Surface Plasmons Excited by Xrays in the Surface Layers of Solids
Abstract
:1. Introduction
1.1. Total External Reflection of Xrays from the Surface of Solids
1.2. Ideas about the Excitation of Surface Plasmons in Solids by Xrays
1.2.1. Theoretical Concepts of Plasma Oscillations in Metals
1.2.2. Plasma Oscillations in Crystalline Semiconductors and Dielectrics
2. Dispersion of Surface Plasmons in Solids
2.1. Comparative Study of Plasmon Dispersion in Amorphous Fused Quartz and in a Single Crystal LiF
2.2. Plasmon Dispersion in Amorphous Vanadium Dioxide VO_{2} Films
2.2.1. Theoretical Calculations of Vanadium Dioxide
 (1)
 Calculation of the depth of the TSE X output.
 (2)
 Calculation of the depth x formation of TER Xrays.
 (3)
 Calculation of the number of electrons N involved in the excitation of plasmons in vanadium dioxide.
2.2.2. Xray Diffraction Analysis of Samples of Vanadium Dioxide thin Films
2.2.3. Investigation of the Dispersion of Surface Plasmons by the Method of Total External Reflection of Xrays from Samples of Vanadium Dioxide Thin Films
3. Conclusions
Funding
Data Availability Statement
Conflicts of Interest
References
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Reflex Number  2θ°  $\mathit{h}\mathit{k}\mathit{l}$  ${\mathit{H}}_{\mathit{h}\mathit{k}\mathit{l}}\times {10}^{4}\mathbf{c}\mathbf{m}$  $(\frac{\mathit{x}}{{\mathit{H}}_{\mathit{h}\mathit{k}\mathit{l}}})\times {10}^{4}$  ${\mathit{N}}_{\mathit{c}\mathit{r}\mathit{s}}\times {10}^{9}$  $\mathit{d},\mathbf{\AA}$  δ × 10^{−8} 

1  38.5274  110  1.2273  5.2636  5.9057  2.3348  
2  55.6190  200  1.7355  29.329  3842.3  1.6511  23.1 
3  69.6765  211  2.1251  3.0398  46.219  1.3484  
4  10.771  222  3.0052  2.1496  971.91  0.9535  13.3 
Metal 
$$\mathsf{\delta}\times {10}^{8}$$
 d, Å 
$$\mathit{C}=\frac{\mathbf{\delta}}{\mathit{d}}\times {10}^{8}{\mathbf{\AA}}^{1}$$

$$\mathbf{\u2206}\mathit{C}\times {10}^{8}{\mathbf{\AA}}^{1}$$

$$\mathit{x},\mathbf{\AA}$$


Ni  21.1  1.7542  12  1  143.4 
Cu  12.8  1.2786  10  3  52.5 
Ag  26.3  2.0234  13  0  72.18 
Pt  33.8  2.2537  15  −2  17.90 
Bi  54.2  3.9482  14  −1  10.99 
Metal  ${\mathsf{\alpha}}^{\mathsf{\xb0}}$  $\mathit{h}\mathit{k}\mathit{l}$  ${\mathbf{E}}_{\mathbf{P}},\mathbf{e}\mathbf{V}$  $\mathit{x},\mathbf{\AA}$  $\mathit{N}\times {10}^{28}{\mathbf{m}}^{3}$ 

Cu  0.0178  111  2.06  26  4.062 
0.0261  200  4.06  52  8.707  
Mo  0.0776  200  10.9  42  7.723 
Ta  0.0095  200  1.4  6.5  1.274 
0.0785  222  11.0  50  7.865  
Pt  0.0141  111  1.98  5.35  2.548 
0.0878  222  12.33  35.0  9.909  
Ag  0.0124  111  1.74  4.5  1.168 
Au  0.0612  222  8.60  20.1  4.807 
Semiconductor Crystals  ${\mathbf{E}}_{\mathbf{P}},\mathbf{e}\mathbf{V}$  $\mathit{x},\mathbf{\AA}$  ${\mathit{N}}_{2}$  ${\mathbf{E}}_{\mathbf{g}},\mathbf{e}\mathbf{V}$ 

Si  2.146  90.5  $60.56\times {10}^{16}$  1.120 
Ge  2.135  32  $40.87\times {10}^{16}$  0.665 
GaSb  1.896  12  $13.25\times {10}^{16}$  0.810 
Dielectric Crystal  
LiF  3.174  62.3  $20.15\times {10}^{21}$  14.50 
${\mathsf{\beta}}^{\mathsf{\xb0}}$  ${\mathsf{\alpha}}^{\mathsf{\xb0}}$  ${\mathbf{E}}_{\mathbf{P}},\mathbf{eV}$  $\mathit{x},\AA $  ${\mathit{N}}_{1}\times {10}^{21}\mathbf{Electrons}$  Electron Asymmetry 

