diff --git a/SolidState/GraphenePhonons.ipynb b/SolidState/GraphenePhonons.ipynb
index 1eb1e2de5f0ef9381239f37cb4957e94cbbf0ea2..0b690e1312f4125ce3e4324786885b85b0e571ae 100644
--- a/SolidState/GraphenePhonons.ipynb
+++ b/SolidState/GraphenePhonons.ipynb
@@ -13,19 +13,148 @@
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Análisis analÃtico"
+ "## Desarrollo analÃtico"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
- "## Análisis numérico"
+ "El grafeno es un material bidimensional compuesto por átomos de carbono organizados en una estructura hexagonal, formando una sola capa atómica. Esta disposición le otorga propiedades únicas, tanto electrónicas como térmicas, que lo convierten en un tema de interés en el estudio de materiales bidimensionales.\n",
+ "\n",
+ "Para caracterizar las vibraciones en la red de grafeno nos planteamos construir su matriz dinámica, que describe los modos de vibración para cada valor del vector de onda $\\mathbf{K}$ en el espacio recÃproco. En este proyecto, derivaremos la matriz dinámica de grafeno considerando únicamente interacciones de primeros vecinos, siguiendo el enfoque presentado en la Sección 7 del libro Quantum Theory of Materials, E. Kaxiras (2019)."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### EnergÃa Potencial en la Red\n",
+ "\n",
+ "La energÃa potencial $\\Delta U$ del sistema se expresa en términos de la interacción entre átomos de carbono vecinos en la red. Consideramos dos tipos de interacciones en el modelo de primeros vecinos:\n",
+ "\n",
+ "- **Interacciones radiales**: fuerzas que actúan a lo largo de la dirección del enlace entre átomos vecinos, modificando la longitud de separación entre los átomos.\n",
+ "- **Interacciones tangenciales**: fuerzas que actúan perpendicularmente al enlace, reflejando las deformaciones angulares de la red.\n",
+ "\n",
+ "Para cada par de átomos de carbono vecinos, la energÃa potencial de la interacción puede escribirse como:\n",
+ "\n",
+ "$$\\Delta U = \\frac{1}{2} (c_r-c_t) \\sum_{\\langle i,j \\rangle} [(\\mathbf{S}_i-\\mathbf{S}_i) \\cdot \\hat{r}_{ij}]^2 + \\frac{1}{2} c_t \\sum_{\\langle i,j \\rangle} |\\mathbf{S}_i-\\mathbf{S}_j|^2,$$\n",
+ "\n",
+ "donde:\n",
+ "- $ c_r $ y $ c_t $ son las constantes de resorte para las interacciones radial y tangencial, respectivamente,\n",
+ "- $ \\mathbf{S}_i $ es el desplazamiento del átomo $i$ respecto a su posición de equilibrio,\n",
+ "- $ \\hat{r}_{ij} $ es el vector unitario que une los átomos $i$ y $j$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Definición de la Matriz Dinámica\n",
+ "\n",
+ "La matriz dinámica en el espacio recÃproco, $D(\\mathbf{K})$, se define a partir de las segundas derivadas de la energÃa potencial con respecto a los desplazamientos de los átomos:\n",
+ "\n",
+ "$$\n",
+ "D_{i\\alpha,j\\beta}(\\mathbf{K}) = \\frac{1}{\\sqrt{m_i m_j}} \\sum_{n} \\frac{\\partial^2 \\Delta U}{\\partial S_{ni\\alpha} \\partial S_{0j\\beta}} e^{i \\mathbf{K} \\cdot \\mathbf{R}_n},\n",
+ "$$\n",
+ "\n",
