30:T3237,crystalView = { // ─── Configuration ─── const [Nx, Ny, Nz] = [3, 3, 3]; const isoLevel = 0.3; const a = 2; const radius = 0.3; const cameraFov = 45, cameraAspect = 1, cameraNear = 0.1, cameraFar = 1000; const backgroundColor = 0xffffff; // ─── Scene Setup ─── const scene = new three.Scene(); const camera = new three.PerspectiveCamera(cameraFov, cameraAspect, cameraNear, cameraFar); camera.position.set(3, 3, 3); const renderer = new three.WebGLRenderer({ antialias: true, alpha: true }); renderer.setSize(width, width); renderer.setPixelRatio(devicePixelRatio); renderer.setClearColor(backgroundColor, 1); renderer.localClippingEnabled = true; const container = html`

`; container.appendChild(renderer.domElement); const controls = new OrbitControls(camera, renderer.domElement); controls.enablePan = false; controls.enableZoom = true; controls.minPolarAngle = 0; controls.maxPolarAngle = Math.PI / 2; controls.enableDamping = true; scene.add(new three.AmbientLight(0xffffff, 0.5)); const dl = new three.DirectionalLight(0xffffff, 0.8); dl.position.set(5, 5, 5); scene.add(dl); // ─── Lattice Setup ─── const [lattice, basisName] = latticeKey.split(" | "); const entry = lattices[lattice].bases[basisName]; const params = lattices[lattice].parameters.map(p => lattices[lattice].defaults[p]); const vectors = (entry.vectors || lattices[lattice].vectors)(params); const basis = entry.basis; const species = entry.species; const scaled = vectors.map(v => new three.Vector3(...v).multiplyScalar(a)); const scaledLengths = scaled.map(v => v.length()); const shift = scaled.reduce((acc, vec) => acc.addScaledVector(vec, -0.5), new three.Vector3()); // ─── Planes ─── const planes = []; for (let i = 0; i < 3; i++) { const normal = scaled[(i + 1) % 3].clone().cross(scaled[(i + 2) % 3]).normalize(); const half = scaled[i].clone().multiplyScalar(0.5); planes.push(new three.Plane().setFromNormalAndCoplanarPoint(normal, half)); planes.push(new three.Plane().setFromNormalAndCoplanarPoint(normal.clone().negate(), half.clone().negate())); } planes.forEach(p => { if (p.distanceToPoint(new three.Vector3(0, 0, 0)) < 0) p.negate(); }); const exteriorPlanes = planes; const interiorPlanes = planes.map(p => p.clone().negate()); // ─── Materials ─── const speciesMats = {}; species.forEach(sp => { if (!speciesMats[sp]) { const col = new three.Color(colorMap[sp]?.color ?? 0x008080); speciesMats[sp] = { outside: new three.MeshStandardMaterial({ color: col, transparent: true, opacity: 0.2, side: three.DoubleSide, clippingPlanes: interiorPlanes, clipIntersection: true, depthWrite: false }), inside: new three.MeshStandardMaterial({ color: col, transparent: false, opacity: 0.6, side: three.DoubleSide, clippingPlanes: exteriorPlanes, clipIntersection: false, depthWrite: true }) }; } }); // ─── Groups ─── const atomsGroup = new three.Group(); const cellEdgesGroup = new three.Group(); const supercellEdgesGroup = new three.Group(); scene.add(atomsGroup, cellEdgesGroup, supercellEdgesGroup); // ─── Atoms ─── const atoms = []; for (let ix = 0; ix <= Nx; ix++) { for (let iy = 0; iy <= Ny; iy++) { for (let iz = 0; iz <= Nz; iz++) { basis.forEach(([u, v, w], i) => { if ((ix < Nx || u === 0) && (iy < Ny || v === 0) && (iz < Nz || w === 0)) { const fx = ix + u, fy = iy + v, fz = iz + w; const