Nanodiamonds are materials of strong topical interest because of their unusual properties and diverse potential applications such as in biomedical, communications, sensing devices, and quantum computing. Their dimensions range from a few to several hundred nanometers.  There is special interest in color centers in nanodiamonds, which give them unique photonic and spin characteristics. These characteristics are useful for their applications in optical and quantum devices.
Color centers are lattice defects such as vacancies. A lattice defect  causes a distortion or strain in the lattice, which also distorts the electronic wave functions and perturbs the associated energy levels. This effect is likely to be a serious material issue, which can affect the reliability and the performance of the finished device based upon the use of nanodiamonds.  It is, therefore, of paramount importance to develop modeling and measurement techniques of the lattice distortion/strain field due to a color center in nanodiamond, which is the objective of this work.
A unified theory for lattice defects in nanodiamonds is a challenging problem because the nanodiamonds can be too small or too big for a conventional theoretical treatment. A 4-5 nm nanodiamond is too small for the standard continuum model, which is the usual model for bulk materials. One must use a discrete lattice theory such as the molecular dynamics (MD). On the other hand, if we attempt to model a 100 nm nanodiamond by using ordinary MD, we note that it may contain up to a billion atoms. Modeling such a large number of atoms by using a standard MD may be a formidable task.
Further, in addition to variations in the size, there is also a need for seamless linking of the length scales in the same nanodiamond. Lattice distortion is expressed as the displacement of atoms from their positions of equilibrium. It is a discrete function defined only at the discrete atomistic sites. This discrete function needs to be calculated by accounting for the discrete structure of the lattice. On the other hand, strain is a continuum model parameter, which is defined in terms of the derivatives of the continuous displacement field.  The inherent assumption in a continuum model is that the discrete lattice distortion is smeared out into a continuum. This assumption is valid only at distances much larger than the interatomic separations. Thus, modeling the lattice distortion/strain field requires near field calculation using the discrete lattice model and the far field calculations using a suitable continuum model. For the results to be physically realistic, the near field and far field formulation must be linked seamlessly.
We will develop a Green’s function (GF) method for modeling color centers and other defects in nanodiamonds. The GF technique is computationally efficient and can simulate even several million atoms on an ordinary computer. It links the different length scales smoothly and seamlessly.Such a model should be useful for many industrial applications of nanodiamnds. The ultimate objective is to develop a computational/simulation technqiue  which can be used for virtual experimentaion on nanodiamonds.  
References
1. V. K. Tewary and E.J. Garboczi, in Modeling, Characterization and Production of Nanomaterials (V. K. Tewary and Z. Yong, eds.), Elsevier, Amsterdam, 2023, p. 89-124.
2. V. K. Tewary and E.. J. Garboczi, "Lattice Green’s Function for Multiscale Modeling of  Strain Field Due to a Vacancy or Other Point Defects in Graphene; " Materials Research Advances 5 (2020) 2717-2725.