Stefan Hildebrandt,
Editor-in-Chief
Phys. Status Solidi B
Dear Mr. Editor, I am writing to you regarding the paper by F. Kh. Mirzade “Surface wave propagation in an elastic laser-excited half-space with small-scale effects” published in Phys. Status Solidi B 250, No. 10, 2185–2193 (2013). Below please read my comment on this paper. The conclusion made is that this is a plagiarized work containing also rude errors, inconsistences and cheating. This paper adds to a list of plagiarized papers published by this author (under the name F.Mirzoev) previously in Russian physical journals.
I do not know whether PSSb journal is publishing comments at all. In any case, I feel that the following comments look too extended to be published. I deliberately give detailed exposition of results of examination of Mirzade’paper to substantiate my assertions given in the text in bold (you may skim them first). This comment can be given in a more concise form.
With best regards,
Professor Emel’yanov V.I.
Physics Faculty, Moscow State University,
Moscow, Russia
Comment on the paper of F.Kh.Mirzade “Surface wave propagation in an elastic laser-excited half-space with small-scale effects”, published in Phys. Status Solidi B 250, No. 10, 2185–2193 (2013).
1.Introduction.
In the paper by F.Kh.Mirzade [1], the nonlocal-elastic theory of Rayleigh wave propagation on the surface of solids in the presence of point defects is presented. In it, the author claims introducing a number of fundamentally new elements: 1) he shows that the presence of mobile point defects renormalizes the classical Rayleigh determinant equation leading to occurrence of two new types of its solution: a defect-renormalized dynamic solution describing surface propagating waves and quasistatic solution describing formation of static surface Concentration-Strain (CS) nanostructures (in the following referred to as Defect-Deformational (DD) nanostructures) ; 2) he predicts softening of frequencies of Rayleigh waves due to defect generation; 2) a fundamentally new element of the theory [1] is the introduction, besides the conventional nanoscale parameter of the nonlocal elastic theory (the length of atom-atom interaction, g), also of a new nanoscale parameter: the length of defect-atom interaction h (in notations of Ref.[1]). 3)He obtains the growth rate and period of the static surface DD nanostructures which are determined by g and h; 4) he predicts the transition with the variation of control parameters of the DD system from occurrence of one to two maxima in the dependence of the growth rate of the surface DD nanograting on its wavenumber, that corresponds to formation of either single mode or two-modal static surface DD nanostructures; 5) he applies obtained formulas for the interpretation of literature data on surface nanostructure formation in СdTe under the action of a nanosecond laser pulse and gets a satisfactory agreement regarding the growth rate and period of the nanostructure; 6) at the end of the paper [1], the author put forward an unconventional idea of the possible relation of the growth rate of the DD nanogratings to the nanoparticle size distribution function.
In all these issues (1)-(6), F.Kh.Mirzade positions himself as a discoverer because he does not cite any previous works of other authors addressing these particular questions.
It is the aim of my comment to show that: (1) all above questions were addressed previously by another authors and corresponding nonlocal theories of the surface and bulk instabilities have been developed with taking into account of both scaling parameters g and h; (2) renormalization of Rayleigh determinant equation by defect generation leading to the softening of frequencies and occurrence of static surface structures were predicted and studied by other authors earlier; (3) the formulas for the critical defect concentration, the growth rate and the period of surface DD nanostructure, corresponding to the longwave maximum of the growth rate of surface DD nanostructure, obtained in [1], are only exact copies of previously obtained results of other authors covered in [1] under cumbersome notations; (4) the occurrence of the second (shortwave) maximum of the growth rate of surface DD nanostructure is an artifact (there is, in principle, no bimodality of static nanostructures in the nonlocal defect-Rayleigh wave system); (5) the agreement between the theory and literature experimental results on nanoparticle formation in СdTe, obtained in Ref.[1] is the result of gross errors in numerical estimates and (6) the idea of the possible relation between the DD nanostructure growth rate and nanoparticle size distribution was not only put forward previously but corresponding theories has been developed and published in several papers and reviews and results of this unconventional theory of formation of bimodal nanoparticle size distribution function were extensively compared with experiment.
I also comment on one earlier publication episode connected with the author Kh.F.Mirzade, when he published his papers in physical journals under the name of Kh.F. Mirzoev.
