lattice mismatch and matching standard?

[njuxyh]

Hi all:

i have searched a paper named "contact effects of nickel and copper on electron transport through graphene", http://http://journals.aps.org/prb/abstract/10.1103/PhysRevB.86.155434
in which two probe system is attached. the central region is one-dimension GNRs, the period direction is x direction.

and i want to practice to construct such system,
in my case, the cell of the substrate plane is a  orthorhombic cell, and in the z direction: lattice z1=4.5087 angstrom, x direction: x1=2.5955 angstrom.
the central region consists of a one-dimensional material, the length in the z direction consists several repeat unit, and every repeat is 4.6363 angstrom,
the cell of film on the substrate is also orthorombic cell,  in the x direction,lattice x2=3.3010 angstrom.

and the first step for me is to solve the lattice matching issue.
1. how to define the mismatching?
 for example, if i choose 1 repeat unit in the z direction,  4 repeats in the x direction for substrate cell and 3 repeats in the x direction) for  film cell.is it the mismatching computed like this
 in the x direction (2.5955-3.3010)/=0.21=21%, in the z direction, (4.5087-4.6363)/4.5078= -0.02=2% ?


2. the limits of mismatch can be accepted? 21% is too large?
 

3 I saw some theoretical references, in order to get better matching, the substrate  or the film is compressed, so the plane has strain.
i am not familiar with the practical experimental condition, to compress the substrate or film is reasonable or not? 

i need your help!

thanks very much

[zh]

For such questions correlated strongly to a specific paper, it is much better to contact the authors of that paper to clarify your doubt if you want to repeat their calculations.

[zh]

in my case, the cell of the substrate plane is a  orthorhombic cell, and in the z direction: lattice z1=4.5087 angstrom, x direction: x1=2.5955 angstrom.
the central region consists of a one-dimensional material, the length in the z direction consists several repeat unit, and every repeat is 4.6363 angstrom,
the cell of film on the substrate is also orthorombic cell,  in the x direction,lattice x2=3.3010 angstrom.
and the first step for me is to solve the lattice matching issue.
1. how to define the mismatching?
 for example, if i choose 1 repeat unit in the z direction,  4 repeats in the x direction for substrate cell and 3 repeats in the x direction) for  film cell.is it the mismatching computed like this
 in the x direction (2.5955-3.3010)/=0.21=21%, in the z direction, (4.5087-4.6363)/4.5078= -0.02=2% ?

The z direction is assumed to be the transport direction. The simulated system contains just a short length and a finite width of GNR in the center region. Indeed you may take it as a relatively "special" molecule. You can neglect the lattice match issue in your simulated device.

2. the limits of mismatch can be accepted? 21% is too large?
 

It is too huge.

3 I saw some theoretical references, in order to get better matching, the substrate  or the film is compressed, so the plane has strain.
i am not familiar with the practical experimental condition, to compress the substrate or film is reasonable or not?  

You had better check the literature by yourself.

[njuxyh]

in my case, the cell of the substrate plane is a  orthorhombic cell, and in the z direction: lattice z1=4.5087 angstrom, x direction: x1=2.5955 angstrom.
the central region consists of a one-dimensional material, the length in the z direction consists several repeat unit, and every repeat is 4.6363 angstrom,
the cell of film on the substrate is also orthorombic cell,  in the x direction,lattice x2=3.3010 angstrom.
and the first step for me is to solve the lattice matching issue.
1. how to define the mismatching?
 for example, if i choose 1 repeat unit in the z direction,  4 repeats in the x direction for substrate cell and 3 repeats in the x direction) for  film cell.is it the mismatching computed like this
 in the x direction (2.5955-3.3010)/=0.21=21%, in the z direction, (4.5087-4.6363)/4.5078= -0.02=2% ?

The z direction is assumed to be the transport direction. The simulated system contains just a short length and a finite width of GNR in the center region. Indeed you may take it as a relatively "special" molecule. You can neglect the lattice match issue in your simulated device.

2. the limits of mismatch can be accepted? 21% is too large?
 

It is too huge.

3 I saw some theoretical references, in order to get better matching, the substrate  or the film is compressed, so the plane has strain.
i am not familiar with the practical experimental condition, to compress the substrate or film is reasonable or not?  

You had better check the literature by yourself.

to 1.
No, the GNR indeed constains a short length(in the z direction,i.e.transport direction),but it is infinite in the x direction,(its period direction) so i should discussion the lattice matching issues  
to 2
yes, i feel it is huge.
to 3
thanks, in fact, i saw the interface tool in the vnl, the matching parameters include the stain parameter, so i want to know about it.
plus:
the lattice matching formula:
(Lattice constant of film / Lattice constant of substrate)-1
few people also define it as,
(Lattice constant of substrate / Lattice constant of film)-1 [Faux et al. JAP94]
is it so?

[zh]

For your question 1:
The length of GNR is usually defined along the periodic direction. 

the central region consists of a one-dimensional material, the length in the z direction consists several repeat unit, and every repeat is 4.6363 angstrom,

the GNR indeed constains a short length(in the z direction,i.e.transport direction),but it is infinite in the x direction,(its period direction)

Your second statement may be wrong. The GNR is just an one-dimensional system. From the first quoted statement, it should be not infinite in the x direction. Indeed, the x direction gives the width of the GNR. You should clearly describe your system. Or you may not yet understand your system.

For your 3dr question,

There is no significant difference in two formulas to define the lattice mismatch. It just means which one (substrate or film) is used as reference.
Conventionally, substrate is used as reference.