+ "donde:\n",
+ "- $ i $ y $ j $ indican los diferentes sitios de la celda primitiva,\n",
+ "- $ \\alpha, \\beta $ son las direcciones $x$, $y$, $z$,\n",
+ "- $ m_i $ es la masa de los átomos,\n",
+ "- $ \\mathbf{K} $ es el vector de onda en el espacio recÃproco,\n",
+ "- $ \\mathbf{R}_n $ es el vector de traslación que identifica la celda $n$.\n",
+ "\n",
+ "Este enfoque nos permite capturar los efectos de las interacciones entre los primeros vecinos en la estructura vibracional de la red de grafeno resolviendo la ecuación de valores propios:\n",
+ "\n",
+ "$$\n",
+ "\\sum_{j\\beta} D_{i\\alpha,j\\beta}(\\mathbf{K}) u_{j\\beta}(\\mathbf{K}) = \\omega^2 u_{i\\alpha}(\\mathbf{K}),\n",
+ "$$\n",
+ "\n",
+ "donde $ u_{i\\alpha}(\\mathbf{K}) $ es la amplitud de desplazamiento del átomo $i$ en dirección $\\alpha$ y $ \\omega $ es la frecuencia de vibración."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "<!-- A partir de la energÃa potencial, es posible derivar una expresión explÃcita para la matriz dinámica de grafeno. En el código, esto se implementa en la función `D(Kx, Ky, Kz, params)`, donde:\n",
+ "\n",
+ "- **Parámetros del modelo**: Los parámetros de interacción $c_1$, $c_2$, $c_3$ y la masa atómica $m$ están predefinidos en el código, junto con los vectores de red $\\mathbf{a_1}$ y $\\mathbf{a_2}$.\n",
+ "- **Construcción de la matriz dinámica**: La matriz dinámica se descompone en componentes radiales y tangenciales usando los vectores de red $\\mathbf{a_1}$ y $\\mathbf{a_2}$, y los valores de la función de onda. -->\n",
+ "<!-- ### Expresión de la Matriz Dinámica\n",
+ "\n",
+ "La matriz dinámica $D(\\mathbf{K})$ se puede expresar en función de las constantes de interacción y los vectores de red. Algunos de los elementos de la matriz dinámica en el código se presentan como:\n",
+ "\n",
+ "$$\n",
+ "D_{xx}(\\mathbf{K}) = \\frac{3(c_1 + c_2)}{2m} - \\frac{c_1}{m} \\left( 1 + e^{-i \\mathbf{K} \\cdot \\mathbf{a}_1} + e^{-i \\mathbf{K} \\cdot \\mathbf{a}_2} \\right)\n",
+ "$$\n",
+ "\n",
+ "$$\n",
+ "D_{xy}(\\mathbf{K}) = \\frac{\\sqrt{3}}{4m} (c_1 - c_2) \\left( e^{-i \\mathbf{K} \\cdot \\mathbf{a}_1} - e^{-i \\mathbf{K} \\cdot \\mathbf{a}_2} \\right)\n",
+ "$$\n",
+ "\n",
+ "Los términos fuera de la diagonal reflejan las interacciones tangenciales entre átomos vecinos, mientras que los términos en la diagonal corresponden a las interacciones radiales. -->"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Descripción de la Red de Grafeno\n",
+ "\n",
+ "Consideramos una celda primitiva de grafeno con dos átomos de carbono, donde los átomos están dispuestos en una red hexagonal. Los vectores de red son:\n",
+ "\n",
+ "$$\n",
+ "\\mathbf{a}_1 = \\frac{a}{2} (\\sqrt{3} \\hat{x} - \\hat{y}), \\quad \\mathbf{a}_2 = \\frac{a}{2} (\\sqrt{3} \\hat{x} + \\hat{y}),\n",
+ "$$\n",
+ "\n",
+ "donde $a$ es el parámetro de red. La base de la celda primitiva es:\n",
+ "\n",
+ "$$\n",
+ "\\mathbf{t}_1 = \\vec{0} \\quad \\text{y} \\quad \\mathbf{t}_2 = \\frac{1}{3} (\\mathbf{a}_1 + \\mathbf{a}_2) = \\frac{a}{\\sqrt{3}} \\hat{x}.\n",
