Reliable first-principles alloy thermodynamics via truncated cluster expansions

Machine Learning Force Field-Aided Cluster Expansion Approach to Phase Diagram of Alloyed Materials

First-principles approaches based on density functional theory (DFT) have played important roles in the theoretical study of multicomponent alloyed materials. Considering the highly demanding computational cost of direct DFT-based sampling of the configurational space, it is crucial to build efficient and low-cost surrogate Hamiltonian models with DFT accuracy for efficient simulation of alloyed systems with configurational disorder. Recently, the machine learning force field (MLFF) method has been proposed to tackle complicated multicomponent disordered systems. However, the importance of integrating significant physical considerations, including, in particular, convex hull preservation, which is the prerequisite for the accurate prediction of phase diagrams, into the training process of the MLFF remains rarely addressed. In this work, a workflow is proposed to train a convex-hull-preserved (CHP) MLFF for binary alloy systems, based on which the order-disorder phase boundary is predicted by using the Wang-Landau Monte Carlo (WLMC) technique. The predicted values for order-disorder phase transition temperatures agree well with the experiment. The CHP-MLFF is further used to build CE models with the same accuracy as the MLFF and higher efficiency in sampling configurational space. Using the results obtained from the MLFF-based WLMC simulation as a reference, the performances of different schemes for constructing CE models were evaluated in a transparent manner, which revealed the close correlation between the prediction accuracy of ground-state configurations and that of the order-disorder phase transition temperature. This work clearly indicates the great importance of reproducing the convex hull and energetics of ground-state configurations when constructing surrogate Hamiltonians for the statistical modeling of alloyed systems.

Exploring the Phase Stability of Li2Mn1-x TM x O3 (TM = Ni, Co, Cr, Ru) Cathode Materials in Lithium-Ion Batteries via the Cluster Expansion Method

Li2MnO3 has garnered significant interest as a potential cathode material due to its high electrochemical capacity, cost-effectiveness, and eco-friendliness. Nonetheless, its practical utilization is hindered by structural deterioration, which results in rapid capacity and voltage decay during cycling. To mitigate these challenges, cationic dopants have been incorporated to minimize structural collapse and enhance cathode material performance. Consequently, there is a strong desire to identify novel doped configurations as a remedial strategy for optimizing Li2MnO3 properties. In this study, the stability of the Li2Mn1-x TM x O3 system (TM = Ni, Co, Cr, Ru) was explored using cluster expansion and Monte Carlo simulations. By employing cluster expansion, binary ground state diagrams were generated, revealing 73, 65, 90, and 83 newly stable phases in Li2Mn1-x Ni x O3, Li2Mn1-x Co x O3, Li2Mn1-x Cr x O3, and Li2Mn1-x Ru x O3, respectively. The outcomes indicated that Li2Mn0.83Ni0.17O3, Li2Mn0.5Co0.5O3, Li2Mn0.5Cr0.5O3, and Li2Mn0.5Ru0.5O3 represent the most stable doped phases within the Li2MnO3 system. The application of Monte Carlo simulations enabled the assessment of high-temperature characteristics across the entire range of TM concentrations (0 ≤ x ≤ 1), facilitating the construction of phase diagrams. The Li2Mn1-x Ni x O3, Li2Mn1-x Co x O3, Li2Mn1-x Cr x O3, and Li2Mn1-x Ru x O3 systems exhibited favorable mixing at temperatures of 850, 700, 1700, and 1300 K, respectively. These discoveries present a clear trajectory for optimizing the properties of Li2MnO3, offering valuable insights into conceptualizing innovative cathode materials characterized by enhanced stability and performance.

Block sparsity promoting algorithm for efficient construction of cluster expansion models for multicomponent alloys

Multicomponent alloys are gaining significance as drivers of technological breakthroughs especially in structural and energy storage materials. The vast configuration space of these materials prohibit computational modeling using first-principles based methods alone. The cluster expansion (CE) method is the most widely used tool for modeling configurational disorder in alloys. CE relies on machine learning algorithms to train Hamiltonians and uses first-principles calculated data as training sets. In this paper we present a new compressive sensing-based algorithm for the efficient construction of CE Hamiltonians of multicomponent alloys. Our algorithm constructs highly sparse and physically reasonable models from a carefully selected small training set of alloy structures. Compared to conventional fitting algorithms, the algorithm achieves more than 50% reduction in the training set size. The resultant sparse models can sample the configuration space at least 3 × faster. We demonstrate this algorithm on 4 different alloy systems, namely Ag-Au, Ag-Au-Cu, Ag-Au-Cu-Pd and (Ge,Sn)(S,Se,Te).The sparse CE models for these alloys can rapidly reproduce known ground state orderings and order-disorder transitions. Our method can truly enable high-throughput multicomponent alloy thermodynamics by reducing the cost associated with model construction and configuration sampling.

