Carrying the Planet on their Backs: How Minerals Respond to Stress

1811-5209/26/0022-096$2.50 DOI: 10.2138/gselements.22.2.96

Keywords: Elasticity; rheology; stress; strain

MINERALS AND ROCKS UNDER GRAVITY

To a first approximation, the Earth is a gravitating, self-compressed body (Turcotte and Schubert 2002). Gravity draws particles inward, while interatomic forces, described by interatomic potentials (Fig. 1), oppose further compression. This interplay creates pressure that ensures that every point of the Earth remains in mechanical equilibrium by counterbalancing the inward gravitational forces with an outward pressure gradient. As a result, pressure and density must increase with depth in the Earth, and this is confirmed by comparing the mean density of the Earth (~ 5,500 kg/m³), obtained by the ratio of the mean mass of the Earth to its volume, and the average density of rocks at the Earth’s surface (~ 2,700 kg/m³). Most of the Earth’s interior consists of minerals, and understanding their response to temperature (T), pressure (P), and non-hydrostatic stress (see Box 1 for the definition of hydrostatic P and stress) is crucial to inferring the planet’s internal structure. One key property is compressibility, which measures how a material’s volume and density change under P. More than 100 years ago, Williamson and Adams (1923) had already realized that the compressibility of a homogeneous mantle could not explain the Earth’s density profile, suggesting instead an internal structure with denser phases at greater depths.

The elastic response of minerals gives us a way to image the structure of the inaccessible inner part of the Earth. Earthquakes generate seismic (i.e., mechanical) waves, which impose stresses on minerals lasting seconds to minutes. Under low differential stress (see Box 1) and short time scales, minerals behave elastically: atoms are displaced only slightly from their equilibrium positions, and the interatomic forces restore them to their initial positions once stress is removed (Fig. 1). By experimentally determining the elastic properties of the minerals that compose the Earth, we can derive seismic wave velocities of rocks, and, in turn, when the velocity, amplitude, and frequency of seismic waves are measured through seismometers, we can infer the structure, density, and mineralogy of the inner parts of the Earth (Fig. 2).

Single Crystal Elasticity

The linear elastic behavior of an ideal, isotropic solid at a given P and T is described by just two elastic moduli*. The bulk modulus controls how much its volume changes under hydrostatic P. The shear modulus governs how the solid responds to a shear (shape-changing) stress. However, minerals are elastically anisotropic: their response to stress depends on direction within the crystal. Depending on their crystal symmetry, up to 21 independent elastic moduli are required to capture their full anisotropic elastic and seismic response at a given P and T (Cordier and Jackson 2026 this issue). Temperature also affects elastic behavior by causing thermal agitation, which displaces atoms from equilibrium. Interatomic forces act to restore equilibrium, resulting in atomic oscillations. Ideally, this leads to harmonic motion (Fig. 1A, blue dashed line) with no volume change. However, real crystals show anharmonicity (Fig. 1A, blue solid line; Anderson 1995), which leads to thermal expansion and affects both the elastic and thermal properties of minerals (Jackson et al. 2026 this issue).

A major challenge in determining the elastic properties of minerals in planetary studies is to reproduce the high P and T of Earth’s (or other planets) interior. With devices such as multianvil presses and diamond anvil cells, P can be gradually increased to tens or even hundreds of gigapascals while concomitant heating can raise T to thousands of kelvin.

Bulk elastic properties and variations of volume are measured with techniques such as X-ray diffraction. Anisotropic elastic properties are typically obtained by measuring the velocity of acoustic waves propagating through the material, or the scattering of an incident light beam that interacts with the normal modes of vibration of the crystal (Bass and Zhang 2015).

Laboratory measurements of the elastic properties of minerals are essential for constructing physically based models that describe the elasticity of minerals in the Earth’s interior and allow for extrapolation to extreme conditions at which accurate measurements are difficult to obtain. Equations of state, which account for the non-linear elastic response at large strains (Fig. 1B), relate volume, compressibility, and thermal expansion to P and T while enforcing specific thermodynamic relationships (Birch 1952; Anderson 1995; Angel et al. 2014). Elastic properties also vary with chemical composition and crystal structure. Laboratory measurements and first-principles calculations (Prencipe 2019) provide elastic properties and P-derivatives for mineral end-members as well as for solid solutions, with T-derivatives constrained experimentally. These results are included in self-consistent databases, from which phase diagrams for typical compositions of the Earth’s interior, together with their elastic and seismic properties, can be calculated (e.g., Connolly 2005).