2. Outline of previous relevant works of other authors
To assess the originality of the paper [1] by Kh.F.Mirzade, we first compare it briefly with previously published relevant papers of other authors. The coupling of Rayleigh wave to diffusion type variable (point defect concentration or temperature) leading to the renormalization of Rayleigh determinant equation with two new types of its solution: (a) the dynamical one, describing defect-renormalized Rayleigh waves with softened frequencies and (b) DD surface static structures, was for the first time considered in Ref. [2] for the case of electron-hole pairs as defects. The introduction of two nonlocal scaling parameters and in the theory of DD nanostructure selforganization in the bulk of solids was for the first time done in Ref.[3,4] (notations and are from [3,4]). The nonlocal theory of surface DD nanostructure selforganization with the participation of quasi-Rayleigh wave with taking into account of the scaling parameter was developed in Ref. [5]. Two maxima of the growth rate of the surface DD instability involving coupled quasi-Lamb flexural and quasi-Rayleigh waves were obtained previously and the relation between the growth rate and the nanoparticle size distribution function was suggested and studied in [6]. The review of the DD theory of laser-induced formation of bimodal size distribution function and extensive comparison with experimental results are given in [7]. None of these works [2]-[7] is cited by Kh.F.Mirzade in his paper [1].
Now, let us compare in more detail the mechanism of surface DD instability, equations and results obtained in Ref. [1] with those from listed above Refs.[2]-[7].
3. Papers [1] and [5] explore one and the same mechanism of surface Defect-Deformational instability
Let us compare, first, physical mechanisms of the surface instabilities considered in Refs.[5] and [1].
From Introduction in Ref. [5]:
“The mechanism of the surface DD (Defect-Deformational) instability consists of the following. An initial surface fluctuation strain gives rise to strain-induced surface defect fluxes. This leads to the formation of spatially nonuniform field of surface defect concentration, which via the defect deformation potential and also via the local renormalization of the surface energy nonuniformly deforms the surface and underlying elastic continuum, increasing thus the initial strain. Exceeding a certain critical value of surface defect concentration such positive feedback leads to the onset of the DD instability with arising of nanometer scale surface relief modulations and piling up of defects at extrema of this modulation, which serve as periodic nucleation sites for the subsequent growth of nanoclusters.”
From Sec.6 of Ref. [1]:
“Laser radiation (or, in general, a flux of particles) generates high concentrations of mobile atomic defects in the surface layer of the irradiated solid. When a fluctuation harmonic of the elastic deformation field appears in a medium because of the generation of atomic defects, the strain-induced drift of atomic defects occurs. This is a consequence of nonlocal defect–strain interaction. The strain-induced flux of defects leads to the formation of spatially nonuniform fields of the defect concentration. The redistribution of defects creates forces proportional to their gradients. These forces lead in turn to additional growth of strain fluctuations. When the defect density or a critical rate of defect generation exceeds the critical value, diffusion–elastic instabilities develop as a result of positive feedback, which result in the self-organization of ordered Concentration-Strain structures.”
Evidently, the paper [1] relies on the same physical mechanism of surface DD instability as was studied in [5]. Similar are also model equations involving the equation for the vector of displacement in the medium and diffusion equation for point defects. We note that Kh.F.Mirzade in [1], in contradistinction to [5], uses boundary conditions for medium displacement vector at defect-free surface that is inadmissible for defect-elastic continuum problem and makes all obtained results inconclusive.
Both models [5] and [1] starts from the nonlocal Hooks’s law which takes into account of nonlocality of atom-atom and defect-atom interactions leading to occurrence of two nonlocality parameters and (compare eq.(1) from [5] and Eq. (2) from [1]). Without citing any previous works, Kh.F.Mirzade in [1] claims to introduce the second parameter for the first time. This claim does not correspond to facts.
4. Two scaling parameters of nonlocal elasticity theory with taking into account of point defects, and , have been introduced for the first time in Ref. [3,4] for the bulk DD instability and in Ref.[5] for surface DD instability.