Compositional Glass: A State with Inherent Chemical Disorder, Exemplified by Ti-rich Ni3(Al,Ti)1 D024 Phase

A compositional glass is a state with an unavoidable disorder in chemical compositions on each site, characterized by frustration and freezing of the compositional degrees of freedom at low temperature. From this state a full atomic long-range order is unachievable by a reasonable thermodynamic treatment. There is a similarity between a spin glass (a magnetic state with disorder in spin orientations) and a compositional glass (with disorder in site occupations by chemical elements): both have frustrated ground states and a frozen disorder at low temperatures T < Tf (here Tf is called the freezing temperature). While it is possible to perform a ground-state search in a compositional glass, the resulting set of the fully ordered structures does not adequately represent the real solid with an inherent atomic disorder. Compositional glasses constitute a class of materials, which is insufficiently understood, but is of high industrial importance. Some of the phases in the precipitated alloys (including steels, high-entropy alloys, and superalloys) might be compositional glasses, and their better understanding would facilitate materials design. Due to their strength at high operating temperatures, superalloys are used in combustion engines and particularly in jet turbine engines. Precipitation strengthening of nickel superalloys is an area of active research. Local phase transformations inside Ni3Al-based precipitates are of particular interest due to their impact on creep strength. In the Ni3(Al1−xTix)1 ternary system, the competing phases are Ni3Al-type L12 (γʹ) and Ni3Ti-type D024 (η), while D019 (χ) is higher in energy. These three phases differ by the stacking of atomic layers: locally, the last two look like the internal and external stacking faults in L12. We compute enthalpies of disordered and ordered Ni3(Al1−xTix)1 ternary structures, examine phase stability, investigate the ground states and competing structures, and predict that the Ti-rich Ni3(Al1−xTix)1 D024 phase is a compositional glass with the atomic disorder on the Al/Ti sublattice. To resolve apparent contradictions among the previous experiments and to confirm our prediction, we perform X-ray diffraction and scanning electron microscopy analysis of the cast Ni3(Ti0.917Al0.083)1 sample. Our measurements appear to confirm the ab initio computed results. Our results elucidate properties of compositional glasses and provide a better understanding of precipitation strengthening mechanisms in Ni superalloys.

Theoretical methods for structural phase transitions in elemental solids at extreme conditions: statics and dynamics

In recent years, theoretical studies have moved from a traditionally supporting role to a more proactive role in the research of phase transitions at high pressures. In many cases, theoretical prediction leads the experimental exploration. This is largely owing to the rapid progress of computer power and theoretical methods, particularly the structure prediction methods tailored for high-pressure applications. This review introduces commonly used structure searching techniques based on static and dynamic approaches, their applicability in studying phase transitions at high pressure, and new developments made toward predicting complex crystalline phases. Successful landmark studies for each method are discussed, with an emphasis on elemental solids and their behaviors under high pressure. The review concludes with a perspective on outstanding challenges and opportunities in the field.

Machine Learning Force Field Aided Cluster Expansion Approach to Configurationally Disordered Materials: Critical Assessment of Training Set Selection and Size Convergence

Cluster expansion (CE) is a powerful theoretical tool to study the configuration-dependent properties of substitutionally disordered systems. Typically, a CE model is built by fitting a few tens or hundreds of target quantities calculated by first-principles approaches. To validate the reliability of the model, a convergence test of the cross-validation (CV) score to the training set size is commonly conducted to verify the sufficiency of the training data. However, such a test only confirms the convergence of the predictive capability of the CE model within the training set, and it is unknown whether the convergence of the CV score would lead to robust thermodynamic simulation results such as order-disorder phase transition temperature T_c. In this work, using carbon defective MoC_1-x as a model system and aided by the machine-learning force field technique, a training data pool with about 13000 configurations has been efficiently obtained and used to generate different training sets of the same size randomly. By conducting parallel Monte Carlo simulations with the CE models trained with different randomly selected training sets, the uncertainty in calculated T_c can be evaluated at different training set sizes. It is found that the training set size that is sufficient for the CV score to converge still leads to a significant uncertainty in the predicted T_c and that the latter can be considerably reduced by enlarging the training set to that of a few thousand configurations. This work highlights the importance of using a large training set to build the optimal CE model that can achieve robust statistical modeling results and the facility provided by the machine-learning force field approach to efficiently produce adequate training data.