pos = new three.Vector3() .addScaledVector(scaled[0], fx) .addScaledVector(scaled[1], fy) .addScaledVector(scaled[2], fz) .add(shift); atoms.push(pos); const sp = species[i]; const mats = speciesMats[sp]; const Z = colorMap[sp]?.Z || 20; const r = radius * (0.5 + 0.5 * (1 - Math.exp(-Z / 20))); const geo = new three.SphereGeometry(r, 32, 32); const outMesh = new three.Mesh(geo, mats.outside); outMesh.position.copy(pos); outMesh.renderOrder = 0; atomsGroup.add(outMesh); const inMesh = new three.Mesh(geo, mats.inside); inMesh.position.copy(pos); inMesh.renderOrder = 1; atomsGroup.add(inMesh); } }); } } } // ─── Electron Density (only for Diamond) ─── if (showDensity) { // (lattice === "FCC" && basisName === "Diamond (C)") { const Ngrid = 40; // 1) Build density grid in fractional (u,v,w) const grid = Array.from({ length: Ngrid + 1 }, (_, i) => Array.from({ length: Ngrid + 1 }, (_, j) => Array.from({ length: Ngrid + 1 }, (_, k) => { const u = i / Ngrid, v = j / Ngrid, w = k / Ngrid; const pos = new three.Vector3() .addScaledVector(scaled[0], u) .addScaledVector(scaled[1], v) .addScaledVector(scaled[2], w) .add(shift); let rho = 0; atoms.forEach(atomPos => { const d2 = pos.distanceToSquared(atomPos); rho += Math.exp(-5 * d2); }); return rho; }) ) ); const gradientGrid = Array.from({ length: Ngrid + 1 }, (_, i) => Array.from({ length: Ngrid + 1 }, (_, j) => Array.from({ length: Ngrid + 1 }, (_, k) => new three.Vector3()) ) ); for (let i = 1; i < Ngrid; i++) { for (let j = 1; j < Ngrid; j++) { for (let k = 1; k < Ngrid; k++) { const dx = (grid[i+1][j][k] - grid[i-1][j][k]) * 0.5; const dy = (grid[i][j+1][k] - grid[i][j-1][k]) * 0.5; const dz = (grid[i][j][k+1] - grid[i][j][k-1]) * 0.5; gradientGrid[i][j][k].set(dx, dy, dz).normalize(); } } } // 2) Interpolate in fractional space (linear interpolation) function interpolateVerts(p1, p2, i, j, k) { const [dx1, dy1, dz1] = cubeVerts[p1]; const [dx2, dy2, dz2] = cubeVerts[p2]; const idx1 = i + dx1, idy1 = j + dy1, idz1 = k + dz1; const idx2 = i + dx2, idy2 = j + dy2, idz2 = k + dz2; const v1 = grid[idx1][idy1][idz1]; const v2 = grid[idx2][idy2][idz2]; const mu = (v2 === v1) ? 0 : (isoLevel - v1) / (v2 - v1); // Interpolate position const u = (idx1 + mu * (idx2 - idx1)) / Ngrid; const v = (idy1 + mu * (idy2 - idy1)) / Ngrid; const w = (idz1 + mu * (idz2 - idz1)) / Ngrid; const pos = new three.Vector3() .addScaledVector(scaled[0], u) .addScaledVector(scaled[1], v) .addScaledVector(scaled[2], w) .add(shift); // Interpolate normal (gradient vector) const g1 = gradientGrid[idx1][idy1][idz1]; const g2 = gradientGrid[idx2][idy2][idz2]; const normal = g1.clone().lerp(g2, mu).normalize(); return { pos, normal }; } // 3) Run Marching Cubes const vertices = []; const normals = []; const faces = []; for (let i = 0; i < Ngrid; i++) { for (let j = 0; j < Ngrid; j++) { for (let k = 0; k < Ngrid; k++) { let cubeindex = 0; for (let n = 0; n < 8; n++) { const [dx, dy, dz] = cubeVerts[n]; const ii = (i + dx); const jj = (j + dy); const kk = (k + dz); if (grid[ii][jj][kk] < isoLevel) cubeindex |= 1 << n; } const edges = edgeTable[cubeindex]; if (!edges) continue; const vertList = []; for (let e = 0; e < 12; e++) { if (edges & (1 << e)) { const [p1, p2] = edgeConnections[e]; vertList[e] = interpolateVerts(p1, p2, i, j, k); } } for (let t = 0; triTable[cubeindex][t] !