson [3]. Using a di!erent formalism, these authors have obtained a result similar to that of Gomer [2]. Both papers deal with the presentation of a theoretical formula for the current #uctuation autocorrelation function. The autocorrelation function depends on the energy dependent coe$cient of surface di!usion. The direct connection of the physical characteristic of di!usion with "eld emission current #uctuations in the theoretical model o!ers a bene"t to surface research workers. Measurement of the current #uctuations can yield data about some physical parameters related to a given adsorbate deposited on a given substrate. Gomer has successfully used his theory for investigation of some gases [4] on refractory metals. The
0042-207X/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 0 1 ) 0 0 1 7 8 - 6
114
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
same method was employed in studies of alkali metals: potassium layers [5}7] and microcrystals [8], lithium layers [9}11] as well as for selfdi!usion of tungsten [12]. Recently the method of analysis of the autocorrelation function for "eld emission current #uctuations has been employed in a surface di!usion study of titanium [13,14]. Besides treating the autocorrelation function one can analyse the cross-correlation of current #uctuations measured for two emitter surface regions not too far away from each other [15]. Such measurements yield information on the interaction between atoms as well as the material transport on the emitter surface. Gomer's theory has been successfully adopted in the paper [16] to calculate the theoretical cross-correlation function. Not all experimental facts, however, could be understood by an advanced theory based on the adsorbate density #uctuations. Certain phenomena appear which need explanation based on the notion of soliton movement [17,18]. Interpretation of experimental results in the present work goes beyond the explicit formalism of Gesley and Swanson's theory. Part of these results are described by introducing a linear combination of two theoretical functions. In this way the interpretation can be done by referring to the general properties of titanium. Titanium di!usion on a "eld emitter surface was studied many years ago [19,20], such studies included the measurement of material transport caused by the presence of the concentration gradient. The present interest in titanium metal is due to its great importance in power engineering and ultrahigh vacuum technology. Titanium appears to be an ideal material for the power industry to store an ecologically clean fuel. Upon increasing air pollution by exhaust gas the new e$cient means of clean fuel storage has become a clue task. In order to examine the interaction of titanium with gases, the primary data required are ones about the temperature behaviour of the metal under well-de"ned ultrapurity conditions. Bulk titanium itself undergoes a high temperature phase transition from the hcp structure to bcc titanium. The transition occurs at 1156 K, which is well below the melting point of titanium at 1941 K. Measurements in the present
work were carried out at temperatures from 300 K to about 1500 K.
2. Experimental Measurement of "eld emission current #uctuations for titanium adsorbed on the region of the W(1 1 1) plane were carried out using the probehole "eld emission microscope and the experimental arrangement described in Ref. [13]. Titanium was evaporated in situ onto the W tip from a source made of a Ti block which could be heated by electron bombardment. The emitter tip temperature could be changed from room temperature to high values: it was stabilized and controlled using the temperature dependence of the resistance of an emitter loop segment with potential leads. The emission current from the W(1 1 1) plane was magnetically directed via a probe-hole to the Faraday collector for the probe region of approximately 10\ cm. After ampli"cation of the probe-hole current, its a.c. component was processed in an analog-digital converter PC card. The sampling time was 2;10\ s and one realization consisted of 400 000 samples. In order to control the thickness of the titanium adlayers, the work function versus the deposition time (corresponding to Ti coverage) was investigated. The initial portion of saturation of the curve is assumed to correspond to one monolayer of titanium. Data on the work function changes can be found in Ref. [13] and they are in general agreement with former ones [19,20]. The values of average work function versus deposition time of titanium used for investigation of "eld emission current #uctuations in this work are presented in Fig. 1.
3. Results and discussion Typical experimental autocorrelation functions of "eld emission current #uctuations are represented in Fig. 2. These results were obtained for the deposition time of titanium equal to 9 min (Fig. 1, point d). Curves from a to e are shifted by 0.4 of the unit along the vertical axis for better viewing. Each
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
115
Fig. 1. Average work function of tungsten versus the deposition time of titanium. Points a}f correspond to Fig. 4a}f. Point d corresponds to the Figs. 2 and 3.
Fig. 3. Experimental autocorrelation functions of the Ti/W(1 1 1) system for the deposition time of titanium t "9 min (the same as in Fig. 2) in double logarithmic scale (dots). Solid lines represent the theoretical autocorrelation functions "tted to the experimental values. Curves are shifted in the vertical direction by one decade each for better viewing.