CLEASE: a versatile and user-friendly implementation of cluster expansion method

Materials exhibiting a substitutional disorder such as multicomponent alloys and mixed metal oxides/oxyfluorides are of great importance in many scientific and technological sectors. Disordered materials constitute an overwhelmingly large configurational space, which makes it practically impossible to be explored manually using first-principles calculations such as density functional theory due to the high computational costs. Consequently, the use of methods such as cluster expansion (CE) is vital in enhancing our understanding of the disordered materials. CE dramatically reduces the computational cost by mapping the first-principles calculation results on to a Hamiltonian which is much faster to evaluate. In this work, we present our implementation of the CE method, which is integrated as a part of the atomic simulation environment (ASE) open-source package. The versatile and user-friendly code automates the complex set up and construction procedure of CE while giving the users the flexibility to tweak the settings and to import their own structures and previous calculation results. Recent advancements such as regularization techniques from machine learning are implemented in the developed code. The code allows the users to construct CE on any bulk lattice structure, which makes it useful for a wide range of applications involving complex materials. We demonstrate the capabilities of our implementation by analyzing the two example materials with varying complexities: a binary metal alloy and a disordered lithium chromium oxyfluoride.

First-principles study of order-disorder transitions in multicomponent solid-solution alloys

In this review, we will focus on the recent development of the order-disorder transition in metallic materials. The past decades have witnessed fast development in the first-principles methodologies and their applications to ordering transitions in multi-component alloys, particularly the high-entropy alloys. The driving force for the proceedings comes from (i) the advance of algorithms and increasingly cheaper hardware, and also (ii) the great passion to model alloys with increasing number of components. The review starts with a brief introduction of the history for the ordering transitions. More detailed scientific proceedings prior to the 1970s had been well summarized in Krivoglaz and Smirnov (1965 The Theory of Order-Disorder in Alloys (New York: Elsevier)) and Stoloff and Davies (1968 Prog. Mater. Sci. 13 1-84). In the second part, the methods to study the ordering transitions, primarily on the theoretic methods are introduced. These will include (i) KKR-CPA method and supercell methods for energetic calculations; and (ii) thermodynamic and statistical methods to compute the transition temperatures. The third part will focus on representative applications in alloys, including our own work and many others. This part supplies the primary information of this review to the readers. The fourth part will summarize the connections between ordering transitions and broader physical properties (e.g. the mechanical properties). In the last part, some concluding remarks and perspectives will be given.

Cluster expansion based configurational averaging approach to bandgaps of semiconductor alloys

Configurationally disordered semiconducting materials including semiconductor alloys [e.g., (GaN)_1-x(ZnO)_x] and stoichiometric materials with fractional occupation (e.g., LaTiO₂N) have attracted a lot of interest recently in search for efficient visible light photo-catalysts. First-principles modeling of such materials poses great challenges due to the difficulty in treating the configurational disorder efficiently. In this work, a configurational averaging approach based on the cluster expansion technique has been exploited to describe bandgaps of ordered, partially disordered (with short-range order), and fully disordered phases of semiconductor alloys on the same footing. We take three semiconductor alloys [Cd_1-xZn_xS, ZnO_1-xS_x, and (GaN)_1-x(ZnO)_x] as model systems and clearly demonstrate that semiconductor alloys can have a system-dependent short-range order that has significant effects on their electronic properties.