+ "$$\n",
+ "\n",
+ "Nuestra notación será la siguiente: el desplazamiento $S_{mni\\alpha}$ corresponde a la componente $\\alpha$ del átomo $i$ cuyo vector de traslación es $\\mathbf{R}_{mn} = m \\mathbf{a}_1 + n \\mathbf{a}_2$. La red de grafeno se puede visualizar en el siguiente diagrama, con las etiquetas $mni$ de cada átomo ($\\bar{1} = -1$):\n",
+ "\n",
+ "<p align=\"center\">\n",
+ " <img src=\"https://gitmilab.redclara.net/mantillan/TrabajosPregrado/-/raw/main/SolidState/GrapheneLattice.jpg\" width=\"50%\" />\n",
+ "</p>\n",
+ "\n",
+ "en donde se han señalado los primeros vecinos de los átomos $0$ y $1$ de la celda $00$ mediante enlaces color naranja.\n",
+ "\n",
+ "Consecuentemente, los vectores recÃprocos, los cuales cumplen la regla $\\mathbf{a}_i \\cdot \\mathbf{b}_j = 2\\pi \\delta_{ij}$, son:\n",
+ "\n",
+ "$$\n",
+ "\\mathbf{b}_1 = \\frac{2\\pi}{\\sqrt{3}a} (\\hat{x} - \\sqrt{3} \\hat{y}), \\quad \\mathbf{b}_2 = \\frac{2\\pi}{\\sqrt{3}a} (\\hat{x} + \\sqrt{3} \\hat{y}),\n",
+ "$$\n",
+ "\n",
+ "el cual es también una red hexagonal de dos sitios, pero rotado $\\pi/2$, de modo que los puntos de alta simetrÃa en la zona de Brillouin son:\n",
+ "\n",
+ "$$\n",
+ "\\Gamma = \\vec{0}, \\quad M = \\frac{\\mathbf{b}_1+\\mathbf{b}_2}{2}, \\quad K = \\frac{|\\mathbf{b}_1+\\mathbf{b}_2|}{2} (\\hat{x} + \\frac{1}{\\sqrt{3}} \\hat{y}).\n",
+ "$$"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "### Matriz Dinámica del Grafeno\n",
+ "\n",
+ "Para poder escribir la energÃa potencial $\\Delta U$ en términos de los desplazamientos de los átomos, es necesario considerar las direcciones de los enlaces entre átomos vecinos $r_{ij}$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Desarrollo numérico"
]
},
{
"cell_type": "code",
- "execution_count": 1,
+ "execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
@@ -37,162 +166,166 @@
},
{
"cell_type": "code",
- "execution_count": 64,
+ "execution_count": 66,
"metadata": {},
"outputs": [],
"source": [
- "#Definimos la matriz dinamica\n",
+ "# Definimos la matriz dinámica\n",
"def D(Kx, Ky, Kz, params):\n",
" '''\n",
- " Esta función calcula la matriz dinamica de un cristal hexagonal\n",
+ " Esta función calcula la matriz dinámica de un cristal hexagonal\n",
" para un vector de onda K = (Kx, Ky, Kz). La notación de las componentes\n",
- " de la matriz dinamica se puede comprender en la forma:\n",
+ " de la matriz dinámica se puede comprender en la forma:\n",
" D_0x,0x = D_0,0, D_1x,1x = D_3,3, D_0y,1z = D_1,5, etc.\n",
" '''\n",
- " #Definimos las constantes del problema\n",
- " cx, cy, cz, m, a1, a2 = params\n",
+ " # Definimos las constantes del problema\n",
+ " c1, c2, c3, m, a1, a2 = params\n",
"\n",
+ " # Vector de onda\n",
" K = np.array([Kx, Ky, Kz])\n",
- " dinamic = np.zeros((6,6))\n",
- " dinamic[0,0] = 3*cx/m\n",
- " dinamic[1,1] = 3*cy/m\n",
- " dinamic[2,2] = 3*cz/m\n",
- " dinamic[3,3] = 3*cx/m\n",
- " dinamic[4,4] = 3*cy/m\n",
- " dinamic[5,5] = 3*cz/m\n",