In Refs.[3,4] we introduced an expression for the bulk free-energy density of a one-dimensional self-consistently strained crystal with point defects, which takes into account the nonlocal interaction of the lattice atoms with one another and with defects. Using this free-energy expression we studied the formation of periodic and cluster defect-deformational (DD) structures deriving nonlinear mean-field equation for the self-consistent strain. We did not expose in [3,4] the growth rate of obtained DD structures since we studied steady-state solutions of this equation. But it can be easily checked that the corresponding growth rate of the bulk DD grating () reads
, (I)
where is the defect diffusion coefficient, is the characteristic interaction length between lattice atoms (the conventional parameter of nonlocal elasticity theory), is the characteristic interaction length of the defects with the lattice atoms, is the control parameter, is the mean concentration of the point defects, is the critical defect concentration, is the density of the medium, is the longitudinal velocity of sound, is defect deformational potential, is a change in the volume of the crystal as a result of the generation of a single defect, and K is the bulk elastic modulus, T is the temperature, is the Boltzmann constant and is defect lifetime.
The formula (31) for the growth rate, given by Kh.F.Mirzade in his paper [1] for surface instability, in notations of Eq.(I), has the form
, (II)
which virtually coincides with the formula (I), if one takes into account that the unimportant (in this context) factor ( is the transverse sound velocity) appears only in the surface (Rayleigh wave) problem (see below). Note, that in the range of applicability of nonlocal elastic theory [1] the formula (II) at R=1 coincides with Eq.(I) (see Sec.7).
The connection of the Mirzade’s publication [1] to the our earlier papers [3,4] is now obvious. The new scaling parameter of the nonlocality has been introduced for the first time in the works [3,4] on the bulk DD instability and not in [1] and the growth rate involving two nonlocal scaling parameters and in the form of Eq.(I) is quite similar to that given in Ref.[1]. Nevertheless, Kh.F.Mirzade does not cite the works [3,4].
In the next step, we addressed the problem of the DD instability on the surface in Ref.[5], eight years prior to Kh.F.Mirzade’s publication [1], where we take into account only the nonlocality of defect-atom interaction (the scaling parameter ), introduced in [3,4], and disregard the nonlocality of atom-atom interactions putting(see the substantiation of this neglect in Sec. 7). We thus neglected in [5] the influence of nonlocality-induced softening of elastic modules on the DD instability and leading, according to [1], to occurrence of the second, shortwave maximum, see Fig. 2 and Fig.3 from Ref. [1] (the proof , that this is an artifact is given below in Sec.7).
We note that neglect of the atom-atom interaction nonlocality () does not influence also the effect of softening of Rayleigh wave frequencies which was considered for the first time in the framework of local elasticity theory earlier in Ref. [2].
Let us compare problem stating and results of papers [1] and [2].
5. Defect-induced softening of Rayleigh wave frequency and generation of static surface DD structures as solutions of defect-renormalized Rayleigh determinant equation were for the first time considered in [2] in the framework of local elasticity theory.
In Ref. [2] the surface electron-deformation-thermal instability (EDTI) was considered the cause of which is coupling of the Rayleigh wave to surface diffusional field (point defects or temperature) leading to renormalization of classic Rayleigh determinant equation. It is shown that (I cite the abstract from [2]): “ Under certain conditions there can be three qualitatively different types of EDTI: generation of surface acoustic waves, "softening" of the frequencies of surface acoustic waves, and generation of static ordered surface structures”. These are the same problems that are addressed in Ref. [1]. I cite from [1]: “Equation (24) has solutions describing qualitatively different types of instability: (i) instability of frequencies of surface acoustic waves; (ii) generation of spatially ordered surface (static) structures.” Nonetheless, no citation on earlier paper [2] is given in [1]. One must note, that the resulting formula, predicting the softening of the frequencies of Rayleigh wave, presented in [1], is inconclusive because of (a) inadequate defect free surface boundary conditions used in [1], (b) evident error made in the derivation of it (the sign in expression for , following from Eq. (28), must be reversed), and (c) uncertainty of the undiscussed sign of very general form derivative occurring in the final formula (30a)).
Nonetheless, we note that from (30a) it is seen that the term causing frequency softening is independent of nonlocality parameters and and is proportional to defect concentration (or, for steady-state, to the rate of defect generation). These are also salient features of the corresponding formula from the earlier paper [2].