== -1; t += 3) { const a = vertList[triTable[cubeindex][t]]; const b = vertList[triTable[cubeindex][t+1]]; const c = vertList[triTable[cubeindex][t+2]]; if (!a || !b || !c) continue; const idx = vertices.length / 3; // Push positions vertices.push( a.pos.x, a.pos.y, a.pos.z, b.pos.x, b.pos.y, b.pos.z, c.pos.x, c.pos.y, c.pos.z ); // Push normals normals.push( a.normal.x, a.normal.y, a.normal.z, b.normal.x, b.normal.y, b.normal.z, c.normal.x, c.normal.y, c.normal.z ); // Push face indices faces.push(idx, idx+1, idx+2); } } } } // 4) Build isosurface mesh const isoGeometry = new three.BufferGeometry(); isoGeometry.setAttribute('position', new three.Float32BufferAttribute(vertices, 3)); isoGeometry.setAttribute('normal', new three.Float32BufferAttribute(normals, 3)); isoGeometry.setIndex(faces); // merge nearby vertices to stitch faces together if (three.BufferGeometryUtils) { three.BufferGeometryUtils.mergeVertices(isoGeometry, 1e-6); } isoGeometry.computeVertexNormals(); const isoMaterial = new three.MeshStandardMaterial({ color: 0x00ffff, side: three.DoubleSide, transparent: true, opacity: 0.5, clippingPlanes: exteriorPlanes, clipIntersection: false, depthWrite: false }); const isoMesh = new three.Mesh(isoGeometry, isoMaterial); isoMesh.renderOrder = 1; scene.add(isoMesh); } // ─── Helper to Create Corners ─── function createCorners(scaleVectors, signs) { const corners = []; signs.forEach(s1 => signs.forEach(s2 => signs.forEach(s3 => { corners.push( new three.Vector3() .addScaledVector(scaleVectors[0], s1 / 2) .addScaledVector(scaleVectors[1], s2 / 2) .addScaledVector(scaleVectors[2], s3 / 2) ); }))); return corners; } const corners = createCorners(scaled, [-1, 1]); const superCorners = [ new three.Vector3().addScaledVector(scaled[0], -0.5).addScaledVector(scaled[1], -0.5).addScaledVector(scaled[2], -0.5), new three.Vector3().addScaledVector(scaled[0], Nx-0.5).addScaledVector(scaled[1], -0.5).addScaledVector(scaled[2], -0.5), new three.Vector3().addScaledVector(scaled[0], -0.5).addScaledVector(scaled[1], Ny-0.5).addScaledVector(scaled[2], -0.5), new three.Vector3().addScaledVector(scaled[0], Nx-0.5).addScaledVector(scaled[1], Ny-0.5).addScaledVector(scaled[2], -0.5), new three.Vector3().addScaledVector(scaled[0], -0.5).addScaledVector(scaled[1], -0.5).addScaledVector(scaled[2], Nz-0.5), new three.Vector3().addScaledVector(scaled[0], Nx-0.5).addScaledVector(scaled[1], -0.5).addScaledVector(scaled[2], Nz-0.5), new three.Vector3().addScaledVector(scaled[0], -0.5).addScaledVector(scaled[1], Ny-0.5).addScaledVector(scaled[2], Nz-0.5), new three.Vector3().addScaledVector(scaled[0], Nx-0.5).addScaledVector(scaled[1], Ny-0.5).addScaledVector(scaled[2], Nz-0.5) ]; // ─── Draw Edges ─── const edgeMat = new three.LineBasicMaterial({ color: 0x222222, depthTest: true }); corners.forEach((c1, i) => corners.slice(i + 1).forEach(c2 => { const d = c1.distanceTo(c2); if ( Math.abs(d - scaledLengths[0]) < 1e-6 || Math.abs(d - scaledLengths[1]) < 1e-6 || Math.abs(d - scaledLengths[2]) < 1e-6 ) { const line = new three.Line( new three.BufferGeometry().setFromPoints([c1, c2]), edgeMat ); line.renderOrder = 2; cellEdgesGroup.add(line); } }) ); const superMat = new three.LineBasicMaterial({ color: 0xcccccc, depthTest: false }); superCorners.forEach((c1, i) => superCorners.slice(i + 1).forEach(c2 => { const d = c1.distanceTo(c2); if ( Math.abs(d - scaledLengths[0] * Nx) < 1e-6 || Math.abs(d - scaledLengths[1] * Ny) < 1e-6 || Math.abs(d - scaledLengths[2] * Nz) < 1e-6 ) { const superLine = new three.Line( new three.BufferGeometry().setFromPoints([c1, c2]), superMat ); superLine.renderOrder = 1; supercellEdgesGroup.add(superLine); } }) ); // ─── Animate ─── function animate() { controls.update(); renderer.render(scene, camera); requestAnimationFrame(animate); } animate(); return container; }31:T1cb7,lattices = ({ "FCC": { parameters: ["a"], defaults: { a: 1 }, vectors: ([a]) => [[a, 0, 0], [0, a, 0], [0, 0, a]], bases: { "Copper (Cu)": { basis: [[0, 0, 0], [0.5, 0.5, 0], [0.5, 0, 0.5], [0, 0.5, 0.5]], species: ["Cu", "Cu", "Cu", "Cu"], description: "Standard FCC structure with a single copper atom at each face center" }, "Diamond (C)": { basis: [ [0, 0, 0], [0.25, 0.25, 0.25], [0.5, 0.5, 0], [0.75, 0.75, 0.25], [0.5, 0, 0.5], [0.75, 0.25, 0.75], [0, 0.5, 0.5], [0.25, 0.75, 0.75] ], species: Array(8).fill("C"), description: "Diamond cubic structure formed by two interpenetrating FCC sublattices" }, "Nickel (Ni)": { basis: [[0, 0, 0], [0.5, 0.5, 0], [0.5, 0, 0.5], [0, 0.5, 0.5]], species: ["Ni", "Ni", "Ni", "Ni"], description: "Nickel adopts the FCC structure with one atom at each face center" }, "NaCl (Rock Salt)": { basis: [[0, 0, 0], [0.5, 0.5, 0.5]], species: ["Na", "Cl"], description: "Face-centered cubic structure with alternating Na and Cl atoms" }, "Zincblende (ZnS)": { basis: [ [0, 0, 0], [0.25, 0.25, 0.25], [0.5, 0.5, 0], [0.75, 0.75, 0.25], [0.5, 0, 0.5], [0.75, 0.25, 0.75], [0, 0.5, 0.5], [0.25, 0.75, 0.75] ], species: ["Zn", "S", "Zn", "S", "Zn", "S", "Zn", "S"], description: "Zincblende (sphalerite) structure: same geometry as diamond but with alternating Zn and S atoms" }, "Calcium Fluoride (CaF₂)": { basis: [ [0, 0, 0], [0.25, 0.25, 0.25], [0.75, 0.25, 0.25], [0.25, 0.75, 0.25], [0.25, 0.25, 0.75] ], species: ["Ca", "F", "F", "F", "F"], description: "Fluorite structure: Ca at corners, F atoms centered in tetrahedra" } } }, "SC (Simple Cubic)": { parameters: ["a"], defaults: { a: 1 }, vectors: ([a]) => [[a, 0, 0], [0, a, 0], [0, 0, a]], bases: { "CsCl (B2)": { basis: [[0, 0, 0], [0.5, 0.5, 0.5]], species: ["Cs", "Cl"], description: "Simple cubic structure with Cl at corners and Cs at the body center" }, "Polonium (Po)": { basis: [[0, 0, 0]], species: ["Po"], description: "One of the very few elements that crystallizes in the simple cubic lattice" } } }, "BCC (Body-Centered Cubic)": { parameters: ["a"], defaults: { a: 1 }, vectors: ([a]) => [[a, 0, 0], [0, a, 0], [0, 0, a]], bases: { "Iron (Fe α-phase)": { basis: [[0, 0, 0], [0.5, 0.5, 0.5]], species: ["Fe", "Fe"], description: "Body-centered cubic (BCC) structure typical of iron at room temperature" } } }, "Perovskite": { parameters: ["a"], defaults: { a: 1 }, vectors: ([a]) => [[a, 0, 0], [0, a, 0], [0, 0, a]], bases: { "BaTiO₃": { basis: [ [0.5, 0.5, 0.5], [0, 0, 0], [0.5, 0.5, 0], [0.5, 0, 0.5], [0, 0.5, 0.5] ], species: ["Ba", "Ti", "O", "O", "O"], description: "Classic perovskite structure with Ba at corners, Ti at center, and O on faces" } } }, "Hexagonal": { parameters: ["a", "c"], defaults: { a: 1, c: 1.6 }, vectors: ([a, c]) => [ [a, 0, 0], [-a/2, Math.sqrt(3)*a/2, 0], [0, 0, c] ], bases: { "Graphene (C)": { basis: [[0, 0, 0], [1/3, 2/3, 0]], species: ["C", "C"], description: "2D hexagonal lattice of carbon atoms with two atoms per unit cell" }, "MoS₂ (2H phase)": { basis: [[0.0, 0.0, 0.5], [1/3, 2/3, 0.58], [2/3, 1/3, 0.42]], species: ["Mo", "S", "S"], description: "Layered 2D structure with Mo sandwiched between two S layers" }, "Zinc (Zn)": { basis: [[0, 0, 0], [1/3, 2/3, 0.5]], species: ["Zn", "Zn"], description: "Zinc forms a hexagonal close-packed structure with two atoms per unit cell" }, "Boron Nitride (h-BN)": { basis: [[0, 0, 0], [1/3, 2/3, 0]], species: ["B", "N"], description: "Hexagonal boron nitride: structurally like graphene but alternating B and N atoms" }, "Magnesium (Mg)": { basis: [[0, 0, 0], [1/3, 2/3, 0.5]], species: ["Mg", "Mg"], description: "HCP structure typical of magnesium: ABAB stacking in hexagonal close-packing" } } }, "Tetragonal": { parameters: ["a", "c"], defaults: { a: 1, c: 1.5 }, vectors: ([a, c]) => [[a, 0, 0], [0, a, 0], [0, 0, c]], bases: { "Rutile TiO₂": { basis: [ [0, 0, 0], [0.5, 0.5, 0.5], [0.3, 0.3, 0], [0.7, 0.7, 0], [0.3, 0.7, 0.5], [0.7, 0.3, 0.5] ], species: ["Ti", "Ti", "O", "O", "O", "O"], description: "Each Ti is octahedrally coordinated by O atoms, forming a tetragonal structure" }, "SnO₂ (Cassiterite)": { basis: [ [0, 0, 0], [0.5, 0.5, 0.5], [0.306, 0.306, 0], [0.694, 0.694, 0], [0.306, 0.694, 0.5], [0.694, 0.306, 0.5] ], species: ["Sn", "Sn", "O", "O", "O", "O"], description: "Tetragonal rutile-type structure with tin and oxygen atoms" }, "Strontium Titanate (SrTiO₃)": { basis: [ [0, 0, 0], [0.5, 0.5, 0.5], [0.5, 0.5, 0], [0.5, 0, 0.5], [0, 0.5, 0.5] ], species: ["Sr", "Ti", "O", "O", "O"], description: "Perovskite-type structure with Sr at corners, Ti at center, and O atoms on faces" } } }, Triclinic: { parameters: ["a", "b", "c", "alpha", "beta", "gamma"], defaults: { a: 1, b: 1.1, c: 1.2, alpha: 90, beta: 100, gamma: 95 }, vectors: ([a, b, c, alpha, beta, gamma]) => { const rad = deg => deg * Math.PI / 180; const α = rad(alpha), β = rad(beta), γ = rad(gamma); const cosα = Math.cos(α), cosβ = Math.cos(β), cosγ = Math.cos(γ); const sinγ = Math.sin(γ); const v1 = [a, 0, 0]; const v2 = [b * cosγ, b * sinγ, 0]; const cx = c * cosβ; const cy = c * (cosα - cosβ * cosγ) / sinγ; const cz = Math.sqrt(c * c - cx * cx - cy * cy); const v3 = [cx, cy, cz]; return [v1, v2, v3]; }, bases: { "Kyanite (Al₂SiO₅)": { basis: [ [0.0, 0.0, 0.0], [0.25, 0.25, 0.25], [0.5, 0.0, 0.5], [0.75, 0.25, 0.75] ], species: ["Al", "Si", "O", "O"], description: "Triclinic example with Al, Si, and O atoms in a realistic mineral configuration" } } }, "Rhombohedral": { parameters: ["a", "alpha"], defaults: { a: 1, alpha: 60 }, vectors: ([a, alpha]) => { const rad = Math.PI / 180 * alpha; const c = Math.cos(rad), s = Math.sin(rad); return [ [a, 0, 0], [a * c, a * s, 0], [a * c, a * (c - c * c) / s, a * Math.sqrt(1 - 3 * c * c + 2 * c * c * c) / s] ]; }, bases: { "Calcite (CaCO₃)": { basis: [[0, 0, 0], [1/3, 2/3, 0.25], [2/3, 1/3, 0.75]], species: ["Ca", "C", "O"], description: "Rhombohedral structure with layered carbonate ions" } } } })32:Tad0,colorMap = ({ H: { color: 0xFFFFFF, Z: 1 }, // white C: { color: 0x222222, Z: 6 }, // dark gray N: { color: 0x0000FF, Z: 7 }, // blue O: { color: 0xFF0000, Z: 8 }, // red F: { color: 0x00FF00, Z: 9 }, // green Na: { color: 0x0000FF, Z: 11 }, // sodium blue Mg: { color: 0x1E90FF, Z: 12 }, // dodger blue Al: { color: 0xA9A9A9, Z: 13 }, // dark gray Si: { color: 0xDAA520, Z: 14 }, // goldenrod P: { color: 0xFFA500, Z: 15 }, // orange S: { color: 0xFFFF00, Z: 16 }, // yellow Cl: { color: 0x00FF00, Z: 17 }, // lime green K: { color: 0x8B00FF, Z: 19 }, // violet Ca: { color: 0x40E0D0, Z: 20 }, // turquoise Ti: { color: 0xB0C4DE, Z: 22 }, // light steel blue V: { color: 0x228B22, Z: 23 }, // forest green Cr: { color: 0x008080, Z: 24 }, // teal Mn: { color: 0x800080, Z: 25 }, // purple Fe: { color: 0xD2691E, Z: 26 }, // chocolate Co: { color: 0x4169E1, Z: 27 }, // royal blue Ni: { color: 0xA9A9A9, Z: 28 }, // dark gray Cu: { color: 0xB87333, Z: 29 }, // copper Zn: { color: 0x7FFFD4, Z: 30 }, // aquamarine Ga: { color: 0xC0C0C0, Z: 31 }, // silver Ge: { color: 0x696969, Z: 32 }, // dim gray As: { color: 0x556B2F, Z: 33 }, // dark olive green Se: { color: 0xFFA07A, Z: 34 }, // light salmon Br: { color: 0xA52A2A, Z: 35 }, // brown Rb: { color: 0x9932CC, Z: 37 }, // dark orchid Sr: { color: 0x00CED1, Z: 38 }, // dark turquoise Y: { color: 0x708090, Z: 39 }, // slate gray Zr: { color: 0x4682B4, Z: 40 }, // steel blue Nb: { color: 0x2F4F4F, Z: 41 }, // dark slate gray Mo: { color: 0x00FA9A, Z: 42 }, // medium spring green Ag: { color: 0xC0C0C0, Z: 47 }, // silver Cd: { color: 0xFFD700, Z: 48 }, // gold In: { color: 0x7CFC00, Z: 49 }, // lawn green Sn: { color: 0xD3D3D3, Z: 50 }, // light gray Sb: { color: 0x8B4513, Z: 51 }, // saddle brown Te: { color: 0x008B8B, Z: 52 }, // dark cyan I: { color: 0x9400D3, Z: 53 }, // dark violet Cs: { color: 0xFF4500, Z: 55 }, // orange red Ba: { color: 0x00FFEF, Z: 56 }, // cyan La: { color: 0xADD8E6, Z: 57 }, // light blue Hf: { color: 0x4682B4, Z: 72 }, // steel blue Ta: { color: 0x00FFFF, Z: 73 }, // cyan W: { color: 0xDAA520, Z: 74 }, // goldenrod Re: { color: 0xFFDAB9, Z: 75 }, // peach puff Os: { color: 0x1E90FF, Z: 76 }, // dodger blue Ir: { color: 0xBA55D3, Z: 77 }, // medium orchid Pt: { color: 0xE5E4E2, Z: 78 }, // platinum Au: { color: 0xFFD700, Z: 79 }, // gold Hg: { color: 0xB0C4DE, Z: 80 }, // light steel blue Pb: { color: 0x708090, Z: 82 }, // slate gray Bi: { color: 0x8B0000, Z: 83 }, // dark red Po: { color: 0x8B008B, Z: 84 } // dark magenta })33:T2436,triTable = [ [ -1 ], [ 0, 3, 8, -1 ], [ 0, 9, 1, -1 ], [ 3, 8, 1, 1, 8, 9, -1 ], [ 2, 11, 3, -1 ], [ 8, 0, 11, 11, 0, 2, -1 ], [ 3, 2, 11, 1, 0, 9, -1 ], [ 11, 1, 2, 11, 9, 1, 11, 8, 9, -1 ], [ 1, 10, 2, -1 ], [ 0, 3, 8, 2, 1, 10, -1 ], [ 10, 2, 9, 9, 2, 0, -1 ], [ 8, 2, 3, 8, 10, 2, 8, 9, 10, -1 ], [ 11, 3, 10, 10, 3, 1, -1 ], [ 10, 0, 1, 10, 8, 0, 10, 11, 8, -1 ], [ 9, 3, 0, 9, 11, 3, 9, 10, 11, -1 ], [ 8, 9, 11, 11, 9, 10, -1 ], [ 4, 8, 7, -1 ], [ 7, 4, 3, 3, 4, 0, -1 ], [ 4, 8, 7, 0, 9, 1, -1 ], [ 1, 4, 9, 1, 7, 4, 1, 3, 7, -1 ], [ 8, 7, 4, 11, 3, 2, -1 ], [ 4, 11, 7, 4, 2, 11, 4, 0, 2, -1 ], [ 0, 9, 1, 8, 7, 4, 11, 3, 2, -1 ], [ 7, 4, 11, 11, 4, 2, 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0, 2, 5, 6, 10, -1 ], [ 1, 0, 9, 2, 11, 3, 6, 10, 5, -1 ], [ 5, 6, 10, 11, 1, 2, 11, 9, 1, 11, 8, 9, -1 ], [ 5, 6, 1, 1, 6, 2, -1 ], [ 5, 6, 1, 1, 6, 2, 8, 0, 3, -1 ], [ 6, 9, 5, 6, 0, 9, 6, 2, 0, -1 ], [ 6, 2, 5, 2, 3, 8, 5, 2, 8, 5, 8, 9, -1 ], [ 3, 6, 11, 3, 5, 6, 3, 1, 5, -1 ], [ 8, 0, 1, 8, 1, 6, 1, 5, 6, 11, 8, 6, -1 ], [ 11, 3, 6, 6, 3, 5, 5, 3, 0, 5, 0, 9, -1 ], [ 5, 6, 9, 6, 11, 9, 11, 8, 9, -1 ], [ 5, 6, 10, 7, 4, 8, -1 ], [ 0, 3, 4, 4, 3, 7, 10, 5, 6, -1 ], [ 5, 6, 10, 4, 8, 7, 0, 9, 1, -1 ], [ 6, 10, 5, 1, 4, 9, 1, 7, 4, 1, 3, 7, -1 ], [ 7, 4, 8, 6, 10, 5, 2, 11, 3, -1 ], [ 10, 5, 6, 4, 11, 7, 4, 2, 11, 4, 0, 2, -1 ], [ 4, 8, 7, 6, 10, 5, 3, 2, 11, 1, 0, 9, -1 ], [ 1, 2, 10, 11, 7, 6, 9, 5, 4, -1 ], [ 2, 1, 6, 6, 1, 5, 8, 7, 4, -1 ], [ 0, 3, 7, 0, 7, 4, 2, 1, 6, 1, 5, 6, -1 ], [ 8, 7, 4, 6, 9, 5, 6, 0, 9, 6, 2, 0, -1 ], [ 7, 2, 3, 6, 2, 7, 5, 4, 9, -1 ], [ 4, 8, 7, 3, 6, 11, 3, 5, 6, 3, 1, 5, -1 ], [ 5, 0, 1, 4, 0, 5, 7, 6, 11, -1 ], [ 9, 5, 4, 6, 11, 7, 0, 8, 3, -1 ], [ 11, 7, 6, 9, 5, 4, -1 ], [ 6, 10, 4, 4, 10, 9, -1 ], [ 6, 10, 4, 4, 10, 9, 3, 8, 0, -1 ], [ 0, 10, 1, 0, 6, 10, 0, 4, 6, -1 ], [ 6, 10, 1, 6, 1, 8, 1, 3, 8, 4, 6, 8, -1 ], [ 9, 4, 10, 10, 4, 6, 3, 2, 11, -1 ], [ 2, 11, 8, 2, 8, 0, 6, 10, 4, 10, 9, 4, -1 ], [ 11, 3, 2, 0, 10, 1, 0, 6, 10, 0, 4, 6, -1 ], [ 6, 8, 4, 11, 8, 6, 2, 10, 1, -1 ], [ 4, 1, 9, 4, 2, 1, 4, 6, 2, -1 ], [ 3, 8, 0, 4, 1, 9, 4, 2, 1, 4, 6, 2, -1 ], [ 6, 2, 4, 4, 2, 0, -1 ], [ 3, 8, 2, 8, 4, 2, 4, 6, 2, -1 ], [ 4, 6, 9, 6, 11, 3, 9, 6, 3, 9, 3, 1, -1 ], [ 8, 6, 11, 4, 6, 8, 9, 0, 1, -1 ], [ 11, 3, 6, 3, 0, 6, 0, 4, 6, -1 ], [ 8, 6, 11, 4, 6, 8, -1 ], [ 10, 7, 6, 10, 8, 7, 10, 9, 8, -1 ], [ 3, 7, 0, 7, 6, 10, 0, 7, 10, 0, 10, 9, -1 ], [ 6, 10, 7, 7, 10, 8, 8, 10, 1, 8, 1, 0, -1 ], [ 6, 10, 7, 10, 1, 7, 1, 3, 7, -1 ], [ 3, 2, 11, 10, 7, 6, 10, 8, 7, 10, 9, 8, -1 ], [ 2, 9, 0, 10, 9, 2, 6, 11, 7, -1 ], [ 0, 8, 3, 7, 6, 11, 1, 2, 10, -1 ], [ 7, 6, 11, 1, 2, 10, -1 ], [ 2, 1, 9, 2, 9, 7, 9, 8, 7, 6, 2, 7, -1 ], [ 2, 7, 6, 3, 7, 2, 0, 1, 9, -1 ], [ 8, 7, 0, 7, 6, 0, 6, 2, 0, -1 ], [ 7, 2, 3, 6, 2, 7, -1 ], [ 8, 1, 9, 3, 1, 8, 11, 7, 6, -1 ], [ 11, 7, 6, 1, 9, 0, -1 ], [ 6, 11, 7, 0, 8, 3, -1 ], [ 11, 7, 6, -1 ], [ 7, 11, 5, 5, 11, 10, -1 ], [ 10, 5, 11, 11, 5, 7, 0, 3, 8, -1 ], [ 7, 11, 5, 5, 11, 10, 0, 9, 1, -1 ], [ 7, 11, 10, 7, 10, 5, 3, 8, 1, 8, 9, 1, -1 ], [ 5, 2, 10, 5, 3, 2, 5, 7, 3, -1 ], [ 5, 7, 10, 7, 8, 0, 10, 7, 0, 10, 0, 2, -1 ], [ 0, 9, 1, 5, 2, 10, 5, 3, 2, 5, 7, 3, -1 ], [ 9, 7, 8, 5, 7, 9, 10, 1, 2, -1 ], [ 1, 11, 2, 1, 7, 11, 1, 5, 7, -1 ], [ 8, 0, 3, 1, 11, 2, 1, 7, 11, 1, 5, 7, -1 ], [ 7, 11, 2, 7, 2, 9, 2, 0, 9, 5, 7, 9, -1 ], [ 7, 9, 5, 8, 9, 7, 3, 11, 2, -1 ], [ 3, 1, 7, 7, 1, 5, -1 ], [ 8, 0, 7, 0, 1, 7, 1, 5, 7, -1 ], [ 0, 9, 3, 9, 5, 3, 5, 7, 3, -1 ], [ 9, 7, 8, 5, 7, 9, -1 ], [ 8, 5, 4, 8, 10, 5, 8, 11, 10, -1 ], [ 0, 3, 11, 0, 11, 5, 11, 10, 5, 4, 0, 5, -1 ], [ 1, 0, 9, 8, 5, 4, 8, 10, 5, 8, 11, 10, -1 ], [ 10, 3, 11, 1, 3, 10, 9, 5, 4, -1 ], [ 3, 2, 8, 8, 2, 4, 4, 2, 10, 4, 10, 5, -1 ], [ 10, 5, 2, 5, 4, 2, 4, 0, 2, -1 ], [ 5, 4, 9, 8, 3, 0, 10, 1, 2, -1 ], [ 2, 10, 1, 4, 9, 5, -1 ], [ 8, 11, 4, 11, 2, 1, 4, 11, 1, 4, 1, 5, -1 ], [ 0, 5, 4, 1, 5, 0, 2, 3, 11, -1 ], [ 0, 11, 2, 8, 11, 0, 4, 9, 5, -1 ], [ 5, 4, 9, 2, 3, 11, -1 ], [ 4, 8, 5, 8, 3, 5, 3, 1, 5, -1 ], [ 0, 5, 4, 1, 5, 0, -1 ], [ 5, 4, 9, 3, 0, 8, -1 ], [ 5, 4, 9, -1 ], [ 11, 4, 7, 11, 9, 4, 11, 10, 9, -1 ], [ 0, 3, 