Optimizing special quasirandom structure (SQS) models for accurate functional property prediction in disordered 2D alloys

2D materials such as MXenes have garnered attention in a wide field of applications ranging from energy to environment to medical. Properties of 2D materials can be tailored via alloying and in some cases, solid-solutions (disordered alloys) are formed. To predict the disordered alloy properties via first-principles, the model structure needs to imitate the random arrangements of alloyants and yet remains computationally tractable. Using density functional theory and the cluster expansion method, we investigate the accuracy of using of special quasirandom structures (SQSs) for predicting disordered 2D alloy properties, evaluating the effect of SQS supercell size on the prediction quality of formation energies, elastic properties, and structural parameters. We illustrate the findings with 5 different disordered binary [Formula: see text] MXene alloy systems (where M  =  Ti and M'  =  Zr, Hf, V, Nb, or Ta), demonstrating that SQSs around 6-8 times the primitive cell (N  =  6-8) are sufficient to attain convergence in the property predictions versus supercell size. For formation energies, SQSs with N  >  4 are found to reproduce the formation energies of the fully disordered phase within ~2.5 meV. For the simulation of the experimentally-synthesized TiNbCO₂, we find convergence in structural parameters and elastic tensors at N ~ 6. We traced the convergence of the predictions to the convergence in the band structure-related properties via analysis of the electronic densities-of-states and the projected crystal overlap Hamilton population. Our findings suggest that modest sized SQSs would reproduce the properties of disordered MXene alloys. The results should help guide the investigations of structure-property relationships in other disordered 2D materials as well.

Enhancing the Photocatalytic Performance of MXenes via Stoichiometry Engineering of Their Electronic and Optical Properties

Combining both density functional theory and the cluster expansion method, we investigate 3 binary MXene alloy systems of semiconducting Ti₂CO₂, Zr₂CO₂, and Hf₂CO₂, where the transition metals substitute one another (i.e., Ti_{2(1- x)}Zr_{2 x}CO₂, Ti_{2(1- x)}Hf_{2 x}CO₂, and Zr_{2(1- x)}Hf_{2 x}CO₂). We show that this group of MXene alloys forms the solid-solution phase across all compositions. Special quasirandom structures are generated to model the solid-solution phase of these alloys, using which we demonstrate how their structural, mechanical, electronic, and optical properties are tuned via stoichiometry engineering. These alloys exhibit outstanding mechanical strength and stability. They possess indirect band gaps of 1.25-1.80 eV. For Ti_{2(1- x)}Zr_{2 x}CO₂ and Ti_{2(1- x)}Hf_{2 x}CO₂, they display higher absorbance in the solar spectrum than their constituent Zr₂CO₂ and Hf₂CO₂, respectively. Most of the MXene alloys also show appropriately aligned band edges for water splitting. We predict the Ti_{2(1- x)}Zr_{2 x}CO₂ alloy with x = 0.2778 to be the most promising water-splitting photocatalyst among the MXenes studied here, outperforming its constituents, Ti₂CO₂ and Zr₂CO₂, when solar absorbance performance and band-edge alignments are simultaneously considered. This work demonstrates that alloying can be used to effectively tune photocatalytic performance.

High-Throughput Survey of Ordering Configurations in MXene Alloys Across Compositions and Temperatures

2D transition metal carbides and nitrides known as MXenes are gaining increasing attention. About 20 of them have been synthesized (more predicted) and their applications in fields ranging from energy storage and electromagnetic shielding to medicine are being explored. To facilitate the search for double-transition-metal MXenes, we explore the structure-stability relationship for 8 MXene alloy systems, namely, (V_1-xMo_x)₃C₂, (Nb_1-xMo_x)₃C₂, (Ta_1-xMo_x)₃C₂, (Ti_1-xMo_x)₃C₂, (Ti_1-xNb_x)₃C₂, (Ti_1-xTa_x)₃C₂, (Ti_1-xV_x)₃C₂, and (Nb_1-xV_x)₃C_2, with 0 ≤ x ≤ 1, using high-throughput computations. Starting from density-functional theory calculated formation energies, we used the cluster expansion method to build quick-to-compute interactions, enabling us to scan through the formation energies of millions of alloying configurations. For the Mo-rich MXenes, (M1_1-xMo_x)₃C₂ (where M1: Ti, V, Nb, Ta) Mo atoms prefer to occupy the surface layers, and ordering persists to high temperatures, based on our Monte Carlo simulations. When Ti is alloyed with Nb or Ta, in the Ti-rich MXenes, Ti atoms prefer the surface layers (e.g., Ti-C-Nb-C-Ti sequence), and in the Nb- or Ta-rich MXenes, Ti occupies only one surface layer and the other two layers are Nb or Ta (e.g., Ti-C-Nb-C-Nb), exhibiting asymmetric ordering. However, alloying Ti with V results in solid solutions across all compositions. (Nb_1-xV_x)₃C₂ phase separates at lower temperatures but forms solid solutions at synthesis temperatures. Postsynthesis annealing at moderate temperatures (800 to 1000 K) increases the ordering for all the compositions. Lastly, by investigating the stability of their precursor MAX phases and surface-terminated MXenes, we discuss the synthesis possibilities of highly ordered MXenes.

