[Paper Review] Effect of Deformation on Surface Characteristics of Finite Metallic Crystals

В. В. Погосов, O. M. Shtepa|arXiv (Cornell University)|Oct 8, 2003

Metal Forming Simulation Techniques3 citations

TL;DR

This study calculates the effect of elastic deformation on surface stress, work function, and contact potential difference (CPD) in finite metallic crystals (Al, Cu, Au, Ni, Ti) using a self-consistent Kohn–Sham method within a modified stabilized jellium model. It demonstrates that the Kelvin method's assumption (ΔW ≡ −CPD) is incorrect, as CPD reflects changes in effective potential at the image plane, not work function; instead, work function decreases linearly with tensile strain and increases with compression, contradicting the conventional interpretation of experimental CPD data.

ABSTRACT

The surface stress and the contact potential differences of elastically deformed faces of Al, Cu, Au, Ni, and Ti crystals are calculated within the modified stabilized jellium model using the self-consistent Kohn-Sham method. The obtained values of the surface stress are in agreement with the results of the available first-principal calculations. We find that the work function decreases/increases linearly with elongation/compression of crystals. Our results confirm that the available experimental data for the contact potential difference obtained for the deformed surface by the Kelvin method do not correspond to the change of the work function but to the change of the surface potential. The problem of "anisotropy" of the work function and ionization potential of finite sample is discussed.

Motivation & Objective

• To investigate how elastic deformation affects surface stress, work function, and contact potential difference (CPD) in finite metallic crystals.
• To resolve the discrepancy between experimental CPD measurements and theoretical expectations regarding work function changes under strain.
• To challenge the conventional use of the Kelvin method, which equates CPD changes directly to work function changes (ΔW ≡ −CPD).
• To clarify the fundamental definition of work function in finite systems, particularly regarding anisotropy and capacitance effects.
• To provide a corrected theoretical framework for interpreting CPD and work function changes in strained metallic nanostructures.

Proposed method

• The study employs a self-consistent Kohn–Sham density functional theory (DFT) approach within a modified stabilized jellium model to calculate electronic structure and surface properties.
• The total energy is decomposed into kinetic, exchange, correlation, Hartree, pseudopotential, and Madelung contributions, with correlation energy modeled via a standard parametrization.
• Effective potential and work function are calculated by solving the Euler–Lagrange equation for the nonhomogeneous electron gas, including surface and deformation effects.
• The image plane at z₀ = 1 bohr is used to define CPD as ΔV_eff(z₀, u_xx), distinguishing it from bulk potential shifts.
• The ratio ξ = ΔV_eff(z₀)/ΔV_eff(bulk) is computed to quantify the discrepancy between surface and bulk potential responses to strain, yielding ξ ≈ −2.8 for Al.
• Finite-size effects are addressed by modeling the ionization potential as IP = W + e²/(2C), showing work function W is a scalar, not anisotropic, in finite samples.

Experimental results

Research questions

• RQ1 Does the Kelvin method accurately measure work function changes under uniaxial strain in metallic crystals?
• RQ2 How does elastic deformation affect the work function and surface stress in finite metallic crystals of Al, Cu, Au, Ni, and Ti?
• RQ3 Why do experimental CPD measurements show an apparent increase in work function under tensile strain, contradicting known trends in alkali metals?
• RQ4 Is the concept of anisotropic work function valid for finite metallic samples, or is it a spurious artifact of infinite-slab approximations?
• RQ5 What is the true physical origin of the observed CPD changes in strained metals—work function shift or effective potential shift at the image plane?

Key findings

• The work function decreases linearly with tensile strain and increases with compressive strain, consistent with the trend observed in alkali metals (Cs → Na → Al), contradicting the Kelvin method's assumption.
• The Kelvin method's equation ΔW ≡ −CPD is incorrect; experimental CPD changes reflect shifts in the effective potential at the image plane, not the work function itself.
• The ratio ξ = ΔV_eff(surface)/ΔV_eff(bulk) ranges from −3 to −1 across the studied metals, with ξ ≈ −2.8 for Al, indicating a strong enhancement of surface potential response to strain.
• The work function is a scalar quantity in finite systems, not anisotropic; the ionization potential of a finite sample is IP = W + e²/(2C), reducing to W only in the limit of infinite capacitance.
• The conventional definition of anisotropic work function is physically invalid for finite crystals, as it arises from unphysical semi-infinite models.
• The results imply that the Kelvin method is inadequate for measuring temperature or strain-dependent work function changes, as CPD does not directly reflect ΔW.