- " dinamic[0,3] = -cx/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
- " dinamic[1,4] = -cy/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
- " dinamic[2,5] = -cz/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
- " dinamic[3,0] = -cx/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
- " dinamic[4,1] = -cy/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
- " dinamic[5,2] = -cz/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
- " return dinamic\n",
- "\n",
- "#Definimos una función para calcular los valores propios de la matriz dinamica\n",
+ " \n",
+ " # Inicializamos la matriz dinámica con ceros\n",
+ " dinamic = np.zeros((6,6), dtype=complex)\n",
+ "\n",
+ " # Matriz dinámica modelo 1 (descomposición en x y z)\n",
+ " # dinamic[0,0] = 3*c1/m\n",
+ " # dinamic[1,1] = 3*c2/m\n",
+ " # dinamic[2,2] = 3*c3/m\n",
+ " # dinamic[3,3] = 3*c1/m\n",
+ " # dinamic[4,4] = 3*c2/m\n",
+ " # dinamic[5,5] = 3*c3/m\n",
+ " # dinamic[0,3] = -c1/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
+ " # dinamic[1,4] = -c2/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
+ " # dinamic[2,5] = -c3/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
+ " # dinamic[3,0] = -c1/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
+ " # dinamic[4,1] = -c2/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
+ " # dinamic[5,2] = -c3/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
+ "\n",
+ " # Matriz dinámica modelo 2 (descomposición en radial y tangencial)\n",
+ " dinamic[0,0] = 3*(c1+c2)/(2)\n",
+ " dinamic[0,3] = -(c1+1/4*(c1+3*c2)*(np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2))))\n",
+ " dinamic[0,4] = np.sqrt(3)/(4)*(c1-c2)*(np.exp(1j*np.dot(K,a1))-np.exp(1j*np.dot(K,a2)))\n",
+ " dinamic[1,1] = 3*(c1+c2)/(2)\n",
+ " dinamic[1,3] = np.sqrt(3)/(4)*(c1-c2)*(np.exp(1j*np.dot(K,a1))-np.exp(1j*np.dot(K,a2)))\n",
+ " dinamic[1,4] = -(c2+1/4*(3*c1+c2)*(np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2))))\n",
+ " dinamic[2,2] = 3*c3\n",
+ " dinamic[2,5] = -c3*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
+ " dinamic[3,0] = -(c1+1/4*(c1+3*c2)*(np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2))))\n",
+ " dinamic[3,1] = np.sqrt(3)/(4)*(c1-c2)*(np.exp(-1j*np.dot(K,a1))-np.exp(-1j*np.dot(K,a2)))\n",
+ " dinamic[3,3] = 3*(c1+c2)/(2)\n",
+ " dinamic[4,0] = np.sqrt(3)/(4)*(c1-c2)*(np.exp(-1j*np.dot(K,a1))-np.exp(-1j*np.dot(K,a2)))\n",
+ " dinamic[4,1] = -(c2+1/4*(3*c1+c2)*(np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2))))\n",
+ " dinamic[4,4] = 3*(c1+c2)/(2)\n",
+ " dinamic[5,2] = -c3*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
+ " dinamic[5,5] = 3*c3\n",
+ "\n",
+ " # Retornamos la matriz dinámica normalizada por la masa\n",
+ " return dinamic/m\n",
+ "\n",
+ "# Definimos una función para calcular los valores propios de la matriz dinámica\n",
"def eigenvalues(Kx, Ky, Kz, params):\n",
" '''\n",
- " Esta función calcula los valores propios de la matriz dinamica para un\n",
