VelCrys: Interactive web-based application to compute acoustic wave velocity in crystals and its magnetic corrections

TL;DR

VelCrys is a web-based tool that computes acoustic group velocity from the elastic tensor and estimates linear magnetic corrections to velocity via $ΔC_{ij}$. It combines Wang 2023 velocity formulas with the Rinaldi–Turilli magnetoelastic framework to deliver direction-resolved $v$ and $(v-v_0)/v_0$ for arbitrary crystal symmetry. The authors validate VelCrys on dry sandstone, Co-Pt alloy, and hcp Co, showing agreement with literature and experimental data and revealing complex magnetic landscapes and Simon-effect type field dependencies. The work provides an open-source, interactive platform with potential applications in geophysics, magnetoacoustics, and materials design, while noting current limitations in symmetry coverage and higher-order corrections.

Abstract

We present VelCrys, a web-based interactive tool, that allows to perform further post-processing of the elastic tensor in order to compute and plot the group velocity of the acoustic waves for any crystal symmetry. We also implemented the calculation of effective magnetic corrections to the elastic tensor and corresponding fractional change in group velocity under a magnetic field. We apply it to dry sandstone, cubic CoPt and hcp Co to show some of the program features. In the analysis of magnetic corrections, we find complex landscapes of fractional change in group velocity as a function of ray direction, as well as a field dependence consistent with Simon effect.

Figures (7)

• Figure 1: Isoline of the group velocity ($v=2.6$ km/s) of the qP wave for dry sandstone with varied ray angle ($\phi,\theta$) obtained with VelCrys (red open circles) and by Wang et al.wang2023 (blue solid line).
• Figure 2: Group velocity landscape as a function of the ray direction (phase velocity direction) $\boldsymbol{n}=\boldsymbol{k}/k=(\sin\theta\cos\phi,\sin\theta\sin\phi,\cos\theta)$ of the qP wave for dry sandstone generated with VelCrys. The color of the surface corresponds to the magnitude of group velocity $\vert v\vert$.
• Figure 3: Fractional change in ultrasound frequency for a longitudinal wave (qP) under an applied magnetic field parallel or perpendicular to the wave propagation vector for cubic single crystals of disordered Co-Pt alloy. Red stars and orange diamonds show experimental data from Ref.ROUCHY198069 for the cases $H\parallel[001]$ and $H\parallel[100]$, respectively. Red solid and orange dashed lines stand for the theoretical values obtained from Eq.\ref{['eq:dF']} and Table \ref{['table:theory']}. Open blue squares and solid pink circles give the values derived from the computed fractional change in group velocity $(v-v_0)/v_0$ by VelCrys via Eq.\ref{['eq:dv']}. We added experimentally observed $\Delta s$-effect at saturated state ($\Delta^{sat}=0.00435$) both in the theoretical values and VelCrys data.
• Figure 4: Fractional change in ultrasound frequency for a transverse wave (qS1) under an applied magnetic field parallel or perpendicular to the wave propagation vector for cubic single crystals of disordered equiatomic Co-Pt alloy. Red stars and orange diamonds show experimental data from Ref.ROUCHY198069 for the cases $H\parallel[100]$ and $H\parallel[001]$, respectively. Red solid and orange dashed lines stand for the theoretical values obtained from Eq.\ref{['eq:dF']} and Table \ref{['table:theory']}. Open blue squares and solid pink circles give the values derived from the computed fractional change in group velocity $(v-v_0)/v_0$ by VelCrys via Eq.\ref{['eq:dv']}. We added experimentally observed $\Delta s$-effect at saturated state ($\Delta^{sat}=0.00435$) both in the theoretical values and VelCrys data.
• Figure 5: Landscape of the fractional change in group velocity $(v-v_0)/v_0$ for the 3 types of waves (qP, qS1 and qS2) as a function of the ray direction (phase velocity direction) with applied magnetic field $\mu_0\boldsymbol{H}=(0,0,5)$ T for cubic single crystals of disordered equiatomic Co-Pt alloy generated with VelCrys.