0  0.0218  3.062  246  24  N_{1(0)}
/N_{1(180)} = 1.26 N_{1(45)} /N_{1(225)} = 1.8 N_{1(90)} /N_{1(270)} = 2.54 N_{1(135)} /N_{1(335)} = 1.44 
20  0.0223  3.132  252  26  
45  0.0226  3.174  256  27  
65  0.0228  3.202  258  28  
90  0.0230  3.231  260  28  
110  0.0224  3.146  253  26  
135  0.0126  3.034  244  23  
155  0.0210  2.950  238  22  
180  0.0202  2.837  228  19  
200  0.0192  2.700  217  16  
225  0.0185  2.598  209  15  
245  0.0173  2.430  196  12  
270  0.0170  2.388  192  11  
290  0.0178  2.500  201  13  
315  0.0189  2.655  214  16  
335  0.0197  2.767  223  18 
Substance  ${\overline{\mathbf{E}}}_{\mathbf{P}},\mathbf{e}\mathbf{V}$  $\mathsf{\sigma},\mathbf{G}\mathbf{P}\mathbf{a}$ 

fused quartz  0.574  3.129 
quartz glass  0.395  2.153 
uviol glass  0.412  2.246 
molybdenum glass  0.432  2.354 
lithium fluoride  0.0042  0 
sitall  0.361  1.968 
${\mathsf{\beta}}^{\mathsf{\xb0}}$  ${\mathsf{\alpha}}^{\mathsf{\xb0}}$  ${\mathbf{E}}_{\mathbf{P}},\mathbf{e}\mathbf{V}$  $\mathit{x}\mathsf{,}\mathsf{\AA}$  ${\mathit{N}}_{\mathbf{1}}\mathsf{\times}{\mathbf{10}}^{\mathbf{16}}$ Electrons  N_{1(0)}/N_{1(180)} = 1.35 N_{1(45)}/N_{(225)} = 1.95 N_{1(90)}/N_{1(270)} = 2.3 N_{1(135)}/N_{1(335)} = 1.38 
0  0.0170  2.388  23.68  42.36  
20  0.0164  2.304  22.84  38.04  
45  0.0160  2.247  22.28  35.30  
65  0.0154  2.163  21.45  31.76  
90  0.0150  2.107  20.89  29.10  
110  0.0162  2.275  22.56  36.64  
135  0.0168  2.360  23.40  40.89  
155  0.0175  2.458  24.37  46.20  
180  0.0188  2.640  26.18  57.26  
200  0.0198  2.781  27.58  66.92  
225  0.0200  2.809  27.85  68.96  
245  0.0200  2.809  27.85  68.96  
270  0.0198  2.781  27.58  66.92  
290  0.0190  2.669  26.46  59.15  
315  0.0187  2.627  26.04  56.40  
335  0.0180  2.528  25.07  50.20 
${\mathsf{\beta}}^{\mathsf{\xb0}}$  ${\mathsf{\alpha}}^{\mathsf{\xb0}}$  ${\mathbf{E}}_{\mathbf{P}},\mathbf{e}\mathbf{V}$  $\mathit{x}\mathsf{,}\mathbf{\AA}$  ${\mathbf{N}}_{\mathbf{1}}\mathsf{\times}{\mathbf{10}}^{\mathbf{16}}$ Electrons  N_{1(0)}/N_{1(180)} = 2.7 N_{1(45)}/N_{1(225)} = 1.5 N_{1(90)}/N_{1(270)} = 1.53 N_{1(135)}/N_{1(335)} = 2.18 
0  0.0140  1.966  19.50  19.21  
20  0.0150  2.107  20.89  22.64  
45  0.0159  2.233  22,14  28.14  
65  0.0170  2.388  23.68  34.42  
90  0.0188  2.641  26.18  46.55  
110  0.0196  2.753  27.30  52.73  
135  0.0197  2.767  27.48  53.54  
155  0.0198  2.781  27.58  54.36  
180  0.0195  2.739  27.16  51.96  
200  0.0191  2.683  26.60  48.81  
225  0.0182  2.556  25.35  42.21  
245  0.0175  2.458  24.37  37.53  
270  0.0163  2.289  22.70  30.32  
290  0.0155  2.177  21.59  26.08  
315  0.0152  2.135  21.17  24.60  
335  0.0142  1.994  19.78  20.04 
Vanadium Dioxide Films  $\overline{\mathbf{a}\mathbf{s}\mathbf{y}\mathbf{m}}$  ${\overline{\mathbf{E}}}_{\mathbf{P}},\mathbf{e}\mathbf{V}$  $\mathsf{\sigma},\mathbf{G}\mathbf{P}\mathbf{a}$  $\mathit{x},\mathsf{\AA}$ 

№1  1.745  0.517  3.386  27 
№2  1.980  0.230  1.506  27 
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Stozharov, V.M. Surface Plasmons Excited by Xrays in the Surface Layers of Solids. Solids 2022, 3, 122146. https://doi.org/10.3390/solids3010009
Stozharov VM. Surface Plasmons Excited by Xrays in the Surface Layers of Solids. Solids. 2022; 3(1):122146. https://doi.org/10.3390/solids3010009
Chicago/Turabian StyleStozharov, Valery M. 2022. "Surface Plasmons Excited by Xrays in the Surface Layers of Solids" Solids 3, no. 1: 122146. https://doi.org/10.3390/solids3010009