8, 11, 4, 7, 11, 9, 4, 11, 10, 9, -1 ], [ 11, 10, 7, 10, 1, 0, 7, 10, 0, 7, 0, 4, -1 ], [ 3, 10, 1, 11, 10, 3, 7, 8, 4, -1 ], [ 3, 2, 10, 3, 10, 4, 10, 9, 4, 7, 3, 4, -1 ], [ 9, 2, 10, 0, 2, 9, 8, 4, 7, -1 ], [ 3, 4, 7, 0, 4, 3, 1, 2, 10, -1 ], [ 7, 8, 4, 10, 1, 2, -1 ], [ 7, 11, 4, 4, 11, 9, 9, 11, 2, 9, 2, 1, -1 ], [ 1, 9, 0, 4, 7, 8, 2, 3, 11, -1 ], [ 7, 11, 4, 11, 2, 4, 2, 0, 4, -1 ], [ 4, 7, 8, 2, 3, 11, -1 ], [ 9, 4, 1, 4, 7, 1, 7, 3, 1, -1 ], [ 7, 8, 4, 1, 9, 0, -1 ], [ 3, 4, 7, 0, 4, 3, -1 ], [ 7, 8, 4, -1 ], [ 11, 10, 8, 8, 10, 9, -1 ], [ 0, 3, 9, 3, 11, 9, 11, 10, 9, -1 ], [ 1, 0, 10, 0, 8, 10, 8, 11, 10, -1 ], [ 10, 3, 11, 1, 3, 10, -1 ], [ 3, 2, 8, 2, 10, 8, 10, 9, 8, -1 ], [ 9, 2, 10, 0, 2, 9, -1 ], [ 8, 3, 0, 10, 1, 2, -1 ], [ 2, 10, 1, -1 ], [ 2, 1, 11, 1, 9, 11, 9, 8, 11, -1 ], [ 11, 2, 3, 9, 0, 1, -1 ], [ 11, 0, 8, 2, 0, 11, -1 ], [ 3, 11, 2, -1 ], [ 1, 8, 3, 9, 8, 1, -1 ], [ 1, 9, 0, -1 ], [ 8, 3, 0, -1 ], [ -1 ] ];34:[] 2e:{"title":"Crystal DFT","cells":[{"id":0,"value":"# Crystal DFT","pinned":false,"hidden":false,"mode":"md"},{"id":31,"value":"viewof latticeKey = Inputs.select(\n Object.entries(lattices).flatMap(([lattice, { bases }]) =>\n Object.keys(bases).map(basis => `${lattice} | ${basis}`)\n ),\n {\n label: \"Lattice + Atoms\",\n value: \"Tetragonal | Strontium Titanate (SrTiO₃)\"\n }\n)","pinned":false,"hidden":false,"mode":"ojs"},{"id":633,"value":"viewof showDensity = Inputs.toggle({label: \"electron density\", value: true})","pinned":false,"hidden":false,"mode":"ojs"},{"id":741,"value":"Warning: not real electron density, but a mock one with a Gaussian at each atom","pinned":false,"hidden":false,"mode":"md"},{"id":87,"value":"$30","pinned":true,"hidden":false,"mode":"ojs"},{"id":76,"value":"$31","pinned":true,"hidden":false,"mode":"ojs"},{"id":394,"value":"$32","pinned":false,"hidden":false,"mode":"ojs"},{"id":669,"value":"cubeVerts = [\n [0,0,0], // 0\n [1,0,0], // 1\n [0,1,0], // 2\n [1,1,0], // 3\n [0,0,1], // 4\n [1,0,1], // 5\n [0,1,1], // 6\n [1,1,1], // 7\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":671,"value":"edgeConnections = [\n [0,1], // 0\n [1,3], // 1\n [3,2], // 2\n [2,0], // 3\n [4,5], // 4\n [5,7], // 5\n [7,6], // 6\n [6,4], // 7\n [0,4], // 8\n [1,5], // 9\n [3,7], //10\n [2,6], //11\n]","pinned":false,"hidden":false,"mode":"ojs"},{"id":738,"value":"String(edgeTable)","pinned":true,"hidden":false,"mode":"ojs"},{"id":681,"value":"edgeTable = { \n let edgeTable = [];\n for (let cubeindex = 0; cubeindex < 256; cubeindex++) {\n let mask = 0;\n edgeConnections.forEach(([v1, v2], edgeIndex) => {\n const inside1 = (cubeindex >> v1) & 1;\n const inside2 = (cubeindex >> v2) & 1;\n if (inside1 !== inside2) {\n mask |= (1 << edgeIndex);\n }\n });\n edgeTable.push(mask);\n }\n return edgeTable\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":539,"value":"$33","pinned":false,"hidden":false,"mode":"ojs"},{"id":730,"value":"## Imports","pinned":false,"hidden":false,"mode":"md"},{"id":20,"value":"three = require(\"three@0.150.1\")","pinned":false,"hidden":false,"mode":"ojs"},{"id":45,"value":"OrbitControls = (await import(\n \"three@0.150.1/examples/jsm/controls/OrbitControls.js\"\n)).OrbitControls","pinned":false,"hidden":false,"mode":"ojs"}],"files":"$W34","stdlib":"1","titling":"auto"}