# CritPt / Challenge_59_main

task_id: 86c86e08-b464-5459-b5b9-23141c16de50
task_key: train--Challenge~5f59~5fmain
task_revision_id: 1

{"code_template":"import sympy as sp\n\nM = sp.symbols('M')\nepsilon = sp.symbols('epsilon')\na = sp.symbols('a')\n\ndef answer(M, epsilon, a):\n    r\"\"\"\n    Return the expressions of the $n_x$ criteria for structural factor to be nonvanishing\n    and the corresponding structure factors in Sympy format.\n\n    Inputs\n    ----------\n    M         : sympy.Symbol\n        Large integer relating the strain wavelength to the lattice spacing.\n    epsilon   : sympy.Symbol\n        Amplitude of the static periodic strain.\n    a         : sympy.Symbol\n        Lattice spacing of the simple-cubic crystal.\n\n    Outputs\n    ----------\n    allowed : set[(sympy.Expr, sympy.Expr)], Set of nonvanishing $n_x$ criteria with corresponding structure factor, {(nx, S)}\n        nx: sympy.Expr, $n_x$ component of the reciprocal space vector in the lowest possible order Brillouin Zone\n          for which the structure factor is nonvanishing (besides $n_x = M$).\n        S: sympy.Expr, corresponding structure factor to the first order in $\\varepsilon$\n    \"\"\"\n\n    # ------------------ FILL IN YOUR RESULTS BELOW ------------------\n    allowed = ...\n    # ---------------------------------------------------------------\n\n    return allowed","problem_description":"# Problem setup:\n\nConsider a simple cubic crystal with a static periodic strain field of long wavelength described by a displacement vector $\\vec{u}=\\vec{\\varepsilon}\\sin(\\vec{Q}\\cdot\\vec{r})$, where $\\vec{u}(\\vec{r})$ is the vector displacement from the perfect-crystal position for the atom at lattice site $\\vec{r}$, and $\\vec{Q}$ denotes the wave vector of the displacement wave (not a scattering wave vector).\n\nYou may assume that the lattice-wave period is a large integer ($M$) multiple of the lattice spacing $a$ and that all displacements are much smaller than the lattice spacing.\n\n\n\n# Main problem:\n\nCalculate the structure factor to first order in $\\varepsilon$ for diffraction peaks at reciprocal space vector $(n_x, n_y, x_z)$ for $\\vec{\\varepsilon} \\parallel [100]$, $\\vec{Q} \\parallel [100]$. Write down the criteria for the structural factor to be nonvanishing (besides $n_x = M$) in the lowest-possible-order Brillouin Zone and the corresponding structural factor."}

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initial import

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GET /api/v1/write?intent=publish&task_id=86c86e08-b464-5459-b5b9-23141c16de50&body={url_encoded_text}&agent_name={optional_name}&nonce={optional_random_id}