+ " Esta función calcula los valores propios de la matriz dinámica para un\n",
" vector de onda K = (Kx, Ky, Kz)\n",
" '''\n",
+ " # Calculamos la matriz dinámica\n",
" dinamic = D(Kx, Ky, Kz, params)\n",
- " squared = np.linalg.eigvals(dinamic)\n",
+ " \n",
+ " # Calculamos los valores propios de la matriz dinámica\n",
+ " squared = np.linalg.eigvalsh(dinamic)\n",
+ " \n",
+ " # Retornamos la raÃz cuadrada de los valores propios\n",
" return np.sqrt(squared)\n",
"\n",
- "#Definimos la función que calcula la disperción en el camino Gamma-M-K-Gamma\n",
+ "# Definimos la función que calcula la dispersión en el camino Gamma-M-K-Gamma\n",
"def dispersion(params, b1, b2):\n",
" '''\n",
- " Esta función calcula la disperción en el camino Gamma-M-K-Gamma\n",
+ " Esta función calcula la dispersión en el camino Gamma-M-K-Gamma\n",
" '''\n",
- " #Definimos los puntos del camino\n",
+ " # Definimos los puntos del camino\n",
" Gamma = np.array([0,0,0])\n",
- " M = b2/2\n",
+ " M = (b1+b2)/2\n",
" K = np.linalg.norm(b1+b2)/2*np.array([1,1/np.sqrt(3),0])\n",
"\n",
- " #Definimos el número de puntos en cada segmento\n",
+ " # Definimos el número de puntos en cada segmento\n",
" n = 100\n",
"\n",
- " #Definimos los vectores de onda en cada segmento\n",
+ " # Definimos los vectores de onda en cada segmento\n",
" GM = np.array([np.linspace(Gamma[i], M[i], n) for i in range(3)])\n",
" MK = np.array([np.linspace(M[i], K[i], n) for i in range(3)])\n",
" KG = np.array([np.linspace(K[i], Gamma[i], n) for i in range(3)])\n",
"\n",
- " #Calculamos los valores propios en cada segmento\n",
- " GM_eigenvalues = np.array([eigenvalues(GM[0,i], GM[1,i], GM[2,i], params) for i in range(n)]).T\n",
- " MK_eigenvalues = np.array([eigenvalues(MK[0,i], MK[1,i], MK[2,i], params) for i in range(n)]).T\n",
- " KG_eigenvalues = np.array([eigenvalues(KG[0,i], KG[1,i], KG[2,i], params) for i in range(n)]).T\n",
+ " # Calculamos los valores propios en cada segmento\n",
+ " GM_eigenvalues = np.array([np.real(eigenvalues(GM[0,i], GM[1,i], GM[2,i], params)) for i in range(n)]).T\n",
+ " MK_eigenvalues = np.array([np.real(eigenvalues(MK[0,i], MK[1,i], MK[2,i], params)) for i in range(n)]).T\n",
+ " KG_eigenvalues = np.array([np.real(eigenvalues(KG[0,i], KG[1,i], KG[2,i], params)) for i in range(n)]).T\n",
"\n",
- " #Cambiamos los nan por ceros\n",
+ " # Cambiamos los nan por ceros\n",
" GM_eigenvalues = np.nan_to_num(GM_eigenvalues)\n",
" MK_eigenvalues = np.nan_to_num(MK_eigenvalues)\n",
" KG_eigenvalues = np.nan_to_num(KG_eigenvalues)\n",
" \n",
+ " # Retornamos los valores propios para cada segmento\n",
" return np.array([GM_eigenvalues, MK_eigenvalues, KG_eigenvalues])\n",
"\n",
- "#Definimos una función para graficar la disperción en el camino Gamma-M-K-Gamma\n",
+ "# Definimos una función para graficar la dispersión en el camino Gamma-M-K-Gamma\n",
"def plot_dispersion(dispersion):\n",
" '''\n",
- " Esta función grafica la disperción en el camino Gamma-M-K-Gamma\n",
+ " Esta función grafica la dispersión en el camino Gamma-M-K-Gamma\n",
