The procedure for the determination of elastic parameters according to reference nanometer lithographic marks by atomic force microscopy on samples with up to microscopic sizes is proposed. Analysis of dynamic changes of elastic characteristics that makes it possible to establish the critical rotation velocity of a CD without plastic deformations has been made.
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Dobromyslov, M.

Kuzko, A.

Kuzmenko, A.

Timakov, D.

SocioEconomic Challenges Journal (Sumy State University)

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ 
Vol. 5 No 4, 04045(2pp) (2013) Том 5 № 4, 04045(2cc) (2013) 
 
 
The article was reported at the International Conference «Physics and Technology of Nanomaterials and Structures», Kursk, 21-22 November, 2013 
2077-6772/2013/5(4)04045(2) 04045-1  2013 Sumy State University 
Short Communication 
 
Atomic Force Analysis of Elastic Deformations of CD 
 
A. Kuzmenko1, A. Kuzko1, D. Timakov1, M. Dobromyslov2 
 
1 Southwest State University, 94, 50 Let Oktyabrya Str., 305040 Kursk, Russia 
2 Pacific National University, 136, Tihookeanskaya Str., 680035 Khabarovsk, Russia 
 
(Received 24 October 2013; published online 10 December 2013) 
 
The procedure for the determination of elastic parameters according to reference nanometer litho-
graphic marks by atomic force microscopy on samples with up to microscopic sizes is proposed. Analysis of 
dynamic changes of elastic characteristics that makes it possible to establish the critical rotation velocity of 
a CD without plastic deformations has been made. 
 
Keywords: Elastic effects, Atomic force microscopy, Nanoindenter, CD, Polycarbonate. 
 
PACS number: 62.20.F. – 
 
 
1. INTRODUCTION 
 
The transition to data recording of nanometer-scale 
range using devices of either nanometer- or microme-
ter-scale sizes or nanostructured devices has indicated 
challenges of restructuring in materials that are uti-
lized at pre- and critical localized impacts of electronic, 
elastic, and thermal nature [1, 2]. Traditional diagnos-
tic methods, including optical ones, [3] provide scanty 
information about structural changes in materials. 
Now the atomic force microscopy techniques (AFM) of 
microscopic entities are being developed, which are 
based on nano- and microindentation [4]. 
 
2. EXPERIMENTAL SECTION 
 
Rectangular samples (4  4  0.5 mm) of polycar-
bonate, which is intensively used in electronic and 
computer techniques, for example in CD, were influ-
enced by a localized elastic up to plastic deformation 
(Fig. 1a). The check of restructuring was realized by 
using a nanometer lithographic pattern that was made 
by an atomic- force microscope cantilever. The thick-
ness of reference lines was dictated by the geometrical 
size of a probe and was equal to 7-10 nm. The depth of 
lines was determined by the number of probe pricks 
and the indentation power and was within 12-15 nm, 
and their orientation was chosen with consideration for 
directions of deformation. 
The measurement of deformation magnitude is 
based on photoelasticity, in which changes in polarized 
radiation were recorded with a modified confocal micro-
scope (AIST-NT OmegaScope). Stresses were calculated 
according to the technique described in [4] by using 
equation 
 
   N / dK,  
 
where  is normal stress, N is the order of  interference 
stripe proportional to ,  is the wavelength of a light 
source, d is the sample thickness, K is photoelasticity 
coefficient for polycarbonate ( 7 × 10 – 11 m2/Н). 
Fig. 2 shows how nanometer-scale distance between 
reference nanometer lithographic marks (RNMs) 
changes with deformation. Characteristic areas of elas-
tic, plastic deformation up to the sample destruction 
 
 
 
 
Fig. 1 – AFM image of tracks for the formation of pit infor-
mation – a; nanometer lithographic pattern on the polycar-
bonate surface – b 
 
are observed. Elastic modulus determined from the 
relation E  Fl/SΔl (F, S are the load and the area of 
its distribution, respectively, l, Δl are the pattern size 
and the variation of distance between RNMs) was equal 
to 2.4 GPa with the measurement error of 1.6 %. The 
elastic modulus of polycarbonate determined by the 
standard methods is equal to2.2 GPa. The measure-
ment of E-value for the samples with sizes (4  4  0.5), 
which do not meet requirements of the standard meth-
ods, was equal to 4 GPa with the use of Instron 5882 
(Fig. 2) (at a comparable measurement accuracy). 
a 
b 
 A. KUZMENKO, A. KUZKO, D. TIMAKOV, M. DOBROMYSLOV J. NANO- ELECTRON. PHYS. 5, 04045 (2013) 
 
 
04045-2 
 
 
Fig. 2 – Dependence of changes in nanometer-scale sizes on 
the deformation applied 
 
 
 
Fig. 3 – A schematic of a laser disk (a) and its elementary site (b) 
 