From Crystals to Rocks: Effective Properties of Aggregates

Seismic waves travel through Earth with wavelengths on the order of kilometers, therefore sampling the combined elastic response of many mineral grains bound together in rocks. The effective elastic and seismic responses of an aggregate differ from those of individual grains, and depend on the properties, volume fractions, and exact arrangement of its constituent grains. An aggregate of randomly oriented anisotropic grains behaves approximately isotropically, allowing for the use of simple models (e.g., Voigt and Reuss bounds) to estimate the effective elastic properties. However, the shape and/or crystallographic preferred orientations of minerals and other anisotropies (e.g., systematic sets of fractures, material layering, etc.) can strongly affect the elastic response, and more sophisticated models are necessary to describe the resulting effective anisotropic elasticity (Mavko et al. 2020). Once the effective bulk and shear moduli of a polymineralic rock are determined, the propagation velocities of compressional and shear waves can be calculated. However, as seismic waves propagate, part of their energy is attenuated via anelastic damping (Jackson 2015), meaning that the response is not purely elastic. This attenuation arises because, at low frequencies, under relatively high stress, and at elevated T, features such as point defects, dislocations, grain boundaries, and small fluid fraction present at grain contacts (melts or metamorphic fluids) also respond with some delay to stress variations. Therefore, even at relatively short time scales, the macroscopic response of mineral aggregates becomes visco-elastic and time dependent.

The Inner Structure of the Earth Revealed from Seismic Waves

Integrating our knowledge of the physical response of minerals under P and non-hydrostatic stress with seismic observations has been fundamental in revealing the Earth’s inner structure. Birch (1952) pioneered the approach of comparing seismic velocities with the elastic properties of candidate materials to infer the composition of Earth’s interior. For example, seismic discontinuities, defined by sharp variations in wave velocities with depth (Fig. 2), are often interpreted to correspond to mineral phase transitions by comparison with high P–T experimental results, thus providing direct constraints on the mantle’s T and mineralogy at specific depths (e.g., Stixrude 2015). The inversion of seismic observations (travel times, free oscillation frequencies, and waveform data) and astronomical data (Earth’s radius, mass, and moment of inertia) together with the physical properties of minerals allows construction of seismological models that are the basis for seismic tomography and geophysical studies. For decades, the Preliminary Reference Earth Model (PREM) of Dziewonski and Anderson (1981) has been the standard one-dimensional seismic model. This spherically symmetric model characterizes the average elastic properties, seismic velocities, density, and attenuation as functions of radius (Fig. 2). With advances in both laboratory measurements and seismic observational techniques, modern studies now constrain not only radial but also lateral variations in seismic wave velocities, leading to the development of comprehensive three-dimensional models of the Earth’s structure (Stixrude 2015).

EVERYTHING FLOWS: FROM THE PLANETARY SCALE TO GRAINS AND DEFECTS AND BACK

Seismology gives a “snapshot” of Earth’s internal structure, but our planet is far from static. At depth in the Earth’s upper crust, brittle deformation nucleates upon stress loading above the elastic limit of geomaterials, triggering earthquakes. In the lithosphere, deformation is localized especially at, but not restricted to, tectonic plate margins such as rift zones and subduction zones. Observations from rocks exhumed from larger depths in mountain belts and shear zones show that deeper in the lithosphere, at higher T, rocks flow in the solid state. The dynamics of the Earth is largely governed by the viscosity of the mantle (Turcotte and Schubert 2002), which controls convection and the transfer of material and heat between the core and surface (Jackson et al. 2026 this issue).

Therefore, to understand the Earth’s large-scale dynamics, we need to link the behavior of large rock volumes to processes on the mineral scale and down to the scale of defects in crystals. Remarkably, an aggregate of solid crystals can behave like a highly viscous fluid when averaged over kilometers and millions of years, whereas the fundamental mechanisms and processes occur in individual crystals on time scales of seconds. A striking example is the bridgmanite–post-perovskite (ppv) transition in the D” region just above the core–mantle boundary (Fig. 2). Ppv crystals develop strong crystal-lographic preferred orientations (CPO) due to their layered structure, accommodating large deformations by dislocation slip (Wu et al. 2017). The collective behavior of ppv crystals thus reduces viscosity and generates seismic anisotropy, affecting mantle convection and core–mantle interaction. Flow laws are empirical equations obtained from experiments that capture this collective behavior of microscopic processes (Turcotte and Schubert 2002). They relate stress to strain rate by incorporating the contributions of specific microscopic mechanisms into a set of parameters, therefore describing the effective viscosity of rocks. As such, they are an essential ingredient of any quantitative continuum-mechanical description of the deformation and dynamics of the Earth. Yet, this macroscopic rheological behavior relies on the fundamental mechanisms and processes operating in single crystals and aggregates, and the two scales are coupled through direct feedback.