" '''\n",
- " \n",
- " #Separamos los caminos\n",
+ " # Separamos los caminos\n",
" GM = dispersion[0]\n",
" MK = dispersion[1]\n",
" KG = dispersion[2]\n",
"\n",
- " #Inicializamos la figura\n",
- " fig = plt.figure(figsize=(10,10))\n",
+ " # Inicializamos la figura\n",
+ " fig = plt.figure(figsize=(8,6))\n",
"\n",
- " #Graficamos la disperción para cada uno de los 6 modos\n",
- " colors = ['r', 'g', 'b', 'c', 'm', 'y']\n",
+ " # Graficamos la dispersión para cada uno de los 6 valores propios hallados en cada punto\n",
+ " shifting = 0.1\n",
+ " colors = 6*['m']\n",
" for i in range(6):\n",
- " plt.plot(np.linspace(0,1,100), GM[i], str(colors[i])+'.', markersize=2)\n",
- " plt.plot(np.linspace(1,2,100), MK[i], str(colors[i])+'.', markersize=2)\n",
- " plt.plot(np.linspace(2,3,100), KG[i], str(colors[i])+'.', markersize=2)\n",
+ " plt.plot(np.linspace(0,1+shifting,100), GM[i]*1e-2, str(colors[i])+'.', markersize=2.5)\n",
+ " plt.plot(np.linspace(1+shifting,2-shifting,100), MK[i]*1e-2, str(colors[i])+'.', markersize=2.5)\n",
+ " plt.plot(np.linspace(2-shifting,3,100), KG[i]*1e-2, str(colors[i])+'.', markersize=2.5)\n",
"\n",
- " #Lineas verticales para separar los caminos\n",
- " plt.axvline(x=1, color='k', linestyle='--')\n",
- " plt.axvline(x=2, color='k', linestyle='--')\n",
+ " # LÃneas verticales para separar los caminos\n",
+ " plt.axvline(x=1+shifting, color='k', linestyle='--')\n",
+ " plt.axvline(x=2-shifting, color='k', linestyle='--')\n",
" \n",
- " #Agregamos las etiquetas\n",
- " plt.xticks([0,1,2,3], ['$\\Gamma$', 'M', 'K', '$\\Gamma$'])\n",
- " plt.ylabel('Frecuencia (Hz)')\n",
- " plt.title('Dispersión en el camino $\\Gamma$-M-K-$\\Gamma$')\n",
+ " # Agregamos las etiquetas\n",
+ " plt.xticks([0,1+shifting,2-shifting,3], ['$\\Gamma$', 'M', 'K', '$\\Gamma$'], fontsize=12)\n",
+ " plt.xlabel('Camino en el espacio recÃproco', fontsize=14)\n",
+ " plt.yticks(np.arange(0, 1700, 200))\n",
+ " plt.ylabel('Frecuencia (cm$^{-1}$)', fontsize=14)\n",
+ " plt.title('Dispersión en el camino $\\Gamma$-M-K-$\\Gamma$', fontsize=16)\n",
+ " plt.grid(alpha=0.5)\n",
" plt.show()\n"
]
},
{
"cell_type": "code",
- "execution_count": 28,
+ "execution_count": 67,
"metadata": {},
"outputs": [
{
"data": {
+ "image/png": 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",
"text/plain": [
- "(3, 6, 100)"
+ "<Figure size 800x600 with 1 Axes>"
]
},
- "execution_count": 28,
"metadata": {},
- "output_type": "execute_result"
- }
- ],
- "source": [
- "disp.shape"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 42,
- "metadata": {},
- "outputs": [
- {
- "name": "stderr",
- "output_type": "stream",
- "text": [
- "C:\\Users\\nicom\\AppData\\Local\\Temp\\ipykernel_13392\\234641334.py:20: ComplexWarning: Casting complex values to real discards the imaginary part\n",
- " dinamic[0,3] = -cx/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
- "C:\\Users\\nicom\\AppData\\Local\\Temp\\ipykernel_13392\\234641334.py:21: ComplexWarning: Casting complex values to real discards the imaginary part\n",