As a practical application of the obtained nanoscale 
elastic modulus dynamic changes in elastic parameters 
have been analyzed, which correspond to critical (with-
out plastic deformation) rotation velocities of a CD, that 
is in elastic deformation domain. As seen in Fig. 3, the 
external areas of a CD undergo a maximum effect of 
inertial force; as a result these deform most of all. Con-
sider the elementary site of the CD at its edge with  –
a maximum rotation velocity, which is accompanied by 
a shift of the information pit edge through an angle d 
as compared to the nearest edge of another pit (Fig.2). 
Here    ⃗⃗⃗⃗  ⃗    ⃗⃗⃗⃗  ⃗     ⃗⃗ ⃗⃗  are elastic forces that act on this 
site at its maximum deformation when in rotation and 
the resultant force set in opposite direction to the cen-
trifugal force. 
According to D’Alembert’ principle: 
 
  ⃗⃗⃗⃗     ⃗⃗ ⃗⃗     ⃗⃗ ⃗⃗    ⃗⃗⃗⃗     
 
Considering, that                   , pro-
jecting on the Y-axis 
 
          
  
 
            
 
Disk destruction and super critical shift of pits at 
deformation is determined by only two diagonal strain 
components    и   : 
 
                  
               
               ,          . 
 
Considering smallness of       
  
 
 
  
 
: 
 
                         
  
 
           
                     . 
 
Obviously: 
 
   
   
    
 
       
      
        
 
Here     is the difference between two centrifugal 
forces acting on sites with mass dm at a distance dr 
along disk radius. 
 
            
         
     (  
  
 
)     
 
Considering smallness of           and    
         the maximum disk rotation frequency can be 
evaluated, at which irreversible changes still do not 
occur: 
 
 
 
    
√
       
 
 = 1532 rev/s, 
 
where    is the disk radius,           is the elastic limit of 
polycarbonate, ρ is the disk density. 
The elastic limit          obtained in studying na-
nometer-scale deformations makes it possible to deter-
mine the maximum possible shift of pits with respect to 
each other        for error-free reading data: 
 
      
         
 
 
          
 
     nm 
 
3. CONCLUSIONS 
 
The present results indicate the importance of de-
velopment of special ways and methods to determine 
elastic parameters in covers on materials or in small-
sized samples (up to nanometer-scale and microscopic) 
even along one coordinate axis. 
 
 
REFERENCES 
 
1. Yu.I. Golovin, Phys. Solid State 50, 2205 (2008). 
2. A. Kuzmenko, D. Timakov, P. Abakumov, M. Dobro-
myslov, L.V. Odnodvorets, J. Nano- Electron. Phys. 5 No3, 
03024 (2013). 
3. S.I. Gerasimov, Appl. Mech. Tech. Phys. 45, 453 (2004). 
4. A.P. Kuzmenko, Nano Deformation of the CD Material. 
BSU Scientific bulletin 106, 108 (2011). 
 
