Nonmetal ordering in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi mathvariant="normal">Ti</mml:mi><mml:msub><mml:mi mathvariant="normal">C</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi mathvariant="normal">N</mml:mi><mml:mi>x</mml:mi></mml:msub></mml:mrow></mml:math>: Ground-state structure and the effects of finite temperature

Kolb, Brian; Hart, Gus L. W.

doi:10.1103/physrevb.72.224207

Cited by 18 publications

(8 citation statements)

References 41 publications

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“…The energies are then fitted to a generalized Ising model. 22 If care is taken in such a fitting procedure, [24][25][26] the resulting Ising Hamiltonian ͑cluster expansion͒ can predict arbitrary unfitted structures with near first-principles accuracy. The results are iteratively verified ͑and the model improved if necessary͒ using additional first-principles calculations, as described in Ref.…”

Section: Cluster Expansion and Ground State Searchesmentioning

confidence: 99%

Verifying predictions of theL13crystal structure in Cd-Pt and Pd-Pt by exhaustive enumeration

Hart

2009

Phys. Rev. B

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͑2001͔͒ predicted a never-before-observed crystal structure in Ag-Pd. Recently, Curtarolo predicted the same structure to be stable in Pt-Cd and Pt-Pd ͓S. Curtarolo et al., CALPHAD: Comput. Coupling Phase Diagrams Thermochem. 29, 163 ͑2005͔͒. The predicted structure is unique in several ways. Though never seen in any other face-centered-cubic-based intermetallic binary compound or ordered alloy, it is relatively simple-it contains only four atoms per unit cell. Furthermore, the structure is the only one of this small size, except the L1 2 structure, that cannot be characterized as a simple stacking of layers where each layer contains only one kind of atom. We construct a first-principlesbased Hamiltonian and search it for the thermodynamically stable ͑lowest energy͒ structures. Using a ͑practi-cally͒ exhaustive enumeration of about three million of the most likely candidate structures, we find that this new structure, designated L1 3 , is indeed a ground state in both Cd-Pt and Pd-Pt. Experimental efforts to validate the predictions are underway.

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Section: Cluster Expansion and Ground State Searchesmentioning

confidence: 99%

Verifying predictions of theL13crystal structure in Cd-Pt and Pd-Pt by exhaustive enumeration

Hart

2009

Phys. Rev. B

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“…The search of such ground-state structures is beyond the scope of this work and besides ordering temperatures in related structures are reported to be below room temperature. 67 …”

Section: A Phase Stability Of Ti 2 Alc Upon Oxygen Incorporationmentioning

confidence: 99%

Phase stability ofTi2AlCupon oxygen incorporation: A first-principles investigation

et al. 2010

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The phase stability of Ti 2 AlC upon oxygen incorporation has been studied by means of first-principles calculations. Recent experimental observations of this so-called MAX phase ͑M = early transition metal, A = A-group element, and X = C or N͒ show that the characteristic nanolaminated structure is retained upon oxygen incorporation, with strong indications of O substituting for C. Therefore, a solid solution of C and O on the carbon sublattice has been simulated by the so-called special quasirandom structure method. Through a developed systematic approach, the enthalpy of formation of Ti 2 Al͑C 1−x ,O x ͒ has been compared to all experimentally known competing phases, and has been found favorable for all C to O ratios at the composition of the MAX phase. A negative isostructural formation enthalpy has also been predicted for Ti 2 Al͑C 1−x ,O x ͒. Altogether, the results indicate that a large amount of oxygen, at least up to x = 0.75, might be present in the Ti 2 AlC MAX-phase structure without decomposition of the material into its competing phases. Furthermore, an effect of an increased oxygen content is a corresponding increase in the bulk modulus and a change in electronic properties. These results are of importance for further understanding and identification of possible composition range of the MAX-phase oxycarbide, and hence for the prospect of tuning the material properties by a varying incorporation of oxygen.

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“…[2][3][4][5][6][7][8][9][10][11][12] Cluster expansions predict the value of a material property for a given structure very quickly and accurately, making it computationally feasible to search for structures that have optimal property values or perform statistical sampling to arrive at thermodynamic averages. However for each property and each material, a new cluster expansion must be created by fitting a parametrized function to a set of training data.…”

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confidence: 99%

Exact expressions for structure selection in cluster expansions

Mueller

Ceder

2010

Phys. Rev. B

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The cluster expansion has proven to be a valuable tool in materials science to predict properties of configurationally ordered and disordered structures but the generation of cluster expansions can be computationally expensive. In recent years there have been efforts to make the generation of cluster expansions more efficient by selecting training structures in a way that minimizes approximate expressions for the variance of the predicted property values. We demonstrate that in many cases, these approximations are not necessary and exact expressions for the variance of the predicted property values may be derived. To illustrate this result, we present examples based on common applications of the cluster expansion such as bulk binary alloys. In addition we extend these structure selection techniques to Bayesian cluster expansions. These results should enable researchers to better analyze the quality of existing training sets and to select training structures that yield cluster expansions with lower prediction error.

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Nonmetal ordering inTiC1−xNx: Ground-state structure and the effects of finite temperature

Cited by 18 publications

References 41 publications

Verifying predictions of theL13crystal structure in Cd-Pt and Pd-Pt by exhaustive enumeration

Verifying predictions of theL13crystal structure in Cd-Pt and Pd-Pt by exhaustive enumeration

Phase stability ofTi2AlCupon oxygen incorporation: A first-principles investigation

Exact expressions for structure selection in cluster expansions

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