Self-assembly of Carbon Vacancies in Sub-stoichiometric ZrC(1-x)

Sub-stoichiometric interstitial compounds, including binary transition metal carbides (MC(1-x)), maintain structural stability even if they accommodate abundant anion vacancies. This unique character endows them with variable-composition, diverse-configuration and controllable-performance through composition and structure design. Herein, the evolution of carbon vacancy (VC) configuration in sub-stoichiometric ZrC(1-x) is investigated by combining the cluster expansion method and first-principles calculations. We report the interesting self-assembly of VCs and the fingerprint VC configuration (VC triplet constructed by 3(rd) nearest neighboring vacancies) in all the low energy structures of ZrC(1-x). When VC concentration is higher than the critical value of 0.5 (x > 0.5), the 2(nd) nearest neighboring VC configurations with strongly repulsive interaction inevitably appear, and meanwhile, the system energy (or formation enthalpy) of ZrC(1-x) increases sharply which suggests the material may lose phase stability. The present results clarify why ZrC(1-x) bears a huge amount of VCs, tends towards VC ordering, and retains stability up to a stoichiometry of x = 0.5.

Nanoalloy electrocatalysis: simulating cyclic voltammetry from configurational thermodynamics with adsorbates

Simulated 2-dimensional cyclic voltammetry for nanoalloys with a hybrid ensemble scheme in Monte Carlo simulation based on the cluster expansion method.

Configurational thermodynamics of alloyed nanoparticles with adsorbates

Changes in the chemical configuration of alloyed nanoparticle (NP) catalysts induced by adsorbates under working conditions, such as reversal in core-shell preference, are crucial to understand and design NP functionality. We extend the cluster expansion method to predict the configurational thermodynamics of alloyed NPs with adsorbates based on density functional theory data. Exemplified with PdRh NPs having O-coverage up to a monolayer, we fully detail the core-shell behavior across the entire range of NP composition and O-coverage with quantitative agreement to in situ experimental data. Optimally fitted cluster interactions in the heterogeneous system are the key to enable quantitative Monte Carlo simulations and design.

Unveiling stable group IV alloy nanowires via a comprehensive search and their electronic band characteristics

By means of density functional theory calculations, the cluster expansion method, and Monte Carlo simulations, we identify the stable spatial configurations (ground states) for [100] CSi, GeSi, and SnSi alloy nanowires (NWs) across compositions. In particular, we find that stable configurations of GeSiNWs and SnSiNWs exhibit core-shell segregation tendencies, while those of CSiNWs favor ordering. Moreover, we show compositional ranges where the band gaps are expected to vary linearly with composition, allowing predictable band gap fine-tuning. We also predict composition ranges where the spatial separation of near-band gap states are imminent, making it possible for electron-hole charge separation. By addressing both the issues of stability and the compositional trend of electronic band structure, our work should prove useful for designing alloy NWs of smaller dimensions.

A comprehensive search for stable Pt-Pd nanoalloy configurations and their use as tunable catalysts

Using density-functional theory, we predict stable alloy configurations (ground states) for a 1 nm Pt-Pd cuboctahedral nanoparticle across the entire composition range and demonstrate their use as tunable alloy catalysts via hydrogen-adsorption studies. Unlike previous works, we use simulated annealing with a cluster expansion Hamiltonian to perform a rapid and comprehensive search that encompasses both high and low-symmetry configurations. The ground states show Pt(core)-Pd(shell) type configurations across all compositions but with specific Pd patterns. For catalysis studies at room temperatures, the ground states are more realistic structural models than the commonly assumed random alloy configurations. Using the ground states, we reveal that the hydrogen adsorption energy increases (decreases) monotonically with at. % Pt for the {111} hollow ({100} bridge) adsorption site. Such trends are useful for designing tunable Pd-Pt nanocatalysts for the hydrogen evolution reaction.