a 
b 


English

Atomic Force Analysis of Elastic Deformations of CD

Electronic Sumy State University Institutional Repository

JOURNAL OF NANO- AND ELECTRONIC PHYSICS ЖУРНАЛ НАНО- ТА ЕЛЕКТРОННОЇ ФІЗИКИ Vol. 5 No 4, 04045(2pp) (2013) Том 5 № 4, 04045(2cc) (2013)   The article was reported at the International Conference «Physics and Technology of Nanomaterials and Structures», Kursk, 21-22 November, 2013 2077-6772/2013/5(4)04045(2) 04045-1  2013 Sumy State University Short Communication  Atomic Force Analysis of Elastic Deformations of CD  A. Kuzmenko1, A. Kuzko1, D. Timakov1, M. Dobromyslov2  1 Southwest State University, 94, 50 Let Oktyabrya Str., 305040 Kursk, Russia 2 Pacific National University, 136, Tihookeanskaya Str., 680035 Khabarovsk, Russia  (Received 24 October 2013; published online 10 December 2013)  The procedure for the determination of elastic parameters according to reference nanometer litho-graphic marks by atomic force microscopy on samples with up to microscopic sizes is proposed. Analysis of dynamic changes of elastic characteristics that makes it possible to establish the critical rotation velocity of a CD without plastic deformations has been made.  Keywords: Elastic effects, Atomic force microscopy, Nanoindenter, CD, Polycarbonate.  PACS number: 62.20.F. –   1. INTRODUCTION  The transition to data recording of nanometer-scale range using devices of either nanometer- or microme-ter-scale sizes or nanostructured devices has indicated challenges of restructuring in materials that are uti-lized at pre- and critical localized impacts of electronic, elastic, and thermal nature [1, 2]. Traditional diagnos-tic methods, including optical ones, [3] provide scanty information about structural changes in materials. Now the atomic force microscopy techniques (AFM) of microscopic entities are being developed, which are based on nano- and microindentation [4].  2. EXPERIMENTAL SECTION  Rectangular samples (4  4  0.5 mm) of polycar-bonate, which is intensively used in electronic and computer techniques, for example in CD, were influ-enced by a localized elastic up to plastic deformation (Fig. 1a). The check of restructuring was realized by using a nanometer lithographic pattern that was made by an atomic- force microscope cantilever. The thick-ness of reference lines was dictated by the geometrical size of a probe and was equal to 7-10 nm. The depth of lines was determined by the number of probe pricks and the indentation power and was within 12-15 nm, and their orientation was chosen with consideration for directions of deformation. The measurement of deformation magnitude is based on photoelasticity, in which changes in polarized radiation were recorded with a modified confocal micro-scope (AIST-NT OmegaScope). Stresses were calculated according to the technique described in [4] by using equation     N / dK,   where  is normal stress, N is the order of  interference stripe proportional to ,  is the wavelength of a light source, d is the sample thickness, K is photoelasticity coefficient for polycarbonate ( 7 × 10 – 11 m2/Н). Fig. 2 shows how nanometer-scale distance between reference nanometer lithographic marks (RNMs) changes with deformation. Characteristic areas of elas-tic, plastic deformation up to the sample destruction     Fig. 1 – AFM image of tracks for the formation of pit infor-mation – a; nanometer lithographic pattern on the polycar-bonate surface – b  are observed. Elastic modulus determined from the relation E  Fl/SΔl (F, S are the load and the area of its distribution, respectively, l, Δl are the pattern size and the variation of distance between RNMs) was equal to 2.4 GPa with the measurement error of 1.6 %. The elastic modulus of polycarbonate determined by the standard methods is equal to2.2 GPa. The measure-ment of E-value for the samples with sizes (4  4  0.5), which do not meet requirements of the standard meth-ods, was equal to 4 GPa with the use of Instron 5882 (Fig. 2) (at a comparable measurement accuracy). a b  A. KUZMENKO, A. KUZKO, D. TIMAKOV, M. DOBROMYSLOV J. NANO- ELECTRON. PHYS. 5, 04045 (2013)   04045-2   Fig. 2 – Dependence of changes in nanometer-scale sizes on the deformation applied    Fig. 3 – A schematic of a laser disk (a) and its elementary site (b)  As a practical application of the obtained nanoscale elastic modulus dynamic changes in elastic parameters have been analyzed, which correspond to critical (with-out plastic deformation) rotation velocities of a CD, that is in elastic deformation domain. As seen in Fig. 3, the external areas of a CD undergo a maximum effect of inertial force; as a result these deform most of all. Con-sider the elementary site of the CD at its edge with  –a maximum rotation velocity, which is accompanied by a shift of the information pit edge through an angle d as compared to the nearest edge of another pit (Fig.2). Here    ⃗⃗⃗⃗  ⃗    ⃗⃗⃗⃗  ⃗     ⃗⃗ ⃗⃗  are elastic forces that act on this site at its maximum deformation when in rotation and the resultant force set in opposite direction to the cen-trifugal force. According to D’Alembert’ principle:    ⃗⃗⃗⃗     ⃗⃗ ⃗⃗     ⃗⃗ ⃗⃗    ⃗⃗⃗⃗      Considering, that                   , pro-jecting on the Y-axis                            Disk destruction and super critical shift of pits at deformation is determined by only two diagonal strain components    и   :                                                  ,          .  Considering smallness of              :                                                              .  Obviously:                                   Here     is the difference between two centrifugal forces acting on sites with mass dm at a distance dr along disk radius.                            (     )      Considering smallness of           and             the maximum disk rotation frequency can be evaluated, at which irreversible changes still do not occur:        √         = 1532 rev/s,  where    is the disk radius,           is the elastic limit of polycarbonate, ρ is the disk density. The elastic limit          obtained in studying na-nometer-scale deformations makes it possible to deter-mine the maximum possible shift of pits with respect to each other        for error-free reading data:                                   nm  3. CONCLUSIONS  The present results indicate the importance of de-velopment of special ways and methods to determine elastic parameters in covers on materials or in small-sized samples (up to nanometer-scale and microscopic) even along one coordinate axis.   REFERENCES  1. Yu.I. Golovin, Phys. Solid State 50, 2205 (2008). 2. A. Kuzmenko, D. Timakov, P. Abakumov, M. Dobro-myslov, L.V. Odnodvorets, J. Nano- Electron. Phys. 5 No3, 03024 (2013). 3. S.I. Gerasimov, Appl. Mech. Tech. Phys. 45, 453 (2004). 4. A.P. Kuzmenko, Nano Deformation of the CD Material. BSU Scientific bulletin 106, 108 (2011).  a b 

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Atomic Force Analysis of Elastic Deformations of CD

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