Fig. 2. Experimental autocorrelation functions of the Ti/W(1 1 1) system, for the deposition time of titanium t "9 min, determined at the emitter temperatures indicated in the "gure. Curves are shifted in the vertical direction by 0.4 each for better viewing. Plots a}e correspond to plots a}e in Fig. 3 and points a}e in Fig. 4d.
curve starts at a value of 1 and diminishes to 0 with increasing time. The higher the temperature, the faster the autocorrelation functions diminish to
zero. The measurements were made in a broad temperature range of 300}1500 K. Thermally activated di!usion was observed above 875 K. In order to determine the di!usion coe$cient a theoretical curve was "tted to the experimental autocorrelation function by the least squares method. The theoretical autocorrelation function was calculated and given in analytical form in Ref. [3, Eq. (45)]. The diagram in Fig. 3 represents the curves of Fig. 2 in log}log scale. Points show the experimental data (as they were measured) and solid lines represent the theoretical functions. Curves in the "gure are shifted relative to each other by an order of magnitude for better viewing. It is seen that curves a, b and c are all well approximated by the theoretical function A. Curves d and
116
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
e, however, are well approximated by the function A only for long delay times, while for small times, the curves need approximation by introducing an additional function B. At high temperatures only the sum of functions A and B gives a good approximation of the experimental curves. In the "tting procedure described above the diffusion coe$cients were obtained at di!erent temperatures and titanium deposition time. In Fig. 4 the di!usion coe$cients D are shown as a function of reciprocal temperature 1/¹ in a semi-logarithmic diagram. It is clear from the "gure that certain ranges of temperature appear suitable for the di!usion coe$cients D to satisfy the Arrhenius equation with a constant activation energy E. In these temperature ranges the surface di!usion seems to be thermally activated. In Fig. 4 this is represented by the points that lie at the marked straight line segments with the corresponding values of energy and estimation error given at each segment. Filled circles correspond to the di!usion coe$cient computed by "tting with the theoretical function A and empty circles represent "tting by the function B. It may be noticed that the high temperature di!usion coe$cients D (marked by "lled circles) decrease with increasing temperature, while those of low temperature practically remain unchanged. In the range of high temperature, the di!usion coe$cients D represented by empty circles are arranged along a line of negative slope. Based on these results it seems that two di!usion types should be involved, or certainly two processes by which the di!usion proceeds could be discriminated. The di!usion energy for these processes as a function of the titanium layer thickness (which is expressed by the evaporation time) is represented in Fig. 5. Based on the literature [19] one can assume that the maximum thickness of the titanium in the present work corresponds to about two monolayers. It results from Fig. 5 that the energy for the process A is as high as 1.77 eV for small coverage and it diminishes with increasing coverage. For coverages in excess of a monolayer the diminution saturates and the energy reaches a value of approximately 0.3 eV. A similar behaviour is observed for the energy of the process B, where the saturation is reached at about the same value of energy, though this process starts from the initial value of energy
Fig. 4. Temperature dependence of the di!usion coe$cients for di!erent coverages of titanium. The deposition times of titanium are: (a) t "1 min, (b) t 3 min, (c) t "6 min, (d) t "9 min, (e) t "12 min, (f) t "22 min. The activation energies of di!usion calculated from the slope of Arrhenius plots are indicated at the plots.
Fig. 5. Di!usion activation energy versus deposition time of titanium determined from the Arrhenius plots in Fig. 4. Curves A and B correspond to di!erent processes of di!usion for a lower and a higher temperature range, respectively.
1.42 eV. Taking into account the estimation error, both "nal values of energy may be recognized to be equal in the high coverage limit. Besides the surface di!usion energy E also the pre-exponential factor D is obtained (Fig. 6) which
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
117
Fig. 6. Titanium coverage dependence of the pre-exponential factor D determined from the Arrhenius plot in Fig. 4. Filled circles correspond to process A, empty circles correspond to process B.
Fig. 7. Temperature ranges of the thermally activated di!usion yielding an Arrhenius straight line of a semi-log plot (see Fig. 4). Region between the curves marked by "lled circles and triangles corresponds to the process A. Curve of empty circles represents the onset of process B.