How Do Minerals React to Stresses Higher than Their Elastic Limit?

The elastic, reversible response of minerals is restricted to low differential stress (Fig. 1). Beyond the elastic limit, deformation becomes permanent and is accommodated by mechanisms of crystal plasticity, which are strongly T-dependent. In this regime, minerals can accumulate crystal defects (Fig. 3A–3C), which are deviations from their ideal crystallographic structure. For example, a point defect refers to a missing (vacancy) or misplaced (interstitial) atom in the otherwise regular crystallographic structure. Dislocations are linear defects that, by moving in certain planes (known as slip planes), shear the c→rystal by an elementary amount called the Burgers vector (b). As such, they are the agents of crystal plastic deformation and can be seen using transmission electron microscopy (TEM, Fig. 3A–3D). They are generated upon stress concentrations at discontinuities, for example, at the tip of microcracks (Fig. 3B). Upon their movement through the crystal, they interact with each other, commonly leading to a heterogeneous spatial distribution and to heterogeneously strained crystals (Fig. 3C, 3D). Dislocations can arrange into low-angle grain boundaries to reduce the elastic energy associated with these defects (Fig. 3A, 3D). Moreover, rocks are composed of aggregates of grains and various mineral phases and their boundaries become important locations to accommodate strain (Fig. 3D–3F). Strain-induced grain boundary migration, i.e., dynamic recrystallization, modifies the grain boundary network during deformation, continuously renewing the microstructure and controlling grain size evolution. Boundaries of any type are essential in the macroscopic deformation behavior of rocks, during dislocation creep (with dynamic recrystallization; Fig. 3D, 3E), high-stress crystal plasticity (with formation of twin boundaries and cracks; Fig. 3B), as well as dissolution–precipitation creep (Gratier et al. 2013). In addition, grain boundaries accommodate strain through grain boundary sliding, and can host disclinations that play a key role in localizing deformation at the nanoscale (Cordier et al. 2014). Grain boundaries can be both sites of stress/strain concentrations (Fig. 3E, white arrow) as well as sites of stress/strain shadows (Fig. 3E, black arrow), depending on the differences in flow strength of adjacent minerals and on the orientation of the boundaries to the local stress/strain field. Observation of boundaries at all scales, from polarized light microscopy (Fig. 3E) to TEM (Fig. 3D), gives us relevant information on their role in the rheology of rocks. Yet, the real structure of boundaries is resolvable only by high-resolution TEM (Fig. 3F).

What are the Stresses in the Earth’s Interior?

The presence of Earth’s topography together with the associated crustal-thickness variations suggest that, on average, the lithosphere experiences and sustains differential stresses (Moulas et al. 2019). Minerals may develop and sustain significant levels of non-hydrostatic stress, as evidenced from observations on deformed rocks (Fig. 4). For example, electron tomography of [001] dislocations in olivine and field dislocation mechanics have revealed significant variations in the local resolved shear stresses (RSS) on various slip planes on the order ± 400 MPa (Weidner et al. 2024). Such observations allow us to directly investigate the build-up of kinematic hardening and the activation of different dislocation slip systems during deformation. Moving up in scale from individual crystals to mineral aggregates, we observe that rocks may develop non-hydrostatic stresses upon variations of external P and T due to the heterogeneous physical properties of the constituent minerals. For example, due to contrasts in thermo-mechanical properties, minerals included in other host minerals can develop over- or under-pressures exceeding 1 GPa during burial and exhumation (Angel et al. 2015). Residual pressures measured in inclusions (e.g., by Raman spectroscopy, Solomatova et al. 2026 this issue), can be used in inversion models to constrain the pressure of metamorphism and differential stress during geological processes (e.g., Zhong et al. 2021). Metamorphic reactions associated with volume changes, such as the phase transition from coesite to quartz in a polyphase rock during exhumation from ultrahigh-pressure metamorphic conditions, can impose local and short-term differential stresses of several hundred MPa on the surrounding crystals (e.g., Lenze et al. 2005, Fig. 4). On a larger scale, transient differential stresses on the order of hundreds of MPa to GPa and fast strain rates (on the order of  10⁻⁵ s⁻¹) occur especially during the seismic cycle even below the Earth’s upper seismogenic zone from depths at greenschist facies conditions to mantle depths (Fig. 4 (4–7)), as indicated for example by minerals containing twins with high critical resolved shear stress (CRSS) and/or pseudotachylytes. Also, at slower strain rates (on the order of 10⁻¹² s⁻¹ to 10⁻¹⁴ s⁻¹), rocks can experience differential stresses of a few tens to hundreds of MPa, as indicated from deformed rocks exhumed from large depths in combination with experimental rock deformation (Fig. 4).