Cluster expansion approach for transmutative lattice systems

We propose a cluster expansion (CE) technique that can express any function of atomic arrangement on any given lattice with the same number of lattice points in a single formalism. In the proposed CE, two types of spin variable, σ and τ, on the base lattice and virtual lattice, respectively, are introduced. The former spin variable specifies the occupation of the constituent elements for each lattice point. The latter specifies the positions of each lattice point. Basis functions constructed from the two types of spin variable satisfy completeness and orthonormality for any atomic arrangement on given lattices. As examples, the proposed CE is applied to one- and three-dimensional lattices in a binary system, which clarifies the concept of base and virtual lattices, how the functions of atomic arrangements are expressed in terms of the two types of spin variable, and the efficiency and convergence of the proposed CE with a finite number of clusters and input structures.

Thermodynamic theory of epitaxial alloys: first-principles mixed-basis cluster expansion of (In, Ga)N alloy film

Epitaxial growth of semiconductor alloys onto a fixed substrate has become the method of choice to make high quality crystals. In the coherent epitaxial growth, the lattice mismatch between the alloy film and the substrate induces a particular form of strain, adding a strain energy term into the free energy of the alloy system. Such epitaxial strain energy can alter the thermodynamics of the alloy, leading to a different phase diagram and different atomic microstructures. In this paper, we present a general-purpose mixed-basis cluster expansion method to describe the thermodynamics of an epitaxial alloy, where the formation energy of a structure is expressed in terms of pair and many-body interactions. With a finite number of first-principles calculation inputs, our method can predict the energies of various atomic structures with an accuracy comparable to that of first-principles calculations themselves. Epitaxial (In, Ga)N zinc-blende alloy grown on GaN(001) substrate is taken as an example to demonstrate the details of the method. Two (210) superlattice structures, (InN)(2)/(GaN)(2) (at x = 0.50) and (InN)(4)/(GaN)(1) (at x = 0.80), are identified as the ground state structures, in contrast to the phase-separation behavior of the bulk alloy.

Ground-state phase diagram of Na(x)CoO(2): correlation of Na ordering with CoO(2) stacking sequences

We have proposed a Hamiltonian that takes into account both Na-Na interactions and coupling between Na ions and CoO(2) layers. By a combination of the Monte Carlo and first-principles approaches, all the possible stacking sequences of CoO(2) layers together with the Na ordering have been obtained. In particular, an infinite series of ground states of Na ordering has been predicted in P3-Na(x)CoO(2). We have obtained the ground-state phase diagram with the variation of Na concentration, which explains well the complex variation of the CoO(2) stacking sequences. Our calculations show that the ordering of Na ions to minimize the Coulomb interaction is the main cause of the variation of the CoO(2) stacking sequences.

Cluster expansions in multicomponent systems: precise expansions from noisy databases

We have performed a systematic analysis of the numerical errors contained in the databases used in cluster expansions of multicomponent alloys. Our results underscore the importance of numerical noise in the determination of the effective cluster interactions and in the expansion determination. The relevance of the size of and information contained in the input database is highlighted. It is shown that cross-validatory approaches by themselves can produce unphysical expansions characterized by non-negligible, long-ranged coefficients. A selection criterion that combines both forecasting ability and a physical limiting behavior for the expansion is proposed. Expansions performed under this criterion exhibit the remarkable property of noise filtering. A discussion of the impact of this unforeseen characteristic of the cluster expansion method on the modeling of multicomponent alloy systems is presented.

Evolutionary approach for determining first-principles hamiltonians

Modern condensed-matter theory from first principles is highly successful when applied to materials of given structure-type or restricted unit-cell size. But this approach is limited where large cells or searches over millions of structure types become necessary. To treat these with first-principles accuracy, one 'coarse-grains' the many-particle Schrodinger equation into 'model hamiltonians' whose variables are configurational order parameters (atomic positions, spin and so on), connected by a few 'interaction parameters' obtained from a microscopic theory. But to construct a truly quantitative model hamiltonian, one must know just which types of interaction parameters to use, from possibly 10(6)-10(8) alternative selections. Here we show how genetic algorithms, mimicking biological evolution ('survival of the fittest'), can be used to distil reliable model hamiltonian parameters from a database of first-principles calculations. We demonstrate this for a classic dilemma in solid-state physics, structural inorganic chemistry and metallurgy: how to predict the stable crystal structure of a compound given only its composition. The selection of leading parameters based on a genetic algorithm is general and easily applied to construct any other type of complex model hamiltonian from direct quantum-mechanical results.