- " dinamic[1,4] = -cy/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
- "C:\\Users\\nicom\\AppData\\Local\\Temp\\ipykernel_13392\\234641334.py:22: ComplexWarning: Casting complex values to real discards the imaginary part\n",
- " dinamic[2,5] = -cz/m*(1+np.exp(-1j*np.dot(K,a1))+np.exp(-1j*np.dot(K,a2)))\n",
- "C:\\Users\\nicom\\AppData\\Local\\Temp\\ipykernel_13392\\234641334.py:23: ComplexWarning: Casting complex values to real discards the imaginary part\n",
- " dinamic[3,0] = -cx/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
- "C:\\Users\\nicom\\AppData\\Local\\Temp\\ipykernel_13392\\234641334.py:24: ComplexWarning: Casting complex values to real discards the imaginary part\n",
- " dinamic[4,1] = -cy/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
- "C:\\Users\\nicom\\AppData\\Local\\Temp\\ipykernel_13392\\234641334.py:25: ComplexWarning: Casting complex values to real discards the imaginary part\n",
- " dinamic[5,2] = -cz/m*(1+np.exp(1j*np.dot(K,a1))+np.exp(1j*np.dot(K,a2)))\n",
- "C:\\Users\\nicom\\AppData\\Local\\Temp\\ipykernel_13392\\234641334.py:36: RuntimeWarning: invalid value encountered in sqrt\n",
- " return np.sqrt(squared)\n"
- ]
+ "output_type": "display_data"
}
],
"source": [
- "#Definimos las constantes del cristal hexagonal y los vectores de la red y de la red recÃproca\n",
- "a = 1 #constante de red, Angstrom\n",
- "cx = 1 #constantes de resorte, N/m\n",
- "cy = 1\n",
- "cz = 1\n",
- "m = 1 #masa, kg\n",
+ "#Definimos las constantes del cristal hexagonal, los vectores de la red y de la red recÃproca\n",
+ "a = 2e-10 #constante de red, m\n",
+ "c1 = 4.5e-17 #constantes de resorte, N/m\n",
+ "c2 = 12.5e-17\n",
+ "c3 = 2.25e-17\n",
+ "m = 2e-26 #masa atómica del carbono, kg\n",
"\n",
"a1 = np.array(a/2*np.array([np.sqrt(3),-1,0]))\n",
"a2 = np.array(a/2*np.array([np.sqrt(3),1,0]))\n",
@@ -200,62 +333,21 @@
"b1 = 2*np.pi/(a*np.sqrt(3))*np.array([1,-np.sqrt(3),0])\n",
"b2 = 2*np.pi/(a*np.sqrt(3))*np.array([1,np.sqrt(3),0])\n",
"\n",
- "params = [cx, cy, cz, m, a1, a2]\n",
+ "params = [c1, c2, c3, m, a1, a2]\n",
"\n",
"#Calculamos la disperción\n",
- "disp = dispersion(params, b1, b2)"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 65,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 1000x1000 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
+ "disp = dispersion(params, b1, b2)\n",
+ "\n",
"#Graficamos la disperción\n",
"plot_dispersion(disp)"
]
},
{
"cell_type": "code",
- "execution_count": 52,
+ "execution_count": null,
"metadata": {},
- "outputs": [
- {
- "data": {
- "text/plain": [
- "[<matplotlib.lines.Line2D at 0x24afbff0eb0>]"
- ]
- },
- "execution_count": 52,
- "metadata": {},
- "output_type": "execute_result"
- },
- {
- "data": {
- "image/png": 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",
- "text/plain": [
- "<Figure size 640x480 with 1 Axes>"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "plt.plot(np.linspace(0,1,100), disp[0][2])"
- ]
+ "outputs": [],
+ "source": []
}
],
"metadata": {