BEHAVIOR UNDER HIGH STRESS

Minerals are observed to sustain high differential stresses, raising the question of the maximum strength of a defect-free crystal, or one in which defects are inactive, for instance due to the stress time being too short in relation to the response time.

Hypervelocity impacts of large asteroids on the Earth’s surface trigger shock waves with dynamic stress conditions that last for fractions of a second to a few seconds. Traveling faster than the local speed of sound, a shock wave creates a sharp discontinuity in P, T, and density, usually involving irreversible transformations, which makes it different from elastic waves. These shock waves also generate extremely high deviatoric stresses, as indicated by minerals containing twins with high CRSS values (Fig. 4). These intense, short-lived stresses can drive phase transformations, up to melting or vaporization, with the brief duration of the pressure pulse playing a critical role in the transformation process. Early studies found high-pressure silica polymorphs (coesite, stishovite) in impact craters like Meteor Crater (Arizona, USA). The transformation pathways during these very intense but very brief events can be unusual. For example, advanced time-resolved experiments in modern synchrotron facilities have revealed an ultrafast transformation pathway in silica that includes a new intermediate rosiaite-type phase (Otzen et al. 2023). Moreover, minerals may undergo martensitic transformations by diffusionless mechanisms, where deformation and polymorphic phase transitions occur simultaneously, as exemplified by the shock-induced transformation of rutile (Langenhorst and Deutsch 2012). As bonds are stretched, the interatomic force increases to a maximum and then decreases (Fig. 1), marking the onset of bond instability. In a crystalline structure, this can lead to more complex and unexpected behaviors. Under extreme shear, atoms can form new bonds, leading to exceptional strain hardening. This is the case of enstatite (Gouriet et al. 2022), which forms a new, extremely resistant phase when subjected to uniaxial tension (Fig. 5). These considerations raise the question of how the description of thermody- namic equilibria and phase diagrams should incorporate the effects of non-hydrostatic stress states in addition to hydrostatic pressure.

Beyond the instability threshold, predicting outcomes is difficult: very short durations and low T hinder transformation kinetics and may prevent the formation of stable phases. A frequently observed response of minerals is the disruption of long-range crystalline order (i.e., amorphization).

The resulting amorphous material may have structural and rheological characteristics quite different from quenched melts, as is observed in diaplectic glasses from impact craters. They also behave very differently from crystals, generally accommodating greater deformation. A clear example is the amorphization of grain boundaries in olivine under high stresses (Fig. 3F), which promotes grain boundary sliding (Samae et al. 2021).

PERSPECTIVES: THE INTERPLAY BETWEEN STRESS, MINERAL EQUILIBRIA, AND

REACTIONS

The coupled feedback between the mechanical state of rocks, phase transitions, and chemical reactions control many geological processes investigated across multiple disciplines. They include the reactive transport in the lithosphere, equilibria and microstructures in rocks, and rock rheology, among others, with implications for lithospheric evolution, reservoir stability, and earthquake cycles (e.g., Gratier et al. 2013). Thermodynamic equilibria in the Earth are commonly interpreted assuming that stresses are hydrostatic and locally homogeneous (e.g., Connolly 2005). However, stresses in rocks are often heterogeneous and non-hydrostatic (Fig. 4), and the extent to which they influence mineral equilibria and reactions remains an active area of research. At the atomistic scale, both the mechanical state and thermodynamic equilibria are governed by the same underlying physical forces (e.g.,

Frolov and Mishin 2010). Yet, in practice, the appropriate thermodynamic framework for deforming systems remains debated (e.g., Hobbs and Ord 2016; Powell et al. 2018; Wheeler 2020; Mazzucchelli et al. 2026), and the magnitude of non-hydrostatic stress effects on phase stability and reactions has yet to be fully quantified. Experimental studies of phase transitions and dissolution–precipitation creep under differential stress have provided important insights, yet the underlying theoretical frameworks remain incomplete. Developing predictive descriptions of stress–reaction coupling in Earth materials will likely require closer integration of thermodynamics, solid-state physics, and materials science.

ACKNOWLEDGMENTS

P. Cordier has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreement No 787198 – TimeMan. We thank S. Demouchy and F. Langenhorst for their constructive reviews, which improved the clarity of this article. We also acknowledge J. Angel and J. P. Gonzalez for their comments on an earlier version of the manuscript, and N. Campomenosi for providing the banner image. The editorial handling of S. Chakraborty and J. M. Jackson is greatly appreciated.