is related to the entropy di!erence between trough and saddle position of the di!using adparticles. According to Zener [21] and Frenkel [22] the simplest model for D reveals D "a, where a is a jump-length and an attempt frequency. If a is taken as the tungsten lattice constant, a"3.16 As , and "10 s\, the pre-exponential D will be 10\ cm s\ which is not observed for both processes. D for the process A is 10\ cm s\ and D for the process B is 10\ cm s\ when the coverage of titanium tends to zero. Then D for both processes decreases with rising deposition time t more than one order of magnitude to 10\ cm s\ for the process A and 4;10\ cm s\ for process B. It seems that so large D variations are not only due to the adatom oscillation frequency but also due to adatom jump-lengths and may be caused in part by changes in the thermodynamic factor exp(S/k) which is lacking in the above expression of D . For the interpretation of the obtained results it may be understood that bulk titanium metal undergoes at 1156 K the phase transition from the hcp structure to bcc titanium. It is seen from Fig. 4 that the Arrhenius straight lines for both processes are displaced with increasing coverage towards low temperature. This e!ect is clearly seen in Fig. 7, where "lled circles represent the initial temperature and "lled triangles the "nal temperature of the range typical of the process A. The upper curve of
empty circles shows the initial temperature for the process B; its "nal temperature cannot be reasonably represented because of the low accuracy of measurement at higher temperature. The horizontal dashed line in Fig. 7 marks the ordinate 1156 K, or the phase transition point of titanium. Temperature regions of both processes are separated almost entirely by this line. Only for low coverage the process A proceeds at a temperature higher than 1155 K. For coverages in excess of a monolayer each process can be assigned to a di!erent range of temperature. The di!usion process A proceeds at a temperature at which bulk titanium has the hcp structure, while the di!usion B occurs at one where the bcc structure occurs. It can be supposed that adsorption sites or con"gurations of di!erent energy are involved in each process. The occurrence of two processes in the adsorption layers below and above the titanium phase transition point hcp/bcc is in accordance with the FEM results of Ti/W by Anderson and Thompson [23]. In their paper the formation of an alloy was not supposed to be probable. A similar point of view has been expressed in a recent paper [24], although the phase diagram titanium}tungsten [25] admits the possibility of an alloy formation of a bcc structure. A conclusion about the possible occurrence of a Ti/W surface alloy could be made based on LEED examination or atom*probe FIM
T. Biernat, A.M. Da9 browski / Vacuum 63 (2001) 113}118
118
analysis rather than by the interpretation of FEM patterns of the Ti/W adsorption system. It can be concluded that the behaviour of the ultrathin titanium layers on the W(1 1 1) substrate probably is connected with a precursor of the phase transition of titanium at high temperatures. Acknowledgements The work was supported by the University of Wroc"aw, Grant 2016/W/IFD/99. Helpful discussions with Dr. S. Surma are gratefully acknowledged. The authors are also indebted to Krzysztof Biernat for the computer programming. References [1] [2] [3] [4] [5]
Kleint Ch. Surf Sci 1971;25:394,411. Gomer R. Surf Sci 1973;38:373. Gesley MA, Swanson LW. Phys Rev B 1985;32:7703. Gomer R. Rep Prog Phys 1990;53:919. Be9 ben J. Solid State Phenom 1990;12:17.
[6] Da9 browski AM. Solid State Phenom 1990;12:39. [7] Biernat T, Be9 ben J, Me9 clewski R. Surf Sci 1992;17:266. [8] Biernat T, Kleint Ch, Me9 clewski R. Surf Sci 1983;127: 487. [9] Biernat T. Solid State Phenom 1990;12:61. [10] Biernat T, Kleint Ch, Me9 clewski R. Surf Sci 1991; 246:54. [11] Biernat T, Kleint Ch, Me9 clewski R. Applied Surf Sci 1993;67:206. [12] Biernat T, Kleint Ch. Appl Surf Sci 1987;27:411. [13] Da9 browski AM, Biernat T, Be9 ben J, Gubernator W. Acta Phys Polon A 1997;91:1091. [14] Biernat T, Da9 browski AM. Vacuum 1999;54:99. [15] Da9 browski A, Kleint Ch. Surf Sci 1982;119:118. [16] Da9 browski AM, Kleint Ch. Surf Sci 1986;172:372. [17] Kleint Ch. Acta Univ Wratislaw 1986;936:81. [18] B"aszczyszyn R, Kleint Ch. Surf Sci 1986;171:615. [19] Zubenko YuV. Radiotekhn Electron 1963;8:1239. [20] Vladimirov GG, Medvedev BK, Sokolska IL. Solid State Phys 1970;12:1423. [21] Zener C. In: Proceedings of the Symposium on Imperfections in Nearly Perfect Crystals, Pocono Manor, 1950. [22] Frenkel J. Z Phys 1926;35:652. [23] Anderson JR, Thompson N. Surf Sci 1971;26:397. [24] Szczud"o Z, Ciszewski A. Applied Surf Sci, in press. [25] Hansen M. Constitution of binary alloys. New York: McGraw-Hill, 1958.